Finite Group Databasebeta

← #11707349

Subgroups — #11707349

Order 768.

7894 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3517C211yesmaximal, characteristic, complemented
2#87023C211yesmaximal, characteristic, complemented
3#87015C211yesmaximal, characteristic, complemented
4#86913C216yesmaximal, complemented
5#86888C216yesmaximal, complemented
6D3×#550C213yesmaximal, complemented
7#86775C213yesmaximal, complemented
8#86772C212yesmaximal, complemented
9#86770C212yesmaximal, complemented
10#86770C211yesmaximal, characteristic, complemented
11#86768C211yesmaximal, characteristic, complemented
12#86703C213yesmaximal, complemented
13#86674C213yesmaximal, complemented
14#86488C216yesmaximal, complemented
15#86486C216yesmaximal, complemented
16#86245C213yesmaximal, complemented
17#86238C213yesmaximal, complemented
18#86166C213yesmaximal, complemented
19#86152C213yesmaximal, complemented
20#85896C212yesmaximal, complemented
21#85886C212yesmaximal, complemented
22#85845C211yesmaximal, characteristic, complemented
23C4×#1009C211yesmaximal, characteristic, complemented
24#62986—31nomaximal, Sylow
25C2×#1009C2211yescharacteristic
26C2×#1009C2212yes—
27C2×D3×#41C2216yescomplemented
28C3×#557C2211yescharacteristic, complemented
29C3×#553C2216yescomplemented
30C3×#550C2211yescharacteristic, complemented
31C3×#550C2212yescomplemented
32C3×#550C2213yescomplemented
33C3×#547C2213yescomplemented
34C3×#540C2216yescomplemented
35C3×#532C2213yescomplemented
36C3×#529C2213yescomplemented
37C3×#520C2212yescomplemented
38C3×C4×#41C2211yescharacteristic, complemented
39#5834C2212yescomplemented
40#5834C2212yescomplemented
41#5834C2212yescomplemented
42#5834C2216yescomplemented
43#5829C2216yescomplemented
44#5828C2216yescomplemented
45#5827C2211yescharacteristic, complemented
46Dic3×#41C2212yescomplemented
47#5728C2213yescomplemented
48#5727C2213yescomplemented
49#5726C2213yescomplemented
50#5725C2213yescomplemented
51#5719C2216yescomplemented
52#5718C2216yescomplemented
53#5718C2213yescomplemented
54#5717C2216yescomplemented
55#5717C2213yescomplemented
56#5716C2213yescomplemented
57D3×#127C2216yescomplemented
58D3×#127C2213yescomplemented
59#5709C2216yescomplemented
60#5704C22112yescomplemented
61#5702C2216yescomplemented
62#5697C2216yescomplemented
63#5695C2216yescomplemented
64#5695C2213yescomplemented
65#5690C2216yescomplemented
66#5688C2216yescomplemented
67#5685C2211yescharacteristic, complemented
68#5681C2213yescomplemented
69#5677C2213yescomplemented
70#5676C2216yescomplemented
71#5664C22112yescomplemented
72#5664C2216yescomplemented
73#5661C2216yescomplemented
74#5657C22112yescomplemented
75#5656C22112yescomplemented
76#5654C22112yescomplemented
77#5654C22112yescomplemented
78#5641C2213yescomplemented
79#5633C2213yescomplemented
80#5627C2216yescomplemented
81#5619C2216yescomplemented
82#5616C2216yescomplemented
83#5614C2213yescomplemented
84#5614C2216yescomplemented
85#5613C22112yescomplemented
86#5612C2216yescomplemented
87#5611C2216yescomplemented
88#5610C22112yescomplemented
89#5610C22112yescomplemented
90#5609C2216yescomplemented
91#5609C2216yescomplemented
92#5609C2216yescomplemented
93#5607C2216yescomplemented
94#5607C2216yescomplemented
95#5607C2216yescomplemented
96D3×#121C22112yescomplemented
97D3×#121C2216yescomplemented
98#5599C22112yescomplemented
99#5599C2213yescomplemented
100#5599C2216yescomplemented
101#5596C2216yescomplemented
102#5596C2216yescomplemented
103#5580C2213yescomplemented
104#5579C2213yescomplemented
105#5577C2211yescharacteristic, complemented
106#5577C2212yescomplemented
107#5577C2213yescomplemented
108#5574C2211yescharacteristic
109#5574C2211yescharacteristic, complemented
110#5574C2212yescomplemented
111C4×#239C2211yescharacteristic
112C4×#239C2212yes—
113C4×#239C2211yescharacteristic, complemented
114C4×#239C2212yescomplemented
115C4×D3×Q8C2213yescomplemented
116#5569C2212yescomplemented
117Q8×Dic6C2211yescharacteristic, complemented
118#5565C2216yescomplemented
