Finite Group Databasebeta

← #11664536

Subgroups — #11664536

Order 768.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86586C211yesmaximal, characteristic, complemented
2#86340C211yesmaximal, characteristic
3C3×#3137C211yesmaximal, characteristic, complemented
4#83471C211yesmaximal, characteristic, complemented
5#83401C211yesmaximal, characteristic, complemented
6#81739C212yesmaximal, complemented
7#81738C212yesmaximal, complemented
8#81683C212yesmaximal, complemented
9#81681C212yesmaximal, complemented
10#81639C212yesmaximal, complemented
11#81637C212yesmaximal, complemented
12#81599C212yesmaximal, complemented
13D3×#487C212yesmaximal, complemented
14#78957C211yesmaximal, characteristic, complemented
15#78953C211yesmaximal, characteristic, complemented
16#78883C211yesmaximal, characteristic, complemented
17#78878C211yesmaximal, characteristic, complemented
18#78832C211yesmaximal, characteristic, complemented
19#78825C211yesmaximal, characteristic, complemented
20#78790C211yesmaximal, characteristic, complemented
21C2×#4792C211yesmaximal, characteristic, complemented
22#78575C211yesmaximal, characteristic, complemented
23#78549C211yesmaximal, characteristic, complemented
24#60623—31nomaximal, Sylow
25C2×#1010C2211yescharacteristic
26C2×#1007C2211yescharacteristic
27C3×#544C2211yescharacteristic
28C3×#536C2211yescharacteristic
29#5832C2211yescharacteristic
30C2×#944C2211yescharacteristic
31C2×#907C2211yescharacteristic
32C2×#901C2211yescharacteristic
33#5729C2212yes—
34#5727—21no—
35#5724C2212yes—
36D3×C4⋊Q8C2212yes—
37D3×C4⋊Q8C2212yes—
38#5722—21no—
39#5690—21no—
40#5689C2212yes—
41#5688C2212yes—
42#5685—21no—
43#5675C2212yes—
44#5668C2212yes—
45#5655—22no—
46#5655—22no—
47#5636—22no—
48#5632—21no—
49#5632—21no—
50#5632—22no—
51#5631—21no—
52#5631—21no—
53#5526C2211yescharacteristic
54#5523C2211yescharacteristic
55#5522C2211yescharacteristic
56#5519C2211yescharacteristic
57#5517C2211yescharacteristic
58#5504C2211yescharacteristic
59C2×#888C2211yescharacteristic
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×C8×Dic3C2211yescharacteristic
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#4800C2211yescharacteristic
105#4800C2211yescharacteristic
106#4797C2212yes—
107#4797C2212yes—
108#4794C2212yes—
109#4792C2212yes—
110#4792C2212yes—
111#4792C2212yes—
112#4792C2212yes—
113#4792C2211yescharacteristic
114#4792C2212yes—
115#4792C2212yes—
116#4792C2212yes—
117#4792C2211yescharacteristic
118#4772C2212yes—
119#4772C2212yes—
120#4771C2212yes—
121#4771C2212yes—
122#4768C2211yescharacteristic
123#4768C2211yescharacteristic
124#4765C2212yes—
125#4760C2211yescharacteristic
126#4760C2212yes—
127#4760C2211yescharacteristic
128#4714C2212yes—
129#4708C2212yes—
130#4707C2212yes—
