Finite Group Databasebeta

← #11664306

Subgroups — #11664306

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86369C211yesmaximal, characteristic, complemented
2#85887C211yesmaximal, characteristic, complemented
3C3×#3098C211yesmaximal, characteristic, complemented
4#83427C211yesmaximal, characteristic, complemented
5#82574C211yesmaximal, characteristic, complemented
6#81499C212yesmaximal, complemented
7#81492C212yesmaximal, complemented
8#81456C212yesmaximal, complemented
9#81455C212yesmaximal, complemented
10#81355C212yesmaximal, complemented
11#81350C212yesmaximal, complemented
12#81272C212yesmaximal, complemented
13#81269C212yesmaximal, complemented
14#79241C211yesmaximal, characteristic, complemented
15#79202C211yesmaximal, characteristic, complemented
16C2×#4877C211yesmaximal, characteristic, complemented
17#79136C211yesmaximal, characteristic, complemented
18#78913C211yesmaximal, characteristic, complemented
19#78869C211yesmaximal, characteristic, complemented
20#78861C211yesmaximal, characteristic, complemented
21#78821C211yesmaximal, characteristic, complemented
22#78680C211yesmaximal, characteristic, complemented
23#78650C211yesmaximal, characteristic, complemented
24#60598—31nomaximal, Sylow
25C2×#1010C2211yescharacteristic
26C3×#537C2211yescharacteristic
27C3×#520C2211yescharacteristic
28#5833C2211yescharacteristic
29#5832C2211yescharacteristic
30#5827C2211yescharacteristic
31Dic3×#41C2211yescharacteristic
32C2×#951C2211yescharacteristic
33C2×#950C2211yescharacteristic
34C2×#909C2211yescharacteristic
35C2×#904C2211yescharacteristic
36#5642—21no—
37#5639—21no—
38#5625C2212yes—
39#5624C2212yes—
40#5619C2212yes—
41#5618—21no—
42#5618—22no—
43#5614—21no—
44#5601—22no—
45#5600C2212yes—
46#5572—21no—
47C4×D3×Q8—21no—
48#5546—22no—
49#5546—21no—
50C4×#237—22no—
51C4×#237—21no—
52#5522C2211yescharacteristic
53#5522C2212yes—
54#5516C2212yes—
55#5516C2211yescharacteristic
56#5504C2211yescharacteristic
57#5504C2211yescharacteristic
58#5504C2212yes—
59C2×#890C2211yescharacteristic
60C2×#887C2212yes—
61C2×#887C2211yescharacteristic
62C3×#485C2212yes—
63C3×#484C2212yes—
64C3×#482C2212yes—
65C3×#480C2212yes—
66C3×#428C2211yescharacteristic
67C2×C3×#107C2211yescharacteristic
68C3×#417C2211yescharacteristic
69C3×#416C2211yescharacteristic
70C3×#408C2211yescharacteristic
71#5234C2211yescharacteristic
72#5133C2211yescharacteristic
73#5122C2211yescharacteristic
74#5118C2211yescharacteristic
75C2×#816C2211yescharacteristic
76#5101C2211yescharacteristic
77C2×Dic3⋊C8C2211yescharacteristic
78#5050C2212yes—
79#5047C2212yes—
80#5040C2212yes—
81#5037C2212yes—
82#5003C2212yes—
83#5002C2211yescharacteristic
84#4996C2212yes—
85#4995C2211yescharacteristic
86#4971C2212yes—
87C2×#810C2211yescharacteristic
88#4968C2212yes—
89#4966C2211yescharacteristic
90#4966C2211yescharacteristic
91C2×#808C2211yescharacteristic
92#4891C2212yes—
93#4889C2212yes—