119#5563C2213yescomplemented
120#5563C2213yescomplemented
121#5562C2216yescomplemented
122#5559C2216yescomplemented
123#5558C2216yescomplemented
124#5554C2216yescomplemented
125#5553C2213yescomplemented
126#5553C2216yescomplemented
127D4×D12C2216yescomplemented
128D4×D12C2213yescomplemented
129#5548C2216yescomplemented
130#5548C2216yescomplemented
131#5548C2216yescomplemented
132#5548C2213yescomplemented
133#5547C22112yescomplemented
134#5545C2213yescomplemented
135#5545C2213yescomplemented
136#5545C2216yescomplemented
137#5545C2216yescomplemented
138C4×D3×D4C2213yescomplemented
139C4×D3×D4C2213yescomplemented
140C4×D3×D4C2216yescomplemented
141C4×D3×D4C2216yescomplemented
142#5538C2216yescomplemented
143C4×#237C2213yescomplemented
144#5535C2216yescomplemented
145#5532C2216yescomplemented
146#5528C2216yescomplemented
147#5523C2213yescomplemented
148#5522C2216yescomplemented
149#5521C2213yescomplemented
150#5521C2216yescomplemented
151#5514C2216yescomplemented
152#5507C2216yescomplemented
153#5504C2216yescomplemented
154C2×#893C2216yescomplemented
155#5477C2213yescomplemented
156C4×#235C2213yescomplemented
157C4×#235C2213yescomplemented
158C2×C4×D12C2213yescomplemented
159#3519—36no—
160#3519—33no—
161#3519—36no—
162#3519—33no—
163#3517—31no—
164#3517—32no—
165#3517—32no—
166#3517D311yescharacteristic, complemented
167#3508—36no—
168#3508—33no—
169#3506—36no—
170#3506—33no—
171#3498—31no—
172#3498—32no—
173#3483—31no—
174#3483—31no—
175#3480—33no—
176Q8×#41—31no—
177D4×#41—33no—
178D4×#41—33no—
179C2×#550—33no—
180C4×H(5,𝔽2)—32no—
181C4×H(5,𝔽2)—31no—
182C2×C3×#41C2312yes—
183C2×C3×#41C2311yescharacteristic
184C2×C3×#41C2316yes—
185#1009—28no—
186#1009—216no—
187D3×#41—424no—
188C2×#239C2311yescharacteristic
189C2×#239C2312yes—
190C2×#239C2316yes—
191C2×#239C2311yescharacteristic
192C2×D3×Q8C2313yes—
193C2×#237C2313yes—
194C2×#237C23112yes—
195C2×#237C2316yes—
196C2×D3×D4C2313yes—
197C2×D3×D4C2316yes—
198C2×D3×D4C2313yes—
199C2×D3×D4C2316yes—
200C2×D3×D4C23112yes—
201C2×D3×D4C2316yes—
202C2×D3×D4C23112yes—
203C2×D3×D4C2316yes—
204C2×#235C2313yes—
205C2×#235C2313yes—
206C2×#235C2316yes—
207C2×#235C23112yes—
208C2×#235C2316yes—
209C22×D12C2313yes—
210C22×D12C2316yes—
211C22×C4×D3C23112yes—
212C22×C4×D3C2316yes—
213C3×C4⋊Q8C2313yes—
214C3×#127C2313yes—
215C3×#127C2316yes—
216C3×#126C2316yes—
217C3×#125C2311yescharacteristic
218C3×#125C2316yes—
219C3×#124C2313yes—
220C3×#123C2316yes—
221C3×#123C23112yes—
222C3×C22⋊Q8C2313yes—
223C3×#121C2316yes—
224C3×#121C2316yes—
225C3×#121C2313yes—
226C3×#121C23112yes—
227C3×#121C2316yes—
228C3×#121C2316yes—
229C3×C4×Q8C2311yescharacteristic
230C3×C4×Q8C2312yes—
231C3×C4×Q8C2313yes—
232C3×C4×Q8C2311yescharacteristic
233C3×C4×D4C2313yes—
234C3×C4×D4C2316yes—
235C3×C4×D4C2313yes—
236C3×C4×D4C2316yes—
237C3×C4×D4C2316yes—
238C3×C4×D4C2313yes—
239C3×C4×D4C2316yes—
240C3×#117C2316yes—
241C3×#117C2313yes—
242C2×C3×C4⋊C4C2316yes—
243C2×C3×C42C2313yes—
244#947C2313yes—
245#946C2313yes—
246#946C2316yes—
247Q8×Dic3C2313yes—
248Q8×Dic3C2312yes—
249Q8×Dic3C2311yescharacteristic
250Q8×Dic3C2311yescharacteristic
251#940C2316yes—
252#940C23112yes—
253#940C2313yes—
254#940C2316yes—
255#940C2316yes—
256#940C2316yes—
257#940C2316yes—
258#939C23112yes—
259#939C23112yes—
260#939C2316yes—
261#939C23112yes—
262#938C23112yes—
263#938C2316yes—
264#938C2316yes—
265#938C2313yes—
266#938C2316yes—
267#938C2316yes—
268#938C2316yes—
269#937C23112yes—
270#937C23112yes—
271#937C23112yes—
272#936C2316yes—
273#935C2316yes—
274#935C23112yes—
275D4×Dic3C2313yes—
276D4×Dic3C2316yes—
277D4×Dic3C2316yes—
278D4×Dic3C2313yes—
279D4×Dic3C2313yes—
280#930C23112yes—
281#930C2316yes—
282#930C2316yes—
283#930C2316yes—
284#930C2316yes—
285#929C23112yes—
286C4×#67C2313yes—
287C4×#67C2313yes—
288C4×#67C23112yes—
289C4×#67C2313yes—
290C4×#67C2316yes—
291C4×#67C2313yes—
292C4×#67C23112yes—
293C4×#67C23112yes—
294C4×#67C2316yes—
295C4×#67C2316yes—
296C4×#67C2316yes—
297C2×(C2×D3)⋊C4C2316yes—
