Finite Group Databasebeta

← #7679719

Subgroups — #7679719

Order 512.

4732 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59440C214yesmaximal, complemented
2#59329C212yesmaximal, complemented
3#59309C214yesmaximal, complemented
4#59302C212yesmaximal, complemented
5#59256C212yesmaximal, complemented
6#59211C212yesmaximal, complemented
7#45145C214yesmaximal, complemented
8#44958C214yesmaximal, complemented
9#43153C218yesmaximal, complemented
10#38931C212yesmaximal, complemented
11#38930C212yesmaximal, complemented
12#38279C214yesmaximal, complemented
13#38278C214yesmaximal, complemented
14#36314C212yesmaximal, complemented
15#36301C212yesmaximal, complemented
16#35618C212yesmaximal
17#35545C212yesmaximal, complemented
18#35339C212yesmaximal, complemented
19#35280C211yesmaximal, characteristic, complemented
20#34947C211yesmaximal, characteristic, complemented
21C2×#2571C211yesmaximal, characteristic, complemented
22#34253C212yesmaximal, complemented
23#34213C211yesmaximal, characteristic, complemented
24#34183C211yesmaximal, characteristic, complemented
25#34121C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic
27C2×#537C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C2×#520C2212yes—
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32#2864C2214yes—
33#2864C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2794C2218yes—
37#2793C2218yes—
38#2779C2218yes—
39#2772C2218yes—
40#2770C2218yes—
41#2766C2218yes—
42#2761C2218yes—
43#2758C2218yes—
44#2743C2218yes—
45#2739C2218yes—
46#2738C2218yes—
47#2698C2218yes—
48#2647C2214yes—
49#2647C2214yes—
50#2629C2214yes—
51#2601C2218yes—
52#2590C2218yes—
53#2582C2212yes—
54#2582C2212yes—
55#2571C2212yes—
56#2571C2212yes—
57#2571C2214yes—
58#2571C2212yes—
59#2571C2214yes—
60#2571C2212yes—
61#2570C2214yes—
62#2570C2214yes—
63#2570C2214yes—
64#2570C2214yes—
65#2570C2214yes—
66#2569C2218yes—
67#2569C2218yes—
68#2568C2211yescharacteristic
69#2567C2211yescharacteristic
70#2566C2212yes—
71#2565C2212yes—
72#2564C2214yes—
73#2563C2211yescharacteristic
74#2542C2211yescharacteristic
75#2538C2212yes—
76#2538C2212yes—
77#2536C2214yes—
78#2533C2218yes—
79#2530C2218yes—
80#2529C2218yes—
81#2528C2218yes—
82#2527C2218yes—
83#2525C2218yes—
84#2515C2218yes—
85#2514C2214yes—
86#2513C2214yes—
87#2512C2214yes—
88#2511C2214yes—
89#2511C2214yes—
90#2510C2218yes—
91#2508C2214yes—
92#2504C2214yes—
93#2503C2214yes—
94#2503C2214yes—
95#2500C2214yes—
96#2499C2214yes—
97#2499C2214yes—
98#2497C2214yes—
99#2496C2214yes—
100#2496C2214yes—
101#2495C2214yes—
102#2495C2214yes—
103#2494C2214yes—
104#2494C2214yes—
105#2485C2214yes—
106#2484C2218yes—
107#2481C2218yes—
108#2481C2218yes—
109#2477C2218yes—
110#2444C2218yes—
111#2444C2218yes—
112#2421C2214yes—
113#2421C2214yes—
114#2421C2214yes—
115#2420C2214yes—
116#2420C2214yes—
117#2417C2214yes—
118#2417C2212yes—
119#2417C2214yes—
120#2417C2212yes—
121#2417C2214yes—
122#2396C2214yes—
123C2×#400C2214yes—
124#2370C2214yes—
125#2369C2212yes—
126#2365C2212yes—
127#2362C2214yes—
128#2357C2212yes—
129#2356C2212yes—
130#2356C2214yes—
131#2355C2211yescharacteristic
132#2355C2211yescharacteristic
133#2355C2214yes—
134#2355C2212yes—
135#2354C2211yescharacteristic
136#2354C2211yescharacteristic
137#2353C2214yes—
138#2353C2218yes—
139#2352C2212yes—
140#2352C2218yes—
141#2352C2212yes—
142#2352C2214yes—
143Q8×C4⋊C4C2212yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146D4×C4⋊C4C2212yes—
147D4×C4⋊C4C2214yes—
148D4×C4⋊C4C2212yes—
149D4×C4⋊C4C2214yes—
150#2347C2214yes—
151#2346C2214yes—
152#2345C2214yes—
153#2344C2214yes—
154#2344C2214yes—
155#2329C2214yes—
156#2325C2214yes—
157#2324C2212yes—
158#2324C2212yes—
159#2323C2212yes—
160#2323C2212yes—
161#2320C2214yes—
162#2319C2214yes—
163#2317C2212yes—
164#2317C2212yes—
165#2317C2214yes—
166#2316C2211yescharacteristic
167#2316C2212yes—
168#2311C2212yes—
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2212yes—
173C4×C22⋊Q8C2214yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×#121C2212yes—
177C4×#121C2214yes—
178C4×#121C2212yes—
179#2298C2214yes—
180#2297C2212yes—
181#2297C2212yes—
182#2295C2214yes—
183#2293C2214yes—
184C2×#389C2212yes—
185C2×#389C2212yes—
186#2285C2212yes—
187#2285C2211yescharacteristic
188#2285C2212yes—
189C2×#384C2211yescharacteristic
190C2×#384C2212yes—
191#2283C2212yes—
192C2×#382C2212yes—
193C2×#382C2212yes—
194#2274C2212yes—
