Finite Group Databasebeta

← #7987056

Subgroups — #7987056

Order 512.

4345 conjugacy classes of subgroups.

The subgroup lattice has 1083 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59672C212yesmaximal, complemented
3#59256C212yesmaximal, complemented
4#59243C212yesmaximal, complemented
5#49132C218yesmaximal, complemented
6#45640C214yesmaximal, complemented
7#45218C214yesmaximal, complemented
8#44990C214yesmaximal, complemented
9#42750C214yesmaximal, complemented
10#42655C214yesmaximal, complemented
11#39928C214yesmaximal, complemented
12#39480C212yesmaximal, complemented
13#39480C212yesmaximal, complemented
14#39203C212yesmaximal, complemented
15#38921C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36194C211yesmaximal, characteristic, complemented
18#36194C211yesmaximal, characteristic, complemented
19#36176C212yesmaximal, complemented
20#36175C212yesmaximal, complemented
21#35207C212yesmaximal
22#35181C212yesmaximal, complemented
23#34941C211yesmaximal, characteristic, complemented
24#34932C211yesmaximal, characteristic
25#34383C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#554C2211yescharacteristic
28C2×#529C2212yes—
29#2868C2211yescharacteristic
30#2862C2212yes—
31#2857C2212yes—
32#2857C2212yes—
33#2854C2214yes—
34#2851C2214yes—
35#2851C2214yes—
36#2827C2218yes—
37#2809C2218yes—
38#2806C2214yes—
39#2798C2218yes—
40#2793C2218yes—
41#2786C2218yes—
42#2777C2218yes—
43#2776C2218yes—
44#2770C2218yes—
45#2762C2218yes—
46#2762C2218yes—
47#2754C2218yes—
48#2744C2218yes—
49#2707C2218yes—
50#2698C2218yes—
51#2690C2218yes—
52#2690C2218yes—
53#2680C2218yes—
54#2653C2218yes—
55#2652C2218yes—
56#2646C2218yes—
57#2625C2214yes—
58#2625C2214yes—
59#2594C2218yes—
60#2584C2214yes—
61#2582C2212yes—
62#2582C2214yes—
63#2574C2214yes—
64#2571C2214yes—
65#2571C2212yes—
66#2571C2212yes—
67#2571C2212yes—
68#2570C2214yes—
69#2570C2214yes—
70#2570C2214yes—
71#2570C2214yes—
72#2570C2218yes—
73#2568C2212yes—
74#2567C2212yes—
75#2567C2211yescharacteristic
76#2565C2218yes—
77#2563C2212yes—
78#2563C2212yes—
79#2563C2211yescharacteristic
80#2553C2214yes—
81#2552C2214yes—
82#2552C2211yescharacteristic
83#2552C2214yes—
84#2552C2212yes—
85#2552C2212yes—
86#2552C2211yescharacteristic
87#2547C2211yescharacteristic
88#2542C2211yescharacteristic
89#2538C2212yes—
90#2538C2212yes—
91#2538C2211yescharacteristic
92#2537C2211yescharacteristic
93#2532C2218yes—
94#2528C2218yes—
95#2528C2218yes—
96#2527C2218yes—
97#2523C2218yes—
98#2514C2214yes—
99#2514C2214yes—
100#2513C2214yes—
101#2513C2214yes—
102#2511C2214yes—
103#2508C2214yes—
104#2508C2214yes—
105#2508C2212yes—
106#2507C2214yes—
107#2506C2214yes—
108#2506C2214yes—
109#2506C2214yes—
110#2499C2214yes—
111#2497C2214yes—
112#2497C2214yes—
113#2497C2212yes—
114#2496C2212yes—
115#2495C2214yes—
116#2495C2214yes—
117#2494C2214yes—
118#2494C2214yes—
119#2494C2214yes—
120#2494C2214yes—
121#2492C2214yes—
122#2492C2214yes—
123#2490C2214yes—
124#2489C2214yes—
125#2489C2212yes—
126#2488C2218yes—
127#2486C2214yes—
128#2458C2218yes—
129#2454C2212yes—
130#2447C2214yes—
131#2446C2214yes—
132#2439C2214yes—
133#2439C2214yes—
134#2427C2212yes—
135#2423C2212yes—
136#2422C2214yes—
137#2422C2212yes—
138#2421C2214yes—
139#2415C2214yes—
140#2396C2214yes—
141#2395C2214yes—
142#2376C2218yes—
143#2370C2214yes—
144#2370C2214yes—
145#2370C2212yes—
146#2369C2212yes—
147#2369C2212yes—
148#2369C2211yescharacteristic
149#2369C2212yes—
150#2368C2214yes—
151#2367C2214yes—
152#2365C2212yes—
153#2365C2212yes—
154#2360C2212yes—
155#2356C2214yes—
156#2355C2212yes—
157#2355C2212yes—
158#2355C2212yes—
159#2355C2212yes—
