Finite Group Databasebeta

← #7672917

Subgroups — #7672917

Order 512.

4664 conjugacy classes of subgroups.

The subgroup lattice has 1391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43557C214yesmaximal, complemented
2#43556C214yesmaximal, complemented
3#43130C214yesmaximal, complemented
4#43129C214yesmaximal, complemented
5#39679C212yesmaximal, complemented
6#39678C212yesmaximal, complemented
7#39677C212yesmaximal, complemented
8#39676C212yesmaximal, complemented
9#39640C212yesmaximal, complemented
10#39639C212yesmaximal, complemented
11#39636C212yesmaximal, complemented
12#39636C212yesmaximal, complemented
13#39179C214yesmaximal, complemented
14#39178C214yesmaximal, complemented
15#39175C214yesmaximal, complemented
16#39175C214yesmaximal, complemented
17#35391C212yesmaximal
18#35368C212yesmaximal
19#35020C211yesmaximal, characteristic
20#35002C211yesmaximal, characteristic
21#34994C212yesmaximal
22C2×#2646C211yesmaximal, characteristic
23#34270C212yesmaximal
24#34212C211yesmaximal, characteristic
25#34212C211yesmaximal, characteristic
26C2×#2329C211yesmaximal, characteristic
27C2×#2329C211yesmaximal, characteristic
28C2×#543C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31#2857C2212yes—
32#2857C2212yes—
33#2851C2214yes—
34#2851C2214yes—
35#2851C2212yes—
36#2851C2212yes—
37#2809C2214yescomplemented
38#2809C2214yescomplemented
39#2806C2214yescomplemented
40#2806C2214yescomplemented
41#2805C2214yescomplemented
42#2805C2214yescomplemented
43#2802C2214yescomplemented
44#2802C2214yescomplemented
45#2802C2214yescomplemented
46#2802C2214yescomplemented
47#2799C2214yescomplemented
48#2799C2214yescomplemented
49#2799C2214yescomplemented
50#2799C2214yescomplemented
51#2791C2214yescomplemented
52#2791C2214yescomplemented
53#2791C2214yescomplemented
54#2791C2214yescomplemented
55#2774C2214yescomplemented
56#2774C2214yescomplemented
57#2774C2214yescomplemented
58#2774C2214yescomplemented
59#2755C2214yescomplemented
60#2755C2214yescomplemented
61#2755C2214yescomplemented
62#2755C2214yescomplemented
63#2726C2214yescomplemented
64#2726C2214yescomplemented
65#2713C2214yescomplemented
66#2713C2214yescomplemented
67#2713C2214yescomplemented
68#2713C2214yescomplemented
69#2659C2212yes—
70#2659C2212yes—
71#2646C2214yes—
72#2646C2214yes—
73#2646C2212yes—
74#2646C2212yes—
75#2646C2212yes—
76#2646C2212yes—
77#2646C2214yes—
78#2646C2214yes—
79#2646C2212yes—
80#2646C2212yes—
81#2590C2214yescomplemented
82#2590C2214yescomplemented
83#2588C2214yescomplemented
84#2588C2214yescomplemented
85#2585C2214yescomplemented
86#2585C2214yescomplemented
87#2585C2214yescomplemented
88#2585C2214yescomplemented
89#2584C2214yescomplemented
90#2583C2214yes—
91#2583C2214yes—
92#2582C2214yescomplemented
93#2581C2214yescomplemented
94#2569C2214yes—
95#2569C2214yes—
96#2569C2214yes—
97#2569C2214yes—
98#2568C2214yescomplemented
99#2565C2214yescomplemented
100#2552C2214yescomplemented
101#2550C2214yescomplemented
102#2549C2214yes—
103#2549C2214yes—
104#2549C2214yes—
105#2549C2214yes—
106#2549C2214yes—
107#2549C2214yes—
108#2546C2214yescomplemented
109#2520C2214yescomplemented
110#2520C2214yescomplemented
111#2511C2214yescomplemented
112#2511C2214yescomplemented
113#2509C2214yescomplemented
114#2509C2214yescomplemented
115#2508C2214yescomplemented
116#2506C2214yescomplemented
117#2505C2214yes—
118#2505C2214yes—
119#2505C2214yes—
120#2505C2214yes—
121#2505C2214yes—
122#2505C2214yes—
123#2505C2214yes—
124#2505C2214yes—
125#2502C2214yes—
126#2473C2214yes—
127#2473C2214yes—
128#2473C2214yes—
129#2473C2214yes—
130#2473C2214yes—
131#2473C2214yes—
132#2473C2214yes—
133#2473C2214yes—
134#2462C2214yescomplemented
135#2462C2214yescomplemented
136#2453C2214yescomplemented
137#2453C2214yescomplemented
