Finite Group Databasebeta

← #7987057

Subgroups — #7987057

Order 512.

4617 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59435C212yesmaximal, complemented
3#59312C212yesmaximal, complemented
4#59258C212yesmaximal, complemented
5#50429C218yesmaximal, complemented
6#46180C214yesmaximal, complemented
7#45030C214yesmaximal, complemented
8#44956C214yesmaximal, complemented
9#42939C214yesmaximal, complemented
10#42773C214yesmaximal, complemented
11#39955C214yesmaximal, complemented
12#39737C212yesmaximal, complemented
13#39642C212yesmaximal, complemented
14#39489C212yesmaximal
15#38932C212yesmaximal, complemented
16#36593C211yesmaximal, characteristic, complemented
17#36314C212yesmaximal, complemented
18#36287C212yesmaximal, complemented
19#36194C211yesmaximal, characteristic, complemented
20#36180C211yesmaximal, characteristic, complemented
21#35286C212yesmaximal, complemented
22#35202C212yesmaximal, complemented
23#34945C211yesmaximal, characteristic, complemented
24#34941C211yesmaximal, characteristic, complemented
25#34484C212yesmaximal, complemented
26C4×#555C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#555C2211yescharacteristic
29C2×#554C2212yes—
30C2×#552C2214yes—
31#2868C2212yes—
32#2868C2211yescharacteristic
33#2864C2214yes—
34#2859C2214yes—
35#2859C2214yes—
36#2857C2212yes—
37#2857C2212yes—
38#2836C2218yes—
39#2806C2214yes—
40#2775C2218yes—
41#2772C2218yes—
42#2766C2218yes—
43#2765C2218yes—
44#2764C2218yes—
45#2741C2218yes—
46#2721C2218yes—
47#2719C2218yes—
48#2713C2218yes—
49#2713C2218yes—
50#2707C2218yes—
51#2695C2218yes—
52#2694C2218yes—
53#2687C2218yes—
54#2674C2218yes—
55#2674C2218yes—
56#2667C2218yes—
57#2664C2218yes—
58#2647C2214yes—
59#2647C2218yes—
60#2620C2214yes—
61#2612C2218yes—
62#2611C2218yes—
63#2606C2218yes—
64#2604C2218yes—
65#2584C2214yes—
66#2582C2214yes—
67#2574C2214yes—
68#2573C2214yes—
69#2571C2214yes—
70#2571C2212yes—
71#2571C2211yescharacteristic
72#2568C2211yescharacteristic
73#2567C2212yes—
74#2567C2212yes—
75#2567C2211yescharacteristic
76#2563C2211yescharacteristic
77#2563C2212yes—
78#2562C2214yes—
79#2556C2218yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2214yes—
83#2552C2212yes—
84#2552C2212yes—
85#2552C2212yes—
86#2552C2211yescharacteristic
87#2552C2214yes—
88#2552C2214yes—
89#2552C2212yes—
90#2552C2214yes—
91#2547C2211yescharacteristic
92#2546C2212yes—
93#2546C2214yes—
94#2538C2212yes—
95#2538C2211yescharacteristic
96#2538C2211yescharacteristic
97#2533C2218yes—
98#2530C2218yes—
99#2514C2212yes—
100#2512C2214yes—
101#2511C2214yes—
102#2511C2214yes—
103#2508C2212yes—
104#2507C2214yes—
105#2506C2214yes—
106#2506C2214yes—
107#2502C2214yes—
108#2501C2214yes—
109#2499C2214yes—
110#2497C2214yes—
111#2497C2214yes—
112#2497C2212yes—
113#2496C2214yes—
114#2495C2214yes—
115#2495C2214yes—
116#2494C2212yes—
117#2492C2214yes—
118#2486C2214yes—
119#2485C2214yes—
120#2475C2218yes—
121#2454C2212yes—
122#2448C2214yes—
123#2447C2212yes—
124#2442C2214yes—
125#2442C2214yes—
126#2442C2218yes—
127#2441C2214yes—
128#2441C2214yes—
129#2441C2214yes—
130#2441C2214yes—
131#2441C2214yes—
132#2440C2214yes—
133#2440C2214yes—
134#2439C2214yes—
135#2423C2212yes—
136#2423C2214yes—
137#2422C2214yes—
138#2422C2214yes—
139#2421C2212yes—
140#2421C2214yes—
141#2413C2218yes—
142#2401C2214yes—
143#2396C2214yes—
144#2378C2218yes—
145#2372C2214yes—
146#2370C2214yes—
147#2369C2212yes—
148#2369C2212yes—
149#2369C2211yescharacteristic
150#2365C2212yes—
151#2363C2212yes—
152#2363C2212yes—
153#2362C2214yes—
154#2356C2214yes—
155#2355C2212yes—
156#2354C2211yescharacteristic
157#2354C2212yes—
158#2354C2211yescharacteristic
159#2354C2214yes—
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2212yes—
