Finite Group Databasebeta

← #8508893

Subgroups — #8508893

Order 512.

4555 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#58421C214yesmaximal, complemented
3#58345C214yesmaximal, complemented
4#57212C214yesmaximal, complemented
5#55532C214yesmaximal, complemented
6#55135C214yesmaximal, complemented
7#53376C212yesmaximal, complemented
8#53359C212yesmaximal, complemented
9#53109C212yesmaximal, complemented
10#52162C211yesmaximal, characteristic, complemented
11#47945C214yesmaximal, complemented
12#45998C212yesmaximal, complemented
13#45485C212yesmaximal, complemented
14#45435C212yesmaximal, complemented
15#45197C212yesmaximal, complemented
16#42762C212yesmaximal, complemented
17#42525C212yesmaximal, complemented
18#42427C212yesmaximal, complemented
19#39756C211yesmaximal, characteristic, complemented
20#39596C212yesmaximal, complemented
21#39509C211yesmaximal, characteristic, complemented
22#39270C212yesmaximal
23#39247C212yesmaximal, complemented
24#37349C212yesmaximal, complemented
25#37275C212yesmaximal, complemented
26#37153C212yesmaximal, complemented
27#36535C211yesmaximal, characteristic, complemented
28#35208C211yesmaximal, characteristic, complemented
29#35198C211yesmaximal, characteristic
30C2×#563C2214yes—
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×#542C2212yes—
34C2×#533C2212yes—
35#2864C2212yes—
36#2863C2212yes—
37#2860C2212yes—
38#2859C2211yescharacteristic
39#2859C2212yes—
40#2858C2212yes—
41#2857C2212yes—
42#2855C2212yes—
43#2854C2212yes—
44#2835C2214yes—
45#2832C2214yes—
46#2830C2214yes—
47#2830C2214yes—
48#2821C2214yes—
49#2820C2214yes—
50#2817C2214yes—
51#2814C2214yes—
52#2810C2212yes—
53#2808C2212yes—
54#2808C2212yes—
55#2808C2212yes—
56#2805C2212yes—
57#2803C2214yes—
58#2800C2214yes—
59#2797C2214yes—
60#2796C2214yes—
61#2793C2214yes—
62#2792C2214yes—
63#2792C2214yes—
64#2790C2214yes—
65#2777C2214yes—
66#2775C2214yes—
67#2774C2214yes—
68#2772C2214yes—
69#2761C2214yes—
70#2761C2214yes—
71#2758C2214yes—
72#2757C2214yes—
73#2751C2214yes—
74#2751C2214yes—
75#2740C2214yes—
76#2739C2214yes—
77#2737C2214yes—
78#2737C2214yes—
79#2734C2211yescharacteristic
80#2734C2214yes—
81#2734C2214yes—
82#2732C2211yescharacteristic
83#2729C2212yes—
84#2729C2214yes—
85#2729C2214yes—
86#2727C2212yes—
87#2727C2212yes—
88#2727C2212yes—
89#2726C2211yescharacteristic
90#2725C2214yes—
91#2723C2214yes—
92#2723C2214yes—
93#2723C2214yes—
94#2721C2214yes—
95#2720C2214yes—
96#2720C2214yes—
97#2720C2214yes—
98#2720C2212yes—
99#2718C2214yes—
100#2716C2214yes—
101#2716C2214yes—
102#2716C2214yes—
103#2716C2214yes—
104#2715C2214yes—
105#2713C2212yes—
106#2709C2214yes—
107#2704C2212yes—
108#2700C2214yes—
109#2698C2214yes—
110#2695C2214yes—
111#2692C2214yes—
112#2692C2214yes—
113#2692C2212yes—
114#2690C2214yes—
115#2690C2214yes—
116#2689C2214yes—
117#2689C2214yes—
118#2689C2214yes—
119#2687C2214yes—
120#2683C2212yes—
121#2683C2212yes—
122#2683C2211yescharacteristic
123#2680C2214yes—
124#2677C2212yes—
125#2677C2214yes—
126#2674C2214yes—
127#2674C2214yes—
128#2674C2214yes—
129#2674C2214yes—
130#2666C2214yes—
131#2663C2214yes—
132#2662C2214yes—
133#2652C2214yes—
134#2651C2214yes—
135#2650C2214yes—
136#2650C2214yes—
137#2641C2212yes—
138#2638C2214yes—
139#2628C2212yes—
140#2628C2212yes—
141#2625C2212yes—
142#2624C2212yes—
143#2614C2214yes—
144#2602C2214yes—
145#2596C2214yes—
146#2595C2214yes—
147#2592C2212yes—
148#2592C2212yes—
149#2590C2214yes—
150#2588C2214yes—
151#2586C2214yes—
152#2586C2214yes—
153#2582C2211yescharacteristic
154#2581C2212yes—
155#2580C2212yes—
156#2580C2212yes—
157#2577C2214yes—
158#2571C2211yescharacteristic
159#2570C2212yes—
160#2567C2212yes—
161#2567C2212yes—
162#2567C2211yescharacteristic
163#2567C2211yescharacteristic
164#2565C2212yes—
165#2562C2212yes—
166#2560C2214yes—
167#2552C2211yescharacteristic
168#2552C2211yescharacteristic
169#2551C2214yes—
170#2551C2212yes—
171#2551C2211yescharacteristic
172#2551C2214yes—
173#2551C2212yes—
174#2551C2212yes—
175#2550C2212yes—
176#2548C2211yescharacteristic
177#2546C2212yes—
178#2546C2212yes—
179#2542C2214yes—
180#2541C2211yescharacteristic
181#2538C2212yes—
182#2538C2211yescharacteristic
183#2538C2212yes—
184#2538C2212yes—
185#2525C2214yes—
186#2513C2212yes—
187#2512C2212yes—
188#2512C2214yes—
189#2512C2212yes—
190#2512C2214yes—
191#2512C2212yes—
192#2511C2212yes—
193#2507C2212yes—
194#2506C2212yes—
195#2497C2212yes—
196#2496C2212yes—
197#2496C2212yes—
198#2495C2212yes—
199#2492C2212yes—
200#2492C2214yes—
201#2492C2212yes—
202#2491C2212yes—
203#2490C2212yes—
204#2490C2212yes—
205#2469C2214yes—
206#2468C2214yes—
207#2468C2214yes—
208#2466C2214yes—
209#2466C2214yes—
210#2462C2214yes—
211#2461C2214yes—
212#2455C2214yes—
213#2453C2212yes—
214#2452C2212yes—
215#2452C2214yes—
216#2452C2214yes—
217#2452C2212yes—
218#2452C2212yes—
219#2447C2212yes—
220#2447C2212yes—
221#2445C2214yes—
