Finite Group Databasebeta

← #8157147

Subgroups — #8157147

Order 512.

4288 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59454C212yesmaximal, complemented
2#59332C212yesmaximal, complemented
3#56682C214yesmaximal, complemented
4#54098C214yesmaximal, complemented
5#53807C214yesmaximal, complemented
6#53405C214yesmaximal, complemented
7#52996C212yesmaximal, complemented
8#52989C212yesmaximal, complemented
9#52800C214yesmaximal, complemented
10#45426C212yesmaximal, complemented
11#45376C212yesmaximal, complemented
12#42723C212yesmaximal, complemented
13#42687C212yesmaximal, complemented
14#42614C212yesmaximal, complemented
15#42496C212yesmaximal, complemented
16#40890C214yesmaximal, complemented
17#39421C212yesmaximal, complemented
18#39384C211yesmaximal, characteristic
19#39376C212yesmaximal, complemented
20#39368C211yesmaximal, characteristic, complemented
21#38068C212yesmaximal, complemented
22#38067C212yesmaximal, complemented
23#37464C212yesmaximal, complemented
24#36742C212yesmaximal, complemented
25#36599C211yesmaximal, characteristic, complemented
26#36587C211yesmaximal, characteristic
27#35006C211yesmaximal, characteristic
28C2×#2509C211yesmaximal, characteristic, complemented
29#34595C211yesmaximal, characteristic, complemented
30C2×#544C2212yes—
31C2×#539C2212yes—
32C2×#539C2212yes—
33#2857C2212yes—
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2854C2212yes—
37#2850C2212yes—
38#2841C2214yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2836C2214yes—
44#2832C2214yes—
45#2831C2214yes—
46#2831C2214yes—
47#2830C2214yes—
48#2827C2214yes—
49#2827C2214yes—
50#2810C2214yes—
51#2791C2214yes—
52#2790C2214yes—
53#2790C2214yes—
54#2788C2214yes—
55#2783C2214yes—
56#2777C2214yes—
57#2775C2214yes—
58#2773C2214yes—
59#2773C2214yes—
60#2772C2214yes—
61#2770C2214yes—
62#2768C2214yes—
63#2755C2214yes—
64#2755C2214yes—
65#2754C2214yes—
66#2750C2214yes—
67#2747C2214yes—
68#2744C2214yes—
69#2743C2214yes—
70#2742C2214yes—
71#2741C2214yes—
72#2739C2214yes—
73#2739C2214yes—
74#2738C2214yes—
75#2734C2212yes—
76#2732C2212yes—
77#2729C2214yes—
78#2728C2214yes—
79#2727C2212yes—
80#2726C2214yes—
81#2726C2212yes—
82#2725C2214yes—
83#2724C2214yes—
84#2721C2214yes—
85#2719C2214yes—
86#2719C2214yes—
87#2716C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2698C2214yes—
91#2694C2214yes—
92#2694C2214yes—
93#2690C2214yes—
94#2689C2214yes—
95#2689C2214yes—
96#2689C2214yes—
97#2677C2214yes—
98#2674C2214yes—
99#2674C2214yes—
100#2666C2212yes—
101#2666C2212yes—
102#2666C2212yes—
103#2666C2212yes—
104#2665C2214yes—
105#2659C2211yescharacteristic
106#2659C2211yescharacteristic
107#2654C2214yes—
108#2654C2214yes—
109#2652C2214yes—
110#2652C2214yes—
111#2650C2214yes—
112#2647C2212yes—
113#2647C2212yes—
114#2646C2212yes—
115#2644C2212yes—
116#2644C2212yes—
117#2639C2212yes—
118#2637C2214yes—
119#2627C2214yes—
120#2627C2212yes—
121#2627C2211yescharacteristic
122#2627C2211yescharacteristic
123#2627C2212yes—
124#2618C2212yes—
125#2618C2212yes—
126#2597C2214yes—
127#2589C2214yes—
128#2588C2214yes—
129#2585C2214yes—
130#2583C2214yes—
131#2580C2212yes—
132#2580C2212yes—
133#2575C2214yes—
134#2571C2211yescharacteristic
135#2571C2212yes—
136#2570C2212yes—
137#2570C2212yes—
138#2569C2214yes—
139#2567C2212yes—
140#2564C2214yes—
141#2560C2214yes—
142#2558C2214yes—
143#2558C2214yes—
144#2552C2212yes—
145#2552C2211yescharacteristic
146#2551C2212yes—
147#2550C2214yes—
148#2548C2211yescharacteristic
149#2546C2211yescharacteristic
150#2546C2212yes—
151#2538C2212yes—
152#2520C2214yes—
153#2519C2214yes—
154#2517C2214yes—
155#2513C2212yes—
156#2513C2212yes—
157#2513C2212yes—
158#2513C2212yes—
159#2513C2212yes—
160#2512C2212yes—
161#2512C2212yes—
162#2512C2212yes—
163#2511C2212yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2509C2214yes—
170#2509C2212yes—
171#2509C2214yes—
172#2509C2212yes—
173#2508C2212yes—
174#2507C2212yes—
175#2507C2212yes—
176#2507C2212yes—
177#2506C2212yes—
178#2506C2212yes—
179#2506C2214yes—
180#2506C2212yes—
181#2504C2212yes—
182#2501C2212yes—
183#2498C2214yes—
184#2498C2214yes—
185#2496C2214yes—
186#2488C2214yes—
187#2488C2214yes—
188#2486C2214yes—
189#2486C2214yes—
190#2481C2214yes—
191#2481C2214yes—
192#2468C2214yes—
193#2454C2212yes—
194#2454C2212yes—
195#2452C2212yes—
196#2452C2212yes—
197#2452C2212yes—
198#2450C2214yes—
199#2449C2214yes—
200#2447C2212yes—
201#2446C2212yes—
202#2445C2212yes—
203#2445C2212yes—
204#2444C2214yes—
205#2442C2212yes—
206#2440C2214yes—
207#2440C2212yes—
208#2438C2214yes—
