Finite Group Databasebeta

← #7688548

Subgroups — #7688548

Order 512.

5137 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59652C212yesmaximal, complemented
3#59581C214yesmaximal, complemented
4#59306C214yesmaximal, complemented
5#59303C212yesmaximal, complemented
6#59259C212yesmaximal, complemented
7#45259C214yesmaximal, complemented
8#44057C218yesmaximal, complemented
9#39900C214yesmaximal, complemented
10#39481C212yesmaximal, complemented
11#39033C214yesmaximal, complemented
12#38909C212yesmaximal, complemented
13#36598C211yesmaximal, characteristic, complemented
14#36534C212yesmaximal, complemented
15#36504C212yesmaximal, complemented
16#36302C212yesmaximal, complemented
17#36187C211yesmaximal, characteristic, complemented
18#36185C212yesmaximal, complemented
19#36180C211yesmaximal, characteristic, complemented
20#36000C214yesmaximal, complemented
21#34941C212yesmaximal, complemented
22#34932C211yesmaximal, characteristic, complemented
23#34242C212yesmaximal, complemented
24#34188C212yesmaximal, complemented
25C4×#556C211yesmaximal, characteristic, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27C2×#556C2211yescharacteristic
28C2×#556C2212yes—
29C2×#555C2212yes—
30C2×#554C2212yes—
31C2×#550C2211yescharacteristic
32C2×#529C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2862C2212yes—
36#2861C2214yes—
37#2857C2212yes—
38#2856C2212yes—
39#2850C2214yes—
40#2795C2218yes—
41#2773C2218yes—
42#2768C2218yes—
43#2753C2218yes—
44#2747C2218yes—
45#2741C2218yes—
46#2741C2218yes—
47#2730C2218yes—
48#2727C2214yes—
49#2691C2218yes—
50#2671C2218yes—
51#2651C2218yes—
52#2624C2214yes—
53#2597C2218yes—
54#2591C2218yes—
55#2585C2218yes—
56#2582C2212yes—
57#2578C2218yes—
58#2574C2218yes—
59#2571C2212yes—
60#2570C2214yes—
61#2568C2212yes—
62#2567C2212yes—
63#2565C2214yes—
64#2563C2212yes—
65#2560C2218yes—
66#2560C2218yes—
67#2553C2214yes—
68#2552C2212yes—
69#2552C2212yes—
70#2552C2211yescharacteristic
71#2548C2212yes—
72#2547C2211yescharacteristic
73#2544C2214yes—
74#2542C2212yes—
75#2542C2211yescharacteristic
76#2540C2214yes—
77#2538C2212yes—
78#2537C2211yescharacteristic
79#2537C2212yes—
80#2537C2212yes—
81#2536C2214yes—
82#2536C2214yes—
83#2531C2218yes—
84#2525C2218yes—
85#2521C2218yes—
86#2521C2218yes—
87#2513C2214yes—
88#2512C2214yes—
89#2511C2214yes—
90#2508C2214yes—
91#2507C2214yes—
92#2502C2214yes—
93#2500C2214yes—
94#2500C2214yes—
95#2500C2214yes—
96#2499C2214yes—
97#2497C2214yes—
98#2497C2214yes—
99#2496C2212yes—
100#2491C2214yes—
101#2491C2214yes—
102#2490C2214yes—
103#2489C2212yes—
104#2479C2218yes—
105#2476C2218yes—
106#2476C2218yes—
107#2467C2218yes—
108#2454C2214yes—
109#2448C2214yes—
110#2446C2214yes—
111#2441C2214yes—
112#2440C2214yes—
113#2440C2214yes—
114#2428C2214yes—
115#2427C2214yes—
116#2427C2214yes—
117#2427C2212yes—
118#2426C2218yes—
119#2423C2214yes—
120#2423C2214yes—
121#2422C2212yes—
122#2416C2214yes—
123#2416C2214yes—
124#2415C2214yes—
125#2415C2214yes—
126#2407C2214yes—
127#2396C2218yes—
128#2395C2214yes—
129#2373C2214yes—
130#2373C2218yes—
131#2367C2212yes—
132#2366C2212yes—
133#2366C2211yescharacteristic
134#2365C2211yescharacteristic
135#2365C2212yes—
136#2363C2214yes—
137#2363C2214yes—
138#2363C2212yes—
139#2363C2214yes—
140#2362C2214yes—
141#2362C2214yes—
142#2362C2212yes—
143#2356C2212yes—
144#2355C2211yescharacteristic
145#2355C2214yes—
146#2355C2212yes—
147#2355C2212yes—
148#2354C2212yes—
149#2354C2212yes—
150#2354C2212yes—
151#2354C2211yescharacteristic
152#2354C2211yescharacteristic
153#2354C2214yes—
154#2354C2212yes—
155#2354C2214yes—
156#2352C2214yes—
157#2352C2218yes—
158#2352C2214yes—
159#2352C2214yes—
160#2352C2214yes—
161Q8×C4⋊C4C2211yescharacteristic
162Q8×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165#2347C2212yes—
166#2341C2212yes—
167#2335C2218yes—
168#2314C2218yes—
169#2314C2214yes—
170#2311C2214yes—
171C4×C4⋊Q8C2212yes—
172C4×C4⋊Q8C2211yescharacteristic
173C4×C4⋊Q8C2211yescharacteristic
174C4×#127C2212yes—
175C4×#127C2211yescharacteristic
176C4×#125C2214yes—
177C4×#126C2214yes—
178C4×#124C2212yes—
179C4×#124C2214yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2214yes—
183C4×#121C2212yes—
184C4×#121C2214yes—
185C4×#121C2212yes—
186#2293C2214yes—
187#2285C2212yes—
188#2285C2214yes—
189#2285C2212yes—
190#2285C2214yes—
191C2×#384C2212yes—
192#2274C2214yes—
193C42×Q8C2211yescharacteristic
194C42×Q8C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2212yes—
197C42×D4C2211yescharacteristic
198C4×#117C2212yes—
199C22×#41C2312yes—
200#556—28no—
201#556—48no—
202#555—48no—
203#554—48no—
204#550—28no—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#127C2311yescharacteristic
211C2×#127C2312yes—
212#529—216no—
213C2×#126C2314yes—
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#124C2312yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#124C2318yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×#121C2312yes—
