Finite Group Databasebeta

← #7656496

Subgroups — #7656496

Order 512.

4628 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42901C213yesmaximal, complemented
2#42898C213yesmaximal, complemented
3#42849C213yesmaximal, complemented
4#42845C213yesmaximal, complemented
5#42684C213yesmaximal, complemented
6#42656C213yesmaximal, complemented
7#42521C213yesmaximal, complemented
8#42464C213yesmaximal, complemented
9#40123C213yesmaximal, complemented
10#40105C213yesmaximal, complemented
11#39239C213yesmaximal, complemented
12#39223C213yesmaximal, complemented
13#37521C213yesmaximal, complemented
14#37508C213yesmaximal, complemented
15#36448C211yesmaximal, characteristic, complemented
16#36447C211yesmaximal, characteristic, complemented
17#36432C211yesmaximal, characteristic, complemented
18#36431C211yesmaximal, characteristic, complemented
19#35971C211yesmaximal, characteristic, complemented
20#35898C211yesmaximal, characteristic, complemented
21#35845C211yesmaximal, characteristic, complemented
22#35801C211yesmaximal, characteristic, complemented
23#35801C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#35771C211yesmaximal, characteristic
26#35723C211yesmaximal, characteristic, complemented
27#35045C213yesmaximal, complemented
28#34592C213yesmaximal, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34249C211yesmaximal, characteristic, complemented
31C4×#548C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2863C2213yes—
42#2859C2213yes—
43#2855C2213yes—
44#2851C2213yes—
45#2838C2216yes—
46#2836C2216yes—
47#2827C2216yes—
48#2826C2216yes—
49#2810C2216yes—
50#2802C2216yes—
51#2796C2216yes—
52#2793C2216yes—
53#2793C2216yes—
54#2790C2216yes—
55#2789C2216yes—
56#2785C2216yes—
57#2783C2216yes—
58#2783C2216yes—
59#2775C2216yes—
60#2773C2216yes—
61#2771C2216yes—
62#2765C2216yes—
63#2727C2216yes—
64#2721C2216yes—
65#2667C2213yes—
66#2666C2213yes—
67#2664C2213yes—
68#2663C2213yes—
69#2655C2213yes—
70#2654C2213yes—
71#2654C2216yes—
72#2653C2216yes—
73#2653C2213yes—
74#2652C2213yes—
75#2652C2213yes—
76#2652C2213yes—
77#2651C2216yes—
78#2649C2211yescharacteristic
79#2649C2213yes—
80#2649C2216yes—
81#2647C2213yes—
82#2644C2213yes—
83#2638C2213yes—
84#2636C2213yes—
85#2633C2213yes—
86#2633C2216yes—
87#2630C2213yes—
88#2629C2213yes—
89#2628C2213yes—
90#2625C2213yes—
91#2624C2213yes—
92#2624C2213yes—
93#2620C2213yes—
94#2590C2216yes—
95#2582C2213yes—
96#2581C2213yes—
97#2580C2213yes—
98#2577C2216yes—
99#2575C2216yes—
100#2573C2216yes—
101#2571C2213yes—
102#2571C2213yes—
103#2570C2213yes—
104#2567C2213yes—
105#2566C2213yes—
106#2565C2213yes—
107#2558C2216yes—
108#2556C2216yes—
109#2552C2213yes—
110#2545C2213yes—
111#2538C2213yes—
112#2517C2216yes—
113#2514C2213yes—
114#2514C2213yes—
115#2513C2213yes—
116#2512C2213yes—
117#2512C2213yes—
118#2511C2213yes—
119#2509C2213yes—
120#2508C2213yes—
121#2508C2213yes—
122#2508C2213yes—
123#2508C2213yes—
124#2507C2213yes—
125#2506C2213yes—
126#2506C2213yes—
127#2500C2213yes—
128#2500C2213yes—
129#2499C2213yes—
130#2499C2213yes—
131#2497C2213yes—
132#2496C2213yes—
133#2496C2213yes—
134#2495C2213yes—
135#2494C2213yes—
136#2494C2213yes—
137#2485C2213yes—
138#2485C2213yes—
139#2485C2213yes—
140#2485C2213yes—
141#2466C2216yes—
142#2454C2213yes—
143#2453C2213yes—
144#2453C2213yes—
145#2453C2213yes—
146#2452C2213yes—
147#2451C2213yes—
148#2448C2213yes—
149#2448C2213yes—
150#2448C2213yes—
151#2448C2213yes—
152#2447C2213yes—
153#2447C2213yes—
154#2446C2213yes—
155#2446C2213yes—
156#2441C2213yes—
157#2441C2213yes—
158#2441C2213yes—
159#2441C2213yes—
160#2439C2213yes—
161#2439C2213yes—
