Finite Group Databasebeta

← #8726484

Subgroups — #8726484

Order 512.

4387 conjugacy classes of subgroups.

The subgroup lattice has 1410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59925C211yesmaximal, characteristic, complemented
2#59627C212yesmaximal, complemented
3#59557C212yesmaximal, complemented
4#59152C212yesmaximal, complemented
5#59036C212yesmaximal, complemented
6#58726C214yesmaximal, complemented
7#58630C214yesmaximal, complemented
8#54502C214yesmaximal, complemented
9#53642C212yesmaximal, complemented
10#53081C211yesmaximal, characteristic, complemented
11#53035C212yesmaximal, complemented
12#52302C211yesmaximal, characteristic, complemented
13#47541C212yesmaximal, complemented
14#47476C214yesmaximal, complemented
15#45435C211yesmaximal, characteristic, complemented
16#45351C212yesmaximal, complemented
17#45193C212yesmaximal, complemented
18#45037C214yesmaximal, complemented
19#42729C212yesmaximal, complemented
20#42481C211yesmaximal, characteristic, complemented
21#42285C212yesmaximal, complemented
22#40923C214yesmaximal, complemented
23#40174C212yesmaximal, complemented
24#40121C212yesmaximal, complemented
25#39891C212yesmaximal, complemented
26#39746C211yesmaximal, characteristic, complemented
27#39029C212yesmaximal, complemented
28#36051C211yesmaximal, characteristic
29#35963C212yesmaximal, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#555C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#533C2212yes—
35#2858C2211yescharacteristic
36#2854C2212yes—
37#2841C2214yes—
38#2838C2214yes—
39#2837C2214yes—
40#2832C2212yes—
41#2831C2214yes—
42#2831C2214yes—
43#2823C2212yes—
44#2821C2214yes—
45#2814C2212yes—
46#2800C2214yes—
47#2800C2214yes—
48#2799C2211yescharacteristic
49#2799C2212yes—
50#2797C2214yes—
51#2796C2214yes—
52#2794C2211yescharacteristic
53#2794C2212yes—
54#2793C2214yes—
55#2792C2214yes—
56#2792C2212yes—
57#2786C2214yes—
58#2777C2214yes—
59#2776C2212yes—
60#2770C2214yes—
61#2770C2212yes—
62#2762C2214yes—
63#2754C2214yes—
64#2754C2214yes—
65#2745C2214yes—
66#2745C2212yes—
67#2742C2214yes—
68#2741C2214yes—
69#2740C2214yes—
70#2738C2214yes—
71#2737C2214yes—
72#2737C2214yes—
73#2734C2212yes—
74#2734C2212yes—
75#2734C2212yes—
76#2731C2214yes—
77#2729C2212yes—
78#2728C2211yescharacteristic
79#2727C2214yes—
80#2722C2214yes—
81#2718C2214yes—
82#2717C2214yes—
83#2716C2214yes—
84#2716C2214yes—
85#2705C2214yes—
86#2705C2214yes—
87#2704C2214yes—
88#2700C2214yes—
89#2700C2214yes—
90#2695C2212yes—
91#2694C2214yes—
92#2694C2214yes—
93#2692C2214yes—
94#2692C2214yes—
95#2689C2212yes—
96#2686C2214yes—
97#2681C2214yes—
98#2680C2214yes—
99#2680C2211yescharacteristic
100#2677C2214yes—
101#2674C2214yes—
102#2672C2214yes—
103#2672C2214yes—
104#2667C2214yes—
105#2662C2214yes—
106#2661C2212yes—
107#2658C2212yes—
108#2653C2214yes—
109#2650C2214yes—
110#2650C2214yes—
111#2647C2212yes—
112#2640C2211yescharacteristic
113#2640C2211yescharacteristic
114#2638C2212yes—
115#2632C2214yes—
116#2630C2214yes—
117#2614C2212yes—
118#2602C2214yes—
119#2599C2214yes—
120#2596C2214yes—
121#2594C2214yes—
122#2594C2214yes—
123#2592C2211yescharacteristic
124#2589C2214yes—
125#2587C2214yes—
126#2586C2212yes—
127#2586C2214yes—
128#2586C2212yes—
129#2586C2212yes—
130#2584C2212yes—
131#2573C2214yes—
132#2569C2214yes—
133#2567C2211yescharacteristic
134#2567C2212yes—
135#2565C2212yes—
136#2563C2212yes—
137#2557C2214yes—
138#2556C2214yes—
139#2552C2212yes—
140#2551C2212yes—
141#2551C2212yes—
142#2551C2214yes—
143#2550C2212yes—
144#2550C2212yes—
145#2550C2212yes—
146#2548C2211yescharacteristic
147#2547C2212yes—
148#2546C2211yescharacteristic
149#2546C2211yescharacteristic