209#2429C2214yes—
210#2425C2214yes—
211#2419C2214yes—
212#2419C2214yes—
213#2419C2214yes—
214#2417C2214yes—
215#2413C2214yes—
216#2402C2212yes—
217#2402C2212yes—
218#2399C2212yes—
219#2399C2212yes—
220C2×#400C2212yes—
221C2×#400C2212yes—
222#2370C2212yes—
223#2370C2212yes—
224#2366C2211yescharacteristic
225#2365C2211yescharacteristic
226#2361C2212yes—
227#2361C2212yes—
228#2359C2214yes—
229#2357C2212yes—
230#2357C2212yes—
231#2355C2211yescharacteristic
232#2355C2212yes—
233#2355C2211yescharacteristic
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2214yes—
236#2345C2212yes—
237#2344C2212yes—
238#2331C2212yes—
239#2330C2212yes—
240#2325C2212yes—
241#2319C2212yes—
242#2319C2212yes—
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2211yescharacteristic
245C4×C22⋊Q8C2211yescharacteristic
246C4×C22⋊Q8C2212yes—
247C4×#121C2212yes—
248C4×#121C2212yes—
249C2×#389C2211yescharacteristic
250C2×#389C2211yescharacteristic
251C2×#389C2211yescharacteristic
252C2×#389C2211yescharacteristic
253C2×#389C2212yes—
254C2×#387C2212yes—
255#2283C2212yes—
256C2×#382C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259#544—48no—
260#539—48no—
261#539—48no—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×#127C2311yescharacteristic
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#125C2312yes—
272C2×#125C2314yes—
273C2×#125C2314yes—
274C2×#125C2314yes—
275C2×#125C2314yes—
276C2×#124C2312yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2311yescharacteristic
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2314yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×#117C2314yes—
306C22×C4⋊C4C2311yescharacteristic
307C22×C4⋊C4C2311yescharacteristic
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2314yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2312yes—
351#400C2312yes—
352#400C2312yes—
353#400C2312yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2312yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#398C2314yes—
397#398C2312yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2312yes—
402#398C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2314yes—
439#395C2312yes—
440#395C2314yes—
441#395C2314yes—
442#395C2312yes—
443#395C2312yes—
444#395C2312yes—
445#395C2312yes—
446#395C2312yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#391C2312yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2312yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2311yescharacteristic
469#391C2311yescharacteristic
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
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#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
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#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2312yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2312yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#384C2314yes—
626#384C2312yes—
627#384C2312yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2312yes—
632#383C2312yes—
633#383C2312yes—
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2314yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2312yes—
651#381C2312yes—
652#380C2312yes—
653#380C2314yes—
654#380C2312yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661#380C2311yescharacteristic
662#380C2311yescharacteristic
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704#376C2312yes—
705#376C2312yes—
706C2×#95C2312yes—
707C2×#95C2312yes—
708C2×#95C2311yescharacteristic
709C2×#95C2312yes—
710C2×#95C2311yescharacteristic
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2411yescharacteristic
718C22×Q8C2412yes—
719C22×Q8C2414yes—
720C22×D4C2414yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2411yescharacteristic
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2414yes—
733C23×C4C2411yescharacteristic
734C23×C4C2411yescharacteristic
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2411yescharacteristic
738C4⋊Q8—42no—
739C4⋊Q8—44no—
740C4⋊Q8—48no—
741C4⋊Q8—48no—
742C4⋊Q8—82no—
743#127—42no—
744#126—48no—
745#126—48no—
746#126—84no—
747#125—28no—
748#125—48no—
749#125—48no—
750#125—48no—
751#125—48no—
752#124—82no—
753#123—48no—
754#123—48no—
755#123—48no—
756#123—48no—
757#123—48no—
758C22⋊Q8—24no—
759C22⋊Q8—28no—
760C22⋊Q8—24no—
761C22⋊Q8—44no—
762C22⋊Q8—48no—
763C22⋊Q8—48no—
764C22⋊Q8—48no—
765C22⋊Q8—84no—
766C22⋊Q8—84no—
767#121—28no—
768#121—28no—
769#121—44no—
770C4×Q8—44no—
771C4×Q8—42no—
772C4×Q8—42no—
773C4×Q8—82no—
774C4×D4—28no—
775C4×D4—44no—
776C4×D4—44no—