162Q8×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2212yes—
165#2346C2212yes—
166#2346C2214yes—
167#2346C2212yes—
168#2344C2214yes—
169#2330C2214yes—
170#2330C2214yes—
171#2323C2218yes—
172#2323C2214yes—
173#2319C2214yes—
174#2317C2214yes—
175#2316C2214yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2211yescharacteristic
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×#125C2212yes—
181C4×#124C2214yes—
182C4×#124C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×#121C2212yes—
186C4×#121C2212yes—
187#2295C2214yes—
188#2295C2212yes—
189#2293C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192C2×#384C2212yes—
193#2283C2212yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C4×#117C2212yes—
198C4×#117C2212yes—
199#557—48no—
200#555—28no—
201#554—216no—
202#552—416no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2312yes—
211C2×#126C2318yes—
212C2×#125C2312yes—
213C2×#125C2314yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2318yes—
217C2×#125C2318yes—
218C2×#125C2318yes—
219C2×#124C2314yes—
220C2×#124C2312yes—
221C2×#123C2318yes—
222C2×#123C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2314yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2314yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2314yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2318yes—
253C2×#117C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2314yes—
257C22×C42C2312yes—
258C22×C42C2312yes—
259#401C2314yes—
260#400C2318yes—
261#400C2314yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2314yes—
269#400C2318yes—
270#400C2318yes—
271#399C2318yes—
272#399C2318yes—
273#399C2314yes—
274#399C2318yes—
275#398C2314yes—
276#398C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#397C2314yes—
290#397C2314yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2314yes—
295#397C2318yes—
296#396C2314yes—
297#396C2314yes—
298#396C2318yes—
299#396C2318yes—
300#396C2318yes—
301#396C2314yes—
302#396C2318yes—
303#395C2314yes—
304#395C2318yes—
305#395C2318yes—
306#394C2318yes—
307#394C2318yes—
308#393C2314yes—
309#393C2318yes—
310#391C2312yes—
311#391C2312yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#391C2318yes—
323#391C2314yes—
324#391C2314yes—
325#390C2312yes—
326#390C2314yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2314yes—
331#390C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2314yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2314yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2312yes—
347#389C2312yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2312yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2314yes—
358#389C2318yes—
359#389C2318yes—
360#389C2318yes—
361#389C2314yes—
362#389C2314yes—
363#389C2312yes—
364#389C2318yes—
365#389C2318yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#389C2318yes—
374#389C2318yes—
375#389C2312yes—
376#388C2318yes—
377#388C2318yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2314yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2318yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2318yes—
392#388C2314yes—
393#388C2318yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#386C2314yes—
415#386C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2314yes—
426#384C2314yes—
427#384C2312yes—
428#384C2312yes—
429#384C2314yes—
430#384C2314yes—
431#384C2314yes—
432#384C2312yes—
433#384C2314yes—
434#384C2312yes—
435#384C2312yes—
436#384C2314yes—
437#384C2314yes—
438#384C2312yes—
439#384C2314yes—
440#383C2314yes—
441#383C2318yes—
442#382C2312yes—
443#382C2314yes—
444#382C2312yes—
445#382C2312yes—
446#382C2318yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#381C2314yes—