131#4703C2212yes—
132#4697C2212yes—
133#4689C2212yes—
134C4×D3×C8C2212yes—
135#4681C2212yes—
136#3503—31no—
137#3499—31no—
138#3141—32no—
139#3141—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#3131—32no—
151#3131—31no—
152C2×#487—32no—
153C2×#487—31no—
154#2898—31no—
155#2898—31no—
156#2898—31no—
157#2898—31no—
158C4×#131—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—22no—
168C2×D3×Q8—21no—
169C2×D3×Q8C2312yes—
170C2×D3×Q8C2312yes—
171C2×#237—22no—
172C2×#237C2312yes—
173C2×#235—22no—
174C2×#235—21no—
175C2×#235C2311yescharacteristic
176C2×#235C2311yescharacteristic
177C22×Dic6—21no—
178C22×Dic6—21no—
179C22×Dic6C2311yescharacteristic
180C2×C3×M16C2311yescharacteristic
181C22×C3×C8C2311yescharacteristic
182C3×C4⋊Q8—21no—
183C3×C4⋊Q8C2312yes—
184C3×C4⋊Q8C2312yes—
185C3×#125—21no—
186C3×#125C2312yes—
187C3×#124C2312yes—
188C3×#123—22no—
189C3×C22⋊Q8—21no—
190C3×C22⋊Q8—21no—
191C3×C22⋊Q8—22no—
192C3×#117C2311yescharacteristic
193C3×#117C2311yescharacteristic
194C2×C3×C4⋊C4C2311yescharacteristic
195#947C2311yescharacteristic
196#946—22no—
197#944—22no—
198#944—21no—
199#944—21no—
200#944—22no—
201#944C2312yes—
202#944C2312yes—
203#944C2311yescharacteristic
204#940C2311yescharacteristic
205#939—21no—
206#939—21no—
207#936C2311yescharacteristic
208C4×#67—22no—
209C4×#67—21no—
210C4×#67—21no—
211#926C2311yescharacteristic
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—21no—
226#897—21no—
227#897—22no—
228#896—22no—
229#896—22no—
230#896—22no—
231#896—22no—
232#896—22no—
233#896—22no—
234#894—22no—
235#894—22no—
236#893—21no—
237#893D411yescharacteristic
238#893D411yescharacteristic
239#892C2312yes—
240#892C2312yes—
241D3×C4⋊C4—22no—
242D3×C4⋊C4—22no—
243D3×C4⋊C4—22no—
244D3×C4⋊C4C2312yes—
245D3×C4⋊C4C2312yes—
246#890—21no—
247#890C2311yescharacteristic
248#890C2311yescharacteristic
249#889—22no—
250#889—22no—
251#888—21no—
252#888—22no—
253#888—22no—
254#888—22no—
255#888—22no—
256#888—21no—
257#888—21no—
258#888C2311yescharacteristic
259#888C2312yes—
260#888C2312yes—
261#888C2311yescharacteristic
262#887—21no—
263#887—22no—
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×#102C2312yes—
300C3×#102C2311yescharacteristic
301C3×#102C2311yescharacteristic
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#815C2312yes—
325C8×Dic3C2311yescharacteristic
326C8×Dic3C2312yes—
327C8×Dic3C2311yescharacteristic
328C8×Dic3C2311yescharacteristic
329C8×Dic3C2311yescharacteristic
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—
346Q82—61no—
347#557—61no—
348#554—62no—
349#554—61no—
350D4×Q8—62no—
351D4×Q8—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—32no—
371C2×C4⋊Q8—31no—
372C2×C4⋊Q8—31no—
373C2×C4⋊Q8—32no—
374#520—31no—
375#520—31no—
376C4×#41—31no—
