Finite Group Databasebeta

← #7675036

Subgroups — #7675036

Order 512.

4562 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59963C212yesmaximal, complemented
2#59922C212yesmaximal, complemented
3#59714C212yesmaximal, complemented
4#59593C212yesmaximal, complemented
5#59557C212yesmaximal, complemented
6#59467C212yesmaximal, complemented
7#59293C212yesmaximal, complemented
8#59249C212yesmaximal, complemented
9#44391C214yesmaximal, complemented
10#44304C214yesmaximal, complemented
11#43850C214yesmaximal, complemented
12#43789C214yesmaximal, complemented
13#39759C211yesmaximal, characteristic
14#39639C211yesmaximal, characteristic, complemented
15#39075C214yesmaximal, complemented
16#38919C212yesmaximal, complemented
17#37886C212yesmaximal, complemented
18#37708C212yesmaximal
19#36489C212yesmaximal, complemented
20#36186C211yesmaximal, characteristic
21#36133C211yesmaximal, characteristic, complemented
22#35380C214yesmaximal, complemented
23#35042C212yesmaximal
24#35015C211yesmaximal, characteristic, complemented
25#34772C212yesmaximal, complemented
26#34314C212yesmaximal, complemented
27#34213C212yesmaximal, complemented
28C2×#2370C211yesmaximal, characteristic, complemented
29C4×#539C211yesmaximal, characteristic
30C2×#552C2212yes—
31C2×#539C2211yescharacteristic
32C2×#533C2212yes—
33C22×#125C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2855C2212yes—
37#2855C2212yes—
38#2854C2212yes—
39#2852C2214yes—
40#2810C2212yes—
41#2809C2212yes—
42#2802C2214yes—
43#2798C2214yes—
44#2794C2214yes—
45#2793C2214yes—
46#2791C2214yes—
47#2791C2214yes—
48#2768C2214yes—
49#2767C2214yes—
50#2767C2214yes—
51#2767C2214yes—
52#2762C2214yes—
53#2758C2214yes—
54#2754C2214yes—
55#2738C2214yes—
56#2729C2214yes—
57#2727C2212yes—
58#2726C2212yes—
59#2721C2214yes—
60#2721C2214yes—
61#2719C2214yes—
62#2719C2214yes—
63#2719C2214yes—
64#2716C2214yes—
65#2707C2214yes—
66#2646C2212yes—
67#2646C2212yes—
68#2639C2212yes—
69#2627C2212yes—
70#2623C2214yes—
71#2604C2214yes—
72#2597C2214yes—
73#2596C2214yes—
74#2596C2214yes—
75#2594C2214yes—
76#2594C2214yes—
77#2590C2214yes—
78#2590C2214yes—
79#2590C2214yes—
80#2590C2214yes—
81#2589C2214yes—
82#2589C2214yes—
83#2588C2214yes—
84#2588C2214yes—
85#2588C2214yes—
86#2587C2214yes—
87#2585C2214yes—
88#2585C2214yes—
89#2582C2212yes—
90#2575C2214yes—
91#2565C2214yes—
92#2552C2212yes—
93#2552C2212yes—
94#2552C2211yescharacteristic
95#2552C2212yes—
96#2551C2211yescharacteristic
97#2546C2211yescharacteristic
98#2542C2211yescharacteristic
99#2533C2214yes—
100#2533C2214yes—
101#2533C2214yes—
102#2533C2214yes—
103#2532C2214yes—
104#2528C2214yes—
105#2528C2214yes—
106#2525C2214yes—
107#2524C2214yes—
108#2524C2214yes—
109#2524C2214yes—
110#2522C2214yes—
111#2520C2214yes—
112#2520C2214yes—
113#2519C2214yes—
114#2519C2214yes—
115#2514C2212yes—
116#2512C2212yes—
117#2511C2212yes—
118#2511C2212yes—
119#2511C2212yes—
120#2509C2212yes—
121#2509C2214yes—
122#2509C2212yes—
123#2507C2212yes—
124#2507C2212yes—
125#2506C2212yes—
126#2506C2212yes—
127#2505C2214yes—
128#2502C2212yes—
129#2498C2214yes—
130#2497C2212yes—
131#2496C2214yes—
132#2496C2212yes—
133#2496C2212yes—
134#2493C2214yes—
135#2492C2212yes—
136#2492C2212yes—
137#2489C2212yes—
138#2489C2212yes—
139#2489C2212yes—
140#2488C2214yes—
141#2487C2212yes—
142#2485C2212yes—
143#2484C2214yes—
144#2481C2214yes—
145#2479C2214yes—
146#2478C2214yes—
147#2478C2214yes—
148#2475C2214yes—
149#2473C2214yes—
150#2469C2214yes—
151#2469C2214yes—
152#2469C2214yes—
153#2462C2214yes—
154#2458C2214yes—
155#2453C2212yes—
