Finite Group Databasebeta

← #11664311

Subgroups — #11664311

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#86087C211yesmaximal, characteristic, complemented
2C4×#1007C211yesmaximal, characteristic, complemented
3C2×C3×#479C211yesmaximal, characteristic, complemented
4#83017C211yesmaximal, characteristic, complemented
5#82441C211yesmaximal, characteristic, complemented
6#81211C212yesmaximal, complemented
7#81210C212yesmaximal, complemented
8#81209C212yesmaximal, complemented
9#81208C212yesmaximal, complemented
10#81207C212yesmaximal, complemented
11#81206C212yesmaximal, complemented
12#81205C212yesmaximal, complemented
13#81204C212yesmaximal, complemented
14#79141C211yesmaximal, characteristic, complemented
15#79136C211yesmaximal, characteristic, complemented
16#79112C211yesmaximal, characteristic, complemented
17#79106C211yesmaximal, characteristic, complemented
18#79021C211yesmaximal, characteristic, complemented
19#79000C211yesmaximal, characteristic, complemented
20#78795C211yesmaximal, characteristic, complemented
21#78795C211yesmaximal, characteristic, complemented
22#78774C211yesmaximal, characteristic, complemented
23#78774C211yesmaximal, characteristic, complemented
24#60598—31nomaximal, Sylow
25C2×#1007C2211yescharacteristic
26C2×C3×#125C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28#5812C2211yescharacteristic
29C2×#942C2211yescharacteristic
30C2×#942C2211yescharacteristic
31C2×#904C2211yescharacteristic
32C2×#904C2211yescharacteristic
33#5698C2212yes—
34#5697C2212yes—
35#5695—21no—
36#5695—21no—
37#5694—21no—
38#5694—21no—
39#5691C2212yes—
40#5691C2212yes—
41#5574—21no—
42#5574C2212yes—
43C4×#239—21no—
44C4×#239C2212yes—
45#5572—21no—
46#5572C2212yes—
47C4×D3×Q8—21no—
48C4×D3×Q8C2212yes—
49#5514—22no—
50#5514—22no—
51#5510C2211yescharacteristic
52#5510C2211yescharacteristic
53#5504—22no—
54#5504C2211yescharacteristic
55#5504C2211yescharacteristic
56#5504C2211yescharacteristic
57#5504C2211yescharacteristic
58#5477C2211yescharacteristic
59C4×#235—22no—
60C4×#235C2211yescharacteristic
61C4×#235C2211yescharacteristic
62C3×#479C2212yes—
63C3×#479C2212yes—
64C3×#479C2212yes—
65C3×#479C2212yes—
66C2×C3×#107C2211yescharacteristic
67C2×C3×#106C2211yescharacteristic
68C2×C3×C4⋊C8C2211yescharacteristic
69C2×C3×#103C2211yescharacteristic
70C2×C3×#103C2211yescharacteristic
71#5113C2211yescharacteristic
72#5113C2211yescharacteristic
73#5110C2211yescharacteristic
74#5110C2211yescharacteristic
75#5101C2211yescharacteristic
76#5101C2211yescharacteristic
77#5066C2212yes—
78#5066C2212yes—
79#5063C2212yes—
80#5063C2212yes—
81#5031C2212yes—
82#5028C2212yes—
83#5028C2212yes—
84#5027C2212yes—
85#4966C2211yescharacteristic
86#4966C2211yescharacteristic
87#4966C2211yescharacteristic
88#4966C2211yescharacteristic
89#4964C2211yescharacteristic
90#4964C2211yescharacteristic
