Finite Group Databasebeta

← #8097200

Subgroups — #8097200

Order 512.

4341 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53139C212yesmaximal, complemented
2#53028C212yesmaximal, complemented
3#53017C211yesmaximal, characteristic, complemented
4#53009C211yesmaximal, characteristic, complemented
5#52817C212yesmaximal, complemented
6#52721C214yesmaximal, complemented
7#52568C212yesmaximal, complemented
8#52377C214yesmaximal, complemented
9#52306C211yesmaximal, characteristic, complemented
10C2×#2769C212yesmaximal, complemented
11#46344C212yesmaximal, complemented
12#46336C214yesmaximal, complemented
13#46190C211yesmaximal, characteristic, complemented
14#46145C212yesmaximal, complemented
15#46119C214yesmaximal, complemented
16#46116C212yesmaximal, complemented
17#46069C212yesmaximal, complemented
18#46045C212yesmaximal, complemented
19#46041C214yesmaximal, complemented
20#45983C214yesmaximal, complemented
21#36261C212yesmaximal, complemented
22#36241C212yesmaximal, complemented
23#36239C212yesmaximal, complemented
24#36166C212yesmaximal, complemented
25#36164C211yesmaximal, characteristic
26#36067C211yesmaximal, characteristic
27#36031C212yesmaximal, complemented
28#35998C211yesmaximal, characteristic
29#35806C212yesmaximal, complemented
30C2×#554C2211yescharacteristic
31C2×#554C2212yes—
32C2×#547C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic
35#2864C2212yes—
36#2863C2212yes—
37#2863C2212yes—
38#2862C2211yescharacteristic
39#2859C2212yes—
40#2857C2214yes—
41#2852C2214yes—
42#2852C2214yes—
43#2851C2214yes—
44#2850C2212yes—
45#2844C2212yes—
46#2843C2214yes—
47#2841C2212yes—
48#2839C2214yes—
49#2839C2214yes—
50#2839C2214yes—
51#2839C2214yes—
52#2838C2214yes—
53#2838C2214yes—
54#2836C2214yes—
55#2836C2214yes—
56#2835C2212yes—
57#2833C2212yes—
58#2833C2214yes—
59#2833C2214yes—
60#2833C2214yes—
61#2831C2214yes—
62#2822C2212yes—
63#2821C2214yes—
64#2809C2211yescharacteristic
65#2793C2214yes—
66#2791C2214yes—
67#2791C2214yes—
68#2789C2214yes—
69#2787C2214yes—
70#2787C2214yes—
71#2777C2214yes—
72#2777C2214yes—
73#2776C2214yes—
74#2775C2212yes—
75#2775C2212yes—
76#2774C2214yes—
77#2774C2214yes—
78#2774C2214yes—
79#2771C2214yes—
80#2770C2214yes—
81#2769C2214yes—
82#2769C2212yes—
83#2769C2212yes—
84#2769C2214yes—
85#2769C2214yes—
86#2769C2214yes—
87#2769C2211yescharacteristic
88#2769C2212yes—
89#2769C2211yescharacteristic
90#2769C2214yes—
91#2769C2214yes—
92#2766C2214yes—
93#2766C2214yes—
94#2766C2214yes—
95#2764C2212yes—
96#2762C2214yes—
97#2762C2214yes—
98#2759C2214yes—
99#2758C2214yes—
100#2758C2214yes—
101#2738C2214yes—
102#2738C2214yes—
103#2734C2211yescharacteristic
104#2731C2212yes—
105#2727C2212yes—
106#2723C2214yes—
107#2722C2214yes—
108#2721C2212yes—
109#2721C2212yes—
110#2717C2212yes—
111#2713C2214yes—
112#2713C2214yes—
113#2707C2214yes—
114#2689C2214yes—
115#2677C2212yes—
116#2629C2212yes—
117#2628C2212yes—
118#2627C2214yes—
119#2627C2214yes—
120#2625C2211yescharacteristic
121#2625C2211yescharacteristic
122#2623C2212yes—
123#2623C2212yes—
124#2584C2212yes—
125#2584C2212yes—
126#2583C2214yes—
127#2583C2214yes—
128#2582C2212yes—
129#2581C2212yes—
130#2579C2214yes—
131#2570C2212yes—
132#2570C2212yes—
133#2569C2214yes—
134#2569C2214yes—
135#2568C2211yescharacteristic
136#2568C2212yes—
137#2565C2212yes—
138#2564C2214yes—
139#2563C2211yescharacteristic
140#2552C2212yes—
141#2551C2212yes—
142#2550C2212yes—
143#2550C2212yes—
144#2549C2214yes—
145#2549C2214yes—
146#2514C2212yes—
