Finite Group Databasebeta

← #8751626

Subgroups — #8751626

Order 512.

4941 conjugacy classes of subgroups.

The subgroup lattice has 1511 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59692C212yesmaximal, complemented
3#58957C214yesmaximal, complemented
4#58942C212yesmaximal, complemented
5#58131C214yesmaximal, complemented
6#56775C214yesmaximal, complemented
7#53900C214yesmaximal, complemented
8#53053C212yesmaximal, complemented
9#53008C211yesmaximal, characteristic, complemented
10#52904C212yesmaximal, complemented
11#52477C214yesmaximal, complemented
12#47752C212yesmaximal, complemented
13#45332C212yesmaximal, complemented
14#45321C211yesmaximal, characteristic, complemented
15#45321C212yesmaximal, complemented
16#45309C212yesmaximal, complemented
17#45248C212yesmaximal, complemented
18#42995C211yesmaximal, characteristic, complemented
19#42933C212yesmaximal, complemented
20#42867C212yesmaximal, complemented
21#42796C212yesmaximal, complemented
22#42787C212yesmaximal, complemented
23#42714C212yesmaximal, complemented
24#41137C214yesmaximal, complemented
25#39663C212yesmaximal, complemented
26#39491C211yesmaximal, characteristic, complemented
27#36696C211yesmaximal, characteristic, complemented
28#36077C211yesmaximal, characteristic, complemented
29#35700C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×D4×Q8C2212yes—
35C2×#548C2212yes—
36C2×#547C2211yescharacteristic
37C2×#536C2212yes—
38C2×#536C2211yescharacteristic
39C2×#536C2212yes—
40C2×#519C2211yescharacteristic
41#2862C2211yescharacteristic
42#2843C2212yes—
43#2843C2211yescharacteristic
44#2838C2214yes—
45#2837C2214yes—
46#2837C2214yes—
47#2834C2212yes—
48#2832C2214yes—
49#2830C2211yescharacteristic
50#2830C2212yes—
51#2829C2212yes—
52#2829C2214yes—
53#2829C2212yes—
54#2829C2212yes—
55#2828C2214yes—
56#2828C2211yescharacteristic
57#2828C2212yes—
58#2826C2214yes—
59#2823C2211yescharacteristic
60#2819C2212yes—
61#2818C2212yes—
62#2814C2214yes—
63#2813C2214yes—
64#2807C2212yes—
65#2807C2214yes—
66#2806C2214yes—
67#2803C2214yes—
68#2803C2214yes—
69#2801C2214yes—
70#2800C2214yes—
71#2793C2214yes—
72#2792C2212yes—
73#2788C2214yes—
74#2788C2214yes—
75#2783C2214yes—
76#2777C2214yes—
77#2777C2214yes—
78#2777C2214yes—
79#2775C2214yes—
80#2774C2214yes—
81#2772C2214yes—
82#2772C2214yes—
83#2768C2214yes—
84#2759C2214yes—
85#2757C2214yes—
86#2757C2214yes—
87#2757C2214yes—
88#2756C2214yes—
89#2733C2214yes—
90#2732C2214yes—
91#2731C2214yes—
92#2730C2214yes—
93#2729C2214yes—
94#2729C2214yes—
95#2729C2214yes—
96#2728C2214yes—
97#2710C2214yes—
98#2710C2214yes—
99#2710C2214yes—
100#2703C2214yes—
101#2683C2212yes—
102#2683C2214yes—
103#2683C2212yes—
104#2681C2214yes—
105#2681C2214yes—
106#2680C2214yes—
107#2680C2212yes—
108#2680C2214yes—
109#2677C2214yes—
110#2677C2212yes—
111#2677C2214yes—
112#2674C2214yes—
113#2674C2214yes—
114#2674C2214yes—
115#2674C2214yes—
116#2674C2214yes—
117#2672C2214yes—
118#2666C2214yes—
119#2666C2214yes—
120#2663C2214yes—
121#2661C2214yes—
122#2653C2214yes—
123#2651C2214yes—
124#2651C2214yes—
125#2640C2212yes—
126#2632C2212yes—
127#2630C2214yes—
128#2630C2214yes—
129#2628C2212yes—
130#2625C2212yes—
131#2624C2211yescharacteristic
132#2621C2212yes—
133#2621C2214yes—
134#2619C2212yes—
135#2615C2211yescharacteristic
136#2610C2212yes—
137#2606C2214yes—
138#2602C2214yes—
139#2602C2214yes—
140#2601C2214yes—
141#2599C2212yes—
142#2597C2214yes—
143#2594C2214yes—
144#2593C2214yes—
145#2593C2214yes—
146#2592C2212yes—
147#2589C2214yes—
148#2586C2214yes—
149#2563C2211yescharacteristic
150#2551C2212yes—
151#2551C2214yes—
152#2551C2212yes—
153#2546C2212yes—
154#2546C2212yes—