91#4924C2211yescharacteristic
92#4889C2212yes—
93#4889C2212yes—
94#4888C2212yes—
95#4885C2212yes—
96#4884C2212yes—
97#4882C2212yes—
98#4873C2212yes—
99#4872C2212yes—
100#4869C2212yes—
101#4868C2212yes—
102#4866C2212yes—
103#4863C2212yes—
104#4862C2212yes—
105#4853C2212yes—
106#4852C2212yes—
107#4852C2212yes—
108#4849C2211yescharacteristic
109#4848C2211yescharacteristic
110#4845C2211yescharacteristic
111#4845C2211yescharacteristic
112#4844C2211yescharacteristic
113#4844C2211yescharacteristic
114#4843C2211yescharacteristic
115#4841C2211yescharacteristic
116#4840C2212yes—
117#4840C2212yes—
118#4835C2212yes—
119#4833C2212yes—
120#4817C2212yes—
121#4817C2212yes—
122#4810C2212yes—
123#4810C2212yes—
124#4809C2212yes—
125#4809C2212yes—
126#4808C2212yes—
127#4808C2212yes—
128#4806C2212yes—
129#4806C2212yes—
130#4790C2212yes—
131#4790C2212yes—
132#4789C2212yes—
133#4789C2212yes—
134#4788C2212yes—
135#4788C2212yes—
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#3098—31no—
148#3080—31no—
149C2×#479D311yescharacteristic, complemented
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—
159C22×C3×Q8C2311yescharacteristic
160#1007—24no—
161#1007—24no—
162C2×#239—21no—
163C2×#239C2312yes—
164C2×D3×Q8—21no—
165C2×D3×Q8C2312yes—
166C2×#235—22no—
167C2×#235C2311yescharacteristic
168C2×#235C2311yescharacteristic
169C2×#235C2311yescharacteristic
170C2×#235C2311yescharacteristic
171C22×C3×C8C2311yescharacteristic
172C22×C3×C8C2311yescharacteristic
173C3×#125—21no—
174C3×#125—21no—
175C3×#125C2312yes—
176C3×#125C2312yes—
177C3×C4×Q8—21no—
178C3×C4×Q8—21no—
179C3×C4×Q8C2312yes—
180C3×C4×Q8C2312yes—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—21no—
183C2×C3×C4⋊C4—21no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C4⋊C4C2311yescharacteristic
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C42—21no—
188C2×C3×C42C2311yescharacteristic
189Q8×Dic3—21no—
190Q8×Dic3—21no—
191Q8×Dic3C2312yes—
192Q8×Dic3C2312yes—
193C2×#216C2312yes—
194C2×#216C2312yes—
195#942—24no—
196#942—24no—
197C2×#215C2312yes—
198C2×#215C2312yes—
199#930—21no—
200#930—21no—
201#930—22no—
202#930—22no—
203C4×#67—21no—
204C4×#67—21no—
205C4×#67—22no—
206C4×#67—22no—
207C4×#67—22no—
208C4×#67—22no—
209C4×#67D412yes—
210C4×#67D412yes—
211#926—22no—
212#926C2311yescharacteristic
213#926C2311yescharacteristic
214C2×#208C2311yescharacteristic
215C2×#208C2311yescharacteristic
216C2×Dic12C2311yescharacteristic
217C2×Dic12C2311yescharacteristic
218#904—24no—
219#904—24no—
220C2×D24C2311yescharacteristic
221C2×D24C2311yescharacteristic
222C2×#204C2311yescharacteristic
223C2×#204C2311yescharacteristic
224C2×#204C2311yescharacteristic
225C2×#204C2311yescharacteristic
226#898—22no—
227#898—22no—
228#898—22no—
229#898—22no—
230#897—21no—
231#897—21no—
232#897C2312yes—
233#897C2312yes—
234#895—21no—
235#895—21no—
