Finite Group Databasebeta

← #7674843

Subgroups — #7674843

Order 512.

4720 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59664C214yesmaximal, complemented
2#59662C214yesmaximal, complemented
3#59661C214yesmaximal, complemented
4#59325C214yesmaximal, complemented
5#43557C214yesmaximal, complemented
6#43557C214yesmaximal, complemented
7#43556C214yesmaximal, complemented
8#43129C214yesmaximal, complemented
9#39679C212yesmaximal, complemented
10#39679C212yesmaximal, complemented
11#39678C212yesmaximal, complemented
12#39676C212yesmaximal, complemented
13#39640C212yesmaximal, complemented
14#39636C212yesmaximal, complemented
15#36571C212yesmaximal, complemented
16#36552C212yesmaximal, complemented
17#35391C212yesmaximal
18#35368C212yesmaximal
19#35002C211yesmaximal, characteristic
20#34994C211yesmaximal, characteristic
21#34994C211yesmaximal, characteristic
22C2×#2505C212yesmaximal
23#34270C212yesmaximal
24#34270C211yesmaximal, characteristic
25#34270C211yesmaximal, characteristic
26C2×#2368C211yesmaximal, characteristic
27C4×#543C211yesmaximal, characteristic
28C2×#543C2212yes—
29C2×#543C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31#2857C2212yes—
32#2857C2212yes—
33#2851C2212yes—
34#2851C2212yes—
35#2851C2212yes—
36#2851C2212yes—
37#2809C2214yescomplemented
38#2809C2214yescomplemented
39#2806C2214yescomplemented
40#2805C2214yescomplemented
41#2805C2214yescomplemented
42#2805C2214yescomplemented
43#2802C2214yescomplemented
44#2802C2214yescomplemented
45#2799C2214yescomplemented
46#2799C2214yescomplemented
47#2799C2214yescomplemented
48#2791C2214yescomplemented
49#2791C2214yescomplemented
50#2791C2214yescomplemented
51#2774C2214yescomplemented
52#2774C2214yescomplemented
53#2774C2214yescomplemented
54#2774C2214yescomplemented
55#2755C2214yescomplemented
56#2755C2214yescomplemented
57#2755C2214yescomplemented
58#2713C2214yescomplemented
59#2713C2214yescomplemented
60#2713C2214yescomplemented
61#2659C2212yes—
62#2659C2212yes—
63#2646C2212yes—
64#2646C2212yes—
65#2646C2212yes—
66#2646C2212yes—
67#2590C2214yescomplemented
68#2590C2214yescomplemented
69#2590C2214yescomplemented
70#2590C2214yescomplemented
71#2588C2214yescomplemented
72#2588C2214yescomplemented
73#2588C2214yescomplemented
74#2585C2214yescomplemented
75#2585C2214yescomplemented
76#2585C2214yescomplemented
77#2583C2214yes—
78#2583C2214yes—
79#2581C2214yescomplemented
80#2581C2214yescomplemented
81#2569C2214yes—
82#2569C2214yes—
83#2568C2212yescomplemented
84#2568C2214yescomplemented
85#2565C2212yescomplemented
86#2565C2214yescomplemented
87#2552C2212yescomplemented
88#2550C2212yescomplemented
89#2550C2214yescomplemented
90#2549C2214yes—
91#2549C2214yes—
92#2549C2214yes—
93#2549C2214yes—
94#2549C2214yes—
95#2549C2214yes—
96#2546C2214yescomplemented
97#2520C2214yescomplemented
98#2520C2214yescomplemented
99#2520C2214yescomplemented
100#2511C2214yescomplemented
101#2511C2214yescomplemented
102#2509C2212yescomplemented
103#2509C2214yescomplemented
104#2508C2214yescomplemented
105#2508C2212yescomplemented
106#2508C2214yescomplemented
107#2508C2212yescomplemented
108#2506C2214yescomplemented
109#2506C2212yescomplemented
110#2505C2214yes—
111#2505C2214yes—
112#2505C2214yes—
113#2505C2214yes—
114#2505C2214yes—
115#2505C2214yes—
116#2505C2214yes—
117#2505C2214yes—
118#2505C2214yes—
119#2505C2214yes—
120#2505C2214yes—
121#2505C2214yes—
122#2505C2214yes—