160#2355C2211yescharacteristic
161#2354C2212yes—
162#2354C2214yes—
163#2354C2212yes—
164#2352C2214yes—
165Q8×C4⋊C4C2212yes—
166#2349C2212yes—
167D4×C4⋊C4C2211yescharacteristic
168#2346C2214yes—
169#2345C2212yes—
170#2334C2218yes—
171#2324C2214yes—
172#2323C2214yes—
173#2317C2214yes—
174#2317C2214yes—
175#2314C2214yes—
176#2314C2214yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×#125C2212yes—
182C4×#125C2212yes—
183C4×C22⋊Q8C2212yes—
184C4×C22⋊Q8C2212yes—
185C4×C22⋊Q8C2212yes—
186C4×C22⋊Q8C2214yes—
187C4×#121C2212yes—
188#2293C2212yes—
189#2285C2212yes—
190#2285C2212yes—
191#2285C2212yes—
192#2285C2212yes—
193#2283C2214yes—
194C42×Q8C2211yescharacteristic
195C42×D4C2212yes—
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199#554—28no—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2311yescharacteristic
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206#529—216no—
207C2×#126C2314yes—
208C2×#125C2312yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2318yes—
213C2×#124C2312yes—
214C2×#123C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2314yes—
245C2×#117C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C42C2312yes—
249C22×C42C2312yes—
250C22×C42C2314yes—
251#401C2318yes—
252#401C2318yes—
253#400C2318yes—
254#400C2318yes—
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#400C2314yes—
262#400C2314yes—
263#400C2318yes—
264#400C2318yes—
265#399C2314yes—
266#399C2314yes—
267#398C2314yes—
268#398C2318yes—
269#398C2318yes—
270#398C2318yes—
271#398C2314yes—
272#398C2318yes—
273#398C2318yes—
274#398C2318yes—
275#398C2318yes—
276#398C2318yes—
277#398C2318yes—
278#398C2314yes—
279#397C2318yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2314yes—
286#397C2314yes—
287#397C2314yes—
288#397C2318yes—
289#397C2318yes—
290#396C2318yes—
291#396C2318yes—
292#396C2314yes—
293#396C2314yes—
294#395C2314yes—
295#395C2318yes—
296#394C2314yes—
297#394C2318yes—
298#394C2314yes—
299#393C2314yes—
300#393C2318yes—
301#393C2318yes—
302#391C2314yes—
303#391C2312yes—
304#391C2312yes—
305#391C2312yes—
306#391C2318yes—
307#391C2318yes—
308#391C2314yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2318yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#390C2314yes—
322#390C2312yes—
323#390C2314yes—
324#390C2318yes—
325#390C2312yes—
326#390C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2312yes—
330#389C2312yes—
331#389C2312yes—
332#389C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2312yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2318yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2318yes—
355#389C2318yes—
356#389C2314yes—
357#389C2318yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2314yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#387C2314yes—
379#387C2314yes—
380#387C2314yes—
381#387C2314yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#386C2318yes—
406#386C2314yes—
407#385C2314yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#384C2311yescharacteristic
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2318yes—
420#384C2312yes—
421#384C2314yes—
422#384C2312yes—
423#384C2312yes—
424#384C2312yes—
425#384C2314yes—
426#384C2312yes—
427#384C2312yes—
428#384C2312yes—
429#384C2312yes—
430#383C2318yes—
431#383C2318yes—
432#382C2312yes—
433#382C2312yes—
434#382C2314yes—
435#382C2314yes—
436#382C2318yes—
437#382C2314yes—
438#382C2314yes—
439#382C2314yes—
440#382C2314yes—
441#382C2314yes—
442#382C2314yes—
443#382C2318yes—
444#382C2314yes—
445#381C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2314yes—
455#380C2314yes—
456#380C2312yes—
