Finite Group Databasebeta

← #7716055

Subgroups — #7716055

Order 512.

4668 conjugacy classes of subgroups.

The subgroup lattice has 1457 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#50581C214yesmaximal, complemented
2#50521C214yesmaximal, complemented
3#49467C214yesmaximal, complemented
4#49367C214yesmaximal, complemented
5#45087C212yesmaximal, complemented
6#45080C212yesmaximal, complemented
7#45026C212yesmaximal, complemented
8#45021C212yesmaximal, complemented
9#44967C212yesmaximal, complemented
10#44960C212yesmaximal, complemented
11#44924C212yesmaximal, complemented
12#44918C212yesmaximal, complemented
13#39752C211yesmaximal, characteristic, complemented
14#39743C211yesmaximal, characteristic
15#39145C212yesmaximal, complemented
16#39141C214yesmaximal, complemented
17#37771C212yesmaximal, complemented
18#37763C212yesmaximal, complemented
19#37000C214yesmaximal, complemented
20#36483C212yesmaximal, complemented
21#36117C211yesmaximal, characteristic, complemented
22#36116C211yesmaximal, characteristic, complemented
23#35229C212yesmaximal, complemented
24#35119C212yesmaximal, complemented
25#35099C212yesmaximal, complemented
26#35006C211yesmaximal, characteristic, complemented
27#34584C211yesmaximal, characteristic, complemented
28#34472C212yesmaximal, complemented
29C2×#2356C211yesmaximal, characteristic, complemented
30C2×#548C2212yes—
31C2×#539C2212yes—
32C2×#529C2212yes—
33C2×#529C2212yes—
34C22×C4×Q8C2211yescharacteristic
35#2857C2211yescharacteristic
36#2856C2211yescharacteristic
37#2855C2212yes—
38#2854C2212yes—
39#2854C2214yes—
40#2854C2214yes—
41#2854C2212yes—
42#2853C2214yes—
43#2809C2212yes—
44#2806C2212yes—
45#2799C2214yes—
46#2797C2214yes—
47#2793C2214yes—
48#2793C2214yes—
49#2791C2214yes—
50#2791C2214yes—
51#2786C2214yes—
52#2783C2214yes—
53#2782C2214yes—
54#2781C2214yes—
55#2777C2214yes—
56#2776C2214yes—
57#2776C2214yes—
58#2773C2214yes—
59#2770C2214yes—
60#2770C2214yes—
61#2768C2214yes—
62#2765C2214yes—
63#2757C2214yes—
64#2757C2214yes—
65#2752C2214yes—
66#2749C2214yes—
67#2749C2214yes—
68#2748C2214yes—
69#2743C2214yes—
70#2741C2214yes—
71#2740C2214yes—
72#2740C2214yes—
73#2738C2214yes—
74#2733C2212yes—
75#2732C2212yes—
76#2730C2214yes—
77#2730C2214yes—
78#2722C2214yes—
79#2721C2214yes—
80#2721C2214yes—
81#2719C2214yes—
82#2717C2214yes—
83#2705C2214yes—
84#2698C2214yes—
85#2659C2212yes—
86#2656C2212yes—
87#2655C2212yes—
88#2654C2212yes—
89#2654C2214yes—
90#2651C2212yes—
91#2651C2214yes—
92#2650C2212yes—
93#2646C2211yescharacteristic
94#2643C2212yes—
95#2643C2214yes—
96#2639C2211yescharacteristic
97#2639C2212yes—
98#2627C2211yescharacteristic
99#2623C2212yes—
100#2618C2211yescharacteristic
101#2618C2212yes—
102#2611C2214yes—
103#2611C2214yes—
104#2610C2214yes—
105#2610C2214yes—
106#2604C2214yes—
107#2604C2214yes—
108#2603C2214yes—
109#2603C2214yes—
110#2581C2212yes—
111#2578C2214yes—
112#2578C2214yes—
113#2570C2212yes—
114#2569C2214yes—
115#2566C2212yes—
116#2565C2212yes—
117#2560C2214yes—
118#2558C2214yes—
119#2552C2211yescharacteristic
120#2552C2211yescharacteristic
121#2548C2211yescharacteristic
122#2547C2211yescharacteristic
123#2543C2214yes—
124#2533C2214yes—
125#2532C2214yes—
126#2531C2214yes—
127#2530C2214yes—
128#2529C2214yes—
129#2528C2214yes—
130#2527C2214yes—
131#2526C2214yes—
132#2525C2214yes—
133#2525C2214yes—
134#2522C2214yes—
135#2516C2214yes—
136#2515C2214yes—
137#2515C2214yes—
138#2513C2212yes—
139#2513C2212yes—
140#2512C2212yes—
141#2512C2212yes—
142#2510C2214yes—
143#2510C2214yes—
144#2509C2212yes—
145#2507C2212yes—
146#2506C2212yes—
147#2504C2212yes—
148#2501C2212yes—
149#2501C2214yes—
150#2497C2212yes—
151#2496C2212yes—
152#2494C2212yes—