236#895—22no—
237#895—22no—
238#895C2312yes—
239#895C2312yes—
240#894—22no—
241#894—22no—
242#894—22no—
243#894—22no—
244#893—21no—
245#893—22no—
246#893—22no—
247#893—22no—
248#893—22no—
249#893C2312yes—
250#893C2312yes—
251#893C2312yes—
252#892—22no—
253#892—21no—
254#892—21no—
255#892—21no—
256#892—22no—
257#892—22no—
258#892—22no—
259#892C2312yes—
260D3×C4⋊C4—22no—
261D3×C4⋊C4—21no—
262D3×C4⋊C4—21no—
263D3×C4⋊C4—21no—
264D3×C4⋊C4—22no—
265D3×C4⋊C4C2312yes—
266#890—22no—
267#890—22no—
268#887—21no—
269#887—22no—
270#887—22no—
271#887C2312yes—
272#887C2312yes—
273#887C2312yes—
274#875C2311yescharacteristic
275#875C2311yescharacteristic
276#874C2311yescharacteristic
277C4×D12—22no—
278C4×D12—21no—
279C4×D12—21no—
280C4×D12—22no—
281C4×D12D411yescharacteristic
282C4×D12D411yescharacteristic
283C4×D12C2311yescharacteristic
284C4×D12C2311yescharacteristic
285#872—21no—
286#872—22no—
287#872—22no—
288#872C2312yes—
289C42×D3—22no—
290C42×D3—21no—
291C42×D3—22no—
292C42×D3C2312yes—
293#869C2311yescharacteristic
294C4×Dic6—22no—
295C4×Dic6—22no—
296C4×Dic6D411yescharacteristic
297C4×Dic6D411yescharacteristic
298C4×Dic6C2311yescharacteristic
299C4×Dic6C2311yescharacteristic
300C3×#107C2312yes—
301C3×#107C2312yes—
302C3×#106C2312yes—
303C3×#106C2312yes—
304C3×C4⋊C8C2311yescharacteristic
305C3×C4⋊C8C2311yescharacteristic
306C3×C4⋊C8C2311yescharacteristic
307C3×C4⋊C8C2311yescharacteristic
308C3×#103C2312yes—
309C3×#103C2312yes—
310C3×#103C2312yes—
311C3×#103C2312yes—
312#821C2311yescharacteristic
313#821C2311yescharacteristic
314#821C2311yescharacteristic
315#821C2311yescharacteristic
316(C2×D3)⋊C8C2312yes—
317(C2×D3)⋊C8C2312yes—
318(C2×D3)⋊C8C2312yes—
319(C2×D3)⋊C8C2312yes—
320#816C2311yescharacteristic
321#816C2311yescharacteristic
322#816C2311yescharacteristic
323#816C2311yescharacteristic
324#815C2312yes—
325#815C2312yes—
326C8×Dic3C2312yes—
327C8×Dic3C2312yes—
328#810C2312yes—
329#810C2312yes—
330#810C2312yes—
331#810C2312yes—
332#809C2312yes—
333#809C2312yes—
334#809C2312yes—
335#809C2312yes—
336#808C2312yes—
337#808C2312yes—
338#807C2312yes—
339#807C2312yes—
340C4⋊(C3⋊C8)C2312yes—
341C4⋊(C3⋊C8)C2312yes—
342C2×2−1+4—31no—
343C2×#137—31no—
344C2×#137—31no—
345C2×#135—31no—
346C2×#135—31no—
347#553—62no—
348#553—62no—
349#553—61no—
350#553—61no—
351#552—61no—
352#552—61no—
353#541—32no—
354#540—32no—
355#537—31no—
356#537—31no—
357#532—31no—
358#529—32no—
359#529—32no—
360C2×#125C2×D311yescharacteristic
361#520—31no—
362#520—32no—
363#520—31no—
364#520—31no—
365#520—31no—
366#520—62no—
367#520—61no—
368#519—31no—
369#519—32no—
370#519—61no—
371C4×#41—31no—
372C4×#41—32no—
373C4×#41—31no—
374C4×#41—62no—
375C4×#41—61no—
376C2×C4×Q8—32no—
377C2×C4×Q8—61no—
378C2×C4×Q8C2×D311yescharacteristic
379#485—32no—
380#485—32no—
381#484—32no—
382#483—32no—
383#482—32no—
384#482—32no—