222#2445C2212yes—
223#2434C2214yes—
224#2434C2214yes—
225#2426C2212yes—
226#2422C2212yes—
227#2422C2212yes—
228#2409C2214yes—
229#2409C2214yes—
230#2399C2212yes—
231#2396C2212yes—
232#2396C2212yes—
233#2370C2212yes—
234#2370C2212yes—
235#2370C2212yes—
236#2370C2212yes—
237#2366C2212yes—
238#2357C2212yes—
239#2355C2211yescharacteristic
240#2355C2211yescharacteristic
241#2355C2212yes—
242#2332C2214yes—
243#2330C2212yes—
244#2330C2212yes—
245#2324C2212yes—
246#2324C2212yes—
247#2320C2212yes—
248#2314C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2211yescharacteristic
251C4×#127C2211yescharacteristic
252C4×#125C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×#121C2212yes—
255#2295C2211yescharacteristic
256#2293C2211yescharacteristic
257#2290C2212yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2314yes—
260#563—416no—
261D4×Q8—48no—
262D4×Q8—48no—
263#542—48no—
264#533—48no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×#127C2311yescharacteristic
279C2×#127C2312yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2314yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×#121C2312yes—
315C2×#121C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2311yescharacteristic
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C22×C42C2312yes—
335#400C2312yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#399C2314yes—
355#399C2314yes—
356#399C2312yes—
357#399C2312yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
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#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
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#396C2312yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2312yes—
410#396C2312yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2312yes—
426#395C2314yes—
427#395C2314yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2312yes—
433#395C2312yes—
434#395C2312yes—
435#395C2312yes—
436#395C2314yes—
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#393C2312yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2312yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#392C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2311yescharacteristic
481#391C2314yes—
482#391C2312yes—
483#391C2311yescharacteristic
484#390C2314yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2314yes—
489#390C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2311yescharacteristic
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2314yes—
506#389C2311yescharacteristic
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2312yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2311yescharacteristic
544#389C2314yes—
545#389C2311yescharacteristic
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
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#388C2312yes—
574#388C2314yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
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#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2312yes—
629#386C2314yes—
630#386C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2312yes—
645#385C2312yes—
646#385C2312yes—
647#385C2312yes—
648#384C2311yescharacteristic
649#384C2311yescharacteristic
650#384C2311yescharacteristic
651#384C2312yes—
652#384C2312yes—
653#384C2312yes—
654#384C2314yes—
655#384C2314yes—
656#384C2311yescharacteristic
657#384C2311yescharacteristic
658#384C2312yes—
659#383C2314yes—
660#383C2314yes—
661#382C2312yes—
662#382C2312yes—
663#382C2312yes—
664#382C2312yes—
665#382C2314yes—
666#382C2312yes—
667#381C2314yes—
668#381C2314yes—
669#381C2314yes—
670#381C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715C43C2312yes—
716C43C2311yescharacteristic
717C22×Q8—48no—
718C22×Q8—48no—
719C22×Q8—84no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2412yes—
722C22×Q8C2412yes—
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2414yes—
729C22×D4C2412yes—
730C22×D4C2412yes—
731C22×D4C2414yes—
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2414yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2412yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C4⋊Q8—24no—
742C4⋊Q8—24no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—48no—
749C4⋊Q8—48no—
750C4⋊Q8—48no—
751C4⋊Q8—84no—
752C4⋊Q8—84no—
753C4⋊Q8—82no—
754#127—24no—
755#127—82no—
756#126—48no—
757#126—48no—
758#126—48no—
759#126—48no—
760#126—48no—
761#126—84no—
762#125—28no—
763#125—28no—
764#125—28no—
765#125—48no—
766#125—44no—
767#125—44no—
768#124—48no—
769#124—48no—
770#124—44no—
771#123—48no—
772#123—48no—
773#123—48no—
774#123—84no—
775C22⋊Q8—216no—
776C22⋊Q8—28no—
777C22⋊Q8—44no—
778C22⋊Q8—44no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—44no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—44no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790#121—28no—
791#121—44no—
792C4×Q8—24no—
793C4×Q8—24no—
