Finite Group Databasebeta

← C67×#61790 #30741041

Subgroups — C67×#61790 #30741041

Order 17152.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3551C211yesmaximal, characteristic, complemented
2C67×#3512C211yesmaximal, characteristic, complemented
3C67×#3355C211yesmaximal, characteristic, complemented
4C67×#3352C211yesmaximal, characteristic, complemented
5C67×#3351C211yesmaximal, characteristic, complemented
6C67×#3351C211yesmaximal, characteristic, complemented
7C67×#3339C211yesmaximal, characteristic, complemented
8C67×#3337C211yesmaximal, characteristic, complemented
9C67×#3337C211yesmaximal, characteristic, complemented
10C67×#3336C211yesmaximal, characteristic, complemented
11C67×#3327C211yesmaximal, characteristic, complemented
12C67×#3326C211yesmaximal, characteristic, complemented
13C67×#3323C211yesmaximal, characteristic, complemented
14C67×#3322C211yesmaximal, characteristic, complemented
15C67×#3301C211yesmaximal, characteristic, complemented
16C67×#3300C211yesmaximal, characteristic, complemented
17C67×#3297C211yesmaximal, characteristic, complemented
18C67×#3296C211yesmaximal, characteristic, complemented
19C67×#3232C211yesmaximal, characteristic, complemented
20C67×#3232C211yesmaximal, characteristic, complemented
21C67×#3204C211yesmaximal, characteristic, complemented
22C67×#3203C211yesmaximal, characteristic, complemented
23C67×#3201C211yesmaximal, characteristic, complemented
24C67×#3198C211yesmaximal, characteristic, complemented
25C67×#3102C211yesmaximal, characteristic, complemented
26C67×#3102C211yesmaximal, characteristic, complemented
27C67×#3099C211yesmaximal, characteristic, complemented
28C67×#3098C211yesmaximal, characteristic, complemented
29C67×#3097C211yesmaximal, characteristic, complemented
30C67×#3096C211yesmaximal, characteristic, complemented
31C67×#2979C211yesmaximal, characteristic, complemented
32#563×C67—21no—
33#560×C67—21no—
34#555×C67—21no—
35#553×C67—21no—
36#553×C67—21no—
37#553×C67—21no—
38#553×C67—21no—
39#553×C67C2211yescharacteristic
40#553×C67C2211yescharacteristic
41#553×C67C2211yescharacteristic
42#553×C67C2211yescharacteristic
43#553×C67C2211yescharacteristic, complemented
44#553×C67C2211yescharacteristic, complemented
45#552×C67C2211yescharacteristic
46#552×C67C2211yescharacteristic
47#552×C67C2211yescharacteristic
48#552×C67C2211yescharacteristic
49#552×C67C2211yescharacteristic, complemented
50#552×C67C2211yescharacteristic, complemented
51#551×C67—21no—
52#548×C67C2211yescharacteristic
53#548×C67C2211yescharacteristic
54#546×C67C2211yescharacteristic
55#546×C67C2211yescharacteristic
56#541×C67—21no—
57#540×C67—21no—
58#540×C67—21no—
59#540×C67—21no—
60#538×C67—21no—
61#538×C67—21no—
62#537×C67C2211yescharacteristic
63#537×C67C2211yescharacteristic
64#537×C67C2211yescharacteristic
65#537×C67C2211yescharacteristic, complemented
66#536×C67C2211yescharacteristic
67#535×C67C2211yescharacteristic
68#532×C67C2211yescharacteristic
69#529×C67—21no—
70#529×C67—21no—
71#529×C67C2211yescharacteristic
72#529×C67C2211yescharacteristic
73C2×#125×C67C2211yescharacteristic, complemented
74#520×C67C2211yescharacteristic
75#520×C67C2211yescharacteristic, complemented
76C4×#41×C67C2211yescharacteristic, complemented
77#499×C67C2211yescharacteristic, complemented
78#499×C67C2211yescharacteristic, complemented
79#499×C67C2211yescharacteristic, complemented
80#499×C67C2211yescharacteristic, complemented
81#488×C67C2211yescharacteristic
82#488×C67C2211yescharacteristic
83#488×C67C2211yescharacteristic
84#488×C67C2211yescharacteristic
85#485×C67C2211yescharacteristic
86#485×C67C2211yescharacteristic
87#485×C67C2211yescharacteristic
88#485×C67C2211yescharacteristic, complemented
89#485×C67C2211yescharacteristic, complemented
90#485×C67C2211yescharacteristic, complemented
91#485×C67C2211yescharacteristic, complemented
92#485×C67C2211yescharacteristic, complemented
93#484×C67C2211yescharacteristic
94#484×C67C2211yescharacteristic, complemented
95#484×C67C2211yescharacteristic, complemented
96#484×C67C2211yescharacteristic, complemented
97#484×C67C2211yescharacteristic, complemented
98#483×C67C2211yescharacteristic
99#483×C67C2211yescharacteristic, complemented
100#483×C67C2211yescharacteristic, complemented
101#483×C67C2211yescharacteristic, complemented
102#483×C67C2211yescharacteristic, complemented
103#482×C67C2211yescharacteristic
104#482×C67C2211yescharacteristic
105#482×C67C2211yescharacteristic
106#482×C67C2211yescharacteristic
107#482×C67C2211yescharacteristic
108#482×C67C2211yescharacteristic
109#482×C67C2211yescharacteristic
110#482×C67C2211yescharacteristic, complemented
111#481×C67C2211yescharacteristic
112#481×C67C2211yescharacteristic
113#481×C67C2211yescharacteristic
114#481×C67C2211yescharacteristic
115#481×C67C2211yescharacteristic, complemented
116#480×C67C2211yescharacteristic
117#480×C67C2211yescharacteristic
118#480×C67C2211yescharacteristic
119#480×C67C2211yescharacteristic
120#480×C67C2211yescharacteristic, complemented
121#479×C67C2211yescharacteristic, complemented
122#479×C67C2211yescharacteristic, complemented
123#479×C67C2211yescharacteristic, complemented
124#479×C67C2211yescharacteristic, complemented
125#479×C67C2211yescharacteristic, complemented
126#479×C67C2211yescharacteristic, complemented
127#478×C67C2211yescharacteristic
128#478×C67C2211yescharacteristic
129#478×C67C2211yescharacteristic
130#478×C67C2211yescharacteristic
131#478×C67C2211yescharacteristic, complemented
132#478×C67C2211yescharacteristic, complemented
133#470×C67C2211yescharacteristic
134#470×C67C2211yescharacteristic, complemented
135#469×C67C2211yescharacteristic
136#469×C67C2211yescharacteristic
137#468×C67C2211yescharacteristic
138#468×C67C2211yescharacteristic
139#468×C67C2211yescharacteristic
140#468×C67C2211yescharacteristic, complemented
141#467×C67C2211yescharacteristic
142#467×C67C2211yescharacteristic, complemented
143#466×C67C2211yescharacteristic
144#466×C67C2211yescharacteristic
145#465×C67C2211yescharacteristic
146#465×C67C2211yescharacteristic
147#465×C67C2211yescharacteristic
148#465×C67C2211yescharacteristic, complemented
149#464×C67C2211yescharacteristic
150#464×C67C2211yescharacteristic
151#463×C67C2211yescharacteristic
152#463×C67C2211yescharacteristic
153#452×C67C2211yescharacteristic
154#452×C67C2211yescharacteristic
155#452×C67C2211yescharacteristic, complemented
156#452×C67C2211yescharacteristic, complemented
157#451×C67C2211yescharacteristic, complemented
158#450×C67C2211yescharacteristic
159#449×C67C2211yescharacteristic
