Finite Group Databasebeta

← #9236426

Subgroups — #9236426

Order 512.

3727 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58752C212yesmaximal, complemented
2#57733C214yesmaximal, complemented
3#57731C214yesmaximal, complemented
4#57598C212yesmaximal
5#51293C214yesmaximal, complemented
6#51195C212yesmaximal
7#50981C214yesmaximal, complemented
8#50915C212yesmaximal, complemented
9#50325C214yesmaximal
10#49535C214yesmaximal, complemented
11#49443C214yesmaximal, complemented
12#49260C214yesmaximal, complemented
13#49094C214yesmaximal, complemented
14#48989C214yesmaximal, complemented
15#46245C212yesmaximal
16#46244C212yesmaximal
17#46243C212yesmaximal, complemented
18#46157C212yesmaximal, complemented
19#46152C211yesmaximal, characteristic
20#37612C211yesmaximal, characteristic
21#37603C212yesmaximal, complemented
22#36601C211yesmaximal, characteristic
23#36567C212yesmaximal, complemented
24#2864C2212yes—
25#2864C2212yes—
26#2861C2212yes—
27#2859C2212yes—
28#2859C2211yescharacteristic
29#2844C2212yes—
30#2844C2214yes—
31#2844C2211yescharacteristic
32#2843C2212yes—
33#2838C2214yes—
34#2835C2212yes—
35#2822C2212yes—
36#2822C2212yes—
37#2822C2211yescharacteristic
38#2820C2212yes—
39#2810C2214yes—
40#2810C2214yes—
41#2809C2212yes—
42#2809C2214yes—
43#2805C2214yes—
44#2805C2214yes—
45#2794C2214yes—
46#2794C2212yes—
47#2792C2212yes—
48#2789C2214yes—
49#2789C2214yes—
50#2787C2214yes—
51#2787C2214yes—
52#2786C2214yes—
53#2783C2214yes—
54#2783C2214yes—
55#2777C2214yes—
56#2777C2214yes—
57#2777C2214yes—
58#2776C2214yes—
59#2776C2214yes—
60#2774C2214yes—
61#2774C2214yes—
62#2773C2214yes—
63#2773C2214yes—
64#2773C2214yes—
65#2772C2214yes—
66#2772C2214yes—
67#2771C2214yes—
68#2769C2214yes—
69#2767C2214yes—
70#2767C2214yes—
71#2767C2214yes—
72#2766C2214yes—
73#2765C2214yes—
74#2763C2212yes—
75#2762C2214yes—
76#2758C2214yes—
77#2758C2214yes—
78#2755C2214yes—
79#2755C2214yes—
80#2755C2214yes—
81#2754C2214yes—
82#2744C2214yes—
83#2742C2212yes—
84#2740C2214yes—
85#2739C2214yes—
86#2738C2214yes—
87#2738C2214yes—
88#2726C2214yes—
89#2725C2214yes—
90#2720C2214yes—
91#2720C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2713C2214yes—
98#2704C2214yes—
99#2698C2214yes—
100#2698C2214yes—
101#2690C2214yes—
102#2683C2212yes—
103#2667C2212yes—
104#2666C2214yes—
105#2666C2214yes—
106#2666C2214yes—
107#2655C2214yes—
108#2655C2214yes—
109#2655C2214yes—
110#2655C2214yes—
111#2654C2214yes—
112#2654C2214yes—
113#2650C2214yes—
114#2642C2212yes—
115#2638C2212yes—
116#2634C2212yes—
117#2606C2212yes—
118#2596C2214yes—
119#2596C2214yes—
120#2595C2214yes—
121#2594C2214yes—
122#2594C2214yes—
123#2593C2212yes—
124#2590C2214yes—
125#2590C2214yes—
126#2590C2214yes—
127#2588C2214yes—
128#2588C2214yes—
129#2588C2214yes—
130#2588C2214yes—
131#2587C2214yes—
132#2586C2214yes—
133#2586C2214yes—
134#2586C2212yes—
135#2585C2214yes—
136#2585C2214yes—
137#2584C2212yes—
138#2584C2212yes—
139#2581C2211yescharacteristic
140#2580C2211yescharacteristic
141#2577C2214yes—
142#2577C2214yes—
143#2575C2214yes—
144#2573C2214yes—
145#2573C2214yes—
146#2571C2212yes—
147#2570C2214yes—
148#2570C2214yes—
149#2570C2214yes—
150#2567C2212yes—
151#2556C2214yes—
152#2556C2214yes—
153#2528C2214yes—
154#2525C2214yes—
155#2525C2214yes—
156#2524C2214yes—
157#2524C2214yes—
158#2524C2214yes—
159#2524C2214yes—
160#2524C2214yes—
161#2522C2214yes—
162#2520C2214yes—
163#2520C2214yes—
164#2520C2214yes—
165#2520C2214yes—
166#2519C2214yes—
167#2517C2212yes—
168#2516C2214yes—
169#2515C2214yes—
170#2514C2214yes—
171#2512C2212yes—
172#2511C2212yes—
173#2509C2214yes—
174#2509C2214yes—
175#2509C2214yes—
176#2508C2214yes—
177#2508C2214yes—
178#2507C2212yes—
179#2507C2214yes—
180#2507C2212yes—
181#2506C2214yes—
182#2506C2212yes—
183#2506C2212yes—
184#2503C2212yes—
185#2497C2214yes—
186#2489C2214yes—
187#2489C2214yes—
188#2487C2212yes—
189#2473C2214yes—
190#2469C2214yes—
191#2462C2214yes—
192#2462C2214yes—
193#2440C2214yes—
194#2382C2212yes—
195#2382C2212yes—
196#2382C2214yes—
