Finite Group Databasebeta

← #7987094

Subgroups — #7987094

Order 512.

5053 conjugacy classes of subgroups.

The subgroup lattice has 1155 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59652C212yesmaximal, complemented
3#59304C212yesmaximal, complemented
4#59214C212yesmaximal, complemented
5#50793C218yesmaximal, complemented
6#46078C214yesmaximal, complemented
7#45313C214yesmaximal, complemented
8#44972C214yesmaximal, complemented
9#42554C214yesmaximal, complemented
10#42460C214yesmaximal, complemented
11#40177C214yesmaximal, complemented
12#39489C212yesmaximal, complemented
13#39156C212yesmaximal, complemented
14#39147C212yesmaximal, complemented
15#39136C212yesmaximal, complemented
16#36593C211yesmaximal, characteristic, complemented
17#36559C212yesmaximal, complemented
18#36472C212yesmaximal, complemented
19#36187C211yesmaximal, characteristic, complemented
20#36180C211yesmaximal, characteristic, complemented
21#35202C212yesmaximal, complemented
22#35185C212yesmaximal, complemented
23#34943C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34384C212yesmaximal, complemented
26C4×#556C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#556C2211yescharacteristic
29C2×#555C2212yes—
30C2×#554C2212yes—
31C2×#554C2212yes—
32C2×#553C2214yes—
33C2×#529C2212yes—
34#2868C2212yes—
35#2868C2211yescharacteristic
36#2864C2214yes—
37#2860C2214yes—
38#2859C2214yes—
39#2857C2212yes—
40#2856C2212yes—
41#2837C2218yes—
42#2780C2218yes—
43#2777C2218yes—
44#2770C2218yes—
45#2757C2218yes—
46#2757C2218yes—
47#2740C2218yes—
48#2732C2214yes—
49#2730C2218yes—
50#2727C2218yes—
51#2725C2218yes—
52#2718C2218yes—
53#2711C2218yes—
54#2707C2218yes—
55#2705C2218yes—
56#2701C2218yes—
57#2674C2218yes—
58#2674C2218yes—
59#2667C2218yes—
60#2650C2218yes—
61#2644C2214yes—
62#2630C2218yes—
63#2620C2214yes—
64#2606C2218yes—
65#2603C2218yes—
66#2587C2218yes—
67#2572C2214yes—
68#2571C2211yescharacteristic
69#2567C2212yes—
70#2566C2214yes—
71#2566C2214yes—
72#2563C2211yescharacteristic
73#2563C2212yes—
74#2563C2211yescharacteristic
75#2554C2214yes—
76#2552C2212yes—
77#2552C2212yes—
78#2552C2212yes—
79#2552C2211yescharacteristic
80#2552C2212yes—
81#2552C2212yes—
82#2552C2214yes—
83#2552C2214yes—
84#2548C2211yescharacteristic
85#2546C2212yes—
86#2546C2214yes—
87#2542C2212yes—
88#2541C2211yescharacteristic
89#2540C2214yes—
90#2538C2214yes—
91#2538C2214yes—
92#2538C2212yes—
93#2538C2211yescharacteristic
94#2538C2214yes—
95#2538C2214yes—
96#2537C2211yescharacteristic
97#2537C2212yes—
98#2537C2212yes—
99#2513C2214yes—
100#2512C2212yes—
101#2509C2214yes—
102#2502C2214yes—
103#2501C2214yes—
104#2500C2214yes—
105#2499C2214yes—
106#2497C2214yes—
107#2496C2214yes—
108#2495C2212yes—
109#2495C2212yes—
110#2491C2214yes—
111#2491C2214yes—
112#2490C2214yes—
113#2490C2214yes—
114#2490C2212yes—
115#2487C2214yes—
116#2469C2218yes—
117#2464C2218yes—
118#2460C2218yes—
119#2454C2214yes—
120#2452C2218yes—
121#2452C2218yes—
122#2445C2212yes—
123#2443C2218yes—
124#2441C2214yes—
125#2441C2214yes—
126#2441C2214yes—
127#2441C2214yes—
128#2441C2214yes—
129#2440C2214yes—
130#2440C2214yes—
131#2428C2214yes—
132#2426C2212yes—
133#2426C2218yes—
134#2426C2214yes—
135#2422C2214yes—
136#2422C2214yes—
137#2422C2214yes—
138#2421C2214yes—
139#2420C2212yes—
140#2420C2212yes—
141#2417C2214yes—
142#2416C2214yes—
143#2415C2214yes—
144#2414C2214yes—
145#2398C2214yes—
146#2392C2214yes—
147#2383C2218yes—
148#2373C2214yes—
149#2367C2212yes—
150#2366C2212yes—
151#2365C2211yescharacteristic
152#2363C2214yes—
153#2362C2212yes—
154#2361C2214yes—
155#2360C2214yes—
156#2356C2212yes—
157#2355C2211yescharacteristic
158#2354C2212yes—
159#2354C2212yes—
160#2354C2211yescharacteristic
161#2352C2214yes—
162Q8×C4⋊C4C2212yes—
163Q8×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2214yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2214yes—
169#2347C2212yes—
170#2330C2214yes—
171#2330C2214yes—
172#2326C2214yes—
173#2323C2214yes—
174#2322C2218yes—
175#2317C2214yes—
176#2314C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#127C2212yes—
181C4×#127C2211yescharacteristic
182C4×#127C2214yes—
183C4×#126C2214yes—
184C4×#124C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×#121C2212yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189#2293C2212yes—
190#2285C2212yes—
191C2×#384C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194C42×Q8C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199#557—48no—
200#556—28no—
201#555—48no—