155#2546C2214yes—
156#2545C2212yes—
157#2542C2211yescharacteristic
158#2542C2212yes—
159#2540C2212yes—
160#2538C2212yes—
161#2538C2212yes—
162#2536C2212yes—
163#2536C2214yes—
164#2529C2214yes—
165#2522C2214yes—
166#2518C2214yes—
167#2514C2212yes—
168#2511C2212yes—
169#2509C2214yes—
170#2507C2212yes—
171#2507C2214yes—
172#2504C2212yes—
173#2500C2212yes—
174#2500C2212yes—
175#2495C2212yes—
176#2492C2212yes—
177#2485C2212yes—
178#2476C2214yes—
179#2474C2214yes—
180#2464C2214yes—
181#2463C2214yes—
182#2461C2214yes—
183#2461C2214yes—
184#2461C2214yes—
185#2461C2214yes—
186#2456C2214yes—
187#2455C2214yes—
188#2455C2212yes—
189#2455C2214yes—
190#2452C2214yes—
191#2452C2214yes—
192#2452C2214yes—
193#2451C2212yes—
194#2449C2214yes—
195#2448C2212yes—
196#2446C2212yes—
197#2440C2214yes—
198#2436C2211yescharacteristic
199#2436C2211yescharacteristic
200#2434C2212yes—
201#2434C2212yes—
202#2434C2212yes—
203#2432C2212yes—
204#2429C2212yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2429C2214yes—
210#2429C2214yes—
211#2427C2212yes—
212#2426C2212yes—
213#2426C2212yes—
214#2423C2212yes—
215#2421C2212yes—
216#2415C2212yes—
217#2415C2212yes—
218#2415C2212yes—
219#2415C2214yes—
220#2415C2212yes—
221#2415C2214yes—
222#2415C2212yes—
223#2409C2212yes—
224#2409C2211yescharacteristic
225#2409C2211yescharacteristic
226#2409C2212yes—
227#2407C2212yes—
228#2407C2212yes—
229#2407C2212yes—
230#2396C2212yes—
231#2395C2211yescharacteristic
232#2395C2212yes—
233#2392C2212yes—
234#2392C2212yes—
235#2392C2212yes—
236#2392C2214yes—
237#2388C2212yes—
238#2388C2211yescharacteristic
239#2367C2212yes—
240#2366C2212yes—
241#2365C2212yes—
242#2362C2212yes—
243#2362C2212yes—
244#2362C2212yes—
245#2351C2212yes—
246#2347C2214yes—
247#2347C2211yescharacteristic
248#2346C2211yescharacteristic
249Q8×C22⋊C4C2212yes—
250Q8×C22⋊C4C2212yes—
251#2334C2214yes—
252#2323C2212yes—
253#2323C2212yes—
254#2317C2212yes—
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#126C2212yes—
258#2293C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2311yescharacteristic
262C23×Q8C2312yes—
263C23×Q8C2312yes—
264C23×Q8C2311yescharacteristic
265#555—44no—
266D4×Q8—48no—
267D4×Q8—48no—
268D4×Q8—48no—
269D4×Q8—48no—
270#548—48no—
271#547—44no—
272#536—44no—
273#536—48no—
274#536—48no—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×C4⋊Q8C2312yes—
287C2×#127C2311yescharacteristic
288C2×#126C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2314yes—
295C2×#124C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×#121C2311yescharacteristic
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2311yescharacteristic
329C2×#121C2314yes—
330#519—44no—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2314yes—
351C2×C4×D4C2314yes—
352C2×#117C2312yes—
353C2×#117C2311yescharacteristic
354C2×#117C2311yescharacteristic
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2311yescharacteristic
359C2×#117C2314yes—
360C22×C4⋊C4C2312yes—
361#401C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#399C2314yes—
373#399C2312yes—
374#399C2311yescharacteristic
375#399C2312yes—
376#399C2312yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#398C2311yescharacteristic
383#398C2312yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#397C2314yes—
411#397C2314yes—
412#397C2311yescharacteristic
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2312yes—
431#396C2314yes—
432#396C2314yes—
433#396C2312yes—
434#396C2312yes—
435#396C2312yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#395C2311yescharacteristic
448#395C2312yes—
449#395C2314yes—
450#395C2314yes—
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2312yes—
