Finite Group Databasebeta

← #7726833

Subgroups — #7726833

Order 512.

4346 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51628C214yesmaximal, complemented
2#51627C214yesmaximal, complemented
3#47739C214yesmaximal, complemented
4#47738C214yesmaximal, complemented
5#45434C211yesmaximal, characteristic, complemented
6#45431C211yesmaximal, characteristic, complemented
7#45350C211yesmaximal, characteristic, complemented
8#45347C211yesmaximal, characteristic, complemented
9#45306C211yesmaximal, characteristic, complemented
10#45276C211yesmaximal, characteristic, complemented
11#45083C211yesmaximal, characteristic, complemented
12#44979C211yesmaximal, characteristic, complemented
13#39811C212yesmaximal, complemented
14#39802C212yesmaximal, complemented
15#39761C212yesmaximal, complemented
16#39753C212yesmaximal, complemented
17#39639C212yesmaximal, complemented
18#39075C214yesmaximal, complemented
19#38982C212yesmaximal
20#38259C214yesmaximal, complemented
21#37615C211yesmaximal, characteristic
22#36810C214yesmaximal, complemented
23#36552C212yesmaximal, complemented
24#36255C212yesmaximal
25#35398C214yesmaximal, complemented
26#35326C211yesmaximal, characteristic
27#35281C211yesmaximal, characteristic, complemented
28#34878C211yesmaximal, characteristic, complemented
29#34399C211yesmaximal, characteristic, complemented
30#34229C211yesmaximal, characteristic
31C2×#2331C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2868C2212yes—
36#2862C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2852C2214yes—
40#2851C2214yes—
41#2850C2211yescharacteristic
42#2850C2211yescharacteristic
43#2821C2212yes—
44#2821C2212yes—
45#2809C2214yes—
46#2802C2214yes—
47#2802C2214yes—
48#2798C2214yes—
49#2793C2214yes—
50#2793C2214yes—
51#2791C2214yes—
52#2791C2214yes—
53#2789C2214yes—
54#2787C2214yes—
55#2783C2214yes—
56#2777C2214yes—
57#2777C2214yes—
58#2774C2214yes—
59#2773C2214yes—
60#2773C2214yes—
61#2768C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2766C2214yes—
65#2762C2214yes—
66#2762C2214yes—
67#2762C2214yes—
68#2758C2214yes—
69#2758C2214yes—
70#2758C2214yes—
71#2755C2214yes—
72#2754C2214yes—
73#2754C2214yes—
74#2738C2214yes—
75#2726C2214yes—
76#2716C2214yes—
77#2716C2214yes—
78#2713C2214yes—
79#2713C2214yes—
80#2704C2214yes—
81#2698C2214yes—
82#2690C2214yes—
83#2689C2214yes—
84#2689C2214yes—
85#2660C2211yescharacteristic
86#2660C2212yes—
87#2660C2212yes—
88#2660C2212yes—
89#2658C2211yescharacteristic
90#2646C2214yes—
91#2643C2214yes—
92#2642C2211yescharacteristic
93#2640C2211yescharacteristic
94#2640C2212yes—
95#2623C2212yes—
96#2623C2212yes—
97#2621C2214yes—
98#2612C2212yes—
99#2612C2212yes—
100#2612C2214yes—
101#2611C2214yes—
102#2611C2214yes—
103#2607C2214yes—
104#2606C2212yes—
105#2605C2212yes—
106#2605C2214yes—
107#2605C2214yes—
108#2604C2214yes—
109#2604C2214yes—
110#2594C2214yes—
111#2592C2212yes—
112#2590C2214yes—
113#2590C2214yes—
114#2590C2214yes—
115#2589C2214yes—
116#2588C2214yes—
117#2586C2214yes—
118#2582C2212yes—
119#2582C2212yes—
120#2581C2212yes—
121#2577C2214yes—
122#2575C2214yes—
123#2571C2212yes—
124#2570C2212yes—
125#2570C2212yes—
126#2569C2212yes—
127#2568C2211yescharacteristic
128#2568C2212yes—
129#2568C2211yescharacteristic
130#2567C2211yescharacteristic
131#2567C2211yescharacteristic
132#2567C2211yescharacteristic
133#2567C2211yescharacteristic
134#2565C2214yes—
135#2564C2214yes—
136#2556C2214yes—
137#2556C2214yes—
138#2552C2212yes—
139#2552C2212yes—
140#2552C2212yes—
141#2550C2214yes—
142#2549C2212yes—
143#2549C2214yes—
144#2546C2214yes—
145#2542C2211yescharacteristic
146#2542C2211yescharacteristic
147#2538C2212yes—
148#2533C2214yes—