123#2505C2214yes—
124#2505C2214yes—
125#2505C2214yes—
126#2502C2214yes—
127#2473C2214yes—
128#2473C2214yes—
129#2473C2214yes—
130#2473C2214yes—
131#2473C2214yes—
132#2473C2214yes—
133#2473C2214yes—
134#2473C2214yes—
135#2462C2214yescomplemented
136#2462C2214yescomplemented
137#2453C2212yescomplemented
138#2453C2214yescomplemented
139#2453C2212yescomplemented
140#2453C2212yescomplemented
141#2451C2214yescomplemented
142#2451C2212yescomplemented
143#2446C2214yescomplemented
144#2442C2214yes—
145#2442C2214yes—
146#2440C2214yes—
147#2440C2214yes—
148#2440C2214yes—
149#2440C2214yes—
150#2440C2214yes—
151#2440C2214yes—
152#2434C2214yes—
153C2×#400C2212yes—
154C2×#400C2212yes—
155C2×#400C2212yes—
156C2×#398C2212yes—
157#2370C2214yescomplemented
158#2370C2212yescomplemented
159#2368C2214yes—
160#2368C2214yes—
161#2368C2214yes—
162#2368C2214yes—
163#2368C2214yes—
164#2368C2214yes—
165#2368C2214yes—
166#2368C2214yes—
167#2368C2214yes—
168#2368C2214yes—
169#2368C2214yes—
170#2368C2214yes—
171#2365C2212yescomplemented
172#2360C2214yes—
173#2360C2214yes—
174#2360C2214yes—
175#2360C2214yes—
176#2360C2214yes—
177#2360C2214yes—
178#2360C2214yes—
179#2360C2214yes—
180#2355C2214yescomplemented
181#2351C2212yescomplemented
182Q8×C4⋊C4C2212yescomplemented
183#2329C2214yes—
184#2329C2214yes—
185#2329C2214yes—
186#2329C2214yes—
187#2329C2212yes—
188#2329C2212yes—
189#2329C2212yes—
190#2329C2212yes—
191#2329C2212yes—
192#2329C2212yes—
193#2315C2212yes—
194#2315C2212yes—
195#2315C2212yes—
196#2315C2211yescharacteristic
197#2315C2211yescharacteristic
198#2315C2211yescharacteristic
199C4×C22⋊Q8C2214yes—
200C4×C22⋊Q8C2214yes—
201C4×C22⋊Q8C2214yes—
202C4×C22⋊Q8C2214yes—
203C4×C22⋊Q8C2212yes—
204C4×C22⋊Q8C2212yes—
205C4×C22⋊Q8C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C2×#391C2211yescharacteristic
210C2×#391C2211yescharacteristic
211C2×#389C2212yes—
212C2×#387C2212yes—
213C2×#387C2212yes—
214C2×#387C2211yescharacteristic
215C2×#387C2211yescharacteristic
216C2×#387C2211yescharacteristic
217C2×#387C2211yescharacteristic
218C2×#385C2211yescharacteristic
219C2×#385C2212yes—
220C2×#385C2212yes—
221C2×#385C2212yes—
222C2×#385C2211yescharacteristic
223C2×#385C2212yes—
224C2×#382C2212yes—
225C2×#380C2212yes—
226#2273C2212yes—
227#2273C2212yes—
228C2×C4×C4⋊C4C2211yescharacteristic
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C22⋊C4C2211yescharacteristic
231C2×C4×C22⋊C4C2212yes—
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C22×#95C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C24×C4C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239#543—216no—
240#543Q8116yescomplemented
241C2×C4⋊Q8C2312yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2314yes—
245C2×#125C2312yes—
246C2×#125C2314yes—
247C2×#125C2314yes—
248C2×#125C2312yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×C22⋊Q8—28no—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2314yes—
263C2×C22⋊Q8C2314yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2314yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×Q8C2312yes—
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2312yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2312yes—
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2312yes—
291C22×C22⋊C4C2312yes—
292C22×C22⋊C4C2312yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2312yes—
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#395C2314yes—