202#554—48no—
203#554—48no—
204#553—416no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×#127C2312yes—
213C2×#127C2311yescharacteristic
214#529—216no—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2318yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2318yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×#123C2318yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#121C2318yes—
244C2×#121C2314yes—
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2318yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2314yes—
270C2×C4×D4C2318yes—
271C2×#117C2314yes—
272C2×#117C2312yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C4⋊C4C2314yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#399C2318yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2314yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2314yes—
311#396C2318yes—
312#396C2318yes—
313#396C2314yes—
314#396C2318yes—
315#396C2318yes—
316#395C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#394C2318yes—
328#393C2314yes—
329#393C2314yes—
330#393C2318yes—
331#392C2314yes—
332#392C2318yes—
333#391C2312yes—
334#391C2312yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2318yes—
344#390C2314yes—
345#390C2312yes—
346#390C2312yes—
347#390C2314yes—
348#390C2318yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2318yes—
357#390C2314yes—
358#390C2312yes—
359#390C2312yes—
360#390C2318yes—
361#389C2312yes—
362#389C2314yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2312yes—
377#389C2314yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2312yes—
385#389C2318yes—
386#389C2318yes—
387#389C2314yes—
388#389C2312yes—
389#389C2314yes—
390#389C2312yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2318yes—
395#388C2318yes—
396#388C2314yes—
397#388C2314yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2314yes—
438#384C2312yes—
439#384C2314yes—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2314yes—
444#384C2314yes—
445#384C2314yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2314yes—
454#383C2314yes—
455#383C2314yes—
456#383C2314yes—
457#382C2312yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#381C2314yes—
464#381C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2318yes—
477#380C2314yes—
478#380C2314yes—
479#380C2312yes—
480#380C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2318yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522#376C2314yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C22×Q8C2412yes—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2414yes—
530C22×D4C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2414yes—
534C22×D4C2414yes—
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C22×D4C2412yes—
538C22×D4C2418yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C23×C4C2418yes—
548C4⋊Q8—24no—
549C4⋊Q8—24no—
550C4⋊Q8—28no—
551C4⋊Q8—44no—
552C4⋊Q8—48no—
553C4⋊Q8—82no—
554C4⋊Q8—84no—
555#127—28no—
556#127—24no—
557#126—216no—
558#126—216no—
559#126—416no—
560#125—28no—
561#125—216no—
562#125—48no—
563#125—48no—
564#125—416no—
565#124—28no—
566#124—28no—
567#124—416no—
568#123—216no—
569#123—416no—
570#123—88no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—48no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578#121—28no—
579#121—28no—
580#121—28no—
581#121—416no—
582#121—44no—
583#121—48no—
584#121—48no—
585#121—48no—
586#121—84no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—24no—
591C4×Q8—44no—
592C4×Q8—48no—
593C4×Q8—44no—
594C4×Q8—48no—
595C4×Q8#4118yes—
596C4×D4—24no—
597C4×D4—28no—
598C4×D4—216no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—28no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—42no—
605C4×D4—416no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—48no—
609C4×D4—44no—
610C4×D4—48no—
611C4×D4—48no—
612C4×D4—88no—
613#117—28no—
614#117—28no—
615#117—216no—
616#117—48no—
617#117—48no—
618C2×C4⋊C4—48no—
619C2×C4⋊C4—48no—
620C2×C4⋊C4—48no—
621C2×C4⋊C4—84no—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2411yescharacteristic
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C42—28no—
710C2×C42—28no—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2411yescharacteristic
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2418yes—
729C2×C42C2414yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#95C2412yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2412yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2418yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2512yes—
