Finite Group Databasebeta

← #7699914

Subgroups — #7699914

Order 512.

5543 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C211yesmaximal, characteristic, complemented
2#59765C214yesmaximal, complemented
3#59761C218yesmaximal, complemented
4#59678C212yesmaximal, complemented
5#59567C214yesmaximal, complemented
6#59220C212yesmaximal, complemented
7#59215C214yesmaximal, complemented
8#59033C212yesmaximal, complemented
9#36598C211yesmaximal, characteristic, complemented
10#36586C212yesmaximal, complemented
11#36526C214yesmaximal, complemented
12#36492C212yesmaximal, complemented
13#36415C212yesmaximal, complemented
14#36314C212yesmaximal, complemented
15#36301C212yesmaximal, complemented
16#36254C214yesmaximal, complemented
17#36229C214yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19#36175C212yesmaximal, complemented
20#36127C211yesmaximal, characteristic, complemented
21C4×#554C211yesmaximal, characteristic, complemented
22C4×#555C211yesmaximal, characteristic, complemented
23C4×#550C211yesmaximal, characteristic, complemented
24C4×#547C212yesmaximal, complemented
25#34141C212yesmaximal, complemented
26#34127C212yesmaximal, complemented
27C2×#556C2212yes—
28C2×#555C2211yescharacteristic
29C2×#554C2211yescharacteristic
30C2×#550C2211yescharacteristic
31C2×#547C2212yes—
32C2×#532C2212yes—
33C2×C4×#41C2212yes—
34C2×C4×#41C2214yes—
35#2868C2211yescharacteristic
36#2864C2214yes—
37#2862C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2852C2218yes—
41#2851C2214yes—
42#2850C2214yes—
43#2804C2214yes—
44#2796C2218yes—
45#2782C2218yes—
46#2746C2218yes—
47#2688C2218yes—
48#2603C2218yes—
49#2598C2218yes—
50#2597C2218yes—
51#2596C2218yes—
52#2582C2212yes—
53#2580C2214yes—
54#2580C2214yes—
55#2578C2218yes—
56#2575C2218yes—
57#2571C2212yes—
58#2571C2212yes—
59#2570C2214yes—
60#2568C2212yes—
61#2568C2212yes—
62#2563C2212yes—
63#2563C2212yes—
64#2562C2214yes—
65#2557C2218yes—
66#2557C2218yes—
67#2547C2212yes—
68#2547C2212yes—
69#2547C2212yes—
70#2544C2214yes—
71#2537C2212yes—
72#2537C2212yes—
73#2535C2214yes—
74#2535C2214yes—
75#2535C2214yes—
76#2533C2218yes—
77#2530C2218yes—
78#2527C2218yes—
79#2527C2218yes—
80#2523C2218yes—
81#2514C2214yes—
82#2511C2214yes—
83#2511C2214yes—
84#2510C2218yes—
85#2505C2218yes—
86#2499C2214yes—
87#2499C2214yes—
88#2496C2214yes—
89#2496C2214yes—
90#2495C2214yes—
91#2495C2214yes—
92#2494C2214yes—
93#2494C2214yes—
94#2487C2214yes—
95#2487C2214yes—
96#2487C2214yes—
97#2485C2214yes—
98#2479C2218yes—
99#2477C2218yes—
100#2477C2218yes—
101#2467C2218yes—
102#2463C2218yes—
103#2448C2214yes—
104#2447C2214yes—
105#2446C2214yes—
106#2444C2218yes—
107#2432C2214yes—
108#2431C2214yes—
109#2422C2214yes—
110#2422C2214yes—
111#2421C2214yes—
112#2420C2214yes—
113#2407C2214yes—
114#2372C2214yes—
115#2370C2212yes—
116#2369C2211yescharacteristic
117#2369C2211yescharacteristic
118#2368C2214yes—
119#2367C2214yes—
120#2367C2214yes—
121#2366C2211yescharacteristic
122#2366C2212yes—
123#2366C2212yes—
124#2365C2212yes—
125#2365C2212yes—
126#2365C2212yes—
127#2364C2218yes—
128#2363C2212yes—
129#2363C2214yes—
130#2363C2212yes—
131#2363C2212yes—
132#2362C2214yes—
133#2361C2214yes—
134#2361C2214yes—
135#2361C2214yes—
136#2360C2212yes—
137#2359C2218yes—
138#2356C2214yes—
139#2355C2211yescharacteristic
140#2355C2212yes—
141#2355C2212yes—
142#2354C2211yescharacteristic
143#2354C2211yescharacteristic
144#2354C2212yes—
145#2354C2211yescharacteristic
146#2352C2214yes—
147#2352C2214yes—
148#2352C2214yes—
149#2352C2214yes—
150Q8×C4⋊C4C2211yescharacteristic
151#2349C2212yes—
152D4×C4⋊C4C2212yes—
153D4×C4⋊C4C2212yes—
154D4×C4⋊C4C2212yes—
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2211yescharacteristic
157#2347C2214yes—
158#2346C2212yes—
159#2346C2212yes—
160#2345C2212yes—
161#2344C2214yes—