150#2545C2212yes—
151#2545C2214yes—
152#2543C2212yes—
153#2540C2211yescharacteristic
154#2538C2214yes—
155#2533C2214yes—
156#2532C2214yes—
157#2524C2214yes—
158#2521C2214yes—
159#2521C2214yes—
160#2521C2214yes—
161#2517C2214yes—
162#2516C2214yes—
163#2514C2212yes—
164#2513C2214yes—
165#2512C2214yes—
166#2512C2212yes—
167#2512C2212yes—
168#2511C2212yes—
169#2507C2214yes—
170#2500C2212yes—
171#2498C2212yes—
172#2497C2212yes—
173#2497C2214yes—
174#2496C2214yes—
175#2496C2212yes—
176#2494C2214yes—
177#2491C2214yes—
178#2491C2212yes—
179#2491C2214yes—
180#2490C2212yes—
181#2490C2212yes—
182#2490C2212yes—
183#2489C2212yes—
184#2489C2212yes—
185#2485C2212yes—
186#2477C2214yes—
187#2470C2214yes—
188#2469C2214yes—
189#2465C2214yes—
190#2465C2214yes—
191#2465C2214yes—
192#2462C2214yes—
193#2462C2214yes—
194#2454C2212yes—
195#2454C2212yes—
196#2454C2212yes—
197#2454C2212yes—
198#2454C2212yes—
199#2452C2212yes—
200#2451C2214yes—
201#2451C2212yes—
202#2451C2212yes—
203#2448C2212yes—
204#2448C2212yes—
205#2447C2212yes—
206#2445C2212yes—
207#2441C2212yes—
208#2439C2212yes—
209#2439C2212yes—
210#2439C2212yes—
211#2438C2214yes—
212#2428C2212yes—
213#2427C2212yes—
214#2423C2214yes—
215#2423C2214yes—
216#2409C2212yes—
217#2409C2214yes—
218#2402C2212yes—
219#2401C2212yes—
220#2399C2211yescharacteristic
221#2398C2211yescharacteristic
222#2396C2214yes—
223#2395C2212yes—
224#2370C2212yes—
225#2370C2212yes—
226#2370C2212yes—
227#2370C2212yes—
228#2370C2212yes—
229#2369C2212yes—
230#2365C2214yes—
231#2365C2212yes—
232#2363C2212yes—
233#2363C2212yes—
234#2362C2212yes—
235#2362C2212yes—
236#2357C2212yes—
237#2357C2214yes—
238#2355C2214yes—
239#2354C2212yes—
240#2347C2212yes—
241Q8×C22⋊C4C2214yes—
242#2335C2214yes—
243#2330C2212yes—
244#2326C2212yes—
245#2324C2214yes—
246#2323C2214yes—
247#2319C2211yescharacteristic
248#2314C2214yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×#125C2212yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256C4×#121C2212yes—
257#2295C2211yescharacteristic
258#2275C2211yescharacteristic
259C23×Q8C2312yes—
260#559—44no—
261#557—44no—
262#555—44no—
263D4×Q8—44no—
264#533—48no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2312yes—
276C2×#127C2311yescharacteristic
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2314yes—
289C2×#124C2311yescharacteristic
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#123C2314yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2312yes—
298C2×#123C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×#121C2312yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2314yes—
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2312yes—
330C2×#117C2312yes—
331C22×C42C2312yes—
332#401C2314yes—
333#401C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2311yescharacteristic
347#400C2312yes—
348#400C2311yescharacteristic
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2312yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2312yes—
376#398C2311yescharacteristic
377#398C2312yes—
378#398C2311yescharacteristic
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2312yes—
388#397C2312yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2312yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2312yes—
404#397C2312yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2312yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2311yescharacteristic
430#395C2311yescharacteristic
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2312yes—
436#395C2314yes—
437#394C2311yescharacteristic
438#394C2314yes—
439#394C2311yescharacteristic
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#393C2312yes—
458#393C2314yes—
