Finite Group Databasebeta

← #7695519

Subgroups — #7695519

Order 512.

4561 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60001C214yesmaximal, complemented
2#59866C212yesmaximal, complemented
3#59828C211yesmaximal, characteristic, complemented
4#59479C212yesmaximal, complemented
5#52281C212yesmaximal, complemented
6#52272C211yesmaximal, characteristic, complemented
7#45335C212yesmaximal
8#45192C212yesmaximal, complemented
9#44924C212yesmaximal, complemented
10#44471C214yesmaximal, complemented
11#44054C214yesmaximal, complemented
12#43321C214yesmaximal, complemented
13#39629C211yesmaximal, characteristic, complemented
14#39583C212yesmaximal, complemented
15#39501C211yesmaximal, characteristic, complemented
16#39283C212yesmaximal, complemented
17#38748C214yesmaximal, complemented
18#38465C212yesmaximal, complemented
19#38230C212yesmaximal, complemented
20#38188C214yesmaximal, complemented
21#36554C212yesmaximal, complemented
22#36476C211yesmaximal, characteristic, complemented
23#35919C212yesmaximal, complemented
24#35911C212yesmaximal, complemented
25#35846C212yesmaximal, complemented
26#34328C212yesmaximal, complemented
27#34324C211yesmaximal, characteristic, complemented
28#34308C211yesmaximal, characteristic
29#34263C212yesmaximal, complemented
30C2×#557C2212yes—
31C2×#556C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#520C2212yes—
34#2863C2214yes—
35#2863C2212yes—
36#2862C2211yescharacteristic
37#2855C2212yes—
38#2810C2211yescharacteristic
39#2809C2212yes—
40#2809C2212yes—
41#2808C2211yescharacteristic
42#2808C2212yes—
43#2808C2212yes—
44#2806C2212yes—
45#2806C2212yes—
46#2805C2211yescharacteristic
47#2805C2212yes—
48#2805C2212yes—
49#2802C2214yes—
50#2800C2212yes—
51#2798C2212yes—
52#2793C2212yes—
53#2791C2214yes—
54#2787C2214yes—
55#2786C2214yes—
56#2777C2214yes—
57#2776C2212yes—
58#2776C2214yes—
59#2773C2214yes—
60#2772C2214yes—
61#2770C2214yes—
62#2766C2214yes—
63#2764C2214yes—
64#2759C2212yes—
65#2751C2214yes—
66#2745C2214yes—
67#2738C2214yes—
68#2738C2214yes—
69#2737C2214yes—
70#2727C2211yescharacteristic
71#2726C2212yes—
72#2726C2212yes—
73#2723C2214yes—
74#2721C2214yes—
75#2716C2212yes—
76#2711C2214yes—
77#2711C2214yes—
78#2694C2214yes—
79#2694C2214yes—
80#2655C2214yes—
81#2655C2214yes—
82#2647C2212yes—
83#2645C2212yes—
84#2638C2214yes—
85#2621C2212yes—
86#2611C2214yes—
87#2607C2214yes—
88#2604C2214yes—
89#2596C2214yes—
90#2594C2214yes—
91#2590C2214yes—
92#2590C2214yes—
93#2589C2214yes—
94#2589C2214yes—
95#2589C2214yes—
96#2588C2214yes—
97#2585C2214yes—
98#2585C2214yes—
99#2585C2214yes—
100#2583C2214yes—
101#2582C2212yes—
102#2581C2212yes—
103#2580C2212yes—
104#2575C2214yes—
105#2575C2214yes—
106#2574C2214yes—
107#2570C2212yes—
108#2569C2214yes—
109#2563C2211yescharacteristic
110#2560C2214yes—
111#2552C2212yes—
112#2546C2212yes—
113#2542C2211yescharacteristic
114#2536C2212yes—
115#2532C2214yes—
116#2532C2214yes—
117#2531C2214yes—
118#2530C2214yes—
119#2528C2214yes—
120#2528C2214yes—
121#2527C2214yes—
122#2527C2214yes—
123#2527C2214yes—
124#2527C2214yes—
125#2525C2214yes—
126#2522C2214yes—
127#2520C2214yes—
128#2520C2214yes—
129#2520C2214yes—
130#2516C2214yes—
131#2507C2212yes—
132#2506C2214yes—
133#2506C2212yes—
134#2496C2212yes—
135#2494C2212yes—
136#2493C2214yes—
137#2492C2212yes—
138#2492C2212yes—
139#2492C2212yes—
140#2484C2214yes—
141#2484C2214yes—
142#2479C2214yes—
143#2478C2214yes—
144#2478C2214yes—
145#2478C2214yes—
146#2475C2214yes—
147#2473C2214yes—
148#2473C2214yes—
149#2473C2214yes—
150#2468C2214yes—
151#2466C2214yes—
152#2466C2214yes—
153#2462C2214yes—
154#2458C2214yes—
155#2458C2214yes—
156#2453C2214yes—
157#2453C2214yes—
