Finite Group Databasebeta

← #7688392

Subgroups — #7688392

Order 512.

5673 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59676C214yesmaximal, complemented
3#59483C214yesmaximal, complemented
4#59419C212yesmaximal, complemented
5#59410C212yesmaximal, complemented
6#59057C212yesmaximal, complemented
7#45087C214yesmaximal, complemented
8#44259C218yesmaximal, complemented
9#40177C214yesmaximal, complemented
10#40175C214yesmaximal, complemented
11#39194C212yesmaximal, complemented
12#39191C212yesmaximal, complemented
13#36563C211yesmaximal, characteristic, complemented
14#36559C211yesmaximal, characteristic, complemented
15#36555C212yesmaximal, complemented
16#36453C212yesmaximal, complemented
17#36301C212yesmaximal, complemented
18#36275C212yesmaximal, complemented
19#36127C211yesmaximal, characteristic, complemented
20#35715C214yesmaximal, complemented
21#34977C212yesmaximal, complemented
22#34954C211yesmaximal, characteristic, complemented
23#34313C212yesmaximal, complemented
24#34308C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#554C2212yes—
29C2×#550C2212yes—
30C2×#550C2211yescharacteristic
31C2×#547C2212yes—
32C2×#547C2212yes—
33C2×#532C2212yes—
34C2×#520C2214yes—
35C2×C4×#41C2212yes—
36#2868C2211yescharacteristic
37#2864C2214yes—
38#2859C2212yes—
39#2859C2212yes—
40#2857C2212yes—
41#2855C2214yes—
42#2801C2218yes—
43#2800C2218yes—
44#2757C2218yes—
45#2753C2218yes—
46#2740C2218yes—
47#2740C2218yes—
48#2730C2218yes—
49#2711C2218yes—
50#2705C2218yes—
51#2699C2218yes—
52#2682C2214yes—
53#2630C2218yes—
54#2624C2214yes—
55#2610C2218yes—
56#2602C2218yes—
57#2593C2214yes—
58#2587C2218yes—
59#2582C2212yes—
60#2582C2211yescharacteristic
61#2576C2218yes—
62#2571C2211yescharacteristic
63#2567C2212yes—
64#2566C2214yes—
65#2563C2212yes—
66#2554C2218yes—
67#2552C2212yes—
68#2550C2214yes—
69#2548C2211yescharacteristic
70#2548C2211yescharacteristic
71#2547C2212yes—
72#2543C2218yes—
73#2541C2212yes—
74#2540C2214yes—
75#2538C2212yes—
76#2538C2212yes—
77#2538C2212yes—
78#2537C2212yes—
79#2537C2212yes—
80#2537C2212yes—
81#2527C2218yes—
82#2522C2218yes—
83#2513C2212yes—
84#2513C2212yes—
85#2510C2218yes—
86#2507C2214yes—
87#2500C2214yes—
88#2497C2214yes—
89#2494C2214yes—
90#2494C2214yes—
91#2494C2214yes—
92#2490C2214yes—
93#2487C2214yes—
94#2485C2214yes—
95#2477C2218yes—
96#2471C2218yes—
97#2460C2218yes—
98#2454C2214yes—
99#2453C2214yes—
100#2452C2214yes—
101#2452C2214yes—
102#2451C2214yes—
103#2449C2218yes—
104#2448C2212yes—
105#2448C2212yes—
106#2445C2214yes—
107#2443C2218yes—
108#2441C2214yes—
109#2438C2218yes—
110#2432C2214yes—
111#2431C2214yes—
112#2431C2214yes—
113#2428C2214yes—
114#2428C2214yes—
115#2427C2214yes—
116#2426C2214yes—
117#2423C2214yes—
118#2422C2214yes—
119#2422C2214yes—
120#2420C2214yes—
121#2420C2214yes—
122#2417C2214yes—
123#2416C2214yes—
124#2416C2214yes—
125#2414C2214yes—
126#2414C2214yes—
127#2407C2214yes—
128#2407C2218yes—
129#2395C2214yes—
130#2388C2218yes—
131#2373C2214yes—
132#2369C2212yes—
133#2367C2212yes—
134#2366C2211yescharacteristic
135#2366C2214yes—
136#2366C2212yes—
137#2365C2211yescharacteristic
138#2363C2214yes—
139#2363C2212yes—
140#2362C2212yes—
141#2361C2214yes—
142#2361C2218yes—
143#2361C2214yes—
144#2360C2214yes—
145#2359C2218yes—
146#2356C2212yes—
147#2355C2212yes—
148#2355C2211yescharacteristic
149#2354C2211yescharacteristic
150#2354C2211yescharacteristic
151#2354C2212yes—
152#2352C2214yes—
153Q8×C4⋊C4C2212yes—
154Q8×C4⋊C4C2211yescharacteristic
155D4×C4⋊C4C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2212yes—
158D4×C4⋊C4C2214yes—
159D4×C4⋊C4C2212yes—
160D4×C4⋊C4C2212yes—
161#2347C2212yes—
162#2345C2214yes—
163#2344C2214yes—
164#2341C2214yes—
165#2341C2212yes—
166#2339C2214yes—
167#2339C2214yes—
168#2324C2214yes—
169#2324C2218yes—
170#2323C2214yes—
171#2322C2218yes—
172C4×C4⋊Q8C2212yes—
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2212yes—
175C4×#127C2214yes—
176C4×#127C2212yes—
177C4×#127C2211yescharacteristic
178C4×#127C2211yescharacteristic
179C4×#126C2214yes—
180C4×#124C2212yes—
181C4×#124C2212yes—
182C4×#124C2212yes—
183C4×#124C2214yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2214yes—