195C4×#117C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201#537—28no—
202#533—28no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×#126C2318yes—
206C2×#125C2312yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2314yes—
215C2×#121C2312yes—
216C2×#121C2312yes—
217C2×#121C2314yes—
218#520—216no—
219C4×#41—28no—
220C4×#41—28no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2314yes—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2314yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2312yes—
235C2×C4×D4C2318yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2314yes—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2314yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2318yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2314yes—
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265C22×C42C2311yescharacteristic
266#401C2318yes—
267#400C2314yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#396C2314yes—
298#396C2314yes—
299#396C2318yes—
300#396C2318yes—
301#396C2318yes—
302#395C2314yes—
303#394C2318yes—
304#394C2318yes—
305#393C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2312yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2318yes—
316#391C2312yes—
317#391C2312yes—
318#391C2314yes—
319#390C2312yes—
320#390C2312yes—
321#390C2312yes—
322#390C2312yes—
323#390C2314yes—
324#390C2314yes—
325#390C2312yes—
326#390C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2314yes—
335#389C2318yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2314yes—
343#389C2312yes—
344#389C2312yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2318yes—
354#389C2314yes—
355#388C2318yes—
356#388C2318yes—
357#388C2314yes—
358#388C2314yes—
359#388C2314yes—
360#388C2314yes—
361#388C2314yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#387C2314yes—
373#387C2314yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2314yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2314yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#387C2318yes—
399#387C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2314yes—
406#386C2314yes—
407#386C2318yes—
408#386C2314yes—
409#386C2314yes—
410#386C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2314yes—
418#385C2314yes—
419#384C2312yes—
420#384C2312yes—
421#384C2314yes—
422#384C2314yes—
423#384C2314yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2314yes—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#383C2318yes—
432#383C2314yes—
433#383C2318yes—
434#382C2312yes—
435#382C2312yes—
436#382C2314yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2314yes—
445#382C2318yes—
446#382C2312yes—
447#382C2318yes—
448#382C2312yes—
449#381C2318yes—
450#381C2318yes—
451#381C2314yes—
452#381C2318yes—
453#380C2312yes—
454#380C2312yes—
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2318yes—
465#380C2318yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2312yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2318yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515#376C2314yes—
516#376C2318yes—
517#376C2314yes—
518C2×#95C2312yes—
519C2×#95C2314yes—
520C2×#95C2314yes—
521C2×#95C2312yes—
522C2×#95C2314yes—
523C43C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41#4118yes—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2411yescharacteristic
533C22×Q8C2412yes—
534C22×D4C2412yes—
535C22×D4C2411yescharacteristic
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2411yescharacteristic
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2418yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C4⋊Q8—24no—
555C4⋊Q8—24no—
556#126—88no—
557#125—28no—
558C22⋊Q8—28no—
559C22⋊Q8—28no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—48no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—84no—
566#121—28no—
567#121—216no—
568#121—28no—
569C4×Q8—216no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—48no—
577C4×D4—216no—
578C4×D4—232no—
579C4×D4—28no—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—28no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—48no—
588#117—24no—
589#117—24no—
590#117—216no—
591#117—28no—
592#117—28no—
593#117—28no—
594#117—28no—
595#117—44no—
596#117—44no—
597#117—88no—
598C2×C4⋊C4—216no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—48no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4—42no—
605C2×C4⋊C4—42no—
606C2×C4⋊C4—82no—
607C2×C4⋊C4—84no—
