Finite Group Databasebeta

← #11664576

Subgroups — #11664576

Order 768.

1998 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86587C211yesmaximal, characteristic, complemented
2#86340C211yesmaximal, characteristic
3C3×#3137C211yesmaximal, characteristic, complemented
4#83471C211yesmaximal, characteristic, complemented
5#83401C211yesmaximal, characteristic, complemented
6#81738C212yesmaximal, complemented
7D3×#491C212yesmaximal, complemented
8#81681C212yesmaximal, complemented
9#81679C212yesmaximal, complemented
10#81641C212yesmaximal, complemented
11#81639C212yesmaximal, complemented
12#81600C212yesmaximal, complemented
13#81599C212yesmaximal, complemented
14#78957C211yesmaximal, characteristic, complemented
15#78953C211yesmaximal, characteristic, complemented
16#78883C211yesmaximal, characteristic, complemented
17#78879C211yesmaximal, characteristic, complemented
18#78832C211yesmaximal, characteristic, complemented
19#78826C211yesmaximal, characteristic, complemented
20#78790C211yesmaximal, characteristic, complemented
21C2×#4797C211yesmaximal, characteristic, complemented
22#78575C211yesmaximal, characteristic, complemented
23#78550C211yesmaximal, characteristic, complemented
24#60627—31nomaximal, Sylow
25C2×#1010C2211yescharacteristic
26C2×#1007C2211yescharacteristic
27C3×#544C2211yescharacteristic
28C3×#536C2211yescharacteristic
29#5832C2211yescharacteristic
30C2×#944C2211yescharacteristic
31C2×#907C2211yescharacteristic
32C2×#901C2211yescharacteristic
33#5730—21no—
34#5729C2212yes—
35#5728C2212yes—
36#5724C2212yes—
37D3×C4⋊Q8C2212yes—
38#5721—21no—
39#5690—21no—
40#5689C2212yes—
41D3×#125C2212yes—
42#5685—21no—
43#5675C2212yes—
44#5668C2212yes—
45#5655—22no—
46#5655—22no—
47#5636—22no—
48#5635—22no—
49#5632—21no—
50#5632—21no—
51#5631—21no—
52#5631—21no—
53#5526C2211yescharacteristic
54#5523C2211yescharacteristic
55#5522C2211yescharacteristic
56#5519C2211yescharacteristic
57#5517C2211yescharacteristic
58#5504C2211yescharacteristic
59C2×#890C2211yescharacteristic
60C3×#491C2212yes—
61C3×#489C2212yes—
62C3×#488C2212yes—
63C3×#487C2212yes—
64C3×#419C2211yescharacteristic
65C3×#417C2211yescharacteristic
66C3×#416C2211yescharacteristic
67C2×C3×#103C2211yescharacteristic
68C3×#405C2211yescharacteristic
69#5233C2211yescharacteristic
70#5232C2211yescharacteristic
71#5225C2211yescharacteristic
72C2×#835C2211yescharacteristic
73#5133C2211yescharacteristic
74#5120C2211yescharacteristic
75Dic3×M16C2211yescharacteristic
76#5113C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×#815C2211yescharacteristic
79#5093C2212yes—
80#5089C2212yes—
81#5082C2212yes—
82#5079C2212yes—
83#5069C2212yes—
84#5068C2212yes—
85#5056C2212yes—
86#5055C2212yes—
87#5004C2211yescharacteristic
88#5002C2211yescharacteristic
89#4997C2211yescharacteristic
90C2×#810C2211yescharacteristic
91#4966C2211yescharacteristic
92#4804C2212yes—
93#4804C2212yes—