94#4889C2212yes—
95#4889C2212yes—
96#4877C2212yes—
97#4877C2212yes—
98#4877C2212yes—
99#4877C2212yes—
100#4877C2212yes—
101#4873C2212yes—
102#4873C2212yes—
103#4872C2212yes—
104#4871C2212yes—
105#4857C2212yes—
106#4853C2212yes—
107#4852C2212yes—
108#4819C2211yescharacteristic
109#4818C2211yescharacteristic
110#4798C2211yescharacteristic
111#4798C2212yes—
112#4795C2211yescharacteristic
113#4795C2212yes—
114#4790C2212yes—
115#4789C2212yes—
116#4789C2212yes—
117#4788C2212yes—
118#4787C2211yescharacteristic
119#4786C2211yescharacteristic
120#4785C2212yes—
121#4767C2211yescharacteristic
122#4767C2212yes—
123#4762C2211yescharacteristic
124#4762C2212yes—
125#4758C2212yes—
126#4758C2212yes—
127#4757C2212yes—
128#4739C2212yes—
129#4738C2212yes—
130#4734C2212yes—
131#4733C2212yes—
132#4720C2212yes—
133#4720C2212yes—
134#4719C2212yes—
135#4718C2212yes—
136#3512—31no—
137C4×2−1+4—31no—
138#3127—32no—
139#3126—32no—
140#3120—32no—
141#3119—32no—
142#3117—32no—
143#3111—32no—
144#3108—32no—
145#3102—32no—
146#3099—31no—
147#3098D311yescharacteristic, complemented
148#3080—31no—
149C2×#479—31no—
150#3037—31no—
151#3035—31no—
152#3013—31no—
153#3013—31no—
154#2952—31no—
155#2951—31no—
156#2947—31no—
157#2947—31no—
158#2925—31no—
159C2×C3×#41C2311yescharacteristic
160C2×C3×#41C2311yescharacteristic
161#1010—24no—
162#1010—24no—
163C2×D3×Q8—21no—
164C2×#237—21no—
165C2×#237—22no—
166C2×#235C2312yes—
167C2×#235C2311yescharacteristic
168C2×#235C2311yescharacteristic
169C22×Dic6C2312yes—
170C22×Dic6C2311yescharacteristic
171C2×C3×M16C2311yescharacteristic
172C22×C3×C8C2311yescharacteristic
173C3×C22⋊Q8—21no—
174C3×C22⋊Q8C2312yes—
175C3×#121—22no—
176C3×#121—21no—
177C3×#121C2312yes—
178C3×C4×Q8—21no—
179C3×C4×D4—21no—
180C3×C4×D4—22no—
181C3×#117C2311yescharacteristic
182C3×#117C2312yes—
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2312yes—
186#951—24no—
187#950—24no—
188#947C2311yescharacteristic
189#946—21no—
190Q8×Dic3D411yescharacteristic
191Q8×Dic3D411yescharacteristic
192Q8×Dic3C2312yes—
193#944C2311yescharacteristic
194C2×#216C2311yescharacteristic
195C2×#216C2312yes—
196C2×#215C2311yescharacteristic
197#940C2311yescharacteristic
198#939—22no—
199#939—21no—
200#939—21no—
201#939—22no—
202#938—21no—
203#938—22no—
204#936C2311yescharacteristic
205#935—22no—
206D4×Dic3—22no—
207D4×Dic3—22no—
208D4×Dic3D412yes—
209D4×Dic3D411yescharacteristic
210D4×Dic3D412yes—
211D4×Dic3D411yescharacteristic
212D4×Dic3C2312yes—
213C2×#214C2312yes—
214C2×#214C2311yescharacteristic
215C2×#213C2311yescharacteristic
216#930C2312yes—
217C4×#67—22no—
218C4×#67—22no—
219C4×#67—22no—
220C4×#67—22no—
221C4×#67—21no—
222C4×#67—21no—
223#926—21no—
224#926C2311yescharacteristic
225#926C2312yes—
226C2×C4⋊Dic3—21no—
227C2×C4⋊Dic3—21no—
228C2×C4⋊Dic3C2311yescharacteristic
229#924C2312yes—
230C2×Dic3⋊C4—22no—
231C2×Dic3⋊C4—21no—
232C2×Dic3⋊C4—21no—
233C2×C4×Dic3—22no—
234C2×C4×Dic3—21no—