149#2533C2214yes—
150#2532C2214yes—
151#2528C2214yes—
152#2528C2214yes—
153#2524C2214yes—
154#2520C2214yes—
155#2519C2214yes—
156#2517C2214yes—
157#2514C2212yes—
158#2514C2212yes—
159#2512C2212yes—
160#2512C2212yes—
161#2511C2212yes—
162#2511C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2510C2214yes—
166#2508C2214yes—
167#2506C2214yes—
168#2505C2214yes—
169#2505C2214yes—
170#2504C2212yes—
171#2502C2212yes—
172#2502C2212yes—
173#2502C2212yes—
174#2499C2214yes—
175#2498C2214yes—
176#2496C2214yes—
177#2492C2214yes—
178#2481C2214yes—
179#2478C2214yes—
180#2473C2214yes—
181#2473C2214yes—
182#2465C2214yes—
183#2453C2214yes—
184#2451C2214yes—
185#2450C2214yes—
186#2449C2214yes—
187#2448C2212yes—
188#2447C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2439C2214yes—
192#2438C2214yes—
193#2438C2212yes—
194#2438C2212yes—
195#2434C2212yes—
196#2434C2212yes—
197#2409C2214yes—
198#2402C2211yescharacteristic
199#2402C2211yescharacteristic
200#2399C2211yescharacteristic
201#2399C2211yescharacteristic
202#2382C2214yes—
203#2367C2212yes—
204#2365C2212yes—
205#2361C2212yes—
206#2360C2212yes—
207#2360C2212yes—
208#2360C2212yes—
209#2359C2214yes—
210#2357C2211yescharacteristic
211#2356C2211yescharacteristic
212#2356C2211yescharacteristic
213#2356C2211yescharacteristic
214#2356C2212yes—
215#2355C2212yes—
216#2355C2212yes—
217#2355C2212yes—
218#2354C2212yes—
219#2351C2211yescharacteristic
220#2351C2211yescharacteristic
221#2351C2211yescharacteristic
222Q8×C4⋊C4C2212yes—
223#2349C2211yescharacteristic
224#2346C2212yes—
225#2343C2212yes—
226#2343C2212yes—
227#2343C2212yes—
228#2334C2214yes—
229#2331C2211yescharacteristic
230#2331C2211yescharacteristic
231#2331C2212yes—
232#2331C2212yes—
233#2331C2211yescharacteristic
234#2331C2214yes—
235#2331C2214yes—
236#2331C2211yescharacteristic
237#2331C2212yes—
238#2329C2214yes—
239#2329C2214yes—
240#2327C2211yescharacteristic
241#2327C2212yes—
242#2327C2211yescharacteristic
243#2326C2211yescharacteristic
244#2326C2211yescharacteristic
245#2320C2212yes—
246#2320C2212yes—
247#2318C2214yes—
248#2318C2212yes—
249#2317C2214yes—
250C4×#125C2212yes—
251C4×#124C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2214yes—
255#2295C2212yes—
256#2295C2212yes—
257C2×#391C2214yes—
258C2×#389C2212yes—
259#2290C2214yes—
260C2×#387C2214yes—
261#2283C2211yescharacteristic
262C2×#382C2211yescharacteristic
263#2275C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2211yescharacteristic
267C23×Q8C2312yes—
268#533—28no—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2314yes—
280C2×C4⋊Q8C2314yes—
281#529—28no—
282C2×#126C2312yes—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#124C2311yescharacteristic
291C2×#124C2311yescharacteristic
292C2×#124C2311yescharacteristic
293C2×#123C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2311yescharacteristic
298C2×C22⋊Q8C2311yescharacteristic
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×#121C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2314yes—
322C22×C4⋊C4C2312yes—
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2314yes—
329C22×C42C2311yescharacteristic
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2312yes—
365#399C2312yes—
366#399C2314yes—
367#399C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2312yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2312yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2311yescharacteristic
452#391C2311yescharacteristic
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2311yescharacteristic
457#391C2311yescharacteristic
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#390C2311yescharacteristic
474#390C2311yescharacteristic