162#2429C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2423C2213yes—
167#2422C2213yes—
168#2421C2213yes—
169#2421C2213yes—
170#2421C2213yes—
171#2420C2213yes—
172#2415C2213yes—
173#2414C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2396C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2395C2213yes—
181#2392C2213yes—
182#2367C2213yes—
183#2365C2213yes—
184#2362C2213yes—
185#2362C2213yes—
186#2361C2213yes—
187#2360C2213yes—
188#2352C2213yes—
189#2352C2213yes—
190#2351C2211yescharacteristic
191#2351C2213yes—
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197#2351C2211yescharacteristic
198#2351C2213yes—
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2213yes—
204Q8×C4⋊C4C2211yescharacteristic
205Q8×C4⋊C4C2213yes—
206Q8×C4⋊C4C2211yescharacteristic
207Q8×C4⋊C4C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2336C2216yes—
219#2334C2216yes—
220#2327C2213yes—
221#2323C2213yes—
222#2317C2213yes—
223#2317C2213yes—
224C4×#125C2213yes—
225C4×#126C2213yes—
226C4×#124C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×C22⋊Q8C2213yes—
230C4×#123C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233#2296C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242D4×Q8—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#126C2313yes—
248C2×#126C2316yes—
249C2×#125C2313yes—
250C2×#125C2313yes—
251C2×#125C2313yes—
252C2×#125C2316yes—
253C2×#124C2313yes—
254C2×#124C2313yes—
255C2×#123C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×#121C2313yes—
262C2×#121C2313yes—
263#519—28no—
264#519—44no—
265#519—44no—
266C4×#41—44no—
267C2×C4×Q8—44no—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C2×#117C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C22×C4⋊C4C2313yes—
304C22×C42C2313yes—
305C22×C42C2313yes—
306#401C2316yes—
307#401C2313yes—
308#400C2316yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2316yes—
313#400C2316yes—
314#400C2316yes—
315#400C2316yes—
316#400C2313yes—
317#400C2313yes—
318#400C2316yes—
319#400C2313yes—
320#400C2313yes—
321#400C2313yes—
322#400C2311yescharacteristic
323#400C2311yescharacteristic
324#400C2313yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#399C2316yes—
329#399C2316yes—
330#399C2316yes—
331#399C2316yes—
332#399C2311yescharacteristic
333#399C2313yes—
334#399C2313yes—
335#399C2313yes—
336#399C2313yes—
337#398C2313yes—
338#398C2316yes—
339#398C2313yes—
340#398C2316yes—
341#398C2313yes—
342#398C2316yes—
343#398C2316yes—
344#398C2316yes—
345#398C2313yes—
346#398C2316yes—
347#398C2313yes—
348#398C2313yes—
349#398C2313yes—
350#398C2313yes—
351#398C2313yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2316yes—
359#397C2316yes—
360#397C2316yes—
361#397C2316yes—
362#397C2313yes—
363#397C2316yes—
364#397C2313yes—
365#397C2316yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2313yes—
370#397C2313yes—
371#397C2311yescharacteristic
372#397C2311yescharacteristic
373#397C2313yes—
374#397C2313yes—
375#397C2313yes—
376#397C2313yes—
377#396C2316yes—
378#396C2316yes—
379#396C2316yes—
380#396C2313yes—
381#396C2316yes—
382#396C2316yes—
383#396C2316yes—
384#396C2313yes—
385#396C2313yes—
386#396C2313yes—
387#396C2313yes—
388#396C2313yes—
389#396C2311yescharacteristic
390#395C2313yes—
391#395C2316yes—
392#395C2313yes—
393#394C2313yes—
394#394C2316yes—
395#394C2316yes—
396#394C2316yes—
397#394C2313yes—
398#394C2316yes—
399#394C2313yes—
400#394C2313yes—
401#394C2313yes—
402#394C2311yescharacteristic
403#394C2313yes—
404#394C2311yescharacteristic
405#394C2313yes—
406#393C2316yes—
407#393C2313yes—
408#393C2313yes—