459#393C2312yes—
460#393C2314yes—
461#393C2312yes—
462#393C2312yes—
463#392C2312yes—
464#392C2314yes—
465#391C2311yescharacteristic
466#391C2311yescharacteristic
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2314yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#390C2314yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2314yes—
500#390C2314yes—
501#390C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#388C2312yes—
537#388C2312yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
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#388C2312yes—
573#388C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2312yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2314yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2312yes—
624#386C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2314yes—
636#385C2312yes—
637#385C2312yes—
638#384C2311yescharacteristic
639#384C2312yes—
640#384C2312yes—
641#384C2314yes—
642#384C2312yes—
643#384C2314yes—
644#383C2312yes—
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#381C2312yes—
652#381C2314yes—
653#381C2312yes—
654#381C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2311yescharacteristic
713#376C2312yes—
714#376C2311yescharacteristic
715C2×#95C2312yes—
716C43C2311yescharacteristic
717C22×Q8—44no—
718C22×Q8—48no—
719C22×Q8C2411yescharacteristic
720C22×Q8C2414yes—
721C22×Q8C2411yescharacteristic
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×D4C2411yescharacteristic
729C22×D4C2411yescharacteristic
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2414yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C4⋊Q8—28no—
743C4⋊Q8—44no—
744C4⋊Q8—42no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—44no—
750C4⋊Q8—48no—
751C4⋊Q8—82no—
752C4⋊Q8—84no—
753#127—42no—
754#126—44no—
755#126—84no—
756#126—84no—
757#126—84no—
758#125—28no—
759#125—28no—
760#125—28no—
761#125—44no—
762#125—48no—
763#124—48no—
764#124—44no—
765#124—44no—
766#124—42no—
767#124—42no—
768#124—82no—
769#124—84no—
770#124—82no—
771#123—48no—
772#123—44no—
773#123—44no—
774#123—44no—
775#123—84no—
776C22⋊Q8—28no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—48no—
782C22⋊Q8—48no—
783C22⋊Q8—44no—
784#121—28no—
785#121—44no—
786#121—48no—
787#121—44no—
788C4×Q8—24no—
789C4×Q8—42no—
790C4×Q8—42no—
791C4×Q8—42no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—48no—
796C4×Q8—44no—
797C4×D4—24no—
798C4×D4—24no—
799C4×D4—28no—
800C4×D4—44no—
801C4×D4—48no—
802C4×D4—42no—
803C4×D4—44no—
804#117—28no—
805#117—44no—
806#117—48no—
807#117—44no—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C42—44no—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2411yescharacteristic
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2414yes—
944#95C2411yescharacteristic
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015C24C2512yes—
1016C24C2512yes—
1017C24C2512yes—
1018C2×Q8—22no—
1019C2×Q8—28no—
1020C2×Q8—24no—
1021C2×Q8—28no—
1022C2×Q8—24no—
1023C2×Q8—22no—
1024C2×Q8—24no—
1025C2×Q8—22no—
1026C2×Q8—41no—
1027C2×Q8—44no—
1028C2×Q8—44no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—41no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—42no—
1041C2×Q8—42no—
1042C2×Q8—816no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—24no—
1046C2×D4—24no—
1047C2×D4—28no—
1048C2×D4—24no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—28no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2514yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—44no—
1126C4⋊C4—41no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—41no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—42no—
1134C4⋊C4—41no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—41no—