197#2381C2212yes—
198#2379C2211yescharacteristic
199#2379C2211yescharacteristic
200#2378C2212yes—
201#2378C2214yes—
202#2373C2214yes—
203#2370C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2370C2214yes—
207#2357C2211yescharacteristic
208#2356C2211yescharacteristic
209#2336C2212yes—
210#2336C2214yes—
211#2332C2214yes—
212#2313C2212yes—
213C4×#125C2212yes—
214C4×#125C2212yes—
215C4×#125C2212yes—
216C4×#125C2212yes—
217C4×#124C2211yescharacteristic
218C42×Q8C2211yescharacteristic
219C2×C4⋊Q8C2312yes—
220C2×#126C2314yes—
221C2×#125C2312yes—
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#125C2312yes—
226C2×#125C2314yes—
227C2×#125C2314yes—
228C2×#125C2314yes—
229C2×#125C2314yes—
230C2×#124C2311yescharacteristic
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×D4C2311yescharacteristic
238C22×C4⋊C4C2312yes—
239#401C2314yes—
240#401C2314yes—
241#401C2314yes—
242#400C2314yes—
243#400C2314yes—
244#400C2314yes—
245#400C2314yes—
246#400C2314yes—
247#400C2314yes—
248#400C2314yes—
249#400C2314yes—
250#400C2314yes—
251#400C2314yes—
252#400C2312yes—
253#400C2312yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2312yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2314yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2314yes—
283#400C2314yes—
284#399C2314yes—
285#399C2312yes—
286#399C2314yes—
287#399C2314yes—
288#399C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2312yes—
293#398C2314yes—
294#398C2312yes—
295#398C2314yes—
296#398C2314yes—
297#398C2314yes—
298#398C2314yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#398C2314yes—
306#398C2314yes—
307#398C2314yes—
308#398C2314yes—
309#398C2314yes—
310#398C2314yes—
311#398C2314yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2314yes—
316#398C2314yes—
317#398C2314yes—
318#398C2314yes—
319#398C2312yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#397C2314yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#397C2314yes—
329#397C2314yes—
330#397C2312yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#396C2314yes—
337#396C2314yes—
338#396C2314yes—
339#396C2314yes—
340#396C2314yes—
341#396C2314yes—
342#396C2314yes—
343#395C2314yes—
344#395C2314yes—
345#395C2314yes—
346#395C2314yes—
347#395C2312yes—
348#395C2314yes—
349#395C2314yes—
350#395C2312yes—
351#395C2314yes—
352#395C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#394C2314yes—
357#393C2312yes—
358#393C2312yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2314yes—
364#391C2311yescharacteristic
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2312yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#390C2312yes—
375#390C2311yescharacteristic
376#390C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2312yes—
403#389C2312yes—
404#389C2314yes—
405#389C2312yes—
406#389C2314yes—
407#389C2314yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2314yes—
413#389C2314yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2312yes—
422#389C2312yes—
423#389C2314yes—
424#389C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#386C2312yes—
531#386C2312yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2312yes—
538#385C2314yes—
539#385C2312yes—
540#384C2312yes—
541#384C2312yes—
542#384C2312yes—
543#384C2312yes—
544#384C2312yes—
545#383C2312yes—
546#383C2312yes—
547#383C2314yes—
548#383C2314yes—
549#383C2314yes—
550#383C2314yes—
551#383C2314yes—
552#382C2311yescharacteristic
553#382C2312yes—
554#382C2312yes—
555#382C2312yes—
556#382C2314yes—
557#382C2314yes—
558#382C2314yes—
559#382C2314yes—
560#382C2314yes—
561#382C2314yes—
562#382C2314yes—
563#382C2311yescharacteristic
564#382C2311yescharacteristic
565#382C2314yes—
566#382C2314yes—
567#382C2314yes—
568#382C2314yes—
569#381C2312yes—
570#381C2312yes—
571#381C2314yes—
572#381C2314yes—
573#380C2314yes—
574#380C2314yes—
575#380C2314yes—
576#380C2312yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2311yescharacteristic
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2312yes—
611#376C2312yes—
