Finite Group Databasebeta

← #7688155

Subgroups — #7688155

Order 512.

5381 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59678C212yesmaximal, complemented
3#59315C214yesmaximal, complemented
4#59304C212yesmaximal, complemented
5#59249C212yesmaximal, complemented
6#59086C214yesmaximal, complemented
7#44920C214yesmaximal, complemented
8#44019C218yesmaximal, complemented
9#39902C214yesmaximal, complemented
10#39479C212yesmaximal, complemented
11#39029C214yesmaximal, complemented
12#38909C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36492C212yesmaximal, complemented
15#36468C212yesmaximal, complemented
16#36192C212yesmaximal, complemented
17#36187C211yesmaximal, characteristic, complemented
18#36180C211yesmaximal, characteristic, complemented
19#36117C212yesmaximal, complemented
20#35989C214yesmaximal, complemented
21#34932C212yesmaximal, complemented
22#34932C211yesmaximal, characteristic, complemented
23#34243C212yesmaximal, complemented
24#34188C212yesmaximal, complemented
25C4×#554C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27C2×#555C2212yes—
28C2×#554C2211yescharacteristic
29C2×#554C2212yes—
30C2×#553C2214yes—
31C2×#550C2211yescharacteristic
32C2×#529C2212yes—
33C2×#529C2214yes—
34C2×C4×#41C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2857C2212yes—
38#2856C2212yes—
39#2854C2214yes—
40#2851C2214yes—
41#2808C2214yes—
42#2796C2218yes—
43#2767C2218yes—
44#2754C2218yes—
45#2742C2218yes—
46#2723C2218yes—
47#2718C2218yes—
48#2717C2218yes—
49#2702C2218yes—
50#2691C2218yes—
51#2671C2218yes—
52#2650C2218yes—
53#2624C2214yes—
54#2602C2218yes—
55#2597C2218yes—
56#2592C2214yes—
57#2582C2212yes—
58#2567C2212yes—
59#2567C2212yes—
60#2563C2212yes—
61#2563C2212yes—
62#2562C2214yes—
63#2562C2214yes—
64#2559C2218yes—
65#2553C2218yes—
66#2553C2214yes—
67#2552C2212yes—
68#2552C2212yes—
69#2552C2212yes—
70#2552C2211yescharacteristic
71#2550C2214yes—
72#2548C2212yes—
73#2547C2211yescharacteristic
74#2547C2212yes—
75#2544C2214yes—
76#2542C2211yescharacteristic
77#2537C2212yes—
78#2537C2212yes—
79#2537C2211yescharacteristic
80#2535C2214yes—
81#2522C2218yes—
82#2522C2218yes—
83#2521C2218yes—
84#2513C2214yes—
85#2512C2214yes—
86#2511C2214yes—
87#2509C2214yes—
88#2507C2214yes—
89#2502C2214yes—
90#2501C2214yes—
91#2500C2214yes—
92#2496C2214yes—
93#2496C2214yes—
94#2496C2214yes—
95#2496C2212yes—
96#2491C2214yes—
97#2491C2214yes—
98#2489C2214yes—
99#2489C2212yes—
100#2487C2214yes—
101#2485C2214yes—
102#2485C2214yes—
103#2479C2218yes—
104#2478C2218yes—
105#2477C2218yes—
106#2477C2218yes—
107#2463C2218yes—
108#2461C2218yes—
109#2454C2214yes—
110#2454C2214yes—
111#2451C2214yes—
112#2448C2214yes—
113#2443C2218yes—
114#2441C2214yes—
115#2441C2214yes—
116#2440C2214yes—
117#2440C2214yes—
118#2428C2214yes—
119#2427C2214yes—
120#2427C2212yes—
121#2427C2218yes—
122#2425C2218yes—
123#2422C2214yes—
124#2422C2212yes—
125#2421C2214yes—
126#2416C2214yes—
127#2407C2214yes—
128#2395C2214yes—
129#2395C2218yes—
130#2370C2214yes—
131#2370C2214yes—
132#2370C2212yes—
133#2369C2211yescharacteristic
134#2369C2212yes—
135#2368C2214yes—
136#2367C2214yes—
137#2366C2211yescharacteristic
138#2366C2212yes—
139#2363C2212yes—
140#2363C2214yes—
141#2361C2214yes—
142#2360C2212yes—
143#2359C2218yes—
144#2355C2214yes—
145#2355C2212yes—
146#2355C2211yescharacteristic
147#2355C2212yes—
148#2354C2214yes—
149#2354C2212yes—
150#2354C2212yes—
151#2354C2212yes—
152#2354C2212yes—
153#2354C2211yescharacteristic
154#2354C2212yes—
155#2352C2214yes—
156#2352C2214yes—
157#2352C2218yes—
158#2352C2214yes—
159Q8×C4⋊C4C2212yes—
160Q8×C4⋊C4C2211yescharacteristic
161#2349C2212yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2211yescharacteristic
165D4×C4⋊C4C2214yes—
166#2345C2212yes—
167#2341C2212yes—
168#2334C2218yes—
169#2314C2214yes—
170#2314C2218yes—
171#2311C2214yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×C4⋊Q8C2211yescharacteristic
175C4×#127C2212yes—
176C4×#127C2211yescharacteristic
177C4×#125C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×C22⋊Q8C2214yes—
181C4×C22⋊Q8C2214yes—
182C4×#121C2212yes—
183C4×#121C2214yes—
184C4×#121C2212yes—
185C4×#121C2214yes—
186C4×#121C2214yes—
187#2285C2212yes—
188#2285C2212yes—
189#2285C2214yes—
190#2285C2214yes—
191C2×#384C2212yes—
192#2274C2214yes—
193C42×Q8C2211yescharacteristic
194C42×D4C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200#555—48no—
201#554—28no—
202#554—48no—
203#553—416no—
204#550—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212#529—216no—
213#529—416no—
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#126C2318yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2318yes—
