Finite Group Databasebeta

← #7985583

Subgroups — #7985583

Order 512.

5187 conjugacy classes of subgroups.

The subgroup lattice has 1167 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59444C212yesmaximal, complemented
3#59258C212yesmaximal, complemented
4#59039C212yesmaximal, complemented
5#49657C218yesmaximal, complemented
6#45664C214yesmaximal, complemented
7#45060C214yesmaximal, complemented
8#45050C214yesmaximal, complemented
9#42577C214yesmaximal, complemented
10#42556C214yesmaximal, complemented
11#39607C212yesmaximal, complemented
12#39479C212yesmaximal, complemented
13#39191C212yesmaximal, complemented
14#39126C212yesmaximal, complemented
15#38950C214yesmaximal, complemented
16#36563C211yesmaximal, characteristic, complemented
17#36290C212yesmaximal, complemented
18#36275C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#36127C211yesmaximal, characteristic, complemented
21#35196C212yesmaximal, complemented
22#35189C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic, complemented
25#34368C212yesmaximal, complemented
26C4×#550C211yesmaximal, characteristic, complemented
27C2×#554C2212yes—
28C2×#552C2214yes—
29C2×#550C2211yescharacteristic
30C2×#547C2212yes—
31C2×#532C2212yes—
32C2×#529C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2851C2214yes—
40#2850C2214yes—
41#2827C2218yes—
42#2786C2218yes—
43#2755C2218yes—
44#2754C2218yes—
45#2753C2218yes—
46#2747C2218yes—
47#2739C2218yes—
48#2732C2214yes—
49#2711C2218yes—
50#2707C2218yes—
51#2705C2218yes—
52#2704C2218yes—
53#2702C2218yes—
54#2702C2218yes—
55#2695C2218yes—
56#2694C2218yes—
57#2686C2218yes—
58#2681C2218yes—
59#2649C2218yes—
60#2630C2218yes—
61#2629C2214yes—
62#2624C2214yes—
63#2618C2218yes—
64#2601C2218yes—
65#2582C2212yes—
66#2574C2214yes—
67#2571C2212yes—
68#2567C2211yescharacteristic
69#2567C2212yes—
70#2563C2212yes—
71#2563C2211yescharacteristic
72#2562C2214yes—
73#2553C2214yes—
74#2552C2214yes—
75#2552C2212yes—
76#2552C2212yes—
77#2552C2211yescharacteristic
78#2552C2211yescharacteristic
79#2550C2214yes—
80#2547C2212yes—
81#2547C2211yescharacteristic
82#2542C2211yescharacteristic
83#2542C2212yes—
84#2538C2212yes—
85#2538C2214yes—
86#2538C2211yescharacteristic
87#2538C2212yes—
88#2537C2211yescharacteristic
89#2537C2212yes—
90#2537C2212yes—
91#2537C2214yes—
92#2536C2214yes—
93#2516C2218yes—
94#2512C2214yes—
95#2509C2214yes—
96#2508C2212yes—
97#2507C2214yes—
98#2507C2214yes—
99#2506C2214yes—
100#2505C2218yes—
101#2498C2218yes—
102#2497C2214yes—
103#2497C2214yes—
104#2497C2214yes—
105#2497C2212yes—
106#2496C2214yes—
107#2496C2212yes—
108#2492C2214yes—
109#2489C2212yes—
110#2487C2214yes—
111#2485C2214yes—
112#2485C2214yes—
113#2479C2218yes—
114#2475C2218yes—
115#2473C2218yes—
116#2454C2214yes—
117#2454C2212yes—
118#2453C2214yes—
119#2451C2214yes—
120#2449C2218yes—
121#2445C2214yes—
122#2442C2214yes—
123#2442C2214yes—
124#2441C2214yes—
125#2439C2214yes—
126#2438C2218yes—
127#2432C2214yes—
128#2430C2218yes—
129#2428C2214yes—
130#2427C2212yes—
131#2426C2214yes—
132#2423C2212yes—
133#2422C2214yes—
134#2422C2214yes—
135#2422C2212yes—
136#2422C2214yes—
137#2421C2214yes—
138#2420C2214yes—
139#2417C2214yes—
140#2417C2214yes—
141#2416C2214yes—
142#2415C2214yes—
143#2414C2214yes—
144#2407C2214yes—
145#2396C2214yes—
146#2395C2214yes—
147#2379C2218yes—
148#2369C2212yes—
149#2369C2212yes—
150#2366C2212yes—
151#2366C2211yescharacteristic
152#2366C2212yes—
153#2363C2212yes—
154#2363C2214yes—
155#2355C2212yes—
156#2355C2212yes—
157#2354C2214yes—
158#2354C2212yes—
159#2354C2214yes—
160#2354C2211yescharacteristic
161#2354C2212yes—
162Q8×C4⋊C4C2211yescharacteristic
163Q8×C4⋊C4C2212yes—
164#2349C2214yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2212yes—
