Finite Group Databasebeta

← #11664338

Subgroups — #11664338

Order 768.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85893C211yesmaximal, characteristic, complemented
2#85873C211yesmaximal, characteristic, complemented
3C3×#2947C211yesmaximal, characteristic, complemented
4#83984C211yesmaximal, characteristic, complemented
5#83966C211yesmaximal, characteristic, complemented
6#82557C211yesmaximal, characteristic, complemented
7#82547C211yesmaximal, characteristic, complemented
8#79848C212yesmaximal, complemented
9#79835C212yesmaximal, complemented
10#79813C212yesmaximal, complemented
11#79781C212yesmaximal, complemented
12#79749C212yesmaximal, complemented
13#79722C212yesmaximal, complemented
14#79695C212yesmaximal, complemented
15#79658C212yesmaximal, complemented
16#79240C211yesmaximal, characteristic, complemented
17#79221C211yesmaximal, characteristic, complemented
18#78861C211yesmaximal, characteristic, complemented
19#78843C211yesmaximal, characteristic, complemented
20#78795C211yesmaximal, characteristic, complemented
21C2×#4793C211yesmaximal, characteristic, complemented
22#78562C211yesmaximal, characteristic, complemented
23#78552C211yesmaximal, characteristic, complemented
24#60600—31nomaximal, Sylow
25C2×#1007C2211yescharacteristic
26C2×C3×#137C2211yescharacteristic
27C3×#520C2211yescharacteristic
28C3×#519C2211yescharacteristic
29#5833C2211yescharacteristic
30#5832C2211yescharacteristic
31C2×#950C2211yescharacteristic
32C2×Q8×Dic3C2211yescharacteristic
33C2×#942C2211yescharacteristic
34C2×#904C2211yescharacteristic
35#5582C2212yes—
36#5578C2212yes—
37#5574—21no—
38#5574C2212yes—
39C4×#239—21no—
40C4×#239C2212yes—
41#5572—21no—
42#5572C2212yes—
43C4×D3×Q8—21no—
44C4×D3×Q8C2212yes—
45#5561C2212yes—
46#5552—22no—
47#5548C2212yes—
48#5540—22no—
49#5533—21no—
50#5532—21no—
51#5523—22no—
52#5523C2211yescharacteristic
53#5523C2211yescharacteristic
54#5523C2211yescharacteristic
55#5522—22no—
56#5522C2211yescharacteristic
57#5522C2211yescharacteristic
58#5511—21no—
59#5510C2211yescharacteristic
60#5507—21no—
61C2×#888C2211yescharacteristic
62C3×#441C2212yes—
63C3×#440C2212yes—
64C3×C4×Q16C2212yes—
65C3×C4×SD16C2212yes—
66C3×#428C2211yescharacteristic
67C3×#416C2211yescharacteristic
68C2×C3×#103C2211yescharacteristic
69C3×#405C2211yescharacteristic
70#5232C2211yescharacteristic
71C2×#835C2211yescharacteristic
72#5187C2212yes—
73#5186C2212yes—
74#5185C2212yes—
75#5182C2212yes—
76#5172C2212yes—
77#5170C2212yes—
78#5166C2212yes—
79#5163C2212yes—
80#5133C2211yescharacteristic
81#5133C2211yescharacteristic
82#5129C2211yescharacteristic
83#5118C2211yescharacteristic
84#5110C2211yescharacteristic
85C2×#818C2211yescharacteristic
86C2×Dic3⋊C8C2211yescharacteristic
87#5030C2212yes—
88C4×#216C2212yes—
89C4×#216C2212yes—
90#5026C2212yes—
91#5026C2212yes—
92C4×#215C2212yes—
93#5018C2212yes—
94C4×#213C2212yes—
95#5002C2211yescharacteristic
96#4997C2211yescharacteristic
97#4995C2211yescharacteristic