235C2×C4×Dic3C2312yes—
236C2×C4×Dic3C2311yescharacteristic
237C2×#208C2311yescharacteristic
238C22×C3⋊C8C2311yescharacteristic
239#909—24no—
240C2×Dic12C2311yescharacteristic
241C2×Dic12C2312yes—
242#904—24no—
243C2×D24C2311yescharacteristic
244C2×#204C2311yescharacteristic
245C2×#204C2311yescharacteristic
246C2×#204C2312yes—
247#898—22no—
248#893C2311yescharacteristic
249#893C2312yes—
250#893C2312yes—
251#893C2311yescharacteristic
252#892—21no—
253#892—22no—
254#892—21no—
255#892—22no—
256D3×C4⋊C4—21no—
257D3×C4⋊C4—22no—
258D3×C4⋊C4—21no—
259#890—22no—
260#890—21no—
261#890—21no—
262#890C2312yes—
263#890C2312yes—
264#889—22no—
265#887—22no—
266#887—21no—
267#887—22no—
268#887—21no—
269#887C2312yes—
270#887C2312yes—
271#887C2312yes—
272#887C2312yes—
273#887C2311yescharacteristic
274#887C2312yes—
275#887C2312yes—
276#887C2311yescharacteristic
277#886—22no—
278#886—22no—
279#883—22no—
280#67⋊C4—22no—
281#67⋊C4—21no—
282#67⋊C4—22no—
283#67⋊C4—21no—
284#67⋊C4—22no—
285#879—22no—
286#879—22no—
287#879—22no—
288#877—22no—
289#877—22no—
290#877—22no—
291#877—22no—
292#872—22no—
293#872—21no—
294C42×D3—22no—
295C42×D3—21no—
296C4×Dic6—22no—
297C4×Dic6—21no—
298C4×Dic6—22no—
299C4×Dic6—21no—
300C3×#107C2312yes—
301C3×#107C2312yes—
302C3×#107C2312yes—
303C3×#106C2312yes—
304C3×#103C2311yescharacteristic
305C3×#103C2311yescharacteristic
306C3×#103C2312yes—
307C3×#102C2311yescharacteristic
308C3×#102C2311yescharacteristic
309C3×#102C2312yes—
310C3×C22⋊C8C2312yes—
311C3×C22⋊C8C2312yes—
312#830C2312yes—
313#830C2312yes—
314#821C2312yes—
315#816C2312yes—
316#816C2312yes—
317#816C2312yes—
318#815C2312yes—
319#815C2312yes—
320Dic3⋊C8C2312yes—
321Dic3⋊C8C2311yescharacteristic
322Dic3⋊C8C2311yescharacteristic
323Dic3⋊C8C2311yescharacteristic
324Dic3⋊C8C2311yescharacteristic
325Dic3⋊C8C2312yes—
326C8×Dic3C2312yes—
327C8×Dic3C2312yes—
328#810C2311yescharacteristic
329#810C2312yes—
330#810C2312yes—
331#810C2312yes—
332#810C2312yes—
333#810C2311yescharacteristic
334#809C2312yes—
335#809C2312yes—
336#809C2311yescharacteristic
337#809C2311yescharacteristic
338#808C2312yes—
339#808C2312yes—
340#808C2312yes—
341#807C2312yes—
342C2×2−1+4—31no—
343C2×#137—31no—
344C2×#137—31no—
345C2×#135—31no—
346C2×#135—31no—
347#553—62no—
348#553—61no—
349#553—61no—
350#553—62no—
351#552—61no—
352#552—61no—
353#541—32no—
354#540—32no—
355#537—31no—
356#537C2×D311yescharacteristic
357#532—31no—
358#529—32no—
359#529—32no—
360C2×#125—31no—
361#520—31no—
362#520—32no—
363#520—31no—
364#520—31no—
365#520—61no—
366#520—62no—
367#520C2×D311yescharacteristic
368#519—32no—
369#519—31no—
370#519—61no—
371C4×#41—31no—
372C4×#41—31no—
373C4×#41—32no—
374C4×#41—62no—
375C4×#41—61no—
376C2×C4×Q8—31no—
377C2×C4×Q8—32no—
378C2×C4×Q8—61no—
379#485—32no—
380#485C2×D312yes—
381#484C2×D312yes—
382#483—32no—
383#482—32no—
384#482C2×D312yes—
385#481—32no—
386#480C2×D312yes—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479—32no—
