Finite Group Databasebeta

← #7711634

Subgroups — #7711634

Order 512.

5022 conjugacy classes of subgroups.

The subgroup lattice has 1159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59871C211yesmaximal, characteristic, complemented
3#59863C211yesmaximal, characteristic, complemented
4#59823C211yesmaximal, characteristic, complemented
5#59312C212yesmaximal, complemented
6#59136C212yesmaximal, complemented
7#46347C214yesmaximal, complemented
8#46098C214yesmaximal, complemented
9#40167C214yesmaximal, complemented
10#40166C214yesmaximal, complemented
11#39200C212yesmaximal, complemented
12#39180C212yesmaximal, complemented
13#38985C212yesmaximal, complemented
14#38965C212yesmaximal, complemented
15#38067C214yesmaximal, complemented
16#38043C214yesmaximal, complemented
17#37637C212yesmaximal, complemented
18#37265C214yesmaximal, complemented
19#36635C211yesmaximal, characteristic, complemented
20#36631C211yesmaximal, characteristic
21#36193C212yesmaximal, complemented
22#36186C212yesmaximal, complemented
23#36117C212yesmaximal
24#36116C212yesmaximal, complemented
25#35247C214yesmaximal, complemented
26#34484C212yesmaximal, complemented
27C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#552C2214yes—
30C22×C4⋊Q8C2211yescharacteristic
31C2×#529C2214yes—
32C2×#529C2212yes—
33C22×C4×Q8C2212yes—
34#2864C2212yes—
35#2863C2212yes—
36#2863C2212yes—
37#2862C2211yescharacteristic
38#2861C2212yes—
39#2860C2212yes—
40#2860C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2855C2214yes—
49#2855C2212yes—
50#2855C2212yes—
51#2854C2214yes—
52#2854C2212yes—
53#2854C2212yes—
54#2851C2212yes—
55#2850C2212yes—
56#2831C2218yes—
57#2808C2214yes—
58#2806C2214yes—
59#2806C2214yes—
60#2777C2218yes—
61#2773C2218yes—
62#2768C2218yes—
63#2755C2218yes—
64#2754C2218yes—
65#2738C2218yes—
66#2732C2214yes—
67#2729C2218yes—
68#2726C2218yes—
69#2725C2218yes—
70#2722C2218yes—
71#2721C2218yes—
72#2715C2218yes—
73#2704C2218yes—
74#2700C2218yes—
75#2647C2214yes—
76#2644C2214yes—
77#2637C2218yes—
78#2637C2218yes—
79#2629C2214yes—
80#2625C2214yes—
81#2592C2214yes—
82#2592C2214yes—
83#2584C2214yes—
84#2584C2214yes—
85#2584C2214yes—
86#2582C2214yes—
87#2582C2214yes—
88#2582C2214yes—
89#2567C2212yes—
90#2567C2212yes—
91#2563C2212yes—
92#2552C2212yes—
93#2552C2212yes—
94#2552C2212yes—
95#2552C2214yes—
96#2552C2212yes—
97#2552C2212yes—
98#2550C2214yes—
99#2548C2212yes—
100#2547C2212yes—
101#2542C2212yes—
102#2538C2212yes—
103#2538C2214yes—
104#2538C2214yes—
105#2520C2218yes—
106#2519C2218yes—
107#2513C2214yes—
108#2512C2214yes—
109#2512C2214yes—
110#2512C2214yes—
111#2511C2214yes—
112#2508C2214yes—
113#2507C2214yes—
114#2507C2214yes—
115#2507C2214yes—
116#2506C2214yes—
117#2501C2214yes—
118#2498C2218yes—
119#2496C2214yes—
120#2492C2214yes—
121#2489C2214yes—
122#2486C2214yes—
123#2486C2218yes—
124#2485C2214yes—
125#2479C2218yes—
126#2478C2218yes—
127#2454C2214yes—
128#2454C2214yes—
129#2453C2214yes—
130#2452C2214yes—
131#2448C2214yes—
132#2447C2214yes—
133#2442C2214yes—
134#2441C2214yes—
135#2440C2214yes—
136#2438C2218yes—
137#2425C2218yes—
138#2423C2214yes—
139#2419C2218yes—
140#2417C2214yes—
141#2417C2214yes—
142#2413C2218yes—
143#2413C2218yes—
144#2409C2218yes—
145#2378C2218yes—
146#2370C2214yes—
147#2369C2212yes—
148#2369C2212yes—
149#2366C2212yes—
150#2365C2212yes—
151#2365C2212yes—
152#2362C2214yes—
153#2361C2214yes—
154#2355C2212yes—
155#2354C2214yes—
156#2354C2212yes—
157#2354C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160D4×C4⋊C4C2214yes—
161D4×C4⋊C4C2212yes—
162#2344C2214yes—
163#2344C2214yes—
164#2330C2214yes—
165#2323C2214yes—
166#2323C2218yes—
167#2323C2218yes—
168#2319C2214yes—
169#2316C2214yes—
170C4×C4⋊Q8C2211yescharacteristic
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×C4⋊Q8C2211yescharacteristic
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192C2×#391C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195C2×#389C2212yes—
196C2×#389C2212yes—
197#2285C2214yes—
198C2×#384C2211yescharacteristic
199#2283C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2312yes—
204#554—216no—
205#552—416no—
206C2×C4⋊Q8—28no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#127C2311yescharacteristic
216#529—48no—
217#529—416no—
218C2×#126C2314yes—
219C2×#126C2318yes—
220C2×#126C2318yes—
221C2×#125C2314yes—
222C2×#125C2312yes—
223C2×#125C2314yes—
224C2×#125C2314yes—
225C2×#125C2312yes—