98#4966C2211yescharacteristic
99C2×#807C2211yescharacteristic
100#4890C2212yes—
101#4884C2212yes—
102#4882C2212yes—
103#4875C2212yes—
104#4870C2212yes—
105#4868C2212yes—
106#4866C2212yes—
107#4854C2212yes—
108#4819C2211yescharacteristic
109#4818C2211yescharacteristic
110#4814C2212yes—
111#4811C2212yes—
112#4810C2212yes—
113#4809C2212yes—
114#4808C2212yes—
115#4806C2212yes—
116#4798C2211yescharacteristic
117#4795C2211yescharacteristic
118#4793C2212yes—
119#4793C2212yes—
120#4793C2212yes—
121#4793C2212yes—
122#4787C2211yescharacteristic
123#4786C2211yescharacteristic
124#4784C2212yes—
125#4774C2212yes—
126#4767C2211yescharacteristic
127#4762C2211yescharacteristic
128#4710C2212yes—
129#4710C2212yes—
130#4709C2212yes—
131#4705C2212yes—
132C4×Dic12C2212yes—
133C4×D24C2212yes—
134#4690C2212yes—
135#4685C2212yes—
136#3511—31no—
137C4×2−1+4—31no—
138#3124—32no—
139#3124—32no—
140#3121—32no—
141#3121—32no—
142#3116—32no—
143#3112—32no—
144#3106—32no—
145#3104—32no—
146#3098—31no—
147#3098—31no—
148#3079—31no—
149C2×#477—31no—
150#3037—31no—
151#3035—31no—
152#3013—31no—
153#3013—31no—
154#2951—31no—
155#2951—31no—
156#2947—31no—
157#2947D311yescharacteristic, complemented
158#2925—31no—
159C2×C3×#41C2311yescharacteristic
160C22×C3×Q8C2311yescharacteristic
161#1007—24no—
162#1007—24no—
163C2×#239—21no—
164C2×#239C2312yes—
165C2×D3×Q8—21no—
166C2×D3×Q8C2312yes—
167C2×#235—22no—
168C2×#235—22no—
169C2×#235C2311yescharacteristic
170C2×#235C2311yescharacteristic
171C2×#235C2311yescharacteristic
172C22×Dic6—21no—
173C3×#137—24no—
174C2×C3×Q16C2312yes—
175C2×C3×SD16C2312yes—
176C2×C3×M16C2311yescharacteristic
177C22×C3×C8C2311yescharacteristic
178C3×C4×Q8—21no—
179C3×C4×Q8—21no—
180C3×C4×Q8C2312yes—
181C3×C4×Q8C2312yes—
182C3×C4×Q8C2312yes—
183C3×C4×D4—22no—
184C3×C4×D4C2312yes—
185C3×#117—21no—
186C3×#117—22no—
187C3×#117C2311yescharacteristic
188C3×#117C2311yescharacteristic
189C2×C3×C4⋊C4—21no—
190C2×C3×C4⋊C4C2311yescharacteristic
191#950—24no—
192#947C2311yescharacteristic
193#946C2312yes—
194Q8×Dic3—21no—
195Q8×Dic3—21no—
196Q8×Dic3C2312yes—
197Q8×Dic3C2312yes—
198#944C2311yescharacteristic
199C2×#216C2312yes—
200C2×#216C2311yescharacteristic
201#942—24no—
202C2×#215C2312yes—
203C2×#215C2311yescharacteristic
204#940C2311yescharacteristic
205#939—22no—
206#939—21no—
207#939—21no—
208#938C2312yes—
209#936C2311yescharacteristic
210C2×#214C2311yescharacteristic
211C2×#213C2311yescharacteristic
212#930—22no—
213#930—21no—
214#929—22no—
215C4×#67—21no—
216C4×#67—21no—
217C4×#67—22no—
218C2×C4⋊Dic3—21no—
219C2×C4⋊Dic3C2311yescharacteristic
220C2×C4⋊Dic3C2311yescharacteristic
221#924—21no—
222#924—22no—
223C2×Dic3⋊C4—21no—
224C2×C4×Dic3—21no—
225C2×C4×Dic3C2311yescharacteristic
226C2×#208C2311yescharacteristic
227C22×C3⋊C8C2311yescharacteristic
228C2×Dic12C2311yescharacteristic
229#904—24no—
230C2×D24C2311yescharacteristic
231C2×#204C2311yescharacteristic
232C2×#204C2311yescharacteristic
233#897—21no—
234#897C2312yes—
