Finite Group Databasebeta

← #7655140

Subgroups — #7655140

Order 512.

4770 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42947C214yesmaximal, complemented
2#42250C218yesmaximal, complemented
3#39736C212yesmaximal, complemented
4#39554C214yesmaximal, complemented
5#39480C212yesmaximal, complemented
6#39437C214yesmaximal, complemented
7#39379C212yesmaximal, complemented
8#39194C212yesmaximal, complemented
9#38219C214yesmaximal, complemented
10#37973C214yesmaximal, complemented
11#37640C211yesmaximal, characteristic, complemented
12#37627C212yesmaximal, complemented
13#36477C212yesmaximal, complemented
14#36460C212yesmaximal, complemented
15#36287C212yesmaximal, complemented
16#36174C212yesmaximal, complemented
17#36073C214yesmaximal, complemented
18#35286C211yesmaximal, characteristic, complemented
19#35273C211yesmaximal, characteristic
20#35209C212yesmaximal, complemented
21#35196C212yesmaximal, complemented
22#34979C211yesmaximal, characteristic, complemented
23#34945C212yesmaximal, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34155C211yesmaximal, characteristic, complemented
26#34129C211yesmaximal, characteristic, complemented
27C2×#541C2214yes—
28C2×#537C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2860C2214yes—
33#2859C2212yes—
34#2859C2212yes—
35#2859C2214yes—
36#2857C2212yes—
37#2856C2212yes—
38#2855C2214yes—
39#2850C2214yes—
40#2837C2218yes—
41#2820C2214yes—
42#2801C2218yes—
43#2800C2218yes—
44#2762C2218yes—
45#2761C2218yes—
46#2757C2218yes—
47#2750C2218yes—
48#2725C2218yes—
49#2725C2218yes—
50#2711C2218yes—
51#2691C2218yes—
52#2691C2218yes—
53#2690C2218yes—
54#2664C2218yes—
55#2651C2218yes—
56#2649C2218yes—
57#2647C2214yes—
58#2629C2214yes—
59#2625C2214yes—
60#2624C2214yes—
61#2624C2214yes—
62#2620C2214yes—
63#2620C2214yes—
64#2620C2214yes—
65#2616C2214yes—
66#2612C2218yes—
67#2611C2214yes—
68#2608C2218yes—
69#2587C2218yes—
70#2576C2218yes—
71#2573C2218yes—
72#2571C2212yes—
73#2571C2212yes—
74#2570C2214yes—
75#2568C2211yescharacteristic
76#2567C2212yes—
77#2566C2214yes—
78#2559C2218yes—
79#2559C2218yes—
80#2556C2218yes—
81#2552C2212yes—
82#2552C2212yes—
83#2548C2212yes—
84#2547C2212yes—
85#2547C2211yescharacteristic
86#2546C2211yescharacteristic
87#2542C2212yes—
88#2542C2211yescharacteristic
89#2538C2212yes—
90#2538C2212yes—
91#2538C2212yes—
92#2538C2212yes—
93#2537C2212yes—
94#2537C2212yes—
95#2531C2218yes—
96#2526C2218yes—
97#2526C2218yes—
98#2519C2218yes—
99#2518C2218yes—
100#2516C2218yes—
101#2514C2214yes—
102#2512C2214yes—
103#2512C2214yes—
104#2512C2214yes—
105#2506C2214yes—
106#2506C2214yes—
107#2506C2214yes—
108#2500C2214yes—
109#2499C2212yes—
110#2497C2214yes—
111#2497C2214yes—
112#2495C2214yes—
113#2494C2214yes—
114#2494C2214yes—
115#2490C2218yes—
116#2490C2214yes—
117#2490C2214yes—
118#2489C2214yes—
119#2447C2214yes—
120#2442C2214yes—
121#2442C2214yes—
122#2441C2214yes—
123#2432C2212yes—
124#2429C2214yes—
125#2426C2214yes—
126#2426C2214yes—
127#2423C2214yes—
128#2421C2214yes—
129#2421C2214yes—
130#2420C2214yes—
131#2420C2214yes—
132#2416C2214yes—
133#2416C2214yes—
134#2415C2212yes—
135#2415C2212yes—
136#2401C2218yes—
137#2395C2214yes—
138#2372C2214yes—
139#2370C2214yes—
140#2369C2211yescharacteristic
141#2369C2211yescharacteristic
142#2366C2211yescharacteristic
143#2366C2211yescharacteristic
144#2363C2212yes—
145#2363C2214yes—
146#2363C2212yes—
147#2363C2212yes—
148#2363C2212yes—
149#2360C2214yes—
150#2360C2214yes—
151#2357C2214yes—
152#2355C2212yes—
153#2355C2212yes—
154#2354C2211yescharacteristic
155#2354C2211yescharacteristic
156#2354C2212yes—
157#2354C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2211yescharacteristic
160Q8×C4⋊C4C2211yescharacteristic
161Q8×C4⋊C4C2212yes—
162#2346C2214yes—
163#2346C2214yes—
164#2346C2212yes—
165#2341C2212yes—
166#2330C2214yes—
167#2324C2214yes—
168#2323C2214yes—
169#2317C2212yes—
170#2317C2212yes—
171#2316C2212yes—
172#2314C2214yes—
173#2311C2212yes—
174C4×C4⋊Q8C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×#124C2212yes—
178C4×#124C2214yes—
179C4×C22⋊Q8C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182#2297C2214yes—