226C2×#125C2318yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×#123C2318yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2318yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8—48no—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2318yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C2×#117C2318yes—
265C2×#117C2318yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C42C2311yescharacteristic
274C22×C42C2311yescharacteristic
275C22×C42C2314yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2318yes—
286#399C2318yes—
287#399C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#395C2318yes—
316#395C2318yes—
317#395C2318yes—
318#394C2318yes—
319#393C2318yes—
320#393C2318yes—
321#391C2312yes—
322#391C2312yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#391C2318yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2318yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2312yes—
346#390C2314yes—
347#390C2312yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2312yes—
355#390C2312yes—
356#390C2312yes—
357#390C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2312yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2318yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#389C2312yes—
410#389C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2318yes—
428#388C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#387C2314yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2314yes—
439#387C2314yes—
440#387C2318yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#386C2314yes—
448#386C2314yes—
449#386C2318yes—
450#386C2318yes—
451#385C2314yes—
452#385C2314yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#384C2311yescharacteristic
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#384C2311yescharacteristic
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#384C2314yes—
467#384C2314yes—
468#384C2314yes—
469#384C2314yes—
470#384C2314yes—
471#383C2314yes—
472#382C2312yes—
473#382C2314yes—
474#382C2312yes—
475#382C2312yes—
476#382C2312yes—
477#382C2318yes—
478#381C2318yes—
479#381C2314yes—
480#381C2318yes—
481#380C2314yes—
482#380C2314yes—
483#380C2318yes—
484#380C2318yes—
485#380C2314yes—
486#380C2318yes—
487#380C2312yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492#380C2312yes—
493#380C2314yes—
494#380C2318yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2318yes—
517C4×C4⋊C4C2314yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C4⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2314yes—
524C4×C22⋊C4C2314yes—
525#376C2314yes—
526C2×#95C2314yes—
527C2×#95C2314yes—
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2311yescharacteristic
533C43C2311yescharacteristic
534C43C2311yescharacteristic
535C43C2311yescharacteristic
536C22×Q8—28no—
537C22×Q8—44no—
538C22×Q8—44no—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2414yes—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2412yes—
549C23×C4C2414yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2418yes—
560C4⋊Q8—28no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—24no—
564C4⋊Q8—24no—
565C4⋊Q8—24no—
566C4⋊Q8—24no—
567C4⋊Q8#4118yes—
568#127—24no—
569#126—416no—
570#126—48no—
571#126—416no—
572#125—216no—
573#125—44no—
574#125—48no—
575#125—44no—
576#125—48no—
577#125—416no—
578#124—44no—
579#124—44no—
580#124—48no—
581#123—48no—
582#123—416no—
583#123—416no—
584C22⋊Q8—232no—
585C22⋊Q8—28no—
586C22⋊Q8—28no—
587C22⋊Q8—216no—
588C22⋊Q8—44no—
589C22⋊Q8—416no—
590C22⋊Q8—48no—
591#121—28no—
592#121—28no—
593#121—44no—
594C4×Q8—28no—
595C4×Q8—28no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×Q8—44no—
599C4×Q8—48no—
600C4×Q8—44no—
601C4×Q8—44no—
602C4×Q8—44no—
603C4×Q8—48no—
604C4×Q8—48no—
605C4×D4—216no—
606C4×D4—216no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—416no—
612#117—48no—
613#117—416no—
614#117—416no—
615#117—48no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4—28no—
618C2×C4⋊C4—28no—
619C2×C4⋊C4—28no—
620C2×C4⋊C4—216no—
621C2×C4⋊C4—44no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C42—24no—
702C2×C42—216no—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42—42no—
709C2×C42C2411yescharacteristic
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2414yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2418yes—
740C2×C42C2418yes—
741C2×C42C2418yes—
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2418yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24C2514yes—
786C24C2511yescharacteristic
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—28no—