457#380C2312yes—
458#380C2314yes—
459#380C2314yes—
460#380C2312yes—
461#380C2314yes—
462#380C2314yes—
463#380C2314yes—
464#380C2312yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C22⋊C4C2312yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517#376C2318yes—
518C2×#95C2314yes—
519C43C2312yes—
520C43C2311yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2412yes—
523C22×Q8C2412yes—
524C22×Q8C2412yes—
525C22×Q8C2414yes—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2414yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2412yes—
533C23×C4C2414yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2414yes—
537C4⋊Q8—24no—
538C4⋊Q8—24no—
539C4⋊Q8—24no—
540C4⋊Q8—28no—
541C4⋊Q8—44no—
542C4⋊Q8—82no—
543#126—216no—
544#125—28no—
545#125—28no—
546#125—44no—
547#125—48no—
548#125—88no—
549#124—28no—
550#123—216no—
551#123—88no—
552C22⋊Q8—28no—
553C22⋊Q8—28no—
554C22⋊Q8—216no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—84no—
558C22⋊Q8—84no—
559#121—28no—
560#121—44no—
561C4×Q8—28no—
562C4×Q8—24no—
563C4×Q8—24no—
564C4×Q8—44no—
565C4×Q8—44no—
566C4×Q8—48no—
567C4×Q8—42no—
568C4×Q8—84no—
569C4×D4—28no—
570C4×D4—216no—
571C4×D4—24no—
572C4×D4—24no—
573C4×D4—24no—
574C4×D4—44no—
575C4×D4—42no—
576C4×D4—42no—
577C4×D4#4118yes—
578#117—216no—
579#117—48no—
580#117—48no—
581#117—48no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—44no—
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2414yes—
645C2×C22⋊C4C2414yes—
646C2×C22⋊C4C2414yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2414yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2414yes—
654C2×C22⋊C4C2414yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2418yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C42—28no—
665C2×C42—28no—
666C2×C42—48no—
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2414yes—
670C2×C42C2414yes—
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2412yes—
674C2×C42C2414yes—
675C2×C42C2411yescharacteristic
676C2×C42C2412yes—
677C2×C42C2412yes—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2418yes—
684C2×C42C2418yes—
685C2×C42C2412yes—
686C2×C42C2418yes—
687C2×C42C2412yes—
688C2×C42C2418yes—
689C2×C42C2411yescharacteristic
690C2×C42C2414yes—
691C2×C42C2414yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#95C2412yes—
696#95C2414yes—
697#95C2414yes—
698#95C2414yes—
699#95C2414yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2412yes—
704#95C2414yes—
705#95C2414yes—
706#95C2412yes—
707#95C2412yes—
708#95C2414yes—
709#95C2414yes—
710#95C2412yes—
711#95C2412yes—
712#95C2412yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2412yes—
718#95C2412yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2414yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743C24C2512yes—
744C24C2512yes—
745C2×Q8—22no—
746C2×Q8—24no—
747C2×Q8—24no—
748C2×Q8—22no—
749C2×Q8—24no—
750C2×Q8—24no—
751C2×Q8—28no—
752C2×Q8—24no—
753C2×Q8—22no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—44no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—44no—
760C2×D4—28no—
761C2×D4—22no—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4C2×#4114yes—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—28no—
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—24no—
782C22×C4—24no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—42no—
787C22×C4—42no—
788C22×C4—44no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—44no—
792C22×C4C2×#4118yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2512yes—
797C22×C4C2512yes—
798C22×C4C2512yes—
799C22×C4C2514yes—
800C22×C4C2518yes—
801C22×C4C2512yes—
802C22×C4C2512yes—