452#381C2318yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2314yes—
459#380C2312yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2318yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C22⋊C4C2312yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2312yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2318yes—
518#376C2314yes—
519#376C2314yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C43C2314yes—
523C22×Q8C2412yes—
524C22×Q8C2411yescharacteristic
525C22×Q8C2414yes—
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2414yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2418yes—
537C23×C4C2412yes—
538C4⋊Q8—28no—
539C4⋊Q8—24no—
540C4⋊Q8—24no—
541C4⋊Q8—24no—
542C4⋊Q8—44no—
543C4⋊Q8—48no—
544C4⋊Q8—82no—
545C4⋊Q8—84no—
546#126—416no—
547#125—216no—
548#125—28no—
549#125—48no—
550#125—416no—
551#125—48no—
552#125—416no—
553#125—88no—
554#124—216no—
555#124—44no—
556#123—416no—
557#123—88no—
558C22⋊Q8—28no—
559C22⋊Q8—28no—
560C22⋊Q8—216no—
561C22⋊Q8—232no—
562C22⋊Q8—84no—
563#121—28no—
564#121—28no—
565C4×Q8—216no—
566C4×Q8—24no—
567C4×Q8—28no—
568C4×Q8—24no—
569C4×Q8—24no—
570C4×Q8—44no—
571C4×Q8—48no—
572C4×Q8—44no—
573C4×Q8—48no—
574C4×D4—216no—
575C4×D4—24no—
576C4×D4—24no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—42no—
580C4×D4—48no—
581C4×D4#4118yes—
582#117—28no—
583#117—28no—
584#117—28no—
585#117—48no—
586#117—416no—
587#117—44no—
588#117—48no—
589C2×C4⋊C4—216no—
590C2×C4⋊C4—48no—
591C2×C4⋊C4—84no—
592C2×C4⋊C4C2412yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2414yes—
595C2×C4⋊C4C2418yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2414yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C42—28no—
675C2×C42—28no—
676C2×C42C2414yes—
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2414yes—
681C2×C42C2414yes—
682C2×C42C2411yescharacteristic
683C2×C42C2414yes—
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2418yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705#95C2412yes—
706#95C2412yes—
707#95C2414yes—
708#95C2414yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2414yes—
719#95C2418yes—
720#95C2414yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2412yes—
732#95C2414yes—
733#95C2412yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751C24C2512yes—
752C24C2512yes—
753C2×Q8—24no—
754C2×Q8—28no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—22no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—24no—
761C2×Q8—44no—
762C2×Q8—42no—
763C2×Q8—42no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—44no—
767C2×Q8H(5,𝔽2)14yes—
768C2×D4—28no—
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—44no—
775C2×D4—44no—
776C2×D4C2×#4114yes—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—216no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—24no—
784C22×C4—24no—
785C22×C4—24no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—24no—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—42no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4C2×#4118yes—
798C22×C4C2512yes—
799C22×C4C2512yes—
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2512yes—
803C22×C4C2512yes—
804C22×C4C2514yes—
805C22×C4C2512yes—
806C22×C4C2514yes—
807C22×C4C2511yescharacteristic
808C22×C4C2512yes—
809C22×C4C2514yes—
810C22×C4C2514yes—
811C22×C4C2518yes—
812C22×C4C2514yes—
813C22×C4C2511yescharacteristic
814C22×C4C2512yes—
815C22×C4C2512yes—
816C22×C4C2511yescharacteristic
817C22×C4C2511yescharacteristic
818C22×C4C2512yes—
819C22×C4C2511yescharacteristic
820C22×C4C2511yescharacteristic
821C22×C4C2511yescharacteristic
822C4⋊C4—24no—
823C4⋊C4—216no—
824C4⋊C4—28no—
825C4⋊C4—22no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—216no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—216no—
