Finite Group Databasebeta

← #7673884

Subgroups — #7673884

Order 512.

5006 conjugacy classes of subgroups.

The subgroup lattice has 1089 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45131C214yesmaximal, complemented
2#45121C214yesmaximal, complemented
3#44923C214yesmaximal, complemented
4#44908C214yesmaximal, complemented
5#39687C218yesmaximal, complemented
6#39685C218yesmaximal, complemented
7#39498C214yesmaximal, complemented
8#39493C214yesmaximal, complemented
9#37879C214yesmaximal, complemented
10#37874C214yesmaximal, complemented
11#35627C211yesmaximal, characteristic, complemented
12#35620C211yesmaximal, characteristic, complemented
13#35555C211yesmaximal, characteristic, complemented
14#35532C211yesmaximal, characteristic, complemented
15#35334C211yesmaximal, characteristic, complemented
16#35330C211yesmaximal, characteristic, complemented
17#35224C211yesmaximal, characteristic, complemented
18#35151C211yesmaximal, characteristic, complemented
19#34634C211yesmaximal, characteristic, complemented
20#34214C211yesmaximal, characteristic, complemented
21#34201C211yesmaximal, characteristic
22#34200C211yesmaximal, characteristic
23#34183C211yesmaximal, characteristic, complemented
24#34065C211yesmaximal, characteristic
25C2×#2317C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2862C2212yescomplemented
37#2859C2212yescomplemented
38#2855C2214yes—
39#2851C2214yescomplemented
40#2848C2214yes—
41#2807C2218yes—
42#2807C2218yescomplemented
43#2806C2218yescomplemented
44#2805C2218yescomplemented
45#2804C2218yes—
46#2792C2218yescomplemented
47#2791C2218yescomplemented
48#2790C2218yes—
49#2788C2218yes—
50#2788C2218yescomplemented
51#2788C2218yescomplemented
52#2784C2218yes—
53#2780C2218yes—
54#2768C2218yescomplemented
55#2732C2218yes—
56#2720C2218yes—
57#2660C2212yescomplemented
58#2660C2212yescomplemented
59#2629C2212yes—
60#2629C2212yes—
61#2628C2212yes—
62#2628C2212yes—
63#2628C2214yescomplemented
64#2627C2214yes—
65#2627C2214yes—
66#2626C2214yes—
67#2626C2214yes—
68#2589C2218yes—
69#2589C2218yescomplemented
70#2588C2218yescomplemented
71#2587C2218yes—
72#2585C2218yescomplemented
73#2584C2218yescomplemented
74#2583C2218yescomplemented
75#2581C2214yescomplemented
76#2580C2218yes—
77#2580C2214yescomplemented
78#2579C2218yes—
79#2574C2218yes—
80#2571C2214yescomplemented
81#2570C2214yescomplemented
82#2570C2214yescomplemented
83#2568C2212yescomplemented
84#2567C2212yescomplemented
85#2566C2212yescomplemented
86#2566C2212yescomplemented
87#2565C2212yescomplemented
88#2565C2212yescomplemented
89#2564C2218yes—
90#2563C2212yescomplemented
91#2552C2214yescomplemented
92#2550C2214yescomplemented
93#2550C2214yescomplemented
94#2549C2218yes—
95#2542C2212yescomplemented
96#2509C2218yescomplemented
97#2509C2214yescomplemented
98#2508C2214yescomplemented
99#2507C2214yescomplemented
100#2506C2214yescomplemented
101#2505C2218yes—
102#2473C2218yes—
103#2473C2218yescomplemented
104#2465C2218yes—
105#2465C2218yescomplemented
106#2454C2218yes—
107#2450C2218yes—
108#2449C2218yes—
109#2449C2218yes—
110#2442C2214yes—
111#2442C2214yes—
112#2442C2214yescomplemented
113#2441C2214yes—
114#2441C2214yes—
115#2441C2214yescomplemented
116#2440C2214yes—
117#2440C2214yes—
118#2440C2214yescomplemented
119#2439C2214yes—
120#2439C2214yes—
121#2439C2214yescomplemented
122#2396C2214yes—
123#2396C2214yes—
124#2363C2214yes—
125#2362C2214yes—
126#2361C2214yes—
127#2360C2218yes—
128#2360C2214yes—
129#2355C2214yescomplemented
130#2354C2214yes—
131#2352C2214yes—
132#2352C2214yes—
133Q8×C4⋊C4C2214yescomplemented
134Q8×C4⋊C4C2214yescomplemented
135D4×C4⋊C4C2218yes—
136D4×C4⋊C4C2214yes—
137D4×C4⋊C4C2214yescomplemented
138#2330C2214yescomplemented
139#2324C2212yes—
140#2324C2212yes—
141#2323C2212yes—
142#2323C2212yes—
143#2322C2214yes—
144#2322C2214yes—
145#2321C2214yes—
146#2321C2214yes—
147#2317C2211yescharacteristic
148#2317C2211yescharacteristic
149#2317C2214yes—
150#2317C2214yes—
151#2317C2214yes—
152#2317C2214yes—
153#2317C2211yescharacteristic
154#2317C2211yescharacteristic
155#2317C2211yescharacteristic
156#2317C2211yescharacteristic
157#2317C2212yescomplemented
158#2317C2212yescomplemented
159#2316C2211yescharacteristic