167D4×C4⋊C4C2212yes—
168D4×C4⋊C4C2214yes—
169D4×C4⋊C4C2214yes—
170#2341C2212yes—
171#2339C2214yes—
172#2324C2214yes—
173#2324C2214yes—
174#2324C2214yes—
175#2324C2214yes—
176#2323C2214yes—
177#2314C2214yes—
178#2311C2218yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×#127C2212yes—
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×#121C2214yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2293C2212yes—
191C2×#389C2214yes—
192#2285C2212yes—
193#2285C2212yes—
194#2285C2212yes—
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2212yes—
199C22×#41C2312yes—
200C22×#41C2314yes—
201#554—48no—
202#552—416no—
203#550—28no—
204#547—48no—
205#532—216no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2312yes—
212C2×#127C2311yescharacteristic
213#529—48no—
214C2×#126C2314yes—
215C2×#126C2318yes—
216C2×#125C2312yes—
217C2×#125C2314yes—
218C2×#125C2312yes—
219C2×#125C2318yes—
220C2×#125C2314yes—
221C2×#124C2314yes—
222C2×#124C2312yes—
223C2×#123C2318yes—
224C2×#123C2318yes—
225C2×#123C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2318yes—
242C4×#41—48no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2314yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2312yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2311yescharacteristic
270C2×#117C2318yes—
271C2×#117C2314yes—
272C2×#117C2314yes—
273C2×#117C2314yes—
274C2×#117C2312yes—
275C2×#117C2314yes—
276C22×C4⋊C4C2314yes—
277C22×C4⋊C4C2314yes—
278C22×C4⋊C4C2318yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281C22×C42C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2314yes—
285#400C2318yes—
286#400C2314yes—
287#400C2318yes—
288#400C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#399C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#397C2314yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2314yes—
310#396C2318yes—
311#396C2318yes—
312#396C2314yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#395C2314yes—
319#395C2318yes—
320#394C2318yes—
321#394C2318yes—
322#394C2318yes—
323#394C2318yes—
324#394C2314yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2314yes—
330#393C2314yes—
331#393C2318yes—
332#392C2318yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2318yes—
337#391C2318yes—
338#391C2314yes—
339#391C2312yes—
340#391C2312yes—
341#391C2314yes—
342#391C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2312yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#390C2314yes—
351#390C2312yes—
352#390C2318yes—
353#390C2318yes—
354#390C2312yes—
355#390C2314yes—
356#390C2314yes—
357#390C2312yes—
358#390C2314yes—
359#390C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2318yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2314yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2318yes—
406#388C2314yes—
407#387C2314yes—
408#387C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2314yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2314yes—
418#387C2318yes—
419#386C2314yes—
420#386C2318yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2311yescharacteristic
444#384C2311yescharacteristic
445#384C2312yes—
446#384C2314yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#382C2312yes—
455#382C2314yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#382C2314yes—
460#381C2318yes—
461#380C2312yes—
462#380C2312yes—
463#380C2314yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2318yes—
470#380C2318yes—
471#380C2312yes—
472#380C2314yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2318yes—
482#380C2318yes—
483#380C2314yes—
484#380C2312yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522C4×C22⋊C4C2312yes—
523C2×#95C2318yes—
524C43C2312yes—
525C43C2311yescharacteristic