409#392C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2316yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2316yes—
433#389C2311yescharacteristic
434#389C2313yes—
435#389C2316yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2316yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2316yes—
457#389C2313yes—
458#389C2316yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#389C2313yes—
477#388C2311yescharacteristic
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2313yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2316yes—
492#388C2313yes—
493#388C2311yescharacteristic
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#387C2313yes—
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2313yes—
505#387C2313yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2313yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2313yes—
526#387C2313yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2311yescharacteristic
531#387C2313yes—
532#386C2313yes—
533#386C2316yes—
534#386C2311yescharacteristic
535#386C2313yes—
536#385C2313yes—
537#385C2316yes—
538#385C2316yes—
539#385C2313yes—
540#385C2313yes—
541#385C2313yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#385C2316yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2311yescharacteristic
550#384C2313yes—
551#384C2313yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2316yes—
556#384C2313yes—
557#384C2313yes—
558#383C2313yes—
559#383C2316yes—
560#382C2313yes—
561#382C2313yes—
562#382C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2316yes—
568#382C2316yes—
569#382C2316yes—
570#382C2313yes—
571#381C2313yes—
572#381C2316yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2316yes—
598C4×C4⋊C4C2316yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2316yes—
624C4×C22⋊C4C2311yescharacteristic
625#376C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2411yescharacteristic
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C23×C4C2413yes—
650C23×C4C2413yes—
651C4⋊Q8—212no—
652C4⋊Q8—46no—
653#126—46no—
654#126—412no—
655#125—412no—
656#125—46no—
657#125—46no—
658#125—46no—
659#124—212no—
660#124—46no—
661#123—46no—
662C22⋊Q8—212no—
663C22⋊Q8—212no—
664C22⋊Q8—212no—
665C22⋊Q8—46no—
666C22⋊Q8—46no—
667#121—212no—
668#121—46no—
669C4×Q8—212no—
670C4×Q8—212no—
671C4×Q8—24no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—46no—
684C4×Q8—46no—
685C4×Q8—46no—
686C4×Q8—46no—
687C4×Q8—46no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×D4—212no—
691C4×D4—212no—
692C4×D4—46no—
693C4×D4—46no—
694C4×D4—46no—
695C4×D4—46no—
696C4×D4—46no—
697#117—212no—
698#117—212no—
699#117—46no—
700#117—46no—
701#117—46no—
702#117—46no—
703#117—46no—
704C2×C4⋊C4—46no—
705C2×C4⋊C4C2413yes—
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2416yes—
747C2×C4⋊C4C2416yes—
748C2×C4⋊C4C2416yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2411yescharacteristic
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2416yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C22⋊C4C2411yescharacteristic
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2411yescharacteristic
770C2×C22⋊C4C2411yescharacteristic
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2413yes—
773C2×C22⋊C4C2413yes—
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2411yescharacteristic
777C2×C22⋊C4C2411yescharacteristic
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2416yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2416yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C42—46no—
807C2×C42—46no—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2416yes—
