Finite Group Databasebeta

← #7671573

Subgroups — #7671573

Order 512.

4784 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59869C211yesmaximal, characteristic, complemented
3#59864C211yesmaximal, characteristic, complemented
4#59827C211yesmaximal, characteristic, complemented
5#59567C214yesmaximal, complemented
6#59437C212yesmaximal, complemented
7#59436C212yesmaximal, complemented
8#59256C212yesmaximal, complemented
9#59064C212yesmaximal
10#40010C214yesmaximal, complemented
11#39581C214yesmaximal, complemented
12#39536C214yesmaximal, complemented
13#38472C214yesmaximal, complemented
14#36635C211yesmaximal, characteristic, complemented
15#36449C212yesmaximal, complemented
16#36394C214yesmaximal, complemented
17#36301C212yesmaximal, complemented
18#36175C212yesmaximal, complemented
19#36171C214yesmaximal, complemented
20#36165C212yesmaximal, complemented
21#35632C214yesmaximal, complemented
22#35200C212yesmaximal, complemented
23#35187C212yesmaximal, complemented
24#34331C212yesmaximal, complemented
25#34191C212yesmaximal, complemented
26C4×#533C211yesmaximal, characteristic, complemented
27C4×#532C211yesmaximal, characteristic
28C2×#559C2212yes—
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×C4×#41C2212yes—
32#2864C2212yes—
33#2864C2214yes—
34#2863C2212yes—
35#2863C2212yes—
36#2863C2214yes—
37#2862C2211yescharacteristic
38#2859C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2211yescharacteristic
41#2855C2212yes—
42#2855C2212yes—
43#2851C2212yes—
44#2851C2214yes—
45#2851C2214yes—
46#2809C2214yes—
47#2805C2214yes—
48#2804C2214yes—
49#2787C2218yes—
50#2782C2218yes—
51#2770C2218yes—
52#2746C2218yes—
53#2745C2218yes—
54#2724C2214yes—
55#2708C2218yes—
56#2655C2218yes—
57#2638C2218yes—
58#2599C2218yes—
59#2599C2218yes—
60#2582C2212yes—
61#2581C2214yes—
62#2580C2214yes—
63#2580C2214yes—
64#2578C2218yes—
65#2577C2218yes—
66#2577C2218yes—
67#2575C2218yes—
68#2575C2218yes—
69#2571C2212yes—
70#2571C2212yes—
71#2571C2212yes—
72#2570C2214yes—
73#2568C2214yes—
74#2568C2212yes—
75#2567C2212yes—
76#2563C2212yes—
77#2563C2212yes—
78#2547C2214yes—
79#2547C2212yes—
80#2547C2212yes—
81#2546C2212yes—
82#2546C2212yes—
83#2530C2218yes—
84#2528C2218yes—
85#2527C2218yes—
86#2527C2218yes—
87#2524C2218yes—
88#2523C2218yes—
89#2517C2218yes—
90#2514C2214yes—
91#2514C2214yes—
92#2514C2214yes—
93#2511C2214yes—
94#2509C2214yes—
95#2508C2214yes—
96#2508C2214yes—
97#2508C2214yes—
98#2508C2214yes—
99#2505C2218yes—
100#2505C2218yes—
101#2499C2214yes—
102#2495C2214yes—
103#2495C2214yes—
104#2494C2214yes—
105#2494C2214yes—
106#2494C2214yes—
107#2493C2218yes—
108#2487C2214yes—
109#2486C2214yes—
110#2485C2214yes—
111#2485C2214yes—
112#2477C2218yes—
113#2447C2214yes—
114#2447C2214yes—
115#2447C2214yes—
116#2447C2214yes—
117#2446C2214yes—
118#2442C2214yes—
119#2442C2214yes—
120#2432C2214yes—
121#2427C2214yes—
122#2421C2214yes—
123#2420C2214yes—
124#2419C2218yes—
125#2369C2212yes—
126#2367C2214yes—
127#2367C2214yes—
128#2366C2212yes—
129#2365C2212yes—
130#2359C2218yes—
131#2356C2214yes—
132#2355C2212yes—
133#2355C2212yes—
134#2355C2212yes—
135#2354C2214yes—
136#2352C2214yes—
137#2352C2214yes—
138Q8×C4⋊C4C2212yes—
139#2349C2214yes—
140#2349C2214yes—
141D4×C4⋊C4C2212yes—
142D4×C4⋊C4C2212yes—
143D4×C4⋊C4C2212yes—
144D4×C4⋊C4C2212yes—
145#2346C2214yes—
146#2345C2214yes—
147#2344C2214yes—
148#2343C2218yes—
149#2343C2218yes—
150#2339C2214yes—
151#2335C2218yes—
152#2327C2214yes—
153#2326C2214yes—
154#2320C2214yes—
155#2318C2218yes—
156C4×C4⋊Q8C2211yescharacteristic
157C4×C4⋊Q8C2211yescharacteristic
158C4×C4⋊Q8C2211yescharacteristic
159C4×C4⋊Q8C2211yescharacteristic
160C4×C4⋊Q8C2211yescharacteristic
161C4×C4⋊Q8C2211yescharacteristic
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2211yescharacteristic
164C4×#127C2211yescharacteristic
165C4×#127C2211yescharacteristic
166C4×#125C2212yes—
167C4×#125C2212yes—
168C4×#125C2212yes—
169C4×#124C2214yes—
170C4×#124C2212yes—
171C4×#124C2212yes—
172C4×C22⋊Q8C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×C22⋊Q8C2212yes—
178C4×#121C2212yes—
179C4×#121C2212yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182#2297C2212yes—
183#2296C2212yes—
184#2295C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187#2295C2212yes—
188#2293C2214yes—
189#2293C2212yes—
190#2293C2212yes—
191#2285C2211yescharacteristic
192#2285C2211yescharacteristic
193#2283C2212yes—
194#2283C2214yes—
195C2×#382C2214yes—
196#2275C2214yes—
197C42×Q8C2212yes—
198C42×Q8C2212yes—
199C42×D4C2212yes—