153#2490C2212yes—
154#2486C2212yes—
155#2486C2214yes—
156#2479C2214yes—
157#2478C2214yes—
158#2478C2214yes—
159#2471C2214yes—
160#2467C2214yes—
161#2462C2214yes—
162#2454C2212yes—
163#2453C2212yes—
164#2453C2212yes—
165#2452C2212yes—
166#2451C2212yes—
167#2448C2212yes—
168#2448C2214yes—
169#2448C2212yes—
170#2448C2214yes—
171#2448C2212yes—
172#2448C2212yes—
173#2447C2212yes—
174#2445C2212yes—
175#2442C2212yes—
176#2442C2212yes—
177#2441C2214yes—
178#2438C2214yes—
179#2431C2212yes—
180#2425C2214yes—
181#2425C2214yes—
182#2425C2214yes—
183#2423C2212yes—
184#2423C2212yes—
185#2423C2214yes—
186#2423C2212yes—
187#2423C2214yes—
188#2423C2214yes—
189#2420C2212yes—
190#2419C2214yes—
191#2419C2214yes—
192#2419C2214yes—
193#2419C2214yes—
194#2416C2212yes—
195#2407C2212yes—
196#2402C2212yes—
197#2401C2212yes—
198#2396C2212yes—
199#2395C2212yes—
200#2379C2214yes—
201#2378C2214yes—
202#2367C2212yes—
203#2366C2211yescharacteristic
204#2365C2211yescharacteristic
205#2364C2214yes—
206#2361C2212yes—
207#2360C2212yes—
208#2356C2212yes—
209#2356C2212yes—
210#2356C2214yes—
211#2356C2214yes—
212#2356C2212yes—
213#2356C2212yes—
214#2355C2212yes—
215#2354C2212yes—
216Q8×C4⋊C4C2211yescharacteristic
217Q8×C4⋊C4C2212yes—
218Q8×C4⋊C4C2212yes—
219#2349C2214yes—
220D4×C4⋊C4C2211yescharacteristic
221D4×C4⋊C4C2212yes—
222#2344C2212yes—
223#2341C2212yes—
224#2341C2212yes—
225Q8×C22⋊C4C2212yes—
226#2339C2212yes—
227#2337C2214yes—
228#2330C2212yes—
229#2329C2212yes—
230#2329C2214yes—
231#2326C2212yes—
232#2325C2212yes—
233#2325C2214yes—
234#2325C2214yes—
235#2325C2212yes—
236#2324C2212yes—
237#2323C2212yes—
238#2320C2212yes—
239#2319C2212yes—
240#2318C2214yes—
241#2314C2212yes—
242#2311C2212yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×#123C2212yes—
245C4×#123C2214yes—
246C4×#121C2211yescharacteristic
247C4×#121C2212yes—
248C2×#391C2211yescharacteristic
249C2×#391C2211yescharacteristic
250#2290C2212yes—
251C2×#387C2212yes—
252C2×#387C2212yes—
253C2×#383C2212yes—
254C2×#382C2211yescharacteristic
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2212yes—
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261#548—216no—
262#539—48no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×#127C2311yescharacteristic
265#529—48no—
266#529—48no—
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
272C2×#125C2312yes—
273C2×#125C2314yes—
274C2×#124C2312yes—
275C2×#124C2314yes—
276C2×#124C2312yes—
277C2×#124C2312yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2314yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292C2×#121C2311yescharacteristic
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×C4×Q8—28no—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2314yes—
318C2×#117C2314yes—
319C22×C4⋊C4C2311yescharacteristic
320C22×C4⋊C4C2311yescharacteristic
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2311yescharacteristic
324C22×C4⋊C4C2311yescharacteristic
325C22×C4⋊C4C2311yescharacteristic
326C22×C42C2312yes—
327C22×C42C2311yescharacteristic
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332#401C2312yes—
333#401C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2312yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2312yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2312yes—
356#399C2312yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#397C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2312yes—
413#396C2314yes—
414#396C2314yes—
415#396C2312yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2312yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2312yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#393C2314yes—
432#393C2312yes—
433#392C2314yes—
434#392C2314yes—