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2312yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2312yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
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#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#384C2314yes—
627#384C2312yes—
628#384C2312yes—
629#384C2312yes—
630#384C2312yes—
631#384C2314yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2312yes—
636#383C2311yescharacteristic
637#383C2311yescharacteristic
638#383C2312yes—
639#383C2314yes—
640#383C2312yes—
641#383C2312yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2314yes—
649#382C2311yescharacteristic
650#382C2311yescharacteristic
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2311yescharacteristic
659#382C2311yescharacteristic
660#382C2314yes—
661#382C2314yes—
662#382C2312yes—
663#381C2314yes—
664#381C2312yes—
665#381C2311yescharacteristic
666#381C2311yescharacteristic
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2312yes—
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2311yescharacteristic
716#376C2312yes—
717#376C2312yes—
718#376C2311yescharacteristic
719#376C2311yescharacteristic
720#376C2312yes—
721#376C2312yes—
722#376C2312yes—
723#376C2311yescharacteristic
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2311yescharacteristic
727#376C2312yes—
728#376C2314yes—
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2314yes—
732C2×#95C2312yes—
733C2×#95C2312yes—
734C2×#95C2312yes—
735C2×#95C2314yes—
736C43C2312yes—
737C22×Q8—28no—
738C22×Q8—84no—
739C22×Q8C2411yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2412yes—
743C22×Q8C2412yes—
744C22×Q8C2412yes—
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×Q8C2414yes—
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2414yes—
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2414yes—
758C23×C4C2411yescharacteristic
759C4⋊Q8—28no—
760C4⋊Q8—24no—
761C4⋊Q8—24no—
762C4⋊Q8—28no—
763C4⋊Q8—28no—
764C4⋊Q8—24no—
765C4⋊Q8—24no—
766C4⋊Q8—24no—
767C4⋊Q8—42no—
768C4⋊Q8—84no—
769C4⋊Q8—84no—
770#126—28no—
771#126—84no—
772#126—84no—
773#125—24no—
774#125—28no—
775#125—84no—
776#125—84no—
777#125—84no—
778#124—24no—
779#124—24no—
780#124—42no—
781#123—28no—
782C22⋊Q8—24no—
783C22⋊Q8—24no—
784C22⋊Q8—24no—
785C22⋊Q8—28no—
786C22⋊Q8—28no—
787C22⋊Q8—28no—
788C22⋊Q8—84no—
789C22⋊Q8—84no—
790C22⋊Q8—84no—
791#121—24no—
792C4×Q8—24no—
793C4×Q8—24no—
794C4×Q8—24no—
795C4×Q8—28no—
796C4×Q8—28no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—84no—
802C4×D4—28no—
803C4×D4—216no—
804C4×D4—24no—
805C4×D4—44no—
806#117—28no—
807#117—28no—
808#117—28no—
809#117—84no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4—84no—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
909C2×C42—24no—
910C2×C42—42no—
911C2×C42—84no—
912C2×C42#4118yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2411yescharacteristic
970#95C2411yescharacteristic
971#95C2411yescharacteristic
972#95C2412yes—
973#95C2414yes—
974#95C2411yescharacteristic
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2411yescharacteristic
997#95C2411yescharacteristic
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2512yes—
1034C24C2511yescharacteristic
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—28no—
1042C2×Q8—24no—
1043C2×Q8—24no—
1044C2×Q8—22no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—24no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—22no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—816no—
1060C2×D4—24no—
1061C2×D4—28no—
1062C2×D4—22no—
1063C2×D4—22no—
