Finite Group Databasebeta

← #8323584

Subgroups — #8323584

Order 512.

4298 conjugacy classes of subgroups.

The subgroup lattice has 1404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59567C212yesmaximal, complemented
2#59325C212yesmaximal, complemented
3#59073C212yesmaximal, complemented
4#58133C214yesmaximal, complemented
5#57824C212yesmaximal, complemented
6#55610C212yesmaximal, complemented
7#54733C214yesmaximal, complemented
8#54137C214yesmaximal, complemented
9#53140C212yesmaximal, complemented
10#52414C212yesmaximal, complemented
11#52288C211yesmaximal, characteristic, complemented
12#51680C214yesmaximal, complemented
13#50403C214yesmaximal, complemented
14#45517C212yesmaximal, complemented
15#45132C212yesmaximal, complemented
16#44795C212yesmaximal, complemented
17#42981C211yesmaximal, characteristic, complemented
18#42724C212yesmaximal, complemented
19#42695C211yesmaximal, characteristic, complemented
20#42672C212yesmaximal, complemented
21#40878C214yesmaximal, complemented
22#40220C212yesmaximal, complemented
23#39561C212yesmaximal, complemented
24#38911C212yesmaximal, complemented
25#37784C212yesmaximal
26#37514C211yesmaximal, characteristic, complemented
27#35846C211yesmaximal, characteristic, complemented
28#35739C211yesmaximal, characteristic, complemented
29#35618C211yesmaximal, characteristic
30C2×#556C2211yescharacteristic
31C2×D4×Q8C2211yescharacteristic
32C2×#537C2211yescharacteristic
33C2×#529C2212yes—
34C2×#520C2211yescharacteristic
35#2857C2212yes—
36#2855C2212yes—
37#2844C2212yes—
38#2839C2214yes—
39#2839C2214yes—
40#2838C2214yes—
41#2835C2214yes—
42#2834C2212yes—
43#2833C2212yes—
44#2831C2214yes—
45#2831C2214yes—
46#2830C2212yes—
47#2817C2214yes—
48#2810C2214yes—
49#2807C2212yes—
50#2806C2212yes—
51#2806C2214yes—
52#2804C2211yescharacteristic
53#2799C2211yescharacteristic
54#2799C2211yescharacteristic
55#2798C2214yes—
56#2796C2214yes—
57#2796C2214yes—
58#2791C2214yes—
59#2789C2214yes—
60#2789C2212yes—
61#2788C2214yes—
62#2787C2214yes—
63#2787C2214yes—
64#2782C2214yes—
65#2781C2214yes—
66#2780C2212yes—
67#2780C2212yes—
68#2776C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2773C2214yes—
72#2772C2214yes—
73#2770C2214yes—
74#2770C2214yes—
75#2769C2212yes—
76#2767C2214yes—
77#2762C2214yes—
78#2759C2214yes—
79#2758C2214yes—
80#2755C2214yes—
81#2755C2214yes—
82#2755C2214yes—
83#2755C2214yes—
84#2751C2214yes—
85#2748C2212yes—
86#2746C2214yes—
87#2745C2214yes—
88#2744C2214yes—
89#2742C2212yes—
90#2738C2214yes—
91#2737C2214yes—
92#2728C2214yes—
93#2723C2214yes—
94#2722C2214yes—
95#2708C2214yes—
96#2701C2214yes—
97#2698C2214yes—
98#2698C2214yes—
99#2692C2212yes—
100#2692C2212yes—
101#2691C2214yes—
102#2689C2214yes—
103#2689C2214yes—
104#2689C2214yes—
105#2687C2214yes—
106#2687C2214yes—
107#2683C2211yescharacteristic
108#2666C2214yes—
109#2655C2214yes—
110#2653C2214yes—
111#2652C2214yes—
112#2652C2214yes—
113#2649C2214yes—
114#2649C2214yes—
115#2647C2214yes—
116#2643C2214yes—
117#2638C2212yes—
118#2628C2211yescharacteristic
119#2627C2212yes—
120#2625C2214yes—
121#2625C2212yes—
122#2621C2211yescharacteristic
123#2621C2212yes—
124#2616C2212yes—
125#2612C2212yes—
126#2605C2214yes—
127#2593C2212yes—
128#2588C2214yes—
129#2586C2212yes—
130#2585C2214yes—
131#2584C2212yes—
132#2583C2212yes—
133#2582C2212yes—
134#2581C2211yescharacteristic
135#2581C2211yescharacteristic
136#2581C2212yes—
137#2580C2212yes—
138#2578C2214yes—
139#2578C2214yes—
140#2575C2214yes—
141#2575C2214yes—
142#2570C2212yes—
143#2568C2212yes—
144#2568C2212yes—
145#2567C2211yescharacteristic
146#2565C2212yes—
147#2564C2212yes—