777C4×D4—48no—
778C4×D4—48no—
779C4×D4—48no—
780C4×D4—82no—
781#117—48no—
782C2×C4⋊C4—24no—
783C2×C4⋊C4—28no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—42no—
790C2×C4⋊C4—82no—
791C2×C4⋊C4—84no—
792C2×C4⋊C4—82no—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C42—24no—
901C2×C42—42no—
902C2×C42—42no—
903C2×C42—82no—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2414yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2514yes—
1004C24C2511yescharacteristic
1005C2×Q8—22no—
1006C2×Q8—24no—
1007C2×Q8—22no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—42no—
1011C2×Q8—42no—
1012C2×Q8—42no—
1013C2×Q8—41no—
1014C2×Q8—42no—
1015C2×Q8—41no—
1016C2×Q8—42no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×D4—28no—
1021C2×D4—28no—
1022C2×D4—28no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—24no—
1027C2×D4—42no—
1028C2×D4—42no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—22no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—24no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—24no—
1048C22×C4—28no—
1049C22×C4—41no—
1050C22×C4—41no—
1051C22×C4—42no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—41no—
1058C22×C4—42no—
1059C22×C4—41no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4H(5,𝔽2)14yes—
1073C22×C42−1+414yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2514yes—
1094C22×C4C2514yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—22no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—41no—
1150C4⋊C4—41no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—41no—
1158C4⋊C4—44no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C42−1+414yes—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—22no—
1214C42—22no—
1215C42—24no—
1216C42—24no—
1217C42—41no—
1218C42—41no—
1219C42—42no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—42no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—21no—
1235C23—24no—
1236C23—24no—
1237C23—24no—
1238C23—24no—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23C2×H(5,𝔽2)12yes—
1243C23C2×2−1+412yes—
1244C23#58512yes—
1245C23C2611yescharacteristic
1246Q8—82no—
1247Q8—82no—
1248Q8—84no—
1249Q8—84no—
1250Q8—164no—
1251D4—416no—
1252D4—48no—
1253D4—84no—
1254D4—162no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—28no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—44no—
1331C2×C4—48no—
1332C2×C4—48no—
1333C2×C4—44no—
1334C2×C4—88no—
1335C2×C4—82no—
1336C2×C4—84no—
1337C2×C4—82no—
1338C2×C4—84no—
1339C2×C4—82no—
1340C2×C4—82no—
1341C2×C4—164no—
1342C2×C4—164no—
1343C2×C4C2×H(5,𝔽2)12yes—
1344C2×C4C2×H(5,𝔽2)12yes—
1345C2×C4C2×2−1+412yes—
1346C2×C4C2×2−1+414yes—
1347C2×C4C2×2−1+412yes—
1348C2×C4C2×2−1+412yes—
1349C2×C4#58512yes—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22#355414yes—
1364C22C22×H(5,𝔽2)11yescharacteristic
1365C22C22×2−1+411yescharacteristic
1366C22C22×2−1+411yescharacteristic
1367C22C2×#58511yescharacteristic
1368C22C2×#58511yescharacteristic
1369C22H(7,𝔽2)11yescharacteristic
1370C222−1+611yescharacteristic
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—44no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—41no—
1387C4—41no—
1388C4—42no—
1389C4—42no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—42no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4#356314yes—
1398C2—24no—
1399C2—84no—
1400C2C2×#356311yescharacteristic
1401C2C2×#355411yescharacteristic
1402C2#6287911yescharacteristic
1403C2#6290511yescharacteristic
1404C2#6291111yescharacteristic
1405C2#6294611yescharacteristic
1406C2#6294811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59454C2semidirect
2. #59332C2semidirect
3. #56682C2semidirect
4. #54098C2semidirect
5. #53807C2semidirect
6. #53405C2semidirect
7. #52996C2semidirect
8. #52989C2semidirect
9. #52800C2semidirect
10. #45426C2semidirect
11. #45376C2semidirect
12. #42723C2semidirect
13. #42687C2semidirect
14. #42614C2semidirect
15. #42496C2semidirect
16. #40890C2semidirect
17. #39421C2semidirect
19. #39376C2semidirect
20. #39368C2semidirect
21. #38068C2semidirect
22. #38067C2semidirect
23. #37464C2semidirect
24. #36742C2semidirect
25. #36599C2semidirect
28. C2×#2509C2semidirect
29. #34595C2semidirect

Maximal subgroups

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

subgroupindex
#594542
#593322
#566822
#540982
#538072
#534052
#529962
#529892
#528002
#454262
#453762
#427232
#426872
#426142
#424962
#408902
#394212
#393842
#393762
#393682
#380682
#380672
#374642
#367422
#365992
#365872
#350062
C2×#25092
#345952