377#491—32no—
378#491—32no—
379#491—32no—
380#491—32no—
381#491—32no—
382#491C2×D312yes—
383#489—32no—
384#489—32no—
385#489—32no—
386#489—32no—
387#489—32no—
388#489C2×D312yes—
389#488—32no—
390#488—32no—
391#488—31no—
392#488—31no—
393#488—31no—
394#488—31no—
395#488—32no—
396#488C2×D312yes—
397#487—32no—
398#487—32no—
399#487—31no—
400#487—32no—
401#487—32no—
402#487—32no—
403#487—32no—
404#487—32no—
405#487—32no—
406#487—32no—
407#487—31no—
408#487—32no—
409#487C2×D312yes—
410#486—31no—
411#486—32no—
412#486—31no—
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×C4×C8—31no—
452C2×C4×C8—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—
485D3×Q8—84no—
486#237—24no—
487#237—24no—
488#237—48no—
489#235—22no—
490#235—22no—
491#235—48no—
492#235—44no—
493#235#4114yes—
494#235#4114yes—
495C2×D12—22no—
496C2×D12C2×D411yescharacteristic
497C2×D12C2411yescharacteristic
498C2×C4×D3—22no—
499C2×C4×D3—22no—
500C2×C4×D3—21no—
501C2×C4×D3—22no—
502C2×C4×D3—22no—
503C2×C4×D3—22no—
504C2×C4×D3C2×D412yes—
505C2×C4×D3C2×D412yes—
506C2×C4×D3C2412yes—
507C2×Dic6—22no—
508C2×Dic6—22no—
509C2×Dic6—21no—
510C2×Dic6—21no—
511C2×Dic6—21no—
512C2×Dic6—22no—
513C2×Dic6—22no—
514C2×Dic6—22no—
515C2×Dic6—22no—
516C2×Dic6—22no—
517C2×Dic6—44no—
518C2×Dic6—82no—
519C2×Dic6C2×D411yescharacteristic
520C2×Dic6C2411yescharacteristic
521C2×Dic6C2412yes—
522C3×M16—22no—
523C2×C3×C8—22no—
524C2×C3×C8C2411yescharacteristic
525C2×C3×C8C2411yescharacteristic
526C2×C3×C8C2412yes—
527C3×C4⋊C4—21no—
528C3×C4⋊C4—22no—
529C3×C4⋊C4—22no—
530C3×C4⋊C4—22no—
531C3×C4⋊C4—22no—
532C3×C4⋊C4—22no—
533C3×C4⋊C4C2×D411yescharacteristic
534C3×C4⋊C4C2×D411yescharacteristic
535C3×C4⋊C4C2412yes—
536C3×C4⋊C4C2411yescharacteristic
537C3×C4⋊C4C2411yescharacteristic
538C3×C22⋊C4—21no—
539C3×C22⋊C4—22no—
540C3×C22⋊C4—22no—
541C3×C22⋊C4C2×D412yes—
542C3×C42—21no—
543C3×C42C2412yes—
544#217—21no—
545#217—21no—
546#217—21no—
547(C2×D3)⋊C4—22no—
548(C2×D3)⋊C4—22no—
549(C2×D3)⋊C4—22no—
550(C2×D3)⋊C4—22no—
551(C2×D3)⋊C4—21no—
552(C2×D3)⋊C4—21no—
553(C2×D3)⋊C4C2×D412yes—
554(C2×D3)⋊C4C2×D412yes—
555C4⋊Dic3—21no—
556C4⋊Dic3—22no—
557C4⋊Dic3—22no—
558C4⋊Dic3—22no—
559C4⋊Dic3—21no—
560C4⋊Dic3—21no—
561C4⋊Dic3C2411yescharacteristic
562C4⋊Dic3C2412yes—
563C4⋊Dic3C2411yescharacteristic
564Dic3⋊C4—22no—
565Dic3⋊C4—22no—
566Dic3⋊C4—21no—
567Dic3⋊C4—21no—
568Dic3⋊C4—21no—
569Dic3⋊C4—21no—
570Dic3⋊C4—22no—
571Dic3⋊C4—22no—
572Dic3⋊C4—22no—
573Dic3⋊C4—22no—
574Dic3⋊C4—22no—
575Dic3⋊C4—22no—
576Dic3⋊C4—22no—
577Dic3⋊C4—21no—
578Dic3⋊C4—21no—
579Dic3⋊C4—22no—
580Dic3⋊C4C2×D412yes—
581Dic3⋊C4C2×D412yes—
582C4×Dic3—21no—
583C4×Dic3—22no—
584C4×Dic3—22no—
585C4×Dic3C2×D411yescharacteristic
586C4×Dic3C2×D411yescharacteristic
587C4×Dic3C2×D412yes—