825C2×C42C2416yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2411yescharacteristic
830C2×C42C2413yes—
831C2×C42C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2411yescharacteristic
837#95C2411yescharacteristic
838#95C2411yescharacteristic
839#95C2411yescharacteristic
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2416yes—
850#95C2416yes—
851#95C2413yes—
852#95C2413yes—
853#95C2416yes—
854#95C2416yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2411yescharacteristic
863#95C2413yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2411yescharacteristic
867#95C2416yes—
868#95C2413yes—
869#95C2411yescharacteristic
870#95C2411yescharacteristic
871#95C2416yes—
872#95C2413yes—
873#95C2416yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2416yes—
893#95C2416yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897#95C2416yes—
898C24C2511yescharacteristic
899C24C2513yes—
900C24C2511yescharacteristic
901#41—416no—
902C2×Q8—232no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—26no—
907C2×Q8—26no—
908C2×Q8—43no—
909C2×Q8—43no—
910C2×Q8—43no—
911C2×Q8—416no—
912C2×Q8C2×#41112yes—
913C2×Q8C2×#4114yes—
914C2×Q8H(5,𝔽2)14yes—
915C2×Q82−1+414yes—
916C2×D4—22no—
917C2×D4—26no—
918C2×D4—26no—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—43no—
922C2×D4—43no—
923C2×D4—41no—
924C2×D4—41no—
925C2×D4—43no—
926C2×D4—43no—
927C2×D4—43no—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—22no—
937C22×C4—26no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—43no—
941C22×C4—43no—
942C22×C4—43no—
943C22×C4—43no—
944C22×C4—43no—
945C22×C4—43no—
946C22×C4—43no—
947C22×C4—43no—
948C22×C4C2×#41112yes—
949C22×C4C2511yescharacteristic
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2513yes—
953C22×C4C2511yescharacteristic
954C22×C4C2513yes—
955C22×C4C2511yescharacteristic
956C22×C4C2511yescharacteristic
957C22×C4C2511yescharacteristic
958C22×C4C2513yes—
959C22×C4C2511yescharacteristic
960C22×C4C2513yes—
961C22×C4C2513yes—
962C22×C4C2513yes—
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2511yescharacteristic
966C22×C4C2513yes—
967C22×C4C2513yes—
968C22×C4C2513yes—
969C22×C4C2513yes—
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2513yes—
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C4⋊C4—26no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—26no—
981C4⋊C4—26no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—26no—
985C4⋊C4—212no—
986C4⋊C4—26no—
987C4⋊C4—26no—
988C4⋊C4—26no—
989C4⋊C4—26no—
990C4⋊C4—26no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—22no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—22no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—46no—
1001C4⋊C4—41no—
1002C4⋊C4—43no—
1003C4⋊C4—41no—
1004C4⋊C4—41no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—46no—
1008C4⋊C4—41no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—43no—
1012C4⋊C4—46no—
1013C4⋊C4—43no—
1014C4⋊C4—41no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—41no—
1023C4⋊C4—43no—
1024C4⋊C4—43no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—46no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4—46no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—46no—
1039C22⋊C4—22no—
1040C22⋊C4—26no—
1041C22⋊C4—22no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—26no—
1045C22⋊C4—212no—
1046C22⋊C4—22no—
1047C22⋊C4—26no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—43no—
1051C22⋊C4—46no—
1052C22⋊C4—41no—
1053C22⋊C4—43no—
1054C22⋊C4—41no—
1055C22⋊C4—43no—
1056C22⋊C4—43no—
1057C22⋊C4—43no—
1058C22⋊C4—46no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—43no—
1063C22⋊C4—43no—