385#481—32no—
386#480—32no—
387#479—32no—
388#479—32no—
389#479C2×D312yes—
390#479C2×D312yes—
391#479C2×D312yes—
392#479C2×D312yes—
393#478—32no—
394#478—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#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#428—31no—
437C2×#107C2×D311yescharacteristic
438C2×#106C2×D311yescharacteristic
439#423—31no—
440C2×C4⋊C8C2×D311yescharacteristic
441#417—31no—
442#417—31no—
443#417—31no—
444#417—31no—
445#416—31no—
446#416—31no—
447C2×#103C2×D311yescharacteristic
448C2×#103C2×D311yescharacteristic
449#408—31no—
450#408—31no—
451#405—31no—
452#405—31no—
453C2×C3×Q8—21no—
454C2×C3×Q8—22no—
455C2×C3×Q8#4114yes—
456C2×C3×Q8C2412yes—
457C22×C3×C4—21no—
458C22×C3×C4—21no—
459C22×C3×C4—21no—
460C22×C3×C4—21no—
461C22×C3×C4C2×D411yescharacteristic
462C22×C3×C4C2×D411yescharacteristic
463C22×C3×C4C2411yescharacteristic
464C2×#67—21no—
465C2×#67—21no—
466C2×#67—21no—
467C2×#67C2×D412yes—
468#239—28no—
469#239—24no—
470#239—24no—
471D3×Q8—28no—
472D3×Q8—24no—
473D3×Q8—24no—
474#235—216no—
475#235—22no—
476#235—22no—
477#235—22no—
478#235—22no—
479#235—22no—
480#235—22no—
481#235—22no—
482#235#4114yes—
483C2×D12—22no—
484C2×D12—22no—
485C2×D12—22no—
486C2×D12—21no—
487C2×D12—21no—
488C2×D12C2×D411yescharacteristic
489C2×D12C2411yescharacteristic
490C2×D12C2411yescharacteristic
491C2×D12C2411yescharacteristic
492C2×C4×D3—22no—
493C2×C4×D3—21no—
494C2×C4×D3—22no—
495C2×C4×D3—21no—
496C2×C4×D3—21no—
497C2×C4×D3—21no—
498C2×C4×D3—22no—
499C2×C4×D3—21no—
500C2×C4×D3—22no—
501C2×C4×D3—22no—
502C2×C4×D3—22no—
503C2×C4×D3C2×D412yes—
504C2×C4×D3C2×D412yes—
505C2×C4×D3C2412yes—
506C2×Dic6—22no—
507C2×Dic6C2×D411yescharacteristic
508C2×Dic6C2411yescharacteristic
509C2×Dic6C2411yescharacteristic
510C2×Dic6C2411yescharacteristic
511C2×C3×C8—22no—
512C2×C3×C8—22no—
513C2×C3×C8C2411yescharacteristic
514C2×C3×C8C2411yescharacteristic
515C2×C3×C8C2411yescharacteristic
516C2×C3×C8C2411yescharacteristic
517C3×C4⋊C4—22no—
518C3×C4⋊C4—22no—
519C3×C4⋊C4—21no—
520C3×C4⋊C4—22no—
521C3×C4⋊C4—22no—
522C3×C4⋊C4—21no—
523C3×C4⋊C4—21no—
524C3×C4⋊C4—22no—
525C3×C4⋊C4—22no—
526C3×C4⋊C4C2412yes—
527C3×C4⋊C4C2412yes—
528C3×C4⋊C4C2412yes—
529C3×C42—22no—
530C3×C42—22no—
531C3×C42C2×D411yescharacteristic
532C3×C42C2×D411yescharacteristic
533C3×C42C2411yescharacteristic
534C3×C42C2411yescharacteristic
535#217—21no—
536#217C2×D412yes—
537#216—24no—
538#216—24no—
539#215—24no—
540#215—24no—
541(C2×D3)⋊C4—22no—
542(C2×D3)⋊C4—22no—
543(C2×D3)⋊C4—22no—
544(C2×D3)⋊C4—21no—
545(C2×D3)⋊C4—21no—
546(C2×D3)⋊C4—21no—
547(C2×D3)⋊C4—21no—
548(C2×D3)⋊C4—21no—
549(C2×D3)⋊C4—21no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—22no—
552(C2×D3)⋊C4—22no—
553(C2×D3)⋊C4—22no—
554(C2×D3)⋊C4—22no—
555(C2×D3)⋊C4C2×D412yes—
556(C2×D3)⋊C4C2×D412yes—
557C4⋊Dic3—21no—
558C4⋊Dic3—21no—
559C4⋊Dic3—22no—
