Finite Group Databasebeta

← #8429478

Subgroups — #8429478

Order 512.

4233 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C212yesmaximal, complemented
2#59828C211yesmaximal, characteristic, complemented
3#59668C212yesmaximal, complemented
4#59249C212yesmaximal, complemented
5#58725C218yesmaximal, complemented
6#53140C214yesmaximal, complemented
7#53131C214yesmaximal, complemented
8#52965C214yesmaximal, complemented
9#42713C214yesmaximal, complemented
10#42582C214yesmaximal
11#42558C214yesmaximal, complemented
12#39724C212yesmaximal, complemented
13#39643C212yesmaximal, complemented
14#39599C212yesmaximal, complemented
15#39203C212yesmaximal
16#39192C212yesmaximal
17#39181C212yesmaximal, complemented
18#37641C212yesmaximal, complemented
19#37637C212yesmaximal
20#37628C212yesmaximal
21#36598C211yesmaximal, characteristic, complemented
22#36563C211yesmaximal, characteristic, complemented
23#36194C211yesmaximal, characteristic
24#34951C211yesmaximal, characteristic, complemented
25#34929C211yesmaximal, characteristic
26#34929C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#533C2212yes—
29C2×#533C2212yes—
30#2868C2211yescharacteristic
31#2862C2212yes—
32#2859C2212yes—
33#2857C2212yes—
34#2839C2218yes—
35#2839C2218yes—
36#2839C2218yes—
37#2836C2218yes—
38#2831C2218yes—
39#2831C2218yes—
40#2822C2218yes—
41#2809C2218yes—
42#2806C2218yes—
43#2799C2218yes—
44#2798C2218yes—
45#2774C2218yes—
46#2772C2218yes—
47#2772C2218yes—
48#2767C2218yes—
49#2767C2218yes—
50#2755C2218yes—
51#2754C2218yes—
52#2726C2214yes—
53#2726C2218yes—
54#2725C2218yes—
55#2719C2218yes—
56#2716C2218yes—
57#2713C2218yes—
58#2704C2218yes—
59#2690C2218yes—
60#2654C2218yes—
61#2650C2218yes—
62#2647C2214yes—
63#2647C2214yes—
64#2644C2214yes—
65#2637C2218yes—
66#2629C2214yes—
67#2625C2214yes—
68#2625C2214yes—
69#2625C2214yes—
70#2625C2214yes—
71#2621C2218yes—
72#2621C2214yes—
73#2585C2214yes—
74#2584C2214yes—
75#2582C2211yescharacteristic
76#2582C2212yes—
77#2582C2212yes—
78#2582C2212yes—
79#2582C2214yes—
80#2581C2214yes—
81#2571C2212yes—
82#2571C2214yes—
83#2571C2212yes—
84#2570C2214yes—
85#2570C2214yes—
86#2568C2214yes—
87#2568C2214yes—
88#2568C2211yescharacteristic
89#2568C2214yes—
90#2568C2212yes—
91#2567C2212yes—
92#2563C2212yes—
93#2556C2214yes—
94#2556C2214yes—
95#2552C2212yes—
96#2552C2211yescharacteristic
97#2552C2212yes—
98#2551C2211yescharacteristic
99#2551C2214yes—
100#2551C2211yescharacteristic
101#2550C2214yes—
102#2550C2214yes—
103#2546C2214yes—
104#2546C2214yes—
105#2546C2211yescharacteristic
106#2546C2211yescharacteristic
107#2546C2211yescharacteristic
108#2546C2214yes—
109#2546C2212yes—
110#2542C2211yescharacteristic
111#2542C2211yescharacteristic
112#2538C2211yescharacteristic
113#2538C2211yescharacteristic
114#2538C2212yes—
115#2513C2214yes—
116#2513C2214yes—
117#2512C2214yes—
118#2511C2212yes—
119#2511C2214yes—
120#2511C2214yes—
121#2509C2214yes—
122#2509C2214yes—
123#2509C2212yes—
124#2508C2214yes—
125#2508C2214yes—
126#2508C2218yes—
127#2507C2214yes—
128#2507C2214yes—
129#2507C2214yes—
130#2506C2214yes—
131#2506C2212yes—
132#2506C2212yes—
133#2497C2214yes—
134#2496C2214yes—
135#2496C2214yes—
136#2492C2212yes—
137#2492C2214yes—
138#2492C2212yes—
139#2489C2214yes—
140#2489C2214yes—
141#2478C2218yes—
142#2453C2212yes—
143#2453C2214yes—
144#2452C2212yes—
145#2452C2212yes—
146#2451C2214yes—
147#2451C2218yes—
148#2451C2214yes—
149#2446C2214yes—
150#2446C2214yes—
151#2446C2214yes—
152#2446C2212yes—
153#2439C2214yes—
154#2429C2214yes—
155#2429C2214yes—
156#2429C2212yes—
157#2429C2212yes—
158#2421C2214yes—
159#2421C2214yes—
160#2402C2214yes—
161#2396C2214yes—
162#2396C2214yes—
163#2370C2214yes—
164#2369C2212yes—
165#2369C2214yes—
166#2369C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2355C2212yes—
170#2355C2212yes—
171#2355C2212yes—
172#2355C2214yes—
173#2355C2212yes—
174#2354C2212yes—
175Q8×C4⋊C4C2212yes—
176Q8×C4⋊C4C2212yes—
177#2331C2214yes—
178#2323C2214yes—
179#2323C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2211yescharacteristic
186C4×C4⋊Q8C2211yescharacteristic
187C4×C4⋊Q8C2212yes—
188C4×#125C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×C22⋊Q8C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#557—48no—
200#533—48no—
201#533—48no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2318yes—
217C2×#126C2318yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#125C2318yes—
223C2×#125C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C22×C42C2312yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2314yes—
262#400C2318yes—
263#400C2318yes—
264#400C2318yes—
265#400C2318yes—