1064C22⋊C4—46no—
1065C22⋊C4—43no—
1066C22⋊C4—43no—
1067C22⋊C4—41no—
1068C22⋊C4—43no—
1069C22⋊C4—46no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—43no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—46no—
1077C22⋊C4—46no—
1078C42—212no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—41no—
1094C42—43no—
1095C42—43no—
1096C42—43no—
1097C42—41no—
1098C42—43no—
1099C42—46no—
1100C42—46no—
1101C42—46no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—23no—
1110C23—21no—
1111C23—23no—
1112C23—21no—
1113C23—23no—
1114C23—21no—
1115C23—23no—
1116C23—21no—
1117C23—23no—
1118C23—23no—
1119C23—21no—
1120C23—23no—
1121C23—21no—
1122C23C22×#4112yes—
1123C23C2611yescharacteristic
1124Q8—224no—
1125Q8—412no—
1126Q8—86no—
1127Q8#539116yes—
1128D4—412no—
1129D4—44no—
1130D4—412no—
1131D4—86no—
1132C2×C4—21no—
1133C2×C4—23no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—224no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—21no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—23no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—23no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—44no—
1212C2×C4—412no—
1213C2×C4—412no—
1214C2×C4—86no—
1215C2×C4—86no—
1216C2×C4—86no—
1217C2×C4C22×#4116yes—
1218C2×C4C22×#4116yes—
1219C2×C4C2×H(5,𝔽2)16yes—
1220C2×C4C2×2−1+416yes—
1221C2×C4#58512yes—
1222C2×C4#58512yes—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—43no—
1231C22—41no—
1232C22—41no—
1233C22—43no—
1234C22—43no—
1235C22—41no—
1236C22—43no—
1237C22—41no—
1238C22—41no—
1239C22—43no—
1240C22—41no—
1241C22—43no—
1242C22—41no—
1243C22—43no—
1244C22C23×#4111yescharacteristic
1245C22C22×H(5,𝔽2)11yescharacteristic
1246C22C22×2−1+411yescharacteristic
1247C22C2×#58511yescharacteristic
1248C22C2×#58511yescharacteristic
1249C222−1+611yescharacteristic
1250C222−1+611yescharacteristic
1251C4—22no—
1252C4—26no—
1253C4—22no—
1254C4—41no—
1255C4—43no—
1256C4—43no—
1257C4—43no—
1258C4—41no—
1259C4—41no—
1260C4—43no—
1261C4—41no—
1262C4—41no—
1263C4—43no—
1264C4—43no—
1265C4—43no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—43no—
1270C4—43no—
1271C4—43no—
1272C4—41no—
1273C4—41no—
1274C4—43no—
1275C4—43no—
1276C4—41no—
1277C4—43no—
1278C4C2×#539112yes—
1279C2—42no—
1280C2—83no—
1281C2—81no—
1282C2C22×#53911yescharacteristic
1283C2#6279311yescharacteristic
1284C2#6285011yescharacteristic
1285C2#6289711yescharacteristic
1286C2#6292211yescharacteristic
1287C2#6294911yescharacteristic
1288C2#6295311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35771C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42901C2semidirect
2. #42898C2semidirect
3. #42849C2semidirect
4. #42845C2semidirect
5. #42684C2semidirect
6. #42656C2semidirect
7. #42521C2semidirect
8. #42464C2semidirect
9. #40123C2semidirect
10. #40105C2semidirect
11. #39239C2semidirect
12. #39223C2semidirect
13. #37521C2semidirect
14. #37508C2semidirect
15. #36448C2semidirect
16. #36447C2semidirect
17. #36432C2semidirect
18. #36431C2semidirect
19. #35971C2semidirect
20. #35898C2semidirect
21. #35845C2semidirect
22. #35801C2semidirect
23. #35801C2semidirect
24. #35786C2semidirect
26. #35723C2semidirect
27. #35045C2semidirect
28. #34592C2semidirect
29. #34291C2semidirect
30. #34249C2semidirect
31. C4×#548C2semidirect

Maximal subgroups

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

subgroupindex
#429012
#428982
#428492
#428452
#426842
#426562
#425212
#424642
#401232
#401052
#392392
#392232
#375212
#375082
#364482
#364472
#364322
#364312
#359712
#358982
#358452
#358012
#357862
#357712
#357232
#350452
#345922
#342912
#342492
C4×#5482