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—216no—
529C2×#41—48no—
530C2×#41—44no—
531C2×#41—84no—
532C22×Q8C2412yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2412yes—
535C22×Q8C2414yes—
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2418yes—
543C22×D4C2414yes—
544C22×D4C2412yes—
545C23×C4C2414yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2418yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2414yes—
555C23×C4C2418yes—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559C4⋊Q8—44no—
560C4⋊Q8—82no—
561#127—28no—
562#127#4118yes—
563#126—48no—
564#126—416no—
565#125—28no—
566#125—44no—
567#125—48no—
568#125—416no—
569#125—84no—
570#124—216no—
571#124—44no—
572#123—48no—
573#123—416no—
574#123—416no—
575C22⋊Q8—28no—
576C22⋊Q8—28no—
577C22⋊Q8—416no—
578C22⋊Q8—48no—
579C22⋊Q8—44no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582C22⋊Q8—84no—
583#121—216no—
584#121—216no—
585#121—28no—
586#121—216no—
587#121—44no—
588#121—44no—
589#121—48no—
590#121—88no—
591C4×Q8—24no—
592C4×Q8—24no—
593C4×Q8—24no—
594C4×Q8—28no—
595C4×Q8—44no—
596C4×Q8—44no—
597C4×Q8—48no—
598C4×D4—216no—
599C4×D4—216no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—28no—
604C4×D4—24no—
605C4×D4—28no—
606C4×D4—24no—
607C4×D4—24no—
608C4×D4—44no—
609C4×D4—48no—
610C4×D4—42no—
611C4×D4—44no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615C4×D4—44no—
616C4×D4—48no—
617C4×D4—48no—
618#117—48no—
619#117—48no—
620#117—48no—
621#117—44no—
622#117—48no—
623#117—416no—
624C2×C4⋊C4—216no—
625C2×C4⋊C4—48no—
626C2×C4⋊C4—88no—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2412yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2412yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2412yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2414yes—
714C2×C42—28no—
715C2×C42—28no—
716C2×C42—48no—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2411yescharacteristic
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2418yes—
734C2×C42C2414yes—
735C2×C42C2418yes—
736C2×C42C2414yes—
737C2×C42C2412yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2412yes—
747#95C2412yes—
748#95C2412yes—
749#95C2414yes—
750#95C2412yes—
751#95C2412yes—
752#95C2414yes—
753#95C2412yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2412yes—
758#95C2412yes—
759#95C2412yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2418yes—
773#95C2418yes—
774#95C2414yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778C24C2512yes—
779C24C2512yes—
780C24C2514yes—
781#41—432no—
782#41—832no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—42no—
791C2×Q8—44no—
792C2×Q8—42no—
793C2×Q8—44no—
794C2×Q82−1+414yes—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—216no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—28no—
807C2×D4—24no—
808C2×D4—22no—
809C2×D4—44no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—48no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—48no—
819C2×D4C2×#4118yes—
820C2×D4C2×#4118yes—
821C2×D4C2×#4118yes—
822C22×C4—216no—
823C22×C4—28no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—28no—
831C22×C4—216no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—28no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—28no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—42no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2514yes—
862C22×C4C2518yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2514yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2511yescharacteristic
871C22×C4C2512yes—
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C22×C4C2511yescharacteristic
877C22×C4C2511yescharacteristic