231C2×#121C2312yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2318yes—
238C2×#121C2314yes—
239C4×#41—216no—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2312yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2312yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2312yes—
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C2×#117C2314yes—
275C2×#117C2318yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2314yes—
279C22×C42C2314yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#399C2318yes—
287#399C2314yes—
288#399C2318yes—
289#399C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#397C2314yes—
298#397C2314yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2314yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#395C2318yes—
308#394C2318yes—
309#394C2318yes—
310#394C2318yes—
311#394C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#393C2318yes—
320#392C2318yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2312yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2312yes—
333#390C2314yes—
334#390C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2314yes—
341#390C2314yes—
342#390C2314yes—
343#390C2318yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2314yes—
348#390C2312yes—
349#390C2314yes—
350#390C2318yes—
351#390C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2318yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#388C2314yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
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#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2314yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2314yes—
413#387C2314yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2314yes—
418#386C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2314yes—
428#385C2314yes—
429#384C2312yes—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2314yes—
434#384C2314yes—
435#384C2314yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#384C2312yes—
443#383C2314yes—
444#382C2314yes—
445#382C2314yes—
446#382C2314yes—
447#382C2314yes—
448#382C2314yes—
449#382C2318yes—
450#382C2312yes—
451#380C2314yes—
452#380C2314yes—
453#380C2318yes—
454#380C2318yes—
455#380C2312yes—
456#380C2314yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2312yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523C43C2314yes—
524C43C2311yescharacteristic
525C43C2312yes—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—44no—
529C22×Q8C2412yes—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2414yes—
533C22×D4C2411yescharacteristic
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2414yes—
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2412yes—
541C22×D4C2418yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2418yes—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—24no—
555C4⋊Q8—44no—
556C4⋊Q8—82no—
557#127—28no—
558#127—24no—
559#126—216no—
560#126—216no—
561#126—416no—
562#125—28no—
563#125—48no—
564#124—28no—
565#124—28no—
566#124—48no—
567#124—416no—
568#123—216no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—416no—
573C22⋊Q8—48no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—28no—
577#121—28no—
578#121—216no—
579#121—48no—
580#121—44no—
581#121—48no—
582#121—48no—
583#121—84no—
584#121—88no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—44no—
591C4×Q8—42no—
592C4×Q8—48no—
593C4×Q8—84no—
594C4×Q8#4118yes—
595C4×D4—216no—
596C4×D4—28no—
597C4×D4—216no—
598C4×D4—28no—
599C4×D4—24no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—216no—
603C4×D4—24no—
604C4×D4—24no—
605C4×D4—24no—
606C4×D4—28no—
607C4×D4—42no—
608C4×D4—48no—
609C4×D4—44no—
610C4×D4—48no—
611C4×D4#4118yes—
612#117—216no—
613#117—28no—
614#117—216no—
615#117—28no—
616#117—44no—
617#117—48no—
618#117—48no—
619#117—48no—
620#117—88no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4—48no—
623C2×C4⋊C4—84no—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2418yes—
706C2×C22⋊C4C2412yes—
707C2×C42—28no—
708C2×C42—216no—
709C2×C42—28no—
710C2×C42C2414yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2412yes—
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2418yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2414yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2414yes—
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2412yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2414yes—
753#95C2418yes—
754#95C2414yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2412yes—
765#95C2412yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2418yes—
770#95C2414yes—
771#95C2418yes—
772#95C2418yes—
773#95C2414yes—
774#95C2414yes—
775#95C2418yes—
776C24C2512yes—
777C24C2514yes—
778C24C2512yes—