366#395C2314yes—
367#395C2314yes—
368#395C2314yes—
369#395C2314yes—
370#395C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2312yes—
380#391C2312yes—
381#391C2314yes—
382#391C2312yes—
383#391C2314yes—
384#391C2314yes—
385#391C2314yes—
386#391C2314yes—
387#391C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2312yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2312yes—
416#389C2314yes—
417#389C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2314yes—
429#389C2314yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#384C2312yes—
554#384C2314yes—
555#384C2312yes—
556#384C2314yes—
557#382C2312yes—
558#382C2314yes—
559#382C2312yes—
560#382C2312yes—
561#382C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2312yes—
566#382C2314yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2314yes—
572#380C2312yes—
573#380C2312yes—
574#380C2312yes—
575#380C2312yes—
576#380C2312yes—
577#380C2312yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2314yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C2×#95C2312yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2311yescharacteristic
636C2×#95C2311yescharacteristic
637C2×#95C2311yescharacteristic
638C2×#95C2311yescharacteristic
639C2×#95C2311yescharacteristic
640C2×#95C2311yescharacteristic
641C2×#95C2311yescharacteristic
642C2×#95C2311yescharacteristic
643C2×#95C2312yes—
644C2×#95C2312yes—
645C2×#95C2312yes—
646C2×#95C2312yes—
647C2×#95C2312yes—
648C2×#95C2312yes—
649C2×#95C2312yes—
650C2×#95C2312yes—
651C2×#95C2312yes—
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C25C2411yescharacteristic
662C22×Q8—24no—
663C22×Q8—81no—
664C22×Q8—81no—
665C22×Q8C2414yes—
666C22×Q8C2414yes—
667C22×Q8C2414yes—
668C22×Q8C2412yes—
669C22×Q8C2412yes—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—42no—
674C23×C4—42no—
675C23×C4—81no—
676C23×C4—81no—
677C23×C4—81no—
678C23×C4—81no—
679C23×C4C2412yes—
680C23×C4C2411yescharacteristic
681C23×C4C2412yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C23×C4C2411yescharacteristic
691C23×C4C2411yescharacteristic
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2412yes—
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C4⋊Q8—44no—
708C4⋊Q8—82no—
709C4⋊Q8—84no—
710C4⋊Q8—84no—
711#125—44no—
712#125—48no—
713#125—82no—
714#125—82no—
715#125—82no—
716#125—84no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8C2×Q8116yes—
726C22⋊Q8C2×Q8116yes—
727C22⋊Q8C2×Q8132yescomplemented
728C22⋊Q8C2×Q8132yescomplemented
729C4×Q8—44no—
730C4×Q8—48no—
731C4×Q8—44no—
732C4×Q8—82no—
733C4×Q8—82no—
734C4×Q8—84no—
735C4×Q8—82no—
736C4×Q8—82no—
737C2×C4⋊C4—24no—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—42no—
741C2×C4⋊C4—44no—
742C2×C4⋊C4—44no—
743C2×C4⋊C4—42no—
744C2×C4⋊C4—44no—
745C2×C4⋊C4—81no—
746C2×C4⋊C4—82no—
747C2×C4⋊C4—82no—
748C2×C4⋊C4—82no—
749C2×C4⋊C4—82no—
750C2×C4⋊C4—81no—
751C2×C4⋊C4—82no—
752C2×C4⋊C4—82no—
753C2×C4⋊C4—82no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C22⋊C4—24no—
820C2×C22⋊C4—28no—
821C2×C22⋊C4—28no—
822C2×C22⋊C4—28no—
823C2×C22⋊C4—24no—
824C2×C22⋊C4C2×Q8116yes—
825C2×C22⋊C4C2×Q818yes—
826C2×C22⋊C4#4118yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C42—44no—
840C2×C42—42no—
841C2×C42—42no—
842C2×C42—82no—
843C2×C42—81no—
844C2×C42—81no—
845C2×C42—81no—
846C2×C42—81no—
847C2×C42C2414yes—
848C2×C42C2412yes—
849C2×C42C2412yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2412yes—