94#4803C2212yes—
95#4803C2212yes—
96#4802C2212yes—
97#4802C2212yes—
98#4802C2212yes—
99#4802C2212yes—
100D3×#103C2212yes—
101D3×#103C2212yes—
102D3×#103C2212yes—
103D3×#103C2212yes—
104#4800C2212yes—
105#4797C2212yes—
106#4797C2212yes—
107#4797C2212yes—
108#4797C2212yes—
109#4797C2211yescharacteristic
110#4797C2212yes—
111#4797C2212yes—
112#4797C2212yes—
113#4797C2211yescharacteristic
114#4794C2211yescharacteristic
115#4794C2211yescharacteristic
116#4792C2212yes—
117#4792C2212yes—
118#4772C2212yes—
119#4772C2212yes—
120#4771C2212yes—
121#4771C2212yes—
122#4768C2212yes—
123#4765C2211yescharacteristic
124#4765C2211yescharacteristic
125#4764C2211yescharacteristic
126#4764C2212yes—
127#4764C2211yescharacteristic
128#4714C2212yes—
129#4708C2212yes—
130D3×#97C2212yes—
131#4703C2212yes—
132#4697C2212yes—
133#4689C2212yes—
134C4×ΓL(1,𝔽25)C2212yes—
135#4681C2212yes—
136#3504—31no—
137#3499—31no—
138#3142—32no—
139#3142—31no—
140#3139—32no—
141#3139—31no—
142#3137—32no—
143#3137—32no—
144#3137—32no—
145#3137—32no—
146#3137—31no—
147#3137—31no—
148#3137—31no—
149#3137D311yescharacteristic, complemented
150#3135—32no—
151#3135—31no—
152C2×#491—32no—
153C2×#491—31no—
154#2898—31no—
155#2898—31no—
156#2898—31no—
157#2898—31no—
158#2875—31no—
159C2×C3×#41C2311yescharacteristic
160C22×C3×Q8C2311yescharacteristic
161#1010—24no—
162#1010—24no—
163#1007—24no—
164#1007—24no—
165C2×#239—21no—
166C2×#239C2312yes—
167C2×D3×Q8—21no—
168C2×D3×Q8C2312yes—
169C2×D3×Q8C2312yes—
170C2×#237—22no—
171C2×#237C2312yes—
172C2×#235—22no—
173C2×#235—21no—
174C2×#235C2311yescharacteristic
175C2×#235C2311yescharacteristic
176C22×Dic6—21no—
177C22×Dic6C2311yescharacteristic
178C2×C3×M16C2311yescharacteristic
179C22×C3×C8C2311yescharacteristic
180C3×C4⋊Q8—21no—
181C3×C4⋊Q8C2312yes—
182C3×C4⋊Q8C2312yes—
183C3×#125—21no—
184C3×#125C2312yes—
185C3×#124C2312yes—
186C3×#123—22no—
187C3×C22⋊Q8—21no—
188C3×C22⋊Q8—21no—
189C3×C22⋊Q8—22no—
190C3×#117C2311yescharacteristic
191C3×#117C2311yescharacteristic
192C2×C3×C4⋊C4C2311yescharacteristic
193#947C2311yescharacteristic
194#946—22no—
195#946—22no—
196Q8×Dic3—22no—
197#944—22no—
198#944—21no—
199#944—21no—
200#944C2312yes—
201#944C2312yes—
202#944C2311yescharacteristic
203#940C2311yescharacteristic
204#939—21no—
205#939—21no—
206#936C2311yescharacteristic
207C4×#67—22no—
208C4×#67—21no—
209C4×#67—21no—
210#926C2311yescharacteristic
211C2×C4⋊Dic3—21no—
212C2×C4⋊Dic3C2311yescharacteristic
213C2×Dic3⋊C4—21no—
214C2×Dic3⋊C4—21no—
215C2×Dic3⋊C4—21no—
216C2×C4×Dic3C2311yescharacteristic
217C2×#208C2311yescharacteristic
218C22×C3⋊C8C2311yescharacteristic
219#907—24no—
220#901—24no—
221C2×ΓL(1,𝔽25)C2312yes—
222C2×ΓL(1,𝔽25)C2312yes—
223C2×D3×C8C2312yes—
224C2×D3×C8C2312yes—
225#897—22no—
226#897—21no—
227#897—21no—
228#897—22no—
229#896—22no—
230#896—22no—
231#896—22no—
232#896—22no—
233#894—22no—
234#894—22no—
235#893—21no—