1064C2×D4—22no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—28no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—28no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4C2×#4114yes—
1087C22×C4C2×#4114yes—
1088C22×C4C2×#4114yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C22×C4C2511yescharacteristic
1112C22×C4C2511yescharacteristic
1113C22×C4C2511yescharacteristic
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2511yescharacteristic
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—22no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—24no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C42−1+418yes—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—22no—
1218C42—24no—
1219C42—24no—
1220C42—28no—
1221C42—24no—
1222C42—24no—
1223C42—22no—
1224C42—22no—
1225C42—24no—
1226C42—24no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—42no—
1240C42C2×#4114yes—
1241C42C2×#4114yes—
1242C42C2×#4114yes—
1243C42C2×#4114yes—
1244C422−1+414yes—
1245C23—21no—
1246C23—21no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—24no—
1251C23—22no—
1252C23—24no—
1253C23C22×#4112yes—
1254C23C2×2−1+414yes—
1255C23C2611yescharacteristic
1256Q8—48no—
1257Q8—44no—
1258Q8—44no—
1259Q8—44no—
1260Q8—84no—
1261Q8—84no—
1262Q8—84no—
1263Q8—84no—
1264Q8—88no—
1265D4—48no—
1266D4—44no—
1267C2×C4—21no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—21no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—28no—
1280C2×C4—28no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
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—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—44no—
1338C2×C4—48no—
1339C2×C4—416no—
1340C2×C4—84no—
1341C2×C4—88no—
1342C2×C4—88no—
1343C2×C4—84no—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C22×#4112yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C22×#4112yes—
1350C2×C4C2×2−1+414yes—
1351C2×C4C2×2−1+414yes—
1352C2×C4C2×2−1+414yes—
1353C2×C4C2×2−1+412yes—
1354C2×C4#58512yes—
1355C22—22no—
1356C22—22no—
1357C22—24no—
1358C22—24no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—44no—
1363C22—44no—
1364C22#350914yes—
1365C22C23×#4111yescharacteristic
1366C22C22×2−1+411yescharacteristic
1367C22C22×2−1+412yes—
1368C22C2×#58511yescharacteristic
1369C22H(7,𝔽2)12yes—
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—22no—
1375C4—24no—
1376C4—24no—
1377C4—24no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—44no—
1384C4—42no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—42no—
1393C4—44no—
1394C4—42no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4#350714yes—
1399C2—24no—
1400C2—82no—
1401C2C2×#350711yescharacteristic
1402C2C2×#350911yescharacteristic
1403C2#6285511yescharacteristic
1404C2#6294512yes—
1405C2#6295112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51628C2semidirect
2. #51627C2semidirect
3. #47739C2semidirect
4. #47738C2semidirect
5. #45434C2semidirect
6. #45431C2semidirect
7. #45350C2semidirect
8. #45347C2semidirect
9. #45306C2semidirect
10. #45276C2semidirect
11. #45083C2semidirect
12. #44979C2semidirect
13. #39811C2semidirect
14. #39802C2semidirect
15. #39761C2semidirect
16. #39753C2semidirect
17. #39639C2semidirect
18. #39075C2semidirect
20. #38259C2semidirect
22. #36810C2semidirect
23. #36552C2semidirect
25. #35398C2semidirect
27. #35281C2semidirect
28. #34878C2semidirect
29. #34399C2semidirect
31. C2×#2331C2semidirect

Maximal subgroups

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

subgroupindex
#516282
#516272
#477392
#477382
#454342
#454312
#453502
#453472
#453062
#452762
#450832
#449792
#398112
#398022
#397612
#397532
#396392
#390752
#389822
#382592
#376152
#368102
#365522
#362552
#353982
#353262
#352812
#348782
#343992
#342292
C2×#23312