298C2×(C2×D3)⋊C4C23112yes—
299#926C2313yes—
300#926C2313yes—
301#926C2316yes—
302C2×C4⋊Dic3C2313yes—
303C2×C4×Dic3C2316yes—
304#898C2316yes—
305#898C2316yes—
306#898C2316yes—
307#897C2316yes—
308#896C2316yes—
309#896C23112yes—
310#896C23112yes—
311#895C2313yes—
312#895C2316yes—
313#895C23112yes—
314#895C2316yes—
315#895C2316yes—
316#895C2316yes—
317#895C2313yes—
318#895C2316yes—
319#894C2316yes—
320#894C23112yes—
321#894C23112yes—
322#894C2316yes—
323#893C2316yes—
324#893C2316yes—
325#893C2316yes—
326#893C23112yes—
327#893C2313yes—
328#893C2316yes—
329#893C2313yes—
330#893C2316yes—
331#893C2313yes—
332#893C2316yes—
333#893C2313yes—
334#892C2313yes—
335#892C2313yes—
336#892C2316yes—
337#892C2313yes—
338#892C2316yes—
339D3×C4⋊C4C2316yes—
340D3×C4⋊C4C2316yes—
341D3×C4⋊C4C2313yes—
342D3×C4⋊C4C2313yes—
343D3×C4⋊C4C2313yes—
344#890C2311yescharacteristic
345#890C2316yes—
346#889C2312yes—
347#889C2312yes—
348#888C2311yescharacteristic
349#888C2312yes—
350#888C2316yes—
351#888C2316yes—
352#887C2311yescharacteristic
353#887C2316yes—
354#887C2312yes—
355#887C2316yes—
356#887C2316yes—
357#887C2311yescharacteristic
358#886C2316yes—
359#885C2316yes—
360#885C2316yes—
361#885C23112yes—
362#885C23112yes—
363#885C2316yes—
364#885C2316yes—
365#885C2316yes—
366#884C2316yes—
367#884C23112yes—
368#884C23112yes—
369#884C2316yes—
370#884C2316yes—
371#884C23112yes—
372#884C2316yes—
373#883C2316yes—
374#883C23112yes—
375#882C23112yes—
376#882C23112yes—
377#882C23112yes—
378#67⋊C4C2316yes—
379#67⋊C4C23112yes—
380#67⋊C4C2316yes—
381#67⋊C4C2316yes—
382#67⋊C4C2316yes—
383#67⋊C4C2316yes—
384#67⋊C4C2316yes—
385#67⋊C4C2316yes—
386D3×C22⋊C4C2316yes—
387D3×C22⋊C4C23112yes—
388D3×C22⋊C4C2316yes—
389D3×C22⋊C4C23112yes—
390#879C2316yes—
391#879C2316yes—
392#878C2316yes—
393#877C2316yes—
394#875C2316yes—
395#874C2316yes—
396#874C2313yes—
397C4×D12C2313yes—
398C4×D12C2313yes—
399C4×D12C2316yes—
400C4×D12C2316yes—
401C4×D12C2316yes—
402C4×D12C2316yes—
403C4×D12C2313yes—
404C4×D12C2313yes—
405C4×D12C2313yes—
406C4×D12C2313yes—
407C4×D12C2313yes—
408C4×D12C2313yes—
409C4×D12C2316yes—
410#872C2316yes—
411#872C2316yes—
412#872C2313yes—
413#872C2313yes—
414C42×D3C2316yes—
415C42×D3C2313yes—
416C42×D3C2313yes—
417C42×D3C2316yes—
418#870C2316yes—
419#869C2313yes—
420C4×Dic6C2311yescharacteristic
421C4×Dic6C2311yescharacteristic
422C4×Dic6C2316yes—
423C4×Dic6C2313yes—
424C4×Dic6C2313yes—
425C2×H(5,𝔽2)—32no—
426C2×H(5,𝔽2)—31no—
427C22×#41—36no—
428#559—33no—
429#559—36no—
430#559—312no—
431#559—36no—
432Q82—31no—
433#557—31no—
434#557—32no—
435#557C2×D311yescharacteristic, complemented
436#556—36no—
437#556—33no—
438#555—36no—
439#555—33no—
440#555—33no—
441#555—36no—
442#554—36no—
443#554—33no—
444#553—36no—
445#553—33no—
446#553—36no—
447#553—36no—
448#553—33no—
449#553—36no—
450#553—36no—
451#553—36no—
452#553—36no—
453#553C2×D316yescomplemented
454#550—36no—
455#550—32no—
456#550—32no—
457#550—32no—
458#550—33no—
459#550—36no—
460#550—33no—
461#550—312no—
462#550—36no—
463#550—33no—
464#550—31no—
465#550—32no—
466#550—33no—
467#550—36no—
468#550C2×D313yescomplemented
469#550C2×D311yescharacteristic, complemented
470#550C2×D312yescomplemented
471D4×Q8—33no—
472#548—33no—
473#548—33no—
474#547—33no—
475#547—36no—
476#547—36no—
477#547C2×D313yescomplemented
478#546—36no—
479#546—36no—
480#546—312no—
481#546—312no—
482#546—312no—
483#546—312no—
484#546—36no—
485#546—36no—
486D42—33no—
487D42—36no—
488D42—36no—
489D42—36no—
490D42—36no—
491D42—33no—
492D42—36no—
493#540—36no—
494#540—36no—
495#540—36no—
496#540—36no—
497#540—36no—
498#540C2×D316yescomplemented
499#538—312no—
500#538—312no—
501#538—312no—
502#535—36no—
503#535—36no—
504#535—36no—
505#533—33no—
506#533—36no—
507#532—33no—
508#532—33no—
509#532—36no—
510#532—36no—
511#532—36no—
512#532—36no—
513#532—33no—
514#532—36no—
515#532—33no—
516#532C2×D313yescomplemented
517C2×#127—36no—
518C2×#127—33no—
519#529—33no—
520#529—36no—
521#529—36no—
522#529C2×D313yescomplemented
523#525—36no—