148#2560C2214yes—
149#2553C2214yes—
150#2550C2212yes—
151#2550C2212yes—
152#2549C2214yes—
153#2546C2211yescharacteristic
154#2531C2214yes—
155#2527C2214yes—
156#2525C2214yes—
157#2523C2212yes—
158#2520C2214yes—
159#2514C2212yes—
160#2514C2212yes—
161#2511C2212yes—
162#2509C2212yes—
163#2509C2212yes—
164#2509C2212yes—
165#2508C2212yes—
166#2508C2214yes—
167#2505C2214yes—
168#2505C2214yes—
169#2505C2214yes—
170#2504C2212yes—
171#2503C2212yes—
172#2500C2212yes—
173#2499C2212yes—
174#2499C2212yes—
175#2496C2212yes—
176#2495C2212yes—
177#2494C2212yes—
178#2493C2214yes—
179#2492C2212yes—
180#2492C2212yes—
181#2489C2212yes—
182#2484C2212yes—
183#2484C2214yes—
184#2481C2214yes—
185#2479C2214yes—
186#2478C2214yes—
187#2478C2214yes—
188#2477C2214yes—
189#2476C2214yes—
190#2470C2214yes—
191#2468C2214yes—
192#2466C2214yes—
193#2451C2212yes—
194#2449C2214yes—
195#2449C2214yes—
196#2447C2212yes—
197#2447C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2444C2214yes—
201#2444C2214yes—
202#2444C2214yes—
203#2442C2212yes—
204#2440C2212yes—
205#2438C2214yes—
206#2438C2214yes—
207#2432C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2427C2212yes—
211#2423C2212yes—
212#2421C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2420C2212yes—
216#2420C2212yes—
217#2420C2212yes—
218#2420C2214yes—
219#2415C2214yes—
220#2409C2212yes—
221#2409C2214yes—
222#2396C2211yescharacteristic
223#2396C2212yes—
224#2396C2211yescharacteristic
225#2396C2212yes—
226#2395C2212yes—
227C2×#395C2212yes—
228#2378C2214yes—
229#2368C2214yes—
230#2367C2212yes—
231#2365C2212yes—
232#2360C2212yes—
233#2360C2212yes—
234#2357C2211yescharacteristic
235#2355C2212yes—
236#2354C2212yes—
237#2351C2212yes—
238#2349C2211yescharacteristic
239D4×C4⋊C4C2212yes—
240#2346C2212yes—
241#2344C2214yes—
242#2343C2214yes—
243#2339C2212yes—
244#2334C2214yes—
245#2324C2212yes—
246#2317C2211yescharacteristic
247#2314C2212yes—
248#2311C2211yescharacteristic
249#2310C2214yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255#2297C2211yescharacteristic
256#2297C2211yescharacteristic
257#2297C2212yes—
258C2×#382C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2312yes—
262#556—44no—
263D4×Q8—44no—
264#537—44no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269#529—48no—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#124C2312yes—
275C2×#123C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292#520—44no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2312yes—
302C2×C4×D4C2311yescharacteristic
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×#117C2311yescharacteristic
309C2×#117C2314yes—
310C2×#117C2314yes—
311C2×#117C2312yes—
312C2×#117C2311yescharacteristic
313C2×#117C2312yes—
314C2×#117C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2314yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2311yescharacteristic
355#400C2311yescharacteristic
356#400C2314yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#399C2311yescharacteristic
361#399C2314yes—
362#399C2314yes—
363#399C2312yes—
364#399C2311yescharacteristic
365#399C2312yes—
366#399C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2314yes—
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#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#396C2314yes—
421#396C2312yes—
422#396C2314yes—
423#396C2312yes—
424#396C2312yes—
425#396C2312yes—
426#396C2312yes—
427#396C2312yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#395C2312yes—
439#395C2314yes—
440#395C2311yescharacteristic
441#395C2314yes—
442#395C2311yescharacteristic
443#395C2312yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2314yes—