236#893D411yescharacteristic
237#893D411yescharacteristic
238#892C2312yes—
239#892C2312yes—
240D3×C4⋊C4—22no—
241D3×C4⋊C4—22no—
242D3×C4⋊C4—22no—
243D3×C4⋊C4—22no—
244D3×C4⋊C4C2312yes—
245D3×C4⋊C4C2312yes—
246#890—21no—
247#890—21no—
248#890—21no—
249#890C2311yescharacteristic
250#890C2312yes—
251#890C2312yes—
252#890C2311yescharacteristic
253#889—22no—
254#889—22no—
255#889—22no—
256#889—22no—
257#888—21no—
258#888—22no—
259#888—22no—
260#888—22no—
261#888C2311yescharacteristic
262#888C2311yescharacteristic
263#887—21no—
264#887—22no—
265#887D411yescharacteristic
266#887D411yescharacteristic
267#886—22no—
268#884—22no—
269#884—22no—
270#883—22no—
271#883—22no—
272#67⋊C4—22no—
273#67⋊C4—22no—
274#67⋊C4—22no—
275#67⋊C4D412yes—
276#67⋊C4D412yes—
277#878—21no—
278#878—21no—
279#878—22no—
280#878—22no—
281#878—22no—
282#875C2312yes—
283C4×D12—21no—
284#872C2312yes—
285C42×D3C2312yes—
286#870C2312yes—
287#869C2312yes—
288#869C2312yes—
289C4×Dic6—21no—
290C4×Dic6—21no—
291C4×Dic6—21no—
292C3×#103C2312yes—
293C3×#103C2312yes—
294C3×#103C2311yescharacteristic
295C3×#103C2311yescharacteristic
296C3×#103C2312yes—
297C3×#103C2312yes—
298C3×#103C2312yes—
299C3×#102C2311yescharacteristic
300C3×#102C2311yescharacteristic
301C3×#102C2312yes—
302C3×#97C2312yes—
303C3×C4×C8C2312yes—
304#835C2312yes—
305#835C2312yes—
306#835C2312yes—
307#835C2312yes—
308#835C2312yes—
309#835C2311yescharacteristic
310#835C2311yescharacteristic
311#832C2312yes—
312#832C2311yescharacteristic
313#832C2311yescharacteristic
314#821C2312yes—
315#821C2311yescharacteristic
316#821C2311yescharacteristic
317#816C2312yes—
318#816C2312yes—
319#816C2312yes—
320#816C2311yescharacteristic
321#816C2312yes—
322#816C2311yescharacteristic
323#816C2312yes—
324#815C2311yescharacteristic
325#815C2312yes—
326#815C2311yescharacteristic
327#815C2311yescharacteristic
328#815C2311yescharacteristic
329C8×Dic3C2312yes—
330#810C2312yes—
331#810C2312yes—
332#810C2312yes—
333#810C2311yescharacteristic
334#810C2311yescharacteristic
335#810C2312yes—
336#810C2312yes—
337#809C2312yes—
338#809C2311yescharacteristic
339#809C2311yescharacteristic
340#803C2312yes—
341C4×C3⋊C8C2312yes—
342C2×2−1+4—31no—
343C2×2−1+4—31no—
344C2×#131—31no—
345C2×#131—31no—
346#557—61no—
347#557—61no—
348#554—62no—
349#554—62no—
350#554—61no—
351#554—61no—
352D4×Q8—61no—
353D4×Q8—61no—
354#547—61no—
355#547—61no—
356#547—62no—
357#547—62no—
358#544—32no—
359#544—32no—
360#544—31no—
361#544C2×D311yescharacteristic
362#536—32no—
363#536—32no—
364#536—31no—
365#536C2×D311yescharacteristic
366#533—32no—
367#533—31no—
368#532—31no—
369#532—32no—
370C2×C4⋊Q8—31no—
371C2×C4⋊Q8—32no—
372C2×#125—32no—
373C2×#125—31no—
374#520—31no—
375#520—31no—
376C4×#41—31no—
377#491—32no—
378#491—32no—
379#491—31no—
380#491—32no—
381#491—32no—
382#491—32no—
383#491—32no—
384#491—32no—
385#491—32no—
386#491—32no—
387#491—31no—
388#491—32no—