138#2453C2214yescomplemented
139#2451C2214yescomplemented
140#2446C2214yescomplemented
141#2446C2214yescomplemented
142#2442C2212yes—
143#2442C2214yes—
144#2442C2212yes—
145#2442C2214yes—
146#2442C2212yes—
147#2442C2212yes—
148#2440C2212yes—
149#2440C2214yes—
150#2440C2212yes—
151#2440C2214yes—
152#2440C2212yes—
153#2440C2214yes—
154#2440C2214yes—
155#2440C2212yes—
156#2434C2214yes—
157C2×#400C2212yes—
158C2×#400C2212yes—
159C2×#398C2212yes—
160C2×#398C2212yes—
161#2368C2214yes—
162#2368C2214yes—
163#2368C2214yes—
164#2368C2214yes—
165#2368C2214yes—
166#2368C2214yes—
167#2360C2212yes—
168#2360C2214yes—
169#2360C2212yes—
170#2360C2212yes—
171#2360C2214yes—
172#2360C2212yes—
173#2360C2214yes—
174#2360C2214yes—
175#2345C2212yes—
176#2345C2212yes—
177#2345C2214yes—
178#2345C2214yes—
179Q8×C22⋊C4C2212yes—
180Q8×C22⋊C4C2212yes—
181#2329C2214yes—
182#2329C2214yes—
183#2329C2214yes—
184#2329C2214yes—
185#2329C2214yes—
186#2329C2214yes—
187#2329C2214yes—
188#2329C2214yes—
189#2329C2212yes—
190#2329C2212yes—
191#2329C2212yes—
192#2329C2212yes—
193#2329C2212yes—
194#2329C2212yes—
195#2329C2212yes—
196#2329C2212yes—
197#2315C2212yes—
198#2315C2212yes—
199#2315C2212yes—
200#2315C2212yes—
201#2315C2212yes—
202C4×C22⋊Q8C2214yes—
203C4×C22⋊Q8C2214yes—
204C4×C22⋊Q8C2212yes—
205C4×C22⋊Q8C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C2×#391C2212yes—
209C2×#391C2211yescharacteristic
210C2×#391C2211yescharacteristic
211C2×#389C2212yes—
212C2×#389C2211yescharacteristic
213C2×#389C2211yescharacteristic
214C2×#387C2212yes—
215C2×#387C2212yes—
216C2×#387C2211yescharacteristic
217C2×#387C2211yescharacteristic
218C2×#387C2211yescharacteristic
219C2×#387C2211yescharacteristic
220C2×#385C2212yes—
221C2×#385C2212yes—
222C2×#385C2212yes—
223C2×#385C2211yescharacteristic
224C2×#385C2211yescharacteristic
225C2×#380C2211yescharacteristic
226C2×#380C2211yescharacteristic
227C2×#380C2211yescharacteristic
228C2×#380C2211yescharacteristic
229#2273C2212yes—
230#2273C2212yes—
231C2×C4×C22⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2212yes—
234C22×#95C2211yescharacteristic
235C23×Q8C2311yescharacteristic
236C23×Q8C2311yescharacteristic
237C24×C4C2311yescharacteristic
238C24×C4C2311yescharacteristic
239C24×C4C2311yescharacteristic
240#543—216no—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2314yes—
245C2×#125C2314yes—
246C2×#125C2314yes—
247C2×#125C2312yes—
248C2×#125C2312yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×C22⋊Q8—28no—
252C2×C22⋊Q8Q8116yescomplemented
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2314yes—
260C2×C22⋊Q8C2314yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×Q8C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2312yes—
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2312yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2312yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2312yes—
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2311yescharacteristic
302C22×C42C2312yes—
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
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#400C2314yes—
334#400C2314yes—
335#400C2314yes—
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#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#391C2314yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#391C2314yes—
393#391C2314yes—
394#391C2314yes—
395#391C2314yes—
396#391C2314yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2314yes—
407#391C2314yes—
408#391C2314yes—
409#391C2312yes—
410#391C2312yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2312yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
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#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