455#395C2312yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2312yes—
469#394C2311yescharacteristic
470#394C2312yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2312yes—
475#394C2312yes—
476#394C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2312yes—
480#394C2314yes—
481#394C2314yes—
482#394C2312yes—
483#394C2312yes—
484#394C2312yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#393C2314yes—
496#393C2314yes—
497#393C2312yes—
498#393C2312yes—
499#393C2311yescharacteristic
500#393C2312yes—
501#393C2314yes—
502#393C2314yes—
503#393C2312yes—
504#393C2312yes—
505#393C2312yes—
506#393C2312yes—
507#393C2312yes—
508#392C2312yes—
509#392C2312yes—
510#392C2312yes—
511#392C2312yes—
512#392C2312yes—
513#392C2312yes—
514#392C2311yescharacteristic
515#392C2314yes—
516#392C2312yes—
517#392C2312yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2314yes—
525#391C2312yes—
526#391C2312yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2314yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#390C2311yescharacteristic
540#390C2312yes—
541#390C2311yescharacteristic
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2312yes—
550#390C2312yes—
551#390C2314yes—
552#390C2314yes—
553#390C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2312yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2312yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2312yes—
672#385C2314yes—
673#384C2311yescharacteristic
674#384C2312yes—
675#384C2312yes—
676#384C2314yes—
677#383C2312yes—
678#383C2314yes—
679#383C2312yes—
680#383C2314yes—
681#382C2312yes—
682#382C2312yes—
683#382C2312yes—
684#382C2312yes—
685#382C2312yes—
686#382C2314yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2314yes—
692#380C2314yes—
693#380C2311yescharacteristic
694#380C2311yescharacteristic
695#380C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2314yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2311yescharacteristic
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2311yescharacteristic
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721#376C2312yes—
722C43C2311yescharacteristic
723C2×#41—42no—
724C2×#41—44no—
725C2×#41—44no—
726C2×#41—44no—
727C2×#41—44no—
728C22×Q8—28no—
729C22×Q8—28no—
730C22×Q8—28no—
731C22×Q8—42no—
732C22×Q8—42no—
733C22×Q8—44no—
734C22×Q8—44no—
735C22×Q8—44no—
736C22×Q8—44no—
737C22×Q8—44no—
738C22×Q8C2412yes—
739C22×Q8C2412yes—
740C22×Q8C2412yes—
741C22×Q8C2412yes—
742C22×Q8C2414yes—
743C22×Q8C2414yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×D4C2411yescharacteristic
748C22×D4C2412yes—
749C22×D4C2412yes—
750C22×D4C2411yescharacteristic
751C22×D4C2411yescharacteristic
752C22×D4C2412yes—
753C22×D4C2412yes—
754C22×D4C2414yes—
755C22×D4C2412yes—
756C22×D4C2414yes—
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2412yes—
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2412yes—
766C23×C4C2412yes—
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2414yes—
770C23×C4C2412yes—
771C4⋊Q8—28no—
772C4⋊Q8—28no—
773C4⋊Q8—44no—
774C4⋊Q8—48no—
775C4⋊Q8—42no—
776C4⋊Q8—44no—
777C4⋊Q8—42no—
778C4⋊Q8—44no—
779C4⋊Q8—48no—
780C4⋊Q8—48no—
781C4⋊Q8—48no—
782C4⋊Q8—48no—
783#127—24no—
784#126—28no—
785#124—28no—
786#124—44no—
787#124—44no—
788#124—44no—
789#124—44no—
790#124—48no—
791#124—48no—
792#123—48no—
793#123—48no—
794#123—48no—
795#123—48no—
796#123—48no—
797#123—48no—
798C22⋊Q8—28no—
799C22⋊Q8—28no—
800C22⋊Q8—28no—
801C22⋊Q8—28no—
802C22⋊Q8—28no—
803C22⋊Q8—48no—
804C22⋊Q8—48no—
805C22⋊Q8—48no—
806C22⋊Q8—48no—
807C22⋊Q8—48no—
808C22⋊Q8—48no—
809C22⋊Q8—48no—
810C22⋊Q8—48no—
811C22⋊Q8—48no—