162#2343C2218yes—
163#2341C2212yes—
164#2339C2214yes—
165#2339C2214yes—
166C4×C4⋊Q8C2212yes—
167C4×C4⋊Q8C2211yescharacteristic
168C4×C4⋊Q8C2211yescharacteristic
169C4×#127C2212yes—
170C4×#127C2211yescharacteristic
171C4×#125C2212yes—
172C4×#124C2214yes—
173C4×C22⋊Q8C2214yes—
174C4×C22⋊Q8C2214yes—
175C4×C22⋊Q8C2212yes—
176C4×#123C2218yes—
177C4×#121C2214yes—
178C4×#121C2214yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182#2297C2214yes—
183#2295C2214yes—
184#2293C2214yes—
185#2290C2218yes—
186#2290C2218yes—
187#2285C2212yes—
188#2283C2214yes—
189C42×Q8C2211yescharacteristic
190C42×D4C2211yescharacteristic
191C42×D4C2212yes—
192C42×D4C2214yes—
193C42×D4C2212yes—
194C42×D4C2211yescharacteristic
195C4×#117C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2214yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C22×#41C2314yes—
201#556—48no—
202#555—28no—
203#554—28no—
204#550—28no—
205#547—216no—
206#532—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2311yescharacteristic
214C2×#126C2318yes—
215C2×#125C2312yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#124C2314yes—
219C2×#123C2318yes—
220C2×C22⋊Q8C2314yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2312yes—
228C2×#121C2314yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C4×#41—216no—
232C4×#41—416no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2314yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2318yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2311yescharacteristic
265C2×#117C2314yes—
266C2×#117C2312yes—
267C2×#117C2312yes—
268C2×#117C2312yes—
269C2×#117C2312yes—
270C2×#117C2314yes—
271C2×#117C2318yes—
272C2×#117C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2314yes—
276C22×C4⋊C4C2312yes—
277C22×C42C2314yes—
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2314yes—
281C22×C42C2318yes—
282#401C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#399C2318yes—
291#399C2318yes—
292#398C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#394C2318yes—
305#393C2318yes—
306#393C2318yes—
307#392C2318yes—
308#392C2318yes—
309#391C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2314yes—
328#390C2314yes—
329#390C2312yes—
330#390C2312yes—
331#390C2314yes—
332#390C2314yes—
333#390C2314yes—
334#390C2312yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2314yes—
345#389C2312yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2312yes—
350#389C2314yes—
351#389C2314yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2314yes—
362#388C2314yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2314yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#388C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#386C2318yes—
398#386C2318yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2318yes—
406#386C2318yes—
407#386C2314yes—
408#386C2314yes—
409#386C2318yes—
410#386C2314yes—
411#386C2314yes—
412#386C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2318yes—
421#385C2314yes—
422#385C2314yes—
423#385C2318yes—
424#385C2318yes—
425#384C2311yescharacteristic
426#384C2312yes—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#384C2312yes—
433#383C2318yes—
434#383C2318yes—
435#382C2312yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#381C2318yes—
444#381C2318yes—
445#380C2312yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2312yes—
453#380C2314yes—
454#380C2312yes—
455#380C2314yes—
456#380C2312yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2318yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C22⋊C4C2318yes—
499C4×C22⋊C4C2318yes—
500C4×C22⋊C4C2318yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2318yes—
518C4×C22⋊C4C2312yes—
519#376C2314yes—
520#376C2314yes—
521#376C2318yes—
522C2×#95C2318yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C43C2314yes—
527C2×#41—28no—
