Finite Group Databasebeta

← C67×#61771 #30741022

Subgroups — C67×#61771 #30741022

Order 17152.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3541C211yesmaximal, characteristic
2C67×#3495C211yesmaximal, characteristic, complemented
3C67×#3349C211yesmaximal, characteristic, complemented
4C67×#3349C211yesmaximal, characteristic, complemented
5C67×#3346C211yesmaximal, characteristic, complemented
6C67×#3344C211yesmaximal, characteristic, complemented
7C67×#3342C211yesmaximal, characteristic, complemented
8C67×#3338C211yesmaximal, characteristic, complemented
9C67×#3337C211yesmaximal, characteristic, complemented
10C67×#3336C211yesmaximal, characteristic, complemented
11C67×#3316C211yesmaximal, characteristic, complemented
12C67×#3315C211yesmaximal, characteristic, complemented
13C67×#3313C211yesmaximal, characteristic, complemented
14C67×#3312C211yesmaximal, characteristic, complemented
15C67×#3302C211yesmaximal, characteristic, complemented
16C67×#3300C211yesmaximal, characteristic, complemented
17C67×#3300C211yesmaximal, characteristic, complemented
18C67×#3299C211yesmaximal, characteristic, complemented
19C67×#3243C211yesmaximal, characteristic, complemented
20C67×#3242C211yesmaximal, characteristic, complemented
21C67×#3202C211yesmaximal, characteristic, complemented
22C67×#3201C211yesmaximal, characteristic, complemented
23C67×#3190C211yesmaximal, characteristic, complemented
24C67×#3189C211yesmaximal, characteristic, complemented
25C67×#3127C211yesmaximal, characteristic, complemented
26C67×#3121C211yesmaximal, characteristic, complemented
27C67×#3098C211yesmaximal, characteristic, complemented
28C67×#3097C211yesmaximal, characteristic, complemented
29C67×#3091C211yesmaximal, characteristic, complemented
30C2×#485×C67C211yesmaximal, characteristic, complemented
31C67×#2977C211yesmaximal, characteristic, complemented
32#563×C67—21no—
33#562×C67—21no—
34#556×C67C2211yescharacteristic
35#556×C67C2211yescharacteristic
36#556×C67C2211yescharacteristic
37#554×C67—21no—
38#554×C67C2211yescharacteristic
39#554×C67C2211yescharacteristic
40#554×C67C2211yescharacteristic
41#553×C67—21no—
42#553×C67C2211yescharacteristic
43#552×C67—21no—
44#552×C67—21no—
45#552×C67C2211yescharacteristic
46#552×C67C2211yescharacteristic
47#552×C67C2211yescharacteristic
48#552×C67C2211yescharacteristic
49#552×C67C2211yescharacteristic
50#551×C67—21no—
51#551×C67—21no—
52D4×Q8×C67C2211yescharacteristic
53#548×C67C2211yescharacteristic
54#548×C67C2211yescharacteristic
55#547×C67C2211yescharacteristic
56#544×C67C2211yescharacteristic
57#542×C67—21no—
58#542×C67—21no—
59#542×C67C2211yescharacteristic
60#541×C67—21no—
61#541×C67C2211yescharacteristic
62#539×C67—21no—
63#538×C67—21no—
64#538×C67—21no—
65#537×C67C2211yescharacteristic
66#536×C67C2211yescharacteristic
67#536×C67C2211yescharacteristic
68#533×C67—21no—
69#529×C67—21no—
70#525×C67C2211yescharacteristic
71#525×C67C2211yescharacteristic
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×C22⋊Q8×C67C2211yescharacteristic
74#520×C67C2211yescharacteristic
75#519×C67C2211yescharacteristic
76C2×#117×C67C2211yescharacteristic
77#501×C67C2211yescharacteristic, complemented
78#501×C67C2211yescharacteristic, complemented
79#500×C67C2211yescharacteristic, complemented
80#499×C67C2211yescharacteristic, complemented
81#491×C67C2211yescharacteristic, complemented
82#489×C67C2211yescharacteristic, complemented
83#488×C67C2211yescharacteristic, complemented
84#487×C67C2211yescharacteristic, complemented
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#485×C67C2211yescharacteristic
97#485×C67C2211yescharacteristic, complemented
98#485×C67C2211yescharacteristic, complemented
99#485×C67C2211yescharacteristic, complemented
100#485×C67C2211yescharacteristic, complemented
101#485×C67C2211yescharacteristic, complemented
102#484×C67C2211yescharacteristic
103#484×C67C2211yescharacteristic
104#484×C67C2211yescharacteristic
105#484×C67C2211yescharacteristic
106#484×C67C2211yescharacteristic
107#484×C67C2211yescharacteristic, complemented
108#484×C67C2211yescharacteristic, complemented
109#484×C67C2211yescharacteristic, complemented
110#483×C67C2211yescharacteristic
111#483×C67C2211yescharacteristic
112#483×C67C2211yescharacteristic, complemented
113#483×C67C2211yescharacteristic, complemented
114#482×C67C2211yescharacteristic
115#482×C67C2211yescharacteristic
116#482×C67C2211yescharacteristic, complemented
117#481×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#478×C67C2211yescharacteristic, complemented
127#477×C67C2211yescharacteristic, complemented
128#477×C67C2211yescharacteristic, complemented
129#477×C67C2211yescharacteristic, complemented
130#475×C67C2211yescharacteristic, complemented
131#475×C67C2211yescharacteristic, complemented
132#474×C67C2211yescharacteristic, complemented
133#470×C67C2211yescharacteristic, complemented
134#470×C67C2211yescharacteristic, complemented
135#470×C67C2211yescharacteristic, complemented
136#468×C67C2211yescharacteristic, complemented
137#467×C67C2211yescharacteristic
138#467×C67C2211yescharacteristic
139#467×C67C2211yescharacteristic
140#467×C67C2211yescharacteristic
141#467×C67C2211yescharacteristic
142#467×C67C2211yescharacteristic
143#467×C67C2211yescharacteristic, complemented
144#467×C67C2211yescharacteristic, complemented