456#393C2312yes—
457#393C2314yes—
458#393C2311yescharacteristic
459#393C2311yescharacteristic
460#393C2312yes—
461#391C2314yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2312yes—
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2311yescharacteristic
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2311yescharacteristic
497#390C2312yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
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#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#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2312yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2312yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2314yes—
610#386C2312yes—
611#386C2314yes—
612#386C2312yes—
613#386C2312yes—
614#385C2314yes—
615#385C2312yes—
616#385C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2312yes—
638#385C2312yes—
639#385C2312yes—
640#384C2312yes—
641#384C2312yes—
642#384C2312yes—
643#383C2314yes—
644#383C2314yes—
645#383C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2312yes—
650#382C2312yes—
651#382C2311yescharacteristic
652#382C2312yes—
653#382C2314yes—
654#382C2314yes—
655#382C2311yescharacteristic
656#382C2314yes—
657#382C2314yes—
658#382C2312yes—
659#382C2312yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2314yes—
664#381C2314yes—
665#381C2314yes—
666#381C2314yes—
667#381C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677#380C2312yes—
678#380C2314yes—
679#380C2312yes—
680#380C2312yes—
681#380C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2311yescharacteristic
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2314yes—
714C2×#95C2312yes—
715C2×#95C2314yes—
716C2×#95C2314yes—
717C2×#41—24no—
718C2×#41—24no—
719C2×#41—24no—
720C2×#41—42no—
721C2×#41—42no—
722C2×#41—42no—
723C22×Q8—44no—
724C22×Q8—48no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C4⋊Q8—44no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8—42no—
754#126—48no—
755#126—48no—
756#126—48no—
757#125—44no—
758#124—28no—
759#123—48no—
760C22⋊Q8—28no—
761C22⋊Q8—44no—
762C22⋊Q8—48no—
763C22⋊Q8—44no—
764C22⋊Q8—44no—
765C22⋊Q8—44no—
766C22⋊Q8—48no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—48no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773#121—28no—
774#121—48no—
775#121—44no—
776C4×Q8—44no—
777C4×Q8—42no—
778C4×Q8—42no—
779C4×Q8—44no—
780C4×Q8—42no—
781C4×Q8—42no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×D4—24no—
785C4×D4—24no—
786C4×D4—28no—
787C4×D4—44no—
788C4×D4—44no—
789C4×D4—44no—
790C4×D4—48no—
791#117—24no—
792#117—44no—
793#117—42no—
794#117—44no—
795#117—48no—
796#117—44no—
797#117—48no—
798C2×C4⋊C4—48no—
799C2×C4⋊C4—42no—
800C2×C4⋊C4—42no—
801C2×C4⋊C4—44no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—44no—
905C2×C42—42no—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2414yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2414yes—
928#95C2412yes—
929#95C2411yescharacteristic
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2411yescharacteristic
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2411yescharacteristic
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2414yes—
1008C24C2512yes—
1009C24C2512yes—
1010C24C2511yescharacteristic
1011#41—416no—
1012#41—88no—
1013C2×Q8—22no—
1014C2×Q8—24no—
1015C2×Q8—24no—
1016C2×Q8—22no—
1017C2×Q8—22no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—22no—
1021C2×Q8—28no—
1022C2×Q8—41no—
1023C2×Q8—41no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—42no—
1033C2×Q8—41no—
1034C2×Q8—816no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—28no—