524#525—312no—
525#525—36no—
526#525—312no—
527C2×#121—312no—
528C2×#121—36no—
529#520—31no—
530#520—31no—
531#520—32no—
532#520—31no—
533#520—33no—
534#520—36no—
535#520C2×D312yescomplemented
536#518—33no—
537#518—36no—
538#518—33no—
539#518—36no—
540#518—33no—
541#518—36no—
542C4×#41—32no—
543C4×#41—32no—
544C4×#41—31no—
545C4×#41—32no—
546C4×#41—31no—
547C4×#41—33no—
548C4×#41—36no—
549C4×#41—33no—
550C4×#41—33no—
551C4×#41C2×D311yescharacteristic, complemented
552C2×C4×Q8—33no—
553C2×C4×D4—36no—
554C2×C4×D4—33no—
555C2×C4×D4—36no—
556C2×C4×D4—33no—
557C2×C4×D4—36no—
558C2×C4×D4—33no—
559C23×D3C2416yes—
560C23×D3C24112yes—
561C3×#41—28no—
562C3×#41—24no—
563C3×#41—412no—
564C2×C3×Q8C2413yes—
565C2×C3×Q8C2411yescharacteristic
566C2×C3×D4C2416yes—
567C2×C3×D4C2413yes—
568C2×C3×D4C2413yes—
569C2×C3×D4C24112yes—
570C2×C3×D4C2416yes—
571C2×C3×D4C2416yes—
572C22×C3×C4C2416yes—
573C22×C3×C4C2413yes—
574C22×C3×C4C2413yes—
575C22×C3×C4C2413yes—
576C22×C3×C4C24112yes—
577C2×#67C2413yes—
578C2×#67C2416yes—
579C2×#67C2413yes—
580C2×#67C2416yes—
581C2×#67C2416yes—
582C2×#67C2416yes—
583C2×#67C24112yes—
584C2×#67C24112yes—
585C2×#67C24112yes—
586C2×#67C2416yes—
587C22×Dic3C2416yes—
588C22×Dic3C2416yes—
589C22×Dic3C2416yes—
590#239—24no—
591#239—28no—
592#239—412no—
593#239#4118yescomplemented
594D3×Q8—212no—
595#237—212no—
596#237—424no—
597#237—86no—
598D3×D4—212no—
599D3×D4—224no—
600D3×D4—212no—
601D3×D4—224no—
602D3×D4—412no—
603D3×D4—424no—
604D3×D4—86no—
605D3×D4—812no—
606#235—212no—
607#235—224no—
608#235—212no—
609#235—424no—
610#235—86no—
611C2×D12—212no—
612C2×D12—224no—
613C2×D12C2413yes—
614C2×D12C2416yes—
615C2×D12C2413yes—
616C2×D12C2413yes—
617C2×D12C2416yes—
618C2×D12C2416yes—
619C2×D12C2416yes—
620C2×D12C24112yes—
621C2×D12C2413yes—
622C2×C4×D3—424no—
623C2×C4×D3—412no—
624C2×C4×D3C2413yes—
625C2×C4×D3C2416yes—
626C2×C4×D3C2416yes—
627C2×C4×D3C2413yes—
628C2×C4×D3C2413yes—
629C2×C4×D3C2416yes—
630C2×C4×D3C2416yes—
631C2×C4×D3C2416yes—
632C2×C4×D3C2413yes—
633C2×C4×D3C2413yes—
634C2×C4×D3C2416yes—
635C2×C4×D3C2416yes—
636C2×C4×D3C24112yes—
637C2×C4×D3C2413yes—
638C2×Dic6C2411yescharacteristic
639C2×Dic6C2416yes—
640C2×Dic6C2412yes—
641C2×Dic6C2416yes—
642C2×Dic6C2411yescharacteristic
643C3×C4⋊C4C2411yescharacteristic
644C3×C4⋊C4C2412yes—
645C3×C4⋊C4C2411yescharacteristic
646C3×C4⋊C4C2416yes—
647C3×C4⋊C4C2416yes—
648C3×C4⋊C4C2416yes—
649C3×C4⋊C4C2413yes—
650C3×C4⋊C4C2412yes—
651C3×C4⋊C4C2416yes—
652C3×C4⋊C4C2413yes—
653C3×C22⋊C4C2416yes—
654C3×C22⋊C4C2416yes—
655C3×C22⋊C4C2416yes—
656C3×C22⋊C4C2416yes—
657C3×C22⋊C4C2416yes—
658C3×C22⋊C4C2416yes—
659C3×C42C2411yescharacteristic
660C3×C42C2413yes—
661C3×C42C2416yes—
662C3×C42C2413yes—
663C3×C42C2413yes—
664#217C2416yes—
665#217C2416yes—
666#217C2413yes—
667#217C2416yes—
668#217C24112yes—
669#217C2413yes—
670(C2×D3)⋊C4C2413yes—
671(C2×D3)⋊C4C2413yes—
672(C2×D3)⋊C4C2416yes—
673(C2×D3)⋊C4C2416yes—
674(C2×D3)⋊C4C2413yes—
675(C2×D3)⋊C4C2413yes—
676(C2×D3)⋊C4C2416yes—
677(C2×D3)⋊C4C2416yes—
678(C2×D3)⋊C4C2416yes—
679(C2×D3)⋊C4C2416yes—
680(C2×D3)⋊C4C24112yes—
681(C2×D3)⋊C4C24112yes—
682(C2×D3)⋊C4C2416yes—
683(C2×D3)⋊C4C2416yes—
684(C2×D3)⋊C4C2416yes—
685(C2×D3)⋊C4C2416yes—
686C4⋊Dic3C2413yes—
687C4⋊Dic3C2413yes—
688C4⋊Dic3C2411yescharacteristic
689C4⋊Dic3C2411yescharacteristic
690C4⋊Dic3C2416yes—
691C4⋊Dic3C2416yes—
692C4⋊Dic3C2413yes—
693C4⋊Dic3C2413yes—
694C4⋊Dic3C2412yes—
695Dic3⋊C4C2412yes—
696Dic3⋊C4C2416yes—
697Dic3⋊C4C2412yes—
698Dic3⋊C4C2411yescharacteristic
699Dic3⋊C4C2411yescharacteristic
700Dic3⋊C4C2416yes—
701Dic3⋊C4C2413yes—
702Dic3⋊C4C2413yes—
703Dic3⋊C4C24112yes—
704Dic3⋊C4C2412yes—
705Dic3⋊C4C2416yes—
706Dic3⋊C4C2412yes—
707Dic3⋊C4C2412yes—
708C4×Dic3C2416yes—
709C4×Dic3C2413yes—
710C4×Dic3C2412yes—
711C4×Dic3C2411yescharacteristic
712C4×Dic3C2411yescharacteristic
713C4×Dic3C2413yes—
714C4×Dic3C2413yes—
715C4×Dic3C2412yes—
716C4×Dic3C2413yes—
717C4×Dic3C2416yes—
718C4×Dic3C2416yes—
719C4×Dic3C2416yes—
720C4×Dic3C2412yes—