145#467×C67C2211yescharacteristic, complemented
146#465×C67C2211yescharacteristic
147#465×C67C2211yescharacteristic
148#465×C67C2211yescharacteristic, complemented
149#464×C67C2211yescharacteristic, complemented
150#464×C67C2211yescharacteristic, complemented
151#462×C67C2211yescharacteristic, complemented
152#462×C67C2211yescharacteristic, complemented
153#452×C67C2211yescharacteristic
154#452×C67C2211yescharacteristic
155#452×C67C2211yescharacteristic, complemented
156#452×C67C2211yescharacteristic, complemented
157#451×C67C2211yescharacteristic
158#451×C67C2211yescharacteristic
159#451×C67C2211yescharacteristic
160#451×C67C2211yescharacteristic
161#451×C67C2211yescharacteristic
162#451×C67C2211yescharacteristic, complemented
163#451×C67C2211yescharacteristic, complemented
164#448×C67C2211yescharacteristic
165#441×C67C2211yescharacteristic, complemented
166#441×C67C2211yescharacteristic, complemented
167#441×C67C2211yescharacteristic, complemented
168#440×C67C2211yescharacteristic, complemented
169C4×Q16×C67C2211yescharacteristic, complemented
170C4×Q16×C67C2211yescharacteristic, complemented
171C4×Q16×C67C2211yescharacteristic, complemented
172C4×SD16×C67C2211yescharacteristic, complemented
173#435×C67C2211yescharacteristic
174#435×C67C2211yescharacteristic
175#435×C67C2211yescharacteristic
176#435×C67C2211yescharacteristic
177C8×D4×C67C2211yescharacteristic
178C8×D4×C67C2211yescharacteristic
179C8×D4×C67C2211yescharacteristic
180C8×D4×C67C2211yescharacteristic
181#433×C67C2211yescharacteristic
182#433×C67C2211yescharacteristic
183#428×C67C2211yescharacteristic, complemented
184#428×C67C2211yescharacteristic, complemented
185#427×C67C2211yescharacteristic
186#427×C67C2211yescharacteristic
187#427×C67C2211yescharacteristic, complemented
188C2×#107×C67C2211yescharacteristic
189C2×#107×C67C2211yescharacteristic, complemented
190C2×#106×C67C2211yescharacteristic
191#419×C67C2211yescharacteristic, complemented
192#417×C67C2211yescharacteristic, complemented
193#416×C67C2211yescharacteristic
194#416×C67C2211yescharacteristic
195#416×C67C2211yescharacteristic, complemented
196C2×#103×C67C2211yescharacteristic
197C2×#103×C67C2211yescharacteristic
198C2×#103×C67C2211yescharacteristic, complemented
199#408×C67C2211yescharacteristic
200#408×C67C2211yescharacteristic
201C2×C22⋊C8×C67C2211yescharacteristic
202C2×C22⋊C8×C67C2211yescharacteristic
203C2×#41×C67C2311yescharacteristic
204C2×#41×C67C2311yescharacteristic
205C2×#41×C67C2311yescharacteristic
206C22×Q8×C67C2311yescharacteristic
207C22×Q8×C67C2311yescharacteristic
208C22×Q8×C67C2311yescharacteristic
209C23×C4×C67C2311yescharacteristic
210C2×Q16×C67C2311yescharacteristic
211C2×Q16×C67C2311yescharacteristic
212C2×Q16×C67C2311yescharacteristic
213C2×Q16×C67C2311yescharacteristic
214C2×Q16×C67C2311yescharacteristic
215C2×Q16×C67C2311yescharacteristic
216C2×SD16×C67C2311yescharacteristic
217C2×SD16×C67C2311yescharacteristic
218C2×M16×C67C2311yescharacteristic
219C2×M16×C67C2311yescharacteristic
220C22×C8×C67C2311yescharacteristic
221C22×C8×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×C67—21no—
230C4⋊Q8×C67C2311yescharacteristic
231C4⋊Q8×C67C2311yescharacteristic
232C4⋊Q8×C67C2311yescharacteristic
233C4⋊Q8×C67C2311yescharacteristic
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#126×C67—21no—
245#126×C67—21no—
246#126×C67—21no—
247#126×C67—21no—
248#126×C67—21no—
249#125×C67—21no—
250#125×C67—21no—
251#125×C67—21no—
252#125×C67—21no—
253#125×C67—21no—
254#125×C67—21no—
255#125×C67—21no—
256#125×C67—21no—
257#125×C67—21no—
258#125×C67—21no—
259#125×C67—21no—
260#125×C67C2311yescharacteristic
261#125×C67C2311yescharacteristic
262#125×C67C2311yescharacteristic
263#124×C67—21no—
264#124×C67—21no—
265#124×C67—21no—
266#124×C67—21no—
267#124×C67—21no—
268#124×C67—21no—
269#124×C67—21no—
270#124×C67—21no—
271#124×C67C2311yescharacteristic
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—
285#123×C67—21no—
286#123×C67D411yescharacteristic
287#123×C67D411yescharacteristic
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×C67—21no—
297C22⋊Q8×C67—21no—
298C22⋊Q8×C67—21no—
299C22⋊Q8×C67—21no—
300C22⋊Q8×C67—21no—
301C22⋊Q8×C67—21no—
302C22⋊Q8×C67—21no—
303C22⋊Q8×C67—21no—
304C22⋊Q8×C67—21no—
305C22⋊Q8×C67—21no—
306C22⋊Q8×C67D411yescharacteristic
307C22⋊Q8×C67D411yescharacteristic
308C22⋊Q8×C67C2311yescharacteristic
309C22⋊Q8×C67C2311yescharacteristic
310C22⋊Q8×C67C2311yescharacteristic
311C22⋊Q8×C67C2311yescharacteristic
312C22⋊Q8×C67C2311yescharacteristic
313C22⋊Q8×C67C2311yescharacteristic
314C22⋊Q8×C67C2311yescharacteristic
315C22⋊Q8×C67C2311yescharacteristic
316C22⋊Q8×C67C2311yescharacteristic
317C22⋊Q8×C67C2311yescharacteristic
318C22⋊Q8×C67C2311yescharacteristic
319C22⋊Q8×C67C2311yescharacteristic
320C22⋊Q8×C67C2311yescharacteristic
321C22⋊Q8×C67C2311yescharacteristic
322C22⋊Q8×C67C2311yescharacteristic
323C22⋊Q8×C67C2311yescharacteristic
324C22⋊Q8×C67C2311yescharacteristic
325#121×C67—21no—
326#121×C67—21no—
327#121×C67—21no—
328#121×C67—21no—
329#121×C67—21no—
330#121×C67—21no—
331#121×C67—21no—
332#121×C67D411yescharacteristic
333#121×C67D411yescharacteristic
334#121×C67C2311yescharacteristic
335#121×C67C2311yescharacteristic
336#121×C67C2311yescharacteristic
337#120×C67—21no—
338#120×C67D411yescharacteristic
339#120×C67D411yescharacteristic
340C4×Q8×C67—21no—