200C42×D4C2212yes—
201C4×#117C2212yes—
202C2×C43C2211yescharacteristic
203C22×#41C2312yes—
204#559—216no—
205#533—28no—
206#532—28no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2314yes—
213C2×#127C2311yescharacteristic
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#124C2314yes—
217C2×#124C2314yes—
218C2×#124C2312yes—
219C2×#123C2318yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C4×#41—216no—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2318yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C42C2314yes—
260C22×C42C2311yescharacteristic
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#401C2318yes—
268#401C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2318yes—
283#398C2318yes—
284#398C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#395C2318yes—
295#394C2318yes—
296#394C2318yes—
297#393C2318yes—
298#393C2318yes—
299#391C2312yes—
300#391C2312yes—
301#391C2312yes—
302#391C2312yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2318yes—
313#391C2314yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#390C2312yes—
322#390C2312yes—
323#390C2312yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2314yes—
328#390C2314yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2318yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2314yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2314yes—
376#388C2314yes—
377#387C2314yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2318yes—
407#387C2314yes—
408#386C2318yes—
409#386C2318yes—
410#386C2314yes—
411#386C2318yes—
412#386C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2318yes—
426#385C2314yes—
427#385C2314yes—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2314yes—
435#383C2318yes—
436#383C2318yes—
437#383C2318yes—
438#383C2314yes—
439#382C2312yes—
440#382C2312yes—
441#382C2314yes—
442#382C2314yes—
443#382C2314yes—
444#382C2318yes—
445#382C2312yes—
446#382C2314yes—
447#382C2314yes—
448#382C2314yes—
449#382C2318yes—
450#382C2318yes—
451#382C2312yes—
452#382C2312yes—
453#381C2314yes—
454#381C2318yes—
455#381C2318yes—
456#381C2318yes—
457#380C2314yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2318yes—
462#380C2312yes—
463#380C2318yes—
464#380C2312yes—
465#380C2314yes—
466#380C2312yes—
467#380C2312yes—
468#380C2314yes—
469#380C2312yes—
470#380C2318yes—
471#380C2314yes—
472#380C2312yes—
473#380C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2318yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521#376C2318yes—
522#376C2314yes—
523C2×#95C2318yes—
524C2×#95C2318yes—
525C43C2311yescharacteristic
526C43C2311yescharacteristic
527C43C2311yescharacteristic
528C43C2311yescharacteristic
529C43C2311yescharacteristic
530C43C2311yescharacteristic
531C43C2311yescharacteristic
532C43C2314yes—
533C43C2311yescharacteristic
534C2×#41—28no—
535C2×#41—28no—
536C2×#41—44no—
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2412yes—
541C22×Q8C2412yes—
542C22×D4C2414yes—
543C22×D4C2412yes—
544C22×D4C2412yes—
545C22×D4C2412yes—
546C23×C4C2414yes—
547C23×C4C2411yescharacteristic
548C23×C4C2414yes—
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2418yes—
553C23×C4C2414yes—
554C23×C4C2411yescharacteristic
555C23×C4C2418yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C4⋊Q8—24no—
559C4⋊Q8—24no—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—48no—
564#127#4118yes—
565#125—28no—
566#125—44no—
567#124—28no—
568#124—216no—
569#124—216no—
570#123—232no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575#121—28no—
576#121—28no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—44no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×Q8—44no—
587C4×Q8—48no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—216no—
591C4×D4—216no—
592C4×D4—216no—
593C4×D4—216no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—44no—
598C4×D4—44no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—44no—
602#117—28no—
603#117—28no—
604#117—216no—
605#117—416no—
606#117—44no—
607C2×C4⋊C4—48no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C42—216no—
677C2×C42—24no—
678C2×C42—24no—
679C2×C42—42no—
680C2×C42—42no—
681C2×C42—42no—
682C2×C42—42no—
683C2×C42#4118yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2414yes—
695C2×C42C2414yes—
696C2×C42C2414yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2414yes—
708C2×C42C2418yes—
709C2×C42C2414yes—
710C2×C42C2418yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771C24C2514yes—
772C24C2511yescharacteristic