186C4×#121C2214yes—
187C4×#121C2214yes—
188C4×#121C2212yes—
189#2293C2212yes—
190#2293C2212yes—
191#2293C2214yes—
192C2×#389C2214yes—
193C42×Q8C2212yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2312yes—
200C22×#41C2314yes—
201C22×#41C2314yes—
202#556—28no—
203#554—48no—
204#550—216no—
205#550—28no—
206#547—216no—
207#547—48no—
208#532—48no—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2312yes—
214C2×#127C2314yes—
215C2×#127C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#126C2314yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#124C2312yes—
221C2×#124C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#123C2318yes—
225C2×#123C2318yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2314yes—
232C2×#121C2318yes—
233C2×#121C2314yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2318yes—
241#520—416no—
242C4×#41—48no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2312yes—
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2312yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2318yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2312yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2318yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2318yes—
278C2×#117C2312yes—
279C2×#117C2314yes—
280C2×#117C2318yes—
281C2×#117C2314yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C22×C4⋊C4C2314yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2318yes—
287C22×C4⋊C4C2314yes—
288C22×C42C2312yes—
289C22×C42C2314yes—
290#401C2318yes—
291#400C2314yes—
292#400C2318yes—
293#399C2318yes—
294#399C2314yes—
295#399C2318yes—
296#398C2318yes—
297#398C2314yes—
298#398C2318yes—
299#398C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#396C2318yes—
311#396C2318yes—
312#395C2318yes—
313#394C2318yes—
314#394C2314yes—
315#394C2314yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#393C2318yes—
325#392C2318yes—
326#392C2318yes—
327#392C2318yes—
328#392C2318yes—
329#391C2314yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2312yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2318yes—
338#390C2314yes—
339#390C2312yes—
340#390C2312yes—
341#390C2312yes—
342#390C2318yes—
343#390C2314yes—
344#390C2312yes—
345#390C2318yes—
346#390C2314yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#390C2318yes—
355#390C2314yes—
356#390C2312yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2318yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2312yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2318yes—
376#389C2314yes—
377#389C2312yes—
378#389C2314yes—
379#389C2312yes—
380#389C2314yes—
381#389C2314yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2312yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2318yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2314yes—
402#388C2318yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#388C2318yes—
414#388C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2314yes—
437#386C2314yes—
438#386C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2314yes—
448#384C2314yes—
449#384C2311yescharacteristic
450#384C2312yes—
451#384C2311yescharacteristic
452#384C2312yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#383C2314yes—
458#382C2314yes—
459#382C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2312yes—
463#381C2318yes—
464#381C2318yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2318yes—
476#380C2314yes—
477#380C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523C2×#95C2318yes—
524C43C2314yes—
525C43C2311yescharacteristic
526C43C2312yes—
527C43C2312yes—
528C2×#41—216no—
529C2×#41—28no—
530C2×#41—28no—
531C2×#41—216no—
532C2×#41—48no—
533C2×#41—44no—
534C2×#41—48no—
535C2×#41—48no—
536C2×#41—84no—
537C22×Q8C2411yescharacteristic
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2414yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2412yes—
544C22×D4C2418yes—
545C22×D4C2414yes—
546C22×D4C2412yes—
547C22×D4C2412yes—
548C22×D4C2414yes—
549C22×D4C2418yes—
550C22×D4C2412yes—
551C22×D4C2418yes—
552C22×D4C2412yes—
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2418yes—
558C23×C4C2414yes—
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2418yes—
562C23×C4C2418yes—