224C2×#123C2314yes—
225C2×#123C2318yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2318yes—
233C2×#121C2312yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2318yes—
242C4×#41—216no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2312yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2312yes—
255C2×C4×D4C2314yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2318yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2318yes—
270C2×C4×D4C2311yescharacteristic
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2318yes—
277C2×#117C2314yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2314yes—
283C22×C42C2314yes—
284C22×C42C2312yes—
285C22×C42C2312yes—
286C22×C42C2314yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2314yes—
291#400C2318yes—
292#399C2318yes—
293#399C2314yes—
294#399C2318yes—
295#399C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#398C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2318yes—
310#396C2318yes—
311#396C2318yes—
312#395C2318yes—
313#395C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2314yes—
321#394C2318yes—
322#394C2318yes—
323#393C2318yes—
324#393C2318yes—
325#392C2318yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#390C2312yes—
337#390C2314yes—
338#390C2312yes—
339#390C2314yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2314yes—
349#390C2312yes—
350#390C2314yes—
351#390C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2314yes—
369#389C2314yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2312yes—
375#389C2314yes—
376#389C2312yes—
377#389C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2314yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2318yes—
420#386C2314yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#384C2311yescharacteristic
432#384C2312yes—
433#384C2311yescharacteristic
434#384C2312yes—
435#384C2311yescharacteristic
436#384C2314yes—
437#384C2314yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2314yes—
443#384C2312yes—
444#384C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#382C2318yes—
451#380C2314yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2318yes—
471#380C2314yes—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2312yes—
524C2×#95C2314yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—28no—
528C2×#41—28no—
529C2×#41—44no—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2418yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2418yes—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560#127—28no—
561#127—24no—
562#126—216no—
563#126—416no—
564#126—416no—
565#125—28no—
566#125—216no—
567#125—28no—
568#125—48no—
569#124—28no—
570#124—48no—
571#124—416no—
572#123—216no—
573#123—416no—
574#123—416no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—216no—
578C22⋊Q8—28no—
579C22⋊Q8—416no—
580C22⋊Q8—48no—
581#121—28no—
582#121—28no—
583#121—216no—
584#121—28no—
585#121—216no—
586#121—416no—
587#121—48no—
588#121—48no—
589#121—48no—
590C4×Q8—28no—
591C4×Q8—28no—
592C4×Q8—24no—
593C4×Q8—44no—
594C4×Q8—42no—
595C4×Q8—48no—
596C4×Q8#4118yes—
597C4×D4—28no—
598C4×D4—24no—
599C4×D4—216no—
600C4×D4—28no—
601C4×D4—216no—
602C4×D4—28no—
603C4×D4—28no—
604C4×D4—24no—
605C4×D4—216no—
606C4×D4—28no—
607C4×D4—28no—
608C4×D4—24no—
609C4×D4—24no—
610C4×D4—24no—
611C4×D4—28no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—44no—
615C4×D4—416no—
616C4×D4—416no—
617C4×D4#4118yes—
618#117—216no—
619#117—28no—
620#117—216no—
621#117—48no—
622#117—416no—
623#117—48no—
624#117—48no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—48no—
628C2×C4⋊C4—48no—
629C2×C4⋊C4—48no—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2412yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2418yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2412yes—
713C2×C42—216no—
714C2×C42—28no—
715C2×C42—28no—
716C2×C42—48no—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2418yes—
734C2×C42C2414yes—
735C2×C42C2418yes—
736C2×C42C2418yes—
737C2×C42C2412yes—
738C2×C42C2414yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2412yes—
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2414yes—
751#95C2412yes—
752#95C2414yes—
753#95C2412yes—
754#95C2412yes—
755#95C2414yes—
756#95C2414yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2412yes—
769#95C2412yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2414yes—
774#95C2418yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779#95C2414yes—
780#95C2418yes—
781C24C2514yes—
782C24C2512yes—
783C24C2512yes—
784#41—432no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—22no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—44no—