1139C4⋊C4—41no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—42no—
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—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4H(5,𝔽2)14yes—
1169C4⋊C42−1+418yes—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—28no—
1176C22⋊C4—28no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—42no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—44no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—44no—
1211C22⋊C4—42no—
1212C22⋊C4—44no—
1213C42—24no—
1214C42—24no—
1215C42—28no—
1216C42—22no—
1217C42—22no—
1218C42—24no—
1219C42—22no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—28no—
1224C42—22no—
1225C42—42no—
1226C42—42no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—41no—
1233C42—44no—
1234C42—42no—
1235C42—42no—
1236C42—42no—
1237C42—44no—
1238C42—42no—
1239C42—44no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—24no—
1246C23—22no—
1247C23—22no—
1248C23—24no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—24no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23C2611yescharacteristic
1258Q8—416no—
1259Q8—44no—
1260Q8—44no—
1261Q8—82no—
1262Q8—82no—
1263Q8—84no—
1264Q8—88no—
1265Q8—84no—
1266Q8—162no—
1267D4—44no—
1268D4—44no—
1269D4—88no—
1270D4—84no—
1271D4—82no—
1272D4—162no—
1273D4—164no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—21no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—21no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—48no—
1341C2×C4—84no—
1342C2×C4—84no—
1343C2×C4—88no—
1344C2×C4—88no—
1345C2×C4—84no—
1346C2×C4—84no—
1347C2×C4C2×H(5,𝔽2)14yes—
1348C2×C4C2×H(5,𝔽2)12yes—
1349C2×C4C2×2−1+418yes—
1350C2×C4C2×2−1+414yes—
1351C2×C4#58514yes—
1352C2×C4#58512yes—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—44no—
1360C22—42no—
1361C22—44no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—44no—
1368C22—44no—
1369C22—42no—
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22C22×2−1+412yes—
1372C22C2×#58512yes—
1373C22C2×#58511yescharacteristic
1374C22H(7,𝔽2)11yescharacteristic
1375C4—24no—
1376C4—24no—
1377C4—28no—
1378C4—22no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—41no—
1383C4—41no—
1384C4—44no—
1385C4—41no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—44no—
1392C4—41no—
1393C4—44no—
1394C4—41no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—44no—
1400C4#355014yes—
1401C2—82no—
1402C2—82no—
1403C2—82no—
1404C2C2×#355011yescharacteristic
1405C2#6289911yescharacteristic
1406C2#6295212yes—
1407C2#6301711yescharacteristic
1408C2#6302512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36051C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59925C2semidirect
2. #59627C2semidirect
3. #59557C2semidirect
4. #59152C2semidirect
5. #59036C2semidirect
6. #58726C2semidirect
7. #58630C2semidirect
8. #54502C2semidirect
9. #53642C2semidirect
10. #53081C2semidirect
11. #53035C2semidirect
12. #52302C2semidirect
13. #47541C2semidirect
14. #47476C2semidirect
15. #45435C2semidirect
16. #45351C2semidirect
17. #45193C2semidirect
18. #45037C2semidirect
19. #42729C2semidirect
20. #42481C2semidirect
21. #42285C2semidirect
22. #40923C2semidirect
23. #40174C2semidirect
24. #40121C2semidirect
25. #39891C2semidirect
26. #39746C2semidirect
27. #39029C2semidirect
29. #35963C2semidirect

Maximal subgroups

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

subgroupindex
#599252
#596272
#595572
#591522
#590362
#587262
#586302
#545022
#536422
#530812
#530352
#523022
#475412
#474762
#454352
#453512
#451932
#450372
#427292
#424812
#422852
#409232
#401742
#401212
#398912
#397462
#390292
#360512
#359632