235#896—22no—
236#896—22no—
237#895—21no—
238#895C2312yes—
239#894—22no—
240#893—22no—
241#893—22no—
242#893D411yescharacteristic
243#893D411yescharacteristic
244#893C2311yescharacteristic
245#893C2311yescharacteristic
246#892—21no—
247#892—21no—
248#892—22no—
249#892—22no—
250#892C2312yes—
251D3×C4⋊C4—22no—
252D3×C4⋊C4—21no—
253D3×C4⋊C4—21no—
254D3×C4⋊C4—22no—
255D3×C4⋊C4C2312yes—
256#889—22no—
257#888—21no—
258#888—21no—
259#888C2312yes—
260#888C2312yes—
261#887—22no—
262#887—22no—
263#887D411yescharacteristic
264#887D411yescharacteristic
265#887C2311yescharacteristic
266#887C2311yescharacteristic
267#885—22no—
268#885—22no—
269#884—22no—
270#67⋊C4—22no—
271#67⋊C4—21no—
272#67⋊C4—21no—
273#67⋊C4—22no—
274#67⋊C4—22no—
275#67⋊C4D412yes—
276#67⋊C4D412yes—
277#879—22no—
278#876—22no—
279#875—22no—
280C4×D12—21no—
281C4×D12—22no—
282C4×D12—22no—
283C4×D12C2312yes—
284C4×D12C2312yes—
285#872—22no—
286#872—22no—
287#872—22no—
288#872—21no—
289#872C2312yes—
290C42×D3—22no—
291C42×D3—22no—
292C42×D3—21no—
293C42×D3C2312yes—
294C4×Dic6—21no—
295C4×Dic6—22no—
296C4×Dic6—22no—
297C4×Dic6—22no—
298C4×Dic6C2312yes—
299C4×Dic6C2312yes—
300C3×#107C2312yes—
301C3×#106C2312yes—
302C3×#103C2312yes—
303C3×#103C2312yes—
304C3×#103C2311yescharacteristic
305C3×#103C2311yescharacteristic
306C3×#102C2311yescharacteristic
307C3×#102C2311yescharacteristic
308C3×#97C2312yes—
309C3×C4×C8C2312yes—
310#835C2312yes—
311#835C2312yes—
312#835C2312yes—
313#832C2312yes—
314#821C2312yes—
315#821C2312yes—
316(C2×D3)⋊C8C2312yes—
317(C2×D3)⋊C8C2312yes—
318(C2×D3)⋊C8C2312yes—
319(C2×D3)⋊C8C2312yes—
320#818C2312yes—
321#818C2312yes—
322#816C2312yes—
323#816C2312yes—
324Dic3⋊C8C2312yes—
325Dic3⋊C8C2312yes—
326Dic3⋊C8C2311yescharacteristic
327Dic3⋊C8C2311yescharacteristic
328Dic3⋊C8C2311yescharacteristic
329Dic3⋊C8C2311yescharacteristic
330#810C2311yescharacteristic
331#810C2312yes—
332#810C2311yescharacteristic
333#809C2311yescharacteristic
334#809C2312yes—
335#809C2311yescharacteristic
336#808C2312yes—
337#807C2312yes—
338#807C2312yes—
339#807C2312yes—
340#803C2312yes—
341C4×C3⋊C8C2312yes—
342C2×2−1+4—31no—
343C2×#137—31no—
344C2×#137C2×D311yescharacteristic
345C2×#135—31no—
346C2×#135—31no—
347#556—61no—
348#555—61no—
349#554—61no—
350#553—62no—
351#548—62no—
352#547—61no—
353#542—32no—
354#542—32no—
355#537—31no—
356#537—31no—
357#533—32no—
358#532—32no—
359#532—31no—
360C2×C4⋊Q8—31no—
361#520—31no—
362#520—32no—
363#520—31no—
364#520—31no—
365#520—62no—
366#520—61no—
367#520C2×D311yescharacteristic
368#519—32no—
369#519—61no—
370#519C2×D311yescharacteristic
371C4×#41—31no—
372C4×#41—32no—
373C4×#41—31no—
374C4×#41—62no—
375C4×#41—61no—
376C2×C4×Q8—31no—
377C2×C4×Q8—32no—
378C2×C4×Q8—61no—
379#485—32no—
380#485—32no—
381#484—32no—
382#484—32no—
383#482—32no—
384#482—32no—
385#480—32no—
386#480—32no—
387#477—32no—
388#477—32no—
389#477—32no—
390#477—32no—
391#477—32no—
392#476—32no—
393#475—32no—
394#474—32no—
395#464—32no—
396#464—32no—