859C2×C42C2412yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2412yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871#95C2411yescharacteristic
872#95C2411yescharacteristic
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2412yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2412yes—
892#95C2414yes—
893#95C2412yes—
894#95C2414yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2412yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943C24—41no—
944C24—41no—
945C24—41no—
946C24—41no—
947C24C22×Q814yes—
948C24C2×#4114yes—
949C242−1+414yes—
950C24C2511yescharacteristic
951C24C2512yes—
952C2×Q8—28no—
953C2×Q8—28no—
954C2×Q8—28no—
955C2×Q8—42no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—44no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—44no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—88no—
966C2×Q8C22×Q818yes—
967C2×Q8C22×Q818yes—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—24no—
973C22×C4—22no—
974C22×C4—24no—
975C22×C4—22no—
976C22×C4—24no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—22no—
985C22×C4—22no—
986C22×C4—22no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—22no—
993C22×C4—24no—
994C22×C4—42no—
995C22×C4—41no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—41no—
1004C22×C4—41no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—42no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—42no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—42no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—41no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—41no—
1046C22×C4—88no—
1047C22×C4—88no—
1048C22×C4—88no—
1049C22×C4C22×Q814yes—
1050C22×C4C22×Q814yes—
1051C22×C4C22×Q818yes—
1052C22×C4C22×Q818yes—
1053C22×C4C2×#4114yes—
1054C22×C4C2×#4114yes—
1055C22×C4C2511yescharacteristic
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4C22×Q818yes—
1142C4⋊C4C22×Q8116yes—
1143C4⋊C4C22×Q8116yes—
1144C4⋊C4C22×Q818yes—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4C22×Q8116yes—
1154C22⋊C4C22×Q8116yes—
1155C22⋊C4C22×Q8116yes—
1156C22⋊C4C2×#41116yes—
1157C42—28no—
1158C42—24no—
1159C42—24no—
1160C42—44no—
1161C42—42no—
1162C42—42no—
1163C42—44no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42—42no—
1171C42—42no—
1172C42—42no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—44no—
1180C42—44no—
1181C23—21no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—22no—
1188C23—22no—
1189C23—44no—
1190C23—44no—
1191C23—44no—
1192C23—44no—
1193C23—44no—
1194C23—44no—
1195C23#557116yes—
1196C23C23×Q812yes—
1197C23C23×Q814yes—
1198C23C22×#4112yes—
1199C23C22×#4114yes—
1200C23C2×2−1+412yes—
1201C23C2×2−1+414yes—
1202C23C2611yescharacteristic
1203Q8—48no—
1204Q8—48no—
1205Q8—88no—
1206Q8—88no—
1207Q8—88no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—44no—
1276C2×C4—44no—
1277C2×C4—48no—
1278C2×C4—48no—
1279C2×C4—44no—
1280C2×C4—44no—
1281C2×C4—48no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—48no—
1285C2×C4—44no—
1286C2×C4—44no—
1287C2×C4—44no—
1288C2×C4—44no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—84no—
1292C2×C4—84no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—82no—
1300C2×C4—84no—
1301C2×C4—84no—
1302C2×C4—82no—
1303C2×C4C23×Q818yes—
1304C2×C4C23×Q818yes—
1305C2×C4C23×Q814yes—
1306C2×C4C23×Q814yes—
1307C2×C4C22×#4114yes—
1308C2×C4C22×#4114yes—
1309C2×C4#58512yes—
1310C2×C4#58512yes—
1311C22—22no—