775C24C2514yes—
776C24C2512yes—
777C2×Q8—24no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—28no—
782C2×Q8—22no—
783C2×Q8—24no—
784C2×Q8—42no—
785C2×Q8—44no—
786C2×Q8—42no—
787C2×Q8—44no—
788C2×Q8C2×#4114yes—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—28no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—24no—
805C2×D4—22no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—42no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D42−1+414yes—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2518yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C4⋊C4—28no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—22no—
880C4⋊C4—24no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—216no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—216no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—42no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—42no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4C2×#4114yes—
916C4⋊C4C2×#4118yes—
917C4⋊C4H(5,𝔽2)14yes—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—24no—
932C22⋊C4—28no—
933C22⋊C4—24no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—42no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—28no—
957C42—28no—
958C42—28no—
959C42—28no—
960C42—24no—
961C42—22no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—22no—
966C42—24no—
967C42—24no—
968C42—22no—
969C42—24no—
970C42—48no—
971C42—44no—
972C42—44no—
973C42—48no—
974C42—42no—
975C42—41no—
976C42C2×#4114yes—
977C42C2×#4118yes—
978C42H(5,𝔽2)14yes—
979C422−1+414yes—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—24no—
992C23—22no—
993C23—22no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23C2×2−1+414yes—
1001C23C2611yescharacteristic
1002Q8—28no—
1003Q8—48no—
1004Q8—84no—
1005Q8—88no—
1006D4—28no—
1007D4—416no—
1008D4—416no—
1009D4—48no—
1010D4—44no—
1011D4—48no—
1012D4—84no—
1013D4—88no—
1014D4—168no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—21no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—28no—
1069C2×C4—48no—
1070C2×C4—48no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—416no—
1074C2×C4—48no—
1075C2×C4—84no—
1076C2×C4—168no—
1077C2×C4—168no—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4114yes—
1080C2×C4C22×#4114yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C2×H(5,𝔽2)14yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×2−1+412yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4#58512yes—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—44no—
1101C22—42no—
1102C22—42no—
1103C22—44no—
1104C22—44no—
1105C22—42no—
1106C22—44no—
1107C22—42no—
1108C22—42no—
1109C22—44no—
1110C22—44no—
1111C22—42no—
1112C22—42no—
1113C22—44no—
1114C22C23×#4111yescharacteristic
1115C22C22×H(5,𝔽2)11yescharacteristic
1116C22C22×H(5,𝔽2)11yescharacteristic
1117C22C22×2−1+411yescharacteristic
1118C22C22×2−1+411yescharacteristic
1119C22C2×#58511yescharacteristic
1120C22H(7,𝔽2)11yescharacteristic
1121C4—22no—
1122C4—24no—
1123C4—24no—
1124C4—24no—
1125C4—22no—
1126C4—22no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—44no—
1131C4—42no—
1132C4—44no—
1133C4—44no—
1134C4—42no—
1135C4—42no—
1136C4—44no—
1137C4—44no—
1138C4—48no—
1139C4—42no—
1140C4—42no—
1141C4#351114yes—
1142C4#351714yes—
1143C4#355214yes—
1144C2—44no—
1145C2—84no—
1146C2—82no—
1147C2C2×#355211yescharacteristic
1148C2C2×#351711yescharacteristic
1149C2C2×#351111yescharacteristic
1150C2#6291611yescharacteristic
1151C2#6292911yescharacteristic
1152C2#6300011yescharacteristic
1153C2#6301311yescharacteristic
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. #59823C2semidirect
2. #59652C2semidirect
3. #59304C2semidirect
4. #59214C2semidirect
5. #50793C2semidirect
6. #46078C2semidirect
7. #45313C2semidirect
8. #44972C2semidirect
9. #42554C2semidirect
10. #42460C2semidirect
11. #40177C2semidirect
12. #39489C2semidirect
13. #39156C2semidirect
14. #39147C2semidirect
15. #39136C2semidirect
16. #36593C2semidirect
17. #36559C2semidirect
18. #36472C2semidirect
19. #36187C2semidirect
20. #36180C2semidirect
21. #35202C2semidirect
22. #35185C2semidirect
23. #34943C2semidirect
24. #34934C2semidirect
25. #34384C2semidirect
26. C4×#556C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#596522
#593042
#592142
#507932
#460782
#453132
#449722
#425542
#424602
#401772
#394892
#391562
#391472
#391362
#365932
#365592
#364722
#361872
#361802
#352022
#351852
#349432
#349342
#343842
C4×#5562