721H(5,𝔽2)—616no—
722H(5,𝔽2)—68no—
723C2×#41—31no—
724C2×#41—31no—
725C2×#41—32no—
726C2×#41—36no—
727C2×#41—33no—
728C2×#41—312no—
729C2×#41—36no—
730C2×#41—36no—
731C2×#41—33no—
732C2×#41—33no—
733C2×#41—312no—
734C2×#41—36no—
735C2×#41—1224no—
736C2×#41C22×D312yes—
737C2×#41C22×D311yescharacteristic
738C2×#41C22×D316yes—
739C22×Q8—33no—
740C22×D4—33no—
741C22×D4—36no—
742C22×D4—36no—
743C22×D4—33no—
744C22×D4—312no—
745C22×D4—36no—
746C22×D4—312no—
747C22×D4—36no—
748C22×D4—36no—
749C22×D4—33no—
750C23×C4—312no—
751C23×C4—36no—
752C4⋊Q8—32no—
753C4⋊Q8—31no—
754C4⋊Q8—36no—
755C4⋊Q8—36no—
756C4⋊Q8—33no—
757C4⋊Q8C22×D313yes—
758#127—36no—
759#127—33no—
760#127—36no—
761#127—36no—
762#127—312no—
763#127—36no—
764#127—36no—
765#127—33no—
766#127—36no—
767#127C22×D313yes—
768#127C22×D316yes—
769#126—36no—
770#126—36no—
771#126—36no—
772#126—36no—
773#126—36no—
774#126C22×D316yes—
775#125—32no—
776#125—32no—
777#125—31no—
778#125—36no—
779#125—36no—
780#125C22×D311yescharacteristic
781#125C22×D316yes—
782#124—33no—
783#124—36no—
784#124—36no—
785#124—36no—
786#124—36no—
787#124—36no—
788#124—36no—
789#124—312no—
790#124—312no—
791#124—36no—
792#124C22×D313yes—
793#123—312no—
794#123—36no—
795#123—312no—
796#123—312no—
797#123—312no—
798#123—36no—
799#123—36no—
800#123—312no—
801#123—36no—
802#123—36no—
803#123C22×D3112yes—
804#123C22×D316yes—
805C22⋊Q8—33no—
806C22⋊Q8—36no—
807C22⋊Q8—36no—
808C22⋊Q8—312no—
809C22⋊Q8—312no—
810C22⋊Q8—36no—
811C22⋊Q8—36no—
812C22⋊Q8C22×D313yes—
813#121—36no—
814#121—36no—
815#121—312no—
816#121—312no—
817#121—312no—
818#121—33no—
819#121—36no—
820#121—36no—
821#121—36no—
822#121—36no—
823#121—312no—
824#121—36no—
825#121—312no—
826#121—36no—
827#121—36no—
828#121—36no—
829#121—33no—
830#121—312no—
831#121—33no—
832#121—36no—
833#121—36no—
834#121—36no—
835#121—36no—
836#121—36no—
837#121—36no—
838#121—312no—
839#121—312no—
840#121—36no—
841#121—36no—
842#121—36no—
843#121—312no—
844#121C22×D313yes—
845#121C22×D3112yes—
846#121C22×D316yes—
847#121C22×D316yes—
848#121C22×D316yes—
849#121C22×D316yes—
850#120—312no—
851#120—312no—
852#120—312no—
853#120—312no—
854#120—312no—
855#120—312no—
856C4×Q8—33no—
857C4×Q8—31no—
858C4×Q8—32no—
859C4×Q8—31no—
860C4×Q8—31no—
861C4×Q8—36no—
862C4×Q8—31no—
863C4×Q8—32no—
864C4×Q8—36no—
865C4×Q8—36no—
866C4×Q8—33no—
867C4×Q8—36no—
868C4×Q8—31no—
869C4×Q8—31no—
870C4×Q8—33no—
871C4×Q8C22×D313yes—
872C4×Q8C22×D311yescharacteristic
873C4×Q8C22×D311yescharacteristic
874C4×Q8C22×D312yes—
875C4×D4—36no—
876C4×D4—33no—
877C4×D4—33no—
878C4×D4—36no—
879C4×D4—33no—
880C4×D4—33no—
881C4×D4—33no—
882C4×D4—312no—
883C4×D4—312no—
884C4×D4—33no—
885C4×D4—33no—
886C4×D4—36no—
887C4×D4—36no—
888C4×D4—36no—
889C4×D4—312no—
890C4×D4—36no—
891C4×D4—33no—
892C4×D4—36no—
893C4×D4—36no—
894C4×D4—36no—
895C4×D4—312no—
896C4×D4—36no—
897C4×D4—33no—
898C4×D4—33no—
899C4×D4—33no—
900C4×D4—36no—
901C4×D4—36no—
902C4×D4—36no—
903C4×D4—36no—
904C4×D4—36no—
905C4×D4—36no—
906C4×D4—36no—
907C4×D4—36no—
908C4×D4—36no—
909C4×D4—312no—
910C4×D4—33no—
911C4×D4—33no—
912C4×D4—33no—
913C4×D4—33no—
914C4×D4—36no—
915C4×D4—33no—
916C4×D4—36no—
917C4×D4—36no—
918C4×D4—36no—
919C4×D4—33no—
920C4×D4—33no—
921C4×D4—33no—
922C4×D4—36no—
923C4×D4C22×D313yes—
924C4×D4C22×D316yes—
925C4×D4C22×D316yes—
926C4×D4C22×D313yes—
927C4×D4C22×D313yes—
928C4×D4C22×D316yes—
929C4×D4C22×D316yes—
930#117—33no—
931#117—36no—
932#117—33no—
933#117—33no—
934#117—36no—
935#117—33no—
936#117—36no—
937#117—33no—
938#117—36no—
939#117—33no—
940#117—36no—
941#117—33no—
942#117—36no—
943#117C22×D316yes—
944#117C22×D313yes—
945C2×C4⋊C4—33no—
946C2×C4⋊C4—33no—
947C2×C4⋊C4—36no—
948C2×C4⋊C4—33no—
949C2×C4⋊C4—36no—
950C2×C4⋊C4—33no—
951C2×C4⋊C4C22×D316yes—
952C2×C22⋊C4—312no—
953C2×C22⋊C4—36no—
954C2×C22⋊C4—36no—
955C2×C22⋊C4—312no—
956C2×C22⋊C4—312no—
957C2×C22⋊C4—36no—
958C2×C42—36no—
959C2×C42—36no—
960C2×C42—33no—
961C2×C42—33no—
962C2×C42—36no—
963C2×C42C22×D313yes—
964C23×C3C2516yes—
965C23×C3C2513yes—
