Finite Group Databasebeta

← #7739343

Subgroups — #7739343

Order 512.

5086 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C212yesmaximal, complemented
2#59642C212yesmaximal, complemented
3#59451C212yesmaximal, complemented
4#59444C212yesmaximal, complemented
5#51620C218yesmaximal, complemented
6#45393C214yesmaximal, complemented
7#45325C214yesmaximal, complemented
8#45237C214yesmaximal, complemented
9#44905C214yesmaximal, complemented
10#39606C212yesmaximal, complemented
11#39514C212yesmaximal, complemented
12#39481C212yesmaximal, complemented
13#39201C212yesmaximal, complemented
14#37335C214yesmaximal, complemented
15#36563C212yesmaximal, complemented
16#36473C212yesmaximal, complemented
17#36300C212yesmaximal, complemented
18#36272C212yesmaximal, complemented
19#35598C214yesmaximal, complemented
20#35317C211yesmaximal, characteristic, complemented
21#35279C211yesmaximal, characteristic, complemented
22#34978C211yesmaximal, characteristic, complemented
23#34977C211yesmaximal, characteristic
24#34368C211yesmaximal, characteristic, complemented
25#34216C211yesmaximal, characteristic, complemented
26#34129C211yesmaximal, characteristic, complemented
27C2×#556C2214yes—
28C2×#552C2214yes—
29C2×#536C2212yes—
30C2×#536C2212yes—
31C2×#532C2211yescharacteristic
32C22×C4⋊Q8C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34#2868C2212yes—
35#2860C2214yes—
36#2859C2214yes—
37#2858C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2807C2218yes—
41#2773C2218yes—
42#2773C2218yes—
43#2768C2218yes—
44#2748C2218yes—
45#2741C2218yes—
46#2727C2218yes—
47#2716C2218yes—
48#2716C2218yes—
49#2712C2218yes—
50#2710C2218yes—
51#2706C2218yes—
52#2705C2218yes—
53#2695C2218yes—
54#2694C2218yes—
55#2694C2218yes—
56#2658C2214yes—
57#2629C2214yes—
58#2628C2214yes—
59#2624C2214yes—
60#2612C2214yes—
61#2611C2218yes—
62#2610C2214yes—
63#2604C2218yes—
64#2596C2218yes—
65#2589C2218yes—
66#2582C2214yes—
67#2580C2214yes—
68#2571C2211yescharacteristic
69#2570C2214yes—
70#2570C2214yes—
71#2568C2212yes—
72#2567C2211yescharacteristic
73#2567C2212yes—
74#2563C2212yes—
75#2563C2211yescharacteristic
76#2557C2218yes—
77#2554C2218yes—
78#2553C2218yes—
79#2552C2214yes—
80#2552C2211yescharacteristic
81#2552C2211yescharacteristic
82#2551C2211yescharacteristic
83#2550C2218yes—
84#2548C2214yes—
85#2548C2211yescharacteristic
86#2542C2212yes—
87#2542C2212yes—
88#2542C2212yes—
89#2542C2212yes—
90#2542C2212yes—
91#2541C2211yescharacteristic
92#2538C2214yes—
93#2536C2214yes—
94#2521C2218yes—
95#2521C2218yes—
96#2513C2214yes—
97#2513C2214yes—
98#2512C2214yes—
99#2512C2214yes—
100#2512C2214yes—
101#2507C2214yes—
102#2507C2214yes—
103#2502C2214yes—
104#2501C2214yes—
105#2501C2214yes—
106#2500C2212yes—
107#2499C2214yes—
108#2496C2214yes—
109#2496C2214yes—
110#2492C2214yes—
111#2491C2214yes—
112#2489C2214yes—
113#2487C2214yes—
114#2479C2218yes—
115#2474C2218yes—
116#2470C2218yes—
117#2458C2218yes—
118#2454C2214yes—
119#2451C2218yes—
120#2448C2218yes—
121#2448C2214yes—
122#2445C2214yes—
123#2441C2212yes—
124#2441C2212yes—
125#2439C2212yes—
126#2439C2212yes—
127#2431C2212yes—
128#2423C2214yes—
129#2423C2214yes—
130#2422C2214yes—
131#2417C2214yes—
132#2415C2214yes—
133#2415C2214yes—
134#2415C2214yes—
135#2414C2212yes—
136#2414C2212yes—
137#2409C2214yes—
138#2396C2214yes—
139#2388C2214yes—
140#2379C2214yes—
141#2369C2212yes—
142#2369C2212yes—
143#2369C2212yes—
144#2367C2214yes—
145#2366C2212yes—
146#2365C2212yes—
147#2365C2212yes—
148#2362C2214yes—
149#2360C2214yes—
150#2355C2214yes—
151#2354C2212yes—
152#2354C2211yescharacteristic
153#2354C2214yes—
154#2354C2212yes—
155#2354C2212yes—
156#2354C2211yescharacteristic
157#2354C2212yes—
158Q8×C4⋊C4C2211yescharacteristic
159Q8×C4⋊C4C2211yescharacteristic
160Q8×C4⋊C4C2214yes—
161D4×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163#2346C2212yes—
164#2346C2214yes—
165#2345C2214yes—
166#2341C2212yes—
167Q8×C22⋊C4C2214yes—
168#2331C2214yes—
169#2324C2214yes—
170#2324C2214yes—
171#2324C2214yes—
172#2317C2212yes—
173#2316C2212yes—
174#2314C2214yes—
175#2311C2214yes—
176#2311C2212yes—
177C4×C4⋊Q8C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×#127C2212yes—
183C4×#125C2212yes—
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188#2293C2214yes—
189#2293C2214yes—
190#2293C2212yes—
191#2285C2212yes—
192#2285C2211yescharacteristic
193#2285C2211yescharacteristic
194#2274C2212yes—