160#449×C67C2211yescharacteristic
161#449×C67C2211yescharacteristic
162#449×C67C2211yescharacteristic
163#448×C67C2211yescharacteristic, complemented
164#447×C67C2211yescharacteristic
165C4×Q16×C67C2211yescharacteristic, complemented
166C4×Q16×C67C2211yescharacteristic, complemented
167C4×SD16×C67C2211yescharacteristic
168C4×SD16×C67C2211yescharacteristic
169C4×SD16×C67C2211yescharacteristic, complemented
170C4×SD16×C67C2211yescharacteristic, complemented
171C4×D8×C67C2211yescharacteristic
172C4×D8×C67C2211yescharacteristic
173#436×C67C2211yescharacteristic
174#436×C67C2211yescharacteristic
175#436×C67C2211yescharacteristic, complemented
176#436×C67C2211yescharacteristic, complemented
177C8×D4×C67C2211yescharacteristic
178C8×D4×C67C2211yescharacteristic
179C8×D4×C67C2211yescharacteristic, complemented
180C8×D4×C67C2211yescharacteristic, complemented
181#431×C67C2211yescharacteristic, complemented
182#431×C67C2211yescharacteristic, complemented
183#428×C67C2211yescharacteristic
184#428×C67C2211yescharacteristic, complemented
185#428×C67C2211yescharacteristic, complemented
186#428×C67C2211yescharacteristic, complemented
187#427×C67C2211yescharacteristic
188#427×C67C2211yescharacteristic, complemented
189C2×#107×C67C2211yescharacteristic, complemented
190C2×#106×C67C2211yescharacteristic, complemented
191#419×C67C2211yescharacteristic, complemented
192#418×C67C2211yescharacteristic
193#417×C67C2211yescharacteristic
194#417×C67C2211yescharacteristic
195#416×C67C2211yescharacteristic
196#416×C67C2211yescharacteristic
197C2×#103×C67C2211yescharacteristic, complemented
198C2×#102×C67C2211yescharacteristic
199#408×C67C2211yescharacteristic
200#408×C67C2211yescharacteristic
201#408×C67C2211yescharacteristic, complemented
202#408×C67C2211yescharacteristic, complemented
203C2×#41×C67C2311yescharacteristic
204C2×#41×C67C2311yescharacteristic
205C2×#41×C67C2311yescharacteristic
206C2×#41×C67C2311yescharacteristic
207C2×#41×C67C2311yescharacteristic
208C22×Q8×C67C2311yescharacteristic
209C22×D4×C67C2311yescharacteristic
210C2×Q16×C67C2311yescharacteristic
211C2×Q16×C67C2311yescharacteristic
212C2×SD16×C67C2311yescharacteristic
213C2×SD16×C67C2311yescharacteristic
214C2×SD16×C67C2311yescharacteristic
215C2×SD16×C67C2311yescharacteristic
216C2×D8×C67C2311yescharacteristic
217C2×D8×C67C2311yescharacteristic
218C2×M16×C67C2311yescharacteristic
219C2×M16×C67C2311yescharacteristic
220C2×M16×C67C2311yescharacteristic
221C2×M16×C67C2311yescharacteristic
222C22×C8×C67C2311yescharacteristic
223C22×C8×C67C2311yescharacteristic
224C22×C8×C67C2311yescharacteristic
225C22×C8×C67C2311yescharacteristic
226C4⋊Q8×C67—21no—
227C4⋊Q8×C67D411yescharacteristic
228#127×C67—21no—
229#127×C67D411yescharacteristic
230#126×C67—21no—
231#126×C67—21no—
232#126×C67—21no—
233#126×C67—21no—
234#126×C67—21no—
235#126×C67—21no—
236#126×C67—21no—
237#126×C67—21no—
238#126×C67—21no—
239#126×C67—21no—
240#126×C67—21no—
241#126×C67—21no—
242#126×C67—21no—
243#126×C67—21no—
244#125×C67—21no—
245#125×C67—21no—
246#125×C67—21no—
247#125×C67—21no—
248#125×C67—21no—
249#125×C67—21no—
250#125×C67—21no—
251#125×C67—21no—
252#125×C67C2311yescharacteristic
253#125×C67C2311yescharacteristic
254#125×C67C2311yescharacteristic
255#125×C67C2311yescharacteristic
256#125×C67C2311yescharacteristic
257#125×C67C2311yescharacteristic
258#124×C67—21no—
259#124×C67—21no—
260#124×C67—21no—
261#124×C67—21no—
262#124×C67D411yescharacteristic
263#124×C67D411yescharacteristic
264#124×C67C2311yescharacteristic
265#124×C67C2311yescharacteristic
266#123×C67—21no—
267#123×C67—21no—
268#123×C67—21no—
269#123×C67—21no—
270#123×C67—21no—
271#123×C67—21no—
272#123×C67—21no—
273#123×C67—21no—
274#123×C67—21no—
275#123×C67—21no—
276#123×C67—21no—
277#123×C67—21no—
278#123×C67—21no—
279#123×C67—21no—
280#123×C67—21no—
281#123×C67—21no—
282#123×C67—21no—
283#123×C67—21no—
284C22⋊Q8×C67—21no—
285C22⋊Q8×C67—21no—
286C22⋊Q8×C67—21no—
287C22⋊Q8×C67—21no—
288C22⋊Q8×C67—21no—
289C22⋊Q8×C67—21no—
290C22⋊Q8×C67C2311yescharacteristic
291C22⋊Q8×C67C2311yescharacteristic
292C22⋊Q8×C67C2311yescharacteristic
293C22⋊Q8×C67C2311yescharacteristic
294C22⋊Q8×C67C2311yescharacteristic
295C22⋊Q8×C67C2311yescharacteristic
296C22⋊Q8×C67C2311yescharacteristic
297C22⋊Q8×C67C2311yescharacteristic
298C22⋊Q8×C67C2311yescharacteristic
299C22⋊Q8×C67C2311yescharacteristic
300#121×C67—21no—
301#121×C67—21no—
302#121×C67—21no—
303#121×C67—21no—
304#121×C67—21no—
305#121×C67—21no—
306#121×C67—21no—
307#121×C67—21no—
308#121×C67—21no—
309#121×C67—21no—
310#121×C67—21no—
311#121×C67—21no—
312#121×C67—21no—
313#121×C67—21no—
314#121×C67—21no—
315#121×C67—21no—
316#121×C67—21no—
317#121×C67—21no—
318#121×C67—21no—
319#121×C67—21no—
320#121×C67—21no—
321#121×C67—21no—
322#121×C67D411yescharacteristic
323#121×C67D411yescharacteristic
324#121×C67D411yescharacteristic
325#121×C67D411yescharacteristic
326#121×C67C2311yescharacteristic
327#121×C67C2311yescharacteristic
328#121×C67C2311yescharacteristic
329#121×C67C2311yescharacteristic
330#121×C67C2311yescharacteristic
331#121×C67C2311yescharacteristic
332#121×C67C2311yescharacteristic
333#121×C67C2311yescharacteristic
334#121×C67C2311yescharacteristic
335#121×C67C2311yescharacteristic
336#120×C67—21no—
337#120×C67—21no—
338#120×C67—21no—
339#120×C67—21no—
340C4×Q8×C67—21no—
341C4×Q8×C67—21no—
342C4×Q8×C67C2311yescharacteristic
343C4×Q8×C67C2311yescharacteristic
344C4×Q8×C67C2311yescharacteristic
345C4×Q8×C67C2311yescharacteristic
346C4×D4×C67—21no—
347C4×D4×C67—21no—
348C4×D4×C67—21no—
349C4×D4×C67—21no—
350C4×D4×C67—21no—
351C4×D4×C67—21no—
352C4×D4×C67—21no—
353C4×D4×C67—21no—
354C4×D4×C67—21no—
355C4×D4×C67—21no—
356C4×D4×C67—21no—
357C4×D4×C67—21no—
358C4×D4×C67—21no—
359C4×D4×C67—21no—
360C4×D4×C67—21no—
361C4×D4×C67—21no—
362C4×D4×C67—21no—
363C4×D4×C67—21no—
364C4×D4×C67C2311yescharacteristic
365C4×D4×C67C2311yescharacteristic
366C4×D4×C67C2311yescharacteristic
367C4×D4×C67C2311yescharacteristic
368C4×D4×C67C2311yescharacteristic
369C4×D4×C67C2311yescharacteristic
370C4×D4×C67C2311yescharacteristic
371C4×D4×C67C2311yescharacteristic
372#117×C67—21no—
373#117×C67—21no—
374#117×C67—21no—
375#117×C67—21no—
376#117×C67—21no—
377#117×C67—21no—
378#117×C67—21no—
379#117×C67—21no—
380#117×C67—21no—
381#117×C67C2311yescharacteristic
382#117×C67C2311yescharacteristic
383#117×C67C2311yescharacteristic
384#117×C67C2311yescharacteristic
385#117×C67C2311yescharacteristic
386#117×C67C2311yescharacteristic
387#117×C67C2311yescharacteristic
388C2×C4⋊C4×C67—21no—