158#2451C2212yes—
159#2451C2212yes—
160#2447C2212yes—
161#2447C2212yes—
162#2446C2212yes—
163#2446C2212yes—
164#2438C2214yes—
165#2432C2212yes—
166#2432C2212yes—
167#2429C2212yes—
168#2429C2212yes—
169#2423C2212yes—
170#2423C2212yes—
171#2423C2212yes—
172#2423C2212yes—
173#2421C2212yes—
174#2401C2212yes—
175#2398C2212yes—
176#2396C2212yes—
177#2396C2214yes—
178#2395C2214yes—
179#2395C2214yes—
180#2373C2214yes—
181#2371C2214yes—
182#2371C2214yes—
183#2370C2214yes—
184#2369C2211yescharacteristic
185#2368C2214yes—
186#2367C2212yes—
187#2365C2211yescharacteristic
188#2365C2212yes—
189#2365C2212yes—
190#2365C2211yescharacteristic
191#2365C2211yescharacteristic
192#2365C2212yes—
193#2362C2212yes—
194#2361C2212yes—
195#2360C2212yes—
196#2360C2212yes—
197#2360C2212yes—
198#2359C2214yes—
199#2357C2212yes—
200#2357C2214yes—
201#2356C2212yes—
202#2356C2214yes—
203#2356C2212yes—
204#2355C2212yes—
205#2355C2212yes—
206#2355C2212yes—
207#2354C2211yescharacteristic
208#2354C2214yes—
209#2351C2212yes—
210Q8×C4⋊C4C2211yescharacteristic
211Q8×C4⋊C4C2212yes—
212D4×C4⋊C4C2211yescharacteristic
213D4×C4⋊C4C2211yescharacteristic
214#2346C2212yes—
215#2345C2212yes—
216#2345C2214yes—
217#2344C2212yes—
218#2344C2214yes—
219#2344C2212yes—
220#2341C2212yes—
221#2341C2212yes—
222#2339C2212yes—
223#2336C2214yes—
224#2336C2214yes—
225#2334C2214yes—
226#2327C2212yes—
227#2327C2212yes—
228#2326C2212yes—
229#2323C2212yes—
230#2322C2214yes—
231#2319C2212yes—
232#2319C2214yes—
233#2314C2214yes—
234#2314C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237C4×C4⋊Q8C2212yes—
238C4×C4⋊Q8C2211yescharacteristic
239C4×#125C2214yes—
240C4×#126C2212yes—
241C4×#126C2214yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×#121C2212yes—
245#2298C2214yes—
246#2298C2212yes—
247#2296C2212yes—
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2295C2214yes—
251#2293C2211yescharacteristic
252#2293C2214yes—
253#2293C2212yes—
254C2×#389C2212yes—
255#2276C2212yes—
256#2276C2212yes—
257C42×Q8C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260#557—216no—
261#556—28no—
262#547—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#124C2312yes—
278C2×#123C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×#121C2312yes—
286#520—216no—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2314yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2314yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×#117C2312yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2314yes—
314C2×#117C2314yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2312yes—
319C22×C42C2312yes—
320#401C2314yes—
321#401C2312yes—
322#401C2314yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2312yes—
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#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#396C2314yes—
388#396C2312yes—
389#396C2314yes—
390#396C2312yes—
391#396C2312yes—
392#395C2314yes—
393#395C2314yes—
394#395C2312yes—
395#395C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2312yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2312yes—
403#393C2314yes—
404#393C2314yes—
405#393C2314yes—
406#393C2314yes—
407#393C2312yes—
408#393C2312yes—
409#393C2312yes—
410#391C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2314yes—
426#391C2312yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2311yescharacteristic
435#391C2312yes—
436#391C2311yescharacteristic
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2312yes—
442#390C2314yes—
443#390C2314yes—
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#389C2312yes—
447#389C2314yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2311yescharacteristic
453#389C2311yescharacteristic