195C42×Q8C2212yes—
196C4×#117C2212yes—
197C4×#117C2211yescharacteristic
198C4×#117C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×Q8C2312yes—
202#556—416no—
203#552—416no—
204#536—48no—
205#536—48no—
206#532—28no—
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×#127C2311yescharacteristic
218C2×#127C2312yes—
219C2×#126C2318yes—
220C2×#126C2318yes—
221C2×#126C2318yes—
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#125C2318yes—
225C2×#124C2312yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2318yes—
230C2×#123C2318yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C4×#41—28no—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2318yes—
251C2×C4×Q8C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2311yescharacteristic
273C2×#117C2312yes—
274C2×#117C2318yes—
275C22×C4⋊C4C2312yes—
276C22×C4⋊C4C2312yes—
277C22×C4⋊C4C2314yes—
278C22×C42C2312yes—
279C22×C42C2311yescharacteristic
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#399C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2314yes—
290#399C2318yes—
291#399C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2314yes—
309#396C2314yes—
310#396C2318yes—
311#395C2314yes—
312#395C2318yes—
313#395C2314yes—
314#394C2314yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2314yes—
319#394C2318yes—
320#394C2318yes—
321#393C2314yes—
322#393C2318yes—
323#393C2318yes—
324#393C2314yes—
325#392C2314yes—
326#392C2314yes—
327#392C2314yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2318yes—
339#391C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#390C2314yes—
344#390C2314yes—
345#390C2318yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2318yes—
350#390C2312yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2312yes—
356#390C2314yes—
357#390C2314yes—
358#390C2312yes—
359#390C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2314yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2318yes—
388#389C2314yes—
389#389C2314yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2312yes—
444#384C2314yes—
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2314yes—
449#384C2314yes—
450#384C2311yescharacteristic
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2314yes—
457#382C2312yes—
458#382C2312yes—
459#382C2314yes—
460#382C2318yes—
461#382C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2318yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2312yes—
477#380C2312yes—
478#380C2318yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2318yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2312yes—
521#376C2314yes—
522#376C2312yes—
523C43C2312yes—
524C43C2312yes—
525C43C2314yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—28no—
529C2×#41—44no—
530C2×#41—44no—
531C2×#41—42no—
532C22×Q8—28no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8C2414yes—
536C22×Q8C2414yes—
537C22×Q8C2411yescharacteristic
538C22×Q8C2414yes—
539C22×Q8C2412yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2414yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C23×C4C2414yes—
556C23×C4C2418yes—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—24no—
564C4⋊Q8—48no—
565C4⋊Q8—48no—
566#127—24no—
567#127—44no—
568#126—416no—
569#126—416no—
570#126—416no—
571#125—28no—
572#125—44no—
573#125—416no—
574#124—28no—
575#124—28no—
576#124—48no—
577#124—48no—
578#124—416no—
579#123—416no—
580#123—416no—
581#123—416no—
582C22⋊Q8—216no—
583C22⋊Q8—216no—
584C22⋊Q8—48no—
585C22⋊Q8—48no—
586C22⋊Q8—48no—
587C22⋊Q8—48no—
588#121—28no—
589#121—28no—
590#121—28no—
591#121—44no—
592C4×Q8—28no—
593C4×Q8—24no—
594C4×Q8—24no—
595C4×Q8—48no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×Q8—416no—
599C4×Q8—48no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—28no—
605C4×D4—28no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—48no—
610#117—24no—
611#117—24no—
612#117—24no—
613#117—28no—
614#117—28no—
615#117—24no—
616#117—28no—
617#117—44no—
618#117—48no—
619#117—44no—
620#117—416no—
621#117—42no—
622#117—48no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C42—28no—
713C2×C42#4118yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2412yes—
736C2×C42C2418yes—
737C2×C42C2414yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#95C2412yes—
743#95C2414yes—
744#95C2412yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2412yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778C24C2512yes—
779C24C2514yes—