812C22⋊Q8—48no—
813C22⋊Q8—48no—
814C22⋊Q8—44no—
815C22⋊Q8—44no—
816C22⋊Q8—44no—
817C22⋊Q8—44no—
818C22⋊Q8—44no—
819C22⋊Q8—44no—
820#121—44no—
821#121—48no—
822#121—44no—
823#121—44no—
824#121—42no—
825#121—42no—
826C4×Q8—28no—
827C4×Q8—44no—
828C4×Q8—44no—
829C4×Q8—44no—
830C4×Q8—44no—
831C4×Q8—44no—
832C4×Q8—44no—
833C4×Q8—44no—
834C4×D4—24no—
835C4×D4—48no—
836C4×D4—42no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—44no—
841C4×D4—44no—
842C4×D4—42no—
843C4×D4—48no—
844C4×D4—48no—
845C4×D4—48no—
846C4×D4—48no—
847#117—24no—
848#117—24no—
849#117—28no—
850#117—42no—
851#117—44no—
852#117—44no—
853#117—48no—
854#117—44no—
855C2×C4⋊C4—44no—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2411yescharacteristic
950C2×C22⋊C4C2411yescharacteristic
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2412yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2414yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2411yescharacteristic
991C2×C42C2412yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2411yescharacteristic
995#95C2411yescharacteristic
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2411yescharacteristic
1004#95C2411yescharacteristic
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2411yescharacteristic
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2412yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052C24C2511yescharacteristic
1053C24C2512yes—
1054C24C2511yescharacteristic
1055C24C2512yes—
1056C24C2512yes—
1057#41—88no—
1058#41—816no—
1059C2×Q8—24no—
1060C2×Q8—24no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—24no—
1065C2×Q8—24no—
1066C2×Q8—28no—
1067C2×Q8—24no—
1068C2×Q8—28no—
1069C2×Q8—28no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—44no—
1073C2×Q8—44no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—42no—
1077C2×Q8—41no—
1078C2×Q8—42no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—416no—
1082C2×Q8—816no—
1083C2×Q8—816no—
1084C2×Q8—88no—
1085C2×Q8H(5,𝔽2)18yes—
1086C2×D4—22no—
1087C2×D4—24no—
1088C2×D4—24no—
1089C2×D4—24no—
1090C2×D4—22no—
1091C2×D4—22no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—42no—
1099C2×D4—42no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—41no—
1103C2×D4—41no—
1104C2×D4—42no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—42no—
1109C2×D4—42no—
1110C2×D4—42no—
1111C2×D4—44no—
1112C2×D4—41no—
1113C2×D4—42no—
1114C2×D4—41no—
1115C2×D4—41no—
1116C2×D4—42no—
1117C2×D4—44no—
1118C2×D4—44no—
1119C2×D4—42no—
1120C2×D4—42no—
1121C2×D4—42no—
1122C2×D4—44no—
1123C2×D4—44no—
1124C22×C4—24no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—28no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—28no—
1138C22×C4—28no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—42no—
1150C22×C4C2511yescharacteristic
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2514yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2514yes—
1166C22×C4C2514yes—
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2514yes—
1171C22×C4C2511yescharacteristic
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C4⋊C4—28no—
1175C4⋊C4—22no—
1176C4⋊C4—22no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—28no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—41no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—41no—
1206C4⋊C4—44no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—42no—
1210C4⋊C4—42no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—42no—
1232C4⋊C4H(5,𝔽2)14yes—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—42no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—42no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—42no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—42no—