966C22×D3—212no—
967C22×D3—224no—
968C22×D3—412no—
969C22×D3—46no—
970C22×D3—412no—
971C22×D3—46no—
972C22×D3C2516yes—
973C22×D3C2513yes—
974C22×D3C2513yes—
975C3×Q8—26no—
976C3×Q8C2×#4114yescomplemented
977C3×D4—212no—
978C3×D4—26no—
979C3×D4—26no—
980C3×D4—412no—
981C3×D4—46no—
982C3×D4—46no—
983C2×C3×C4—212no—
984C2×C3×C4—26no—
985C2×C3×C4—26no—
986C2×C3×C4—412no—
987C2×C3×C4—43no—
988C2×C3×C4C2512yes—
989C2×C3×C4C2511yescharacteristic
990C2×C3×C4C2513yes—
991C2×C3×C4C2513yes—
992C2×C3×C4C2512yes—
993C2×C3×C4C2516yes—
994C2×C3×C4C2511yescharacteristic
995C2×C3×C4C2513yes—
996C2×C3×C4C2511yescharacteristic
997#67—26no—
998#67—212no—
999#67—26no—
1000#67—212no—
1001#67—212no—
1002#67—212no—
1003#67—412no—
1004#67—412no—
1005#67—46no—
1006#67—412no—
1007C2×Dic3—212no—
1008C2×Dic3—46no—
1009C2×Dic3—46no—
1010C2×Dic3C2511yescharacteristic
1011C2×Dic3C2512yes—
1012C2×Dic3C2511yescharacteristic
1013C2×Dic3C2511yescharacteristic
1014C2×Dic3C2516yes—
1015C2×Dic3C2513yes—
1016C2×Dic3C2513yes—
1017C2×Dic3C2511yescharacteristic
1018C2×Dic3C2512yes—
1019D12—26no—
1020D12—212no—
1021D12—26no—
1022D12—212no—
1023D12—26no—
1024D12—412no—
1025D12—46no—
1026D12—46no—
1027D12C2×#41112yescomplemented
1028C4×D3—26no—
1029C4×D3—212no—
1030C4×D3—26no—
1031C4×D3—26no—
1032C4×D3—212no—
1033C4×D3—212no—
1034C4×D3—46no—
1035C4×D3—46no—
1036C4×D3—412no—
1037C4×D3—46no—
1038C4×D3—46no—
1039C4×D3—43no—
1040C4×D3—43no—
1041C4×D3C2×#41112yescomplemented
1042Dic6—22no—
1043Dic6—24no—
1044Dic6—212no—
1045Dic6—46no—
1046Dic6H(5,𝔽2)14yescomplemented
1047C24—36no—
1048C24—312no—
1049#41—28no—
1050#41—24no—
1051#41—38no—
1052#41—412no—
1053#41—624no—
1054#41—612no—
1055#41—612no—
1056#41—612no—
1057#41—64no—
1058#41—68no—
1059#41—1224no—
1060#41—1224no—
1061#41—1212no—
1062#41—246no—
1063#41—246no—
1064C2×Q8—31no—
1065C2×Q8—32no—
1066C2×Q8—31no—
1067C2×Q8—36no—
1068C2×Q8—36no—
1069C2×Q8—612no—
1070C2×Q8C23×D313yes—
1071C2×Q8C23×D311yescharacteristic
1072C2×D4—33no—
1073C2×D4—36no—
1074C2×D4—33no—
1075C2×D4—36no—
1076C2×D4—36no—
1077C2×D4—36no—
1078C2×D4—312no—
1079C2×D4—312no—
1080C2×D4—36no—
1081C2×D4—312no—
1082C2×D4—33no—
1083C2×D4—36no—
1084C2×D4—33no—
1085C2×D4—36no—
1086C2×D4—33no—
1087C2×D4—33no—
1088C2×D4—36no—
1089C2×D4—36no—
1090C2×D4—312no—
1091C2×D4—624no—
1092C2×D4—612no—
1093C2×D4—624no—
1094C2×D4—612no—
1095C2×D4—624no—
1096C2×D4—612no—
1097C2×D4—1212no—
1098C2×D4—1224no—
1099C2×D4—2412no—
1100C2×D4—246no—
1101C2×D4C23×D316yes—
1102C2×D4C23×D313yes—
1103C2×D4C23×D313yes—
1104C2×D4C23×D316yes—
1105C2×D4C23×D316yes—
1106C2×D4C23×D3112yes—
1107C22×C4—33no—
1108C22×C4—36no—
1109C22×C4—36no—
1110C22×C4—36no—
1111C22×C4—33no—
1112C22×C4—36no—
1113C22×C4—36no—
1114C22×C4—33no—
1115C22×C4—36no—
1116C22×C4—33no—
1117C22×C4—36no—
1118C22×C4—33no—
1119C22×C4—33no—
1120C22×C4—36no—
1121C22×C4—36no—
1122C22×C4—312no—
1123C22×C4—36no—
1124C22×C4—1212no—
1125C22×C4—1224no—
1126C22×C4C23×D316yes—
1127C22×C4C23×D313yes—
1128C22×C4C23×D313yes—
1129C22×C4C23×D313yes—
1130C22×C4C23×D3112yes—
1131C4⋊C4—33no—
1132C4⋊C4—32no—
1133C4⋊C4—33no—
1134C4⋊C4—33no—
1135C4⋊C4—36no—
1136C4⋊C4—33no—
1137C4⋊C4—33no—
1138C4⋊C4—36no—
1139C4⋊C4—33no—
1140C4⋊C4—36no—
1141C4⋊C4—36no—
1142C4⋊C4—31no—
1143C4⋊C4—36no—
1144C4⋊C4—32no—
1145C4⋊C4—32no—
1146C4⋊C4—31no—
1147C4⋊C4—32no—
1148C4⋊C4—31no—
1149C4⋊C4—31no—
1150C4⋊C4—32no—
1151C4⋊C4—32no—
1152C4⋊C4—312no—
1153C4⋊C4C23×D311yescharacteristic
1154C4⋊C4C23×D313yes—
1155C4⋊C4C23×D316yes—
1156C4⋊C4C23×D316yes—
1157C4⋊C4C23×D316yes—
1158C4⋊C4C23×D311yescharacteristic
1159C4⋊C4C23×D313yes—
1160C4⋊C4C23×D312yes—
1161C4⋊C4C23×D316yes—
1162C4⋊C4C23×D312yes—
1163C22⋊C4—33no—
1164C22⋊C4—33no—
1165C22⋊C4—312no—
1166C22⋊C4—36no—
1167C22⋊C4—36no—
1168C22⋊C4—36no—
1169C22⋊C4—33no—
1170C22⋊C4—33no—
1171C22⋊C4—312no—
1172C22⋊C4—36no—
1173C22⋊C4—36no—
1174C22⋊C4—33no—
1175C22⋊C4—36no—
1176C22⋊C4—312no—
1177C22⋊C4—36no—
1178C22⋊C4—33no—
1179C22⋊C4—36no—
1180C22⋊C4—36no—
1181C22⋊C4—36no—
1182C22⋊C4—36no—
1183C22⋊C4—36no—