389#491C2×D312yes—
390#490—31no—
391#490—32no—
392#490—31no—
393#489—32no—
394#489—32no—
395#489—31no—
396#489—31no—
397#489—31no—
398#489—31no—
399#489—32no—
400#489C2×D312yes—
401#488—32no—
402#488—32no—
403#488—32no—
404#488—32no—
405#488—32no—
406#488C2×D312yes—
407#487—32no—
408#487—32no—
409#487—32no—
410#487—32no—
411#487—32no—
412#487C2×D312yes—
413#419—31no—
414#419—31no—
415#419—31no—
416#419—32no—
417#419—32no—
418#419—32no—
419#419—32no—
420#419C2×D311yescharacteristic
421#417—31no—
422#417—31no—
423#417—31no—
424#417—32no—
425#417—32no—
426#417—32no—
427#417—32no—
428#417C2×D311yescharacteristic
429#416—31no—
430#416—31no—
431#416—31no—
432#416—32no—
433#416—32no—
434#416—32no—
435#416—32no—
436#416C2×D311yescharacteristic
437C2×#103—31no—
438C2×#103—31no—
439C2×#103—31no—
440C2×#103—32no—
441C2×#103—32no—
442C2×#103—32no—
443C2×#103—32no—
444C2×#103C2×D311yescharacteristic
445#405—31no—
446#405—32no—
447#405—32no—
448#405C2×D311yescharacteristic
449C4×M16—31no—
450C4×M16—32no—
451C2×#97—31no—
452C2×#97—32no—
453C3×#41—22no—
454C3×#41—22no—
455C2×C3×Q8—21no—
456C2×C3×Q8—22no—
457C2×C3×Q8—22no—
458C2×C3×Q8—22no—
459C2×C3×Q8C2412yes—
460C2×C3×Q8C2411yescharacteristic
461C2×C3×D4—21no—
462C2×C3×D4C2411yescharacteristic
463C22×C3×C4—21no—
464C22×C3×C4—21no—
465C22×C3×C4—21no—
466C22×C3×C4C2411yescharacteristic
467C2×#67—21no—
468C2×#67—22no—
469C2×#67—21no—
470C2×#67—21no—
471C2×#67C2×D412yes—
472C22×Dic3—21no—
473C22×Dic3—21no—
474C22×Dic3—22no—
475C22×Dic3C2×D411yescharacteristic
476C22×Dic3C2×D411yescharacteristic
477#239—24no—
478#239—24no—
479#239—44no—
480D3×Q8—24no—
481D3×Q8—24no—
482D3×Q8—24no—
483D3×Q8—24no—
484D3×Q8—44no—
485#237—24no—
486#237—24no—
487#237—48no—
488#235—22no—
489#235—22no—
490#235—48no—
491#235—44no—
492#235#4114yes—
493#235#4114yes—
494C2×D12—22no—
495C2×D12C2×D411yescharacteristic
496C2×D12C2411yescharacteristic
497C2×C4×D3—22no—
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×Dic6—22no—
508C2×Dic6—21no—
509C2×Dic6—22no—
510C2×Dic6—22no—
511C2×Dic6—22no—
512C2×Dic6—21no—
513C2×Dic6—21no—
514C2×Dic6—44no—
515C2×Dic6C2×D411yescharacteristic
516C2×Dic6C2411yescharacteristic
517C2×Dic6C2412yes—
518C3×M16—22no—
519C2×C3×C8—22no—
520C2×C3×C8C2412yes—
521C2×C3×C8C2411yescharacteristic
522C2×C3×C8C2411yescharacteristic
523C3×C4⋊C4—22no—
524C3×C4⋊C4—21no—
525C3×C4⋊C4—22no—
526C3×C4⋊C4—22no—
527C3×C4⋊C4—22no—
528C3×C4⋊C4—22no—
529C3×C4⋊C4C2×D411yescharacteristic
530C3×C4⋊C4C2×D411yescharacteristic
531C3×C4⋊C4C2411yescharacteristic
532C3×C4⋊C4C2411yescharacteristic
533C3×C4⋊C4C2412yes—
534C3×C22⋊C4—21no—
535C3×C22⋊C4—22no—
536C3×C22⋊C4—22no—
537C3×C22⋊C4C2×D412yes—
538C3×C42—21no—
539C3×C42C2412yes—
540#217—21no—
541#217—21no—
542#217—21no—
543(C2×D3)⋊C4—22no—
544(C2×D3)⋊C4—22no—
545(C2×D3)⋊C4—22no—
546(C2×D3)⋊C4—22no—
547(C2×D3)⋊C4—21no—
548(C2×D3)⋊C4—21no—
549(C2×D3)⋊C4C2×D412yes—