780C24C2511yescharacteristic
781#41—416no—
782#41—816no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—24no—
786C2×Q8—28no—
787C2×Q8—28no—
788C2×Q8—28no—
789C2×Q8—28no—
790C2×Q8—28no—
791C2×Q8—22no—
792C2×Q8—44no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—816no—
798C2×Q82−1+414yes—
799C2×D4—24no—
800C2×D4—28no—
801C2×D4—22no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—28no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—42no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—44no—
822C2×D4—44no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—28no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—42no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4C2×#4114yes—
848C22×C4C2×#4114yes—
849C22×C4C2×#4114yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2518yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—216no—
891C4⋊C4—216no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—22no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—28no—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—48no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4H(5,𝔽2)14yes—
925C4⋊C4H(5,𝔽2)14yes—
926C4⋊C42−1+414yes—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—216no—
937C22⋊C4—216no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—42no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—28no—
964C42—24no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—28no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—24no—
975C42—28no—
976C42—24no—
977C42—24no—
978C42—42no—
979C42—48no—
980C42—48no—
981C42—44no—
982C42—48no—
983C42C2×#4114yes—
984C42C2×#4114yes—
985C42C2×#4114yes—
986C42C2×#4114yes—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—22no—
994C23—24no—
995C23—22no—
996C23—22no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—22no—
1007C23C22×#4112yes—
1008C23C2611yescharacteristic
1009Q8—28no—
1010Q8—416no—
1011Q8—416no—
1012Q8—88no—
1013Q8—84no—
1014D4—48no—
1015D4—48no—
1016D4—44no—
1017D4—48no—
1018D4—88no—
1019D4—84no—
1020D4—88no—
1021D4—88no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—21no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—28no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—48no—
1081C2×C4—416no—
1082C2×C4—88no—
1083C2×C4—816no—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)14yes—
1091C2×C4C2×H(5,𝔽2)14yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4C2×2−1+414yes—
1095C2×C4C2×2−1+414yes—
1096C2×C4C2×2−1+412yes—
1097C2×C4C2×2−1+412yes—
1098C2×C4#58512yes—
1099C2×C4#58512yes—
1100C22—22no—
1101C22—22no—
1102C22—22no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—42no—
1108C22—44no—
1109C22—44no—
1110C22—42no—
1111C22—42no—
1112C22—44no—
1113C22—42no—
1114C22—44no—
1115C22—42no—
1116C22—44no—
1117C22—44no—
1118C22—42no—
1119C22—42no—
1120C22—44no—
1121C22C23×#4111yescharacteristic
1122C22C22×H(5,𝔽2)11yescharacteristic
1123C22C22×H(5,𝔽2)11yescharacteristic
1124C22C22×2−1+411yescharacteristic
1125C22C22×2−1+411yescharacteristic
1126C22C2×#58511yescharacteristic
1127C22C2×#58511yescharacteristic
1128C4—24no—
1129C4—24no—
1130C4—22no—
1131C4—24no—
1132C4—22no—
1133C4—22no—
1134C4—24no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—44no—
1147C4—48no—
1148C4#349514yes—
1149C4#350714yes—
1150C4#350814yes—
1151C2—42no—
1152C2—82no—
1153C2—84no—
1154C2C2×#350711yescharacteristic
1155C2C2×#350811yescharacteristic
1156C2C2×#349511yescharacteristic
1157C2#6301311yescharacteristic
1158C2#6302211yescharacteristic
1159C2#6303711yescharacteristic
1160C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59642C2semidirect
3. #59451C2semidirect
4. #59444C2semidirect
5. #51620C2semidirect
6. #45393C2semidirect
7. #45325C2semidirect
8. #45237C2semidirect
9. #44905C2semidirect
10. #39606C2semidirect
11. #39514C2semidirect
12. #39481C2semidirect
13. #39201C2semidirect
14. #37335C2semidirect
15. #36563C2semidirect
16. #36473C2semidirect
17. #36300C2semidirect
18. #36272C2semidirect
19. #35598C2semidirect
20. #35317C2semidirect
21. #35279C2semidirect
22. #34978C2semidirect
24. #34368C2semidirect
25. #34216C2semidirect
26. #34129C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#596422
#594512
#594442
#516202
#453932
#453252
#452372
#449052
#396062
#395142
#394812
#392012
#373352
#365632
#364732
#363002
#362722
#355982
#353172
#352792
#349782
#349772
#343682
#342162
#341292