397#464—31no—
398#464—31no—
399#463—31no—
400#463—31no—
401#462—32no—
402#462—31no—
403#461—31no—
404#460—32no—
405#460—31no—
406#459—31no—
407#452—32no—
408#452—32no—
409#451—32no—
410#451—32no—
411#449—32no—
412#449—32no—
413#448—32no—
414#448—32no—
415#441—32no—
416#441C2×D312yes—
417#440—32no—
418#440—32no—
419#440—32no—
420#440—32no—
421#440—32no—
422#440C2×D312yes—
423C4×Q16—32no—
424C4×Q16—32no—
425C4×Q16—32no—
426C4×Q16C2×D312yes—
427C4×SD16—32no—
428C4×SD16C2×D312yes—
429C4×D8—32no—
430C4×D8—32no—
431#433—32no—
432#433—32no—
433#432—32no—
434#431—32no—
435#428—31no—
436#428C2×D311yescharacteristic
437C2×#107—31no—
438C2×#107—31no—
439#423—31no—
440C2×C4⋊C8—31no—
441#417—31no—
442#417—31no—
443#417—31no—
444#417—31no—
445#416—31no—
446#416C2×D311yescharacteristic
447C2×#103—31no—
448C2×#103C2×D311yescharacteristic
449#408—31no—
450#408—31no—
451#405—31no—
452#405C2×D311yescharacteristic
453C3×#41—22no—
454C3×#41—22no—
455C2×C3×Q8—21no—
456C2×C3×Q8—22no—
457C2×C3×Q8#4114yescomplemented
458C2×C3×Q8C2411yescharacteristic
459C2×C3×Q8C2412yes—
460C2×C3×D4—21no—
461C2×C3×D4C2411yescharacteristic
462C22×C3×C4—21no—
463C22×C3×C4—21no—
464C22×C3×C4—21no—
465C22×C3×C4—22no—
466C22×C3×C4C2411yescharacteristic
467C2×#67—21no—
468C2×#67—21no—
469C2×#67—22no—
470C2×#67—21no—
471C2×#67—21no—
472C2×#67C2×D412yes—
473C22×Dic3—21no—
474C22×Dic3—21no—
475C22×Dic3C2×D411yescharacteristic
476C22×Dic3C2×D411yescharacteristic
477#239—28no—
478#239—24no—
479#239—24no—
480D3×Q8—28no—
481D3×Q8—24no—
482D3×Q8—24no—
483#235—216no—
484#235—22no—
485#235—22no—
486#235—22no—
487#235—22no—
488#235—22no—
489#235—84no—
490#235#4114yescomplemented
491C2×D12—22no—
492C2×D12—22no—
493C2×D12C2×D411yescharacteristic
494C2×D12C2411yescharacteristic
495C2×D12C2411yescharacteristic
496C2×C4×D3—22no—
497C2×C4×D3—21no—
498C2×C4×D3—22no—
499C2×C4×D3—21no—
500C2×C4×D3—21no—
501C2×C4×D3—22no—
502C2×C4×D3—22no—
503C2×C4×D3—22no—
504C2×C4×D3—21no—
505C2×C4×D3C2×D412yes—
506C2×C4×D3C2×D412yes—
507C2×C4×D3C2412yes—
508C2×Dic6—22no—
509C2×Dic6—22no—
510C2×Dic6—22no—
511C2×Dic6—82no—
512C2×Dic6C2×D411yescharacteristic
513C2×Dic6C2411yescharacteristic
514C2×Dic6C2411yescharacteristic
515C3×Q16—24no—
516C3×SD16—24no—
517C3×M16—22no—
518C2×C3×C8—22no—
519C2×C3×C8C2412yes—
520C2×C3×C8C2411yescharacteristic
521C2×C3×C8C2411yescharacteristic
522C3×C4⋊C4—22no—
523C3×C4⋊C4—22no—
524C3×C4⋊C4—21no—
525C3×C4⋊C4—22no—
526C3×C4⋊C4C2×D411yescharacteristic
527C3×C4⋊C4C2×D411yescharacteristic
528C3×C4⋊C4C2411yescharacteristic
529C3×C4⋊C4C2412yes—
530C3×C4⋊C4C2411yescharacteristic
531C3×C22⋊C4—21no—
532C3×C22⋊C4—22no—
533C3×C22⋊C4C2×D412yes—
534C3×C42—22no—
535C3×C42—22no—
536C3×C42—21no—
537C3×C42—22no—
538C3×C42C2412yes—
539#217—21no—
540#217—22no—
541#217—21no—
542#216—24no—
543#216—22no—
544#215—24no—
545#215—22no—
546#214—22no—
547#213—22no—
548(C2×D3)⋊C4—22no—
549(C2×D3)⋊C4—22no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—22no—
552(C2×D3)⋊C4—22no—