392#479—32no—
393#478—32no—
394#478—32no—
395#464—32no—
396#464—31no—
397#464—31no—
398#464—32no—
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#442—32no—
416#441—32no—
417#441—32no—
418#441—32no—
419#440—32no—
420#440—32no—
421#440—32no—
422#440—32no—
423C4×Q16—32no—
424C4×Q16—32no—
425C4×Q16—32no—
426C4×SD16—32no—
427C4×SD16—32no—
428C4×SD16—32no—
429C4×SD16—32no—
430C4×D8—32no—
431#433—32no—
432#433—32no—
433#432—32no—
434#431—32no—
435#428—31no—
436#428C2×D311yescharacteristic
437C2×#107C2×D311yescharacteristic
438C2×#106—31no—
439#423—31no—
440C2×C4⋊C8—31no—
441#417—31no—
442#417—31no—
443#417—31no—
444#417C2×D311yescharacteristic
445#416—31no—
446#416C2×D311yescharacteristic
447C2×#103—31no—
448C2×#103—31no—
449#408—31no—
450#408C2×D311yescharacteristic
451#405—31no—
452#405—31no—
453C3×#41—22no—
454C3×#41—22no—
455C3×#41—22no—
456C3×#41—22no—
457C2×C3×Q8C2×D411yescharacteristic
458C2×C3×Q8C2411yescharacteristic
459C2×C3×D4—21no—
460C2×C3×D4—22no—
461C2×C3×D4C2×D411yescharacteristic
462C2×C3×D4C2×D412yes—
463C2×C3×D4C2411yescharacteristic
464C22×C3×C4—22no—
465C22×C3×C4—21no—
466C22×C3×C4—21no—
467C22×C3×C4—21no—
468C22×C3×C4C2412yes—
469C22×C3×C4C2411yescharacteristic
470C2×#67—22no—
471C2×#67—21no—
472C2×#67—21no—
473C2×#67—22no—
474C2×#67—21no—
475C2×#67—21no—
476C22×Dic3—22no—
477C22×Dic3—21no—
478C22×Dic3—21no—
479C22×Dic3—22no—
480C22×Dic3C2×D412yes—
481C22×Dic3C2×D412yes—
482C22×Dic3C2×D411yescharacteristic
483C22×Dic3C2×D411yescharacteristic
484D3×Q8—28no—
485#237—216no—
486#237—28no—
487#235—22no—
488#235—24no—
489#235—22no—
490#235—22no—
491#235—24no—
492#235#4114yes—
493C2×D12C2411yescharacteristic
494C2×D12C2411yescharacteristic
495C2×C4×D3—22no—
496C2×C4×D3—21no—
497C2×C4×D3—21no—
498C2×C4×D3—21no—
499C2×C4×D3—22no—
500C2×C4×D3—21no—
501C2×C4×D3—22no—
502C2×Dic6—22no—
503C2×Dic6—21no—
504C2×Dic6—22no—
505C2×Dic6—24no—
506C2×Dic6—24no—
507C2×Dic6#4114yes—
508C2×Dic6C2411yescharacteristic
509C2×Dic6C2411yescharacteristic
510C2×Dic6C2412yes—
511C3×M16—22no—
512C2×C3×C8—22no—
513C2×C3×C8C2411yescharacteristic
514C2×C3×C8C2412yes—
515C2×C3×C8C2411yescharacteristic
516C3×C4⋊C4—22no—
517C3×C4⋊C4—21no—
518C3×C4⋊C4—22no—
519C3×C4⋊C4—21no—
520C3×C4⋊C4C2411yescharacteristic
521C3×C4⋊C4C2412yes—
522C3×C4⋊C4C2411yescharacteristic
523C3×C4⋊C4C2412yes—
524C3×C22⋊C4—22no—
525C3×C22⋊C4—21no—
526C3×C22⋊C4—22no—
527C3×C22⋊C4—22no—
528C3×C42—22no—
529C3×C42—21no—
530#217—22no—
531#217—21no—
532#217—21no—
533#217—22no—
534#217C2×D412yes—
535#217C2×D412yes—
536#217C2×D412yes—
537#216—22no—
538#216—24no—
539#215—22no—
540#214—22no—
541#214—24no—
542#213—22no—
543(C2×D3)⋊C4—22no—
544(C2×D3)⋊C4—21no—
545(C2×D3)⋊C4—22no—
546(C2×D3)⋊C4—21no—
547(C2×D3)⋊C4—21no—
548(C2×D3)⋊C4—21no—
549(C2×D3)⋊C4—22no—
550C4⋊Dic3—21no—
551C4⋊Dic3—22no—
552C4⋊Dic3—22no—
553C4⋊Dic3—22no—
554C4⋊Dic3C2×D412yes—
555C4⋊Dic3C2×D412yes—