183#2295C2214yes—
184#2293C2212yes—
185#2293C2214yes—
186#2293C2212yes—
187#2293C2212yes—
188#2285C2211yescharacteristic
189#2285C2212yes—
190C2×#384C2211yescharacteristic
191#2283C2214yes—
192#2274C2212yes—
193C42×Q8C2212yes—
194C42×D4C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201#541—416no—
202#537—48no—
203#533—28no—
204#532—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126C2318yes—
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2318yes—
216C2×#125C2318yes—
217C2×#124C2312yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2318yes—
235C4×#41—28no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2314yes—
260C2×#117C2311yescharacteristic
261C2×#117C2312yes—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2314yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C42C2312yes—
270C22×C42C2314yes—
271C22×C42C2311yescharacteristic
272#401C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#399C2318yes—
281#399C2314yes—
282#399C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2318yes—
288#398C2318yes—
289#397C2318yes—
290#397C2314yes—
291#397C2318yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2314yes—
319#394C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2314yes—
335#390C2318yes—
336#390C2312yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2318yes—
349#390C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2314yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2318yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#386C2318yes—
421#386C2314yes—
422#386C2318yes—
423#386C2318yes—
424#386C2314yes—
425#386C2314yes—
426#386C2314yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2314yes—
437#384C2312yes—
438#384C2314yes—
439#384C2314yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2312yes—
445#383C2318yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2318yes—
453#382C2314yes—
454#381C2318yes—
455#381C2318yes—
456#380C2314yes—
457#380C2314yes—
458#380C2312yes—
459#380C2314yes—
460#380C2318yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2318yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2318yes—
502C4×C22⋊C4C2318yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517#376C2312yes—
518#376C2314yes—
519#376C2318yes—
520#376C2312yes—
521C43C2312yes—
522C43C2312yes—
523C43C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—42no—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2412yes—
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2418yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C23×C4C2414yes—
549C23×C4C2414yes—
550C23×C4C2414yes—
551C4⋊Q8—28no—
552C4⋊Q8—24no—
553C4⋊Q8—24no—
554C4⋊Q8—24no—
555#127—24no—
556#126—416no—
557#126—416no—
558#125—28no—
559#125—48no—
560#125—48no—
561#125—416no—
562#125—416no—
563#124—28no—
564#124—44no—
565#124—48no—
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—28no—
569C22⋊Q8—48no—
570C22⋊Q8—44no—
571C22⋊Q8—44no—
572C22⋊Q8—48no—
573C22⋊Q8—48no—
574#121—28no—
575#121—28no—
576#121—48no—
577#121—416no—
578#121—48no—
579#121—48no—
580#121—48no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—28no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—28no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—44no—
597C4×D4—44no—
598C4×D4—44no—
599#117—24no—
600#117—28no—
601#117—24no—
602#117—28no—
603#117—28no—
604#117—48no—
605#117—44no—
606#117—48no—
607#117—42no—
608#117—44no—
609#117—42no—
610#117—42no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C42—28no—
699C2×C42—48no—
700C2×C42#4118yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2418yes—
722C2×C42C2414yes—
723C2×C42C2418yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2412yes—
731#95C2414yes—
732#95C2412yes—
733#95C2412yes—
734#95C2412yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768C24C2512yes—
769C24C2514yes—
770C24C2511yescharacteristic
771#41—416no—
772#41—816no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8H(5,𝔽2)14yes—
785C2×D4—24no—
786C2×D4—28no—
787C2×D4—22no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—44no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—48no—