156#2453C2212yes—
157#2453C2214yes—
158#2453C2214yes—
159#2451C2212yes—
160#2451C2212yes—
161#2450C2214yes—
162#2446C2212yes—
163#2446C2212yes—
164#2446C2212yes—
165#2441C2212yes—
166#2441C2212yes—
167#2440C2212yes—
168#2439C2212yes—
169#2438C2214yes—
170#2421C2214yes—
171#2417C2212yes—
172#2413C2214yes—
173#2402C2214yes—
174#2396C2214yes—
175#2373C2214yes—
176#2370C2214yes—
177#2370C2212yes—
178#2370C2214yes—
179#2370C2214yes—
180#2370C2214yes—
181#2370C2212yes—
182#2370C2212yes—
183#2370C2214yes—
184#2370C2212yes—
185#2370C2212yes—
186#2369C2214yes—
187#2365C2212yes—
188#2365C2211yescharacteristic
189#2365C2211yescharacteristic
190#2365C2212yes—
191#2365C2214yes—
192#2362C2212yes—
193#2362C2212yes—
194#2362C2212yes—
195#2360C2212yes—
196#2359C2214yes—
197#2355C2214yes—
198#2355C2212yes—
199#2355C2214yes—
200#2355C2214yes—
201#2354C2211yescharacteristic
202#2352C2212yes—
203#2351C2212yes—
204Q8×C4⋊C4C2214yes—
205Q8×C4⋊C4C2211yescharacteristic
206#2347C2212yes—
207#2347C2212yes—
208#2344C2212yes—
209#2343C2214yes—
210#2336C2214yes—
211#2336C2212yes—
212#2335C2212yes—
213#2334C2214yes—
214#2334C2212yes—
215#2332C2212yes—
216#2329C2211yescharacteristic
217#2329C2212yes—
218#2329C2212yes—
219#2329C2212yes—
220#2325C2211yescharacteristic
221#2322C2214yes—
222#2322C2212yes—
223#2318C2212yes—
224#2317C2214yes—
225#2313C2211yescharacteristic
226#2313C2212yes—
227C4×C4⋊Q8C2212yes—
228C4×#125C2212yes—
229C4×#125C2212yes—
230C4×#126C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235C4×C22⋊Q8C2211yescharacteristic
236C4×C22⋊Q8C2214yes—
237C4×C22⋊Q8C2214yes—
238C4×#123C2212yes—
239C4×#123C2212yes—
240C4×#121C2211yescharacteristic
241#2296C2212yes—
242#2295C2212yes—
243#2295C2212yes—
244C2×#389C2211yescharacteristic
245C2×#389C2212yes—
246C2×#389C2211yescharacteristic
247#2290C2214yes—
248C2×#387C2212yes—
249C2×#387C2212yes—
250#2285C2212yes—
251#2285C2212yes—
252#2274C2214yes—
253C42×D4C2212yes—
254C2×C4×C4⋊C4C2211yescharacteristic
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2212yes—
258C2×C4×C4⋊C4C2211yescharacteristic
259#552—216no—
260#539—28no—
261#533—216no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×#126C2312yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125—28no—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2314yes—
280C2×#123C2314yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2311yescharacteristic
290C2×#121C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2314yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2314yes—
299C2×C4×Q8C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2312yes—
307C2×#117C2312yes—
308C2×#117C2314yes—
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2312yes—
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2311yescharacteristic
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2312yes—
324C22×C42C2312yes—
325C22×C42C2312yes—
326#401C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
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#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#393C2314yes—
396#393C2314yes—
397#393C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2314yes—
405#391C2314yes—
406#391C2311yescharacteristic
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#390C2311yescharacteristic
420#390C2312yes—
421#390C2312yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2312yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2314yes—
447#389C2314yes—
448#389C2311yescharacteristic
449#389C2314yes—
450#389C2312yes—