556C4⋊Dic3C2×D411yescharacteristic
557C4⋊Dic3C2×D411yescharacteristic
558C4⋊Dic3C2412yes—
559Dic3⋊C4—22no—
560Dic3⋊C4—22no—
561Dic3⋊C4—21no—
562Dic3⋊C4—22no—
563Dic3⋊C4—22no—
564Dic3⋊C4—22no—
565Dic3⋊C4—22no—
566Dic3⋊C4—21no—
567Dic3⋊C4—22no—
568Dic3⋊C4—22no—
569Dic3⋊C4—21no—
570Dic3⋊C4—21no—
571Dic3⋊C4—22no—
572C4×Dic3—22no—
573C4×Dic3—21no—
574C4×Dic3—22no—
575C4×Dic3—22no—
576C4×Dic3—22no—
577C4×Dic3—22no—
578C4×Dic3—21no—
579C4×Dic3—22no—
580C4×Dic3—22no—
581C4×Dic3C2×D412yes—
582C4×Dic3C2×D411yescharacteristic
583C4×Dic3C2×D412yes—
584C4×Dic3C2×D411yescharacteristic
585C4×Dic3C2412yes—
586C4×Dic3C2411yescharacteristic
587C4×Dic3C2411yescharacteristic
588#208—22no—
589C2×C3⋊C8—22no—
590C2×C3⋊C8C2412yes—
591C2×C3⋊C8C2411yescharacteristic
592C2×C3⋊C8C2411yescharacteristic
593Dic12—22no—
594Dic12—24no—
595D24—22no—
596#204—22no—
597#204—22no—
598#204—24no—
5992−1+4—64no—
6002−1+4—64no—
601C2×#41—31no—
602C2×#41—32no—
603C2×#41—31no—
604C2×#41—61no—
605C2×#41—62no—
606C2×#41C22×D311yescharacteristic
607C2×#41C22×D311yescharacteristic
608C22×Q8—31no—
609C22×Q8—32no—
610C22×Q8—61no—
611#137—64no—
612#137—64no—
613#135—64no—
614#135—64no—
615C2×Q16—31no—
616C2×Q16—32no—
617C2×Q16—31no—
618C2×Q16—32no—
619C2×SD16—31no—
620C2×SD16—31no—
621C2×SD16—32no—
622C2×SD16—31no—
623C2×SD16—31no—
624C2×SD16—32no—
625C2×D8—31no—
626C2×D8—31no—
627C2×M16—31no—
628C2×M16C22×D311yescharacteristic
629C22×C8—31no—
630C22×C8C22×D311yescharacteristic
631C4⋊Q8—31no—
632#127—31no—
633#126—62no—
634#126—62no—
635#126—62no—
636#126—62no—
637#125—32no—
638#125—32no—
639#125—61no—
640#125—61no—
641#125—62no—
642#125—62no—
643#124—31no—
644#124—31no—
645#123—62no—
646#123—62no—
647#123—62no—
648#123—62no—
649C22⋊Q8—21no—
650C22⋊Q8—32no—
651C22⋊Q8—61no—
652C22⋊Q8C22×D312yes—
653#121—21no—
654#121—22no—
655#121—32no—
656#121—62no—
657#121—62no—
658#121—61no—
659#121—61no—
660#121—61no—
661#121—62no—
662#121C22×D312yes—
663C4×Q8—21no—
664C4×Q8—31no—
665C4×Q8—31no—
666C4×Q8—32no—
667C4×Q8—32no—
668C4×Q8—31no—
669C4×Q8—32no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—32no—
673C4×Q8—31no—
674C4×Q8—32no—
675C4×Q8—61no—
676C4×Q8—62no—
677C4×Q8—61no—
678C4×Q8—62no—
679C4×Q8—62no—
680C4×Q8—61no—
681C4×Q8—62no—
682C4×Q8—61no—
683C4×D4—22no—
684C4×D4—21no—
685C4×D4—32no—
686C4×D4—31no—
687C4×D4—32no—
688C4×D4—31no—
689C4×D4—32no—
690C4×D4—31no—
691C4×D4—32no—
692C4×D4—31no—
693C4×D4—32no—
694C4×D4—61no—
695C4×D4—61no—
696C4×D4—61no—
697C4×D4—62no—
698C4×D4—61no—
699C4×D4—62no—
700C4×D4—62no—
701C4×D4—62no—
702C4×D4—62no—
703C4×D4—62no—
704C4×D4—62no—
705C4×D4—62no—
706C4×D4—62no—
707#117—31no—
708#117—32no—
709#117—62no—
710#117—61no—
711#117—62no—
712#117—62no—
713#117—62no—
714#117—62no—
715#117—62no—
716#117—61no—
717#117—62no—
718#117—61no—
719#117—61no—
720#117C22×D311yescharacteristic
721#117C22×D312yes—
722C2×C4⋊C4—31no—
723C2×C4⋊C4—61no—
724C2×C4⋊C4—62no—
