Finite Group Databasebeta

← C67×#61814 #30741065

Subgroups — C67×#61814 #30741065

Order 17152.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3547C211yesmaximal, characteristic, complemented
2C67×#3512C211yesmaximal, characteristic, complemented
3C67×#3352C211yesmaximal, characteristic, complemented
4C67×#3351C211yesmaximal, characteristic, complemented
5C67×#3348C211yesmaximal, characteristic, complemented
6C67×#3347C211yesmaximal, characteristic, complemented
7C67×#3346C211yesmaximal, characteristic, complemented
8C67×#3344C211yesmaximal, characteristic, complemented
9C67×#3337C211yesmaximal, characteristic, complemented
10C67×#3336C211yesmaximal, characteristic, complemented
11C67×#3327C211yesmaximal, characteristic, complemented
12C67×#3326C211yesmaximal, characteristic, complemented
13C67×#3320C211yesmaximal, characteristic, complemented
14C67×#3315C211yesmaximal, characteristic, complemented
15C67×#3312C211yesmaximal, characteristic, complemented
16C67×#3307C211yesmaximal, characteristic, complemented
17C67×#3301C211yesmaximal, characteristic, complemented
18C67×#3300C211yesmaximal, characteristic, complemented
19C67×#3236C211yesmaximal, characteristic, complemented
20C67×#3232C211yesmaximal, characteristic, complemented
21C67×#3204C211yesmaximal, characteristic, complemented
22C67×#3203C211yesmaximal, characteristic, complemented
23C67×#3201C211yesmaximal, characteristic, complemented
24C67×#3201C211yesmaximal, characteristic, complemented
25C67×#3111C211yesmaximal, characteristic, complemented
26C67×#3107C211yesmaximal, characteristic, complemented
27C67×#3099C211yesmaximal, characteristic, complemented
28C67×#3098C211yesmaximal, characteristic, complemented
29C67×#3097C211yesmaximal, characteristic, complemented
30C67×#3097C211yesmaximal, characteristic, complemented
31C67×#2981C211yesmaximal, characteristic, complemented
32#562×C67—21no—
33#562×C67—21no—
34#555×C67—21no—
35#555×C67C2211yescharacteristic
36#554×C67C2211yescharacteristic
37#553×C67—21no—
38#553×C67—21no—
39#553×C67—21no—
40#553×C67—21no—
41#553×C67—21no—
42#553×C67C2211yescharacteristic
43#553×C67C2211yescharacteristic
44#553×C67C2211yescharacteristic
45#553×C67C2211yescharacteristic
46#552×C67C2211yescharacteristic
47#552×C67C2211yescharacteristic
48#552×C67C2211yescharacteristic
49#552×C67C2211yescharacteristic
50#552×C67C2211yescharacteristic
51#552×C67C2211yescharacteristic
52D4×Q8×C67C2211yescharacteristic
53#548×C67C2211yescharacteristic
54#548×C67C2211yescharacteristic
55#547×C67C2211yescharacteristic
56#544×C67—21no—
57#542×C67—21no—
58#542×C67—21no—
59#541×C67—21no—
60#540×C67—21no—
61#540×C67—21no—
62#537×C67C2211yescharacteristic
63#537×C67C2211yescharacteristic
64#537×C67C2211yescharacteristic
65#537×C67C2211yescharacteristic
66#536×C67C2211yescharacteristic
67#536×C67C2211yescharacteristic
68#533×C67C2211yescharacteristic
69#532×C67C2211yescharacteristic
70#529×C67—21no—
71#529×C67—21no—
72#529×C67C2211yescharacteristic
73C2×#125×C67C2211yescharacteristic
74#520×C67C2211yescharacteristic
75#520×C67C2211yescharacteristic
76C4×#41×C67C2211yescharacteristic
77#501×C67C2211yescharacteristic
78#501×C67C2211yescharacteristic
79#499×C67C2211yescharacteristic
80#499×C67C2211yescharacteristic
81#491×C67C2211yescharacteristic
82#491×C67C2211yescharacteristic
83#488×C67C2211yescharacteristic
84#488×C67C2211yescharacteristic
85#485×C67C2211yescharacteristic
86#485×C67C2211yescharacteristic
87#485×C67C2211yescharacteristic
88#485×C67C2211yescharacteristic
89#485×C67C2211yescharacteristic
90#485×C67C2211yescharacteristic
91#485×C67C2211yescharacteristic
92#485×C67C2211yescharacteristic
93#485×C67C2211yescharacteristic
94#485×C67C2211yescharacteristic
95#485×C67C2211yescharacteristic
96#484×C67C2211yescharacteristic
97#484×C67C2211yescharacteristic
98#484×C67C2211yescharacteristic
99#484×C67C2211yescharacteristic
100#484×C67C2211yescharacteristic
101#484×C67C2211yescharacteristic
102#484×C67C2211yescharacteristic
103#483×C67C2211yescharacteristic
104#483×C67C2211yescharacteristic
105#483×C67C2211yescharacteristic
106#483×C67C2211yescharacteristic
107#483×C67C2211yescharacteristic
108#483×C67C2211yescharacteristic
109#483×C67C2211yescharacteristic
110#482×C67C2211yescharacteristic
111#482×C67C2211yescharacteristic
112#482×C67C2211yescharacteristic
113#482×C67C2211yescharacteristic
114#482×C67C2211yescharacteristic
115#481×C67C2211yescharacteristic
116#481×C67C2211yescharacteristic
117#481×C67C2211yescharacteristic
118#480×C67C2211yescharacteristic
119#480×C67C2211yescharacteristic
120#480×C67C2211yescharacteristic
121#479×C67C2211yescharacteristic
122#479×C67C2211yescharacteristic
123#479×C67C2211yescharacteristic
124#479×C67C2211yescharacteristic