878C4⋊C4—22no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—22no—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—22no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—22no—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—24no—
903C4⋊C4—28no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—24no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—42no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—42no—
930C4⋊C4—44no—
931C4⋊C4H(5,𝔽2)14yes—
932C22⋊C4—28no—
933C22⋊C4—216no—
934C22⋊C4—216no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—48no—
955C22⋊C4—42no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—48no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C42—24no—
966C42—24no—
967C42—24no—
968C42—24no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—28no—
974C42—22no—
975C42—24no—
976C42—24no—
977C42—22no—
978C42—24no—
979C42—28no—
980C42—22no—
981C42—44no—
982C42—44no—
983C42—48no—
984C42—48no—
985C42—42no—
986C42—41no—
987C42C2×#4114yes—
988C42H(5,𝔽2)14yes—
989C422−1+414yes—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23C22×#4118yes—
1011C23C2611yescharacteristic
1012Q8—28no—
1013Q8—48no—
1014Q8—84no—
1015Q8—88no—
1016D4—216no—
1017D4—216no—
1018D4—48no—
1019D4—416no—
1020D4—44no—
1021D4—44no—
1022D4—88no—
1023D4—816no—
1024D4—88no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—28no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—28no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—48no—
1081C2×C4—416no—
1082C2×C4—432no—
1083C2×C4—48no—
1084C2×C4—48no—
1085C2×C4—48no—
1086C2×C4—416no—
1087C2×C4—48no—
1088C2×C4—84no—
1089C2×C4—88no—
1090C2×C4—168no—
1091C2×C4C22×#4112yes—
1092C2×C4C22×#4112yes—
1093C2×C4C22×#4112yes—
1094C2×C4C2×H(5,𝔽2)12yes—
1095C2×C4C2×H(5,𝔽2)14yes—
1096C2×C4C2×H(5,𝔽2)12yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×2−1+414yes—
1100C2×C4C2×2−1+412yes—
1101C2×C4C2×2−1+412yes—
1102C2×C4C2×2−1+412yes—
1103C2×C4C2×2−1+412yes—
1104C2×C4#58512yes—
1105C22—28no—
1106C22—28no—
1107C22—28no—
1108C22—44no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22C23×#4111yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×H(5,𝔽2)11yescharacteristic
1129C22C22×2−1+411yescharacteristic
1130C22C22×2−1+411yescharacteristic
1131C22C2×#58511yescharacteristic
1132C22H(7,𝔽2)11yescharacteristic
1133C4—24no—
1134C4—22no—
1135C4—24no—
1136C4—22no—
1137C4—22no—
1138C4—48no—
1139C4—42no—
1140C4—42no—
1141C4—44no—
1142C4—44no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—41no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—44no—
1152C4—44no—
1153C4#351514yes—
1154C4#352014yes—
1155C4#354814yes—
1156C2—48no—
1157C2—82no—
1158C2—82no—
1159C2C2×#354811yescharacteristic
1160C2C2×#352011yescharacteristic
1161C2C2×#351511yescharacteristic
1162C2#6293011yescharacteristic
1163C2#6294311yescharacteristic
1164C2#6298311yescharacteristic
1165C2#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. #59823C2semidirect
2. #59444C2semidirect
3. #59258C2semidirect
4. #59039C2semidirect
5. #49657C2semidirect
6. #45664C2semidirect
7. #45060C2semidirect
8. #45050C2semidirect
9. #42577C2semidirect
10. #42556C2semidirect
11. #39607C2semidirect
12. #39479C2semidirect
13. #39191C2semidirect
14. #39126C2semidirect
15. #38950C2semidirect
16. #36563C2semidirect
17. #36290C2semidirect
18. #36275C2semidirect
19. #36194C2semidirect
20. #36127C2semidirect
21. #35196C2semidirect
22. #35189C2semidirect
23. #34941C2semidirect
24. #34932C2semidirect
25. #34368C2semidirect
26. C4×#550C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#594442
#592582
#590392
#496572
#456642
#450602
#450502
#425772
#425562
#396072
#394792
#391912
#391262
#389502
#365632
#362902
#362752
#361942
#361272
#351962
#351892
#349412
#349322
#343682
C4×#5502