1312C22—22no—
1313C22—24no—
1314C22—24no—
1315C22—22no—
1316C22—24no—
1317C22—22no—
1318C22—24no—
1319C22—22no—
1320C22—22no—
1321C22—24no—
1322C22—24no—
1323C22—416no—
1324C22C2×#55714yes—
1325C22C2×#55718yes—
1326C22C24×Q811yescharacteristic
1327C22C23×#4111yescharacteristic
1328C22C22×2−1+411yescharacteristic
1329C22C2×#58511yescharacteristic
1330C22C2×#58511yescharacteristic
1331C22H(7,𝔽2)11yescharacteristic
1332C22H(7,𝔽2)11yescharacteristic
1333C4—28no—
1334C4—24no—
1335C4—24no—
1336C4—28no—
1337C4—24no—
1338C4—24no—
1339C4—22no—
1340C4—22no—
1341C4—42no—
1342C4—44no—
1343C4—44no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—44no—
1350C4—42no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—42no—
1355C4—42no—
1356C4—44no—
1357C4—44no—
1358C2—24no—
1359C2—28no—
1360C2C22×#55711yescharacteristic
1361C2#6278111yescharacteristic
1362C2#6284611yescharacteristic
1363C2#6290311yescharacteristic
1364C2#6290311yescharacteristic
1365C2#6298911yescharacteristic
1366C2#6298911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59664C2semidirect
2. #59662C2semidirect
3. #59661C2semidirect
4. #59325C2semidirect
5. #43557C2semidirect
6. #43557C2semidirect
7. #43556C2semidirect
8. #43129C2semidirect
9. #39679C2semidirect
10. #39679C2semidirect
11. #39678C2semidirect
12. #39676C2semidirect
13. #39640C2semidirect
14. #39636C2semidirect
15. #36571C2semidirect
16. #36552C2semidirect
37. #2809C22semidirect
38. #2809C22semidirect
39. #2806C22semidirect
40. #2805C22semidirect
41. #2805C22semidirect
42. #2805C22semidirect
43. #2802C22semidirect
44. #2802C22semidirect
45. #2799C22semidirect
46. #2799C22semidirect
47. #2799C22semidirect
48. #2791C22semidirect
49. #2791C22semidirect
50. #2791C22semidirect
51. #2774C22semidirect
52. #2774C22semidirect
53. #2774C22semidirect
54. #2774C22semidirect
55. #2755C22semidirect
56. #2755C22semidirect
57. #2755C22semidirect
58. #2713C22semidirect
59. #2713C22semidirect
60. #2713C22semidirect
67. #2590C22semidirect
68. #2590C22semidirect
69. #2590C22semidirect
70. #2590C22semidirect
71. #2588C22semidirect
72. #2588C22semidirect
73. #2588C22semidirect
74. #2585C22semidirect
75. #2585C22semidirect
76. #2585C22semidirect
79. #2581C22semidirect
80. #2581C22semidirect
83. #2568C22semidirect
84. #2568C22semidirect
85. #2565C22semidirect
86. #2565C22semidirect
87. #2552C22semidirect
88. #2550C22semidirect
89. #2550C22semidirect
96. #2546C22semidirect
97. #2520C22semidirect
98. #2520C22semidirect
99. #2520C22semidirect
100. #2511C22semidirect
101. #2511C22semidirect
102. #2509C22semidirect
103. #2509C22semidirect
104. #2508C22semidirect
105. #2508C22semidirect
106. #2508C22semidirect
107. #2508C22semidirect
108. #2506C22semidirect
109. #2506C22semidirect
135. #2462C22semidirect
136. #2462C22semidirect
137. #2453C22semidirect
138. #2453C22semidirect
139. #2453C22semidirect
140. #2453C22semidirect
141. #2451C22semidirect
142. #2451C22semidirect
143. #2446C22semidirect
157. #2370C22semidirect
158. #2370C22semidirect
171. #2365C22semidirect
180. #2355C22semidirect
181. #2351C22semidirect
182. Q8×C4⋊C4C22semidirect
240. #543Q8semidirect
727. C22⋊Q8C2×Q8semidirect
728. C22⋊Q8C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#596642
#596622
#596612
#593252
#435572
#435562
#431292
#396792
#396782
#396762
#396402
#396362
#365712
#365522
#353912
#353682
#350022
#349942
C2×#25052
#342702
C2×#23682
C4×#5432