266#400C2314yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#399C2314yes—
277#399C2314yes—
278#398C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2314yes—
301#398C2314yes—
302#398C2314yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#396C2318yes—
312#396C2314yes—
313#396C2314yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2314yes—
318#395C2318yes—
319#395C2318yes—
320#395C2318yes—
321#395C2314yes—
322#395C2314yes—
323#393C2318yes—
324#393C2314yes—
325#393C2314yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2314yes—
336#391C2314yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2314yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2314yes—
345#391C2318yes—
346#391C2314yes—
347#391C2318yes—
348#391C2312yes—
349#391C2312yes—
350#391C2318yes—
351#391C2314yes—
352#391C2314yes—
353#391C2318yes—
354#391C2318yes—
355#391C2312yes—
356#390C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2312yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#389C2312yes—
380#389C2312yes—
381#389C2314yes—
382#389C2312yes—
383#389C2314yes—
384#389C2312yes—
385#389C2318yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2318yes—
392#389C2312yes—
393#389C2312yes—
394#389C2318yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2314yes—
400#389C2312yes—
401#389C2318yes—
402#389C2318yes—
403#389C2314yes—
404#389C2318yes—
405#389C2318yes—
406#389C2314yes—
407#389C2318yes—
408#389C2312yes—
409#389C2312yes—
410#389C2312yes—
411#389C2312yes—
412#388C2314yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2318yes—
422#387C2314yes—
423#387C2314yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2314yes—
429#387C2318yes—
430#387C2318yes—
431#387C2314yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2314yes—
438#387C2314yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2314yes—
445#387C2314yes—
446#385C2314yes—
447#385C2314yes—
448#384C2311yescharacteristic
449#384C2312yes—
450#384C2312yes—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#384C2312yes—
454#384C2312yes—
455#384C2314yes—
456#384C2312yes—
457#384C2312yes—
458#384C2314yes—
459#384C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2314yes—
463#382C2318yes—
464#382C2314yes—
465#382C2318yes—
466#382C2314yes—
467#382C2314yes—
468#382C2318yes—
469#382C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476C4×C4⋊C4C2311yescharacteristic
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2314yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2318yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2312yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2314yes—
519C43C2312yes—
520C43C2312yes—
521C43C2311yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2412yes—
524C22×Q8C2412yes—
525C22×Q8C2412yes—
526C22×Q8C2411yescharacteristic
527C22×Q8C2414yes—
528C22×Q8C2414yes—
529C22×Q8C2414yes—
530C22×D4C2411yescharacteristic
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—28no—
535C4⋊Q8—28no—
536C4⋊Q8—24no—
537C4⋊Q8—24no—
538C4⋊Q8—24no—
539C4⋊Q8—28no—
540C4⋊Q8—44no—
541C4⋊Q8—44no—
542C4⋊Q8—44no—
543C4⋊Q8—44no—
544C4⋊Q8—44no—
545C4⋊Q8—44no—
546C4⋊Q8—48no—
547C4⋊Q8—88no—
548C4⋊Q8—82no—
549#126—88no—
550#125—28no—
551#125—48no—
552#125—48no—
553#125—48no—
554#125—416no—
555#125—84no—
556C22⋊Q8—28no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559C22⋊Q8—44no—
560C22⋊Q8—48no—
561C22⋊Q8—44no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C4×Q8—24no—
566C4×Q8—24no—
567C4×Q8—24no—
568C4×Q8—28no—
569C4×Q8—28no—
570C4×Q8—28no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×Q8—48no—
576C4×Q8—42no—
577C4×Q8—48no—
578C4×Q8—48no—
579C4×Q8—84no—
580C4×D4—24no—
581C4×D4—24no—
582C4×D4—24no—
583#117—48no—
584#117—48no—
585#117—84no—
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2412yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2414yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2418yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C42—28no—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2414yes—
671C2×C42C2414yes—
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2414yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2418yes—
688C2×C42C2412yes—
689C2×C42C2418yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2412yes—
702#95C2412yes—
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2414yes—
707#95C2414yes—
708#95C2412yes—
709#95C2412yes—
710#95C2414yes—
711#95C2412yes—
712#95C2412yes—
713#95C2412yes—
714#95C2412yes—
715#95C2418yes—
716#95C2418yes—
717#95C2414yes—
718#95C2414yes—
719#95C2418yes—
720#95C2418yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747C24C2512yes—