588C4×Dic3C2×D412yes—
589C4×Dic3C2411yescharacteristic
590C4×Dic3C2411yescharacteristic
591#208—22no—
592C2×C3⋊C8—22no—
593C2×C3⋊C8C2411yescharacteristic
594C2×C3⋊C8C2412yes—
595C2×C3⋊C8C2411yescharacteristic
596ΓL(1,𝔽25)—24no—
597ΓL(1,𝔽25)—24no—
598D3×C8—24no—
599D3×C8—24no—
6002−1+4—64no—
6012−1+4—64no—
6022−1+4—64no—
6032−1+4—64no—
604C2×#41—31no—
605C2×#41—32no—
606C2×#41—32no—
607C2×#41—31no—
608C2×#41—62no—
609C2×#41—61no—
610C2×#41—62no—
611C2×#41—61no—
612C2×#41C22×D311yescharacteristic
613C22×Q8—32no—
614C22×Q8—32no—
615C22×Q8—31no—
616C22×Q8—61no—
617C22×Q8—61no—
618C22×Q8—62no—
619C22×Q8—61no—
620C22×Q8C22×D311yescharacteristic
621#131—64no—
622#131—64no—
623C2×M16—31no—
624C2×M16—32no—
625C2×M16—32no—
626C2×M16C22×D311yescharacteristic
627C22×C8—31no—
628C22×C8—32no—
629C22×C8—32no—
630C22×C8C22×D311yescharacteristic
631C4⋊Q8—21no—
632C4⋊Q8—31no—
633C4⋊Q8—32no—
634C4⋊Q8—32no—
635C4⋊Q8—31no—
636C4⋊Q8—31no—
637C4⋊Q8—32no—
638C4⋊Q8—32no—
639C4⋊Q8—32no—
640C4⋊Q8—32no—
641C4⋊Q8—62no—
642C4⋊Q8—62no—
643C4⋊Q8—62no—
644C4⋊Q8—61no—
645C4⋊Q8—61no—
646C4⋊Q8—61no—
647C4⋊Q8—61no—
648C4⋊Q8—62no—
649C4⋊Q8—62no—
650C4⋊Q8—62no—
651C4⋊Q8—61no—
652C4⋊Q8C22×D312yes—
653C4⋊Q8C22×D312yes—
654#127—31no—
655#125—21no—
656#125—31no—
657#125—31no—
658#125—32no—
659#125—62no—
660#125—62no—
661#125—61no—
662#125C22×D312yes—
663#124—31no—
664#124—31no—
665#124—32no—
666#124C22×D312yes—
667#123—22no—
668#123—62no—
669#123—62no—
670#123—62no—
671#123—62no—
672#123—62no—
673C22⋊Q8—21no—
674C22⋊Q8—21no—
675C22⋊Q8—22no—
676C22⋊Q8—62no—
677C22⋊Q8—62no—
678C22⋊Q8—61no—
679C22⋊Q8—61no—
680C22⋊Q8—62no—
681C22⋊Q8—62no—
682C22⋊Q8—62no—
683C22⋊Q8—62no—
684C22⋊Q8—62no—
685C22⋊Q8—62no—
686C22⋊Q8—62no—
687C22⋊Q8—62no—
688C22⋊Q8—61no—
689C22⋊Q8—61no—
690C22⋊Q8—62no—
691#121—62no—
692#121—62no—
693#121—61no—
694#121—61no—
695C4×Q8—31no—
696C4×Q8—31no—
697C4×Q8—61no—
698C4×Q8—61no—
699C4×Q8—61no—
700C4×Q8—62no—
701C4×Q8—62no—
702C4×Q8—61no—
703C4×D4—31no—
704C4×D4—31no—
705C4×D4—32no—
706C4×D4—32no—
707C4×D4—61no—
708C4×D4—62no—
709C4×D4—62no—
710C4×D4—61no—
711C4×D4—61no—
712C4×D4—62no—
713C4×D4—61no—
714C4×D4—62no—
715#117—32no—
716#117—31no—
717#117—32no—
718#117—32no—
719#117C22×D311yescharacteristic
720#117C22×D311yescharacteristic
721C2×C4⋊C4—31no—
722C2×C4⋊C4—32no—
723C2×C4⋊C4—32no—
724C2×C4⋊C4—62no—
725C2×C4⋊C4—62no—
726C2×C4⋊C4—62no—
727C2×C4⋊C4—61no—
728C2×C4⋊C4—61no—
729C2×C4⋊C4—61no—
730C2×C4⋊C4C22×D311yescharacteristic
731C2×C42—31no—
732C2×C42—32no—
733#103—31no—
734#103—32no—
735#103—32no—
736#103—32no—
737#103—32no—
738#103—31no—
739#103—32no—
740#103—31no—
741#103—32no—
742#103—32no—
743#103—32no—
744#103—32no—
745#103—31no—
746#103—32no—
747#103—31no—
748#103—32no—
749#103—32no—
750#103—32no—