608C2×C4⋊C4—84no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C42—28no—
687C2×C42—28no—
688C2×C42—28no—
689C2×C42—44no—
690C2×C42#4118yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2412yes—
717#95C2418yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2414yes—
722#95C2414yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2414yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24C2512yes—
763C24C2512yes—
764C24C2511yescharacteristic
765#41—232no—
766#41—416no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8C2×#4114yes—
779C2×D4—24no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4C2×#4118yes—
793C2×D4C2×#4114yes—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—216no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—41no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—48no—
824C22×C4—44no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4C2×#4114yes—
834C22×C4C2×#4118yes—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4C2×#4114yes—
838C22×C42−1+414yes—
839C22×C4C2512yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2512yes—
844C22×C4C2514yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2518yes—
855C22×C4C2512yes—
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—216no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C22⋊C4—216no—
915C22⋊C4—28no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—28no—
925C22⋊C4—44no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—216no—
946C42—28no—
947C42—28no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—28no—
953C42—44no—
954C42—44no—
955C42—44no—
956C42—44no—
957C42—44no—
958C42—48no—
959C42—48no—
960C42C2×#4114yes—
961C42C2×#4114yes—
962C42C2×#4114yes—
963C42C2×#4114yes—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23C22×#4114yes—
982C23C22×#4112yes—
983C23C22×#4112yes—
984C23C2×2−1+412yes—
985C23C2611yescharacteristic
986Q8—28no—
987Q8—44no—
988Q8—48no—
989Q8—84no—
990D4—216no—
991D4—28no—
992D4—48no—
993D4—44no—
994D4—88no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—216no—
1004C2×C4—28no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—28no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—28no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—44no—
1054C2×C4—48no—
1055C2×C4—48no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—84no—
1059C2×C4—84no—
1060C2×C4—88no—
1061C2×C4—816no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4#552116yes—
1066C2×C4C22×#4114yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4#58512yes—
1078C2×C4#58512yes—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—22no—
1083C22—22no—
1084C22—22no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22C2×#55214yes—
1100C22C23×#4111yescharacteristic
1101C22C23×#4111yescharacteristic
1102C22C22×2−1+411yescharacteristic
1103C22C2×#58511yescharacteristic
1104C22C2×#58511yescharacteristic
1105C22H(7,𝔽2)11yescharacteristic
1106C222−1+611yescharacteristic
1107C4—22no—
1108C4—22no—
1109C4—22no—
1110C4—24no—
1111C4—44no—
1112C4—44no—
1113C4—44no—
1114C4—48no—
1115C4—42no—
1116C4—42no—
1117C4—44no—
1118C4—42no—
1119C4—42no—
1120C4—44no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4C2×#55214yes—
1128C4C2×#55214yes—
1129C4#351214yes—
1130C2—24no—
1131C2—44no—
1132C2—82no—
1133C2C22×#55211yescharacteristic
1134C2C2×#351211yescharacteristic
1135C2#6285611yescharacteristic
1136C2#6292911yescharacteristic
1137C2#6295911yescharacteristic
1138C2#6299511yescharacteristic
1139C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59440C2semidirect
2. #59329C2semidirect
3. #59309C2semidirect
4. #59302C2semidirect
5. #59256C2semidirect
6. #59211C2semidirect
7. #45145C2semidirect
8. #44958C2semidirect
9. #43153C2semidirect
10. #38931C2semidirect
11. #38930C2semidirect
12. #38279C2semidirect
13. #38278C2semidirect
14. #36314C2semidirect
15. #36301C2semidirect
17. #35545C2semidirect
18. #35339C2semidirect
19. #35280C2semidirect
20. #34947C2semidirect
21. C2×#2571C2semidirect
22. #34253C2semidirect
23. #34213C2semidirect
24. #34183C2semidirect
25. #34121C2semidirect

Maximal subgroups

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

subgroupindex
#594402
#593292
#593092
#593022
#592562
#592112
#451452
#449582
#431532
#389312
#389302
#382792
#382782
#363142
#363012
#356182
#355452
#353392
#352802
#349472
C2×#25712
#342532
#342132
#341832
#341212
C4×#5372