612C43C2312yes—
613C43C2311yescharacteristic
614C22×Q8C2411yescharacteristic
615C22×Q8C2411yescharacteristic
616C22×Q8C2414yes—
617C22×Q8C2412yes—
618C22×D4C2411yescharacteristic
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2412yes—
622C4⋊Q8—44no—
623#126—48no—
624#125—28no—
625#125—28no—
626#125—44no—
627#125—44no—
628#125—44no—
629#125—48no—
630#125—48no—
631#125—48no—
632#125—48no—
633#124—24no—
634C22⋊Q8—48no—
635C22⋊Q8—48no—
636C22⋊Q8—44no—
637C4×Q8—42no—
638C4×Q8—42no—
639C4×Q8—44no—
640C4×D4—42no—
641C2×C4⋊C4—44no—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2412yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2412yes—
692C2×C4⋊C4C2412yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2412yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2412yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2412yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2412yes—
723C2×C22⋊C4C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750#95C2411yescharacteristic
751#95C2412yes—
752#95C2414yes—
753#95C2414yes—
754#95C2412yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2412yes—
761#95C2411yescharacteristic
762#95C2412yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2412yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2412yes—
809#95C2412yes—
810#95C2412yes—
811#95C2412yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2412yes—
827#95C2414yes—
828#95C2414yes—
829C24C2512yes—
830C2×Q8—22no—
831C2×Q8—41no—
832C2×Q8—42no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—44no—
836C2×Q8—44no—
837C2×Q8—42no—
838C2×Q8—44no—
839C2×Q8—44no—
840C2×D4—22no—
841C2×D4—41no—
842C2×D4—41no—
843C22×C4—24no—
844C22×C4—44no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2512yes—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—42no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—44no—
934C4⋊C4—44no—
935C4⋊C4—44no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—42no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C42—22no—
954C42—24no—
955C42—24no—
956C42—41no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—44no—
961C42—44no—
962C42—42no—
963C42—44no—
964C42—44no—
965C42—44no—
966C42—42no—
967C42—44no—
968C42—44no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—44no—
977C42—44no—
978C422−1+414yes—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—24no—
983C23—22no—
984C23C2611yescharacteristic
985Q8—44no—
986Q8—82no—
987Q8—162no—
988Q8—164no—
989D4—82no—
990C2×C4—22no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—84no—
1049C2×C4—162no—
1050C2×C4—162no—
1051C2×C4C2×2−1+414yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4#58512yes—
1054C2×C4#58514yes—
1055C22—42no—
1056C22—44no—
1057C22—42no—
1058C22—42no—
1059C22—44no—
1060C22C22×2−1+411yescharacteristic
1061C22C2×#58511yescharacteristic
1062C22C2×#58512yes—
1063C222−1+612yes—
1064C222−1+611yescharacteristic
1065C4—22no—
1066C4—24no—
1067C4—22no—
1068C4—24no—
1069C4—42no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4—44no—
1075C4—44no—
1076C4—44no—
1077C4—44no—
1078C4—44no—
1079C4—41no—
1080C4—42no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—44no—
1085C4—44no—
1086C4—44no—
1087C2—82no—
1088C2#6284111yescharacteristic
1089C2#6293211yescharacteristic
1090C2#6295612yes—
1091C2#6306411yescharacteristic
1092C2#6306812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58752C2semidirect
2. #57733C2semidirect
3. #57731C2semidirect
5. #51293C2semidirect
7. #50981C2semidirect
8. #50915C2semidirect
10. #49535C2semidirect
11. #49443C2semidirect
12. #49260C2semidirect
13. #49094C2semidirect
14. #48989C2semidirect
17. #46243C2semidirect
18. #46157C2semidirect
21. #37603C2semidirect
23. #36567C2semidirect

Maximal subgroups

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

subgroupindex
#587522
#577332
#577312
#575982
#512932
#511952
#509812
#509152
#503252
#495352
#494432
#492602
#490942
#489892
#462452
#462442
#462432
#461572
#461522
#376122
#376032
#366012
#365672