528C2×#41—216no—
529C2×#41—28no—
530C2×#41—216no—
531C2×#41—48no—
532C2×#41—44no—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2412yes—
536C22×Q8C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2418yes—
539C22×D4C2414yes—
540C22×D4C2411yescharacteristic
541C22×D4C2412yes—
542C22×D4C2412yes—
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2418yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2414yes—
556C23×C4C2412yes—
557C23×C4C2418yes—
558C23×C4C2414yes—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—44no—
564#127—28no—
565#127#4118yes—
566#126—416no—
567#125—28no—
568#124—216no—
569#124—216no—
570#124—48no—
571#123—232no—
572C22⋊Q8—28no—
573C22⋊Q8—216no—
574C22⋊Q8—216no—
575C22⋊Q8—48no—
576#121—216no—
577#121—216no—
578#121—216no—
579#121—28no—
580#121—216no—
581#121—28no—
582#121—28no—
583C4×Q8—28no—
584C4×Q8—216no—
585C4×Q8—24no—
586C4×Q8—44no—
587C4×Q8—44no—
588C4×Q8—42no—
589C4×Q8—48no—
590C4×Q8#4118yescomplemented
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—28no—
594C4×D4—28no—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—216no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—28no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—416no—
606C4×D4—44no—
607C4×D4—42no—
608C4×D4—48no—
609C4×D4—48no—
610C4×D4—44no—
611C4×D4—48no—
612C4×D4—48no—
613C4×D4—416no—
614C4×D4#4118yescomplemented
615#117—28no—
616#117—28no—
617#117—216no—
618#117—28no—
619#117—28no—
620#117—48no—
621#117—416no—
622#117—44no—
623C2×C4⋊C4—216no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2412yes—
702C2×C42—216no—
703C2×C42—28no—
704C2×C42—28no—
705C2×C42—416no—
706C2×C42—48no—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2418yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2414yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2418yes—
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2414yes—
734C2×C42C2411yescharacteristic
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#95C2414yes—
739#95C2414yes—
740#95C2412yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2412yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2412yes—
763#95C2418yes—
764#95C2414yes—
765#95C2414yes—
766#95C2412yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2412yes—
772#95C2412yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778C24C2512yes—
779C24C2512yes—
780C24C2514yes—
781#41—464no—
782#41—432no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—28no—
789C2×Q8—22no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8C2×#4114yes—
795C2×D4—216no—
796C2×D4—216no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—28no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—48no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4C2×#4118yes—
819C2×D4C2×#4118yes—
820C2×D4C2×#4114yes—
821C2×D4C2×#4118yes—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—216no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—28no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—216no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—42no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—42no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—42no—
860C22×C4C2×#4118yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2518yes—
871C22×C4C2512yes—
872C22×C4C2514yes—
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2512yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2512yes—
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C4⋊C4—28no—
885C4⋊C4—216no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—22no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—216no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—22no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4C2×#4114yes—
925C4⋊C4C2×#4114yes—
926C4⋊C4C2×#4118yes—