796C2×Q8C2×#4114yes—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C2×D4—216no—
802C2×D4—22no—
803C2×D4—28no—
804C2×D4—24no—
805C2×D4—24no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—24no—
810C2×D4—22no—
811C2×D4—22no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—42no—
817C2×D4—44no—
818C2×D4—48no—
819C2×D4—48no—
820C2×D4—42no—
821C2×D4—44no—
822C2×D4C2×#4114yes—
823C2×D4H(5,𝔽2)14yes—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—28no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—28no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4C2×#4118yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2514yes—
870C22×C4C2514yes—
871C22×C4C2518yes—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—22no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—216no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—216no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—22no—
912C4⋊C4—28no—
913C4⋊C4—42no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—44no—
925C4⋊C4—42no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4C2×#4114yes—
931C4⋊C4C2×#4118yes—
932C4⋊C4C2×#4114yes—
933C4⋊C4H(5,𝔽2)14yes—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—216no—
938C22⋊C4—28no—
939C22⋊C4—24no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—24no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—24no—
952C22⋊C4—24no—
953C22⋊C4—28no—
954C22⋊C4—48no—
955C22⋊C4—48no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4C2×#4118yes—
966C42—24no—
967C42—24no—
968C42—28no—
969C42—24no—
970C42—28no—
971C42—24no—
972C42—24no—
973C42—24no—
974C42—28no—
975C42—24no—
976C42—24no—
977C42—28no—
978C42—24no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42—44no—
983C42—44no—
984C42—42no—
985C42—41no—
986C42—48no—
987C42—48no—
988C42—48no—
989C42—42no—
990C42C2×#4118yes—
991C42C2×#4114yes—
992C42C2×#4114yes—
993C422−1+414yes—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23C22×#4114yes—
1014C23C2×H(5,𝔽2)14yes—
1015C23C2611yescharacteristic
1016Q8—28no—
1017Q8—48no—
1018Q8—84no—
1019Q8—164no—
1020D4—28no—
1021D4—28no—
1022D4—416no—
1023D4—416no—
1024D4—48no—
1025D4—48no—
1026D4—84no—
1027D4—88no—
1028D4—816no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—216no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—416no—
1084C2×C4—48no—
1085C2×C4—416no—
1086C2×C4—48no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—416no—
1091C2×C4—88no—
1092C2×C4—88no—
1093C2×C4—168no—
1094C2×C4C22×#4112yes—
1095C2×C4C22×#4114yes—
1096C2×C4C22×#4114yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4114yes—
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×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×2−1+412yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4C2×2−1+412yes—
1109C2×C4#58512yes—
1110C22—24no—
1111C22—24no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22C23×#4111yescharacteristic
1132C22C23×#4111yescharacteristic
1133C22C22×H(5,𝔽2)11yescharacteristic
1134C22C22×H(5,𝔽2)11yescharacteristic
1135C22C22×2−1+411yescharacteristic
1136C22C2×#58511yescharacteristic
1137C222−1+611yescharacteristic
1138C4—24no—
1139C4—24no—
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—24no—
1144C4—24no—
1145C4—42no—
1146C4—44no—
1147C4—44no—
1148C4—42no—
1149C4—42no—
1150C4—44no—
1151C4—48no—
1152C4—41no—
1153C4—44no—
1154C4—42no—
1155C4—42no—
1156C4—44no—
1157C4—42no—
1158C4#347514yes—
1159C4#351114yes—
1160C4#352214yes—
1161C2—44no—
1162C2—44no—
1163C2—84no—
1164C2C2×#347511yescharacteristic
1165C2C2×#352211yescharacteristic
1166C2C2×#351111yescharacteristic
1167C2#6295611yescharacteristic
1168C2#6298511yescharacteristic
1169C2#6298511yescharacteristic
1170C2#6301411yescharacteristic
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. #59863C2semidirect
2. #59678C2semidirect
3. #59315C2semidirect
4. #59304C2semidirect
5. #59249C2semidirect
6. #59086C2semidirect
7. #44920C2semidirect
8. #44019C2semidirect
9. #39902C2semidirect
10. #39479C2semidirect
11. #39029C2semidirect
12. #38909C2semidirect
13. #36563C2semidirect
14. #36492C2semidirect
15. #36468C2semidirect
16. #36192C2semidirect
17. #36187C2semidirect
18. #36180C2semidirect
19. #36117C2semidirect
20. #35989C2semidirect
21. #34932C2semidirect
22. #34932C2semidirect
23. #34243C2semidirect
24. #34188C2semidirect
25. C4×#554C2semidirect
26. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#596782
#593152
#593042
#592492
#590862
#449202
#440192
#399022
#394792
#390292
#389092
#365632
#364922
#364682
#361922
#361872
#361802
#361172
#359892
#349322
#342432
#341882
C4×#5542
C4×#5502