836C4⋊C4—24no—
837C4⋊C4—22no—
838C4⋊C4—28no—
839C4⋊C4—24no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—28no—
847C4⋊C4—28no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—48no—
856C4⋊C4—42no—
857C4⋊C4—48no—
858C4⋊C4—44no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—42no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—42no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—48no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4C2×#4114yes—
880C4⋊C42−1+414yes—
881C22⋊C4—28no—
882C22⋊C4—216no—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—42no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4C2×#4118yes—
904C42—28no—
905C42—28no—
906C42—216no—
907C42—28no—
908C42—24no—
909C42—22no—
910C42—24no—
911C42—24no—
912C42—24no—
913C42—24no—
914C42—24no—
915C42—24no—
916C42—28no—
917C42—22no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—28no—
923C42—22no—
924C42—44no—
925C42—48no—
926C42—48no—
927C42—44no—
928C42—41no—
929C42—42no—
930C42C2×#4114yes—
931C422−1+414yes—
932C422−1+414yes—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23C22×#4114yes—
947C23C2611yescharacteristic
948Q8—28no—
949Q8—48no—
950Q8—88no—
951Q8—84no—
952Q8—84no—
953D4—28no—
954D4—44no—
955D4—88no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—216no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—24no—
972C2×C4—24no—
973C2×C4—28no—
974C2×C4—24no—
975C2×C4—28no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—21no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—28no—
1014C2×C4—48no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4—48no—
1018C2×C4—84no—
1019C2×C4—816no—
1020C2×C4C22×#4114yes—
1021C2×C4C22×#4112yes—
1022C2×C4C22×#4112yes—
1023C2×C4C22×#4112yes—
1024C2×C4C2×H(5,𝔽2)14yes—
1025C2×C4C2×H(5,𝔽2)12yes—
1026C2×C4C2×2−1+412yes—
1027C2×C4C2×2−1+412yes—
1028C2×C4C2×2−1+414yes—
1029C2×C4C2×2−1+412yes—
1030C2×C4C2×2−1+412yes—
1031C2×C4C2×2−1+412yes—
1032C2×C4C2×2−1+412yes—
1033C2×C4C2×2−1+412yes—
1034C2×C4#58512yes—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22C23×#4111yescharacteristic
1050C22C22×H(5,𝔽2)11yescharacteristic
1051C22C22×2−1+411yescharacteristic
1052C22C22×2−1+411yescharacteristic
1053C22C22×2−1+411yescharacteristic
1054C22C2×#58511yescharacteristic
1055C22H(7,𝔽2)11yescharacteristic
1056C4—22no—
1057C4—24no—
1058C4—24no—
1059C4—22no—
1060C4—22no—
1061C4—24no—
1062C4—44no—
1063C4—48no—
1064C4—44no—
1065C4—42no—
1066C4—42no—
1067C4—44no—
1068C4—44no—
1069C4—41no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—42no—
1077C4#350914yes—
1078C4#351514yes—
1079C4#354414yes—
1080C2—44no—
1081C2—82no—
1082C2C2×#354411yescharacteristic
1083C2C2×#351511yescharacteristic
1084C2C2×#350911yescharacteristic
1085C2#6292911yescharacteristic
1086C2#6294511yescharacteristic
1087C2#6298611yescharacteristic
1088C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59435C2semidirect
3. #59312C2semidirect
4. #59258C2semidirect
5. #50429C2semidirect
6. #46180C2semidirect
7. #45030C2semidirect
8. #44956C2semidirect
9. #42939C2semidirect
10. #42773C2semidirect
11. #39955C2semidirect
12. #39737C2semidirect
13. #39642C2semidirect
15. #38932C2semidirect
16. #36593C2semidirect
17. #36314C2semidirect
18. #36287C2semidirect
19. #36194C2semidirect
20. #36180C2semidirect
21. #35286C2semidirect
22. #35202C2semidirect
23. #34945C2semidirect
24. #34941C2semidirect
25. #34484C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#594352
#593122
#592582
#504292
#461802
#450302
#449562
#429392
#427732
#399552
#397372
#396422
#394892
#389322
#365932
#363142
#362872
#361942
#361802
#352862
#352022
#349452
#349412
#344842
C4×#5552