341C4×Q8×C67—21no—
342C4×Q8×C67—21no—
343C4×Q8×C67—21no—
344C4×Q8×C67—21no—
345C4×Q8×C67—21no—
346C4×Q8×C67C2311yescharacteristic
347C4×Q8×C67C2311yescharacteristic
348C4×Q8×C67C2311yescharacteristic
349C4×Q8×C67C2311yescharacteristic
350C4×Q8×C67C2311yescharacteristic
351C4×Q8×C67C2311yescharacteristic
352C4×Q8×C67C2311yescharacteristic
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
370#117×C67—21no—
371#117×C67—21no—
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×C67C2311yescharacteristic
380#117×C67C2311yescharacteristic
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×C67—21no—
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×C22⋊C4×C67—21no—
401C2×C42×C67—21no—
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#107×C67C2311yescharacteristic
415#107×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#103×C67C2311yescharacteristic
453#103×C67C2311yescharacteristic
454#103×C67C2311yescharacteristic
455#103×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
478C24×C67C2×D411yescharacteristic
479#41×C67—41no—
480#41×C67—41no—
481#41×C67—41no—
482#41×C67—41no—
483#41×C67—41no—
484#41×C67—41no—
485C2×Q8×C67—21no—
486C2×Q8×C67—21no—
487C2×Q8×C67—21no—
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×C67—41no—
496C2×Q8×C67—41no—
497C2×Q8×C67C2×D411yescharacteristic
498C2×Q8×C67C2411yescharacteristic
499C2×Q8×C67C2411yescharacteristic
500C2×Q8×C67C2411yescharacteristic
501C2×Q8×C67C2411yescharacteristic
502C2×Q8×C67C2411yescharacteristic
503C2×D4×C67—21no—
504C2×D4×C67—21no—
505C2×D4×C67—21no—
506C2×D4×C67—21no—
507C2×D4×C67—21no—
508C2×D4×C67C2×D411yescharacteristic
509C2×D4×C67C2×D411yescharacteristic
510C2×D4×C67C2×D411yescharacteristic
511C2×D4×C67C2×D411yescharacteristic
512C2×D4×C67C2×D411yescharacteristic
513C2×D4×C67C2×D411yescharacteristic
514C2×D4×C67C2×D411yescharacteristic
515C2×D4×C67C2411yescharacteristic
516C22×C4×C67—21no—
517C22×C4×C67—21no—
518C22×C4×C67—21no—
519C22×C4×C67—21no—
520C22×C4×C67—21no—
521C22×C4×C67—21no—
522C22×C4×C67—21no—
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—41no—
530C22×C4×C67—41no—
531C22×C4×C67C2×D411yescharacteristic
532C22×C4×C67C2×D411yescharacteristic
533C22×C4×C67C2×D411yescharacteristic
534C22×C4×C67C2411yescharacteristic
535C22×C4×C67C2411yescharacteristic
536C22×C4×C67C2411yescharacteristic
537C22×C4×C67C2411yescharacteristic
538C22×C4×C67C2411yescharacteristic
539Q16×C67—41no—
540Q16×C67—41no—
541Q16×C67—41no—
542Q16×C67—41no—
543Q16×C67—41no—
544Q16×C67—41no—
545SD16×C67—41no—
546SD16×C67—41no—
547M16×C67—41no—
548M16×C67—41no—
549C2×C8×C67—41no—
550C2×C8×C67—41no—
551C2×C8×C67—41no—
552C2×C8×C67—41no—
553C2×C8×C67—41no—
554C2×C8×C67—41no—
555C2×C8×C67C2411yescharacteristic
556C2×C8×C67C2411yescharacteristic
557C2×C8×C67C2411yescharacteristic
558C2×C8×C67C2411yescharacteristic
559C2×C8×C67C2411yescharacteristic
560C2×C8×C67C2411yescharacteristic
561C2×C8×C67C2411yescharacteristic
562C2×C8×C67C2411yescharacteristic
563C4⋊C4×C67—21no—
564C4⋊C4×C67—21no—
565C4⋊C4×C67—21no—
566C4⋊C4×C67—21no—
567C4⋊C4×C67—21no—
568C4⋊C4×C67—21no—
569C4⋊C4×C67—21no—
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×C67C2×D411yescharacteristic
606C4⋊C4×C67C2×D411yescharacteristic
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×C67C2×D411yescharacteristic
653C22⋊C4×C67C2×D411yescharacteristic
654C22⋊C4×C67C2×D411yescharacteristic
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
662C42×C67—21no—
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×C67—21no—
676C42×C67—21no—
677C42×C67C2411yescharacteristic
678C42×C67C2411yescharacteristic
679C23×C67—22no—
680C23×C67—21no—
681C23×C67—41no—
682C23×C67—41no—
683C23×C67C22×D411yescharacteristic
684C23×C67C22×D411yescharacteristic
685C23×C67C22×D411yescharacteristic
686C23×C67C22×D411yescharacteristic
687C23×C67C22×D411yescharacteristic
688Q8×C67—21no—
689Q8×C67—21no—
690Q8×C67—21no—
691Q8×C67—21no—
692Q8×C67—21no—
693Q8×C67—21no—
694Q8×C67—21no—
695Q8×C67—21no—
696Q8×C67—21no—
697Q8×C67—21no—
698Q8×C67—41no—
699Q8×C67—42no—
700Q8×C67—81no—
701Q8×C67—81no—
702Q8×C67—81no—
703Q8×C67—81no—
704Q8×C67—81no—
705D4×C67—22no—
706D4×C67—22no—
707D4×C67—21no—
708D4×C67—21no—
709D4×C67—41no—
710D4×C67—41no—
711D4×C67—41no—
712D4×C67—41no—
713D4×C67—41no—
714D4×C67—42no—
715D4×C67—81no—
716D4×C67—81no—
717D4×C67—81no—
718D4×C67—81no—
719C2×C4×C67—21no—
720C2×C4×C67—21no—
721C2×C4×C67—21no—
722C2×C4×C67—21no—
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—41no—
745C2×C4×C67—41no—
746C2×C4×C67—41no—
747C2×C4×C67—42no—
748C2×C4×C67—42no—
749C2×C4×C67—81no—
750C2×C4×C67—81no—
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×C67C22×D411yescharacteristic
761C2×C4×C67C22×D411yescharacteristic
762C2×C4×C67C22×D411yescharacteristic
763C2×C4×C67C22×D411yescharacteristic
764C2×C4×C67C22×D411yescharacteristic
765C2×C4×C67C22×D411yescharacteristic
766C2×C4×C67C22×D411yescharacteristic
767C2×C4×C67C22×D411yescharacteristic
768C2×C4×C67C22×D411yescharacteristic
769C2×C4×C67C2511yescharacteristic
770C8×C67—21no—
771C8×C67—21no—
772C8×C67—21no—
773C8×C67—21no—
774C8×C67—21no—
775C8×C67—21no—
776C8×C67—21no—
777C8×C67—21no—
778C22×C67—21no—
779C22×C67—21no—
780C22×C67—21no—
781C22×C67—21no—
782C22×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—41no—
793C22×C67—41no—
794C22×C67—41no—