160#2316C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163C4×C4⋊Q8C2214yescomplemented
164C4×#123C2214yes—
165C4×#120C2214yes—
166#2297C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170#2293C2214yes—
171C2×#389C2214yes—
172#2290C2214yes—
173C2×#385C2214yes—
174#2285C2211yescharacteristic
175#2285C2212yescomplemented
176C2×#384C2211yescharacteristic
177C2×#384C2211yescharacteristic
178C2×#384C2212yescomplemented
179C2×#382C2211yescharacteristic
180C2×#382C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C4×#117C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C24×C4C2311yescharacteristic
189C24×C4C2312yes—
190#544—44no—
191#544—44no—
192#533—28no—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×#125C2312yes—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2318yes—
204#525Q8116yescomplemented
205C2×#123C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2314yes—
209C2×C22⋊Q8C2318yes—
210C2×C22⋊Q8C2318yes—
211C2×C22⋊Q8C2312yes—
212C2×#121C2312yes—
213C2×#120C2312yes—
214#520—44no—
215#520—44no—
216C4×#41—28no—
217C2×C4×Q8C2312yes—
218C2×C4×Q8C2314yes—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2318yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2312yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2314yes—
230C2×#117—28no—
231C2×#117—44no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—44no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2312yes—
254C22×C4⋊C4C2314yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2318yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C22⋊C4C2312yes—
263C22×C22⋊C4C2312yes—
264C22×C42C2312yes—
265C22×C42C2311yescharacteristic
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#399C2318yes—
278#399C2318yes—
279#399C2318yes—
280#399C2314yes—
281#399C2314yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#398C2314yes—
291#398C2318yes—
292#398C2314yes—
293#398C2318yes—
294#398C2314yes—
295#398C2318yes—
296#396C2318yes—
297#396C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#396C2314yes—
302#396C2318yes—
303#396C2314yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2314yes—
310#395C2314yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2314yes—
315#393C2314yes—
316#391C2318yes—
317#391C2311yescharacteristic
318#391C2311yescharacteristic
319#391C2312yes—
320#391C2312yes—
321#391C2318yes—
322#391C2318yes—
323#391C2318yes—
324#391C2318yes—
325#390C2311yescharacteristic
326#390C2312yes—
327#390C2311yescharacteristic
328#390C2312yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2312yes—
341#389C2318yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2312yes—
358#389C2312yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2318yes—
365#389C2312yes—
366#388C2314yes—
367#388C2318yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
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#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#386C2314yes—
393#386C2314yes—
394#386C2314yes—
395#386C2314yes—
396#386C2318yes—
397#386C2314yes—
398#386C2318yes—
399#385C2318yes—
400#385C2318yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2314yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2314yes—
423#385C2314yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#384C2314yes—
431#384C2312yes—
432#384C2312yes—
433#384C2314yes—
434#384C2312yes—
435#384C2312yes—
436#384C2318yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382C2312yes—
440#382C2312yes—
441#382C2312yes—
442#382C2312yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2314yes—
447#382C2312yes—
448#382C2318yes—
449#382C2314yes—
450#382C2312yes—
451#382C2312yes—
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#381C2312yes—
455#381C2312yes—
456#381C2312yes—
457#380C2318yes—
458#380C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2318yes—
463#380C2312yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2318yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#379C2312yes—
472#379C2312yes—
473#379C2312yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498#376C2312yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C43C2312yes—
502C25C2411yescharacteristic
503C2×#41—24no—
504C2×#41—24no—
505C2×#41C2×Q818yes—
506C22×Q8C2411yescharacteristic