125#479×C67C2211yescharacteristic
126#479×C67C2211yescharacteristic
127#479×C67C2211yescharacteristic
128#478×C67C2211yescharacteristic
129#478×C67C2211yescharacteristic
130#478×C67C2211yescharacteristic
131#475×C67C2211yescharacteristic
132#474×C67C2211yescharacteristic
133#470×C67C2211yescharacteristic
134#470×C67C2211yescharacteristic
135#470×C67C2211yescharacteristic
136#469×C67C2211yescharacteristic
137#468×C67C2211yescharacteristic
138#468×C67C2211yescharacteristic
139#468×C67C2211yescharacteristic
140#468×C67C2211yescharacteristic
141#467×C67C2211yescharacteristic
142#467×C67C2211yescharacteristic
143#467×C67C2211yescharacteristic
144#466×C67C2211yescharacteristic
145#465×C67C2211yescharacteristic
146#465×C67C2211yescharacteristic
147#465×C67C2211yescharacteristic
148#465×C67C2211yescharacteristic
149#464×C67C2211yescharacteristic
150#463×C67C2211yescharacteristic
151#462×C67C2211yescharacteristic
152#461×C67C2211yescharacteristic
153#452×C67C2211yescharacteristic
154#452×C67C2211yescharacteristic
155#452×C67C2211yescharacteristic
156#452×C67C2211yescharacteristic
157#452×C67C2211yescharacteristic
158#451×C67C2211yescharacteristic
159#451×C67C2211yescharacteristic
160#449×C67C2211yescharacteristic
161#449×C67C2211yescharacteristic
162#449×C67C2211yescharacteristic
163#448×C67C2211yescharacteristic
164#448×C67C2211yescharacteristic
165#442×C67C2211yescharacteristic
166#441×C67C2211yescharacteristic
167#440×C67C2211yescharacteristic
168#440×C67C2211yescharacteristic
169C4×Q16×C67C2211yescharacteristic
170C4×Q16×C67C2211yescharacteristic
171C4×SD16×C67C2211yescharacteristic
172C4×SD16×C67C2211yescharacteristic
173#436×C67C2211yescharacteristic
174#436×C67C2211yescharacteristic
175#435×C67C2211yescharacteristic
176#435×C67C2211yescharacteristic
177#435×C67C2211yescharacteristic
178#435×C67C2211yescharacteristic
179C8×D4×C67C2211yescharacteristic
180C8×D4×C67C2211yescharacteristic
181#432×C67C2211yescharacteristic
182#431×C67C2211yescharacteristic
183#428×C67C2211yescharacteristic
184#428×C67C2211yescharacteristic
185#428×C67C2211yescharacteristic
186#428×C67C2211yescharacteristic
187#427×C67C2211yescharacteristic
188#427×C67C2211yescharacteristic
189C2×#107×C67C2211yescharacteristic
190C2×#106×C67C2211yescharacteristic
191#419×C67C2211yescharacteristic
192#419×C67C2211yescharacteristic
193#417×C67C2211yescharacteristic
194#417×C67C2211yescharacteristic
195#416×C67C2211yescharacteristic
196#416×C67C2211yescharacteristic
197C2×#103×C67C2211yescharacteristic
198C2×#103×C67C2211yescharacteristic
199#408×C67C2211yescharacteristic
200#408×C67C2211yescharacteristic
201#408×C67C2211yescharacteristic
202#408×C67C2211yescharacteristic
203C2×#41×C67C2311yescharacteristic
204C2×#41×C67C2311yescharacteristic
205C2×#41×C67C2311yescharacteristic
206C2×#41×C67C2311yescharacteristic
207C2×#41×C67C2311yescharacteristic
208C22×Q8×C67C2311yescharacteristic
209C22×Q8×C67C2311yescharacteristic
210C2×Q16×C67C2311yescharacteristic
211C2×Q16×C67C2311yescharacteristic
212C2×Q16×C67C2311yescharacteristic
213C2×SD16×C67C2311yescharacteristic
214C2×SD16×C67C2311yescharacteristic
215C2×SD16×C67C2311yescharacteristic
216C2×SD16×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×C67—21no—
228C4⋊Q8×C67—21no—
229C4⋊Q8×C67D411yescharacteristic
230C4⋊Q8×C67C2311yescharacteristic
231C4⋊Q8×C67C2311yescharacteristic
232#127×C67D411yescharacteristic
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×C67—21no—
253#125×C67—21no—
254#125×C67C2311yescharacteristic
255#125×C67C2311yescharacteristic
256#125×C67C2311yescharacteristic
257#125×C67C2311yescharacteristic
258#125×C67C2311yescharacteristic
259#124×C67—21no—
260#124×C67—21no—
261#124×C67—21no—
262#124×C67—21no—
263#124×C67—21no—
264#124×C67—21no—
265#124×C67D411yescharacteristic
266#124×C67D411yescharacteristic
267#124×C67C2311yescharacteristic
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—
284#123×C67—21no—
285C22⋊Q8×C67—21no—
286C22⋊Q8×C67—21no—
287C22⋊Q8×C67—21no—
288C22⋊Q8×C67—21no—
289C22⋊Q8×C67—21no—
290C22⋊Q8×C67—21no—
291C22⋊Q8×C67—21no—
292C22⋊Q8×C67—21no—
293C22⋊Q8×C67—21no—
294C22⋊Q8×C67—21no—
295C22⋊Q8×C67—21no—
296C22⋊Q8×C67C2311yescharacteristic
297C22⋊Q8×C67C2311yescharacteristic
298C22⋊Q8×C67C2311yescharacteristic
299C22⋊Q8×C67C2311yescharacteristic
300C22⋊Q8×C67C2311yescharacteristic
301C22⋊Q8×C67C2311yescharacteristic
302C22⋊Q8×C67C2311yescharacteristic
303C22⋊Q8×C67C2311yescharacteristic
304C22⋊Q8×C67C2311yescharacteristic
305C22⋊Q8×C67C2311yescharacteristic
306C22⋊Q8×C67C2311yescharacteristic
307C22⋊Q8×C67C2311yescharacteristic
308C22⋊Q8×C67C2311yescharacteristic
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×C67—21no—
323#121×C67—21no—
324#121×C67—21no—