795C22×C67—82no—
796C22×C67#57812yes—
797C22×C67C23×D411yescharacteristic
798C4×C67—21no—
799C4×C67—21no—
800C4×C67—21no—
801C4×C67—21no—
802C4×C67—21no—
803C4×C67—21no—
804C4×C67—21no—
805C4×C67—21no—
806C4×C67—21no—
807C4×C67—41no—
808C4×C67—41no—
809C4×C67—41no—
810C4×C67—41no—
811C4×C67—41no—
812C4×C67—41no—
813C4×C67—41no—
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#58511yescharacteristic
823C4×C67#58511yescharacteristic
824#61771C6711yesmaximal, characteristic, direct product factor, Sylow
825C2×C67—22no—
826C2×C67—41no—
827C2×C67—41no—
828C2×C67—41no—
829C2×C67—41no—
830C2×C67—81no—
831C2×C67#348511yescharacteristic
832C2×C67C2×#57811yescharacteristic
833C2×C67#358411yescharacteristic
834#3541C2×C6711yescharacteristic
835#3495C2×C6711yescharacteristic, complemented
836#3349C2×C6711yescharacteristic, complemented
837#3349C2×C6711yescharacteristic, complemented
838#3346C2×C6711yescharacteristic, complemented
839#3344C2×C6711yescharacteristic, complemented
840#3342C2×C6711yescharacteristic, complemented
841#3338C2×C6711yescharacteristic, complemented
842#3337C2×C6711yescharacteristic, complemented
843#3336C2×C6711yescharacteristic, complemented
844#3316C2×C6711yescharacteristic, complemented
845#3315C2×C6711yescharacteristic, complemented
846#3313C2×C6711yescharacteristic, complemented
847#3312C2×C6711yescharacteristic, complemented
848#3302C2×C6711yescharacteristic, complemented
849#3300C2×C6711yescharacteristic, complemented
850#3300C2×C6711yescharacteristic, complemented
851#3299C2×C6711yescharacteristic, complemented
852#3243C2×C6711yescharacteristic, complemented
853#3242C2×C6711yescharacteristic, complemented
854#3202C2×C6711yescharacteristic, complemented
855#3201C2×C6711yescharacteristic, complemented
856#3190C2×C6711yescharacteristic, complemented
857#3189C2×C6711yescharacteristic, complemented
858#3127C2×C6711yescharacteristic, complemented
859#3121C2×C6711yescharacteristic, complemented
860#3098C2×C6711yescharacteristic, complemented
861#3097C2×C6711yescharacteristic, complemented
862#3091C2×C6711yescharacteristic, complemented
863C2×#485C2×C6711yescharacteristic, complemented
864#2977C2×C6711yescharacteristic, complemented
865C67#6177111yescharacteristic, direct product factor, Sylow
866#563—21no—
867#562—21no—
868#556C22×C6711yescharacteristic
869#556C22×C6711yescharacteristic
870#556C22×C6711yescharacteristic
871#554—21no—
872#554C22×C6711yescharacteristic
873#554C22×C6711yescharacteristic
874#554C22×C6711yescharacteristic
875#553—21no—
876#553C22×C6711yescharacteristic
877#552—21no—
878#552—21no—
879#552C22×C6711yescharacteristic
880#552C22×C6711yescharacteristic
881#552C22×C6711yescharacteristic
882#552C22×C6711yescharacteristic
883#552C22×C6711yescharacteristic
884#551—21no—
885#551—21no—
886D4×Q8C22×C6711yescharacteristic
887#548C22×C6711yescharacteristic
888#548C22×C6711yescharacteristic
889#547C22×C6711yescharacteristic
890#544C22×C6711yescharacteristic
891#542—21no—
892#542—21no—
893#542C22×C6711yescharacteristic
894#541—21no—
895#541C22×C6711yescharacteristic
896#539—21no—
897#538—21no—
898#538—21no—
899#537C22×C6711yescharacteristic
900#536C22×C6711yescharacteristic
901#536C22×C6711yescharacteristic
902#533—21no—
903#529—21no—
904#525C22×C6711yescharacteristic
905#525C22×C6711yescharacteristic
906C2×C22⋊Q8C22×C6711yescharacteristic
907C2×C22⋊Q8C22×C6711yescharacteristic
908#520C22×C6711yescharacteristic
909#519C22×C6711yescharacteristic
910C2×#117C22×C6711yescharacteristic
911#501C22×C6711yescharacteristic, complemented
912#501C22×C6711yescharacteristic, complemented
913#500C22×C6711yescharacteristic, complemented
914#499C22×C6711yescharacteristic, complemented
915#491C22×C6711yescharacteristic, complemented
916#489C22×C6711yescharacteristic, complemented
917#488C22×C6711yescharacteristic, complemented
918#487C22×C6711yescharacteristic, complemented
919#485C22×C6711yescharacteristic
920#485C22×C6711yescharacteristic
921#485C22×C6711yescharacteristic
922#485C22×C6711yescharacteristic
923#485C22×C6711yescharacteristic
924#485C22×C6711yescharacteristic
925#485C22×C6711yescharacteristic
926#485C22×C6711yescharacteristic
927#485C22×C6711yescharacteristic
928#485C22×C6711yescharacteristic
929#485C22×C6711yescharacteristic
930#485C22×C6711yescharacteristic
931#485C22×C6711yescharacteristic, complemented
932#485C22×C6711yescharacteristic, complemented
933#485C22×C6711yescharacteristic, complemented
934#485C22×C6711yescharacteristic, complemented
935#485C22×C6711yescharacteristic, complemented
936#484C22×C6711yescharacteristic
937#484C22×C6711yescharacteristic
938#484C22×C6711yescharacteristic
939#484C22×C6711yescharacteristic
940#484C22×C6711yescharacteristic
941#484C22×C6711yescharacteristic, complemented
942#484C22×C6711yescharacteristic, complemented
943#484C22×C6711yescharacteristic, complemented
944#483C22×C6711yescharacteristic
945#483C22×C6711yescharacteristic
946#483C22×C6711yescharacteristic, complemented
947#483C22×C6711yescharacteristic, complemented
948#482C22×C6711yescharacteristic
949#482C22×C6711yescharacteristic
950#482C22×C6711yescharacteristic, complemented
951#481C22×C6711yescharacteristic
952#480C22×C6711yescharacteristic
953#480C22×C6711yescharacteristic
954#480C22×C6711yescharacteristic, complemented
955#479C22×C6711yescharacteristic, complemented