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×Q8C2414yes—
510C22×D4C2412yes—
511C22×D4C2411yescharacteristic
512C22×D4C2414yes—
513C23×C4—24no—
514C23×C4—24no—
515C23×C4—44no—
516C23×C4—84no—
517C23×C4C2×Q818yes—
518C23×C4C2411yescharacteristic
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2412yes—
523C23×C4C2412yes—
524C23×C4C2412yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2414yes—
528C23×C4C2414yes—
529C23×C4C2414yes—
530C23×C4C2418yes—
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C4⋊Q8—28no—
534C4⋊Q8—44no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537C4⋊Q8—44no—
538#125—28no—
539#125—44no—
540#125—44no—
541#125—44no—
542#125—44no—
543#125—88no—
544#123C2×Q8116yes—
545C22⋊Q8—216no—
546C22⋊Q8—48no—
547C22⋊Q8—48no—
548C22⋊Q8—88no—
549C22⋊Q8—88no—
550C22⋊Q8C2×Q8116yes—
551#121C2×Q8116yes—
552#120C2×Q8116yes—
553C4×Q8—28no—
554C4×Q8—216no—
555C4×Q8—44no—
556C4×Q8—44no—
557C4×Q8—88no—
558C4×D4—216no—
559C4×D4—28no—
560C4×D4—44no—
561C4×D4—44no—
562C4×D4—48no—
563C4×D4—48no—
564C4×D4—88no—
565C4×D4C2×Q8132yes—
566#117—24no—
567#117—24no—
568#117—24no—
569#117—24no—
570#117—24no—
571#117—24no—
572#117—28no—
573#117—28no—
574#117—28no—
575#117—28no—
576#117—28no—
577#117—48no—
578#117—48no—
579#117—44no—
580#117—44no—
581#117C2×Q818yes—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4—24no—
587C2×C4⋊C4—48no—
588C2×C4⋊C4—48no—
589C2×C4⋊C4—44no—
590C2×C4⋊C4—44no—
591C2×C4⋊C4—44no—
592C2×C4⋊C4—84no—
593C2×C4⋊C4—88no—
594C2×C4⋊C4—84no—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2412yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C22⋊C4—28no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C42—24no—
681C2×C42—28no—
682C2×C42—44no—
683C2×C42#4118yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2414yes—
694C2×C42C2418yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2418yes—
698C2×C42C2414yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2418yes—
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2418yes—
714#95C2418yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2418yes—
738#95C2418yes—
739C24—22no—
740C24—22no—
741C24—42no—
742C24—42no—
743C24C22×Q814yes—
744C24C2512yes—
745C24C2512yes—
746C24C2511yescharacteristic
747#41—232no—
748C2×Q8—22no—
749C2×Q8—28no—
750C2×Q8—22no—
751C2×Q8—44no—
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—48no—
756C2×Q8—48no—
757C2×Q8C22×Q814yes—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4C22×Q818yes—
765C2×D4C22×Q814yes—
766C2×D4C22×Q8116yes—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—232no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—28no—
782C22×C4—42no—
783C22×C4—44no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—44no—
787C22×C4—42no—
788C22×C4—48no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—816no—
800C22×C4C22×Q818yes—
801C22×C4C22×Q818yes—
802C22×C4C22×Q818yes—
803C22×C4C22×Q814yes—
804C22×C4C22×Q814yes—
805C22×C4C2×#4118yes—
806C22×C4C2×#4114yes—
807C22×C4H(5,𝔽2)14yes—
808C22×C4C2512yes—
809C22×C4C2512yes—
810C22×C4C2514yes—
811C22×C4C2514yes—
812C22×C4C2514yes—
813C22×C4C2512yes—
814C22×C4C2514yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2512yes—
819C22×C4C2514yes—
820C22×C4C2514yes—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C4⋊C4—24no—
831C4⋊C4—24no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—28no—
840C4⋊C4—28no—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—48no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—48no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—48no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—48no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4C22×Q818yes—
885C4⋊C4C22×Q8116yes—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—24no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—24no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—28no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4C22×Q818yes—
911C22⋊C4C22×Q8116yes—
912C22⋊C4C22×Q8116yes—
913C42—22no—
914C42—22no—
915C42—24no—
916C42—24no—
917C42—28no—
918C42—24no—
919C42—24no—
920C42—24no—
921C42—24no—
922C42—24no—
923C42—48no—
924C42—44no—
925C42—44no—
926C42—44no—
927C42—48no—
928C42—44no—
929C42—48no—
930C42C22×Q818yes—