797C2×Q8—42no—
798C2×Q8—44no—
799C2×Q8—42no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—432no—
805C2×Q8C2×#4118yes—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—24no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—42no—
817C2×D4—42no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—28no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—28no—
842C22×C4—216no—
843C22×C4—41no—
844C22×C4—41no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4H(5,𝔽2)14yes—
849C22×C4H(5,𝔽2)14yes—
850C22×C42−1+414yes—
851C22×C4C2511yescharacteristic
852C22×C4C2514yes—
853C22×C4C2511yescharacteristic
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2514yes—
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C4⋊C4—24no—
877C4⋊C4—216no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—42no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—42no—
921C4⋊C4—48no—
922C4⋊C4—42no—
923C4⋊C4—48no—
924C4⋊C4—44no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—44no—
932C4⋊C4C2×#4118yes—
933C4⋊C4C2×#4118yes—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—216no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—28no—
958C42—22no—
959C42—28no—
960C42—22no—
961C42—28no—
962C42—22no—
963C42—22no—
964C42—22no—
965C42—22no—
966C42—28no—
967C42—28no—
968C42—22no—
969C42—22no—
970C42—28no—
971C42—22no—
972C42—22no—
973C42—22no—
974C42—22no—
975C42—22no—
976C42—22no—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—22no—
981C42—28no—
982C42—22no—
983C42—22no—
984C42—41no—
985C42—41no—
986C42—48no—
987C42—48no—
988C42—48no—
989C42C2×#4114yes—
990C422−1+414yes—
991C422−1+414yes—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23C2×H(5,𝔽2)12yes—
1004C23C2×H(5,𝔽2)12yes—
1005C23C2×2−1+412yes—
1006C23C2611yescharacteristic
1007Q8—48no—
1008Q8—416no—
1009Q8—48no—
1010Q8—48no—
1011Q8—48no—
1012Q8—84no—
1013D4—416no—
1014D4—48no—
1015D4—48no—
1016D4—84no—
1017C2×C4—28no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—24no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—416no—
1082C2×C4—44no—
1083C2×C4—416no—
1084C2×C4—416no—
1085C2×C4—816no—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4118yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×H(5,𝔽2)12yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4C2×2−1+412yes—
1095C2×C4C2×2−1+412yes—
1096C2×C4C2×2−1+412yes—
1097C2×C4C2×2−1+412yes—
1098C2×C4C2×2−1+412yes—
1099C2×C4C2×2−1+412yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4#58512yes—
1103C22—22no—
1104C22—22no—
1105C22—22no—
1106C22—22no—
1107C22—22no—
1108C22—22no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—44no—
1113C22—44no—
1114C22—44no—
1115C22—44no—
1116C22#354814yes—
1117C22C23×#4111yescharacteristic
1118C22C22×H(5,𝔽2)11yescharacteristic
1119C22C22×H(5,𝔽2)11yescharacteristic
1120C22C22×2−1+411yescharacteristic
1121C22C22×2−1+411yescharacteristic
1122C22C22×2−1+411yescharacteristic
1123C22C2×#58511yescharacteristic
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—28no—
1128C4—22no—
1129C4—22no—
1130C4—22no—
1131C4—22no—
1132C4—44no—
1133C4—41no—
1134C4—41no—
1135C4—44no—
1136C4—44no—
1137C4—44no—
1138C4—44no—
1139C4—44no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—41no—
1144C4—44no—
1145C4—41no—
1146C4#352214yes—
1147C4#352314yes—
1148C4#354414yes—
1149C2—24no—
1150C2—84no—
1151C2C2×#354411yescharacteristic
1152C2C2×#354811yescharacteristic
1153C2#6277311yescharacteristic
1154C2C2×#352211yescharacteristic
1155C2C2×#352311yescharacteristic
1156C2#6283511yescharacteristic
1157C2#6283711yescharacteristic
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. #59871C2semidirect
2. #59871C2semidirect
3. #59863C2semidirect
4. #59823C2semidirect
5. #59312C2semidirect
6. #59136C2semidirect
7. #46347C2semidirect
8. #46098C2semidirect
9. #40167C2semidirect
10. #40166C2semidirect
11. #39200C2semidirect
12. #39180C2semidirect
13. #38985C2semidirect
14. #38965C2semidirect
15. #38067C2semidirect
16. #38043C2semidirect
17. #37637C2semidirect
18. #37265C2semidirect
19. #36635C2semidirect
21. #36193C2semidirect
22. #36186C2semidirect
24. #36116C2semidirect
25. #35247C2semidirect
26. #34484C2semidirect
27. C2×C4×C4⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#598632
#598232
#593122
#591362
#463472
#460982
#401672
#401662
#392002
#391802
#389852
#389652
#380672
#380432
#376372
#372652
#366352
#366312
#361932
#361862
#361172
#361162
#352472
#344842
C2×C4×C4⋊Q82