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#385C2314yes—
554#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#384C2314yes—
561#384C2312yes—
562#384C2312yes—
563#384C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2312yes—
567#382C2312yes—
568#382C2314yes—
569#382C2314yes—
570#380C2314yes—
571#380C2312yes—
572#380C2314yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2314yes—
583#380C2312yes—
584#380C2312yes—
585#380C2312yes—
586#380C2312yes—
587#380C2312yes—
588#380C2314yes—
589#380C2312yes—
590#380C2312yes—
591#380C2312yes—
592#380C2312yes—
593#380C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2314yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2314yes—
614C4×C22⋊C4C2312yes—
615C4×C22⋊C4C2312yes—
616C4×C22⋊C4C2312yes—
617C4×C22⋊C4C2312yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2312yes—
623C4×C22⋊C4C2312yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2314yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2312yes—
636C2×#95C2312yes—
637C2×#95C2312yes—
638C2×#95C2311yescharacteristic
639C2×#95C2311yescharacteristic
640C2×#95C2312yes—
641C2×#95C2312yes—
642C2×#95C2311yescharacteristic
643C2×#95C2311yescharacteristic
644C2×#95C2311yescharacteristic
645C2×#95C2312yes—
646C2×#95C2311yescharacteristic
647C2×#95C2312yes—
648C2×#95C2311yescharacteristic
649C2×#95C2311yescharacteristic
650C2×#95C2311yescharacteristic
651C2×#95C2311yescharacteristic
652C2×#95C2312yes—
653C2×#95C2312yes—
654C2×#95C2312yes—
655C2×#95C2312yes—
656C2×#95C2312yes—
657C2×#95C2311yescharacteristic
658C2×#95C2311yescharacteristic
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C25C2411yescharacteristic
662C22×Q8—24no—
663C22×Q8—81no—
664C22×Q8—81no—
665C22×Q8—81no—
666C22×Q8—81no—
667C22×Q8C2×Q818yescomplemented
668C22×Q8C2414yes—
669C22×Q8C2414yes—
670C22×Q8C2414yes—
671C22×Q8C2412yes—
672C22×Q8C2412yes—
673C23×C4—24no—
674C23×C4—24no—
675C23×C4—81no—
676C23×C4—81no—
677C23×C4—81no—
678C23×C4—81no—
679C23×C4—81no—
680C23×C4—81no—
681C23×C4C2×Q818yes—
682C23×C4C2412yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2412yes—
689C23×C4C2411yescharacteristic
690C23×C4C2412yes—
691C23×C4C2412yes—
692C23×C4C2411yescharacteristic
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2412yes—
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2412yes—
700C23×C4C2411yescharacteristic
701C23×C4C2412yes—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2411yescharacteristic
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C4⋊Q8—82no—
713C4⋊Q8—82no—
714C4⋊Q8—84no—
715C4⋊Q8—84no—
716#125—82no—
717#125—84no—
718#125—82no—
719#125—84no—
720#125—84no—
721#125—84no—
722C22⋊Q8—216no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—216no—
726C22⋊Q8—216no—
727C22⋊Q8—216no—
728C22⋊Q8—216no—
729C22⋊Q8—216no—
730C22⋊Q8C2×Q8116yes—
731C22⋊Q8C2×Q8116yes—
732C22⋊Q8C2×Q8116yescomplemented
733C22⋊Q8C2×Q8116yescomplemented
734C4×Q8—84no—
735C4×Q8—82no—
736C4×Q8—82no—
737C4×Q8—82no—
738C4×Q8—84no—
739C4×Q8—82no—
740C2×C4⋊C4—24no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—24no—
743C2×C4⋊C4—81no—
744C2×C4⋊C4—81no—
745C2×C4⋊C4—81no—
746C2×C4⋊C4—81no—
747C2×C4⋊C4—82no—
748C2×C4⋊C4—82no—
749C2×C4⋊C4—81no—
750C2×C4⋊C4—81no—
751C2×C4⋊C4—81no—
752C2×C4⋊C4—81no—
753C2×C4⋊C4—81no—
754C2×C4⋊C4—81no—
755C2×C4⋊C4—82no—
756C2×C4⋊C4—81no—
757C2×C4⋊C4—81no—
758C2×C4⋊C4—82no—
759C2×C4⋊C4—82no—
760C2×C4⋊C4—82no—
761C2×C4⋊C4C2×Q818yescomplemented
762C2×C4⋊C4C2×Q8116yescomplemented
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⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C22⋊C4—24no—
827C2×C22⋊C4—28no—
828C2×C22⋊C4—28no—
829C2×C22⋊C4—24no—
830C2×C22⋊C4—28no—
831C2×C22⋊C4—24no—
832C2×C22⋊C4C2×Q8116yes—
833C2×C22⋊C4#4118yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C42—82no—
