Finite Group Databasebeta

← #8096548

Subgroups — #8096548

Order 512.

4637 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53132C212yesmaximal, complemented
2#53118C212yesmaximal, complemented
3#52995C212yesmaximal, complemented
4#52522C214yesmaximal, complemented
5#52502C214yesmaximal, complemented
6#52441C214yesmaximal, complemented
7#52305C211yesmaximal, characteristic, complemented
8#52152C212yesmaximal, complemented
9#46281C212yesmaximal, complemented
10#46131C214yesmaximal, complemented
11#46113C212yesmaximal, complemented
12#46044C212yesmaximal, complemented
13#46014C211yesmaximal, characteristic, complemented
14#45998C212yesmaximal, complemented
15#45998C211yesmaximal, characteristic, complemented
16#45997C211yesmaximal, characteristic
17#45957C212yesmaximal, complemented
18#45939C212yesmaximal, complemented
19#45819C214yesmaximal, complemented
20#45790C214yesmaximal, complemented
21#36527C212yesmaximal, complemented
22#36497C211yesmaximal, characteristic, complemented
23#36407C212yesmaximal, complemented
24#36300C211yesmaximal, characteristic, complemented
25#36300C211yesmaximal, characteristic, complemented
26#36115C212yesmaximal, complemented
27#35871C212yesmaximal, complemented
28#35865C212yesmaximal, complemented
29#35860C212yesmaximal, complemented
30C2×#563C2212yes—
31C2×#563C2214yes—
32C2×#562C2212yes—
33C2×#529C2214yes—
34#2864C2212yes—
35#2861C2212yes—
36#2860C2212yes—
37#2860C2212yes—
38#2859C2212yes—
39#2859C2211yescharacteristic
40#2858C2212yes—
41#2858C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2214yes—
44#2852C2214yes—
45#2850C2214yes—
46#2838C2214yes—
47#2838C2214yes—
48#2838C2214yes—
49#2829C2214yes—
50#2829C2214yes—
51#2827C2214yes—
52#2827C2214yes—
53#2826C2214yes—
54#2824C2214yes—
55#2823C2214yes—
56#2823C2214yes—
57#2821C2214yes—
58#2820C2212yes—
59#2820C2214yes—
60#2820C2212yes—
61#2819C2212yes—
62#2817C2214yes—
63#2816C2214yes—
64#2810C2211yescharacteristic
65#2777C2214yes—
66#2775C2214yes—
67#2767C2212yes—
68#2767C2212yes—
69#2767C2212yes—
70#2765C2214yes—
71#2730C2214yes—
72#2729C2214yes—
73#2727C2214yes—
74#2727C2212yes—
75#2727C2212yes—
76#2726C2211yescharacteristic
77#2726C2211yescharacteristic
78#2726C2211yescharacteristic
79#2725C2214yes—
80#2725C2214yes—
81#2724C2212yes—
82#2723C2214yes—
83#2723C2214yes—
84#2723C2214yes—
85#2720C2214yes—
86#2719C2212yes—
87#2719C2212yes—
88#2719C2212yes—
89#2718C2214yes—
90#2718C2214yes—
91#2715C2214yes—
92#2711C2214yes—
93#2710C2214yes—
94#2708C2214yes—
95#2707C2214yes—
96#2706C2214yes—
97#2701C2214yes—
98#2698C2214yes—
99#2696C2214yes—
100#2695C2214yes—
101#2695C2214yes—
102#2689C2214yes—
103#2686C2214yes—
104#2683C2214yes—
105#2683C2212yes—
106#2682C2212yes—
107#2682C2212yes—
108#2681C2214yes—
109#2677C2214yes—
110#2676C2214yes—
111#2676C2214yes—
112#2674C2214yes—
113#2674C2214yes—
114#2674C2214yes—
115#2672C2214yes—
116#2665C2214yes—
117#2649C2214yes—
118#2648C2214yes—
119#2647C2212yes—
120#2641C2212yes—
121#2640C2212yes—
122#2595C2214yes—
123#2589C2214yes—
124#2587C2214yes—
125#2576C2214yes—
126#2576C2214yes—
127#2574C2214yes—
128#2574C2214yes—
129#2570C2212yes—
130#2567C2211yescharacteristic
131#2567C2211yescharacteristic
132#2566C2212yes—
133#2566C2212yes—
134#2560C2214yes—
135#2559C2214yes—
136#2558C2214yes—
137#2556C2214yes—
138#2556C2214yes—
139#2554C2214yes—
140#2553C2214yes—
141#2552C2212yes—
142#2552C2211yescharacteristic
143#2551C2212yes—
144#2551C2212yes—
145#2551C2211yescharacteristic
146#2550C2212yes—
147#2550C2212yes—
148#2549C2214yes—
149#2548C2211yescharacteristic
150#2548C2211yescharacteristic
151#2544C2212yes—
152#2544C2212yes—
153#2542C2212yes—
154#2542C2212yes—
155#2541C2212yes—
156#2541C2212yes—
157#2521C2214yes—
158#2521C2214yes—
159#2520C2214yes—
160#2518C2214yes—
161#2516C2214yes—
162#2514C2212yes—
163#2513C2212yes—
164#2513C2212yes—
165#2513C2212yes—
166#2512C2212yes—
167#2512C2212yes—
168#2512C2212yes—
169#2512C2212yes—
170#2512C2212yes—
171#2512C2212yes—
172#2512C2212yes—
173#2511C2212yes—
174#2492C2214yes—
175#2488C2214yes—
176#2477C2214yes—
177#2476C2214yes—
178#2474C2214yes—
179#2474C2214yes—
180#2471C2214yes—
181#2471C2214yes—
182#2467C2214yes—
183#2467C2214yes—
184#2466C2214yes—
185#2462C2214yes—