927C4⋊C4H(5,𝔽2)14yes—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—216no—
931C22⋊C4—216no—
932C22⋊C4—216no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—24no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—24no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—48no—
949C22⋊C4—42no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4C2×#4118yes—
959C42—24no—
960C42—24no—
961C42—28no—
962C42—24no—
963C42—24no—
964C42—28no—
965C42—24no—
966C42—24no—
967C42—28no—
968C42—24no—
969C42—28no—
970C42—24no—
971C42—216no—
972C42—28no—
973C42—22no—
974C42—22no—
975C42—24no—
976C42—28no—
977C42—22no—
978C42—44no—
979C42—44no—
980C42—48no—
981C42—42no—
982C42—41no—
983C42—44no—
984C42—44no—
985C42—42no—
986C42C2×#4118yes—
987C42C2×#4114yes—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—22no—
997C23—24no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23C22×#4114yes—
1010C23C22×#4118yes—
1011C23C2611yescharacteristic
1012Q8—28no—
1013Q8—416no—
1014Q8—84no—
1015Q8—84no—
1016D4—216no—
1017D4—28no—
1018D4—216no—
1019D4—48no—
1020D4—416no—
1021D4—432no—
1022D4—44no—
1023D4—88no—
1024D4—88no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—216no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—416no—
1080C2×C4—48no—
1081C2×C4—416no—
1082C2×C4—432no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—416no—
1086C2×C4—48no—
1087C2×C4—88no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4—816no—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4114yes—
1093C2×C4C22×#4112yes—
1094C2×C4C22×#4114yes—
1095C2×C4C22×#4114yes—
1096C2×C4C22×#4112yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C22×#4112yes—
1102C2×C4C22×#4112yes—
1103C2×C4C2×H(5,𝔽2)14yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4#58512yes—
1106C2×C4#58512yes—
1107C22—28no—
1108C22—24no—
1109C22—28no—
1110C22—24no—
1111C22—24no—
1112C22—28no—
1113C22—44no—
1114C22—42no—
1115C22—42no—
1116C22—44no—
1117C22—42no—
1118C22—44no—
1119C22—42no—
1120C22—44no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22C23×#4111yescharacteristic
1129C22C23×#4111yescharacteristic
1130C22C23×#4111yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C2×#58511yescharacteristic
1133C22C2×#58511yescharacteristic
1134C222−1+611yescharacteristic
1135C4—24no—
1136C4—24no—
1137C4—22no—
1138C4—22no—
1139C4—22no—
1140C4—24no—
1141C4—24no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4—44no—
1146C4—41no—
1147C4—42no—
1148C4—44no—
1149C4—44no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—44no—
1154C4—48no—
1155C4#347514yes—
1156C4#348014yes—
1157C4#348114yes—
1158C2—48no—
1159C2—44no—
1160C2—82no—
1161C2C2×#347511yescharacteristic
1162C2C2×#348011yescharacteristic
1163C2C2×#348111yescharacteristic
1164C2#6298511yescharacteristic
1165C2#6299111yescharacteristic
1166C2#6299511yescharacteristic
1167C2#6302211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59864C2semidirect
2. #59765C2semidirect
3. #59761C2semidirect
4. #59678C2semidirect
5. #59567C2semidirect
6. #59220C2semidirect
7. #59215C2semidirect
8. #59033C2semidirect
9. #36598C2semidirect
10. #36586C2semidirect
11. #36526C2semidirect
12. #36492C2semidirect
13. #36415C2semidirect
14. #36314C2semidirect
15. #36301C2semidirect
16. #36254C2semidirect
17. #36229C2semidirect
18. #36188C2semidirect
19. #36175C2semidirect
20. #36127C2semidirect
21. C4×#554C2semidirect
22. C4×#555C2semidirect
23. C4×#550C2semidirect
24. C4×#547C2semidirect
25. #34141C2semidirect
26. #34127C2semidirect
590. C4×Q8#41semidirect
614. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598642
#597652
#597612
#596782
#595672
#592202
#592152
#590332
#365982
#365862
#365262
#364922
#364152
#363142
#363012
#362542
#362292
#361882
#361752
#361272
C4×#5542
C4×#5552
C4×#5502
C4×#5472
#341412
#341272