563C4⋊Q8—28no—
564C4⋊Q8—44no—
565C4⋊Q8—82no—
566C4⋊Q8#4118yescomplemented
567#127—216no—
568#127—28no—
569#127—24no—
570#127#4118yescomplemented
571#126—216no—
572#125—48no—
573#125—84no—
574#124—28no—
575#124—28no—
576#124—44no—
577#124—48no—
578#123—232no—
579#123—416no—
580C22⋊Q8—216no—
581C22⋊Q8—28no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585#121—28no—
586#121—216no—
587#121—232no—
588#121—216no—
589#121—216no—
590#121—48no—
591#121—48no—
592#121—48no—
593#121—48no—
594#121—88no—
595C4×Q8—28no—
596C4×Q8—24no—
597C4×Q8—28no—
598C4×Q8—28no—
599C4×Q8—24no—
600C4×Q8—24no—
601C4×Q8—24no—
602C4×Q8—24no—
603C4×Q8—42no—
604C4×Q8—44no—
605C4×Q8—48no—
606C4×D4—216no—
607C4×D4—28no—
608C4×D4—28no—
609C4×D4—24no—
610C4×D4—28no—
611C4×D4—28no—
612C4×D4—28no—
613C4×D4—24no—
614C4×D4—24no—
615C4×D4—28no—
616C4×D4—44no—
617C4×D4—48no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—44no—
622C4×D4—48no—
623C4×D4—48no—
624C4×D4—416no—
625C4×D4—44no—
626C4×D4—48no—
627C4×D4—416no—
628C4×D4—88no—
629C4×D4—84no—
630#117—28no—
631#117—48no—
632#117—48no—
633#117—416no—
634#117—44no—
635#117—44no—
636C2×C4⋊C4—216no—
637C2×C4⋊C4—216no—
638C2×C4⋊C4—416no—
639C2×C4⋊C4—48no—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2418yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2411yescharacteristic
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C42—28no—
723C2×C42—48no—
724C2×C42C2414yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2412yes—
730C2×C42C2411yescharacteristic
731C2×C42C2412yes—
732C2×C42C2411yescharacteristic
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2412yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2411yescharacteristic
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2414yes—
743C2×C42C2418yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2412yes—
747C2×C42C2414yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2412yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2412yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2412yes—
780#95C2412yes—
781#95C2412yes—
782#95C2412yes—
783#95C2412yes—
784#95C2418yes—
785#95C2418yes—
786#95C2414yes—
787#95C2418yes—
788C24C2512yes—
789C24C2514yes—
790C24C2514yes—
791#41—464no—
792#41—432no—
793#41—832no—
794C2×Q8—24no—
795C2×Q8—22no—
796C2×Q8—22no—
797C2×Q8—24no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—28no—
801C2×Q8—22no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8C2×#4118yes—
805C2×Q82−1+414yes—
806C2×D4—216no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—216no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—22no—
813C2×D4—22no—
814C2×D4—24no—
815C2×D4—216no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—24no—
823C2×D4—24no—
824C2×D4—28no—
825C2×D4—24no—
826C2×D4—44no—
827C2×D4—48no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—48no—
834C2×D4—48no—
835C2×D4—48no—
836C2×D4—48no—
837C2×D4—44no—
838C2×D4—48no—
839C2×D4C2×#4118yes—
840C2×D4C2×#4118yes—
841C2×D4C2×#4118yes—
842C22×C4—216no—
843C22×C4—28no—
844C22×C4—28no—
845C22×C4—216no—
846C22×C4—24no—
847C22×C4—28no—
848C22×C4—24no—
849C22×C4—28no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—24no—
853C22×C4—28no—
854C22×C4—28no—
855C22×C4—24no—
856C22×C4—28no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—28no—
860C22×C4—216no—
861C22×C4—28no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4C2512yes—
873C22×C4C2512yes—
874C22×C4C2512yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2511yescharacteristic
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2512yes—
883C22×C4C2514yes—
884C22×C4C2518yes—
885C22×C4C2512yes—
886C22×C4C2514yes—
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2511yescharacteristic
893C22×C4C2511yescharacteristic
894C22×C4C2511yescharacteristic
895C4⋊C4—24no—
896C4⋊C4—216no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—22no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—22no—
906C4⋊C4—28no—
907C4⋊C4—24no—
908C4⋊C4—216no—
909C4⋊C4—28no—
910C4⋊C4—22no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—24no—
914C4⋊C4—22no—
915C4⋊C4—24no—
916C4⋊C4—28no—
917C4⋊C4—24no—
918C4⋊C4—24no—
919C4⋊C4—22no—