325#121×C67—21no—
326#121×C67—21no—
327#121×C67—21no—
328#121×C67—21no—
329#121×C67D411yescharacteristic
330#121×C67D411yescharacteristic
331#121×C67D411yescharacteristic
332#121×C67D411yescharacteristic
333#121×C67C2311yescharacteristic
334#121×C67C2311yescharacteristic
335#121×C67C2311yescharacteristic
336#121×C67C2311yescharacteristic
337#121×C67C2311yescharacteristic
338#121×C67C2311yescharacteristic
339#121×C67C2311yescharacteristic
340C4×Q8×C67—21no—
341C4×Q8×C67—21no—
342C4×Q8×C67—21no—
343C4×Q8×C67C2311yescharacteristic
344C4×Q8×C67C2311yescharacteristic
345C4×Q8×C67C2311yescharacteristic
346C4×Q8×C67C2311yescharacteristic
347C4×Q8×C67C2311yescharacteristic
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×C67—21no—
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×C67—21no—
382#117×C67C2311yescharacteristic
383#117×C67C2311yescharacteristic
384#117×C67C2311yescharacteristic
385#117×C67C2311yescharacteristic
386#117×C67C2311yescharacteristic
387#117×C67C2311yescharacteristic
388#117×C67C2311yescharacteristic
389C2×C4⋊C4×C67—21no—
390C2×C4⋊C4×C67—21no—
391C2×C4⋊C4×C67—21no—
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×C4⋊C4×C67C2311yescharacteristic
399C2×C4⋊C4×C67C2311yescharacteristic
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#103×C67C2311yescharacteristic
447#103×C67C2311yescharacteristic
448#103×C67C2311yescharacteristic
449#103×C67C2311yescharacteristic
450#103×C67C2311yescharacteristic
451#103×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
474#97×C67C2311yescharacteristic
475#97×C67C2311yescharacteristic
476C4×C8×C67C2311yescharacteristic
477C4×C8×C67C2311yescharacteristic
478#41×C67—41no—
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—
488C2×Q8×C67—21no—
489C2×Q8×C67—21no—
490C2×Q8×C67—21no—
491C2×Q8×C67—41no—
492C2×Q8×C67—41no—
493C2×Q8×C67—41no—
494C2×Q8×C67—41no—
495C2×Q8×C67C2×D411yescharacteristic
496C2×Q8×C67C2×D411yescharacteristic
497C2×Q8×C67C2411yescharacteristic
498C2×Q8×C67C2411yescharacteristic
499C2×Q8×C67C2411yescharacteristic
500C2×Q8×C67C2411yescharacteristic
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×C67C2×D411yescharacteristic
512C2×D4×C67C2×D411yescharacteristic
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×C67C2411yescharacteristic
522C2×D4×C67C2411yescharacteristic
523C22×C4×C67—21no—
524C22×C4×C67—21no—
525C22×C4×C67—21no—
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×C67C2×D411yescharacteristic
540C22×C4×C67C2×D411yescharacteristic
541C22×C4×C67C2411yescharacteristic
542C22×C4×C67C2411yescharacteristic
543C22×C4×C67C2411yescharacteristic
544C22×C4×C67C2411yescharacteristic
545C22×C4×C67C2411yescharacteristic
546Q16×C67—41no—
547Q16×C67—41no—
548Q16×C67—41no—
549SD16×C67—41no—
550SD16×C67—41no—
551SD16×C67—41no—
552SD16×C67—41no—
553D8×C67—41no—
554M16×C67—41no—
555M16×C67—41no—
556M16×C67—41no—
557M16×C67—41no—
558C2×C8×C67—41no—
559C2×C8×C67—41no—
560C2×C8×C67—41no—
561C2×C8×C67—41no—
562C2×C8×C67C2411yescharacteristic
563C2×C8×C67C2411yescharacteristic
564C2×C8×C67C2411yescharacteristic
565C2×C8×C67C2411yescharacteristic
566C2×C8×C67C2411yescharacteristic
567C2×C8×C67C2411yescharacteristic
568C2×C8×C67C2411yescharacteristic
569C2×C8×C67C2411yescharacteristic
570C4⋊C4×C67—21no—
571C4⋊C4×C67—21no—
572C4⋊C4×C67—21no—
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×C67—21no—
608C4⋊C4×C67—21no—
609C4⋊C4×C67C2×D411yescharacteristic
610C4⋊C4×C67C2×D411yescharacteristic
611C4⋊C4×C67C2×D411yescharacteristic
612C4⋊C4×C67C2×D411yescharacteristic
613C4⋊C4×C67C2411yescharacteristic
614C4⋊C4×C67C2411yescharacteristic
615C4⋊C4×C67C2411yescharacteristic
616C4⋊C4×C67C2411yescharacteristic
617C4⋊C4×C67C2411yescharacteristic
618C4⋊C4×C67C2411yescharacteristic
619C4⋊C4×C67C2411yescharacteristic
620C4⋊C4×C67C2411yescharacteristic
621C4⋊C4×C67C2411yescharacteristic
622C4⋊C4×C67C2411yescharacteristic
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×C67C2×D411yescharacteristic
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
663C42×C67—21no—
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×C67C22×D411yescharacteristic
682C23×C67C22×D411yescharacteristic
683C23×C67C22×D411yescharacteristic
684C23×C67C22×D411yescharacteristic
685C23×C67C22×D411yescharacteristic
686Q8×C67—21no—
687Q8×C67—21no—
688Q8×C67—21no—
689Q8×C67—21no—
690Q8×C67—21no—
691Q8×C67—21no—
692Q8×C67—21no—
693Q8×C67—21no—
694Q8×C67—41no—
695Q8×C67—41no—
696Q8×C67—81no—
697Q8×C67—81no—
698Q8×C67—81no—
699D4×C67—21no—
700D4×C67—21no—
701D4×C67—21no—
702D4×C67—21no—
703D4×C67—41no—
704D4×C67—41no—
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—42no—
714D4×C67—81no—
715D4×C67—81no—
716D4×C67—81no—
717D4×C67—81no—
718D4×C67—81no—
719D4×C67—81no—