451#389C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2311yescharacteristic
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#388C2312yes—
476#388C2312yes—
477#388C2312yes—
478#388C2312yes—
479#388C2314yes—
480#388C2314yes—
481#388C2312yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2312yes—
487#388C2312yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#387C2312yes—
503#387C2312yes—
504#387C2312yes—
505#387C2312yes—
506#387C2312yes—
507#387C2312yes—
508#387C2314yes—
509#387C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2312yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#386C2312yes—
579#386C2312yes—
580#386C2314yes—
581#386C2312yes—
582#386C2314yes—
583#386C2314yes—
584#385C2312yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2312yes—
589#385C2314yes—
590#385C2312yes—
591#385C2314yes—
592#385C2312yes—
593#385C2314yes—
594#385C2314yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#384C2312yes—
601#384C2314yes—
602#384C2314yes—
603#384C2312yes—
604#384C2311yescharacteristic
605#384C2311yescharacteristic
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#383C2312yes—
610#383C2314yes—
611#383C2314yes—
612#383C2314yes—
613#382C2312yes—
614#382C2312yes—
615#382C2314yes—
616#382C2314yes—
617#382C2314yes—
618#382C2314yes—
619#382C2314yes—
620#382C2314yes—
621#381C2312yes—
622#381C2314yes—
623#381C2312yes—
624#381C2314yes—
625#380C2311yescharacteristic
626#380C2311yescharacteristic
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2312yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2311yescharacteristic
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706#376C2314yes—
707#376C2314yes—
708C2×#95C2311yescharacteristic
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C43C2312yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×D4C2412yes—
721C22×D4C2411yescharacteristic
722C23×C4C2411yescharacteristic
723C23×C4C2412yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2411yescharacteristic
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C4⋊Q8—28no—
737C4⋊Q8—28no—
738C4⋊Q8—28no—
739C4⋊Q8—42no—
740C4⋊Q8—42no—
741#126—28no—
742#126—216no—
743#126—84no—
744#126—84no—
745#125—28no—
746#125—28no—
747#125—216no—
748#125—216no—
749#125—28no—
750#125—216no—
751#125—28no—
752#125—84no—
753#123—216no—
754#123—28no—
755#123—28no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—28no—
761C22⋊Q8—216no—
762C22⋊Q8#4118yes—
763#121—24no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—216no—
767C4×Q8—28no—
768C4×Q8—42no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—84no—
772C4×Q8—84no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—42no—
777#117—216no—
778#117—28no—
779#117—216no—
780#117—44no—
781#117—84no—
782C2×C4⋊C4—28no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—24no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—82no—
791C2×C4⋊C4#4118yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C42—24no—
891C2×C42—28no—
892C2×C42—42no—
893C2×C42—44no—
894C2×C42—42no—
895C2×C42—82no—
896C2×C42—82no—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2511yescharacteristic
1010C2×Q8—24no—
1011C2×Q8—28no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—28no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—44no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8C2×#4114yes—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—22no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—41no—