779#41—432no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—24no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8C2×#4114yes—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—24no—
806C2×D4—22no—
807C2×D4—24no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—42no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—48no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4C2×#4114yes—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—28no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—28no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—42no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4C2×#4118yes—
849C22×C4C2512yes—
850C22×C4C2511yescharacteristic
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2514yes—
857C22×C4C2518yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C4⋊C4—28no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—22no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—28no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—24no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—42no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—42no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4C2×#4114yes—
918C4⋊C4C2×#4118yes—
919C4⋊C4C2×#4114yes—
920C4⋊C42−1+414yes—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—42no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—48no—
954C22⋊C4C2×#4118yes—
955C42—24no—
956C42—28no—
957C42—24no—
958C42—24no—
959C42—28no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—28no—
964C42—28no—
965C42—24no—
966C42—28no—
967C42—24no—
968C42—22no—
969C42—22no—
970C42—24no—
971C42—22no—
972C42—44no—
973C42—48no—
974C42—48no—
975C42—44no—
976C42—48no—
977C42—42no—
978C42—44no—
979C42—42no—
980C42—41no—
981C42C2×#4114yes—
982C42C2×#4118yes—
983C42C2×#4114yes—
984C42H(5,𝔽2)14yes—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23C22×#4114yes—
1006C23C2611yescharacteristic
1007Q8—28no—
1008Q8—48no—
1009Q8—48no—
1010Q8—88no—
1011D4—28no—
1012D4—416no—
1013D4—48no—
1014D4—48no—
1015D4—44no—
1016D4—84no—
1017D4—88no—
1018D4—88no—
1019D4—168no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—22no—
1034C2×C4—216no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—21no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—28no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—28no—
1074C2×C4—48no—
1075C2×C4—416no—
1076C2×C4—416no—
1077C2×C4—48no—
1078C2×C4—48no—
1079C2×C4—48no—
1080C2×C4—416no—
1081C2×C4—84no—
1082C2×C4—168no—
1083C2×C4C22×#4114yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4114yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4114yes—
1088C2×C4C22×#4112yes—
1089C2×C4C22×#4112yes—
1090C2×C4C22×#4112yes—
1091C2×C4C22×#4112yes—
1092C2×C4C2×H(5,𝔽2)12yes—
1093C2×C4C2×H(5,𝔽2)12yes—
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×2−1+414yes—
1096C2×C4C2×2−1+412yes—
1097C2×C4#58512yes—
1098C2×C4#58512yes—
1099C22—24no—
1100C22—24no—
1101C22—24no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—44no—
1108C22—44no—
1109C22—42no—
1110C22—42no—
1111C22—44no—
1112C22—44no—
1113C22—42no—
1114C22—42no—
1115C22—44no—
1116C22—42no—
1117C22—44no—
1118C22—44no—
1119C22—42no—
1120C22C23×#4111yescharacteristic
1121C22C23×#4111yescharacteristic
1122C22C22×H(5,𝔽2)11yescharacteristic
1123C22C22×2−1+411yescharacteristic
1124C22C2×#58511yescharacteristic
1125C22C2×#58511yescharacteristic
1126C22H(7,𝔽2)11yescharacteristic
1127C4—22no—
1128C4—24no—
1129C4—24no—
1130C4—22no—
1131C4—22no—
1132C4—24no—
1133C4—24no—
1134C4—42no—
1135C4—44no—
1136C4—42no—
1137C4—42no—
1138C4—41no—
1139C4—44no—
1140C4—42no—
1141C4—44no—
1142C4—42no—
1143C4—44no—
1144C4—44no—
1145C4—48no—
1146C4—42no—
1147C4#347514yes—
1148C4#351114yes—
1149C4#351714yes—
1150C2—44no—
1151C2—82no—
1152C2—84no—
1153C2C2×#347511yescharacteristic
1154C2C2×#351711yescharacteristic
1155C2C2×#351111yescharacteristic
1156C2#6296111yescharacteristic
1157C2#6299411yescharacteristic
1158C2#6300011yescharacteristic
1159C2#6303411yescharacteristic
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. #59821C2semidirect
2. #59652C2semidirect
3. #59581C2semidirect
4. #59306C2semidirect
5. #59303C2semidirect
6. #59259C2semidirect
7. #45259C2semidirect
8. #44057C2semidirect
9. #39900C2semidirect
10. #39481C2semidirect
11. #39033C2semidirect
12. #38909C2semidirect
13. #36598C2semidirect
14. #36534C2semidirect
15. #36504C2semidirect
16. #36302C2semidirect
17. #36187C2semidirect
18. #36185C2semidirect
19. #36180C2semidirect
20. #36000C2semidirect
21. #34941C2semidirect
22. #34932C2semidirect
23. #34242C2semidirect
24. #34188C2semidirect
25. C4×#556C2semidirect
26. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#596522
#595812
#593062
#593032
#592592
#452592
#440572
#399002
#394812
#390332
#389092
#365982
#365342
#365042
#363022
#361872
#361852
#361802
#360002
#349412
#349322
#342422
#341882
C4×#5562
C4×#5502