720D4×C67—81no—
721D4×C67—81no—
722D4×C67—81no—
723C2×C4×C67—21no—
724C2×C4×C67—21no—
725C2×C4×C67—21no—
726C2×C4×C67—21no—
727C2×C4×C67—21no—
728C2×C4×C67—21no—
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—41no—
748C2×C4×C67—41no—
749C2×C4×C67—42no—
750C2×C4×C67—42no—
751C2×C4×C67—81no—
752C2×C4×C67—81no—
753C2×C4×C67—81no—
754C2×C4×C67—81no—
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×C67C22×D411yescharacteristic
766C2×C4×C67C22×D411yescharacteristic
767C2×C4×C67C22×D411yescharacteristic
768C2×C4×C67C22×D411yescharacteristic
769C2×C4×C67C22×D411yescharacteristic
770C2×C4×C67C22×D411yescharacteristic
771C2×C4×C67C22×D411yescharacteristic
772C2×C4×C67C22×D411yescharacteristic
773C2×C4×C67C22×D411yescharacteristic
774C2×C4×C67C2511yescharacteristic
775C8×C67—21no—
776C8×C67—21no—
777C8×C67—21no—
778C8×C67—21no—
779C8×C67—21no—
780C8×C67—21no—
781C8×C67—21no—
782C8×C67—21no—
783C22×C67—21no—
784C22×C67—21no—
785C22×C67—21no—
786C22×C67—21no—
787C22×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—41no—
799C22×C67—41no—
800C22×C67—41no—
801C22×C67—41no—
802C22×C67—41no—
803C22×C67—41no—
804C22×C67C23×D411yescharacteristic
805C4×C67—21no—
806C4×C67—21no—
807C4×C67—21no—
808C4×C67—21no—
809C4×C67—21no—
810C4×C67—21no—
811C4×C67—21no—
812C4×C67—21no—
813C4×C67—21no—
814C4×C67—41no—
815C4×C67—41no—
816C4×C67—41no—
817C4×C67—41no—
818C4×C67—41no—
819C4×C67—41no—
820C4×C67—41no—
821C4×C67—41no—
822C4×C67—41no—
823C4×C67—41no—
824C4×C67—41no—
825C4×C67—41no—
826C4×C67—41no—
827C4×C67—41no—
828C4×C67#58511yescharacteristic
829C4×C67#58511yescharacteristic
830#61814C6711yesmaximal, characteristic, direct product factor, Sylow
831C2×C67—41no—
832C2×C67—41no—
833C2×C67—41no—
834C2×C67—41no—
835C2×C67—41no—
836C2×C67—81no—
837C2×C67—81no—
838C2×C67#348511yescharacteristic
839C2×C67#358411yescharacteristic
840C2×C67#358611yescharacteristic
841#3547C2×C6711yescharacteristic, complemented
842#3512C2×C6711yescharacteristic, complemented
843#3352C2×C6711yescharacteristic, complemented
844#3351C2×C6711yescharacteristic, complemented
845#3348C2×C6711yescharacteristic, complemented
846#3347C2×C6711yescharacteristic, complemented
847#3346C2×C6711yescharacteristic, complemented
848#3344C2×C6711yescharacteristic, complemented
849#3337C2×C6711yescharacteristic, complemented
850#3336C2×C6711yescharacteristic, complemented
851#3327C2×C6711yescharacteristic, complemented
852#3326C2×C6711yescharacteristic, complemented
853#3320C2×C6711yescharacteristic, complemented
854#3315C2×C6711yescharacteristic, complemented
855#3312C2×C6711yescharacteristic, complemented
856#3307C2×C6711yescharacteristic, complemented
857#3301C2×C6711yescharacteristic, complemented
858#3300C2×C6711yescharacteristic, complemented
859#3236C2×C6711yescharacteristic, complemented
860#3232C2×C6711yescharacteristic, complemented
861#3204C2×C6711yescharacteristic, complemented
862#3203C2×C6711yescharacteristic, complemented
863#3201C2×C6711yescharacteristic, complemented
864#3201C2×C6711yescharacteristic, complemented
865#3111C2×C6711yescharacteristic, complemented
866#3107C2×C6711yescharacteristic, complemented
867#3099C2×C6711yescharacteristic, complemented
868#3098C2×C6711yescharacteristic, complemented
869#3097C2×C6711yescharacteristic, complemented
870#3097C2×C6711yescharacteristic, complemented
871#2981C2×C6711yescharacteristic, complemented
872C67#6181411yescharacteristic, direct product factor, Sylow
873#562—21no—
874#562—21no—
875#555—21no—
876#555C22×C6711yescharacteristic
877#554C22×C6711yescharacteristic
878#553—21no—
879#553—21no—
880#553—21no—
881#553—21no—
882#553—21no—
883#553C22×C6711yescharacteristic
884#553C22×C6711yescharacteristic
885#553C22×C6711yescharacteristic
886#553C22×C6711yescharacteristic
887#552C22×C6711yescharacteristic
888#552C22×C6711yescharacteristic
889#552C22×C6711yescharacteristic
890#552C22×C6711yescharacteristic
891#552C22×C6711yescharacteristic
892#552C22×C6711yescharacteristic
893D4×Q8C22×C6711yescharacteristic
894#548C22×C6711yescharacteristic
895#548C22×C6711yescharacteristic
896#547C22×C6711yescharacteristic
897#544—21no—
898#542—21no—
899#542—21no—
900#541—21no—
901#540—21no—
902#540—21no—
903#537C22×C6711yescharacteristic
904#537C22×C6711yescharacteristic
905#537C22×C6711yescharacteristic
906#537C22×C6711yescharacteristic
907#536C22×C6711yescharacteristic
908#536C22×C6711yescharacteristic
909#533C22×C6711yescharacteristic
910#532C22×C6711yescharacteristic
911#529—21no—
912#529—21no—
913#529C22×C6711yescharacteristic
914C2×#125C22×C6711yescharacteristic
915#520C22×C6711yescharacteristic
916#520C22×C6711yescharacteristic
917C4×#41C22×C6711yescharacteristic
918#501C22×C6711yescharacteristic
919#501C22×C6711yescharacteristic