560C4⋊Dic3—22no—
561C4⋊Dic3—22no—
562C4⋊Dic3—22no—
563C4⋊Dic3C2×D411yescharacteristic
564C4⋊Dic3C2×D411yescharacteristic
565C4⋊Dic3C2411yescharacteristic
566C4⋊Dic3C2411yescharacteristic
567Dic3⋊C4—21no—
568Dic3⋊C4—21no—
569Dic3⋊C4—22no—
570Dic3⋊C4—22no—
571Dic3⋊C4—22no—
572Dic3⋊C4—22no—
573Dic3⋊C4C2×D412yes—
574Dic3⋊C4C2×D412yes—
575C4×Dic3—21no—
576C4×Dic3—21no—
577C4×Dic3—21no—
578C4×Dic3—22no—
579C4×Dic3—22no—
580C4×Dic3—22no—
581C4×Dic3—22no—
582C4×Dic3—22no—
583C4×Dic3—22no—
584C4×Dic3C2×D412yes—
585C4×Dic3C2×D412yes—
586C4×Dic3C2412yes—
587#208—22no—
588#208—22no—
589C2×C3⋊C8C2412yes—
590C2×C3⋊C8C2412yes—
591Dic12—22no—
592Dic12—22no—
593D24—22no—
594D24—22no—
595#204—22no—
596#204—22no—
597#204—22no—
598#204—22no—
5992−1+4—64no—
6002−1+4—64no—
601C2×#41—31no—
602C2×#41—32no—
603C2×#41—31no—
604C2×#41—31no—
605C2×#41—31no—
606C2×#41—62no—
607C2×#41—61no—
608C22×Q8—32no—
609C22×Q8—61no—
610C22×Q8C22×D311yescharacteristic
611#137—64no—
612#137—64no—
613#135—64no—
614#135—64no—
615C2×Q16—32no—
616C2×Q16—32no—
617C2×Q16—31no—
618C2×Q16—31no—
619C2×SD16—32no—
620C2×SD16—32no—
621C2×SD16—31no—
622C2×SD16—31no—
623C2×SD16—31no—
624C2×SD16—31no—
625C2×D8—31no—
626C2×D8—31no—
627C2×M16—31no—
628C2×M16—31no—
629C22×C8C22×D311yescharacteristic
630C22×C8C22×D311yescharacteristic
631C4⋊Q8—31no—
632#127—31no—
633#126—62no—
634#126—62no—
635#126—62no—
636#126—62no—
637#125—21no—
638#125—21no—
639#125—62no—
640#125—62no—
641#125C22×D312yes—
642#125C22×D312yes—
643#124—31no—
644#124—31no—
645#123—62no—
646#123—62no—
647#123—62no—
648#123—62no—
649C22⋊Q8—32no—
650C22⋊Q8—32no—
651C22⋊Q8—61no—
652C22⋊Q8—61no—
653#121—32no—
654#121—32no—
655#121—62no—
656#121—62no—
657#121—61no—
658#121—61no—
659#121—62no—
660#121—62no—
661#121—61no—
662#121—61no—
663C4×Q8—21no—
664C4×Q8—21no—
665C4×Q8—31no—
666C4×Q8—31no—
667C4×Q8—32no—
668C4×Q8—32no—
669C4×Q8—32no—
670C4×Q8—32no—
671C4×Q8—32no—
672C4×Q8—31no—
673C4×Q8—31no—
674C4×Q8—62no—
675C4×Q8—62no—
676C4×Q8—62no—
677C4×Q8—62no—
678C4×Q8—61no—
679C4×Q8—61no—
680C4×Q8—61no—
681C4×Q8C22×D312yes—
682C4×Q8C22×D312yes—
683C4×D4—32no—
684C4×D4—32no—
685C4×D4—32no—
686C4×D4—32no—
687C4×D4—32no—
688C4×D4—31no—
689C4×D4—31no—
690C4×D4—31no—
691C4×D4—31no—
692C4×D4—62no—
693C4×D4—62no—
694C4×D4—62no—
695C4×D4—62no—
696C4×D4—62no—
697C4×D4—62no—
698C4×D4—62no—
699C4×D4—62no—
700C4×D4—62no—
701C4×D4—61no—
702C4×D4—62no—
703C4×D4—61no—
704C4×D4—61no—
705C4×D4—61no—
706C4×D4—61no—
707#117—31no—
708#117—32no—
709#117—31no—
710#117—32no—
711#117—62no—
712#117—62no—
713#117—62no—
714#117—62no—
715#117—62no—
716#117—62no—
717#117—62no—
718#117—61no—
719#117—61no—
720#117—61no—
721#117—61no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—32no—
726C2×C4⋊C4—62no—
727C2×C4⋊C4—61no—
728C2×C4⋊C4—61no—
729C2×C4⋊C4—61no—
730C2×C4⋊C4—62no—
731C2×C4⋊C4C22×D311yescharacteristic