550(C2×D3)⋊C4C2×D412yes—
551C4⋊Dic3—21no—
552C4⋊Dic3—22no—
553C4⋊Dic3—22no—
554C4⋊Dic3—22no—
555C4⋊Dic3—21no—
556C4⋊Dic3—21no—
557C4⋊Dic3—22no—
558C4⋊Dic3—22no—
559C4⋊Dic3C2411yescharacteristic
560C4⋊Dic3C2412yes—
561C4⋊Dic3C2411yescharacteristic
562Dic3⋊C4—22no—
563Dic3⋊C4—22no—
564Dic3⋊C4—21no—
565Dic3⋊C4—21no—
566Dic3⋊C4—21no—
567Dic3⋊C4—21no—
568Dic3⋊C4—22no—
569Dic3⋊C4—22no—
570Dic3⋊C4—22no—
571Dic3⋊C4—22no—
572Dic3⋊C4—22no—
573Dic3⋊C4—22no—
574Dic3⋊C4—22no—
575Dic3⋊C4—21no—
576Dic3⋊C4—21no—
577Dic3⋊C4—22no—
578Dic3⋊C4C2×D412yes—
579Dic3⋊C4C2×D412yes—
580C4×Dic3—21no—
581C4×Dic3—22no—
582C4×Dic3—22no—
583C4×Dic3C2×D411yescharacteristic
584C4×Dic3C2×D411yescharacteristic
585C4×Dic3C2×D412yes—
586C4×Dic3C2×D412yes—
587C4×Dic3C2411yescharacteristic
588C4×Dic3C2411yescharacteristic
589#208—22no—
590C2×C3⋊C8—22no—
591C2×C3⋊C8C2411yescharacteristic
592C2×C3⋊C8C2412yes—
593C2×C3⋊C8C2411yescharacteristic
594ΓL(1,𝔽25)—24no—
595ΓL(1,𝔽25)—24no—
596D3×C8—24no—
597D3×C8—24no—
5982−1+4—64no—
5992−1+4—64no—
6002−1+4—64no—
6012−1+4—64no—
602C2×#41—31no—
603C2×#41—32no—
604C2×#41—32no—
605C2×#41—31no—
606C2×#41—62no—
607C2×#41—61no—
608C2×#41—62no—
609C2×#41—61no—
610C2×#41C22×D311yescharacteristic
611C22×Q8—32no—
612C22×Q8—32no—
613C22×Q8—31no—
614C22×Q8—61no—
615C22×Q8—61no—
616C22×Q8C22×D311yescharacteristic
617#131—64no—
618#131—64no—
619C2×M16—31no—
620C2×M16—32no—
621C2×M16—32no—
622C2×M16C22×D311yescharacteristic
623C22×C8—31no—
624C22×C8—32no—
625C22×C8—32no—
626C22×C8C22×D311yescharacteristic
627C4⋊Q8—21no—
628C4⋊Q8—31no—
629C4⋊Q8—31no—
630C4⋊Q8—31no—
631C4⋊Q8—32no—
632C4⋊Q8—32no—
633C4⋊Q8—32no—
634C4⋊Q8—32no—
635C4⋊Q8—62no—
636C4⋊Q8—62no—
637C4⋊Q8—61no—
638C4⋊Q8—61no—
639C4⋊Q8—62no—
640C4⋊Q8—62no—
641C4⋊Q8—61no—
642C4⋊Q8C22×D312yes—
643C4⋊Q8C22×D312yes—
644#127—31no—
645#125—21no—
646#125—31no—
647#125—32no—
648#125—32no—
649#125—31no—
650#125—32no—
651#125—62no—
652#125—62no—
653#125—61no—
654#125—61no—
655#125—62no—
656#125—62no—
657#125—61no—
658#125C22×D312yes—
659#124—31no—
660#124—31no—
661#124—32no—
662#124C22×D312yes—
663#123—22no—
664#123—62no—
665#123—62no—
666#123—62no—
667#123—62no—
668#123—62no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—22no—
672C22⋊Q8—62no—
673C22⋊Q8—62no—
674C22⋊Q8—61no—
675C22⋊Q8—61no—
676C22⋊Q8—62no—
677C22⋊Q8—62no—
678C22⋊Q8—62no—
679C22⋊Q8—62no—
680C22⋊Q8—62no—
681C22⋊Q8—62no—
682C22⋊Q8—62no—
683C22⋊Q8—62no—
684C22⋊Q8—61no—
685C22⋊Q8—61no—
686C22⋊Q8—62no—
687#121—62no—
688#121—62no—
689#121—61no—
690#121—61no—
691C4×Q8—31no—
692C4×Q8—31no—
693C4×Q8—61no—
694C4×Q8—61no—
695C4×Q8—61no—
696C4×Q8—62no—
697C4×Q8—62no—
698C4×Q8—61no—
699C4×D4—31no—
700C4×D4—31no—
701C4×D4—32no—
702C4×D4—32no—
703C4×D4—61no—
704C4×D4—62no—
705C4×D4—62no—
706C4×D4—61no—
707C4×D4—61no—
708C4×D4—62no—
709C4×D4—61no—
710C4×D4—62no—
711#117—32no—
712#117—31no—
713#117—32no—
714#117—32no—
715#117C22×D311yescharacteristic