920#499C22×C6711yescharacteristic
921#499C22×C6711yescharacteristic
922#491C22×C6711yescharacteristic
923#491C22×C6711yescharacteristic
924#488C22×C6711yescharacteristic
925#488C22×C6711yescharacteristic
926#485C22×C6711yescharacteristic
927#485C22×C6711yescharacteristic
928#485C22×C6711yescharacteristic
929#485C22×C6711yescharacteristic
930#485C22×C6711yescharacteristic
931#485C22×C6711yescharacteristic
932#485C22×C6711yescharacteristic
933#485C22×C6711yescharacteristic
934#485C22×C6711yescharacteristic
935#485C22×C6711yescharacteristic
936#485C22×C6711yescharacteristic
937#484C22×C6711yescharacteristic
938#484C22×C6711yescharacteristic
939#484C22×C6711yescharacteristic
940#484C22×C6711yescharacteristic
941#484C22×C6711yescharacteristic
942#484C22×C6711yescharacteristic
943#484C22×C6711yescharacteristic
944#483C22×C6711yescharacteristic
945#483C22×C6711yescharacteristic
946#483C22×C6711yescharacteristic
947#483C22×C6711yescharacteristic
948#483C22×C6711yescharacteristic
949#483C22×C6711yescharacteristic
950#483C22×C6711yescharacteristic
951#482C22×C6711yescharacteristic
952#482C22×C6711yescharacteristic
953#482C22×C6711yescharacteristic
954#482C22×C6711yescharacteristic
955#482C22×C6711yescharacteristic
956#481C22×C6711yescharacteristic
957#481C22×C6711yescharacteristic
958#481C22×C6711yescharacteristic
959#480C22×C6711yescharacteristic
960#480C22×C6711yescharacteristic
961#480C22×C6711yescharacteristic
962#479C22×C6711yescharacteristic
963#479C22×C6711yescharacteristic
964#479C22×C6711yescharacteristic
965#479C22×C6711yescharacteristic
966#479C22×C6711yescharacteristic
967#479C22×C6711yescharacteristic
968#479C22×C6711yescharacteristic
969#478C22×C6711yescharacteristic
970#478C22×C6711yescharacteristic
971#478C22×C6711yescharacteristic
972#475C22×C6711yescharacteristic
973#474C22×C6711yescharacteristic
974#470C22×C6711yescharacteristic
975#470C22×C6711yescharacteristic
976#470C22×C6711yescharacteristic
977#469C22×C6711yescharacteristic
978#468C22×C6711yescharacteristic
979#468C22×C6711yescharacteristic
980#468C22×C6711yescharacteristic
981#468C22×C6711yescharacteristic
982#467C22×C6711yescharacteristic
983#467C22×C6711yescharacteristic
984#467C22×C6711yescharacteristic
985#466C22×C6711yescharacteristic
986#465C22×C6711yescharacteristic
987#465C22×C6711yescharacteristic
988#465C22×C6711yescharacteristic
989#465C22×C6711yescharacteristic
990#464C22×C6711yescharacteristic
991#463C22×C6711yescharacteristic
992#462C22×C6711yescharacteristic
993#461C22×C6711yescharacteristic
994#452C22×C6711yescharacteristic
995#452C22×C6711yescharacteristic
996#452C22×C6711yescharacteristic
997#452C22×C6711yescharacteristic
998#452C22×C6711yescharacteristic
999#451C22×C6711yescharacteristic
1000#451C22×C6711yescharacteristic
1001#449C22×C6711yescharacteristic
1002#449C22×C6711yescharacteristic
1003#449C22×C6711yescharacteristic
1004#448C22×C6711yescharacteristic
1005#448C22×C6711yescharacteristic
1006#442C22×C6711yescharacteristic
1007#441C22×C6711yescharacteristic
1008#440C22×C6711yescharacteristic
1009#440C22×C6711yescharacteristic
1010C4×Q16C22×C6711yescharacteristic
1011C4×Q16C22×C6711yescharacteristic
1012C4×SD16C22×C6711yescharacteristic
1013C4×SD16C22×C6711yescharacteristic
1014#436C22×C6711yescharacteristic
1015#436C22×C6711yescharacteristic
1016#435C22×C6711yescharacteristic
1017#435C22×C6711yescharacteristic
1018#435C22×C6711yescharacteristic
1019#435C22×C6711yescharacteristic
1020C8×D4C22×C6711yescharacteristic
1021C8×D4C22×C6711yescharacteristic
1022#432C22×C6711yescharacteristic
1023#431C22×C6711yescharacteristic
1024#428C22×C6711yescharacteristic
1025#428C22×C6711yescharacteristic
1026#428C22×C6711yescharacteristic
1027#428C22×C6711yescharacteristic
1028#427C22×C6711yescharacteristic
1029#427C22×C6711yescharacteristic
1030C2×#107C22×C6711yescharacteristic
1031C2×#106C22×C6711yescharacteristic
1032#419C22×C6711yescharacteristic
1033#419C22×C6711yescharacteristic
1034#417C22×C6711yescharacteristic
1035#417C22×C6711yescharacteristic
1036#416C22×C6711yescharacteristic
1037#416C22×C6711yescharacteristic
1038C2×#103C22×C6711yescharacteristic
1039C2×#103C22×C6711yescharacteristic
1040#408C22×C6711yescharacteristic
1041#408C22×C6711yescharacteristic
1042#408C22×C6711yescharacteristic
1043#408C22×C6711yescharacteristic
1044C2×#41C23×C6711yescharacteristic
1045C2×#41C23×C6711yescharacteristic
1046C2×#41C23×C6711yescharacteristic
1047C2×#41C23×C6711yescharacteristic
1048C2×#41C23×C6711yescharacteristic
1049C22×Q8C23×C6711yescharacteristic
1050C22×Q8C23×C6711yescharacteristic
1051C2×Q16C23×C6711yescharacteristic
1052C2×Q16C23×C6711yescharacteristic
1053C2×Q16C23×C6711yescharacteristic
1054C2×SD16C23×C6711yescharacteristic