1276C22⋊C4—42no—
1277C22⋊C4—42no—
1278C22⋊C4—42no—
1279C22⋊C4—42no—
1280C22⋊C4—44no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—42no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C42—24no—
1294C42—24no—
1295C42—28no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—22no—
1300C42—24no—
1301C42—24no—
1302C42—44no—
1303C42—42no—
1304C42—41no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C422−1+414yes—
1313C23—21no—
1314C23—22no—
1315C23—22no—
1316C23—22no—
1317C23—24no—
1318C23—22no—
1319C23—22no—
1320C23—21no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—21no—
1328C23—22no—
1329C23—21no—
1330C23—21no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—21no—
1336C23—22no—
1337C23—24no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23C2611yescharacteristic
1343Q8—216no—
1344Q8—48no—
1345Q8—48no—
1346Q8—48no—
1347Q8—88no—
1348Q8—88no—
1349Q8—84no—
1350Q8—82no—
1351Q8—162no—
1352D4—48no—
1353D4—48no—
1354D4—48no—
1355D4—48no—
1356D4—44no—
1357D4—82no—
1358D4—82no—
1359D4—84no—
1360D4—88no—
1361D4—82no—
1362D4—84no—
1363D4—88no—
1364D4—162no—
1365D4—162no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—21no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—24no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—22no—
1425C2×C4—22no—
1426C2×C4—48no—
1427C2×C4—48no—
1428C2×C4—44no—
1429C2×C4—48no—
1430C2×C4—44no—
1431C2×C4—48no—
1432C2×C4—88no—
1433C2×C4—88no—
1434C2×C4—84no—
1435C2×C4—88no—
1436C2×C4C2×H(5,𝔽2)14yes—
1437C2×C4C2×H(5,𝔽2)18yes—
1438C2×C4C2×H(5,𝔽2)14yes—
1439C2×C4C2×H(5,𝔽2)12yes—
1440C2×C4C2×2−1+412yes—
1441C2×C4C2×2−1+414yes—
1442C22—41no—
1443C22—42no—
1444C22—42no—
1445C22—41no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—41no—
1457C22—41no—
1458C22—42no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—44no—
1465C22—42no—
1466C22—42no—
1467C22—41no—
1468C22—42no—
1469C22—41no—
1470C22—42no—
1471C22C22×H(5,𝔽2)12yes—
1472C22C22×H(5,𝔽2)11yescharacteristic
1473C22C22×2−1+411yescharacteristic
1474C222−1+611yescharacteristic
1475C222−1+612yes—
1476C4—28no—
1477C4—24no—
1478C4—22no—
1479C4—24no—
1480C4—42no—
1481C4—41no—
1482C4—42no—
1483C4—41no—
1484C4—44no—
1485C4—44no—
1486C4—42no—
1487C4—44no—
1488C4—42no—
1489C4—42no—
1490C4—44no—
1491C4—42no—
1492C4—42no—
1493C4—42no—
1494C4—41no—
1495C4—42no—
1496C4—42no—
1497C4—44no—
1498C4—42no—
1499C4#353714yes—
1500C2—81no—
1501C2—82no—
1502C2—82no—
1503C2—81no—
1504C2—82no—
1505C2C2×#353711yescharacteristic
1506C2#6291312yes—
1507C2#6291511yescharacteristic
1508C2#6304412yes—
1509C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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. #59692C2semidirect
3. #58957C2semidirect
4. #58942C2semidirect
5. #58131C2semidirect
6. #56775C2semidirect
7. #53900C2semidirect
8. #53053C2semidirect
9. #53008C2semidirect
10. #52904C2semidirect
11. #52477C2semidirect
12. #47752C2semidirect
13. #45332C2semidirect
14. #45321C2semidirect
15. #45321C2semidirect
16. #45309C2semidirect
17. #45248C2semidirect
18. #42995C2semidirect
19. #42933C2semidirect
20. #42867C2semidirect
21. #42796C2semidirect
22. #42787C2semidirect
23. #42714C2semidirect
24. #41137C2semidirect
25. #39663C2semidirect
26. #39491C2semidirect
27. #36696C2semidirect
28. #36077C2semidirect
29. #35700C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596922
#589572
#589422
#581312
#567752
#539002
#530532
#530082
#529042
#524772
#477522
#453322
#453212
#453092
#452482
#429952
#429332
#428672
#427962
#427872
#427142
#411372
#396632
#394912
#366962
#360772
#357002