389C2×C4⋊C4×C67—21no—
390C2×C4⋊C4×C67C2311yescharacteristic
391C2×C4⋊C4×C67C2311yescharacteristic
392C2×C4⋊C4×C67C2311yescharacteristic
393C2×C4⋊C4×C67C2311yescharacteristic
394C2×C4⋊C4×C67C2311yescharacteristic
395C2×C4⋊C4×C67C2311yescharacteristic
396C2×C4⋊C4×C67C2311yescharacteristic
397C2×C4⋊C4×C67C2311yescharacteristic
398C2×C22⋊C4×C67—21no—
399C2×C22⋊C4×C67—21no—
400C2×C42×C67—21no—
401C2×C42×C67C2311yescharacteristic
402#107×C67C2311yescharacteristic
403#107×C67C2311yescharacteristic
404#107×C67C2311yescharacteristic
405#107×C67C2311yescharacteristic
406#107×C67C2311yescharacteristic
407#107×C67C2311yescharacteristic
408#107×C67C2311yescharacteristic
409#107×C67C2311yescharacteristic
410#107×C67C2311yescharacteristic
411#107×C67C2311yescharacteristic
412#107×C67C2311yescharacteristic
413#107×C67C2311yescharacteristic
414#106×C67C2311yescharacteristic
415#106×C67C2311yescharacteristic
416#106×C67C2311yescharacteristic
417#106×C67C2311yescharacteristic
418#106×C67C2311yescharacteristic
419#106×C67C2311yescharacteristic
420#106×C67C2311yescharacteristic
421#106×C67C2311yescharacteristic
422#106×C67C2311yescharacteristic
423#106×C67C2311yescharacteristic
424#106×C67C2311yescharacteristic
425#106×C67C2311yescharacteristic
426C4⋊C8×C67C2311yescharacteristic
427C4⋊C8×C67C2311yescharacteristic
428C4⋊C8×C67C2311yescharacteristic
429C4⋊C8×C67C2311yescharacteristic
430#103×C67C2311yescharacteristic
431#103×C67C2311yescharacteristic
432#103×C67C2311yescharacteristic
433#103×C67C2311yescharacteristic
434#103×C67C2311yescharacteristic
435#103×C67C2311yescharacteristic
436#103×C67C2311yescharacteristic
437#103×C67C2311yescharacteristic
438#103×C67C2311yescharacteristic
439#103×C67C2311yescharacteristic
440#103×C67C2311yescharacteristic
441#103×C67C2311yescharacteristic
442#103×C67C2311yescharacteristic
443#103×C67C2311yescharacteristic
444#103×C67C2311yescharacteristic
445#103×C67C2311yescharacteristic
446#102×C67C2311yescharacteristic
447#102×C67C2311yescharacteristic
448#102×C67C2311yescharacteristic
449#102×C67C2311yescharacteristic
450#102×C67C2311yescharacteristic
451#102×C67C2311yescharacteristic
452#102×C67C2311yescharacteristic
453#102×C67C2311yescharacteristic
454#102×C67C2311yescharacteristic
455#102×C67C2311yescharacteristic
456#102×C67C2311yescharacteristic
457#102×C67C2311yescharacteristic
458#102×C67C2311yescharacteristic
459#102×C67C2311yescharacteristic
460#102×C67C2311yescharacteristic
461#102×C67C2311yescharacteristic
462C22⋊C8×C67C2311yescharacteristic
463C22⋊C8×C67C2311yescharacteristic
464C22⋊C8×C67C2311yescharacteristic
465C22⋊C8×C67C2311yescharacteristic
466C22⋊C8×C67C2311yescharacteristic
467C22⋊C8×C67C2311yescharacteristic
468C22⋊C8×C67C2311yescharacteristic
469C22⋊C8×C67C2311yescharacteristic
470C22⋊C8×C67C2311yescharacteristic
471C22⋊C8×C67C2311yescharacteristic
472C22⋊C8×C67C2311yescharacteristic
473C22⋊C8×C67C2311yescharacteristic
474C4×C8×C67C2311yescharacteristic
475C4×C8×C67C2311yescharacteristic
476C4×C8×C67C2311yescharacteristic
477C4×C8×C67C2311yescharacteristic
478C24×C67—21no—
479#41×C67—41no—
480#41×C67—41no—
481#41×C67—41no—
482#41×C67—41no—
483#41×C67—41no—
484#41×C67—41no—
485#41×C67—41no—
486#41×C67—41no—
487#41×C67—41no—
488#41×C67—41no—
489C2×Q8×C67—21no—
490C2×Q8×C67—41no—
491C2×Q8×C67—41no—
492C2×Q8×C67C2×D411yescharacteristic
493C2×Q8×C67C2×D411yescharacteristic
494C2×Q8×C67C2411yescharacteristic
495C2×Q8×C67C2411yescharacteristic
496C2×Q8×C67C2411yescharacteristic
497C2×D4×C67—21no—
498C2×D4×C67—21no—
499C2×D4×C67—21no—
500C2×D4×C67—21no—
501C2×D4×C67—21no—
502C2×D4×C67—21no—
503C2×D4×C67—21no—
504C2×D4×C67—21no—
505C2×D4×C67—21no—
506C2×D4×C67—21no—
507C2×D4×C67—21no—
508C2×D4×C67—21no—
509C2×D4×C67—21no—
510C2×D4×C67—21no—
511C2×D4×C67—41no—
512C2×D4×C67—41no—
513C2×D4×C67C2×D411yescharacteristic
514C2×D4×C67C2×D411yescharacteristic
515C2×D4×C67C2×D411yescharacteristic
516C2×D4×C67C2×D411yescharacteristic
517C2×D4×C67C2×D411yescharacteristic
518C2×D4×C67C2×D411yescharacteristic
519C2×D4×C67C2×D411yescharacteristic
520C2×D4×C67C2×D411yescharacteristic
521C2×D4×C67C2×D411yescharacteristic
522C2×D4×C67C2×D411yescharacteristic
523C2×D4×C67C2411yescharacteristic
524C2×D4×C67C2411yescharacteristic
525C2×D4×C67C2411yescharacteristic
526C22×C4×C67—21no—
527C22×C4×C67—21no—
528C22×C4×C67—21no—
529C22×C4×C67—21no—
530C22×C4×C67—21no—
531C22×C4×C67—21no—
532C22×C4×C67—21no—
533C22×C4×C67—21no—
534C22×C4×C67—21no—
535C22×C4×C67—21no—
536C22×C4×C67—21no—
537C22×C4×C67—21no—
538C22×C4×C67—21no—
539C22×C4×C67—21no—
540C22×C4×C67—21no—
541C22×C4×C67—21no—
542C22×C4×C67C2×D411yescharacteristic
543C22×C4×C67C2×D411yescharacteristic
544C22×C4×C67C2411yescharacteristic
545C22×C4×C67C2411yescharacteristic
546C22×C4×C67C2411yescharacteristic
547C22×C4×C67C2411yescharacteristic
548C22×C4×C67C2411yescharacteristic
549Q16×C67—41no—
550Q16×C67—41no—
551SD16×C67—41no—
552SD16×C67—41no—
553SD16×C67—41no—
554SD16×C67—41no—
555D8×C67—41no—
556D8×C67—41no—
557M16×C67—41no—
558M16×C67—41no—
559M16×C67—41no—
560M16×C67—41no—
561C2×C8×C67—41no—
562C2×C8×C67—41no—
563C2×C8×C67—41no—
564C2×C8×C67—41no—
565C2×C8×C67C2411yescharacteristic
566C2×C8×C67C2411yescharacteristic
567C2×C8×C67C2411yescharacteristic
568C2×C8×C67C2411yescharacteristic
569C2×C8×C67C2411yescharacteristic
570C2×C8×C67C2411yescharacteristic
571C2×C8×C67C2411yescharacteristic
572C2×C8×C67C2411yescharacteristic
573C4⋊C4×C67—21no—
574C4⋊C4×C67—21no—
575C4⋊C4×C67—21no—
576C4⋊C4×C67—21no—
577C4⋊C4×C67—21no—
578C4⋊C4×C67—21no—
579C4⋊C4×C67—21no—
580C4⋊C4×C67—21no—
581C4⋊C4×C67—21no—
582C4⋊C4×C67—21no—
583C4⋊C4×C67—21no—
584C4⋊C4×C67—21no—
585C4⋊C4×C67—21no—
586C4⋊C4×C67—21no—
587C4⋊C4×C67—21no—
588C4⋊C4×C67—21no—
589C4⋊C4×C67—21no—
590C4⋊C4×C67—21no—
591C4⋊C4×C67—21no—
592C4⋊C4×C67—21no—
593C4⋊C4×C67—21no—
594C4⋊C4×C67—21no—
595C4⋊C4×C67—21no—
596C4⋊C4×C67—21no—
597C4⋊C4×C67—21no—
598C4⋊C4×C67—21no—
599C4⋊C4×C67—21no—
600C4⋊C4×C67—21no—
601C4⋊C4×C67—21no—
602C4⋊C4×C67—21no—
603C4⋊C4×C67—21no—
604C4⋊C4×C67—21no—
605C4⋊C4×C67—21no—
606C4⋊C4×C67—21no—
607C4⋊C4×C67C2×D411yescharacteristic
608C4⋊C4×C67C2×D411yescharacteristic
609C4⋊C4×C67C2×D411yescharacteristic
610C4⋊C4×C67C2×D411yescharacteristic
611C4⋊C4×C67C2411yescharacteristic
612C4⋊C4×C67C2411yescharacteristic
613C4⋊C4×C67C2411yescharacteristic
614C4⋊C4×C67C2411yescharacteristic
615C4⋊C4×C67C2411yescharacteristic
616C4⋊C4×C67C2411yescharacteristic
617C4⋊C4×C67C2411yescharacteristic
618C4⋊C4×C67C2411yescharacteristic
619C4⋊C4×C67C2411yescharacteristic