553(C2×D3)⋊C4—21no—
554(C2×D3)⋊C4—21no—
555(C2×D3)⋊C4—21no—
556(C2×D3)⋊C4—21no—
557(C2×D3)⋊C4—22no—
558(C2×D3)⋊C4C2×D412yes—
559(C2×D3)⋊C4C2×D412yes—
560C4⋊Dic3—21no—
561C4⋊Dic3—21no—
562C4⋊Dic3—22no—
563C4⋊Dic3—22no—
564C4⋊Dic3—22no—
565C4⋊Dic3C2412yes—
566C4⋊Dic3C2412yes—
567Dic3⋊C4—22no—
568Dic3⋊C4—22no—
569Dic3⋊C4—22no—
570Dic3⋊C4—21no—
571Dic3⋊C4—21no—
572Dic3⋊C4—22no—
573Dic3⋊C4—21no—
574Dic3⋊C4—21no—
575Dic3⋊C4—22no—
576Dic3⋊C4—22no—
577Dic3⋊C4C2×D412yes—
578Dic3⋊C4C2×D412yes—
579C4×Dic3—22no—
580C4×Dic3—22no—
581C4×Dic3—22no—
582C4×Dic3—21no—
583C4×Dic3—21no—
584C4×Dic3—22no—
585C4×Dic3—22no—
586C4×Dic3C2×D412yes—
587C4×Dic3C2×D412yes—
588C4×Dic3C2×D411yescharacteristic
589C4×Dic3C2×D411yescharacteristic
590C4×Dic3C2411yescharacteristic
591C4×Dic3C2411yescharacteristic
592#208—22no—
593C2×C3⋊C8—22no—
594C2×C3⋊C8C2411yescharacteristic
595C2×C3⋊C8C2412yes—
596C2×C3⋊C8C2411yescharacteristic
597Dic12—22no—
598D24—22no—
599#204—22no—
600#204—22no—
6012−1+4—64no—
6022−1+4—64no—
603C2×#41—31no—
604C2×#41—32no—
605C2×#41—31no—
606C2×#41—31no—
607C2×#41—62no—
608C2×#41—62no—
609C2×#41—61no—
610C2×#41C22×D311yescharacteristic
611C22×Q8—32no—
612C22×Q8—61no—
613C22×Q8—61no—
614C22×Q8C22×D311yescharacteristic
615#137—24no—
616#137—64no—
617#135—64no—
618#135—64no—
619C2×Q16—31no—
620C2×Q16—32no—
621C2×Q16—31no—
622C2×Q16C22×D312yes—
623C2×SD16—31no—
624C2×SD16—32no—
625C2×SD16—31no—
626C2×SD16—31no—
627C2×SD16—31no—
628C2×SD16C22×D312yes—
629C2×D8—31no—
630C2×D8—31no—
631C2×M16—31no—
632C2×M16C22×D311yescharacteristic
633C22×C8—31no—
634C22×C8C22×D311yescharacteristic
635C4⋊Q8—32no—
636C4⋊Q8—32no—
637C4⋊Q8—31no—
638C4⋊Q8—61no—
639C4⋊Q8—61no—
640#127—31no—
641#126—62no—
642#126—62no—
643#125—62no—
644#124—31no—
645#124—31no—
646#124—62no—
647#124—62no—
648#124—62no—
649#123—62no—
650#123—62no—
651C22⋊Q8—32no—
652C22⋊Q8—32no—
653C22⋊Q8—62no—
654C22⋊Q8—62no—
655C22⋊Q8—61no—
656C22⋊Q8—62no—
657C22⋊Q8—61no—
658#121—32no—
659#121—32no—
660#121—62no—
661#121—61no—
662#121—61no—
663#121—62no—
664#121—61no—
665#121—61no—
666#121—62no—
667C4×Q8—21no—
668C4×Q8—21no—
669C4×Q8—31no—
670C4×Q8—31no—
671C4×Q8—32no—
672C4×Q8—32no—
673C4×Q8—31no—
674C4×Q8—31no—
675C4×Q8—32no—
676C4×Q8—32no—
677C4×Q8—62no—
678C4×Q8—62no—
679C4×Q8—62no—
680C4×Q8—61no—
681C4×Q8—62no—
682C4×Q8—61no—
683C4×Q8—61no—
684C4×Q8—62no—
685C4×Q8C22×D312yes—
686C4×Q8C22×D312yes—
687C4×Q8C22×D312yes—
688C4×D4—22no—
689C4×D4—31no—
690C4×D4—31no—
691C4×D4—32no—
692C4×D4—32no—
693C4×D4—31no—
694C4×D4—31no—
695C4×D4—32no—
696C4×D4—32no—
697C4×D4—62no—
698C4×D4—62no—
699C4×D4—61no—
700C4×D4—61no—
701C4×D4—62no—
702C4×D4—61no—
703C4×D4—61no—
704C4×D4—61no—
705C4×D4—62no—
706C4×D4—62no—
707C4×D4—62no—
708C4×D4—62no—
709C4×D4—62no—
710C4×D4C22×D312yes—
711#117—21no—
712#117—22no—
713#117—32no—
714#117—32no—
715#117—61no—
716#117—62no—
717#117—62no—
718#117—62no—
719#117—62no—
720#117—62no—
721#117—61no—
722#117—61no—
723#117C22×D311yescharacteristic