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2312yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2311yescharacteristic
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2311yescharacteristic
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2311yescharacteristic
491#389C2311yescharacteristic
492#388C2312yes—
493#388C2312yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2312yes—
521#388C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2314yes—
530#387C2312yes—
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#387C2314yes—
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#387C2314yes—
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#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2312yes—
590#387C2314yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2314yes—
595#387C2312yes—
596#386C2314yes—
597#386C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#384C2311yescharacteristic
615#384C2312yes—
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2314yes—
619#384C2312yes—
620#383C2312yes—
621#383C2314yes—
622#383C2314yes—
623#383C2314yes—
624#382C2314yes—
625#382C2312yes—
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2312yes—
630#381C2314yes—
631#381C2314yes—
632#381C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2314yes—
640#380C2312yes—
641#380C2314yes—
642#380C2312yes—
643#380C2314yes—
644#380C2312yes—
645#380C2312yes—
646#380C2312yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706#376C2312yes—
707#376C2314yes—
708#376C2312yes—
709#376C2314yes—
710#376C2314yes—
711#376C2314yes—
712C2×#95C2314yes—
713C43C2314yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C2×#41—28no—
717C2×#41—28no—
718C2×#41—44no—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×D4C2414yes—
726C22×D4C2411yescharacteristic
727C22×D4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C4⋊Q8—28no—
736C4⋊Q8—28no—
737C4⋊Q8—24no—
738C4⋊Q8—24no—
739C4⋊Q8—42no—
740C4⋊Q8—42no—
741C4⋊Q8#4118yes—
742#126—28no—
743#126—216no—
744#126—84no—
745#125—216no—
746#125—216no—
747#125—216no—
748#125—84no—
749#124—28no—
750#123—216no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—44no—
755C22⋊Q8—44no—
756C22⋊Q8—82no—
757#121—28no—
758C4×Q8—28no—
759C4×Q8—28no—
760C4×Q8—28no—
761C4×Q8—28no—
762C4×Q8—216no—
763C4×Q8—28no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—28no—
767C4×Q8—44no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—82no—
771C4×Q8—82no—
772C4×D4—28no—
773C4×D4—216no—
774C4×D4—216no—
775C4×D4—24no—
776C4×D4—24no—
777C4×D4—42no—
778C4×D4—82no—
779C4×D4#4118yes—
780#117—28no—
781#117—216no—
782#117—28no—
783#117—82no—
784#117—84no—
785#117—84no—
786C2×C4⋊C4—216no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—82no—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C42—82no—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2411yescharacteristic
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927#95C2412yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004C24C2512yes—
1005C24C2512yes—
1006#41—432no—
1007C2×Q8—24no—
1008C2×Q8—24no—
1009C2×Q8—22no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—24no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—41no—
1019C2×Q8—42no—
1020C2×Q8—42no—
1021C2×Q8—42no—
1022C2×Q8—42no—
1023C2×Q8—42no—
1024C2×Q8C2×#4118yes—
1025C2×D4—28no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—28no—
1029C2×D4—22no—
1030C2×D4—41no—
1031C2×D4—41no—
1032C2×D4—44no—
1033C2×D4C2×#4114yes—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—28no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4C2×#4118yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2514yes—