1055C2×SD16C23×C6711yescharacteristic
1056C2×SD16C23×C6711yescharacteristic
1057C2×SD16C23×C6711yescharacteristic
1058C2×D8C23×C6711yescharacteristic
1059C2×M16C23×C6711yescharacteristic
1060C2×M16C23×C6711yescharacteristic
1061C2×M16C23×C6711yescharacteristic
1062C2×M16C23×C6711yescharacteristic
1063C22×C8C23×C6711yescharacteristic
1064C22×C8C23×C6711yescharacteristic
1065C22×C8C23×C6711yescharacteristic
1066C22×C8C23×C6711yescharacteristic
1067C4⋊Q8—21no—
1068C4⋊Q8—21no—
1069C4⋊Q8—21no—
1070C4⋊Q8D4×C6711yescharacteristic
1071C4⋊Q8C23×C6711yescharacteristic
1072C4⋊Q8C23×C6711yescharacteristic
1073#127D4×C6711yescharacteristic
1074#126—21no—
1075#126—21no—
1076#126—21no—
1077#126—21no—
1078#126—21no—
1079#126—21no—
1080#126—21no—
1081#126—21no—
1082#126—21no—
1083#126—21no—
1084#126—21no—
1085#125—21no—
1086#125—21no—
1087#125—21no—
1088#125—21no—
1089#125—21no—
1090#125—21no—
1091#125—21no—
1092#125—21no—
1093#125—21no—
1094#125—21no—
1095#125C23×C6711yescharacteristic
1096#125C23×C6711yescharacteristic
1097#125C23×C6711yescharacteristic
1098#125C23×C6711yescharacteristic
1099#125C23×C6711yescharacteristic
1100#124—21no—
1101#124—21no—
1102#124—21no—
1103#124—21no—
1104#124—21no—
1105#124—21no—
1106#124D4×C6711yescharacteristic
1107#124D4×C6711yescharacteristic
1108#124C23×C6711yescharacteristic
1109#123—21no—
1110#123—21no—
1111#123—21no—
1112#123—21no—
1113#123—21no—
1114#123—21no—
1115#123—21no—
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—
1126C22⋊Q8—21no—
1127C22⋊Q8—21no—
1128C22⋊Q8—21no—
1129C22⋊Q8—21no—
1130C22⋊Q8—21no—
1131C22⋊Q8—21no—
1132C22⋊Q8—21no—
1133C22⋊Q8—21no—
1134C22⋊Q8—21no—
1135C22⋊Q8—21no—
1136C22⋊Q8—21no—
1137C22⋊Q8C23×C6711yescharacteristic
1138C22⋊Q8C23×C6711yescharacteristic
1139C22⋊Q8C23×C6711yescharacteristic
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#121D4×C6711yescharacteristic
1171#121D4×C6711yescharacteristic
1172#121D4×C6711yescharacteristic
1173#121D4×C6711yescharacteristic
1174#121C23×C6711yescharacteristic
1175#121C23×C6711yescharacteristic
1176#121C23×C6711yescharacteristic
1177#121C23×C6711yescharacteristic
1178#121C23×C6711yescharacteristic
1179#121C23×C6711yescharacteristic
1180#121C23×C6711yescharacteristic
1181C4×Q8—21no—
1182C4×Q8—21no—
1183C4×Q8—21no—
1184C4×Q8C23×C6711yescharacteristic
1185C4×Q8C23×C6711yescharacteristic
1186C4×Q8C23×C6711yescharacteristic
1187C4×Q8C23×C6711yescharacteristic
1188C4×Q8C23×C6711yescharacteristic
1189C4×D4—21no—
1190C4×D4—21no—
1191C4×D4—21no—
1192C4×D4—21no—
1193C4×D4—21no—
1194C4×D4—21no—
1195C4×D4—21no—
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×D4C23×C6711yescharacteristic
1207C4×D4C23×C6711yescharacteristic
1208C4×D4C23×C6711yescharacteristic
1209C4×D4C23×C6711yescharacteristic
1210C4×D4C23×C6711yescharacteristic
1211C4×D4C23×C6711yescharacteristic
1212C4×D4C23×C6711yescharacteristic
1213#117—21no—
1214#117—21no—
1215#117—21no—
1216#117—21no—
1217#117—21no—
1218#117—21no—
1219#117—21no—
1220#117—21no—
1221#117—21no—
1222#117—21no—
1223#117C23×C6711yescharacteristic
1224#117C23×C6711yescharacteristic
1225#117C23×C6711yescharacteristic
1226#117C23×C6711yescharacteristic
1227#117C23×C6711yescharacteristic
1228#117C23×C6711yescharacteristic
1229#117C23×C6711yescharacteristic
1230C2×C4⋊C4—21no—
1231C2×C4⋊C4—21no—
1232C2×C4⋊C4—21no—
1233C2×C4⋊C4C23×C6711yescharacteristic
1234C2×C4⋊C4C23×C6711yescharacteristic
1235C2×C4⋊C4C23×C6711yescharacteristic
1236C2×C4⋊C4C23×C6711yescharacteristic
1237C2×C4⋊C4C23×C6711yescharacteristic
1238C2×C4⋊C4C23×C6711yescharacteristic
1239C2×C4⋊C4C23×C6711yescharacteristic
1240C2×C4⋊C4C23×C6711yescharacteristic
1241C2×C42—21no—
1242C2×C42C23×C6711yescharacteristic
1243#107C23×C6711yescharacteristic
1244#107C23×C6711yescharacteristic
1245#107C23×C6711yescharacteristic
1246#107C23×C6711yescharacteristic
1247#107C23×C6711yescharacteristic
1248#107C23×C6711yescharacteristic
1249#107C23×C6711yescharacteristic
1250#107C23×C6711yescharacteristic
1251#107C23×C6711yescharacteristic
1252#107C23×C6711yescharacteristic
1253#107C23×C6711yescharacteristic
1254#107C23×C6711yescharacteristic
1255#106C23×C6711yescharacteristic
1256#106C23×C6711yescharacteristic
1257#106C23×C6711yescharacteristic
1258#106C23×C6711yescharacteristic
1259#106C23×C6711yescharacteristic
1260#106C23×C6711yescharacteristic
1261#106C23×C6711yescharacteristic
1262#106C23×C6711yescharacteristic
1263#106C23×C6711yescharacteristic
1264#106C23×C6711yescharacteristic
1265#106C23×C6711yescharacteristic
1266#106C23×C6711yescharacteristic
1267C4⋊C8C23×C6711yescharacteristic
1268C4⋊C8C23×C6711yescharacteristic
1269C4⋊C8C23×C6711yescharacteristic
1270C4⋊C8C23×C6711yescharacteristic
1271#103C23×C6711yescharacteristic
1272#103C23×C6711yescharacteristic