724#117C22×D311yescharacteristic
725C2×C4⋊C4—21no—
726C2×C4⋊C4—31no—
727C2×C4⋊C4—31no—
728C2×C4⋊C4—32no—
729C2×C4⋊C4—62no—
730C2×C4⋊C4—62no—
731C2×C4⋊C4—61no—
732C2×C4⋊C4—61no—
733C2×C4⋊C4—61no—
734C2×C4⋊C4—61no—
735C2×C4⋊C4C22×D311yescharacteristic
736C2×C42—31no—
737C2×C42—32no—
738C2×C42—62no—
739C2×C42—61no—
740C2×C42—62no—
741C2×C42—61no—
742#107—32no—
743#107—32no—
744#107—32no—
745#107—32no—
746#107—32no—
747#107C22×D312yes—
748#106—32no—
749#106C22×D312yes—
750C4⋊C8—31no—
751C4⋊C8—31no—
752C4⋊C8—31no—
753C4⋊C8—31no—
754C4⋊C8—32no—
755C4⋊C8—32no—
756#103—32no—
757#103—32no—
758#103—32no—
759#103—32no—
760#103—32no—
761#103—31no—
762#103—31no—
763#103—32no—
764#103C22×D312yes—
765#103C22×D312yes—
766#103C22×D311yescharacteristic
767#103C22×D311yescharacteristic
768#102—32no—
769#102—32no—
770#102—32no—
771#102—31no—
772#102—31no—
773#102—32no—
774#102C22×D311yescharacteristic
775#102C22×D311yescharacteristic
776C22⋊C8—32no—
777C22⋊C8—32no—
778C22⋊C8—32no—
779C22⋊C8—32no—
780#97—32no—
781#97C22×D312yes—
782C4×C8—32no—
783C4×C8C22×D312yes—
784C23×C3—21no—
785C23×C3C22×D411yescharacteristic
786C22×D3—21no—
787C22×D3—21no—
788C22×D3C22×D412yes—
789C3×Q8—24no—
790C3×Q8—22no—
791C3×Q8—21no—
792C3×Q8—21no—
793C3×Q8C2×#4114yes—
794C3×D4—21no—
795C3×D4—21no—
796C3×D4—42no—
797C2×C3×C4—24no—
798C2×C3×C4—22no—
799C2×C3×C4—21no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—22no—
803C2×C3×C4—42no—
804C2×C3×C4—82no—
805C2×C3×C4—81no—
806C2×C3×C4C22×D412yes—
807C2×C3×C4C22×D412yes—
808C2×C3×C4C22×D411yescharacteristic
809C2×C3×C4C2×#4112yes—
810C2×C3×C4C2×#4112yes—
811C2×C3×C4C2511yescharacteristic
812#67—24no—
813#67—24no—
814#67—42no—
815#67—42no—
816#67—42no—
817#67—82no—
818C2×Dic3—21no—
819C2×Dic3—22no—
820C2×Dic3—22no—
821C2×Dic3—21no—
822C2×Dic3—22no—
823C2×Dic3—41no—
824C2×Dic3—81no—
825C2×Dic3—81no—
826C2×Dic3C22×D411yescharacteristic
827C2×Dic3C22×D412yes—
828C2×Dic3C22×D411yescharacteristic
829C2×Dic3C22×D411yescharacteristic
830C2×Dic3C22×D411yescharacteristic
831D12—28no—
832D12—22no—
833D12—21no—
834D12—21no—
835D12—21no—
836D12—82no—
837D12C2×#4112yes—
838C4×D3—28no—
839C4×D3—28no—
840C4×D3—24no—
841C4×D3—22no—
842C4×D3—22no—
843C4×D3—24no—
844C4×D3—42no—
845C4×D3—42no—
846C4×D3—42no—
847C4×D3—81no—
848C4×D3—82no—
849C4×D3—82no—
850C4×D3—82no—
851Dic6—28no—
852Dic6—22no—
853Dic6—21no—
854Dic6—21no—
855Dic6—21no—
856Dic6—44no—
857Dic6—82no—
858Dic6C2×#4112yes—
859C3×C8—21no—
860C3×C8—21no—
861C3×C8—22no—
862C3⋊C8—21no—
863C3⋊C8—21no—
864C3⋊C8—22no—
865#41—22no—
866#41—22no—
867#41—34no—
868#41—616no—
869#41—64no—
870#41—68no—
871#41—64no—
872#41—62no—
873#41—62no—
874#41—62no—
875#41—62no—
876#41—62no—
877#41—244no—
878C2×Q8—21no—
879C2×Q8—22no—
880C2×Q8—31no—
881C2×Q8—31no—
882C2×Q8—31no—
883C2×Q8—62no—
884C2×Q8—62no—
885C2×Q8—62no—
886C2×Q8—64no—
887C2×Q8—68no—
888C2×Q8—64no—
889C2×Q8—242no—
890C2×Q8#23514yescomplemented
891C2×Q8C23×D311yescharacteristic
892C2×Q8C23×D312yes—