751#103—32no—
752#103—31no—
753#103—32no—
754#103C22×D311yescharacteristic
755#103C22×D312yes—
756#103C22×D312yes—
757#103C22×D312yes—
758#103C22×D312yes—
759#103C22×D312yes—
760#103C22×D311yescharacteristic
761#102—31no—
762#102—32no—
763#102—31no—
764#102—31no—
765#102—31no—
766#102—32no—
767#102—31no—
768#102—31no—
769#102—32no—
770#102C22×D311yescharacteristic
771#102C22×D312yes—
772#102C22×D311yescharacteristic
773#97—32no—
774#97—32no—
775#97C22×D312yes—
776C4×C8—31no—
777C4×C8—31no—
778C4×C8—32no—
779C4×C8—31no—
780C4×C8—31no—
781C4×C8—32no—
782C4×C8C22×D312yes—
783C23×C3—21no—
784C23×C3C22×D411yescharacteristic
785C22×D3—21no—
786C22×D3C22×D412yes—
787C3×Q8—21no—
788C3×Q8—21no—
789C3×Q8—22no—
790C3×Q8—22no—
791C3×Q8—42no—
792C3×Q8—82no—
793C3×D4—21no—
794C3×D4—21no—
795C3×D4—42no—
796C2×C3×C4—21no—
797C2×C3×C4—22no—
798C2×C3×C4—21no—
799C2×C3×C4—22no—
800C2×C3×C4—21no—
801C2×C3×C4—42no—
802C2×C3×C4—42no—
803C2×C3×C4—81no—
804C2×C3×C4C22×D412yes—
805C2×C3×C4C22×D412yes—
806C2×C3×C4C22×D411yescharacteristic
807C2×C3×C4C2×#4112yes—
808C2×C3×C4C2×#4112yes—
809C2×C3×C4C2511yescharacteristic
810#67—42no—
811#67—44no—
812#67—42no—
813#67—42no—
814#67#12418yes—
815C2×Dic3—22no—
816C2×Dic3—22no—
817C2×Dic3—21no—
818C2×Dic3—22no—
819C2×Dic3—21no—
820C2×Dic3—22no—
821C2×Dic3—21no—
822C2×Dic3—42no—
823C2×Dic3—44no—
824C2×Dic3—81no—
825C2×Dic3C22×D411yescharacteristic
826C2×Dic3C22×D411yescharacteristic
827C2×Dic3C22×D412yes—
828C2×Dic3C22×D411yescharacteristic
829C2×Dic3C22×D411yescharacteristic
830D12—21no—
831D12—21no—
832D12—44no—
833D12#12414yes—
834C4×D3—24no—
835C4×D3—24no—
836C4×D3—44no—
837C4×D3—44no—
838C4×D3—42no—
839C4×D3—44no—
840C4×D3—82no—
841C4×D3—82no—
842C4×D3C2×#4114yes—
843C4×D3C2×#4114yes—
844Dic6—22no—
845Dic6—22no—
846Dic6—21no—
847Dic6—21no—
848Dic6—42no—
849Dic6—44no—
850Dic6—44no—
851Dic6—44no—
852Dic6—42no—
853Dic6—42no—
854Dic6—82no—
855Dic6—82no—
856Dic6#12414yes—
857C3×C8—21no—
858C3×C8—22no—
859C3×C8—21no—
860C3⋊C8—21no—
861C3⋊C8—22no—
862C3⋊C8—21no—
863#41—22no—
864#41—22no—
865#41—34no—
866#41—34no—
867#41—64no—
868#41—64no—
869#41—64no—
870#41—64no—
871#41—62no—
872#41—62no—
873#41—128no—
874#41—124no—
875#41—128no—
876#41—124no—
877C2×Q8—21no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—31no—
882C2×Q8—31no—
883C2×Q8—32no—
884C2×Q8—61no—
885C2×Q8—61no—
886C2×Q8—62no—
887C2×Q8—62no—
888C2×Q8—62no—
889C2×Q8—62no—
890C2×Q8—64no—
891C2×Q8—64no—
892C2×Q8—64no—
893C2×Q8—64no—
894C2×Q8—61no—
895C2×Q8—62no—
896C2×Q8—62no—
897C2×Q8—62no—
898C2×Q8—124no—
899C2×Q8—124no—
900C2×Q8—242no—
901C2×Q8—244no—
902C2×Q8C23×D311yescharacteristic
903C2×Q8C23×D312yes—
904C2×D4—21no—
905C2×D4—32no—
906C2×D4—31no—
907C2×D4—31no—
908C2×D4—62no—
909C2×D4—61no—