1184C22⋊C4—36no—
1185C22⋊C4C23×D316yes—
1186C22⋊C4C23×D316yes—
1187C22⋊C4C23×D316yes—
1188C22⋊C4C23×D316yes—
1189C22⋊C4C23×D316yes—
1190C22⋊C4C23×D316yes—
1191C42—33no—
1192C42—32no—
1193C42—32no—
1194C42—31no—
1195C42—36no—
1196C42—32no—
1197C42—31no—
1198C42—36no—
1199C42—33no—
1200C42—36no—
1201C42—33no—
1202C42—36no—
1203C42—33no—
1204C42C23×D313yes—
1205C42C23×D313yes—
1206C42C23×D316yes—
1207C42C23×D311yescharacteristic
1208C42C23×D313yes—
1209C22×C3—26no—
1210C22×C3—23no—
1211C22×C3—26no—
1212C22×C3—23no—
1213C22×C3—26no—
1214C22×C3—23no—
1215C22×C3C2611yescharacteristic
1216C2×D3—23no—
1217C2×D3—23no—
1218C2×D3—26no—
1219C2×D3—23no—
1220C2×D3—26no—
1221C2×D3—23no—
1222C2×D3—26no—
1223C2×D3—23no—
1224C2×D3—824no—
1225C2×D3—812no—
1226C2×D3C22×#4116yes—
1227C3×C4—22no—
1228C3×C4—21no—
1229C3×C4—26no—
1230C3×C4—23no—
1231C3×C4—23no—
1232C3×C4—21no—
1233C3×C4—22no—
1234C3×C4C22×#4116yes—
1235C3×C4C2×H(5,𝔽2)12yes—
1236Dic3—21no—
1237Dic3—22no—
1238Dic3—23no—
1239Dic3—23no—
1240Dic3—26no—
1241Dic3—21no—
1242Dic3—21no—
1243Dic3C22×#4112yes—
1244Dic3C2×H(5,𝔽2)14yes—
1245C23—33no—
1246C23—33no—
1247C23—36no—
1248C23—612no—
1249C23—624no—
1250C23—126no—
1251C23—1212no—
1252C23—126no—
1253C23—1212no—
1254C23C24×D313yes—
1255C23C24×D316yes—
1256Q8—26no—
1257Q8—34no—
1258Q8—612no—
1259Q8—64no—
1260Q8—62no—
1261Q8—126no—
1262Q8D3×#4114yescomplemented
1263D4—212no—
1264D4—26no—
1265D4—26no—
1266D4—312no—
1267D4—412no—
1268D4—46no—
1269D4—46no—
1270D4—612no—
1271D4—66no—
1272D4—66no—
1273D4—612no—
1274D4—612no—
1275D4—612no—
1276D4—66no—
1277D4—612no—
1278D4—612no—
1279D4—66no—
1280D4—66no—
1281D4—1212no—
1282D4—126no—
1283D4—126no—
1284D4—1212no—
1285D4—126no—
1286D4—1212no—
1287D4—1212no—
1288C2×C4—212no—
1289C2×C4—26no—
1290C2×C4—26no—
1291C2×C4—31no—
1292C2×C4—32no—
1293C2×C4—312no—
1294C2×C4—31no—
1295C2×C4—31no—
1296C2×C4—32no—
1297C2×C4—36no—
1298C2×C4—33no—
1299C2×C4—31no—
1300C2×C4—33no—
1301C2×C4—412no—
1302C2×C4—43no—
1303C2×C4—612no—
1304C2×C4—612no—
1305C2×C4—612no—
1306C2×C4—66no—
1307C2×C4—612no—
1308C2×C4—66no—
1309C2×C4—66no—
1310C2×C4—126no—
1311C2×C4—126no—
1312C2×C4—1212no—
1313C2×C4—123no—
1314C2×C4—126no—
1315C2×C4—126no—
1316C2×C4—123no—
1317C2×C4—126no—
1318C2×C4—126no—
1319C2×C4C24×D312yes—
1320C2×C4C24×D311yescharacteristic
1321C2×C4C24×D313yes—
1322C2×C4C24×D313yes—
1323C2×C4C24×D312yes—
1324C2×C4C24×D316yes—
1325C2×C4C24×D311yescharacteristic
1326C2×C4C24×D313yes—
1327C2×C4C24×D311yescharacteristic
1328C2×C3—46no—
1329C2×C3—43no—
1330C2×C3C23×#4111yescharacteristic
1331C2×C3C22×H(5,𝔽2)11yescharacteristic
1332C2×C3H(7,𝔽2)11yescharacteristic
1333D3—26no—
1334D3—46no—
1335D3—43no—
1336C22—23no—
1337C22—26no—
1338C22—23no—
1339C22—26no—
1340C22—23no—
1341C22—26no—
1342C22—36no—
1343C22—63no—
1344C22—63no—
1345C22—63no—
1346C22—66no—
1347C22—66no—
1348C22—63no—
1349C22—63no—
1350C22—66no—
1351C22—2412no—
1352C22—2424no—
1353C22C25×D311yescharacteristic
1354C4—22no—
1355C4—21no—
1356C4—23no—
1357C4—26no—
1358C4—21no—
1359C4—23no—
1360C4—22no—
1361C4—32no—
1362C4—34no—
1363C4—61no—
1364C4—62no—
1365C4—63no—
1366C4—63no—
1367C4—61no—
1368C4—61no—
1369C4—66no—
1370C4C2×D3×#4116yes—
1371C4D3×H(5,𝔽2)12yes—
1372C3#6298611yescharacteristic, complemented, Sylow
1373C2—43no—
1374C2—46no—
1375C2—66no—
1376C2—126no—
1377C2—123no—
1378C2C22×D3×#4111yescharacteristic
1379C2C2×D3×H(5,𝔽2)11yescharacteristic
1380C2#8757411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3517C2
hypercenter#3517D3
hypocenterC3#62986
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. C3×#3517C2semidirect
2. #87023C2semidirect
3. #87015C2semidirect
4. #86913C2semidirect
5. #86888C2semidirect
6. D3×#550C2semidirect
7. #86775C2semidirect
8. #86772C2semidirect
9. #86770C2semidirect
10. #86770C2semidirect
11. #86768C2semidirect
12. #86703C2semidirect
13. #86674C2semidirect
14. #86488C2semidirect
15. #86486C2semidirect
16. #86245C2semidirect
17. #86238C2semidirect
18. #86166C2semidirect
19. #86152C2semidirect