1273#103C23×C6711yescharacteristic
1274#103C23×C6711yescharacteristic
1275#103C23×C6711yescharacteristic
1276#103C23×C6711yescharacteristic
1277#103C23×C6711yescharacteristic
1278#103C23×C6711yescharacteristic
1279#103C23×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#102C23×C6711yescharacteristic
1294#102C23×C6711yescharacteristic
1295#102C23×C6711yescharacteristic
1296#102C23×C6711yescharacteristic
1297#102C23×C6711yescharacteristic
1298#102C23×C6711yescharacteristic
1299#102C23×C6711yescharacteristic
1300#102C23×C6711yescharacteristic
1301#102C23×C6711yescharacteristic
1302#102C23×C6711yescharacteristic
1303C22⋊C8C23×C6711yescharacteristic
1304C22⋊C8C23×C6711yescharacteristic
1305C22⋊C8C23×C6711yescharacteristic
1306C22⋊C8C23×C6711yescharacteristic
1307C22⋊C8C23×C6711yescharacteristic
1308C22⋊C8C23×C6711yescharacteristic
1309C22⋊C8C23×C6711yescharacteristic
1310C22⋊C8C23×C6711yescharacteristic
1311C22⋊C8C23×C6711yescharacteristic
1312C22⋊C8C23×C6711yescharacteristic
1313C22⋊C8C23×C6711yescharacteristic
1314C22⋊C8C23×C6711yescharacteristic
1315#97C23×C6711yescharacteristic
1316#97C23×C6711yescharacteristic
1317C4×C8C23×C6711yescharacteristic
1318C4×C8C23×C6711yescharacteristic
1319#41—41no—
1320#41—41no—
1321#41—41no—
1322#41—41no—
1323#41—41no—
1324#41—41no—
1325#41—41no—
1326#41—41no—
1327#41—41no—
1328#41—41no—
1329C2×Q8—21no—
1330C2×Q8—21no—
1331C2×Q8—21no—
1332C2×Q8—41no—
1333C2×Q8—41no—
1334C2×Q8—41no—
1335C2×Q8—41no—
1336C2×Q8C2×D4×C6711yescharacteristic
1337C2×Q8C2×D4×C6711yescharacteristic
1338C2×Q8C24×C6711yescharacteristic
1339C2×Q8C24×C6711yescharacteristic
1340C2×Q8C24×C6711yescharacteristic
1341C2×Q8C24×C6711yescharacteristic
1342C2×D4—21no—
1343C2×D4—21no—
1344C2×D4—21no—
1345C2×D4—21no—
1346C2×D4—21no—
1347C2×D4—21no—
1348C2×D4—21no—
1349C2×D4—21no—
1350C2×D4—21no—
1351C2×D4—21no—
1352C2×D4C2×D4×C6711yescharacteristic
1353C2×D4C2×D4×C6711yescharacteristic
1354C2×D4C2×D4×C6711yescharacteristic
1355C2×D4C2×D4×C6711yescharacteristic
1356C2×D4C2×D4×C6711yescharacteristic
1357C2×D4C2×D4×C6711yescharacteristic
1358C2×D4C2×D4×C6711yescharacteristic
1359C2×D4C2×D4×C6711yescharacteristic
1360C2×D4C2×D4×C6711yescharacteristic
1361C2×D4C2×D4×C6711yescharacteristic
1362C2×D4C24×C6711yescharacteristic
1363C2×D4C24×C6711yescharacteristic
1364C22×C4—21no—
1365C22×C4—21no—
1366C22×C4—21no—
1367C22×C4—21no—
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—21no—
1373C22×C4—21no—
1374C22×C4—21no—
1375C22×C4—21no—
1376C22×C4—21no—
1377C22×C4—21no—
1378C22×C4—21no—
1379C22×C4—21no—
1380C22×C4C2×D4×C6711yescharacteristic
1381C22×C4C2×D4×C6711yescharacteristic
1382C22×C4C24×C6711yescharacteristic
1383C22×C4C24×C6711yescharacteristic
1384C22×C4C24×C6711yescharacteristic
1385C22×C4C24×C6711yescharacteristic
1386C22×C4C24×C6711yescharacteristic
1387Q16—41no—
1388Q16—41no—
1389Q16—41no—
1390SD16—41no—
1391SD16—41no—
1392SD16—41no—
1393SD16—41no—
1394D8—41no—
1395M16—41no—
1396M16—41no—
1397M16—41no—
1398M16—41no—
1399C2×C8—41no—
1400C2×C8—41no—
1401C2×C8—41no—
1402C2×C8—41no—
1403C2×C8C24×C6711yescharacteristic
1404C2×C8C24×C6711yescharacteristic
1405C2×C8C24×C6711yescharacteristic
1406C2×C8C24×C6711yescharacteristic
1407C2×C8C24×C6711yescharacteristic
1408C2×C8C24×C6711yescharacteristic
1409C2×C8C24×C6711yescharacteristic
1410C2×C8C24×C6711yescharacteristic
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—21no—
1416C4⋊C4—21no—
1417C4⋊C4—21no—
1418C4⋊C4—21no—
1419C4⋊C4—21no—
1420C4⋊C4—21no—
1421C4⋊C4—21no—
1422C4⋊C4—21no—
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⋊C4C2×D4×C6711yescharacteristic
1451C4⋊C4C2×D4×C6711yescharacteristic
1452C4⋊C4C2×D4×C6711yescharacteristic
1453C4⋊C4C2×D4×C6711yescharacteristic
1454C4⋊C4C24×C6711yescharacteristic
1455C4⋊C4C24×C6711yescharacteristic
1456C4⋊C4C24×C6711yescharacteristic
1457C4⋊C4C24×C6711yescharacteristic
1458C4⋊C4C24×C6711yescharacteristic
1459C4⋊C4C24×C6711yescharacteristic
1460C4⋊C4C24×C6711yescharacteristic
1461C4⋊C4C24×C6711yescharacteristic
1462C4⋊C4C24×C6711yescharacteristic
1463C4⋊C4C24×C6711yescharacteristic
1464C22⋊C4—21no—
1465C22⋊C4—21no—
1466C22⋊C4—21no—
1467C22⋊C4—21no—
1468C22⋊C4—21no—
1469C22⋊C4—21no—
1470C22⋊C4—21no—
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⋊C4C2×D4×C6711yescharacteristic
1497C22⋊C4C2×D4×C6711yescharacteristic
1498C22⋊C4C2×D4×C6711yescharacteristic
1499C22⋊C4C2×D4×C6711yescharacteristic
1500C22⋊C4C2×D4×C6711yescharacteristic
1501C22⋊C4C2×D4×C6711yescharacteristic
1502C22⋊C4C2×D4×C6711yescharacteristic
1503C22⋊C4C2×D4×C6711yescharacteristic
1504C42—21no—
1505C42—21no—
1506C42—21no—
1507C42—21no—
1508C42—21no—
1509C42—21no—
1510C42—21no—
1511C42—21no—
1512C42—21no—
1513C42—21no—
1514C42—21no—
1515C42—21no—