716#117C22×D311yescharacteristic
717C2×C4⋊C4—31no—
718C2×C4⋊C4—32no—
719C2×C4⋊C4—32no—
720C2×C4⋊C4—62no—
721C2×C4⋊C4—62no—
722C2×C4⋊C4—62no—
723C2×C4⋊C4—62no—
724C2×C4⋊C4—61no—
725C2×C4⋊C4—61no—
726C2×C4⋊C4—61no—
727C2×C4⋊C4—61no—
728C2×C4⋊C4C22×D311yescharacteristic
729C2×C42—31no—
730C2×C42—32no—
731#103—31no—
732#103—32no—
733#103—32no—
734#103—32no—
735#103—32no—
736#103—31no—
737#103—32no—
738#103—31no—
739#103—32no—
740#103—32no—
741#103—32no—
742#103—32no—
743#103—32no—
744#103—31no—
745#103—31no—
746#103—32no—
747#103—32no—
748#103—32no—
749#103—32no—
750#103—31no—
751#103—32no—
752#103C22×D311yescharacteristic
753#103C22×D312yes—
754#103C22×D312yes—
755#103C22×D312yes—
756#103C22×D312yes—
757#103C22×D312yes—
758#103C22×D311yescharacteristic
759#102—31no—
760#102—32no—
761#102—31no—
762#102—31no—
763#102—32no—
764#102—31no—
765#102—31no—
766#102—31no—
767#102—32no—
768#102C22×D311yescharacteristic
769#102C22×D312yes—
770#102C22×D311yescharacteristic
771#97—31no—
772#97—32no—
773#97—31no—
774#97—31no—
775#97—31no—
776#97—32no—
777#97C22×D312yes—
778C4×C8—32no—
779C4×C8—32no—
780C4×C8C22×D312yes—
781C23×C3—21no—
782C23×C3C22×D411yescharacteristic
783C22×D3—21no—
784C22×D3C22×D412yes—
785C3×Q8—21no—
786C3×Q8—21no—
787C3×Q8—22no—
788C3×Q8—22no—
789C3×Q8—42no—
790C3×Q8—82no—
791C3×D4—21no—
792C3×D4—21no—
793C3×D4—42no—
794C2×C3×C4—21no—
795C2×C3×C4—22no—
796C2×C3×C4—21no—
797C2×C3×C4—22no—
798C2×C3×C4—21no—
799C2×C3×C4—42no—
800C2×C3×C4—42no—
801C2×C3×C4—81no—
802C2×C3×C4C22×D412yes—
803C2×C3×C4C22×D412yes—
804C2×C3×C4C22×D411yescharacteristic
805C2×C3×C4C2×#4112yes—
806C2×C3×C4C2×#4112yes—
807C2×C3×C4C2511yescharacteristic
808#67—42no—
809#67—42no—
810#67—42no—
811#67—44no—
812#67#12418yes—
813C2×Dic3—21no—
814C2×Dic3—21no—
815C2×Dic3—22no—
816C2×Dic3—22no—
817C2×Dic3—21no—
818C2×Dic3—41no—
819C2×Dic3—41no—
820C2×Dic3—42no—
821C2×Dic3—44no—
822C2×Dic3—81no—
823C2×Dic3C22×D411yescharacteristic
824C2×Dic3C22×D411yescharacteristic
825C2×Dic3C22×D411yescharacteristic
826C2×Dic3C22×D411yescharacteristic
827C2×Dic3C22×D412yes—
828D12—21no—
829D12—21no—
830D12—44no—
831D12#12414yes—
832C4×D3—42no—
833C4×D3—42no—
834C4×D3—44no—
835C4×D3—44no—
836C4×D3—42no—
837C4×D3—44no—
838C4×D3—82no—
839C4×D3—82no—
840C4×D3C2×#4114yes—
841C4×D3C2×#4114yes—
842Dic6—22no—
843Dic6—22no—
844Dic6—21no—
845Dic6—21no—
846Dic6—42no—
847Dic6—44no—
848Dic6—44no—
849Dic6—81no—
850Dic6—81no—
851Dic6—82no—
852Dic6#12414yes—
853C3×C8—21no—
854C3×C8—22no—
855C3×C8—21no—
856C3⋊C8—21no—
857C3⋊C8—22no—
858C3⋊C8—21no—
859#41—22no—
860#41—22no—
861#41—34no—
862#41—34no—
863#41—64no—
864#41—64no—
865#41—64no—
866#41—64no—
867#41—62no—
868#41—62no—
869#41—128no—
870#41—124no—
871#41—128no—
872#41—124no—
873C2×Q8—21no—
874C2×Q8—22no—
875C2×Q8—22no—
876C2×Q8—22no—
877C2×Q8—31no—
878C2×Q8—31no—
879C2×Q8—32no—
880C2×Q8—62no—
881C2×Q8—62no—
882C2×Q8—61no—