748C2×Q8—24no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—24no—
758C2×Q8—24no—
759C2×Q8—24no—
760C2×Q8—28no—
761C2×Q8—28no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—44no—
771C2×Q8—44no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—22no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—24no—
780C22×C4—24no—
781C22×C4—24no—
782C22×C4—24no—
783C22×C4—42no—
784C22×C4C2511yescharacteristic
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2512yes—
790C22×C4C2512yes—
791C22×C4C2518yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2512yes—
804C22×C4C2512yes—
805C22×C4C2511yescharacteristic
806C22×C4C2511yescharacteristic
807C22×C4C2511yescharacteristic
808C22×C4C2511yescharacteristic
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—22no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—22no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—24no—
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—24no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—24no—
838C4⋊C4—24no—
839C4⋊C4—24no—
840C4⋊C4—24no—
841C4⋊C4—28no—
842C4⋊C4—22no—
843C4⋊C4—28no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—44no—
847C4⋊C4—44no—
848C4⋊C4—42no—
849C4⋊C4—44no—
850C4⋊C4—48no—
851C4⋊C4—42no—
852C4⋊C4—44no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C4⋊C4—48no—
859C4⋊C4—48no—
860C4⋊C4—42no—
861C4⋊C4—48no—
862C4⋊C4—44no—
863C4⋊C4—48no—
864C4⋊C4—48no—
865C4⋊C4—42no—
866C4⋊C4—48no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C42−1+414yes—
876C4⋊C42−1+414yes—
877C22⋊C4—24no—
878C22⋊C4—24no—
879C22⋊C4—24no—
880C22⋊C4—28no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C42—24no—
891C42—24no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—28no—
896C42—28no—
897C42—22no—
898C42—22no—
899C42—24no—
900C42—24no—
901C42—28no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—22no—
908C42—48no—
909C42—48no—
910C42—42no—
911C42—48no—
912C42—42no—
913C42—48no—
914C42—42no—
915C42—41no—
916C42H(5,𝔽2)14yes—
917C422−1+414yes—
918C422−1+414yes—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23C2611yescharacteristic
927Q8—44no—
928Q8—48no—
929Q8—48no—
930Q8—48no—
931Q8—44no—
932Q8—88no—
933Q8—88no—
934Q8—88no—
935D4—44no—
936C2×C4—22no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—24no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—24no—
974C2×C4—24no—
975C2×C4—22no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—28no—
981C2×C4—21no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—22no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—24no—
991C2×C4—24no—
992C2×C4—28no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—48no—
998C2×C4—48no—
999C2×C4—48no—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×H(5,𝔽2)12yes—
1002C2×C4C2×H(5,𝔽2)12yes—
1003C2×C4C2×2−1+414yes—
1004C2×C4C2×2−1+412yes—
1005C2×C4C2×2−1+412yes—
1006C2×C4C2×2−1+414yes—
1007C2×C4C2×2−1+412yes—
1008C2×C4C2×2−1+412yes—
1009C2×C4C2×2−1+412yes—
1010C2×C4C2×2−1+412yes—
1011C2×C4C2×2−1+412yes—
1012C2×C4C2×2−1+412yes—
1013C2×C4#58512yes—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22C22×H(5,𝔽2)11yescharacteristic
1022C22C22×2−1+411yescharacteristic
1023C22C22×2−1+411yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C22×2−1+411yescharacteristic
1026C22C2×#58511yescharacteristic
1027C22H(7,𝔽2)11yescharacteristic
1028C4—24no—
1029C4—22no—
1030C4—22no—
1031C4—24no—
1032C4—22no—
1033C4—42no—
1034C4—42no—
1035C4—44no—
1036C4—44no—
1037C4—42no—
1038C4—44no—
1039C4—42no—
1040C4—41no—
1041C4—42no—
1042C4—42no—
1043C4—44no—
1044C4—44no—
1045C4—44no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—48no—
1050C4#354714yes—
1051C4#355014yes—
1052C4#355614yes—
1053C2—82no—
1054C2C2×#354711yescharacteristic
1055C2C2×#355011yescharacteristic
1056C2C2×#355611yescharacteristic
1057C2#6294311yescharacteristic
1058C2#6294411yescharacteristic
1059C2#6296211yescharacteristic
1060C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59869C2semidirect
2. #59828C2semidirect
3. #59668C2semidirect
4. #59249C2semidirect
5. #58725C2semidirect
6. #53140C2semidirect
7. #53131C2semidirect
8. #52965C2semidirect
9. #42713C2semidirect
11. #42558C2semidirect
12. #39724C2semidirect
13. #39643C2semidirect
14. #39599C2semidirect
17. #39181C2semidirect
18. #37641C2semidirect
21. #36598C2semidirect
22. #36563C2semidirect
24. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598692
#598282
#596682
#592492
#587252
#531402
#531312
#529652
#427132
#425822
#425582
#397242
#396432
#395992
#392032
#391922
#391812
#376412
#376372
#376282
#365982
#365632
#361942
#349512
#349292