893C2×D4—21no—
894C2×D4—32no—
895C2×D4—31no—
896C2×D4—31no—
897C2×D4—31no—
898C2×D4—62no—
899C2×D4—62no—
900C2×D4—61no—
901C2×D4—61no—
902C2×D4—61no—
903C2×D4—61no—
904C2×D4—62no—
905C2×D4C23×D311yescharacteristic
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—22no—
910C22×C4—31no—
911C22×C4—31no—
912C22×C4—32no—
913C22×C4—32no—
914C22×C4—32no—
915C22×C4—62no—
916C22×C4—61no—
917C22×C4—61no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—61no—
923C22×C4—61no—
924C22×C4—62no—
925C22×C4—62no—
926C22×C4C23×D311yescharacteristic
927Q16—24no—
928Q16—62no—
929Q16—62no—
930Q16—64no—
931SD16—24no—
932SD16—62no—
933SD16—62no—
934SD16—62no—
935SD16—62no—
936SD16—64no—
937D8—62no—
938D8—62no—
939M16—22no—
940M16—62no—
941C2×C8—22no—
942C2×C8—31no—
943C2×C8—32no—
944C2×C8—31no—
945C2×C8—62no—
946C2×C8C23×D311yescharacteristic
947C2×C8C23×D312yes—
948C2×C8C23×D311yescharacteristic
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—22no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—32no—
956C4⋊C4—32no—
957C4⋊C4—62no—
958C4⋊C4—61no—
959C4⋊C4—62no—
960C4⋊C4—62no—
961C4⋊C4—62no—
962C4⋊C4—62no—
963C4⋊C4—61no—
964C4⋊C4—61no—
965C4⋊C4—61no—
966C4⋊C4—62no—
967C4⋊C4—62no—
968C4⋊C4—61no—
969C4⋊C4—61no—
970C4⋊C4—62no—
971C4⋊C4—62no—
972C4⋊C4D3×D411yescharacteristic
973C4⋊C4D3×D411yescharacteristic
974C4⋊C4C23×D311yescharacteristic
975C4⋊C4C23×D311yescharacteristic
976C4⋊C4C23×D312yes—
977C22⋊C4—21no—
978C22⋊C4—22no—
979C22⋊C4—32no—
980C22⋊C4—32no—
981C22⋊C4—61no—
982C22⋊C4—61no—
983C22⋊C4—62no—
984C22⋊C4—61no—
985C22⋊C4—61no—
986C22⋊C4—62no—
987C22⋊C4—62no—
988C22⋊C4—62no—
989C22⋊C4—62no—
990C22⋊C4—61no—
991C22⋊C4—61no—
992C22⋊C4—62no—
993C22⋊C4—62no—
994C22⋊C4D3×D412yes—
995C42—22no—
996C42—22no—
997C42—21no—
998C42—22no—
999C42—32no—
1000C42—31no—
1001C42—31no—
1002C42—32no—
1003C42—31no—
1004C42—31no—
1005C42—62no—
1006C42—61no—
1007C42—62no—
1008C42—62no—
1009C42—61no—
1010C42—62no—
1011C42—62no—
1012C42C23×D312yes—
1013C22×C3—21no—
1014C22×C3—21no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3#52512yes—
1019C22×C3C23×D411yescharacteristic
1020C2×D3—22no—
1021C2×D3—22no—
1022C2×D3—22no—
1023C2×D3—22no—
1024C2×D3—41no—
1025C2×D3—41no—
1026C2×D3—41no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C3×C4—22no—
1030C3×C4—24no—
1031C3×C4—22no—
1032C3×C4—42no—
1033C3×C4—41no—
1034C3×C4—41no—
1035C3×C4—41no—
1036C3×C4#52512yes—
1037C3×C4C22×#4111yescharacteristic
1038C3×C4C22×#4111yescharacteristic
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—22no—
1042Dic3—22no—
1043Dic3—21no—
1044Dic3—42no—
1045Dic3—42no—
1046Dic3—41no—
1047Dic3#57812yes—
1048C23—21no—
1049C23—32no—
1050C23—61no—
1051C23—61no—
1052C23C2×D3×D411yescharacteristic
1053Q8—22no—
1054Q8—24no—
1055Q8—21no—
1056Q8—21no—
1057Q8—32no—
1058Q8—68no—
1059Q8—61no—
1060Q8—62no—
1061Q8—61no—
1062Q8—61no—
1063Q8—124no—
1064Q8—242no—
1065Q8C2×#23514yes—
1066D4—21no—
1067D4—21no—
1068D4—32no—
1069D4—42no—
1070D4—68no—
1071D4—64no—
1072D4—64no—