147#2514C2212yes—
148#2514C2212yes—
149#2514C2212yes—
150#2511C2212yes—
151#2511C2212yes—
152#2510C2214yes—
153#2510C2214yes—
154#2510C2214yes—
155#2510C2214yes—
156#2509C2212yes—
157#2508C2212yes—
158#2507C2212yes—
159#2506C2212yes—
160#2505C2214yes—
161#2505C2214yes—
162#2504C2212yes—
163#2503C2212yes—
164#2503C2211yescharacteristic
165#2502C2211yescharacteristic
166#2498C2212yes—
167#2498C2212yes—
168#2497C2212yes—
169#2496C2212yes—
170#2495C2212yes—
171#2495C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2493C2214yes—
175#2493C2214yes—
176#2493C2214yes—
177#2493C2214yes—
178#2493C2214yes—
179#2493C2214yes—
180#2489C2212yes—
181#2489C2212yes—
182#2488C2214yes—
183#2488C2214yes—
184#2487C2214yes—
185#2487C2211yescharacteristic
186#2486C2211yescharacteristic
187#2484C2212yes—
188#2484C2212yes—
189#2481C2214yes—
190#2481C2214yes—
191#2473C2214yes—
192#2473C2214yes—
193#2453C2212yes—
194#2453C2212yes—
195#2453C2212yes—
196#2451C2212yes—
197#2450C2214yes—
198#2450C2214yes—
199#2450C2214yes—
200#2449C2214yes—
201#2446C2212yes—
202#2446C2212yes—
203#2444C2214yes—
204#2443C2214yes—
205#2442C2212yes—
206#2442C2212yes—
207#2442C2212yes—
208#2440C2212yes—
209#2440C2214yes—
210#2440C2214yes—
211#2438C2214yes—
212#2438C2214yes—
213#2438C2214yes—
214#2438C2214yes—
215#2423C2212yes—
216#2421C2212yes—
217#2419C2214yes—
218#2419C2214yes—
219#2417C2214yes—
220#2396C2212yes—
221#2396C2212yes—
222#2395C2211yescharacteristic
223#2395C2211yescharacteristic
224C2×#400C2212yes—
225C2×#400C2214yes—
226C2×#398C2212yes—
227C2×#398C2214yes—
228#2383C2214yes—
229#2382C2214yes—
230#2381C2214yes—
231#2378C2214yes—
232#2376C2212yes—
233#2349C2212yes—
234#2349C2212yes—
235#2349C2212yes—
236#2349C2212yes—
237#2349C2212yes—
238D4×C4⋊C4C2212yes—
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2212yes—
241#2339C2212yes—
242#2339C2212yes—
243#2339C2211yescharacteristic
244#2339C2212yes—
245#2339C2211yescharacteristic
246#2339C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×#125C2212yes—
249C4×#126C2212yes—
250C4×#126C2212yes—
251C4×#124C2211yescharacteristic
252C2×#389C2214yes—
253C2×#387C2214yes—
254C2×#387C2214yes—
255C2×#383C2214yes—
256C2×#382C2212yes—
257C42×D4C2211yescharacteristic
258C42×D4C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261#554—48no—
262#554—44no—
263#547—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2314yes—
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#124C2311yescharacteristic
278C2×#123C2312yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×#121C2312yes—
290#520—44no—
291#520—44no—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×#117C2311yescharacteristic
307C2×#117C2311yescharacteristic
308C2×#117C2312yes—
309C2×#117C2312yes—
310C22×C4⋊C4C2314yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2314yes—
313C22×C4⋊C4C2314yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2311yescharacteristic
320C22×C42C2312yes—
321C22×C42C2314yes—
322#401C2314yes—
323#401C2314yes—
324#401C2314yes—
325#401C2314yes—
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#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2311yescharacteristic
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2312yes—
371#399C2314yes—
372#399C2312yes—
373#399C2314yes—
374#399C2312yes—
375#399C2311yescharacteristic
376#399C2311yescharacteristic
377#399C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2312yes—
411#398C2311yescharacteristic
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2312yes—