1516C42C2×D4×C6711yescharacteristic
1517C42C2×D4×C6711yescharacteristic
1518C42C24×C6711yescharacteristic
1519C42C24×C6711yescharacteristic
1520C23—21no—
1521C23—21no—
1522C23C22×D4×C6711yescharacteristic
1523C23C22×D4×C6711yescharacteristic
1524C23C22×D4×C6711yescharacteristic
1525C23C22×D4×C6711yescharacteristic
1526C23C22×D4×C6711yescharacteristic
1527Q8—21no—
1528Q8—21no—
1529Q8—21no—
1530Q8—21no—
1531Q8—21no—
1532Q8—21no—
1533Q8—21no—
1534Q8—21no—
1535Q8—41no—
1536Q8—41no—
1537Q8—81no—
1538Q8—81no—
1539Q8—81no—
1540D4—21no—
1541D4—21no—
1542D4—21no—
1543D4—21no—
1544D4—41no—
1545D4—41no—
1546D4—41no—
1547D4—41no—
1548D4—41no—
1549D4—41no—
1550D4—41no—
1551D4—41no—
1552D4—41no—
1553D4—41no—
1554D4—42no—
1555D4—81no—
1556D4—81no—
1557D4—81no—
1558D4—81no—
1559D4—81no—
1560D4—81no—
1561D4—81no—
1562D4—81no—
1563D4—81no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
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—41no—
1589C2×C4—41no—
1590C2×C4—42no—
1591C2×C4—42no—
1592C2×C4—81no—
1593C2×C4—81no—
1594C2×C4—81no—
1595C2×C4—81no—
1596C2×C4—81no—
1597C2×C4—81no—
1598C2×C4—81no—
1599C2×C4—81no—
1600C2×C4—81no—
1601C2×C4—81no—
1602C2×C4—81no—
1603C2×C4—81no—
1604C2×C4—81no—
1605C2×C4—81no—
1606C2×C4C22×D4×C6711yescharacteristic
1607C2×C4C22×D4×C6711yescharacteristic
1608C2×C4C22×D4×C6711yescharacteristic
1609C2×C4C22×D4×C6711yescharacteristic
1610C2×C4C22×D4×C6711yescharacteristic
1611C2×C4C22×D4×C6711yescharacteristic
1612C2×C4C22×D4×C6711yescharacteristic
1613C2×C4C22×D4×C6711yescharacteristic
1614C2×C4C22×D4×C6711yescharacteristic
1615C2×C4C25×C6711yescharacteristic
1616C8—21no—
1617C8—21no—
1618C8—21no—
1619C8—21no—
1620C8—21no—
1621C8—21no—
1622C8—21no—
1623C8—21no—
1624C22—21no—
1625C22—21no—
1626C22—21no—
1627C22—21no—
1628C22—21no—
1629C22—21no—
1630C22—21no—
1631C22—21no—
1632C22—21no—
1633C22—21no—
1634C22—21no—
1635C22—21no—
1636C22—21no—
1637C22—21no—
1638C22—21no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22C23×D4×C6711yescharacteristic
1646C4—21no—
1647C4—21no—
1648C4—21no—
1649C4—21no—
1650C4—21no—
1651C4—21no—
1652C4—21no—
1653C4—21no—
1654C4—21no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C4—41no—
1660C4—41no—
1661C4—41no—
1662C4—41no—
1663C4—41no—
1664C4—41no—
1665C4—41no—
1666C4—41no—
1667C4—41no—
1668C4—41no—
1669C4#585×C6711yescharacteristic
1670C4#585×C6711yescharacteristic
1671C2—41no—
1672C2—41no—
1673C2—41no—
1674C2—41no—
1675C2—41no—
1676C2—81no—
1677C2—81no—
1678C2C67×#348511yescharacteristic
1679C2C67×#358411yescharacteristic
1680C2C67×#358611yescharacteristic
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×#3547C2semidirect
2. C67×#3512C2semidirect
3. C67×#3352C2semidirect
4. C67×#3351C2semidirect
5. C67×#3348C2semidirect
6. C67×#3347C2semidirect
7. C67×#3346C2semidirect
8. C67×#3344C2semidirect
9. C67×#3337C2semidirect
10. C67×#3336C2semidirect
11. C67×#3327C2semidirect
12. C67×#3326C2semidirect
13. C67×#3320C2semidirect
14. C67×#3315C2semidirect
15. C67×#3312C2semidirect
16. C67×#3307C2semidirect
17. C67×#3301C2semidirect
18. C67×#3300C2semidirect
19. C67×#3236C2semidirect
20. C67×#3232C2semidirect
21. C67×#3204C2semidirect
22. C67×#3203C2semidirect
23. C67×#3201C2semidirect
24. C67×#3201C2semidirect
25. C67×#3111C2semidirect
26. C67×#3107C2semidirect
27. C67×#3099C2semidirect
28. C67×#3098C2semidirect
29. C67×#3097C2semidirect
30. C67×#3097C2semidirect
31. C67×#2981C2semidirect
830. #61814C67direct (N × H)
841. #3547C2×C67semidirect
842. #3512C2×C67semidirect
843. #3352C2×C67semidirect
844. #3351C2×C67semidirect
845. #3348C2×C67semidirect
846. #3347C2×C67semidirect
847. #3346C2×C67semidirect
848. #3344C2×C67semidirect
849. #3337C2×C67semidirect
850. #3336C2×C67semidirect
851. #3327C2×C67semidirect
852. #3326C2×C67semidirect
853. #3320C2×C67semidirect
854. #3315C2×C67semidirect
855. #3312C2×C67semidirect
856. #3307C2×C67semidirect
857. #3301C2×C67semidirect
858. #3300C2×C67semidirect
859. #3236C2×C67semidirect
860. #3232C2×C67semidirect
861. #3204C2×C67semidirect
862. #3203C2×C67semidirect
863. #3201C2×C67semidirect
864. #3201C2×C67semidirect
865. #3111C2×C67semidirect
866. #3107C2×C67semidirect
867. #3099C2×C67semidirect
868. #3098C2×C67semidirect
869. #3097C2×C67semidirect
870. #3097C2×C67semidirect
871. #2981C2×C67semidirect
872. C67#61814direct (N × H)

Maximal subgroups

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

subgroupindex
C67×#35472
C67×#35122
C67×#33522
C67×#33512
C67×#33482
C67×#33472
C67×#33462
C67×#33442
C67×#33372
C67×#33362
C67×#33272
C67×#33262
C67×#33202
C67×#33152
C67×#33122
C67×#33072
C67×#33012
C67×#33002
C67×#32362
C67×#32322
C67×#32042
C67×#32032
C67×#32012
C67×#31112
C67×#31072
C67×#30992
C67×#30982
C67×#30972
C67×#29812
#6181467