1073D4—61no—
1074D4—61no—
1075D4—61no—
1076D4—62no—
1077D4—122no—
1078D4—122no—
1079D4—122no—
1080D4—242no—
1081D4—242no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—32no—
1093C2×C4—42no—
1094C2×C4—64no—
1095C2×C4—68no—
1096C2×C4—68no—
1097C2×C4—62no—
1098C2×C4—61no—
1099C2×C4—62no—
1100C2×C4—62no—
1101C2×C4—64no—
1102C2×C4—62no—
1103C2×C4—61no—
1104C2×C4—62no—
1105C2×C4—82no—
1106C2×C4—81no—
1107C2×C4—122no—
1108C2×C4—122no—
1109C2×C4—121no—
1110C2×C4—122no—
1111C2×C4—242no—
1112C2×C4—242no—
1113C2×C4—241no—
1114C2×C4—242no—
1115C2×C4—241no—
1116C2×C4—241no—
1117C2×C4C2×#23512yes—
1118C2×C4C2×D3×D412yes—
1119C2×C4C2×D3×D412yes—
1120C2×C4C2×D3×D411yescharacteristic
1121C2×C4D3×#4112yes—
1122C2×C4C24×D311yescharacteristic
1123C8—22no—
1124C8—21no—
1125C8—21no—
1126C8—62no—
1127C8—61no—
1128C8—61no—
1129C2×C3—22no—
1130C2×C3—81no—
1131C2×C3C2×#52511yescharacteristic
1132C2×C3C2×#57811yescharacteristic
1133C2×C3#358511yescharacteristic
1134D3—42no—
1135D3—42no—
1136D3—81no—
1137C22—21no—
1138C22—21no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—62no—
1143C22—62no—
1144C22—62no—
1145C22—62no—
1146C22—121no—
1147C22—121no—
1148C22—121no—
1149C22—121no—
1150C22—121no—
1151C22#554712yes—
1152C22C22×D3×D411yescharacteristic
1153C4—24no—
1154C4—22no—
1155C4—22no—
1156C4—32no—
1157C4—41no—
1158C4—42no—
1159C4—41no—
1160C4—41no—
1161C4—62no—
1162C4—62no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—121no—
1167C4—122no—
1168C4—122no—
1169C4#554712yes—
1170C4C22×#23511yescharacteristic
1171C4C2×D3×#4111yescharacteristic
1172C3#6060011yescharacteristic, complemented, Sylow
1173C2—22no—
1174C2—81no—
1175C2—122no—
1176C2—122no—
1177C2—241no—
1178C2C2×#554711yescharacteristic
1179C2#8720711yescharacteristic
1180C2D3×#57811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2947C2
socleC22×C3C23×D4
hypercenter#2947D3
hypocenterC3#60600
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #2947

Complements

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

NH ≅ G/Ntype
1. #85893C2semidirect
2. #85873C2semidirect
3. C3×#2947C2semidirect
4. #83984C2semidirect
5. #83966C2semidirect
6. #82557C2semidirect
7. #82547C2semidirect
8. #79848C2semidirect
9. #79835C2semidirect
10. #79813C2semidirect
11. #79781C2semidirect
12. #79749C2semidirect
13. #79722C2semidirect
14. #79695C2semidirect
15. #79658C2semidirect
16. #79240C2semidirect
17. #79221C2semidirect
18. #78861C2semidirect
19. #78843C2semidirect
20. #78795C2semidirect
21. C2×#4793C2semidirect
22. #78562C2semidirect
23. #78552C2semidirect
157. #2947D3semidirect
457. C2×C3×Q8#41semidirect
490. #235#41semidirect
890. C2×Q8#235semidirect
1172. C3#60600semidirect

Maximal subgroups

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

subgroupindex
#858932
#858732
C3×#29472
#839842
#839662
#825572
#825472
#798482
#798352
#798132
#797812
#797492
#797222
#796952
#796582
#792402
#792212
#788612
#788432
#787952
C2×#47932
#785622
#785522
#606003