851C2×C42—81no—
852C2×C42—82no—
853C2×C42—81no—
854C2×C42—81no—
855C2×C42—81no—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2414yes—
862C2×C42C2414yes—
863C2×C42C2412yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876#95C2412yes—
877#95C2412yes—
878#95C2412yes—
879#95C2412yes—
880#95C2412yes—
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2414yes—
887#95C2414yes—
888#95C2412yes—
889#95C2412yes—
890#95C2412yes—
891#95C2412yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
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—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948C24—41no—
949C24—41no—
950C24—41no—
951C24—41no—
952C24C22×Q814yes—
953C24C2×#4114yes—
954C242−1+414yes—
955C24C2511yescharacteristic
956C24C2511yescharacteristic
957C24C2511yescharacteristic
958C2×Q8—28no—
959C2×Q8—28no—
960C2×Q8—28no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—44no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—44no—
970C2×Q8—44no—
971C2×Q8—88no—
972C2×Q8—88no—
973C2×Q8C22×Q818yes—
974C2×Q8C22×Q818yes—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—24no—
980C22×C4—24no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—24no—
984C22×C4—24no—
985C22×C4—24no—
986C22×C4—24no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—24no—
990C22×C4—22no—
991C22×C4—22no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—24no—
995C22×C4—42no—
996C22×C4—41no—
997C22×C4—41no—
998C22×C4—41no—
999C22×C4—41no—
1000C22×C4—41no—
1001C22×C4—41no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—42no—
1005C22×C4—41no—
1006C22×C4—41no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—41no—
1010C22×C4—41no—
1011C22×C4—41no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—42no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—42no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—41no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—41no—
1039C22×C4—42no—
1040C22×C4—41no—
1041C22×C4—42no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—42no—
1045C22×C4—41no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—41no—
1051C22×C4—42no—
1052C22×C4—42no—
1053C22×C4—41no—
1054C22×C4—42no—
1055C22×C4—88no—
1056C22×C4—88no—
1057C22×C4—88no—
1058C22×C4C22×Q818yes—
1059C22×C4C22×Q818yes—
1060C22×C4C22×Q814yes—
1061C22×C4C22×Q814yes—
1062C22×C4C22×Q814yes—
1063C22×C4C22×Q814yes—
1064C22×C4C22×Q814yes—
1065C22×C4C22×Q814yes—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4114yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2511yescharacteristic
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4C22×Q818yes—
1152C4⋊C4C22×Q818yes—
1153C4⋊C4C22×Q8116yes—
1154C4⋊C4C22×Q8116yes—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—24no—
1162C22⋊C4—24no—
1163C22⋊C4—28no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4C22×Q8116yes—
1168C22⋊C4C22×Q8116yes—
1169C22⋊C4C2×#4118yes—
1170C22⋊C4C2×#4118yes—
1171C42—44no—
1172C42—42no—
1173C42—44no—
1174C42—42no—
1175C42—42no—
1176C42—42no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—21no—
1198C23—21no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—44no—
1204C23—44no—
1205C23—44no—
1206C23—44no—
1207C23—44no—
1208C23—44no—
1209C23#557116yes—
1210C23C23×Q812yes—
1211C23C23×Q812yes—
1212C23C23×Q812yes—
1213C23C22×#4112yes—
1214C23C22×#4112yes—
1215C23C22×#4112yes—
1216C23C2×2−1+412yes—
1217C23C2×2−1+412yes—
1218C23C2×2−1+412yes—
1219C23C2611yescharacteristic
1220Q8—48no—
1221Q8—48no—
1222Q8—88no—
1223Q8—88no—
1224Q8—88no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—24no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—44no—
1290C2×C4—44no—
1291C2×C4—44no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—44no—
1295C2×C4—48no—
1296C2×C4—48no—