773#41—432no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—44no—
798C2×D4C2×#4118yes—
799C2×D4C2×#4118yes—
800C2×D4C2×#4118yes—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
806C22×C4—216no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—28no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—44no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4C2×#4114yes—
835C22×C4C2×#4114yes—
836C22×C4C2×#4114yes—
837C22×C4C2511yescharacteristic
838C22×C4C2514yes—
839C22×C4C2514yes—
840C22×C4C2514yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C2511yescharacteristic
847C22×C4C2514yes—
848C22×C4C2511yescharacteristic
849C22×C4C2511yescharacteristic
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2511yescharacteristic
853C22×C4C2511yescharacteristic
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2511yescharacteristic
858C22×C4C2511yescharacteristic
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—28no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—216no—
915C22⋊C4—216no—
916C22⋊C4—216no—
917C22⋊C4—28no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—48no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C42—28no—
930C42—22no—
931C42—22no—
932C42—28no—
933C42—28no—
934C42—22no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—22no—
939C42—22no—
940C42—22no—
941C42—22no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—22no—
947C42—22no—
948C42—22no—
949C42—28no—
950C42—28no—
951C42—28no—
952C42—41no—
953C42—41no—
954C42—41no—
955C42—41no—
956C42—41no—
957C42—41no—
958C42—41no—
959C42—41no—
960C42—44no—
961C42—48no—
962C42—44no—
963C42—48no—
964C42C2×#4114yes—
965C42C2×#4114yes—
966C42C2×#4114yes—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C422−1+414yes—
970C23—24no—
971C23—21no—
972C23—24no—
973C23—21no—
974C23—24no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—21no—
982C23C22×#4118yes—
983C23C22×#4112yes—
984C23C2611yescharacteristic
985Q8—48no—
986Q8—48no—
987Q8—48no—
988Q8—48no—
989Q8—84no—
990D4—216no—
991D4—216no—
992D4—48no—
993D4—416no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—21no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—44no—
1056C2×C4—44no—
1057C2×C4—416no—
1058C2×C4—44no—
1059C2×C4—44no—
1060C2×C4—416no—
1061C2×C4—44no—
1062C2×C4—88no—
1063C2×C4—816no—
1064C2×C4—168no—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4112yes—
1067C2×C4C22×#4112yes—
1068C2×C4C22×#4112yes—
1069C2×C4C22×#4112yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C2×2−1+412yes—
1075C2×C4C2×2−1+412yes—
1076C2×C4C2×2−1+412yes—
1077C2×C4#58512yes—
1078C2×C4#58512yes—
1079C2×C4#58512yes—
1080C2×C4#58512yes—
1081C22—22no—
1082C22—28no—
1083C22—28no—
1084C22—22no—
1085C22—22no—
1086C22—28no—
1087C22—44no—
1088C22—41no—
1089C22—41no—
1090C22—44no—
1091C22—41no—
1092C22—44no—
1093C22—41no—
1094C22—44no—
1095C22C23×#4111yescharacteristic
1096C22C23×#4111yescharacteristic
1097C22C22×2−1+411yescharacteristic
1098C22C2×#58511yescharacteristic
1099C22C2×#58511yescharacteristic
1100C22C2×#58511yescharacteristic
1101C22C2×#58511yescharacteristic
1102C4—22no—
1103C4—22no—
1104C4—22no—
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—22no—
1109C4—44no—
1110C4—41no—
1111C4—44no—
1112C4—41no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—41no—
1119C4—41no—
1120C4—44no—
1121C4—44no—
1122C4—44no—
1123C4—44no—
1124C4#347514yes—
1125C4#350714yes—
1126C4#351514yes—
1127C2—42no—
1128C2—48no—
1129C2C2×#347511yescharacteristic
1130C2C2×#350711yescharacteristic
1131C2C2×#351511yescharacteristic
1132C2#6278111yescharacteristic
1133C2#6281511yescharacteristic
1134C2#6283111yescharacteristic
1135C2#6284111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59869C2semidirect
3. #59864C2semidirect
4. #59827C2semidirect
5. #59567C2semidirect
6. #59437C2semidirect
7. #59436C2semidirect
8. #59256C2semidirect
10. #40010C2semidirect
11. #39581C2semidirect
12. #39536C2semidirect
13. #38472C2semidirect
14. #36635C2semidirect
15. #36449C2semidirect
16. #36394C2semidirect
17. #36301C2semidirect
18. #36175C2semidirect
19. #36171C2semidirect
20. #36165C2semidirect
21. #35632C2semidirect
22. #35200C2semidirect
23. #35187C2semidirect
24. #34331C2semidirect
25. #34191C2semidirect
26. C4×#533C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#598692
#598642
#598272
#595672
#594372
#594362
#592562
#590642
#400102
#395812
#395362
#384722
#366352
#364492
#363942
#363012
#361752
#361712
#361652
#356322
#352002
#351872
#343312
#341912
C4×#5332
C4×#5322