956#479C22×C6711yescharacteristic, complemented
957#479C22×C6711yescharacteristic, complemented
958#479C22×C6711yescharacteristic, complemented
959#479C22×C6711yescharacteristic, complemented
960#478C22×C6711yescharacteristic, complemented
961#477C22×C6711yescharacteristic, complemented
962#477C22×C6711yescharacteristic, complemented
963#477C22×C6711yescharacteristic, complemented
964#475C22×C6711yescharacteristic, complemented
965#475C22×C6711yescharacteristic, complemented
966#474C22×C6711yescharacteristic, complemented
967#470C22×C6711yescharacteristic, complemented
968#470C22×C6711yescharacteristic, complemented
969#470C22×C6711yescharacteristic, complemented
970#468C22×C6711yescharacteristic, complemented
971#467C22×C6711yescharacteristic
972#467C22×C6711yescharacteristic
973#467C22×C6711yescharacteristic
974#467C22×C6711yescharacteristic
975#467C22×C6711yescharacteristic
976#467C22×C6711yescharacteristic
977#467C22×C6711yescharacteristic, complemented
978#467C22×C6711yescharacteristic, complemented
979#467C22×C6711yescharacteristic, complemented
980#465C22×C6711yescharacteristic
981#465C22×C6711yescharacteristic
982#465C22×C6711yescharacteristic, complemented
983#464C22×C6711yescharacteristic, complemented
984#464C22×C6711yescharacteristic, complemented
985#462C22×C6711yescharacteristic, complemented
986#462C22×C6711yescharacteristic, complemented
987#452C22×C6711yescharacteristic
988#452C22×C6711yescharacteristic
989#452C22×C6711yescharacteristic, complemented
990#452C22×C6711yescharacteristic, complemented
991#451C22×C6711yescharacteristic
992#451C22×C6711yescharacteristic
993#451C22×C6711yescharacteristic
994#451C22×C6711yescharacteristic
995#451C22×C6711yescharacteristic
996#451C22×C6711yescharacteristic, complemented
997#451C22×C6711yescharacteristic, complemented
998#448C22×C6711yescharacteristic
999#441C22×C6711yescharacteristic, complemented
1000#441C22×C6711yescharacteristic, complemented
1001#441C22×C6711yescharacteristic, complemented
1002#440C22×C6711yescharacteristic, complemented
1003C4×Q16C22×C6711yescharacteristic, complemented
1004C4×Q16C22×C6711yescharacteristic, complemented
1005C4×Q16C22×C6711yescharacteristic, complemented
1006C4×SD16C22×C6711yescharacteristic, complemented
1007#435C22×C6711yescharacteristic
1008#435C22×C6711yescharacteristic
1009#435C22×C6711yescharacteristic
1010#435C22×C6711yescharacteristic
1011C8×D4C22×C6711yescharacteristic
1012C8×D4C22×C6711yescharacteristic
1013C8×D4C22×C6711yescharacteristic
1014C8×D4C22×C6711yescharacteristic
1015#433C22×C6711yescharacteristic
1016#433C22×C6711yescharacteristic
1017#428C22×C6711yescharacteristic, complemented
1018#428C22×C6711yescharacteristic, complemented
1019#427C22×C6711yescharacteristic
1020#427C22×C6711yescharacteristic
1021#427C22×C6711yescharacteristic, complemented
1022C2×#107C22×C6711yescharacteristic
1023C2×#107C22×C6711yescharacteristic, complemented
1024C2×#106C22×C6711yescharacteristic
1025#419C22×C6711yescharacteristic, complemented
1026#417C22×C6711yescharacteristic, complemented
1027#416C22×C6711yescharacteristic
1028#416C22×C6711yescharacteristic
1029#416C22×C6711yescharacteristic, complemented
1030C2×#103C22×C6711yescharacteristic
1031C2×#103C22×C6711yescharacteristic
1032C2×#103C22×C6711yescharacteristic, complemented
1033#408C22×C6711yescharacteristic
1034#408C22×C6711yescharacteristic
1035C2×C22⋊C8C22×C6711yescharacteristic
1036C2×C22⋊C8C22×C6711yescharacteristic
1037C2×#41C23×C6711yescharacteristic
1038C2×#41C23×C6711yescharacteristic
1039C2×#41C23×C6711yescharacteristic
1040C22×Q8C23×C6711yescharacteristic
1041C22×Q8C23×C6711yescharacteristic
1042C22×Q8C23×C6711yescharacteristic
1043C23×C4C23×C6711yescharacteristic
1044C2×Q16C23×C6711yescharacteristic
1045C2×Q16C23×C6711yescharacteristic
1046C2×Q16C23×C6711yescharacteristic
1047C2×Q16C23×C6711yescharacteristic
1048C2×Q16C23×C6711yescharacteristic
1049C2×Q16C23×C6711yescharacteristic
1050C2×SD16C23×C6711yescharacteristic
1051C2×SD16C23×C6711yescharacteristic
1052C2×M16C23×C6711yescharacteristic
1053C2×M16C23×C6711yescharacteristic
1054C22×C8C23×C6711yescharacteristic
1055C22×C8C23×C6711yescharacteristic
1056C22×C8C23×C6711yescharacteristic
1057C22×C8C23×C6711yescharacteristic
1058C22×C8C23×C6711yescharacteristic
1059C22×C8C23×C6711yescharacteristic
1060C4⋊Q8—21no—
1061C4⋊Q8—21no—
1062C4⋊Q8—21no—
1063C4⋊Q8—21no—
1064C4⋊Q8C23×C6711yescharacteristic
1065C4⋊Q8C23×C6711yescharacteristic
1066C4⋊Q8C23×C6711yescharacteristic
1067C4⋊Q8C23×C6711yescharacteristic
1068#126—21no—
1069#126—21no—
1070#126—21no—
1071#126—21no—
1072#126—21no—
1073#126—21no—
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#125—21no—
1084#125—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#125C23×C6711yescharacteristic
1095#125C23×C6711yescharacteristic
1096#125C23×C6711yescharacteristic
1097#124—21no—
1098#124—21no—
1099#124—21no—
1100#124—21no—
1101#124—21no—
1102#124—21no—
1103#124—21no—
1104#124—21no—
1105#124C23×C6711yescharacteristic
1106#123—21no—
1107#123—21no—
1108#123—21no—
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#123D4×C6711yescharacteristic
1121#123D4×C6711yescharacteristic
1122C22⋊Q8—21no—
1123C22⋊Q8—21no—
1124C22⋊Q8—21no—
1125C22⋊Q8—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⋊Q8—21no—
1138C22⋊Q8—21no—
1139C22⋊Q8—21no—
1140C22⋊Q8D4×C6711yescharacteristic