732C2×C4⋊C4C22×D311yescharacteristic
733C2×C4⋊C4C22×D311yescharacteristic
734C2×C42—21no—
735C2×C42—32no—
736C2×C42—62no—
737C2×C42—62no—
738C2×C42—61no—
739C2×C42C22×D311yescharacteristic
740#107—32no—
741#107—32no—
742#107C22×D312yes—
743#107C22×D312yes—
744#106—32no—
745#106—32no—
746#106C22×D312yes—
747#106C22×D312yes—
748C4⋊C8—32no—
749C4⋊C8—32no—
750C4⋊C8C22×D311yescharacteristic
751C4⋊C8C22×D311yescharacteristic
752C4⋊C8C22×D311yescharacteristic
753C4⋊C8C22×D311yescharacteristic
754#103—31no—
755#103—31no—
756#103—31no—
757#103—31no—
758#103—32no—
759#103—32no—
760#103—32no—
761#103—32no—
762#103C22×D312yes—
763#103C22×D312yes—
764#103C22×D312yes—
765#103C22×D312yes—
766#102—31no—
767#102—31no—
768#102—31no—
769#102—31no—
770#102—32no—
771#102—32no—
772#102—32no—
773#102—32no—
774C22⋊C8—32no—
775C22⋊C8—32no—
776C22⋊C8—32no—
777C22⋊C8—32no—
778#97—32no—
779#97—32no—
780C4×C8—32no—
781C4×C8—32no—
782C23×C3C22×D411yescharacteristic
783C22×D3—21no—
784C22×D3—21no—
785C22×D3—21no—
786C22×D3C22×D412yes—
787C3×Q8—24no—
788C3×Q8—22no—
789C3×Q8C2×#4114yes—
790C2×C3×C4—24no—
791C2×C3×C4—22no—
792C2×C3×C4—22no—
793C2×C3×C4—22no—
794C2×C3×C4—22no—
795C2×C3×C4—41no—
796C2×C3×C4—41no—
797C2×C3×C4—81no—
798C2×C3×C4—81no—
799C2×C3×C4—81no—
800C2×C3×C4C22×D411yescharacteristic
801C2×C3×C4C22×D411yescharacteristic
802C2×C3×C4C22×D411yescharacteristic
803C2×C3×C4C22×D411yescharacteristic
804C2×C3×C4C22×D411yescharacteristic
805C2×C3×C4C2×#4112yes—
806C2×C3×C4C2×#4112yes—
807C2×C3×C4C2511yescharacteristic
808#67—24no—
809#67—24no—
810#67—42no—
811#67—42no—
812C2×Dic3—21no—
813C2×Dic3—21no—
814C2×Dic3—21no—
815C2×Dic3—21no—
816C2×Dic3—21no—
817C2×Dic3C22×D412yes—
818C2×Dic3C22×D412yes—
819C2×Dic3C22×D412yes—
820D12—28no—
821D12—22no—
822D12—21no—
823D12—21no—
824D12—21no—
825D12—21no—
826D12—21no—
827D12—81no—
828D12—81no—
829D12—82no—
830D12—82no—
831D12C2×#4112yes—
832C4×D3—28no—
833C4×D3—28no—
834C4×D3—24no—
835C4×D3—22no—
836C4×D3—22no—
837C4×D3—42no—
838C4×D3—42no—
839C4×D3—42no—
840C4×D3—42no—
841C4×D3—42no—
842C4×D3—82no—
843C4×D3—82no—
844C4×D3—82no—
845C4×D3—81no—
846C4×D3—82no—
847Dic6—28no—
848Dic6—22no—
849Dic6—21no—
850Dic6—21no—
851Dic6—21no—
852Dic6—21no—
853Dic6—21no—
854Dic6C2×#4112yes—
855C3×C8—21no—
856C3×C8—21no—
857C3×C8—21no—
858C3×C8—21no—
859C3⋊C8—22no—
860C3⋊C8—22no—
861#41—34no—
862#41—616no—
863#41—64no—
864#41—68no—
865#41—64no—
866#41—62no—
867#41—62no—
868#41—62no—
869#41—62no—
870#41—62no—
871#41—62no—
872#41—62no—
873C2×Q8—21no—
874C2×Q8—22no—
875C2×Q8—31no—
876C2×Q8—31no—
877C2×Q8—31no—
878C2×Q8—31no—
879C2×Q8—62no—
880C2×Q8—64no—
881C2×Q8—68no—
882C2×Q8—64no—
883C2×Q8#23914yes—
884C2×Q8C23×D312yes—
885C2×D4—32no—
886C2×D4—31no—
887C2×D4—31no—
888C2×D4—31no—
889C2×D4—31no—
890C2×D4—62no—
891C2×D4—62no—
892C2×D4—62no—
893C2×D4—61no—