417#398C2312yes—
418#397C2312yes—
419#397C2314yes—
420#397C2312yes—
421#397C2312yes—
422#397C2314yes—
423#397C2311yescharacteristic
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2311yescharacteristic
433#396C2314yes—
434#396C2314yes—
435#396C2312yes—
436#396C2312yes—
437#396C2314yes—
438#396C2312yes—
439#396C2312yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2312yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2314yes—
451#395C2312yes—
452#394C2312yes—
453#394C2312yes—
454#393C2312yes—
455#393C2312yes—
456#393C2312yes—
457#393C2314yes—
458#393C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2311yescharacteristic
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#390C2312yes—
481#390C2311yescharacteristic
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2312yes—
547#387C2312yes—
548#387C2312yes—
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#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#384C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2312yes—
629#384C2314yes—
630#383C2312yes—
631#383C2312yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#383C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2314yes—
653#382C2314yes—
654#382C2311yescharacteristic
655#381C2312yes—
656#381C2312yes—
657#381C2312yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#380C2312yes—
664#380C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2314yes—
672#380C2314yes—
673#380C2311yescharacteristic
674#380C2311yescharacteristic
675#380C2312yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C2×#95C2314yes—
705C2×#95C2314yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—28no—
720C2×#41—28no—
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C4⋊Q8—48no—
745C4⋊Q8—44no—
746C4⋊Q8—42no—
747C4⋊Q8—42no—
748C4⋊Q8—44no—
749#126—44no—
750#126—48no—
751#126—44no—
752#125—48no—
753#125—44no—
754#125—44no—
755#125—44no—
756#125—44no—
757#124—42no—
758#123—44no—
759#123—44no—
760#123—44no—
761C22⋊Q8—48no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—44no—
765C22⋊Q8—48no—
766C22⋊Q8—48no—
767C22⋊Q8—42no—
768C22⋊Q8—42no—
769#121—44no—
770C4×Q8—44no—
771C4×Q8—42no—
772C4×Q8—44no—
773C4×Q8—44no—
774C4×D4—28no—
775C4×D4—28no—
776C4×D4—24no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—42no—
782C4×D4—48no—
783C4×D4—48no—
784#117—42no—
785#117—42no—
786#117—44no—
787#117—44no—
788C2×C4⋊C4—48no—
789C2×C4⋊C4—48no—
790C2×C4⋊C4—48no—
791C2×C4⋊C4—42no—
792C2×C4⋊C4—42no—
793C2×C4⋊C4—44no—
794C2×C4⋊C4—44no—
795C2×C4⋊C4—44no—
796C2×C4⋊C4—44no—
797C2×C4⋊C4—48no—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C42—44no—
899C2×C42—48no—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2411yescharacteristic
924#95C2412yes—
925#95C2411yescharacteristic
926#95C2412yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2412yes—
971#95C2411yescharacteristic
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
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#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24C2511yescharacteristic
1007C24C2511yescharacteristic
1008C24C2512yes—
1009#41—416no—
1010#41—416no—
1011C2×Q8—22no—
1012C2×Q8—22no—
1013C2×Q8—24no—
1014C2×Q8—24no—
1015C2×Q8—22no—
1016C2×Q8—41no—
1017C2×Q8—42no—
1018C2×Q8—42no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—42no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×D4—24no—
1027C2×D4—24no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—22no—
1031C2×D4—41no—
1032C2×D4—41no—