1141C22⋊Q8D4×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
1150C22⋊Q8C23×C6711yescharacteristic
1151C22⋊Q8C23×C6711yescharacteristic
1152C22⋊Q8C23×C6711yescharacteristic
1153C22⋊Q8C23×C6711yescharacteristic
1154C22⋊Q8C23×C6711yescharacteristic
1155C22⋊Q8C23×C6711yescharacteristic
1156C22⋊Q8C23×C6711yescharacteristic
1157C22⋊Q8C23×C6711yescharacteristic
1158C22⋊Q8C23×C6711yescharacteristic
1159#121—21no—
1160#121—21no—
1161#121—21no—
1162#121—21no—
1163#121—21no—
1164#121—21no—
1165#121—21no—
1166#121D4×C6711yescharacteristic
1167#121D4×C6711yescharacteristic
1168#121C23×C6711yescharacteristic
1169#121C23×C6711yescharacteristic
1170#121C23×C6711yescharacteristic
1171#120—21no—
1172#120D4×C6711yescharacteristic
1173#120D4×C6711yescharacteristic
1174C4×Q8—21no—
1175C4×Q8—21no—
1176C4×Q8—21no—
1177C4×Q8—21no—
1178C4×Q8—21no—
1179C4×Q8—21no—
1180C4×Q8C23×C6711yescharacteristic
1181C4×Q8C23×C6711yescharacteristic
1182C4×Q8C23×C6711yescharacteristic
1183C4×Q8C23×C6711yescharacteristic
1184C4×Q8C23×C6711yescharacteristic
1185C4×Q8C23×C6711yescharacteristic
1186C4×Q8C23×C6711yescharacteristic
1187C4×D4—21no—
1188C4×D4—21no—
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×D4C23×C6711yescharacteristic
1200C4×D4C23×C6711yescharacteristic
1201C4×D4C23×C6711yescharacteristic
1202C4×D4C23×C6711yescharacteristic
1203C4×D4C23×C6711yescharacteristic
1204#117—21no—
1205#117—21no—
1206#117—21no—
1207#117—21no—
1208#117—21no—
1209#117—21no—
1210#117—21no—
1211#117—21no—
1212#117—21no—
1213#117C23×C6711yescharacteristic
1214#117C23×C6711yescharacteristic
1215#117C23×C6711yescharacteristic
1216#117C23×C6711yescharacteristic
1217#117C23×C6711yescharacteristic
1218#117C23×C6711yescharacteristic
1219#117C23×C6711yescharacteristic
1220#117C23×C6711yescharacteristic
1221#117C23×C6711yescharacteristic
1222C2×C4⋊C4—21no—
1223C2×C4⋊C4—21no—
1224C2×C4⋊C4—21no—
1225C2×C4⋊C4C23×C6711yescharacteristic
1226C2×C4⋊C4C23×C6711yescharacteristic
1227C2×C4⋊C4C23×C6711yescharacteristic
1228C2×C4⋊C4C23×C6711yescharacteristic
1229C2×C4⋊C4C23×C6711yescharacteristic
1230C2×C4⋊C4C23×C6711yescharacteristic
1231C2×C4⋊C4C23×C6711yescharacteristic
1232C2×C22⋊C4—21no—
1233C2×C22⋊C4—21no—
1234C2×C22⋊C4—21no—
1235C2×C42—21no—
1236#107C23×C6711yescharacteristic
1237#107C23×C6711yescharacteristic
1238#107C23×C6711yescharacteristic
1239#107C23×C6711yescharacteristic
1240#107C23×C6711yescharacteristic
1241#107C23×C6711yescharacteristic
1242#107C23×C6711yescharacteristic
1243#107C23×C6711yescharacteristic
1244#107C23×C6711yescharacteristic
1245#107C23×C6711yescharacteristic
1246#107C23×C6711yescharacteristic
1247#107C23×C6711yescharacteristic
1248#107C23×C6711yescharacteristic
1249#107C23×C6711yescharacteristic
1250#106C23×C6711yescharacteristic
1251#106C23×C6711yescharacteristic
1252#106C23×C6711yescharacteristic
1253#106C23×C6711yescharacteristic
1254#106C23×C6711yescharacteristic
1255#106C23×C6711yescharacteristic
1256#106C23×C6711yescharacteristic
1257#106C23×C6711yescharacteristic
1258#106C23×C6711yescharacteristic
1259#106C23×C6711yescharacteristic
1260C4⋊C8C23×C6711yescharacteristic
1261C4⋊C8C23×C6711yescharacteristic
1262C4⋊C8C23×C6711yescharacteristic
1263C4⋊C8C23×C6711yescharacteristic
1264#103C23×C6711yescharacteristic
1265#103C23×C6711yescharacteristic
1266#103C23×C6711yescharacteristic
1267#103C23×C6711yescharacteristic
1268#103C23×C6711yescharacteristic
1269#103C23×C6711yescharacteristic
1270#103C23×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#102C23×C6711yescharacteristic
1291#102C23×C6711yescharacteristic
1292#102C23×C6711yescharacteristic
1293#102C23×C6711yescharacteristic
1294#102C23×C6711yescharacteristic
1295#102C23×C6711yescharacteristic
1296C22⋊C8C23×C6711yescharacteristic
1297C22⋊C8C23×C6711yescharacteristic
1298C22⋊C8C23×C6711yescharacteristic
1299C22⋊C8C23×C6711yescharacteristic
1300C22⋊C8C23×C6711yescharacteristic
1301C22⋊C8C23×C6711yescharacteristic
1302C22⋊C8C23×C6711yescharacteristic
1303C22⋊C8C23×C6711yescharacteristic
1304C22⋊C8C23×C6711yescharacteristic
1305C22⋊C8C23×C6711yescharacteristic
1306C22⋊C8C23×C6711yescharacteristic
1307C22⋊C8C23×C6711yescharacteristic
1308#97C23×C6711yescharacteristic
1309#97C23×C6711yescharacteristic
1310C4×C8C23×C6711yescharacteristic
1311C4×C8C23×C6711yescharacteristic
1312C24C2×D4×C6711yescharacteristic
1313#41—41no—
1314#41—41no—
1315#41—41no—
1316#41—41no—
1317#41—41no—
1318#41—41no—
1319C2×Q8—21no—
1320C2×Q8—21no—
1321C2×Q8—21no—
1322C2×Q8—21no—
1323C2×Q8—21no—
1324C2×Q8—21no—
1325C2×Q8—41no—
1326C2×Q8—41no—
1327C2×Q8—41no—
1328C2×Q8—41no—
1329C2×Q8—41no—
1330C2×Q8—41no—
1331C2×Q8C2×D4×C6711yescharacteristic
1332C2×Q8C24×C6711yescharacteristic
1333C2×Q8C24×C6711yescharacteristic
1334C2×Q8C24×C6711yescharacteristic
1335C2×Q8C24×C6711yescharacteristic
1336C2×Q8C24×C6711yescharacteristic
1337C2×D4—21no—
1338C2×D4—21no—
1339C2×D4—21no—
1340C2×D4—21no—
1341C2×D4—21no—
1342C2×D4C2×D4×C6711yescharacteristic
1343C2×D4C2×D4×C6711yescharacteristic
1344C2×D4C2×D4×C6711yescharacteristic
1345C2×D4C2×D4×C6711yescharacteristic
1346C2×D4C2×D4×C6711yescharacteristic
1347C2×D4C2×D4×C6711yescharacteristic
1348C2×D4C2×D4×C6711yescharacteristic
1349C2×D4C24×C6711yescharacteristic
1350C22×C4—21no—
1351C22×C4—21no—
1352C22×C4—21no—
1353C22×C4—21no—
1354C22×C4—21no—
1355C22×C4—21no—
1356C22×C4—21no—