1048C22×C4—42no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—41no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—41no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—42no—
1065C22×C4—41no—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4118yes—
1068C22×C4C2×#4114yes—
1069C22×C42−1+414yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—22no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—41no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4C2×#4114yes—
1167C4⋊C4C2×#4114yes—
1168C4⋊C4C2×#4118yes—
1169C4⋊C4C2×#4118yes—
1170C4⋊C4C2×#4114yes—
1171C4⋊C42−1+414yes—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4C2×#4118yes—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—28no—
1202C42—28no—
1203C42—28no—
1204C42—28no—
1205C42—24no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—22no—
1211C42—24no—
1212C42—22no—
1213C42—42no—
1214C42—42no—
1215C42—41no—
1216C42—41no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23C22×#4112yes—
1242C23C22×#4112yes—
1243C23C2×2−1+412yes—
1244C23C2611yescharacteristic
1245Q8—44no—
1246Q8—416no—
1247Q8—48no—
1248Q8—84no—
1249D4—48no—
1250D4—82no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—216no—
1270C2×C4—28no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—21no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—44no—
1323C2×C4—44no—
1324C2×C4—48no—
1325C2×C4—48no—
1326C2×C4—44no—
1327C2×C4—48no—
1328C2×C4—44no—
1329C2×C4—48no—
1330C2×C4—84no—
1331C2×C4—82no—
1332C2×C4—82no—
1333C2×C4—84no—
1334C2×C4C22×#4114yes—
1335C2×C4C22×#4112yes—
1336C2×C4C22×#4112yes—
1337C2×C4C22×#4114yes—
1338C2×C4C22×#4112yes—
1339C2×C4C22×#4114yes—
1340C2×C4C22×#4114yes—
1341C2×C4C22×#4112yes—
1342C2×C4C2×2−1+414yes—
1343C2×C4C2×2−1+414yes—
1344C2×C4C2×2−1+412yes—
1345C2×C4#58512yes—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22#348214yes—
1360C22C23×#4111yescharacteristic
1361C22C23×#4111yescharacteristic
1362C22C22×2−1+411yescharacteristic
1363C22C22×2−1+411yescharacteristic
1364C22C2×#58511yescharacteristic
1365C22H(7,𝔽2)11yescharacteristic
1366C222−1+611yescharacteristic
1367C4—22no—
1368C4—22no—
1369C4—24no—
1370C4—24no—
1371C4—24no—
1372C4—22no—
1373C4—24no—
1374C4—24no—
1375C4—24no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—44no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4—42no—
1385C4—44no—
1386C4—42no—
1387C4—41no—
1388C4—41no—
1389C4—44no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4#350714yes—
1394C2—24no—
1395C2—82no—
1396C2C2×#348211yescharacteristic
1397C2C2×#350711yescharacteristic
1398C2#6285111yescharacteristic
1399C2#6290211yescharacteristic
1400C2#6294711yescharacteristic
1401C2#6299111yescharacteristic
1402C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59963C2semidirect
2. #59922C2semidirect
3. #59714C2semidirect
4. #59593C2semidirect
5. #59557C2semidirect
6. #59467C2semidirect
7. #59293C2semidirect
8. #59249C2semidirect
9. #44391C2semidirect
10. #44304C2semidirect
11. #43850C2semidirect
12. #43789C2semidirect
14. #39639C2semidirect
15. #39075C2semidirect
16. #38919C2semidirect
17. #37886C2semidirect
19. #36489C2semidirect
21. #36133C2semidirect
22. #35380C2semidirect
24. #35015C2semidirect
25. #34772C2semidirect
26. #34314C2semidirect
27. #34213C2semidirect
28. C2×#2370C2semidirect

Maximal subgroups

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

subgroupindex
#599632
#599222
#597142
#595932
#595572
#594672
#592932
#592492
#443912
#443042
#438502
#437892
#397592
#396392
#390752
#389192
#378862
#377082
#364892
#361862
#361332
#353802
#350422
#350152
#347722
#343142
#342132
C2×#23702
C4×#5392