725C2×C4⋊C4—61no—
726C2×C4⋊C4—61no—
727C2×C4⋊C4—61no—
728C2×C4⋊C4—62no—
729C2×C4⋊C4—61no—
730C2×C4⋊C4—61no—
731C2×C4⋊C4C22×D311yescharacteristic
732C2×C4⋊C4C22×D312yes—
733C2×C4⋊C4C22×D311yescharacteristic
734C2×C42—31no—
735C2×C42—32no—
736C2×C42—62no—
737C2×C42—61no—
738C2×C42—61no—
739C2×C42—62no—
740#107—32no—
741#107C22×D312yes—
742#107C22×D312yes—
743#107C22×D312yes—
744#106—32no—
745#106—32no—
746#106—32no—
747#106C22×D312yes—
748C4⋊C8—31no—
749C4⋊C8—31no—
750C4⋊C8—31no—
751C4⋊C8—31no—
752C4⋊C8—32no—
753C4⋊C8—32no—
754#103—32no—
755#103—32no—
756#103—32no—
757#103—32no—
758#103—32no—
759#103—31no—
760#103—31no—
761#103—32no—
762#103—32no—
763#103C22×D311yescharacteristic
764#103C22×D311yescharacteristic
765#103C22×D312yes—
766#102—32no—
767#102—31no—
768#102—31no—
769#102—32no—
770#102—32no—
771#102C22×D311yescharacteristic
772#102C22×D311yescharacteristic
773#102C22×D312yes—
774C22⋊C8—32no—
775C22⋊C8—32no—
776C22⋊C8C22×D312yes—
777C22⋊C8C22×D312yes—
778#97—32no—
779#97—32no—
780C4×C8—32no—
781C4×C8—32no—
782C23×C3—21no—
783C23×C3C22×D412yes—
784C23×C3C22×D411yescharacteristic
785C22×D3—21no—
786C22×D3—21no—
787C3×Q8—22no—
788C3×Q8—21no—
789C3×Q8—21no—
790C3×D4—24no—
791C3×D4—22no—
792C3×D4—21no—
793C3×D4—21no—
794C3×D4—42no—
795C3×D4—82no—
796C2×C3×C4—22no—
797C2×C3×C4—22no—
798C2×C3×C4—21no—
799C2×C3×C4—21no—
800C2×C3×C4—22no—
801C2×C3×C4—21no—
802C2×C3×C4—22no—
803C2×C3×C4—42no—
804C2×C3×C4—81no—
805C2×C3×C4—82no—
806C2×C3×C4—81no—
807C2×C3×C4C22×D412yes—
808C2×C3×C4C22×D411yescharacteristic
809C2×C3×C4C2×#4112yes—
810C2×C3×C4C2×#4112yes—
811C2×C3×C4C2511yescharacteristic
812#67—28no—
813#67—24no—
814#67—42no—
815#67—81no—
816#67—81no—
817#67—82no—
818C2×Dic3—28no—
819C2×Dic3—24no—
820C2×Dic3—21no—
821C2×Dic3—22no—
822C2×Dic3—21no—
823C2×Dic3—22no—
824C2×Dic3—42no—
825C2×Dic3—41no—
826C2×Dic3—42no—
827C2×Dic3—41no—
828C2×Dic3—82no—
829C2×Dic3—81no—
830C2×Dic3C22×D411yescharacteristic
831C2×Dic3C22×D412yes—
832C2×Dic3C22×D412yes—
833C2×Dic3C22×D411yescharacteristic
834C2×Dic3C22×D411yescharacteristic
835C2×Dic3C22×D411yescharacteristic
836D12—21no—
837D12—21no—
838D12—21no—
839D12C2×#4112yes—
840C4×D3—28no—
841C4×D3—24no—
842C4×D3—42no—
843C4×D3—42no—
844C4×D3—82no—
845C4×D3—82no—
846C4×D3—81no—
847Dic6—28no—
848Dic6—24no—
849Dic6—22no—
850Dic6—21no—
851Dic6—21no—
852Dic6—21no—
853Dic6C2×#4112yes—
854Dic6C2×#4114yes—
855C3×C8—21no—
856C3×C8—22no—
857C3×C8—21no—
858C3⋊C8—21no—
859C3⋊C8—21no—
860C3⋊C8—22no—
861#41—22no—
862#41—22no—
863#41—22no—
864#41—22no—
865#41—34no—
866#41—64no—
867#41—64no—
868#41—616no—
869#41—68no—
870#41—62no—
871#41—62no—
872#41—62no—
873C2×Q8—34no—
874C2×Q8—32no—
875C2×Q8—31no—
876C2×Q8—31no—
877C2×Q8—64no—
878C2×Q8—64no—
879C2×Q8—68no—
880C2×Q8—62no—
881C2×Q8—61no—
882C2×Q8—62no—
883C2×Q8D3×D411yescharacteristic
884C2×Q8C23×D311yescharacteristic
885C2×D4—21no—
886C2×D4—22no—
887C2×D4—31no—
888C2×D4—31no—