1357C22×C4—21no—
1358C22×C4—21no—
1359C22×C4—21no—
1360C22×C4—21no—
1361C22×C4—21no—
1362C22×C4—21no—
1363C22×C4—41no—
1364C22×C4—41no—
1365C22×C4C2×D4×C6711yescharacteristic
1366C22×C4C2×D4×C6711yescharacteristic
1367C22×C4C2×D4×C6711yescharacteristic
1368C22×C4C24×C6711yescharacteristic
1369C22×C4C24×C6711yescharacteristic
1370C22×C4C24×C6711yescharacteristic
1371C22×C4C24×C6711yescharacteristic
1372C22×C4C24×C6711yescharacteristic
1373Q16—41no—
1374Q16—41no—
1375Q16—41no—
1376Q16—41no—
1377Q16—41no—
1378Q16—41no—
1379SD16—41no—
1380SD16—41no—
1381M16—41no—
1382M16—41no—
1383C2×C8—41no—
1384C2×C8—41no—
1385C2×C8—41no—
1386C2×C8—41no—
1387C2×C8—41no—
1388C2×C8—41no—
1389C2×C8C24×C6711yescharacteristic
1390C2×C8C24×C6711yescharacteristic
1391C2×C8C24×C6711yescharacteristic
1392C2×C8C24×C6711yescharacteristic
1393C2×C8C24×C6711yescharacteristic
1394C2×C8C24×C6711yescharacteristic
1395C2×C8C24×C6711yescharacteristic
1396C2×C8C24×C6711yescharacteristic
1397C4⋊C4—21no—
1398C4⋊C4—21no—
1399C4⋊C4—21no—
1400C4⋊C4—21no—
1401C4⋊C4—21no—
1402C4⋊C4—21no—
1403C4⋊C4—21no—
1404C4⋊C4—21no—
1405C4⋊C4—21no—
1406C4⋊C4—21no—
1407C4⋊C4—21no—
1408C4⋊C4—21no—
1409C4⋊C4—21no—
1410C4⋊C4—21no—
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⋊C4C2×D4×C6711yescharacteristic
1440C4⋊C4C2×D4×C6711yescharacteristic
1441C4⋊C4C2×D4×C6711yescharacteristic
1442C4⋊C4C2×D4×C6711yescharacteristic
1443C4⋊C4C2×D4×C6711yescharacteristic
1444C4⋊C4C2×D4×C6711yescharacteristic
1445C4⋊C4C24×C6711yescharacteristic
1446C4⋊C4C24×C6711yescharacteristic
1447C4⋊C4C24×C6711yescharacteristic
1448C4⋊C4C24×C6711yescharacteristic
1449C4⋊C4C24×C6711yescharacteristic
1450C4⋊C4C24×C6711yescharacteristic
1451C4⋊C4C24×C6711yescharacteristic
1452C4⋊C4C24×C6711yescharacteristic
1453C4⋊C4C24×C6711yescharacteristic
1454C4⋊C4C24×C6711yescharacteristic
1455C22⋊C4—21no—
1456C22⋊C4—21no—
1457C22⋊C4—21no—
1458C22⋊C4—21no—
1459C22⋊C4—21no—
1460C22⋊C4—21no—
1461C22⋊C4—21no—
1462C22⋊C4—21no—
1463C22⋊C4—21no—
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⋊C4C2×D4×C6711yescharacteristic
1487C22⋊C4C2×D4×C6711yescharacteristic
1488C22⋊C4C2×D4×C6711yescharacteristic
1489C22⋊C4C2×D4×C6711yescharacteristic
1490C22⋊C4C2×D4×C6711yescharacteristic
1491C22⋊C4C2×D4×C6711yescharacteristic
1492C22⋊C4C2×D4×C6711yescharacteristic
1493C22⋊C4C2×D4×C6711yescharacteristic
1494C22⋊C4C2×D4×C6711yescharacteristic
1495C22⋊C4C2×D4×C6711yescharacteristic
1496C42—21no—
1497C42—21no—
1498C42—21no—
1499C42—21no—
1500C42—21no—
1501C42—21no—
1502C42—21no—
1503C42—21no—
1504C42—21no—
1505C42—21no—
1506C42—21no—
1507C42—21no—
1508C42—21no—
1509C42—21no—
1510C42—21no—
1511C42C24×C6711yescharacteristic
1512C42C24×C6711yescharacteristic
1513C23—22no—
1514C23—21no—
1515C23—41no—
1516C23—41no—
1517C23C22×D4×C6711yescharacteristic
1518C23C22×D4×C6711yescharacteristic
1519C23C22×D4×C6711yescharacteristic
1520C23C22×D4×C6711yescharacteristic
1521C23C22×D4×C6711yescharacteristic
1522Q8—21no—
1523Q8—21no—
1524Q8—21no—
1525Q8—21no—
1526Q8—21no—
1527Q8—21no—
1528Q8—21no—
1529Q8—21no—
1530Q8—21no—
1531Q8—21no—
1532Q8—41no—
1533Q8—42no—
1534Q8—81no—
1535Q8—81no—
1536Q8—81no—
1537Q8—81no—
1538Q8—81no—
1539D4—22no—
1540D4—22no—
1541D4—21no—
1542D4—21no—
1543D4—41no—
1544D4—41no—
1545D4—41no—
1546D4—41no—
1547D4—41no—
1548D4—42no—
1549D4—81no—
1550D4—81no—
1551D4—81no—
1552D4—81no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
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—41no—
1579C2×C4—41no—
1580C2×C4—41no—
1581C2×C4—42no—
1582C2×C4—42no—
1583C2×C4—81no—
1584C2×C4—81no—
1585C2×C4—81no—
1586C2×C4—81no—
1587C2×C4—81no—
1588C2×C4—81no—
1589C2×C4—81no—
1590C2×C4—81no—
1591C2×C4—81no—
1592C2×C4—81no—
1593C2×C4—81no—
1594C2×C4C22×D4×C6711yescharacteristic
1595C2×C4C22×D4×C6711yescharacteristic
1596C2×C4C22×D4×C6711yescharacteristic
1597C2×C4C22×D4×C6711yescharacteristic
1598C2×C4C22×D4×C6711yescharacteristic
1599C2×C4C22×D4×C6711yescharacteristic
1600C2×C4C22×D4×C6711yescharacteristic
1601C2×C4C22×D4×C6711yescharacteristic
1602C2×C4C22×D4×C6711yescharacteristic
1603C2×C4C25×C6711yescharacteristic
1604C8—21no—
1605C8—21no—
1606C8—21no—
1607C8—21no—
1608C8—21no—
1609C8—21no—
1610C8—21no—
1611C8—21no—
1612C22—21no—
1613C22—21no—
1614C22—21no—
1615C22—21no—
1616C22—21no—
1617C22—21no—
1618C22—21no—
1619C22—21no—
1620C22—21no—
1621C22—21no—
1622C22—21no—
1623C22—21no—
1624C22—21no—
1625C22—21no—
1626C22—41no—
1627C22—41no—
1628C22—41no—
1629C22—82no—
1630C22#578×C6712yes—
1631C22C23×D4×C6711yescharacteristic
1632C4—21no—
1633C4—21no—
1634C4—21no—
1635C4—21no—
1636C4—21no—
1637C4—21no—
1638C4—21no—
1639C4—21no—
1640C4—21no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4#585×C6711yescharacteristic
1657C4#585×C6711yescharacteristic
1658C2—22no—
1659C2—41no—
1660C2—41no—
1661C2—41no—
1662C2—41no—
1663C2—81no—
1664C2C67×#348511yescharacteristic
1665C2C2×#578×C6711yescharacteristic
1666C2C67×#358411yescharacteristic
subgroupG/H
center, socleC22×C67C23×D4
commutator, Frattini, cosocleC2×C4C25×C67
prime radicalC67×#3541C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ #525×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C67×#3495C2semidirect
3. C67×#3349C2semidirect
4. C67×#3349C2semidirect
5. C67×#3346C2semidirect
6. C67×#3344C2semidirect
7. C67×#3342C2semidirect
8. C67×#3338C2semidirect