1033C2×D4H(5,𝔽2)14yes—
1034C2×D42−1+418yes—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—28no—
1042C22×C4—28no—
1043C22×C4—28no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—28no—
1051C22×C4—24no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—41no—
1116C4⋊C4—41no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
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—42no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—41no—
1141C4⋊C4—41no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—28no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—28no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—42no—
1176C22⋊C4—42no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—41no—
1181C22⋊C4—41no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C42—24no—
1196C42—24no—
1197C42—22no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—24no—
1204C42—24no—
1205C42—28no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—41no—
1210C42—42no—
1211C42—44no—
1212C42—44no—
1213C42—42no—
1214C42—42no—
1215C42—42no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—21no—
1220C23—21no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23—21no—
1229C23C2×H(5,𝔽2)14yes—
1230C23C2×2−1+418yes—
1231C23C2611yescharacteristic
1232Q8—44no—
1233Q8—44no—
1234Q8—82no—
1235Q8—84no—
1236Q8—164no—
1237Q8—162no—
1238D4—48no—
1239D4—48no—
1240D4—82no—
1241D4#563116yes—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—416no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—48no—
1314C2×C4—44no—
1315C2×C4—44no—
1316C2×C4—88no—
1317C2×C4—88no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—162no—
1322C2×C4—162no—
1323C2×C4C2×H(5,𝔽2)12yes—
1324C2×C4C2×2−1+414yes—
1325C2×C4#58514yes—
1326C2×C4#58512yes—
1327C22—28no—
1328C22—24no—
1329C22—24no—
1330C22—28no—
1331C22—42no—
1332C22—42no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22C2×#56318yes—
1342C22C22×H(5,𝔽2)11yescharacteristic
1343C22C22×2−1+412yes—
1344C22C2×#58511yescharacteristic
1345C22C2×#58512yes—
1346C222−1+611yescharacteristic
1347C4—24no—
1348C4—22no—
1349C4—42no—
1350C4—44no—
1351C4—44no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—41no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—41no—
1365C4—41no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—42no—
1372C4C2×#56314yes—
1373C2—28no—
1374C2—81no—
1375C2—81no—
1376C2C22×#56311yescharacteristic
1377C2#6289811yescharacteristic
1378C2#6295012yes—
1379C2#6302312yes—
1380C2#6302411yescharacteristic
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. #53139C2semidirect
2. #53028C2semidirect
3. #53017C2semidirect
4. #53009C2semidirect
5. #52817C2semidirect
6. #52721C2semidirect
7. #52568C2semidirect
8. #52377C2semidirect
9. #52306C2semidirect
10. C2×#2769C2semidirect
11. #46344C2semidirect
12. #46336C2semidirect
13. #46190C2semidirect
14. #46145C2semidirect
15. #46119C2semidirect
16. #46116C2semidirect
17. #46069C2semidirect
18. #46045C2semidirect
19. #46041C2semidirect
20. #45983C2semidirect
21. #36261C2semidirect
22. #36241C2semidirect
23. #36239C2semidirect
24. #36166C2semidirect
27. #36031C2semidirect
29. #35806C2semidirect

Maximal subgroups

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

subgroupindex
#531392
#530282
#530172
#530092
#528172
#527212
#525682
#523772
#523062
C2×#27692
#463442
#463362
#461902
#461452
#461192
#461162
#460692
#460452
#460412
#459832
#362612
#362412
#362392
#361662
#361642
#360672
#360312
#359982
#358062