620C4⋊C4×C67C2411yescharacteristic
621C22⋊C4×C67—21no—
622C22⋊C4×C67—21no—
623C22⋊C4×C67—21no—
624C22⋊C4×C67—21no—
625C22⋊C4×C67—21no—
626C22⋊C4×C67—21no—
627C22⋊C4×C67—21no—
628C22⋊C4×C67—21no—
629C22⋊C4×C67—21no—
630C22⋊C4×C67—21no—
631C22⋊C4×C67—21no—
632C22⋊C4×C67—21no—
633C22⋊C4×C67—21no—
634C22⋊C4×C67—21no—
635C22⋊C4×C67—21no—
636C22⋊C4×C67—21no—
637C22⋊C4×C67—21no—
638C22⋊C4×C67—21no—
639C22⋊C4×C67—21no—
640C22⋊C4×C67—21no—
641C22⋊C4×C67—21no—
642C22⋊C4×C67—21no—
643C22⋊C4×C67—21no—
644C22⋊C4×C67—21no—
645C22⋊C4×C67—21no—
646C22⋊C4×C67—21no—
647C22⋊C4×C67—21no—
648C22⋊C4×C67—21no—
649C22⋊C4×C67—21no—
650C22⋊C4×C67—21no—
651C22⋊C4×C67—21no—
652C22⋊C4×C67—21no—
653C22⋊C4×C67—21no—
654C22⋊C4×C67—21no—
655C22⋊C4×C67—21no—
656C22⋊C4×C67C2×D411yescharacteristic
657C22⋊C4×C67C2×D411yescharacteristic
658C22⋊C4×C67C2×D411yescharacteristic
659C22⋊C4×C67C2×D411yescharacteristic
660C22⋊C4×C67C2×D411yescharacteristic
661C22⋊C4×C67C2×D411yescharacteristic
662C22⋊C4×C67C2×D411yescharacteristic
663C22⋊C4×C67C2×D411yescharacteristic
664C42×C67—21no—
665C42×C67—21no—
666C42×C67—21no—
667C42×C67—21no—
668C42×C67—21no—
669C42×C67—21no—
670C42×C67—21no—
671C42×C67—21no—
672C42×C67—21no—
673C42×C67—21no—
674C42×C67—21no—
675C42×C67C2×D411yescharacteristic
676C42×C67C2×D411yescharacteristic
677C42×C67C2411yescharacteristic
678C42×C67C2411yescharacteristic
679C23×C67—21no—
680C23×C67—21no—
681C23×C67—21no—
682C23×C67—81no—
683C23×C67—81no—
684C23×C67—81no—
685C23×C67C22×D411yescharacteristic
686C23×C67C22×D411yescharacteristic
687C23×C67C22×D411yescharacteristic
688C23×C67C22×D411yescharacteristic
689C23×C67C22×D411yescharacteristic
690Q8×C67—21no—
691Q8×C67—21no—
692Q8×C67—21no—
693Q8×C67—21no—
694Q8×C67—21no—
695Q8×C67—21no—
696Q8×C67—41no—
697Q8×C67—41no—
698Q8×C67—81no—
699D4×C67—21no—
700D4×C67—21no—
701D4×C67—21no—
702D4×C67—21no—
703D4×C67—21no—
704D4×C67—21no—
705D4×C67—41no—
706D4×C67—41no—
707D4×C67—41no—
708D4×C67—41no—
709D4×C67—41no—
710D4×C67—41no—
711D4×C67—41no—
712D4×C67—41no—
713D4×C67—41no—
714D4×C67—41no—
715D4×C67—42no—
716D4×C67—81no—
717D4×C67—81no—
718D4×C67—81no—
719D4×C67—81no—
720D4×C67—81no—
721D4×C67—81no—
722D4×C67—81no—
723D4×C67—81no—
724D4×C67—81no—
725D4×C67—81no—
726D4×C67—81no—
727D4×C67—81no—
728D4×C67—81no—
729C2×C4×C67—21no—
730C2×C4×C67—21no—
731C2×C4×C67—21no—
732C2×C4×C67—21no—
733C2×C4×C67—21no—
734C2×C4×C67—21no—
735C2×C4×C67—21no—
736C2×C4×C67—21no—
737C2×C4×C67—21no—
738C2×C4×C67—21no—
739C2×C4×C67—21no—
740C2×C4×C67—21no—
741C2×C4×C67—21no—
742C2×C4×C67—21no—
743C2×C4×C67—21no—
744C2×C4×C67—21no—
745C2×C4×C67—21no—
746C2×C4×C67—21no—
747C2×C4×C67—21no—
748C2×C4×C67—21no—
749C2×C4×C67—21no—
750C2×C4×C67—21no—
751C2×C4×C67—21no—
752C2×C4×C67—41no—
753C2×C4×C67—41no—
754C2×C4×C67—42no—
755C2×C4×C67—81no—
756C2×C4×C67—81no—
757C2×C4×C67—81no—
758C2×C4×C67—81no—
759C2×C4×C67—81no—
760C2×C4×C67—81no—
761C2×C4×C67—81no—
762C2×C4×C67—81no—
763C2×C4×C67—81no—
764C2×C4×C67—81no—
765C2×C4×C67—81no—
766C2×C4×C67—81no—
767C2×C4×C67—81no—
768C2×C4×C67—81no—
769C2×C4×C67—81no—
770C2×C4×C67C22×D411yescharacteristic
771C2×C4×C67C22×D411yescharacteristic
772C2×C4×C67C22×D411yescharacteristic
773C2×C4×C67C22×D411yescharacteristic
774C2×C4×C67C22×D411yescharacteristic
775C2×C4×C67C22×D411yescharacteristic
776C2×C4×C67C22×D411yescharacteristic
777C2×C4×C67C22×D411yescharacteristic
778C2×C4×C67C22×D411yescharacteristic
779C2×C4×C67C2511yescharacteristic
780C8×C67—21no—
781C8×C67—21no—
782C8×C67—21no—
783C8×C67—21no—
784C8×C67—21no—
785C8×C67—21no—
786C8×C67—21no—
787C8×C67—21no—
788C22×C67—21no—
789C22×C67—21no—
790C22×C67—21no—
791C22×C67—21no—
792C22×C67—21no—
793C22×C67—21no—
794C22×C67—21no—
795C22×C67—21no—
796C22×C67—21no—
797C22×C67—21no—
798C22×C67—21no—
799C22×C67—21no—
800C22×C67—21no—
801C22×C67—21no—
802C22×C67—21no—
803C22×C67—41no—
804C22×C67—41no—
805C22×C67—41no—
806C22×C67—41no—
807C22×C67—41no—
808C22×C67—41no—
809C22×C67—41no—
810C22×C67—41no—
811C22×C67—41no—
812C22×C67—162no—
813C22×C67C23×D411yescharacteristic
814C4×C67—21no—
815C4×C67—21no—
816C4×C67—21no—
817C4×C67—21no—
818C4×C67—21no—
819C4×C67—21no—
820C4×C67—21no—
821C4×C67—21no—
822C4×C67—21no—
823C4×C67—41no—
824C4×C67—41no—
825C4×C67—41no—
826C4×C67—41no—
827C4×C67—41no—
828C4×C67—41no—
829C4×C67—41no—
830C4×C67—41no—
831C4×C67—41no—
832C4×C67—41no—
833C4×C67—41no—
834C4×C67—41no—
835C4×C67—41no—
836C4×C67#58511yescharacteristic
837C4×C67#58511yescharacteristic
838#61790C6711yesmaximal, characteristic, direct product factor, Sylow
839C2×C67—41no—
840C2×C67—41no—
841C2×C67—41no—
842C2×C67—41no—
843C2×C67—41no—
844C2×C67—81no—
845C2×C67—81no—
846C2×C67—81no—
847C2×C67#348511yescharacteristic
848C2×C67#358411yescharacteristic
849C2×C67#358411yescharacteristic
850#3551C2×C6711yescharacteristic, complemented
851#3512C2×C6711yescharacteristic, complemented
852#3355C2×C6711yescharacteristic, complemented
853#3352C2×C6711yescharacteristic, complemented
854#3351C2×C6711yescharacteristic, complemented
855#3351C2×C6711yescharacteristic, complemented
856#3339C2×C6711yescharacteristic, complemented
857#3337C2×C6711yescharacteristic, complemented
858#3337C2×C6711yescharacteristic, complemented
859#3336C2×C6711yescharacteristic, complemented
860#3327C2×C6711yescharacteristic, complemented
861#3326C2×C6711yescharacteristic, complemented
862#3323C2×C6711yescharacteristic, complemented
863#3322C2×C6711yescharacteristic, complemented
864#3301C2×C6711yescharacteristic, complemented
865#3300C2×C6711yescharacteristic, complemented
866#3297C2×C6711yescharacteristic, complemented
867#3296C2×C6711yescharacteristic, complemented
868#3232C2×C6711yescharacteristic, complemented
869#3232C2×C6711yescharacteristic, complemented
870#3204C2×C6711yescharacteristic, complemented
871#3203C2×C6711yescharacteristic, complemented
872#3201C2×C6711yescharacteristic, complemented
873#3198C2×C6711yescharacteristic, complemented
874#3102C2×C6711yescharacteristic, complemented
875#3102C2×C6711yescharacteristic, complemented
876#3099C2×C6711yescharacteristic, complemented
877#3098C2×C6711yescharacteristic, complemented
878#3097C2×C6711yescharacteristic, complemented
879#3096C2×C6711yescharacteristic, complemented
880#2979C2×C6711yescharacteristic, complemented
881C67#6179011yescharacteristic, direct product factor, Sylow
882#563—21no—
883#560—21no—
884#555—21no—
885#553—21no—
886#553—21no—
887#553—21no—
888#553—21no—
889#553C22×C6711yescharacteristic
890#553C22×C6711yescharacteristic
891#553C22×C6711yescharacteristic
892#553C22×C6711yescharacteristic