804C2×D4—48no—
805C2×D4—48no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
816C22×C4—28no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—28no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—42no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4C2×#4114yes—
834C22×C4C2×#4114yes—
835C22×C4C2×#4114yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2514yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2514yes—
847C22×C4C2518yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—28no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C42−1+414yes—
910C22⋊C4—24no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—216no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—42no—
924C22⋊C4—44no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—28no—
947C42—24no—
948C42—24no—
949C42—28no—
950C42—24no—
951C42—28no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—28no—
957C42—24no—
958C42—24no—
959C42—44no—
960C42—44no—
961C42—42no—
962C42—42no—
963C42—42no—
964C42—44no—
965C42—44no—
966C42—48no—
967C42—48no—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C42C2×#4114yes—
971C42C2×#4114yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—22no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—22no—
985C23—24no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23C22×#4112yes—
993C23C2611yescharacteristic
994Q8—28no—
995Q8—48no—
996Q8—48no—
997Q8—84no—
998D4—48no—
999D4—48no—
1000D4—44no—
1001D4—48no—
1002D4—84no—
1003D4—88no—
1004D4—168no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—28no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—28no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—28no—
1062C2×C4—22no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—416no—
1066C2×C4—48no—
1067C2×C4—88no—
1068C2×C4—88no—
1069C2×C4—164no—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C2×H(5,𝔽2)14yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×2−1+414yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4#58512yes—
1081C2×C4#58512yes—
1082C2×C4#58512yes—
1083C2×C4#58512yes—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—41no—
1088C22—41no—
1089C22—41no—
1090C22—41no—
1091C22—44no—
1092C22—42no—
1093C22—44no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—44no—
1098C22—42no—
1099C22—42no—
1100C22—44no—
1101C22—42no—
1102C22—44no—
1103C22—42no—
1104C22—44no—
1105C22C23×#4111yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×2−1+411yescharacteristic
1108C22C2×#58511yescharacteristic
1109C22C2×#58511yescharacteristic
1110C22C2×#58511yescharacteristic
1111C22C2×#58511yescharacteristic
1112C4—24no—
1113C4—22no—
1114C4—24no—
1115C4—22no—
1116C4—22no—
1117C4—42no—
1118C4—44no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—48no—
1124C4—42no—
1125C4—42no—
1126C4—44no—
1127C4—44no—
1128C4—44no—
1129C4—42no—
1130C4—44no—
1131C4—42no—
1132C4#346114yes—
1133C4#349414yes—
1134C4#351214yes—
1135C2—42no—
1136C2—84no—
1137C2—82no—
1138C2C2×#346111yescharacteristic
1139C2C2×#349411yescharacteristic
1140C2C2×#351211yescharacteristic
1141C2#6302511yescharacteristic
1142C2#6303111yescharacteristic
1143C2#6303511yescharacteristic
1144C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42947C2semidirect
2. #42250C2semidirect
3. #39736C2semidirect
4. #39554C2semidirect
5. #39480C2semidirect
6. #39437C2semidirect
7. #39379C2semidirect
8. #39194C2semidirect
9. #38219C2semidirect
10. #37973C2semidirect
11. #37640C2semidirect
12. #37627C2semidirect
13. #36477C2semidirect
14. #36460C2semidirect
15. #36287C2semidirect
16. #36174C2semidirect
17. #36073C2semidirect
18. #35286C2semidirect
20. #35209C2semidirect
21. #35196C2semidirect
22. #34979C2semidirect
23. #34945C2semidirect
24. #34214C2semidirect
25. #34155C2semidirect
26. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#429472
#422502
#397362
#395542
#394802
#394372
#393792
#391942
#382192
#379732
#376402
#376272
#364772
#364602
#362872
#361742
#360732
#352862
#352732
#352092
#351962
#349792
#349452
#342142
#341552
#341292