20. #85896C2semidirect
21. #85886C2semidirect
22. #85845C2semidirect
23. C4×#1009C2semidirect
27. C2×D3×#41C22semidirect
28. C3×#557C22semidirect
29. C3×#553C22semidirect
30. C3×#550C22semidirect
31. C3×#550C22semidirect
32. C3×#550C22semidirect
33. C3×#547C22semidirect
34. C3×#540C22semidirect
35. C3×#532C22semidirect
36. C3×#529C22semidirect
37. C3×#520C22semidirect
38. C3×C4×#41C22semidirect
39. #5834C22semidirect
40. #5834C22semidirect
41. #5834C22semidirect
42. #5834C22semidirect
43. #5829C22semidirect
44. #5828C22semidirect
45. #5827C22semidirect
46. Dic3×#41C22semidirect
47. #5728C22semidirect
48. #5727C22semidirect
49. #5726C22semidirect
50. #5725C22semidirect
51. #5719C22semidirect
52. #5718C22semidirect
53. #5718C22semidirect
54. #5717C22semidirect
55. #5717C22semidirect
56. #5716C22semidirect
57. D3×#127C22semidirect
58. D3×#127C22semidirect
59. #5709C22semidirect
60. #5704C22semidirect
61. #5702C22semidirect
62. #5697C22semidirect
63. #5695C22semidirect
64. #5695C22semidirect
65. #5690C22semidirect
66. #5688C22semidirect
67. #5685C22semidirect
68. #5681C22semidirect
69. #5677C22semidirect
70. #5676C22semidirect
71. #5664C22semidirect
72. #5664C22semidirect
73. #5661C22semidirect
74. #5657C22semidirect
75. #5656C22semidirect
76. #5654C22semidirect
77. #5654C22semidirect
78. #5641C22semidirect
79. #5633C22semidirect
80. #5627C22semidirect
81. #5619C22semidirect
82. #5616C22semidirect
83. #5614C22semidirect
84. #5614C22semidirect
85. #5613C22semidirect
86. #5612C22semidirect
87. #5611C22semidirect
88. #5610C22semidirect
89. #5610C22semidirect
90. #5609C22semidirect
91. #5609C22semidirect
92. #5609C22semidirect
93. #5607C22semidirect
94. #5607C22semidirect
95. #5607C22semidirect
96. D3×#121C22semidirect
97. D3×#121C22semidirect
98. #5599C22semidirect
99. #5599C22semidirect
100. #5599C22semidirect
101. #5596C22semidirect
102. #5596C22semidirect
103. #5580C22semidirect
104. #5579C22semidirect
105. #5577C22semidirect
106. #5577C22semidirect
107. #5577C22semidirect
109. #5574C22semidirect
110. #5574C22semidirect
113. C4×#239C22semidirect
114. C4×#239C22semidirect
115. C4×D3×Q8C22semidirect
116. #5569C22semidirect
117. Q8×Dic6C22semidirect
118. #5565C22semidirect
119. #5563C22semidirect
120. #5563C22semidirect
121. #5562C22semidirect
122. #5559C22semidirect
123. #5558C22semidirect
124. #5554C22semidirect
125. #5553C22semidirect
126. #5553C22semidirect
127. D4×D12C22semidirect
128. D4×D12C22semidirect
129. #5548C22semidirect
130. #5548C22semidirect
131. #5548C22semidirect
132. #5548C22semidirect
133. #5547C22semidirect
134. #5545C22semidirect
135. #5545C22semidirect
136. #5545C22semidirect
137. #5545C22semidirect
138. C4×D3×D4C22semidirect
139. C4×D3×D4C22semidirect
140. C4×D3×D4C22semidirect
141. C4×D3×D4C22semidirect
142. #5538C22semidirect
143. C4×#237C22semidirect
144. #5535C22semidirect
145. #5532C22semidirect
146. #5528C22semidirect
147. #5523C22semidirect
148. #5522C22semidirect
149. #5521C22semidirect
150. #5521C22semidirect
151. #5514C22semidirect
152. #5507C22semidirect
153. #5504C22semidirect
154. C2×#893C22semidirect
155. #5477C22semidirect
156. C4×#235C22semidirect
157. C4×#235C22semidirect
158. C2×C4×D12C22semidirect
166. #3517D3semidirect
435. #557C2×D3semidirect
453. #553C2×D3semidirect
468. #550C2×D3semidirect
469. #550C2×D3semidirect
470. #550C2×D3semidirect
477. #547C2×D3semidirect
498. #540C2×D3semidirect
516. #532C2×D3semidirect
522. #529C2×D3semidirect
535. #520C2×D3semidirect
551. C4×#41C2×D3semidirect
593. #239#41semidirect
976. C3×Q8C2×#41semidirect
1027. D12C2×#41semidirect
1041. C4×D3C2×#41semidirect
1046. Dic6H(5,𝔽2)semidirect
1262. Q8D3×#41semidirect
1372. C3#62986semidirect

Maximal subgroups

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

subgroupindex
C3×#35172
#870232
#870152
#869132
#868882
D3×#5502
#867752
#867722
#867702
#867682
#867032
#866742
#864882
#864862
#862452
#862382
#861662
#861522
#858962
#858862
#858452
C4×#10092
#629863