883C2×Q8—61no—
884C2×Q8—64no—
885C2×Q8—64no—
886C2×Q8—64no—
887C2×Q8—64no—
888C2×Q8—61no—
889C2×Q8—62no—
890C2×Q8—62no—
891C2×Q8—62no—
892C2×Q8—124no—
893C2×Q8—124no—
894C2×Q8C23×D311yescharacteristic
895C2×Q8C23×D312yes—
896C2×D4—21no—
897C2×D4—32no—
898C2×D4—31no—
899C2×D4—31no—
900C2×D4—62no—
901C2×D4—61no—
902C2×D4—61no—
903C2×D4—62no—
904C2×D4—61no—
905C2×D4C23×D311yescharacteristic
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—32no—
910C22×C4—31no—
911C22×C4—31no—
912C22×C4—32no—
913C22×C4—32no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—61no—
921C22×C4—61no—
922C22×C4—61no—
923C22×C4C23×D311yescharacteristic
924M16—22no—
925M16—64no—
926M16—64no—
927M16—62no—
928C2×C8—22no—
929C2×C8—32no—
930C2×C8—31no—
931C2×C8—31no—
932C2×C8—64no—
933C2×C8—64no—
934C2×C8—62no—
935C2×C8C23×D312yes—
936C2×C8C23×D311yescharacteristic
937C2×C8C23×D311yescharacteristic
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—22no—
944C4⋊C4—32no—
945C4⋊C4—32no—
946C4⋊C4—32no—
947C4⋊C4—31no—
948C4⋊C4—31no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4—61no—
954C4⋊C4—61no—
955C4⋊C4—61no—
956C4⋊C4—62no—
957C4⋊C4—61no—
958C4⋊C4—62no—
959C4⋊C4—62no—
960C4⋊C4—62no—
961C4⋊C4—62no—
962C4⋊C4—62no—
963C4⋊C4—61no—
964C4⋊C4—61no—
965C4⋊C4—61no—
966C4⋊C4—61no—
967C4⋊C4—61no—
968C4⋊C4—62no—
969C4⋊C4—62no—
970C4⋊C4—62no—
971C4⋊C4—62no—
972C4⋊C4—62no—
973C4⋊C4D3×D411yescharacteristic
974C4⋊C4D3×D411yescharacteristic
975C4⋊C4C23×D311yescharacteristic
976C4⋊C4C23×D312yes—
977C4⋊C4C23×D311yescharacteristic
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—32no—
982C22⋊C4—32no—
983C22⋊C4—61no—
984C22⋊C4—61no—
985C22⋊C4—62no—
986C22⋊C4—62no—
987C22⋊C4—61no—
988C22⋊C4—61no—
989C22⋊C4—61no—
990C22⋊C4—62no—
991C22⋊C4—62no—
992C22⋊C4D3×D412yes—
993C42—21no—
994C42—32no—
995C42—32no—
996C42—31no—
997C42—31no—
998C42—31no—
999C42—31no—
1000C42—62no—
1001C42—62no—
1002C42—61no—
1003C42C23×D312yes—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—41no—
1007C22×C3—41no—
1008C22×C3—41no—
1009C22×C3C2×#12412yes—
1010C22×C3C23×D411yescharacteristic
1011C2×D3—22no—
1012C2×D3—22no—
1013C2×D3—41no—
1014C2×D3—41no—
1015C2×D3—41no—
1016C2×D3C2×#12414yes—
1017C3×C4—22no—
1018C3×C4—22no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—42no—
1022C3×C4—41no—
1023C3×C4—42no—
1024C3×C4C2×#12412yes—
1025C3×C4C22×#4111yescharacteristic
1026C3×C4C22×#4111yescharacteristic
1027Dic3—21no—
1028Dic3—21no—
1029Dic3—21no—
1030Dic3—21no—
1031Dic3—41no—
1032Dic3—41no—
1033Dic3—42no—
1034Dic3—41no—
1035Dic3—42no—
1036Dic3C2×#12414yes—
1037C23—21no—
1038C23—32no—
1039C23—61no—
1040C23C2×D3×D411yescharacteristic
1041Q8—22no—
1042Q8—22no—
1043Q8—21no—
1044Q8—21no—
1045Q8—34no—
1046Q8—42no—
1047Q8—61no—
1048Q8—61no—
1049Q8—62no—
1050Q8—62no—
1051Q8—82no—
1052Q8—124no—
1053Q8—124no—
1054Q8—122no—
1055Q8—242no—
1056Q8—241no—
1057Q8—241no—
1058D4—21no—
1059D4—21no—