893#553C22×C6711yescharacteristic, complemented
894#553C22×C6711yescharacteristic, complemented
895#552C22×C6711yescharacteristic
896#552C22×C6711yescharacteristic
897#552C22×C6711yescharacteristic
898#552C22×C6711yescharacteristic
899#552C22×C6711yescharacteristic, complemented
900#552C22×C6711yescharacteristic, complemented
901#551—21no—
902#548C22×C6711yescharacteristic
903#548C22×C6711yescharacteristic
904#546C22×C6711yescharacteristic
905#546C22×C6711yescharacteristic
906#541—21no—
907#540—21no—
908#540—21no—
909#540—21no—
910#538—21no—
911#538—21no—
912#537C22×C6711yescharacteristic
913#537C22×C6711yescharacteristic
914#537C22×C6711yescharacteristic
915#537C22×C6711yescharacteristic, complemented
916#536C22×C6711yescharacteristic
917#535C22×C6711yescharacteristic
918#532C22×C6711yescharacteristic
919#529—21no—
920#529—21no—
921#529C22×C6711yescharacteristic
922#529C22×C6711yescharacteristic
923C2×#125C22×C6711yescharacteristic, complemented
924#520C22×C6711yescharacteristic
925#520C22×C6711yescharacteristic, complemented
926C4×#41C22×C6711yescharacteristic, complemented
927#499C22×C6711yescharacteristic, complemented
928#499C22×C6711yescharacteristic, complemented
929#499C22×C6711yescharacteristic, complemented
930#499C22×C6711yescharacteristic, complemented
931#488C22×C6711yescharacteristic
932#488C22×C6711yescharacteristic
933#488C22×C6711yescharacteristic
934#488C22×C6711yescharacteristic
935#485C22×C6711yescharacteristic
936#485C22×C6711yescharacteristic
937#485C22×C6711yescharacteristic
938#485C22×C6711yescharacteristic, complemented
939#485C22×C6711yescharacteristic, complemented
940#485C22×C6711yescharacteristic, complemented
941#485C22×C6711yescharacteristic, complemented
942#485C22×C6711yescharacteristic, complemented
943#484C22×C6711yescharacteristic
944#484C22×C6711yescharacteristic, complemented
945#484C22×C6711yescharacteristic, complemented
946#484C22×C6711yescharacteristic, complemented
947#484C22×C6711yescharacteristic, complemented
948#483C22×C6711yescharacteristic
949#483C22×C6711yescharacteristic, complemented
950#483C22×C6711yescharacteristic, complemented
951#483C22×C6711yescharacteristic, complemented
952#483C22×C6711yescharacteristic, complemented
953#482C22×C6711yescharacteristic
954#482C22×C6711yescharacteristic
955#482C22×C6711yescharacteristic
956#482C22×C6711yescharacteristic
957#482C22×C6711yescharacteristic
958#482C22×C6711yescharacteristic
959#482C22×C6711yescharacteristic
960#482C22×C6711yescharacteristic, complemented
961#481C22×C6711yescharacteristic
962#481C22×C6711yescharacteristic
963#481C22×C6711yescharacteristic
964#481C22×C6711yescharacteristic
965#481C22×C6711yescharacteristic, complemented
966#480C22×C6711yescharacteristic
967#480C22×C6711yescharacteristic
968#480C22×C6711yescharacteristic
969#480C22×C6711yescharacteristic
970#480C22×C6711yescharacteristic, complemented
971#479C22×C6711yescharacteristic, complemented
972#479C22×C6711yescharacteristic, complemented
973#479C22×C6711yescharacteristic, complemented
974#479C22×C6711yescharacteristic, complemented
975#479C22×C6711yescharacteristic, complemented
976#479C22×C6711yescharacteristic, complemented
977#478C22×C6711yescharacteristic
978#478C22×C6711yescharacteristic
979#478C22×C6711yescharacteristic
980#478C22×C6711yescharacteristic
981#478C22×C6711yescharacteristic, complemented
982#478C22×C6711yescharacteristic, complemented
983#470C22×C6711yescharacteristic
984#470C22×C6711yescharacteristic, complemented
985#469C22×C6711yescharacteristic
986#469C22×C6711yescharacteristic
987#468C22×C6711yescharacteristic
988#468C22×C6711yescharacteristic
989#468C22×C6711yescharacteristic
990#468C22×C6711yescharacteristic, complemented
991#467C22×C6711yescharacteristic
992#467C22×C6711yescharacteristic, complemented
993#466C22×C6711yescharacteristic
994#466C22×C6711yescharacteristic
995#465C22×C6711yescharacteristic
996#465C22×C6711yescharacteristic
997#465C22×C6711yescharacteristic
998#465C22×C6711yescharacteristic, complemented
999#464C22×C6711yescharacteristic
1000#464C22×C6711yescharacteristic
1001#463C22×C6711yescharacteristic
1002#463C22×C6711yescharacteristic
1003#452C22×C6711yescharacteristic
1004#452C22×C6711yescharacteristic
1005#452C22×C6711yescharacteristic, complemented
1006#452C22×C6711yescharacteristic, complemented
1007#451C22×C6711yescharacteristic, complemented
1008#450C22×C6711yescharacteristic
1009#449C22×C6711yescharacteristic
1010#449C22×C6711yescharacteristic
1011#449C22×C6711yescharacteristic
1012#449C22×C6711yescharacteristic
1013#448C22×C6711yescharacteristic, complemented
1014#447C22×C6711yescharacteristic
1015C4×Q16C22×C6711yescharacteristic, complemented
1016C4×Q16C22×C6711yescharacteristic, complemented
1017C4×SD16C22×C6711yescharacteristic
1018C4×SD16C22×C6711yescharacteristic
1019C4×SD16C22×C6711yescharacteristic, complemented
1020C4×SD16C22×C6711yescharacteristic, complemented
1021C4×D8C22×C6711yescharacteristic
1022C4×D8C22×C6711yescharacteristic
1023#436C22×C6711yescharacteristic
1024#436C22×C6711yescharacteristic
1025#436C22×C6711yescharacteristic, complemented
1026#436C22×C6711yescharacteristic, complemented
1027C8×D4C22×C6711yescharacteristic
1028C8×D4C22×C6711yescharacteristic
1029C8×D4C22×C6711yescharacteristic, complemented
1030C8×D4C22×C6711yescharacteristic, complemented
1031#431C22×C6711yescharacteristic, complemented
1032#431C22×C6711yescharacteristic, complemented
1033#428C22×C6711yescharacteristic
1034#428C22×C6711yescharacteristic, complemented
1035#428C22×C6711yescharacteristic, complemented
1036#428C22×C6711yescharacteristic, complemented
1037#427C22×C6711yescharacteristic
1038#427C22×C6711yescharacteristic, complemented
1039C2×#107C22×C6711yescharacteristic, complemented
1040C2×#106C22×C6711yescharacteristic, complemented
1041#419C22×C6711yescharacteristic, complemented
1042#418C22×C6711yescharacteristic
1043#417C22×C6711yescharacteristic
1044#417C22×C6711yescharacteristic
1045#416C22×C6711yescharacteristic
1046#416C22×C6711yescharacteristic
1047C2×#103C22×C6711yescharacteristic, complemented
1048C2×#102C22×C6711yescharacteristic
1049#408C22×C6711yescharacteristic
1050#408C22×C6711yescharacteristic
1051#408C22×C6711yescharacteristic, complemented
1052#408C22×C6711yescharacteristic, complemented
1053C2×#41C23×C6711yescharacteristic
1054C2×#41C23×C6711yescharacteristic
1055C2×#41C23×C6711yescharacteristic
1056C2×#41C23×C6711yescharacteristic
1057C2×#41C23×C6711yescharacteristic
1058C22×Q8C23×C6711yescharacteristic