9. C67×#3337C2semidirect
10. C67×#3336C2semidirect
11. C67×#3316C2semidirect
12. C67×#3315C2semidirect
13. C67×#3313C2semidirect
14. C67×#3312C2semidirect
15. C67×#3302C2semidirect
16. C67×#3300C2semidirect
17. C67×#3300C2semidirect
18. C67×#3299C2semidirect
19. C67×#3243C2semidirect
20. C67×#3242C2semidirect
21. C67×#3202C2semidirect
22. C67×#3201C2semidirect
23. C67×#3190C2semidirect
24. C67×#3189C2semidirect
25. C67×#3127C2semidirect
26. C67×#3121C2semidirect
27. C67×#3098C2semidirect
28. C67×#3097C2semidirect
29. C67×#3091C2semidirect
30. C2×#485×C67C2semidirect
31. C67×#2977C2semidirect
77. #501×C67C22semidirect
78. #501×C67C22semidirect
79. #500×C67C22semidirect
80. #499×C67C22semidirect
81. #491×C67C22semidirect
82. #489×C67C22semidirect
83. #488×C67C22semidirect
84. #487×C67C22semidirect
97. #485×C67C22semidirect
98. #485×C67C22semidirect
99. #485×C67C22semidirect
100. #485×C67C22semidirect
101. #485×C67C22semidirect
107. #484×C67C22semidirect
108. #484×C67C22semidirect
109. #484×C67C22semidirect
112. #483×C67C22semidirect
113. #483×C67C22semidirect
116. #482×C67C22semidirect
120. #480×C67C22semidirect
121. #479×C67C22semidirect
122. #479×C67C22semidirect
123. #479×C67C22semidirect
124. #479×C67C22semidirect
125. #479×C67C22semidirect
126. #478×C67C22semidirect
127. #477×C67C22semidirect
128. #477×C67C22semidirect
129. #477×C67C22semidirect
130. #475×C67C22semidirect
131. #475×C67C22semidirect
132. #474×C67C22semidirect
133. #470×C67C22semidirect
134. #470×C67C22semidirect
135. #470×C67C22semidirect
136. #468×C67C22semidirect
143. #467×C67C22semidirect
144. #467×C67C22semidirect
145. #467×C67C22semidirect
148. #465×C67C22semidirect
149. #464×C67C22semidirect
150. #464×C67C22semidirect
151. #462×C67C22semidirect
152. #462×C67C22semidirect
155. #452×C67C22semidirect
156. #452×C67C22semidirect
162. #451×C67C22semidirect
163. #451×C67C22semidirect
165. #441×C67C22semidirect
166. #441×C67C22semidirect
167. #441×C67C22semidirect
168. #440×C67C22semidirect
169. C4×Q16×C67C22semidirect
170. C4×Q16×C67C22semidirect
171. C4×Q16×C67C22semidirect
172. C4×SD16×C67C22semidirect
183. #428×C67C22semidirect
184. #428×C67C22semidirect
187. #427×C67C22semidirect
189. C2×#107×C67C22semidirect
191. #419×C67C22semidirect
192. #417×C67C22semidirect
195. #416×C67C22semidirect
198. C2×#103×C67C22semidirect
824. #61771C67direct (N × H)
835. #3495C2×C67semidirect
836. #3349C2×C67semidirect
837. #3349C2×C67semidirect
838. #3346C2×C67semidirect
839. #3344C2×C67semidirect
840. #3342C2×C67semidirect
841. #3338C2×C67semidirect
842. #3337C2×C67semidirect
843. #3336C2×C67semidirect
844. #3316C2×C67semidirect
845. #3315C2×C67semidirect
846. #3313C2×C67semidirect
847. #3312C2×C67semidirect
848. #3302C2×C67semidirect
849. #3300C2×C67semidirect
850. #3300C2×C67semidirect
851. #3299C2×C67semidirect
852. #3243C2×C67semidirect
853. #3242C2×C67semidirect
854. #3202C2×C67semidirect
855. #3201C2×C67semidirect
856. #3190C2×C67semidirect
857. #3189C2×C67semidirect
858. #3127C2×C67semidirect
859. #3121C2×C67semidirect
860. #3098C2×C67semidirect
861. #3097C2×C67semidirect
862. #3091C2×C67semidirect
863. C2×#485C2×C67semidirect
864. #2977C2×C67semidirect
865. C67#61771direct (N × H)
911. #501C22×C67semidirect
912. #501C22×C67semidirect
913. #500C22×C67semidirect
914. #499C22×C67semidirect
915. #491C22×C67semidirect
916. #489C22×C67semidirect
917. #488C22×C67semidirect
918. #487C22×C67semidirect
931. #485C22×C67semidirect
932. #485C22×C67semidirect
933. #485C22×C67semidirect
934. #485C22×C67semidirect
935. #485C22×C67semidirect
941. #484C22×C67semidirect
942. #484C22×C67semidirect
943. #484C22×C67semidirect
946. #483C22×C67semidirect
947. #483C22×C67semidirect
950. #482C22×C67semidirect
954. #480C22×C67semidirect
955. #479C22×C67semidirect
956. #479C22×C67semidirect
957. #479C22×C67semidirect
958. #479C22×C67semidirect
959. #479C22×C67semidirect
960. #478C22×C67semidirect
961. #477C22×C67semidirect
962. #477C22×C67semidirect
963. #477C22×C67semidirect
964. #475C22×C67semidirect
965. #475C22×C67semidirect
966. #474C22×C67semidirect
967. #470C22×C67semidirect
968. #470C22×C67semidirect
969. #470C22×C67semidirect
970. #468C22×C67semidirect
977. #467C22×C67semidirect
978. #467C22×C67semidirect
979. #467C22×C67semidirect
982. #465C22×C67semidirect
983. #464C22×C67semidirect
984. #464C22×C67semidirect
985. #462C22×C67semidirect
986. #462C22×C67semidirect
989. #452C22×C67semidirect
990. #452C22×C67semidirect
996. #451C22×C67semidirect
997. #451C22×C67semidirect
999. #441C22×C67semidirect
1000. #441C22×C67semidirect
1001. #441C22×C67semidirect
1002. #440C22×C67semidirect
1003. C4×Q16C22×C67semidirect
1004. C4×Q16C22×C67semidirect
1005. C4×Q16C22×C67semidirect
1006. C4×SD16C22×C67semidirect
1017. #428C22×C67semidirect
1018. #428C22×C67semidirect
1021. #427C22×C67semidirect
1023. C2×#107C22×C67semidirect
1025. #419C22×C67semidirect
1026. #417C22×C67semidirect
1029. #416C22×C67semidirect
1032. C2×#103C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35412
C67×#34952
C67×#33492
C67×#33462
C67×#33442
C67×#33422
C67×#33382
C67×#33372
C67×#33362
C67×#33162
C67×#33152
C67×#33132
C67×#33122
C67×#33022
C67×#33002
C67×#32992
C67×#32432
C67×#32422
C67×#32022
C67×#32012
C67×#31902
C67×#31892
C67×#31272
C67×#31212
C67×#30982
C67×#30972
C67×#30912
C2×#485×C672
C67×#29772
#6177167