186#2457C2214yes—
187#2454C2212yes—
188#2454C2212yes—
189#2454C2212yes—
190#2454C2212yes—
191#2454C2212yes—
192#2453C2212yes—
193#2452C2212yes—
194#2452C2212yes—
195#2452C2212yes—
196#2452C2212yes—
197#2452C2212yes—
198#2451C2212yes—
199#2450C2214yes—
200#2448C2212yes—
201#2448C2212yes—
202#2447C2212yes—
203#2447C2212yes—
204#2445C2212yes—
205#2445C2212yes—
206#2445C2212yes—
207#2445C2212yes—
208#2445C2212yes—
209#2445C2212yes—
210#2444C2214yes—
211#2441C2214yes—
212#2439C2214yes—
213#2438C2214yes—
214#2429C2214yes—
215#2427C2214yes—
216#2426C2214yes—
217#2425C2214yes—
218#2402C2212yes—
219#2402C2212yes—
220#2402C2212yes—
221#2396C2214yes—
222#2395C2214yes—
223#2392C2214yes—
224#2383C2214yes—
225#2379C2212yes—
226#2377C2214yes—
227#2370C2212yes—
228#2370C2212yes—
229#2369C2212yes—
230#2369C2211yescharacteristic
231#2369C2211yescharacteristic
232#2367C2212yes—
233#2367C2212yes—
234#2366C2211yescharacteristic
235#2366C2212yes—
236#2366C2212yes—
237#2366C2211yescharacteristic
238#2365C2212yes—
239#2357C2212yes—
240#2355C2211yescharacteristic
241#2355C2211yescharacteristic
242#2354C2212yes—
243#2354C2212yes—
244#2354C2212yes—
245C4×C4⋊Q8C2212yes—
246C4×#125C2212yes—
247C4×#125C2212yes—
248C4×#125C2211yescharacteristic
249C4×#125C2212yes—
250C4×#125C2211yescharacteristic
251C4×#125C2211yescharacteristic
252C4×#123C2214yes—
253#2296C2214yes—
254#2293C2212yes—
255#2293C2212yes—
256#2275C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259#563—416no—
260#563—48no—
261#562—48no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2314yes—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×#127C2312yes—
270C2×#127C2311yescharacteristic
271C2×#127C2311yescharacteristic
272C2×#127C2312yes—
273#529—416no—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2311yescharacteristic
283C2×#125C2311yescharacteristic
284C2×#125C2312yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2314yes—
335C22×C42C2314yes—
336#401C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2314yes—
480#390C2314yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2311yescharacteristic
506#389C2311yescharacteristic
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2312yes—
512#389C2311yescharacteristic
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#384C2312yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2312yes—
641#384C2314yes—
642#384C2312yes—
643#384C2311yescharacteristic
644#383C2314yes—
645#382C2311yescharacteristic
646#382C2312yes—
647#382C2311yescharacteristic
648#382C2312yes—
649#382C2311yescharacteristic
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2312yes—
654#382C2314yes—
655#382C2312yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2311yescharacteristic
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712C2×#95C2314yes—
713C43C2311yescharacteristic
714C43C2312yes—
715C43C2312yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2412yes—
720C22×Q8C2412yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2414yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C4⋊Q8—28no—
738C4⋊Q8—44no—
739C4⋊Q8—44no—
740C4⋊Q8—42no—
741C4⋊Q8—42no—
742C4⋊Q8—48no—
743C4⋊Q8—48no—
744#127—44no—
745#127—44no—
746#127—42no—
747#127—42no—
748#126—216no—
749#126—48no—
750#126—48no—
751#126—48no—
752#126—48no—
753#126—48no—
754#126—48no—
755#125—28no—
756#125—24no—
757#125—24no—
758#125—28no—
759#125—44no—
760#125—44no—
761#125—42no—
762#125—44no—
763#125—48no—
764#125—44no—
765#124—44no—
766#124—48no—
767#124—44no—
768#124—44no—
769#124—44no—
770#124—44no—
771#124—44no—
772#124—48no—
773#123—216no—
774#123—48no—
775#123—48no—
776#123—48no—
777#123—48no—
778#123—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788#121—48no—
789#121—48no—
790#121—48no—
791#121—48no—
792C4×Q8—24no—
793C4×Q8—48no—
794C4×Q8—42no—
795C4×Q8—42no—
796C4×D4—28no—
797C4×D4—28no—
798C4×D4—28no—
799C4×D4—44no—
800C4×D4—44no—
801C4×D4—44no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—48no—
805C4×D4—48no—
806#117—48no—
807#117—48no—
808#117—48no—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C42—48no—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2411yescharacteristic
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018C24C2514yes—