435#392C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2311yescharacteristic
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2311yescharacteristic
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2311yescharacteristic
499#389C2311yescharacteristic
500#389C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2312yes—
534#388C2312yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#387C2314yes—
542#387C2314yes—
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#387C2312yes—
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#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2312yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2312yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2314yes—
630#384C2314yes—
631#383C2314yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2312yes—
647#381C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2311yescharacteristic
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701#376C2312yes—
702#376C2314yes—
703#376C2314yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2312yes—
709C2×#95C2311yescharacteristic
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2311yescharacteristic
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#41—28no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—42no—
721C22×Q8—42no—
722C22×Q8#4118yes—
723C22×Q8C2412yes—
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×D4C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C22×D4C2412yes—
735C23×C4C2411yescharacteristic
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2412yes—
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C23×C4C2411yescharacteristic
746C23×C4C2414yes—
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C4⋊Q8—42no—
752#127—42no—
753#126—48no—
754#126—48no—
755#126—48no—
756#125—44no—
757#125—44no—
758#125—44no—
759#125—48no—
760#124—28no—
761#124—216no—
762#124—44no—
763#124—44no—
764#123—48no—
765#123—44no—
766#123—48no—
767#123—48no—
768#123—48no—
769#123—48no—
770C22⋊Q8—28no—
771C22⋊Q8—216no—
772C22⋊Q8—24no—
773C22⋊Q8—28no—
774C22⋊Q8—48no—
775#121—28no—
776#121—216no—
777#121—24no—
778#121—28no—
779#121—44no—
780#121—48no—
781#121—44no—
782C4×Q8—28no—
783C4×Q8—28no—
784C4×Q8—216no—
785C4×Q8—28no—
786C4×Q8—42no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×D4—28no—
792C4×D4—216no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—44no—
797C4×D4—42no—
798C4×D4—48no—
799C4×D4—48no—
800C4×D4—48no—
801#117—44no—
802#117—48no—
803#117—48no—
804C2×C4⋊C4—24no—
805C2×C4⋊C4—28no—
806C2×C4⋊C4—24no—
807C2×C4⋊C4—42no—
808C2×C4⋊C4—44no—
809C2×C4⋊C4—42no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C42—24no—
918C2×C42—28no—
919C2×C42—28no—
920C2×C42—42no—
921C2×C42—42no—
922C2×C42—44no—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018C24C2512yes—
1019C24C2514yes—
1020C24C2511yescharacteristic
1021#41—816no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—41no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—41no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—416no—
1033C2×Q8C2×#4118yes—
1034C2×Q8C2×#4118yes—
1035C2×D4—24no—
1036C2×D4—28no—
1037C2×D4—24no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—28no—
1043C2×D4—22no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—41no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—28no—
1077C22×C4—41no—
1078C22×C4—41no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—42no—
1096C22×C4—41no—
1097C22×C4—42no—
1098C22×C4—41no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4C2×#4114yes—
1105C22×C4C2×#4118yes—