1038C2×D4—24no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—22no—
1042C2×D4—42no—
1043C2×D4—41no—
1044C2×D4—42no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—41no—
1048C2×D4—42no—
1049C2×D4H(5,𝔽2)14yes—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—28no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—28no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C42−1+414yes—
1082C22×C4C2514yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—42no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—41no—
1143C4⋊C4—41no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
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—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—28no—
1177C22⋊C4—28no—
1178C22⋊C4—28no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—41no—
1196C22⋊C4—41no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—24no—
1211C42—24no—
1212C42—22no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—24no—
1218C42—41no—
1219C42—41no—
1220C42—42no—
1221C42—42no—
1222C42—44no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—42no—
1228C42—42no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C23—21no—
1233C23—22no—
1234C23—22no—
1235C23—24no—
1236C23—22no—
1237C23—21no—
1238C23—22no—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23C2×H(5,𝔽2)14yes—
1248C23C2×2−1+412yes—
1249C23C2611yescharacteristic
1250Q8—44no—
1251Q8—48no—
1252Q8—44no—
1253Q8—88no—
1254Q8—82no—
1255Q8—82no—
1256Q8—84no—
1257Q8—84no—
1258D4—28no—
1259D4—48no—
1260D4—82no—
1261D4—88no—
1262D4—84no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—22no—
1267C2×C4—28no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—416no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—162no—
1341C2×C4—162no—
1342C2×C4C2×H(5,𝔽2)12yes—
1343C2×C4C2×2−1+412yes—
1344C2×C4C2×2−1+412yes—
1345C2×C4#58514yes—
1346C2×C4#58512yes—
1347C22—22no—
1348C22—24no—
1349C22—24no—
1350C22—24no—
1351C22—24no—
1352C22—41no—
1353C22—41no—
1354C22—42no—
1355C22—44no—
1356C22—44no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22C22×H(5,𝔽2)11yescharacteristic
1365C22C22×2−1+411yescharacteristic
1366C22C2×#58511yescharacteristic
1367C22C2×#58512yes—
1368C222−1+612yes—
1369C4—22no—
1370C4—24no—
1371C4—42no—
1372C4—42no—
1373C4—44no—
1374C4—44no—
1375C4—41no—
1376C4—41no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—41no—
1381C4—41no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4#353514yes—
1395C2—42no—
1396C2—44no—
1397C2—82no—
1398C2C2×#353511yescharacteristic
1399C2#6293612yes—
1400C2#6295612yes—
1401C2#6301711yescharacteristic
1402C2#6306311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59567C2semidirect
2. #59325C2semidirect
3. #59073C2semidirect
4. #58133C2semidirect
5. #57824C2semidirect
6. #55610C2semidirect
7. #54733C2semidirect
8. #54137C2semidirect
9. #53140C2semidirect
10. #52414C2semidirect
11. #52288C2semidirect
12. #51680C2semidirect
13. #50403C2semidirect
14. #45517C2semidirect
15. #45132C2semidirect
16. #44795C2semidirect
17. #42981C2semidirect
18. #42724C2semidirect
19. #42695C2semidirect
20. #42672C2semidirect
21. #40878C2semidirect
22. #40220C2semidirect
23. #39561C2semidirect
24. #38911C2semidirect
26. #37514C2semidirect
27. #35846C2semidirect
28. #35739C2semidirect

Maximal subgroups

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

subgroupindex
#595672
#593252
#590732
#581332
#578242
#556102
#547332
#541372
#531402
#524142
#522882
#516802
#504032
#455172
#451322
#447952
#429812
#427242
#426952
#426722
#408782
#402202
#395612
#389112
#377842
#375142
#358462
#357392
#356182