1019C24C2514yes—
1020C2×Q8—28no—
1021C2×Q8—22no—
1022C2×Q8—22no—
1023C2×Q8—22no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—42no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×D4—24no—
1036C2×D4—28no—
1037C2×D4—24no—
1038C2×D4—24no—
1039C2×D4—24no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—24no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—42no—
1055C2×D4—42no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—44no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—28no—
1068C22×C4—28no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—22no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—41no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—41no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4H(5,𝔽2)14yes—
1182C4⋊C4H(5,𝔽2)14yes—
1183C4⋊C42−1+414yes—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C42—24no—
1227C42—28no—
1228C42—24no—
1229C42—22no—
1230C42—24no—
1231C42—22no—
1232C42—24no—
1233C42—24no—
1234C42—24no—
1235C42—22no—
1236C42—24no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—24no—
1242C42—22no—
1243C42—22no—
1244C42—22no—
1245C42—44no—
1246C42—44no—
1247C42—41no—
1248C42—42no—
1249C42—44no—
1250C42—44no—
1251C42—42no—
1252C42—42no—
1253C42—42no—
1254C42—44no—
1255C23—24no—
1256C23—24no—
1257C23—24no—
1258C23—24no—
1259C23—24no—
1260C23—24no—
1261C23—24no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—24no—
1266C23—24no—
1267C23—24no—
1268C23—24no—
1269C23C2611yescharacteristic
1270Q8—44no—
1271Q8—88no—
1272Q8—162no—
1273Q8—164no—
1274Q8—162no—
1275D4—48no—
1276D4—48no—
1277D4—88no—
1278D4—84no—
1279D4—84no—
1280D4—88no—
1281D4—162no—
1282D4—164no—
1283D4—162no—
1284D4—164no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—22no—
1301C2×C4—21no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—416no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4—88no—
1361C2×C4—164no—
1362C2×C4—164no—
1363C2×C4C2×H(5,𝔽2)12yes—
1364C2×C4C2×H(5,𝔽2)14yes—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×H(5,𝔽2)14yes—
1367C2×C4C2×2−1+414yes—
1368C2×C4C2×2−1+412yes—
1369C2×C4#58512yes—
1370C2×C4#58512yes—
1371C2×C4#58512yes—
1372C22—44no—
1373C22—44no—
1374C22—44no—
1375C22—44no—
1376C22—44no—
1377C22—44no—
1378C22—44no—
1379C22—44no—
1380C22—44no—
1381C22—44no—
1382C22—44no—
1383C22—44no—
1384C22—44no—
1385C22—44no—
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C22×H(5,𝔽2)11yescharacteristic
1388C22C22×2−1+411yescharacteristic
1389C22C2×#58511yescharacteristic
1390C22C2×#58511yescharacteristic
1391C22C2×#58511yescharacteristic
1392C222−1+611yescharacteristic
1393C4—24no—
1394C4—24no—
1395C4—24no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—41no—
1400C4—42no—
1401C4—44no—
1402C4—42no—
1403C4—44no—
1404C4—41no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—41no—
1411C4—42no—
1412C4—42no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4#353114yes—
1420C2—84no—
1421C2—84no—
1422C2C2×#353111yescharacteristic
1423C2#6294611yescharacteristic
1424C2#6296011yescharacteristic
1425C2#6296411yescharacteristic
1426C2#6301311yescharacteristic
1427C2#6301411yescharacteristic
1428C2#6303511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45997C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53132C2semidirect
2. #53118C2semidirect
3. #52995C2semidirect
4. #52522C2semidirect
5. #52502C2semidirect
6. #52441C2semidirect
7. #52305C2semidirect
8. #52152C2semidirect
9. #46281C2semidirect
10. #46131C2semidirect
11. #46113C2semidirect
12. #46044C2semidirect
13. #46014C2semidirect
14. #45998C2semidirect
15. #45998C2semidirect
17. #45957C2semidirect
18. #45939C2semidirect
19. #45819C2semidirect
20. #45790C2semidirect
21. #36527C2semidirect
22. #36497C2semidirect
23. #36407C2semidirect
24. #36300C2semidirect
25. #36300C2semidirect
26. #36115C2semidirect
27. #35871C2semidirect
28. #35865C2semidirect
29. #35860C2semidirect

Maximal subgroups

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

subgroupindex
#531322
#531182
#529952
#525222
#525022
#524412
#523052
#521522
#462812
#461312
#461132
#460442
#460142
#459982
#459972
#459572
#459392
#458192
#457902
#365272
#364972
#364072
#363002
#361152
#358712
#358652
#358602