1059C22×D4C23×C6711yescharacteristic
1060C2×Q16C23×C6711yescharacteristic
1061C2×Q16C23×C6711yescharacteristic
1062C2×SD16C23×C6711yescharacteristic
1063C2×SD16C23×C6711yescharacteristic
1064C2×SD16C23×C6711yescharacteristic
1065C2×SD16C23×C6711yescharacteristic
1066C2×D8C23×C6711yescharacteristic
1067C2×D8C23×C6711yescharacteristic
1068C2×M16C23×C6711yescharacteristic
1069C2×M16C23×C6711yescharacteristic
1070C2×M16C23×C6711yescharacteristic
1071C2×M16C23×C6711yescharacteristic
1072C22×C8C23×C6711yescharacteristic
1073C22×C8C23×C6711yescharacteristic
1074C22×C8C23×C6711yescharacteristic
1075C22×C8C23×C6711yescharacteristic
1076C4⋊Q8—21no—
1077C4⋊Q8D4×C6711yescharacteristic
1078#127—21no—
1079#127D4×C6711yescharacteristic
1080#126—21no—
1081#126—21no—
1082#126—21no—
1083#126—21no—
1084#126—21no—
1085#126—21no—
1086#126—21no—
1087#126—21no—
1088#126—21no—
1089#126—21no—
1090#126—21no—
1091#126—21no—
1092#126—21no—
1093#126—21no—
1094#125—21no—
1095#125—21no—
1096#125—21no—
1097#125—21no—
1098#125—21no—
1099#125—21no—
1100#125—21no—
1101#125—21no—
1102#125C23×C6711yescharacteristic
1103#125C23×C6711yescharacteristic
1104#125C23×C6711yescharacteristic
1105#125C23×C6711yescharacteristic
1106#125C23×C6711yescharacteristic
1107#125C23×C6711yescharacteristic
1108#124—21no—
1109#124—21no—
1110#124—21no—
1111#124—21no—
1112#124D4×C6711yescharacteristic
1113#124D4×C6711yescharacteristic
1114#124C23×C6711yescharacteristic
1115#124C23×C6711yescharacteristic
1116#123—21no—
1117#123—21no—
1118#123—21no—
1119#123—21no—
1120#123—21no—
1121#123—21no—
1122#123—21no—
1123#123—21no—
1124#123—21no—
1125#123—21no—
1126#123—21no—
1127#123—21no—
1128#123—21no—
1129#123—21no—
1130#123—21no—
1131#123—21no—
1132#123—21no—
1133#123—21no—
1134C22⋊Q8—21no—
1135C22⋊Q8—21no—
1136C22⋊Q8—21no—
1137C22⋊Q8—21no—
1138C22⋊Q8—21no—
1139C22⋊Q8—21no—
1140C22⋊Q8C23×C6711yescharacteristic
1141C22⋊Q8C23×C6711yescharacteristic
1142C22⋊Q8C23×C6711yescharacteristic
1143C22⋊Q8C23×C6711yescharacteristic
1144C22⋊Q8C23×C6711yescharacteristic
1145C22⋊Q8C23×C6711yescharacteristic
1146C22⋊Q8C23×C6711yescharacteristic
1147C22⋊Q8C23×C6711yescharacteristic
1148C22⋊Q8C23×C6711yescharacteristic
1149C22⋊Q8C23×C6711yescharacteristic
1150#121—21no—
1151#121—21no—
1152#121—21no—
1153#121—21no—
1154#121—21no—
1155#121—21no—
1156#121—21no—
1157#121—21no—
1158#121—21no—
1159#121—21no—
1160#121—21no—
1161#121—21no—
1162#121—21no—
1163#121—21no—
1164#121—21no—
1165#121—21no—
1166#121—21no—
1167#121—21no—
1168#121—21no—
1169#121—21no—
1170#121—21no—
1171#121—21no—
1172#121D4×C6711yescharacteristic
1173#121D4×C6711yescharacteristic
1174#121D4×C6711yescharacteristic
1175#121D4×C6711yescharacteristic
1176#121C23×C6711yescharacteristic
1177#121C23×C6711yescharacteristic
1178#121C23×C6711yescharacteristic
1179#121C23×C6711yescharacteristic
1180#121C23×C6711yescharacteristic
1181#121C23×C6711yescharacteristic
1182#121C23×C6711yescharacteristic
1183#121C23×C6711yescharacteristic
1184#121C23×C6711yescharacteristic
1185#121C23×C6711yescharacteristic
1186#120—21no—
1187#120—21no—
1188#120—21no—
1189#120—21no—
1190C4×Q8—21no—
1191C4×Q8—21no—
1192C4×Q8C23×C6711yescharacteristic
1193C4×Q8C23×C6711yescharacteristic
1194C4×Q8C23×C6711yescharacteristic
1195C4×Q8C23×C6711yescharacteristic
1196C4×D4—21no—
1197C4×D4—21no—
1198C4×D4—21no—
1199C4×D4—21no—
1200C4×D4—21no—
1201C4×D4—21no—
1202C4×D4—21no—
1203C4×D4—21no—
1204C4×D4—21no—
1205C4×D4—21no—
1206C4×D4—21no—
1207C4×D4—21no—
1208C4×D4—21no—
1209C4×D4—21no—
1210C4×D4—21no—
1211C4×D4—21no—
1212C4×D4—21no—
1213C4×D4—21no—
1214C4×D4C23×C6711yescharacteristic
1215C4×D4C23×C6711yescharacteristic
1216C4×D4C23×C6711yescharacteristic
1217C4×D4C23×C6711yescharacteristic
1218C4×D4C23×C6711yescharacteristic
1219C4×D4C23×C6711yescharacteristic
1220C4×D4C23×C6711yescharacteristic
1221C4×D4C23×C6711yescharacteristic
1222#117—21no—
1223#117—21no—
1224#117—21no—
1225#117—21no—
1226#117—21no—
1227#117—21no—
1228#117—21no—
1229#117—21no—
1230#117—21no—
1231#117C23×C6711yescharacteristic
1232#117C23×C6711yescharacteristic
1233#117C23×C6711yescharacteristic
1234#117C23×C6711yescharacteristic
1235#117C23×C6711yescharacteristic
1236#117C23×C6711yescharacteristic
1237#117C23×C6711yescharacteristic
1238C2×C4⋊C4—21no—
1239C2×C4⋊C4—21no—
1240C2×C4⋊C4C23×C6711yescharacteristic
1241C2×C4⋊C4C23×C6711yescharacteristic
1242C2×C4⋊C4C23×C6711yescharacteristic
1243C2×C4⋊C4C23×C6711yescharacteristic
1244C2×C4⋊C4C23×C6711yescharacteristic
1245C2×C4⋊C4C23×C6711yescharacteristic
1246C2×C4⋊C4C23×C6711yescharacteristic
1247C2×C4⋊C4C23×C6711yescharacteristic
1248C2×C22⋊C4—21no—
1249C2×C22⋊C4—21no—
1250C2×C42—21no—
1251C2×C42C23×C6711yescharacteristic
1252#107C23×C6711yescharacteristic
1253#107C23×C6711yescharacteristic
1254#107C23×C6711yescharacteristic
1255#107C23×C6711yescharacteristic
1256#107C23×C6711yescharacteristic
1257#107C23×C6711yescharacteristic
1258#107C23×C6711yescharacteristic
1259#107C23×C6711yescharacteristic
1260#107C23×C6711yescharacteristic
1261#107C23×C6711yescharacteristic
1262#107C23×C6711yescharacteristic
1263#107C23×C6711yescharacteristic
1264#106C23×C6711yescharacteristic
1265#106C23×C6711yescharacteristic
1266#106C23×C6711yescharacteristic
1267#106C23×C6711yescharacteristic
1268#106C23×C6711yescharacteristic
1269#106C23×C6711yescharacteristic
1270#106C23×C6711yescharacteristic
1271#106C23×C6711yescharacteristic
1272#106C23×C6711yescharacteristic
1273#106C23×C6711yescharacteristic
1274#106C23×C6711yescharacteristic
1275#106C23×C6711yescharacteristic
1276C4⋊C8C23×C6711yescharacteristic
1277C4⋊C8C23×C6711yescharacteristic
1278C4⋊C8C23×C6711yescharacteristic
1279C4⋊C8C23×C6711yescharacteristic
1280#103C23×C6711yescharacteristic
1281#103C23×C6711yescharacteristic
1282#103C23×C6711yescharacteristic
1283#103C23×C6711yescharacteristic
1284#103C23×C6711yescharacteristic
1285#103C23×C6711yescharacteristic
1286#103C23×C6711yescharacteristic
1287#103C23×C6711yescharacteristic
1288#103C23×C6711yescharacteristic
1289#103C23×C6711yescharacteristic
1290#103C23×C6711yescharacteristic
1291#103C23×C6711yescharacteristic
1292#103C23×C6711yescharacteristic
1293#103C23×C6711yescharacteristic
1294#103C23×C6711yescharacteristic
1295#103C23×C6711yescharacteristic
1296#102C23×C6711yescharacteristic
1297#102C23×C6711yescharacteristic
1298#102C23×C6711yescharacteristic
1299#102C23×C6711yescharacteristic
1300#102C23×C6711yescharacteristic
1301#102C23×C6711yescharacteristic
1302#102C23×C6711yescharacteristic
1303#102C23×C6711yescharacteristic
1304#102C23×C6711yescharacteristic