920C4⋊C4—22no—
921C4⋊C4—24no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—42no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—42no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—42no—
937C4⋊C4—44no—
938C4⋊C4C2×#4118yes—
939C4⋊C4C2×#4118yes—
940C4⋊C4H(5,𝔽2)14yes—
941C22⋊C4—28no—
942C22⋊C4—216no—
943C22⋊C4—28no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—24no—
949C22⋊C4—216no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—24no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C42—28no—
978C42—24no—
979C42—28no—
980C42—24no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—24no—
985C42—24no—
986C42—28no—
987C42—24no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—22no—
992C42—24no—
993C42—22no—
994C42—24no—
995C42—44no—
996C42—44no—
997C42—44no—
998C42—48no—
999C42—42no—
1000C42—44no—
1001C42—42no—
1002C42—42no—
1003C42—41no—
1004C42C2×#4114yes—
1005C42C2×#4114yes—
1006C42H(5,𝔽2)14yes—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—24no—
1017C23—22no—
1018C23—24no—
1019C23—24no—
1020C23—22no—
1021C23—24no—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—22no—
1027C23C22×#4118yes—
1028C23C2611yescharacteristic
1029Q8—216no—
1030Q8—28no—
1031Q8—44no—
1032Q8—88no—
1033D4—216no—
1034D4—216no—
1035D4—48no—
1036D4—416no—
1037D4—432no—
1038D4—48no—
1039D4—44no—
1040D4—48no—
1041D4—48no—
1042D4—88no—
1043D4—816no—
1044D4—816no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—28no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—28no—
1099C2×C4—48no—
1100C2×C4—416no—
1101C2×C4—432no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—48no—
1105C2×C4—48no—
1106C2×C4—88no—
1107C2×C4—816no—
1108C2×C4—168no—
1109C2×C4C22×#4118yes—
1110C2×C4C22×#4112yes—
1111C2×C4C22×#4112yes—
1112C2×C4C22×#4112yes—
1113C2×C4C22×#4112yes—
1114C2×C4C22×#4112yes—
1115C2×C4C22×#4112yes—
1116C2×C4C2×H(5,𝔽2)12yes—
1117C2×C4C2×H(5,𝔽2)14yes—
1118C2×C4C2×H(5,𝔽2)12yes—
1119C2×C4C2×H(5,𝔽2)12yes—
1120C2×C4C2×H(5,𝔽2)12yes—
1121C2×C4C2×2−1+414yes—
1122C2×C4C2×2−1+412yes—
1123C2×C4#58512yes—
1124C22—28no—
1125C22—28no—
1126C22—28no—
1127C22—44no—
1128C22—44no—
1129C22—44no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22—42no—
1134C22—44no—
1135C22—42no—
1136C22—44no—
1137C22—42no—
1138C22—44no—
1139C22—42no—
1140C22—44no—
1141C22—42no—
1142C22—44no—
1143C22—44no—
1144C22—42no—
1145C22C23×#4111yescharacteristic
1146C22C23×#4111yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×H(5,𝔽2)11yescharacteristic
1149C22C22×2−1+411yescharacteristic
1150C22C2×#58511yescharacteristic
1151C22H(7,𝔽2)11yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—24no—
1155C4—22no—
1156C4—24no—
1157C4—28no—
1158C4—42no—
1159C4—44no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—41no—
1165C4—42no—
1166C4—44no—
1167C4—42no—
1168C4—42no—
1169C4—48no—
1170C4—42no—
1171C4—44no—
1172C4#348114yes—
1173C4#351714yes—
1174C4#352014yes—
1175C2—48no—
1176C2—82no—
1177C2—84no—
1178C2C2×#348111yescharacteristic
1179C2C2×#352011yescharacteristic
1180C2C2×#351711yescharacteristic
1181C2#6291211yescharacteristic
1182C2#6299211yescharacteristic
1183C2#6299911yescharacteristic
1184C2#6303911yescharacteristic
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. #59815C2semidirect
2. #59676C2semidirect
3. #59483C2semidirect
4. #59419C2semidirect
5. #59410C2semidirect
6. #59057C2semidirect
7. #45087C2semidirect
8. #44259C2semidirect
9. #40177C2semidirect
10. #40175C2semidirect
11. #39194C2semidirect
12. #39191C2semidirect
13. #36563C2semidirect
14. #36559C2semidirect
15. #36555C2semidirect
16. #36453C2semidirect
17. #36301C2semidirect
18. #36275C2semidirect
19. #36127C2semidirect
20. #35715C2semidirect
21. #34977C2semidirect
22. #34954C2semidirect
23. #34313C2semidirect
24. #34308C2semidirect
25. C4×#556C2semidirect
26. C4×#550C2semidirect
566. C4⋊Q8#41semidirect
570. #127#41semidirect

Maximal subgroups

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

subgroupindex
#598152
#596762
#594832
#594192
#594102
#590572
#450872
#442592
#401772
#401752
#391942
#391912
#365632
#365592
#365552
#364532
#363012
#362752
#361272
#357152
#349772
#349542
#343132
#343082
C4×#5562
C4×#5502