889C2×D4—61no—
890C2×D4—61no—
891C2×D4—62no—
892C2×D4—61no—
893C2×D4—61no—
894C2×D4—62no—
895C2×D4D3×D412yes—
896C2×D4D3×D411yescharacteristic
897C2×D4C23×D311yescharacteristic
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—31no—
903C22×C4—32no—
904C22×C4—31no—
905C22×C4—32no—
906C22×C4—61no—
907C22×C4—62no—
908C22×C4—61no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—61no—
913C22×C4—62no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4—61no—
917C22×C4C23×D312yes—
918C22×C4C23×D311yescharacteristic
919Q16—62no—
920Q16—64no—
921Q16—62no—
922Q16—64no—
923SD16—62no—
924SD16—62no—
925SD16—64no—
926SD16—62no—
927SD16—64no—
928SD16—62no—
929D8—62no—
930D8—62no—
931M16—22no—
932M16—62no—
933C2×C8—22no—
934C2×C8—31no—
935C2×C8—32no—
936C2×C8—31no—
937C2×C8—62no—
938C2×C8C23×D311yescharacteristic
939C2×C8C23×D312yes—
940C2×C8C23×D311yescharacteristic
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—22no—
945C4⋊C4—31no—
946C4⋊C4—31no—
947C4⋊C4—32no—
948C4⋊C4—32no—
949C4⋊C4—32no—
950C4⋊C4—62no—
951C4⋊C4—61no—
952C4⋊C4—62no—
953C4⋊C4—62no—
954C4⋊C4—62no—
955C4⋊C4—62no—
956C4⋊C4—62no—
957C4⋊C4—62no—
958C4⋊C4—62no—
959C4⋊C4—62no—
960C4⋊C4—62no—
961C4⋊C4—62no—
962C4⋊C4—61no—
963C4⋊C4—61no—
964C4⋊C4—61no—
965C4⋊C4—61no—
966C4⋊C4—62no—
967C4⋊C4C23×D311yescharacteristic
968C4⋊C4C23×D312yes—
969C4⋊C4C23×D311yescharacteristic
970C4⋊C4C23×D312yes—
971C22⋊C4—22no—
972C22⋊C4—21no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—32no—
976C22⋊C4—32no—
977C22⋊C4—32no—
978C22⋊C4—61no—
979C22⋊C4—62no—
980C22⋊C4—61no—
981C22⋊C4—61no—
982C22⋊C4—62no—
983C22⋊C4—61no—
984C22⋊C4—61no—
985C22⋊C4—62no—
986C22⋊C4—61no—
987C22⋊C4—62no—
988C22⋊C4—62no—
989C42—22no—
990C42—21no—
991C42—32no—
992C42—31no—
993C42—32no—
994C42—31no—
995C42—32no—
996C42—31no—
997C42—31no—
998C42—62no—
999C42—61no—
1000C42—62no—
1001C42—61no—
1002C42—62no—
1003C42—62no—
1004C42—62no—
1005C42—62no—
1006C42—62no—
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3—22no—
1010C22×C3—22no—
1011C22×C3—22no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3#52512yes—
1016C22×C3C23×D411yescharacteristic
1017C2×D3—22no—
1018C2×D3—41no—
1019C2×D3—41no—
1020C2×D3—41no—
1021C2×D3—41no—
1022C2×D3—41no—
1023C3×C4—22no—
1024C3×C4—42no—
1025C3×C4—41no—
1026C3×C4—42no—
1027C3×C4—41no—
1028C3×C4—41no—
1029C3×C4#52512yes—
1030C3×C4C22×#4111yescharacteristic
1031C3×C4C22×#4111yescharacteristic
1032Dic3—22no—
1033Dic3—21no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—22no—
1037Dic3—21no—
1038Dic3—22no—
1039Dic3—24no—
1040Dic3—42no—
1041Dic3—41no—
1042C23—21no—
1043C23—61no—
1044C23—61no—
1045C23C2×D3×D412yes—
1046C23C2×D3×D411yescharacteristic
1047Q8—22no—
1048Q8—21no—
1049Q8—21no—
1050Q8—34no—
1051Q8—32no—
1052Q8—68no—
1053Q8—64no—
1054Q8—62no—
1055Q8—61no—
1056Q8—61no—
1057Q8—61no—
1058D4—24no—
1059D4—22no—
1060D4—21no—
1061D4—21no—
1062D4—32no—
1063D4—42no—
1064D4—68no—
1065D4—64no—