1305#102C23×C6711yescharacteristic
1306#102C23×C6711yescharacteristic
1307#102C23×C6711yescharacteristic
1308#102C23×C6711yescharacteristic
1309#102C23×C6711yescharacteristic
1310#102C23×C6711yescharacteristic
1311#102C23×C6711yescharacteristic
1312C22⋊C8C23×C6711yescharacteristic
1313C22⋊C8C23×C6711yescharacteristic
1314C22⋊C8C23×C6711yescharacteristic
1315C22⋊C8C23×C6711yescharacteristic
1316C22⋊C8C23×C6711yescharacteristic
1317C22⋊C8C23×C6711yescharacteristic
1318C22⋊C8C23×C6711yescharacteristic
1319C22⋊C8C23×C6711yescharacteristic
1320C22⋊C8C23×C6711yescharacteristic
1321C22⋊C8C23×C6711yescharacteristic
1322C22⋊C8C23×C6711yescharacteristic
1323C22⋊C8C23×C6711yescharacteristic
1324C4×C8C23×C6711yescharacteristic
1325C4×C8C23×C6711yescharacteristic
1326C4×C8C23×C6711yescharacteristic
1327C4×C8C23×C6711yescharacteristic
1328C24—21no—
1329#41—41no—
1330#41—41no—
1331#41—41no—
1332#41—41no—
1333#41—41no—
1334#41—41no—
1335#41—41no—
1336#41—41no—
1337#41—41no—
1338#41—41no—
1339C2×Q8—21no—
1340C2×Q8—41no—
1341C2×Q8—41no—
1342C2×Q8C2×D4×C6711yescharacteristic
1343C2×Q8C2×D4×C6711yescharacteristic
1344C2×Q8C24×C6711yescharacteristic
1345C2×Q8C24×C6711yescharacteristic
1346C2×Q8C24×C6711yescharacteristic
1347C2×D4—21no—
1348C2×D4—21no—
1349C2×D4—21no—
1350C2×D4—21no—
1351C2×D4—21no—
1352C2×D4—21no—
1353C2×D4—21no—
1354C2×D4—21no—
1355C2×D4—21no—
1356C2×D4—21no—
1357C2×D4—21no—
1358C2×D4—21no—
1359C2×D4—21no—
1360C2×D4—21no—
1361C2×D4—41no—
1362C2×D4—41no—
1363C2×D4C2×D4×C6711yescharacteristic
1364C2×D4C2×D4×C6711yescharacteristic
1365C2×D4C2×D4×C6711yescharacteristic
1366C2×D4C2×D4×C6711yescharacteristic
1367C2×D4C2×D4×C6711yescharacteristic
1368C2×D4C2×D4×C6711yescharacteristic
1369C2×D4C2×D4×C6711yescharacteristic
1370C2×D4C2×D4×C6711yescharacteristic
1371C2×D4C2×D4×C6711yescharacteristic
1372C2×D4C2×D4×C6711yescharacteristic
1373C2×D4C24×C6711yescharacteristic
1374C2×D4C24×C6711yescharacteristic
1375C2×D4C24×C6711yescharacteristic
1376C22×C4—21no—
1377C22×C4—21no—
1378C22×C4—21no—
1379C22×C4—21no—
1380C22×C4—21no—
1381C22×C4—21no—
1382C22×C4—21no—
1383C22×C4—21no—
1384C22×C4—21no—
1385C22×C4—21no—
1386C22×C4—21no—
1387C22×C4—21no—
1388C22×C4—21no—
1389C22×C4—21no—
1390C22×C4—21no—
1391C22×C4—21no—
1392C22×C4C2×D4×C6711yescharacteristic
1393C22×C4C2×D4×C6711yescharacteristic
1394C22×C4C24×C6711yescharacteristic
1395C22×C4C24×C6711yescharacteristic
1396C22×C4C24×C6711yescharacteristic
1397C22×C4C24×C6711yescharacteristic
1398C22×C4C24×C6711yescharacteristic
1399Q16—41no—
1400Q16—41no—
1401SD16—41no—
1402SD16—41no—
1403SD16—41no—
1404SD16—41no—
1405D8—41no—
1406D8—41no—
1407M16—41no—
1408M16—41no—
1409M16—41no—
1410M16—41no—
1411C2×C8—41no—
1412C2×C8—41no—
1413C2×C8—41no—
1414C2×C8—41no—
1415C2×C8C24×C6711yescharacteristic
1416C2×C8C24×C6711yescharacteristic
1417C2×C8C24×C6711yescharacteristic
1418C2×C8C24×C6711yescharacteristic
1419C2×C8C24×C6711yescharacteristic
1420C2×C8C24×C6711yescharacteristic
1421C2×C8C24×C6711yescharacteristic
1422C2×C8C24×C6711yescharacteristic
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—21no—
1433C4⋊C4—21no—
1434C4⋊C4—21no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—21no—
1440C4⋊C4—21no—
1441C4⋊C4—21no—
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—21no—
1445C4⋊C4—21no—
1446C4⋊C4—21no—
1447C4⋊C4—21no—
1448C4⋊C4—21no—
1449C4⋊C4—21no—
1450C4⋊C4—21no—
1451C4⋊C4—21no—
1452C4⋊C4—21no—
1453C4⋊C4—21no—
1454C4⋊C4—21no—
1455C4⋊C4—21no—
1456C4⋊C4—21no—
1457C4⋊C4C2×D4×C6711yescharacteristic
1458C4⋊C4C2×D4×C6711yescharacteristic
1459C4⋊C4C2×D4×C6711yescharacteristic
1460C4⋊C4C2×D4×C6711yescharacteristic
1461C4⋊C4C24×C6711yescharacteristic
1462C4⋊C4C24×C6711yescharacteristic
1463C4⋊C4C24×C6711yescharacteristic
1464C4⋊C4C24×C6711yescharacteristic
1465C4⋊C4C24×C6711yescharacteristic
1466C4⋊C4C24×C6711yescharacteristic
1467C4⋊C4C24×C6711yescharacteristic
1468C4⋊C4C24×C6711yescharacteristic
1469C4⋊C4C24×C6711yescharacteristic
1470C4⋊C4C24×C6711yescharacteristic
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—21no—
1484C22⋊C4—21no—
1485C22⋊C4—21no—
1486C22⋊C4—21no—
1487C22⋊C4—21no—
1488C22⋊C4—21no—
1489C22⋊C4—21no—
1490C22⋊C4—21no—
1491C22⋊C4—21no—
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4C2×D4×C6711yescharacteristic
1507C22⋊C4C2×D4×C6711yescharacteristic
1508C22⋊C4C2×D4×C6711yescharacteristic
1509C22⋊C4C2×D4×C6711yescharacteristic
1510C22⋊C4C2×D4×C6711yescharacteristic
1511C22⋊C4C2×D4×C6711yescharacteristic
1512C22⋊C4C2×D4×C6711yescharacteristic
1513C22⋊C4C2×D4×C6711yescharacteristic
1514C42—21no—
1515C42—21no—
1516C42—21no—
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—21no—
1521C42—21no—
1522C42—21no—
1523C42—21no—
1524C42—21no—
1525C42C2×D4×C6711yescharacteristic
1526C42C2×D4×C6711yescharacteristic
1527C42C24×C6711yescharacteristic
1528C42C24×C6711yescharacteristic
1529C23—21no—
1530C23—21no—
1531C23—21no—
1532C23—81no—
1533C23—81no—
1534C23—81no—
1535C23C22×D4×C6711yescharacteristic
1536C23C22×D4×C6711yescharacteristic
1537C23C22×D4×C6711yescharacteristic
1538C23C22×D4×C6711yescharacteristic
1539C23C22×D4×C6711yescharacteristic
1540Q8—21no—
1541Q8—21no—
1542Q8—21no—
1543Q8—21no—
1544Q8—21no—
1545Q8—21no—
1546Q8—41no—
1547Q8—41no—
1548Q8—81no—
1549D4—21no—
1550D4—21no—
1551D4—21no—
1552D4—21no—
1553D4—21no—
1554D4—21no—
1555D4—41no—
1556D4—41no—
1557D4—41no—
1558D4—41no—
1559D4—41no—
1560D4—41no—
1561D4—41no—
1562D4—41no—
1563D4—41no—
1564D4—41no—
1565D4—42no—
1566D4—81no—
1567D4—81no—
1568D4—81no—
1569D4—81no—
1570D4—81no—
1571D4—81no—
1572D4—81no—
1573D4—81no—
1574D4—81no—
1575D4—81no—
1576D4—81no—
1577D4—81no—
1578D4—81no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—41no—
1603C2×C4—41no—
1604C2×C4—42no—
1605C2×C4—81no—
1606C2×C4—81no—
1607C2×C4—81no—
1608C2×C4—81no—
1609C2×C4—81no—
1610C2×C4—81no—
1611C2×C4—81no—
1612C2×C4—81no—
1613C2×C4—81no—
1614C2×C4—81no—
1615C2×C4—81no—
1616C2×C4—81no—
1617C2×C4—81no—
1618C2×C4—81no—
1619C2×C4—81no—
1620C2×C4C22×D4×C6711yescharacteristic
1621C2×C4C22×D4×C6711yescharacteristic
1622C2×C4C22×D4×C6711yescharacteristic
1623C2×C4C22×D4×C6711yescharacteristic
1624C2×C4C22×D4×C6711yescharacteristic
1625C2×C4C22×D4×C6711yescharacteristic
1626C2×C4C22×D4×C6711yescharacteristic
1627C2×C4C22×D4×C6711yescharacteristic
1628C2×C4C22×D4×C6711yescharacteristic
1629C2×C4C25×C6711yescharacteristic
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—21no—
1634C8—21no—
1635C8—21no—
1636C8—21no—
1637C8—21no—
1638C22—21no—
1639C22—21no—
1640C22—21no—
1641C22—21no—
1642C22—21no—