1060D4—38no—
1061D4—34no—
1062D4—42no—
1063D4—61no—
1064D4—61no—
1065D4—124no—
1066D4—122no—
1067D4—122no—
1068D4—124no—
1069D4—122no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—32no—
1076C2×C4—34no—
1077C2×C4—34no—
1078C2×C4—31no—
1079C2×C4—31no—
1080C2×C4—31no—
1081C2×C4—31no—
1082C2×C4—42no—
1083C2×C4—42no—
1084C2×C4—61no—
1085C2×C4—61no—
1086C2×C4—62no—
1087C2×C4—61no—
1088C2×C4—62no—
1089C2×C4—81no—
1090C2×C4—122no—
1091C2×C4—122no—
1092C2×C4—124no—
1093C2×C4—124no—
1094C2×C4—124no—
1095C2×C4—124no—
1096C2×C4—121no—
1097C2×C4—121no—
1098C2×C4—122no—
1099C2×C4—122no—
1100C2×C4—242no—
1101C2×C4—242no—
1102C2×C4—241no—
1103C2×C4C2×D3×D412yes—
1104C2×C4C2×D3×D412yes—
1105C2×C4C2×D3×D411yescharacteristic
1106C2×C4D3×#4112yes—
1107C2×C4D3×#4112yes—
1108C2×C4C24×D311yescharacteristic
1109C8—21no—
1110C8—21no—
1111C8—22no—
1112C8—61no—
1113C8—62no—
1114C8—61no—
1115C2×C3—22no—
1116C2×C3—81no—
1117C2×C3C22×#12411yescharacteristic
1118C2×C3#358611yescharacteristic
1119C2×C3#358611yescharacteristic
1120D3—24no—
1121D3—81no—
1122C22—21no—
1123C22—21no—
1124C22—34no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—62no—
1129C22—62no—
1130C22—121no—
1131C22—121no—
1132C22—121no—
1133C22D3×#12412yes—
1134C22C22×D3×D411yescharacteristic
1135C4—22no—
1136C4—22no—
1137C4—34no—
1138C4—41no—
1139C4—42no—
1140C4—42no—
1141C4—41no—
1142C4—41no—
1143C4—61no—
1144C4—61no—
1145C4—61no—
1146C4—61no—
1147C4—122no—
1148C4—121no—
1149C4—121no—
1150C4—122no—
1151C4—121no—
1152C4D3×#12412yes—
1153C4C2×D3×#4111yescharacteristic
1154C4C2×D3×#4111yescharacteristic
1155C3#6062711yescharacteristic, complemented, Sylow
1156C2—22no—
1157C2—64no—
1158C2—81no—
1159C2—241no—
1160C2C2×D3×#12411yescharacteristic
1161C2#8720811yescharacteristic
1162C2#8721111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3137C2
socleC22×C3C23×D4
prime radical#86340C2
hypercenter#3137D3
hypocenterC3#60627
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3137

Complements

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

NH ≅ G/Ntype
1. #86587C2semidirect
3. C3×#3137C2semidirect
4. #83471C2semidirect
5. #83401C2semidirect
6. #81738C2semidirect
7. D3×#491C2semidirect
8. #81681C2semidirect
9. #81679C2semidirect
10. #81641C2semidirect
11. #81639C2semidirect
12. #81600C2semidirect
13. #81599C2semidirect
14. #78957C2semidirect
15. #78953C2semidirect
16. #78883C2semidirect
17. #78879C2semidirect
18. #78832C2semidirect
19. #78826C2semidirect
20. #78790C2semidirect
21. C2×#4797C2semidirect
22. #78575C2semidirect
23. #78550C2semidirect
149. #3137D3semidirect
1155. C3#60627semidirect

Maximal subgroups

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

subgroupindex
#865872
#863402
C3×#31372
#834712
#834012
#817382
D3×#4912
#816812
#816792
#816412
#816392
#816002
#815992
#789572
#789532
#788832
#788792
#788322
#788262
#787902
C2×#47972
#785752
#785502
#606273