910C2×D4—61no—
911C2×D4—62no—
912C2×D4—61no—
913C2×D4C23×D311yescharacteristic
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—32no—
918C22×C4—31no—
919C22×C4—31no—
920C22×C4—32no—
921C22×C4—32no—
922C22×C4—62no—
923C22×C4—62no—
924C22×C4—62no—
925C22×C4—62no—
926C22×C4—62no—
927C22×C4—62no—
928C22×C4—61no—
929C22×C4—61no—
930C22×C4—61no—
931C22×C4C23×D311yescharacteristic
932M16—22no—
933M16—64no—
934M16—64no—
935M16—62no—
936C2×C8—22no—
937C2×C8—31no—
938C2×C8—31no—
939C2×C8—32no—
940C2×C8—64no—
941C2×C8—64no—
942C2×C8—62no—
943C2×C8C23×D311yescharacteristic
944C2×C8C23×D311yescharacteristic
945C2×C8C23×D312yes—
946C4⋊C4—22no—
947C4⋊C4—22no—
948C4⋊C4—22no—
949C4⋊C4—21no—
950C4⋊C4—22no—
951C4⋊C4—22no—
952C4⋊C4—32no—
953C4⋊C4—32no—
954C4⋊C4—32no—
955C4⋊C4—31no—
956C4⋊C4—31no—
957C4⋊C4—62no—
958C4⋊C4—62no—
959C4⋊C4—62no—
960C4⋊C4—62no—
961C4⋊C4—61no—
962C4⋊C4—61no—
963C4⋊C4—61no—
964C4⋊C4—62no—
965C4⋊C4—62no—
966C4⋊C4—62no—
967C4⋊C4—62no—
968C4⋊C4—61no—
969C4⋊C4—61no—
970C4⋊C4—61no—
971C4⋊C4—61no—
972C4⋊C4—61no—
973C4⋊C4—61no—
974C4⋊C4—62no—
975C4⋊C4—62no—
976C4⋊C4—62no—
977C4⋊C4—62no—
978C4⋊C4—62no—
979C4⋊C4D3×D411yescharacteristic
980C4⋊C4D3×D411yescharacteristic
981C4⋊C4C23×D311yescharacteristic
982C4⋊C4C23×D312yes—
983C4⋊C4C23×D311yescharacteristic
984C22⋊C4—21no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—32no—
988C22⋊C4—32no—
989C22⋊C4—61no—
990C22⋊C4—61no—
991C22⋊C4—62no—
992C22⋊C4—62no—
993C22⋊C4—61no—
994C22⋊C4—61no—
995C22⋊C4—61no—
996C22⋊C4—62no—
997C22⋊C4—62no—
998C22⋊C4D3×D412yes—
999C42—21no—
1000C42—32no—
1001C42—31no—
1002C42—32no—
1003C42—31no—
1004C42—31no—
1005C42—31no—
1006C42—62no—
1007C42—62no—
1008C42—61no—
1009C42C23×D312yes—
1010C22×C3—21no—
1011C22×C3—21no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3C2×#12412yes—
1016C22×C3C23×D411yescharacteristic
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—41no—
1020C2×D3—41no—
1021C2×D3—41no—
1022C2×D3C2×#12414yes—
1023C3×C4—22no—
1024C3×C4—22no—
1025C3×C4—41no—
1026C3×C4—42no—
1027C3×C4—42no—
1028C3×C4—41no—
1029C3×C4—41no—
1030C3×C4C2×#12412yes—
1031C3×C4C22×#4111yescharacteristic
1032C3×C4C22×#4111yescharacteristic
1033Dic3—21no—
1034Dic3—21no—
1035Dic3—41no—
1036Dic3—42no—
1037Dic3—41no—
1038Dic3—42no—
1039Dic3—41no—
1040Dic3C2×#12414yes—
1041Dic3#57712yes—
1042Dic3#57812yes—
1043C23—21no—
1044C23—32no—
1045C23—61no—
1046C23C2×D3×D411yescharacteristic
1047Q8—22no—
1048Q8—22no—
1049Q8—21no—
1050Q8—21no—
1051Q8—34no—
1052Q8—42no—
1053Q8—61no—
1054Q8—61no—
1055Q8—62no—
1056Q8—62no—
1057Q8—82no—
1058Q8—124no—
1059Q8—124no—
1060Q8—124no—
1061Q8—122no—
1062Q8—122no—
1063Q8—122no—
1064Q8—242no—
1065Q8—242no—
1066D4—21no—
1067D4—21no—
1068D4—38no—
1069D4—34no—
1070D4—42no—
1071D4—61no—