1066D4—61no—
1067D4—61no—
1068D4—61no—
1069D4—82no—
1070D4—122no—
1071D4—241no—
1072D4—241no—
1073D4—242no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—31no—
1082C2×C4—31no—
1083C2×C4—32no—
1084C2×C4—31no—
1085C2×C4—32no—
1086C2×C4—31no—
1087C2×C4—42no—
1088C2×C4—68no—
1089C2×C4—68no—
1090C2×C4—64no—
1091C2×C4—62no—
1092C2×C4—61no—
1093C2×C4—64no—
1094C2×C4—61no—
1095C2×C4—62no—
1096C2×C4—81no—
1097C2×C4—82no—
1098C2×C4—81no—
1099C2×C4—122no—
1100C2×C4—122no—
1101C2×C4—121no—
1102C2×C4—122no—
1103C2×C4—121no—
1104C2×C4—122no—
1105C2×C4—242no—
1106C2×C4—241no—
1107C2×C4—242no—
1108C2×C4—242no—
1109C2×C4—241no—
1110C2×C4C2×D3×D412yes—
1111C2×C4C2×D3×D411yescharacteristic
1112C2×C4D3×#4112yes—
1113C2×C4D3×#4112yes—
1114C2×C4C24×D311yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—22no—
1118C8—61no—
1119C8—61no—
1120C8—62no—
1121C2×C3—22no—
1122C2×C3—42no—
1123C2×C3—81no—
1124C2×C3C2×#52511yescharacteristic
1125C2×C3#358411yescharacteristic
1126C2×C3#358611yescharacteristic
1127D3—42no—
1128D3—81no—
1129C22—21no—
1130C22—21no—
1131C22—22no—
1132C22—22no—
1133C22—22no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—62no—
1138C22—121no—
1139C22—121no—
1140C22—121no—
1141C22—121no—
1142C22—121no—
1143C22#565612yes—
1144C22C22×D3×D411yescharacteristic
1145C4—22no—
1146C4—42no—
1147C4—41no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—61no—
1152C4—62no—
1153C4—61no—
1154C4—61no—
1155C4—62no—
1156C4—61no—
1157C4—64no—
1158C4—62no—
1159C4—122no—
1160C4—121no—
1161C4#565612yes—
1162C4C2×D3×#4111yescharacteristic
1163C4C2×D3×#4111yescharacteristic
1164C3#6059811yescharacteristic, complemented, Sylow
1165C2—22no—
1166C2—42no—
1167C2—81no—
1168C2—122no—
1169C2—241no—
1170C2C2×#565611yescharacteristic
1171C2#8720311yescharacteristic
1172C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3098C2
socleC22×C3C23×D4
hypercenter#3098D3
hypocenterC3#60598
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3098

Complements

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

NH ≅ G/Ntype
1. #86369C2semidirect
2. #85887C2semidirect
3. C3×#3098C2semidirect
4. #83427C2semidirect
5. #82574C2semidirect
6. #81499C2semidirect
7. #81492C2semidirect
8. #81456C2semidirect
9. #81455C2semidirect
10. #81355C2semidirect
11. #81350C2semidirect
12. #81272C2semidirect
13. #81269C2semidirect
14. #79241C2semidirect
15. #79202C2semidirect
16. C2×#4877C2semidirect
17. #79136C2semidirect
18. #78913C2semidirect
19. #78869C2semidirect
20. #78861C2semidirect
21. #78821C2semidirect
22. #78680C2semidirect
23. #78650C2semidirect
147. #3098D3semidirect
1164. C3#60598semidirect

Maximal subgroups

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

subgroupindex
#863692
#858872
C3×#30982
#834272
#825742
#814992
#814922
#814562
#814552
#813552
#813502
#812722
#812692
#792412
#792022
C2×#48772
#791362
#789132
#788692
#788612
#788212
#786802
#786502
#605983