1643C22—21no—
1644C22—21no—
1645C22—21no—
1646C22—21no—
1647C22—21no—
1648C22—21no—
1649C22—21no—
1650C22—21no—
1651C22—21no—
1652C22—21no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—162no—
1663C22C23×D4×C6711yescharacteristic
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—21no—
1668C4—21no—
1669C4—21no—
1670C4—21no—
1671C4—21no—
1672C4—21no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4—41no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—41no—
1686C4#585×C6711yescharacteristic
1687C4#585×C6711yescharacteristic
1688C2—41no—
1689C2—41no—
1690C2—41no—
1691C2—41no—
1692C2—41no—
1693C2—81no—
1694C2—81no—
1695C2—81no—
1696C2C67×#348511yescharacteristic
1697C2C67×#358411yescharacteristic
1698C2C67×#358411yescharacteristic
subgroupG/H
center, socleC22×C67C23×D4
commutator, Frattini, cosocleC2×C4C25×C67
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ #532×C67 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C67×#3551C2semidirect
2. C67×#3512C2semidirect
3. C67×#3355C2semidirect
4. C67×#3352C2semidirect
5. C67×#3351C2semidirect
6. C67×#3351C2semidirect
7. C67×#3339C2semidirect
8. C67×#3337C2semidirect
9. C67×#3337C2semidirect
10. C67×#3336C2semidirect
11. C67×#3327C2semidirect
12. C67×#3326C2semidirect
13. C67×#3323C2semidirect
14. C67×#3322C2semidirect
15. C67×#3301C2semidirect
16. C67×#3300C2semidirect
17. C67×#3297C2semidirect
18. C67×#3296C2semidirect
19. C67×#3232C2semidirect
20. C67×#3232C2semidirect
21. C67×#3204C2semidirect
22. C67×#3203C2semidirect
23. C67×#3201C2semidirect
24. C67×#3198C2semidirect
25. C67×#3102C2semidirect
26. C67×#3102C2semidirect
27. C67×#3099C2semidirect
28. C67×#3098C2semidirect
29. C67×#3097C2semidirect
30. C67×#3096C2semidirect
31. C67×#2979C2semidirect
43. #553×C67C22semidirect
44. #553×C67C22semidirect
49. #552×C67C22semidirect
50. #552×C67C22semidirect
65. #537×C67C22semidirect
73. C2×#125×C67C22semidirect
75. #520×C67C22semidirect
76. C4×#41×C67C22semidirect
77. #499×C67C22semidirect
78. #499×C67C22semidirect
79. #499×C67C22semidirect
80. #499×C67C22semidirect
88. #485×C67C22semidirect
89. #485×C67C22semidirect
90. #485×C67C22semidirect
91. #485×C67C22semidirect
92. #485×C67C22semidirect
94. #484×C67C22semidirect
95. #484×C67C22semidirect
96. #484×C67C22semidirect
97. #484×C67C22semidirect
99. #483×C67C22semidirect
100. #483×C67C22semidirect
101. #483×C67C22semidirect
102. #483×C67C22semidirect
110. #482×C67C22semidirect
115. #481×C67C22semidirect
120. #480×C67C22semidirect
121. #479×C67C22semidirect
122. #479×C67C22semidirect
123. #479×C67C22semidirect
124. #479×C67C22semidirect
125. #479×C67C22semidirect
126. #479×C67C22semidirect
131. #478×C67C22semidirect
132. #478×C67C22semidirect
134. #470×C67C22semidirect
140. #468×C67C22semidirect
142. #467×C67C22semidirect
148. #465×C67C22semidirect
155. #452×C67C22semidirect
156. #452×C67C22semidirect
157. #451×C67C22semidirect
163. #448×C67C22semidirect
165. C4×Q16×C67C22semidirect
166. C4×Q16×C67C22semidirect
169. C4×SD16×C67C22semidirect
170. C4×SD16×C67C22semidirect
175. #436×C67C22semidirect
176. #436×C67C22semidirect
179. C8×D4×C67C22semidirect
180. C8×D4×C67C22semidirect
181. #431×C67C22semidirect
182. #431×C67C22semidirect
184. #428×C67C22semidirect
185. #428×C67C22semidirect
186. #428×C67C22semidirect
188. #427×C67C22semidirect
189. C2×#107×C67C22semidirect
190. C2×#106×C67C22semidirect
191. #419×C67C22semidirect
197. C2×#103×C67C22semidirect
201. #408×C67C22semidirect
202. #408×C67C22semidirect
838. #61790C67direct (N × H)
850. #3551C2×C67semidirect
851. #3512C2×C67semidirect
852. #3355C2×C67semidirect
853. #3352C2×C67semidirect
854. #3351C2×C67semidirect
855. #3351C2×C67semidirect
856. #3339C2×C67semidirect
857. #3337C2×C67semidirect
858. #3337C2×C67semidirect
859. #3336C2×C67semidirect
860. #3327C2×C67semidirect
861. #3326C2×C67semidirect
862. #3323C2×C67semidirect
863. #3322C2×C67semidirect
864. #3301C2×C67semidirect
865. #3300C2×C67semidirect
866. #3297C2×C67semidirect
867. #3296C2×C67semidirect
868. #3232C2×C67semidirect
869. #3232C2×C67semidirect
870. #3204C2×C67semidirect
871. #3203C2×C67semidirect
872. #3201C2×C67semidirect
873. #3198C2×C67semidirect
874. #3102C2×C67semidirect
875. #3102C2×C67semidirect
876. #3099C2×C67semidirect
877. #3098C2×C67semidirect
878. #3097C2×C67semidirect
879. #3096C2×C67semidirect
880. #2979C2×C67semidirect
881. C67#61790direct (N × H)
893. #553C22×C67semidirect
894. #553C22×C67semidirect
899. #552C22×C67semidirect
900. #552C22×C67semidirect
915. #537C22×C67semidirect
923. C2×#125C22×C67semidirect
925. #520C22×C67semidirect
926. C4×#41C22×C67semidirect
927. #499C22×C67semidirect
928. #499C22×C67semidirect
929. #499C22×C67semidirect
930. #499C22×C67semidirect
938. #485C22×C67semidirect
939. #485C22×C67semidirect
940. #485C22×C67semidirect
941. #485C22×C67semidirect
942. #485C22×C67semidirect
944. #484C22×C67semidirect
945. #484C22×C67semidirect
946. #484C22×C67semidirect
947. #484C22×C67semidirect
949. #483C22×C67semidirect
950. #483C22×C67semidirect
951. #483C22×C67semidirect
952. #483C22×C67semidirect
960. #482C22×C67semidirect
965. #481C22×C67semidirect
970. #480C22×C67semidirect
971. #479C22×C67semidirect
972. #479C22×C67semidirect
973. #479C22×C67semidirect
974. #479C22×C67semidirect
975. #479C22×C67semidirect
976. #479C22×C67semidirect
981. #478C22×C67semidirect
982. #478C22×C67semidirect
984. #470C22×C67semidirect
990. #468C22×C67semidirect
992. #467C22×C67semidirect
998. #465C22×C67semidirect
1005. #452C22×C67semidirect
1006. #452C22×C67semidirect
1007. #451C22×C67semidirect
1013. #448C22×C67semidirect
1015. C4×Q16C22×C67semidirect
1016. C4×Q16C22×C67semidirect
1019. C4×SD16C22×C67semidirect
1020. C4×SD16C22×C67semidirect
1025. #436C22×C67semidirect
1026. #436C22×C67semidirect
1029. C8×D4C22×C67semidirect
1030. C8×D4C22×C67semidirect
1031. #431C22×C67semidirect
1032. #431C22×C67semidirect
1034. #428C22×C67semidirect
1035. #428C22×C67semidirect
1036. #428C22×C67semidirect
1038. #427C22×C67semidirect
1039. C2×#107C22×C67semidirect
1040. C2×#106C22×C67semidirect
1041. #419C22×C67semidirect
1047. C2×#103C22×C67semidirect
1051. #408C22×C67semidirect
1052. #408C22×C67semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C67×#35512
C67×#35122
C67×#33552
C67×#33522
C67×#33512
C67×#33392
C67×#33372
C67×#33362
C67×#33272
C67×#33262
C67×#33232
C67×#33222
C67×#33012
C67×#33002
C67×#32972
C67×#32962
C67×#32322
C67×#32042
C67×#32032
C67×#32012
C67×#31982
C67×#31022
C67×#30992
C67×#30982
C67×#30972
C67×#30962
C67×#29792
#6179067