1106C22×C4H(5,𝔽2)14yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2514yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—22no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—24no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—41no—
1161C4⋊C4—41no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—41no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—41no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—28no—
1201C22⋊C4—24no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C42—28no—
1240C42—28no—
1241C42—24no—
1242C42—24no—
1243C42—28no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—24no—
1249C42—24no—
1250C42—22no—
1251C42—22no—
1252C42—24no—
1253C42—24no—
1254C42—41no—
1255C42—41no—
1256C42—42no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—21no—
1268C23—22no—
1269C23—24no—
1270C23—24no—
1271C23—22no—
1272C23—24no—
1273C23—22no—
1274C23—22no—
1275C23—24no—
1276C23—24no—
1277C23—22no—
1278C23—22no—
1279C23—24no—
1280C23—24no—
1281C23—22no—
1282C23C22×#4112yes—
1283C23C2×H(5,𝔽2)12yes—
1284C23#58512yes—
1285C23C2611yescharacteristic
1286Q8—216no—
1287Q8—48no—
1288Q8—44no—
1289Q8—84no—
1290D4—44no—
1291D4—48no—
1292D4—416no—
1293D4—48no—
1294D4—84no—
1295D4—88no—
1296D4—162no—
1297D4—164no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—28no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—48no—
1371C2×C4—44no—
1372C2×C4—44no—
1373C2×C4—44no—
1374C2×C4—48no—
1375C2×C4—44no—
1376C2×C4—48no—
1377C2×C4—88no—
1378C2×C4—82no—
1379C2×C4—82no—
1380C2×C4—84no—
1381C2×C4—84no—
1382C2×C4—88no—
1383C2×C4—88no—
1384C2×C4—164no—
1385C2×C4C22×#4118yes—
1386C2×C4C22×#4112yes—
1387C2×C4C22×#4112yes—
1388C2×C4C2×H(5,𝔽2)12yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4#58512yes—
1391C2×C4#58512yes—
1392C22—22no—
1393C22—22no—
1394C22—22no—
1395C22—22no—
1396C22—22no—
1397C22—22no—
1398C22—42no—
1399C22—44no—
1400C22—42no—
1401C22—44no—
1402C22—42no—
1403C22—44no—
1404C22—44no—
1405C22—42no—
1406C22—44no—
1407C22—42no—
1408C22—42no—
1409C22—44no—
1410C22—42no—
1411C22—44no—
1412C22#351714yes—
1413C22C23×#4111yescharacteristic
1414C22C22×H(5,𝔽2)11yescharacteristic
1415C22C2×#58511yescharacteristic
1416C22C2×#58511yescharacteristic
1417C22C2×#58511yescharacteristic
1418C222−1+611yescharacteristic
1419C222−1+611yescharacteristic
1420C4—22no—
1421C4—28no—
1422C4—22no—
1423C4—22no—
1424C4—42no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—41no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—44no—
1445C4#349114yes—
1446C2—24no—
1447C2—82no—
1448C2—84no—
1449C2C2×#349111yescharacteristic
1450C2C2×#351711yescharacteristic
1451C2#6285011yescharacteristic
1452C2#6290111yescharacteristic
1453C2#6293411yescharacteristic
1454C2#6296011yescharacteristic
1455C2#6296411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #50581C2semidirect
2. #50521C2semidirect
3. #49467C2semidirect
4. #49367C2semidirect
5. #45087C2semidirect
6. #45080C2semidirect
7. #45026C2semidirect
8. #45021C2semidirect
9. #44967C2semidirect
10. #44960C2semidirect
11. #44924C2semidirect
12. #44918C2semidirect
13. #39752C2semidirect
15. #39145C2semidirect
16. #39141C2semidirect
17. #37771C2semidirect
18. #37763C2semidirect
19. #37000C2semidirect
20. #36483C2semidirect
21. #36117C2semidirect
22. #36116C2semidirect
23. #35229C2semidirect
24. #35119C2semidirect
25. #35099C2semidirect
26. #35006C2semidirect
27. #34584C2semidirect
28. #34472C2semidirect
29. C2×#2356C2semidirect

Maximal subgroups

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

subgroupindex
#505812
#505212
#494672
#493672
#450872
#450802
#450262
#450212
#449672
#449602
#449242
#449182
#397522
#397432
#391452
#391412
#377712
#377632
#370002
#364832
#361172
#361162
#352292
#351192
#350992
#350062
#345842
#344722
C2×#23562