1072D4—61no—
1073D4—122no—
1074D4—122no—
1075D4—124no—
1076D4—124no—
1077D4—122no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—31no—
1084C2×C4—31no—
1085C2×C4—32no—
1086C2×C4—34no—
1087C2×C4—34no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—64no—
1093C2×C4—64no—
1094C2×C4—62no—
1095C2×C4—62no—
1096C2×C4—61no—
1097C2×C4—62no—
1098C2×C4—61no—
1099C2×C4—61no—
1100C2×C4—62no—
1101C2×C4—81no—
1102C2×C4—124no—
1103C2×C4—124no—
1104C2×C4—124no—
1105C2×C4—124no—
1106C2×C4—122no—
1107C2×C4—122no—
1108C2×C4—242no—
1109C2×C4—242no—
1110C2×C4—241no—
1111C2×C4C2×D3×D412yes—
1112C2×C4C2×D3×D412yes—
1113C2×C4C2×D3×D411yescharacteristic
1114C2×C4D3×#4112yes—
1115C2×C4D3×#4112yes—
1116C2×C4C24×D311yescharacteristic
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—61no—
1121C8—62no—
1122C8—61no—
1123C2×C3—22no—
1124C2×C3—81no—
1125C2×C3C22×#12411yescharacteristic
1126C2×C3C2×#57711yescharacteristic
1127C2×C3C2×#57811yescharacteristic
1128D3—24no—
1129D3—81no—
1130C22—21no—
1131C22—21no—
1132C22—34no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—62no—
1137C22—62no—
1138C22—121no—
1139C22—121no—
1140C22—121no—
1141C22D3×#12412yes—
1142C22C22×D3×D411yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—34no—
1146C4—32no—
1147C4—32no—
1148C4—41no—
1149C4—42no—
1150C4—42no—
1151C4—41no—
1152C4—41no—
1153C4—61no—
1154C4—61no—
1155C4—122no—
1156C4—121no—
1157C4—121no—
1158C4—122no—
1159C4—121no—
1160C4D3×#12412yes—
1161C4C2×D3×#4111yescharacteristic
1162C4C2×D3×#4111yescharacteristic
1163C3#6062311yescharacteristic, complemented, Sylow
1164C2—22no—
1165C2—64no—
1166C2—81no—
1167C2—241no—
1168C2C2×D3×#12411yescharacteristic
1169C2D3×#57711yescharacteristic
1170C2D3×#57811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3137C2
socleC22×C3C23×D4
prime radical#86340C2
hypercenter#3137D3
hypocenterC3#60623
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. #86586C2semidirect
3. C3×#3137C2semidirect
4. #83471C2semidirect
5. #83401C2semidirect
6. #81739C2semidirect
7. #81738C2semidirect
8. #81683C2semidirect
9. #81681C2semidirect
10. #81639C2semidirect
11. #81637C2semidirect
12. #81599C2semidirect
13. D3×#487C2semidirect
14. #78957C2semidirect
15. #78953C2semidirect
16. #78883C2semidirect
17. #78878C2semidirect
18. #78832C2semidirect
19. #78825C2semidirect
20. #78790C2semidirect
21. C2×#4792C2semidirect
22. #78575C2semidirect
23. #78549C2semidirect
149. #3137D3semidirect
1163. C3#60623semidirect

Maximal subgroups

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

subgroupindex
#865862
#863402
C3×#31372
#834712
#834012
#817392
#817382
#816832
#816812
#816392
#816372
#815992
D3×#4872
#789572
#789532
#788832
#788782
#788322
#788252
#787902
C2×#47922
#785752
#785492
#606233