894C2×D4—61no—
895C2×D4—61no—
896C2×D4—61no—
897C2×D4—61no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—32no—
903C22×C4—32no—
904C22×C4—32no—
905C22×C4—62no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—62no—
910C22×C4—62no—
911C22×C4—61no—
912C22×C4—61no—
913C22×C4—61no—
914C22×C4—61no—
915C22×C4—61no—
916C22×C4D3×D411yescharacteristic
917C22×C4D3×D411yescharacteristic
918C22×C4C23×D311yescharacteristic
919Q16—62no—
920Q16—62no—
921Q16—64no—
922Q16—64no—
923SD16—62no—
924SD16—62no—
925SD16—62no—
926SD16—62no—
927SD16—64no—
928SD16—64no—
929D8—62no—
930D8—62no—
931M16—62no—
932M16—62no—
933C2×C8—22no—
934C2×C8—22no—
935C2×C8—32no—
936C2×C8—32no—
937C2×C8C23×D311yescharacteristic
938C2×C8C23×D311yescharacteristic
939C2×C8C23×D311yescharacteristic
940C2×C8C23×D311yescharacteristic
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—31no—
951C4⋊C4—31no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—31no—
955C4⋊C4—31no—
956C4⋊C4—62no—
957C4⋊C4—62no—
958C4⋊C4—62no—
959C4⋊C4—62no—
960C4⋊C4—62no—
961C4⋊C4—62no—
962C4⋊C4—62no—
963C4⋊C4—62no—
964C4⋊C4—61no—
965C4⋊C4—61no—
966C4⋊C4—61no—
967C4⋊C4—61no—
968C4⋊C4C23×D312yes—
969C4⋊C4C23×D312yes—
970C4⋊C4C23×D312yes—
971C22⋊C4—32no—
972C22⋊C4—32no—
973C22⋊C4—32no—
974C22⋊C4—62no—
975C22⋊C4—62no—
976C22⋊C4—62no—
977C22⋊C4—62no—
978C22⋊C4—62no—
979C22⋊C4—62no—
980C22⋊C4—62no—
981C22⋊C4—62no—
982C22⋊C4—61no—
983C22⋊C4—61no—
984C22⋊C4—61no—
985C22⋊C4—61no—
986C22⋊C4—61no—
987C22⋊C4—61no—
988C22⋊C4—61no—
989C42—22no—
990C42—22no—
991C42—32no—
992C42—32no—
993C42—32no—
994C42—62no—
995C42—62no—
996C42—62no—
997C42—62no—
998C42—62no—
999C42—62no—
1000C42—61no—
1001C42—61no—
1002C42—61no—
1003C42D3×D411yescharacteristic
1004C42D3×D411yescharacteristic
1005C42C23×D311yescharacteristic
1006C42C23×D311yescharacteristic
1007C22×C3—21no—
1008C22×C3—21no—
1009C22×C3#52512yes—
1010C22×C3C23×D411yescharacteristic
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—22no—
1015C2×D3—41no—
1016C2×D3—41no—
1017C2×D3—41no—
1018C2×D3—41no—
1019C2×D3—41no—
1020C2×D3—41no—
1021C2×D3—41no—
1022C2×D3—41no—
1023C3×C4—21no—
1024C3×C4—21no—
1025C3×C4—21no—
1026C3×C4—21no—
1027C3×C4—24no—
1028C3×C4—42no—
1029C3×C4—42no—
1030C3×C4—42no—
1031C3×C4#52512yes—
1032C3×C4C22×#4111yescharacteristic
1033C3×C4C22×#4111yescharacteristic
1034Dic3—22no—
1035Dic3—22no—
1036Dic3—22no—
1037Dic3—22no—
1038Dic3—41no—
1039Dic3—41no—
1040Dic3—41no—
1041Dic3—41no—
1042C23—32no—
1043C23—61no—
1044C23—61no—
1045C23—61no—
1046C23C2×D3×D411yescharacteristic
1047Q8—22no—
1048Q8—24no—
1049Q8—32no—
1050Q8—68no—
1051Q8—61no—
1052Q8—62no—
1053Q8—61no—
1054Q8—61no—
1055Q8—61no—
1056Q8—61no—
1057Q8C2×#23914yes—
1058D4—32no—
1059D4—68no—
1060D4—64no—
1061D4—64no—
1062D4—61no—
1063D4—61no—
1064D4—61no—
1065D4—61no—
1066D4—61no—
1067D4—62no—
1068D4—122no—
1069D4—122no—
1070D4—241no—