1077C22×C4C2511yescharacteristic
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—22no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—22no—
1091C4⋊C4—24no—
1092C4⋊C4—22no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—41no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—41no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4C2×#4114yes—
1150C4⋊C4C2×#4118yes—
1151C4⋊C4C2×#4118yes—
1152C4⋊C42−1+414yes—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4C2×#4118yes—
1184C42—28no—
1185C42—28no—
1186C42—24no—
1187C42—28no—
1188C42—24no—
1189C42—28no—
1190C42—28no—
1191C42—28no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—22no—
1196C42—22no—
1197C42—24no—
1198C42—41no—
1199C42—42no—
1200C42—42no—
1201C42—42no—
1202C42—44no—
1203C42—42no—
1204C42—41no—
1205C42—41no—
1206C42—42no—
1207C42—44no—
1208C42—44no—
1209C42—42no—
1210C42—44no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—44no—
1215C42—44no—
1216C42C2×#4114yes—
1217C42C2×#4114yes—
1218C23—22no—
1219C23—22no—
1220C23—22no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—22no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23C22×#4114yes—
1232C23C2611yescharacteristic
1233Q8—216no—
1234Q8—48no—
1235Q8—44no—
1236Q8—48no—
1237Q8—84no—
1238Q8—162no—
1239D4—28no—
1240D4—416no—
1241D4—44no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—48no—
1313C2×C4—416no—
1314C2×C4—48no—
1315C2×C4—48no—
1316C2×C4—88no—
1317C2×C4—84no—
1318C2×C4—88no—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4114yes—
1322C2×C4C22×#4118yes—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4112yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4112yes—
1327C2×C4C2×2−1+414yes—
1328C2×C4C2×2−1+412yes—
1329C2×C4#58512yes—
1330C22—24no—
1331C22—24no—
1332C22—24no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22C23×#4111yescharacteristic
1345C22C23×#4111yescharacteristic
1346C22C22×2−1+411yescharacteristic
1347C22C2×#58511yescharacteristic
1348C22H(7,𝔽2)11yescharacteristic
1349C222−1+611yescharacteristic
1350C222−1+611yescharacteristic
1351C4—22no—
1352C4—24no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—22no—
1357C4—22no—
1358C4—28no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—41no—
1365C4—42no—
1366C4—44no—
1367C4—42no—
1368C4—44no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4—44no—
1377C4#347514yes—
1378C2—44no—
1379C2—82no—
1380C2C2×#347511yescharacteristic
1381C2#6284711yescharacteristic
1382C2#6285111yescharacteristic
1383C2#6296211yescharacteristic
1384C2#6299811yescharacteristic
1385C2#6300111yescharacteristic
1386C2#6306211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#547C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #60001C2semidirect
2. #59866C2semidirect
3. #59828C2semidirect
4. #59479C2semidirect
5. #52281C2semidirect
6. #52272C2semidirect
8. #45192C2semidirect
9. #44924C2semidirect
10. #44471C2semidirect
11. #44054C2semidirect
12. #43321C2semidirect
13. #39629C2semidirect
14. #39583C2semidirect
15. #39501C2semidirect
16. #39283C2semidirect
17. #38748C2semidirect
18. #38465C2semidirect
19. #38230C2semidirect
20. #38188C2semidirect
21. #36554C2semidirect
22. #36476C2semidirect
23. #35919C2semidirect
24. #35911C2semidirect
25. #35846C2semidirect
26. #34328C2semidirect
27. #34324C2semidirect
29. #34263C2semidirect

Maximal subgroups

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

subgroupindex
#600012
#598662
#598282
#594792
#522812
#522722
#453352
#451922
#449242
#444712
#440542
#433212
#396292
#395832
#395012
#392832
#387482
#384652
#382302
#381882
#365542
#364762
#359192
#359112
#358462
#343282
#343242
#343082
#342632