931C42C2×#4114yes—
932C42C2×#4114yes—
933C42C2×#4118yes—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—22no—
946C23—28no—
947C23—48no—
948C23—44no—
949C23—48no—
950C23—44no—
951C23C23×Q814yes—
952C23C23×Q814yes—
953C23C23×Q812yes—
954C23C22×#4112yes—
955C23C2×H(5,𝔽2)12yes—
956C23C2611yescharacteristic
957Q8—28no—
958Q8—416no—
959Q8—164no—
960Q8—164no—
961D4—216no—
962D4—28no—
963D4—416no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—24no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—22no—
974C2×C4—28no—
975C2×C4—216no—
976C2×C4—216no—
977C2×C4—216no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—24no—
981C2×C4—24no—
982C2×C4—24no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—28no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—48no—
1014C2×C4—416no—
1015C2×C4—48no—
1016C2×C4—84no—
1017C2×C4—84no—
1018C2×C4—84no—
1019C2×C4—84no—
1020C2×C4—816no—
1021C2×C4—164no—
1022C2×C4—164no—
1023C2×C4#554116yes—
1024C2×C4C23×Q818yes—
1025C2×C4C23×Q814yes—
1026C2×C4C23×Q814yes—
1027C2×C4C23×Q812yes—
1028C2×C4C23×Q812yes—
1029C2×C4C22×#4114yes—
1030C2×C4C22×#4114yes—
1031C2×C4C22×#4112yes—
1032C2×C4C22×#4112yes—
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C22—24no—
1036C22—24no—
1037C22—22no—
1038C22—22no—
1039C22—24no—
1040C22—28no—
1041C22—24no—
1042C22—24no—
1043C22—24no—
1044C22—416no—
1045C22—44no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22C2×#55414yes—
1053C22C24×Q811yescharacteristic
1054C22C23×#4111yescharacteristic
1055C22C22×H(5,𝔽2)11yescharacteristic
1056C22H(7,𝔽2)12yes—
1057C222−1+612yes—
1058C4—24no—
1059C4—24no—
1060C4—28no—
1061C4—24no—
1062C4—24no—
1063C4—42no—
1064C4—44no—
1065C4—42no—
1066C4—44no—
1067C4—44no—
1068C4—44no—
1069C4—44no—
1070C4—44no—
1071C4—42no—
1072C4—42no—
1073C4—42no—
1074C4—42no—
1075C4—44no—
1076C4—42no—
1077C4—42no—
1078C4C2×#55414yes—
1079C4C2×#55414yes—
1080C2—24no—
1081C2—44no—
1082C2—44no—
1083C2C22×#55411yescharacteristic
1084C2#6284512yes—
1085C2#6285412yes—
1086C2#6287611yescharacteristic
1087C2#6288711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45131C2semidirect
2. #45121C2semidirect
3. #44923C2semidirect
4. #44908C2semidirect
5. #39687C2semidirect
6. #39685C2semidirect
7. #39498C2semidirect
8. #39493C2semidirect
9. #37879C2semidirect
10. #37874C2semidirect
11. #35627C2semidirect
12. #35620C2semidirect
13. #35555C2semidirect
14. #35532C2semidirect
15. #35334C2semidirect
16. #35330C2semidirect
17. #35224C2semidirect
18. #35151C2semidirect
19. #34634C2semidirect
20. #34214C2semidirect
23. #34183C2semidirect
25. C2×#2317C2semidirect
36. #2862C22semidirect
37. #2859C22semidirect
39. #2851C22semidirect
42. #2807C22semidirect
43. #2806C22semidirect
44. #2805C22semidirect
46. #2792C22semidirect
47. #2791C22semidirect
50. #2788C22semidirect
51. #2788C22semidirect
54. #2768C22semidirect
57. #2660C22semidirect
58. #2660C22semidirect
63. #2628C22semidirect
69. #2589C22semidirect
70. #2588C22semidirect
72. #2585C22semidirect
73. #2584C22semidirect
74. #2583C22semidirect
75. #2581C22semidirect
77. #2580C22semidirect
80. #2571C22semidirect
81. #2570C22semidirect
82. #2570C22semidirect
83. #2568C22semidirect
84. #2567C22semidirect
85. #2566C22semidirect
86. #2566C22semidirect
87. #2565C22semidirect
88. #2565C22semidirect
90. #2563C22semidirect
91. #2552C22semidirect
92. #2550C22semidirect
93. #2550C22semidirect
95. #2542C22semidirect
96. #2509C22semidirect
97. #2509C22semidirect
98. #2508C22semidirect
99. #2507C22semidirect
100. #2506C22semidirect
103. #2473C22semidirect
105. #2465C22semidirect
112. #2442C22semidirect
115. #2441C22semidirect
118. #2440C22semidirect
121. #2439C22semidirect
129. #2355C22semidirect
133. Q8×C4⋊C4C22semidirect
134. Q8×C4⋊C4C22semidirect
137. D4×C4⋊C4C22semidirect
138. #2330C22semidirect
157. #2317C22semidirect
158. #2317C22semidirect
163. C4×C4⋊Q8C22semidirect
175. #2285C22semidirect
178. C2×#384C22semidirect
204. #525Q8semidirect

Maximal subgroups

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

subgroupindex
#451312
#451212
#449232
#449082
#396872
#396852
#394982
#394932
#378792
#378742
#356272
#356202
#355552
#355322
#353342
#353302
#352242
#351512
#346342
#342142
#342012
#342002
#341832
#340652
C2×#23172