1071D4—241no—
1072D4—242no—
1073D4—242no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—32no—
1080C2×C4—32no—
1081C2×C4—32no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—68no—
1085C2×C4—68no—
1086C2×C4—61no—
1087C2×C4—62no—
1088C2×C4—62no—
1089C2×C4—64no—
1090C2×C4—61no—
1091C2×C4—61no—
1092C2×C4—61no—
1093C2×C4—61no—
1094C2×C4—81no—
1095C2×C4—81no—
1096C2×C4—81no—
1097C2×C4—122no—
1098C2×C4—122no—
1099C2×C4—122no—
1100C2×C4—122no—
1101C2×C4—122no—
1102C2×C4—241no—
1103C2×C4—242no—
1104C2×C4—242no—
1105C2×C4—242no—
1106C2×C4—242no—
1107C2×C4C2×D3×D411yescharacteristic
1108C2×C4C2×D3×D411yescharacteristic
1109C2×C4C2×D3×D411yescharacteristic
1110C2×C4C2×D3×D411yescharacteristic
1111C2×C4C2×D3×D411yescharacteristic
1112C2×C4C2×#23912yes—
1113C2×C4D3×#4112yes—
1114C2×C4C24×D311yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—62no—
1120C8—62no—
1121C2×C3—22no—
1122C2×C3C2×#52511yescharacteristic
1123C2×C3#358411yescharacteristic
1124C2×C3#358611yescharacteristic
1125D3—42no—
1126D3—42no—
1127D3—81no—
1128D3—81no—
1129C22—21no—
1130C22—21no—
1131C22—62no—
1132C22—62no—
1133C22—62no—
1134C22—62no—
1135C22—121no—
1136C22—121no—
1137C22—121no—
1138C22—121no—
1139C22—121no—
1140C22—121no—
1141C22—121no—
1142C22—121no—
1143C22#562712yes—
1144C22C22×D3×D411yescharacteristic
1145C4—21no—
1146C4—21no—
1147C4—21no—
1148C4—21no—
1149C4—24no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—62no—
1154C4—62no—
1155C4—62no—
1156C4—62no—
1157C4—121no—
1158C4—121no—
1159C4—121no—
1160C4—121no—
1161C4#562712yes—
1162C4C22×#23911yescharacteristic
1163C4C2×D3×#4111yescharacteristic
1164C3#6059811yescharacteristic, complemented, Sylow
1165C2—22no—
1166C2—122no—
1167C2—122no—
1168C2—241no—
1169C2—241no—
1170C2C2×#562711yescharacteristic
1171C2#8718711yescharacteristic
1172C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#479C2
socleC22×C3C23×D4
hypercenterC2×#479D3
hypocenterC3#60598
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. #86087C2semidirect
2. C4×#1007C2semidirect
3. C2×C3×#479C2semidirect
4. #83017C2semidirect
5. #82441C2semidirect
6. #81211C2semidirect
7. #81210C2semidirect
8. #81209C2semidirect
9. #81208C2semidirect
10. #81207C2semidirect
11. #81206C2semidirect
12. #81205C2semidirect
13. #81204C2semidirect
14. #79141C2semidirect
15. #79136C2semidirect
16. #79112C2semidirect
17. #79106C2semidirect
18. #79021C2semidirect
19. #79000C2semidirect
20. #78795C2semidirect
21. #78795C2semidirect
22. #78774C2semidirect
23. #78774C2semidirect
149. C2×#479D3semidirect
1164. C3#60598semidirect

Maximal subgroups

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

subgroupindex
#860872
C4×#10072
C2×C3×#4792
#830172
#824412
#812112
#812102
#812092
#812082
#812072
#812062
#812052
#812042
#791412
#791362
#791122
#791062
#790212
#790002
#787952
#787742
#605983