794C4×Q8—28no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×D4—28no—
801C4×D4—24no—
802C4×D4—44no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—48no—
806C4×D4—82no—
807C4×D4—84no—
808#117—28no—
809#117—44no—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2411yescharacteristic
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C42—44no—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2411yescharacteristic
955C2×C42C2411yescharacteristic
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019C24C2512yes—
1020C24C2514yes—
1021C2×Q8—22no—
1022C2×Q8—24no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—22no—
1026C2×Q8—24no—
1027C2×Q8—28no—
1028C2×Q8—22no—
1029C2×Q8—22no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—832no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—22no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—44no—
1062C2×D4—42no—
1063C2×D4—41no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—24no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—22no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—22no—
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—41no—
1145C4⋊C4—42no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
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—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—41no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4H(5,𝔽2)14yes—
1189C4⋊C42−1+414yes—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—28no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—42no—
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—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—24no—
1234C42—22no—
1235C42—24no—
1236C42—24no—
1237C42—22no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—42no—
1242C42—42no—
1243C42—42no—
1244C42—41no—
1245C42—44no—
1246C42—41no—
1247C42—44no—
1248C42—44no—
1249C42—41no—
1250C42—44no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—42no—
1255C42H(5,𝔽2)14yes—
1256C422−1+414yes—
1257C23—22no—
1258C23—22no—
1259C23—24no—
1260C23—24no—
1261C23—22no—
1262C23—24no—
1263C23—22no—
1264C23—24no—
1265C23—24no—
1266C23—22no—
1267C23—24no—
1268C23—22no—
1269C23—24no—
1270C23—22no—
1271C23C2611yescharacteristic
1272Q8—48no—
1273Q8—48no—
1274Q8—44no—
1275Q8—82no—
1276Q8—84no—
1277Q8—88no—
1278Q8—84no—
1279Q8—88no—
1280Q8—164no—
1281D4—48no—
1282D4—48no—
1283D4—88no—
1284D4—82no—
1285D4—84no—
1286D4—164no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
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—24no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—21no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—48no—
1359C2×C4—84no—
1360C2×C4—88no—
1361C2×C4—88no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4C2×H(5,𝔽2)12yes—
1365C2×C4C2×H(5,𝔽2)12yes—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4C2×H(5,𝔽2)14yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×2−1+412yes—
1370C2×C4C2×2−1+414yes—
1371C2×C4C2×2−1+412yes—
1372C2×C4C2×2−1+412yes—
1373C2×C4C2×2−1+412yes—
1374C22—42no—
1375C22—44no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—44no—
1380C22—42no—
1381C22—44no—
1382C22—44no—
1383C22—42no—
1384C22—44no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22C22×H(5,𝔽2)11yescharacteristic
1389C22C22×H(5,𝔽2)11yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22C22×2−1+411yescharacteristic
1392C22H(7,𝔽2)11yescharacteristic
1393C222−1+611yescharacteristic
1394C222−1+611yescharacteristic
1395C4—24no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—24no—
1400C4—22no—
1401C4—22no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—41no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—44no—
1421C4#355014yes—
1422C2—82no—
1423C2—84no—
1424C2C2×#355011yescharacteristic
1425C2#6287911yescharacteristic
1426C2#6288811yescharacteristic
1427C2#6291211yescharacteristic
1428C2#6291311yescharacteristic
1429C2#6294611yescharacteristic
1430C2#6305811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59817C2semidirect
2. #58421C2semidirect
3. #58345C2semidirect
4. #57212C2semidirect
5. #55532C2semidirect
6. #55135C2semidirect
7. #53376C2semidirect
8. #53359C2semidirect
9. #53109C2semidirect
10. #52162C2semidirect
11. #47945C2semidirect
12. #45998C2semidirect
13. #45485C2semidirect
14. #45435C2semidirect
15. #45197C2semidirect
16. #42762C2semidirect
17. #42525C2semidirect
18. #42427C2semidirect
19. #39756C2semidirect
20. #39596C2semidirect
21. #39509C2semidirect
23. #39247C2semidirect
24. #37349C2semidirect
25. #37275C2semidirect
26. #37153C2semidirect
27. #36535C2semidirect
28. #35208C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#584212
#583452
#572122
#555322
#551352
#533762
#533592
#531092
#521622
#479452
#459982
#454852
#454352
#451972
#427622
#425252
#424272
#397562
#395962
#395092
#392702
#392472
#373492
#372752
#371532
#365352
#352082
#351982