1297C2×C4—44no—
1298C2×C4—44no—
1299C2×C4—44no—
1300C2×C4—44no—
1301C2×C4—48no—
1302C2×C4—44no—
1303C2×C4—44no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—84no—
1307C2×C4—84no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—84no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—84no—
1314C2×C4—84no—
1315C2×C4—84no—
1316C2×C4—82no—
1317C2×C4—84no—
1318C2×C4—82no—
1319C2×C4C23×Q818yes—
1320C2×C4C23×Q818yes—
1321C2×C4C23×Q812yes—
1322C2×C4C23×Q812yes—
1323C2×C4C23×Q812yes—
1324C2×C4C23×Q812yes—
1325C2×C4C22×#4114yes—
1326C2×C4C22×#4114yes—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—416no—
1346C22C2×#55714yes—
1347C22C2×#55714yes—
1348C22C2×#55714yes—
1349C22C24×Q811yescharacteristic
1350C22C23×#4111yescharacteristic
1351C22C22×2−1+411yescharacteristic
1352C22H(7,𝔽2)11yescharacteristic
1353C22H(7,𝔽2)11yescharacteristic
1354C22H(7,𝔽2)11yescharacteristic
1355C222−1+611yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—22no—
1360C4—28no—
1361C4—24no—
1362C4—24no—
1363C4—28no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—44no—
1368C4—44no—
1369C4—42no—
1370C4—44no—
1371C4—44no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—44no—
1380C2—24no—
1381C2—24no—
1382C2—24no—
1383C2C22×#55711yescharacteristic
1384C2#6284311yescharacteristic
1385C2#6284611yescharacteristic
1386C2#6284711yescharacteristic
1387C2#6285411yescharacteristic
1388C2#6286411yescharacteristic
1389C2#6286511yescharacteristic
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. #43557C2semidirect
2. #43556C2semidirect
3. #43130C2semidirect
4. #43129C2semidirect
5. #39679C2semidirect
6. #39678C2semidirect
7. #39677C2semidirect
8. #39676C2semidirect
9. #39640C2semidirect
10. #39639C2semidirect
11. #39636C2semidirect
12. #39636C2semidirect
13. #39179C2semidirect
14. #39178C2semidirect
15. #39175C2semidirect
16. #39175C2semidirect
37. #2809C22semidirect
38. #2809C22semidirect
39. #2806C22semidirect
40. #2806C22semidirect
41. #2805C22semidirect
42. #2805C22semidirect
43. #2802C22semidirect
44. #2802C22semidirect
45. #2802C22semidirect
46. #2802C22semidirect
47. #2799C22semidirect
48. #2799C22semidirect
49. #2799C22semidirect
50. #2799C22semidirect
51. #2791C22semidirect
52. #2791C22semidirect
53. #2791C22semidirect
54. #2791C22semidirect
55. #2774C22semidirect
56. #2774C22semidirect
57. #2774C22semidirect
58. #2774C22semidirect
59. #2755C22semidirect
60. #2755C22semidirect
61. #2755C22semidirect
62. #2755C22semidirect
63. #2726C22semidirect
64. #2726C22semidirect
65. #2713C22semidirect
66. #2713C22semidirect
67. #2713C22semidirect
68. #2713C22semidirect
81. #2590C22semidirect
82. #2590C22semidirect
83. #2588C22semidirect
84. #2588C22semidirect
85. #2585C22semidirect
86. #2585C22semidirect
87. #2585C22semidirect
88. #2585C22semidirect
89. #2584C22semidirect
92. #2582C22semidirect
93. #2581C22semidirect
98. #2568C22semidirect
99. #2565C22semidirect
100. #2552C22semidirect
101. #2550C22semidirect
108. #2546C22semidirect
109. #2520C22semidirect
110. #2520C22semidirect
111. #2511C22semidirect
112. #2511C22semidirect
113. #2509C22semidirect
114. #2509C22semidirect
115. #2508C22semidirect
116. #2506C22semidirect
134. #2462C22semidirect
135. #2462C22semidirect
136. #2453C22semidirect
137. #2453C22semidirect
138. #2453C22semidirect
139. #2451C22semidirect
140. #2446C22semidirect
141. #2446C22semidirect
252. C2×C22⋊Q8Q8semidirect
667. C22×Q8C2×Q8semidirect
732. C22⋊Q8C2×Q8semidirect
733. C22⋊Q8C2×Q8semidirect
761. C2×C4⋊C4C2×Q8semidirect
762. C2×C4⋊C4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#435572
#435562
#431302
#431292
#396792
#396782
#396772
#396762
#396402
#396392
#396362
#391792
#391782
#391752
#353912
#353682
#350202
#350022
#349942
C2×#26462
#342702
#342122
C2×#23292