803C22×C4C2514yes—
804C22×C4C2512yes—
805C22×C4C2514yes—
806C22×C4C2511yescharacteristic
807C22×C4C2514yes—
808C22×C4C2514yes—
809C22×C4C2512yes—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2511yescharacteristic
813C22×C4C2511yescharacteristic
814C22×C4C2511yescharacteristic
815C22×C4C2511yescharacteristic
816C22×C4C2511yescharacteristic
817C4⋊C4—22no—
818C4⋊C4—28no—
819C4⋊C4—24no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—24no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—28no—
827C4⋊C4—28no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—22no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—28no—
835C4⋊C4—24no—
836C4⋊C4—24no—
837C4⋊C4—24no—
838C4⋊C4—28no—
839C4⋊C4—22no—
840C4⋊C4—24no—
841C4⋊C4—24no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—22no—
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—44no—
849C4⋊C4—44no—
850C4⋊C4—44no—
851C4⋊C4—42no—
852C4⋊C4—42no—
853C4⋊C4—44no—
854C4⋊C4—44no—
855C4⋊C4—48no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—48no—
859C4⋊C4—44no—
860C4⋊C4—44no—
861C4⋊C4—48no—
862C4⋊C4—48no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C4⋊C4—48no—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—48no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4C2×#4114yes—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—24no—
881C22⋊C4—24no—
882C22⋊C4—24no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—44no—
888C22⋊C4—42no—
889C22⋊C4—42no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4C2×#4118yes—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—28no—
901C42—24no—
902C42—24no—
903C42—24no—
904C42—24no—
905C42—24no—
906C42—24no—
907C42—28no—
908C42—24no—
909C42—28no—
910C42—22no—
911C42—22no—
912C42—22no—
913C42—44no—
914C42—44no—
915C42—48no—
916C42—48no—
917C42—42no—
918C42—48no—
919C42—42no—
920C42—48no—
921C42—41no—
922C42C2×#4114yes—
923C422−1+414yes—
924C422−1+414yes—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23C22×#4114yes—
939C23C2611yescharacteristic
940Q8—48no—
941Q8—44no—
942Q8—84no—
943Q8—84no—
944Q8—88no—
945D4—28no—
946D4—44no—
947D4—88no—
948C2×C4—22no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—216no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—24no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—24no—
973C2×C4—24no—
974C2×C4—28no—
975C2×C4—24no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—24no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—28no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—48no—
1009C2×C4—48no—
1010C2×C4—48no—
1011C2×C4—84no—
1012C2×C4—84no—
1013C2×C4—88no—
1014C2×C4—88no—
1015C2×C4C22×#4112yes—
1016C2×C4C22×#4114yes—
1017C2×C4C22×#4112yes—
1018C2×C4C22×#4112yes—
1019C2×C4C2×2−1+412yes—
1020C2×C4C2×2−1+412yes—
1021C2×C4C2×2−1+412yes—
1022C2×C4C2×2−1+412yes—
1023C2×C4C2×2−1+412yes—
1024C2×C4C2×2−1+412yes—
1025C2×C4#58512yes—
1026C2×C4#58512yes—
1027C2×C4#58512yes—
1028C22—24no—
1029C22—24no—
1030C22—24no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—42no—
1042C22C23×#4111yescharacteristic
1043C22C22×2−1+411yescharacteristic
1044C22C22×2−1+411yescharacteristic
1045C22C2×#58511yescharacteristic
1046C22C2×#58511yescharacteristic
1047C22C2×#58511yescharacteristic
1048C22H(7,𝔽2)11yescharacteristic
1049C4—22no—
1050C4—24no—
1051C4—22no—
1052C4—22no—
1053C4—42no—
1054C4—42no—
1055C4—44no—
1056C4—44no—
1057C4—42no—
1058C4—41no—
1059C4—44no—
1060C4—44no—
1061C4—42no—
1062C4—42no—
1063C4—44no—
1064C4—42no—
1065C4—42no—
1066C4—42no—
1067C4—42no—
1068C4—44no—
1069C4—48no—
1070C4#350714yes—
1071C4#351514yes—
1072C4#355514yes—
1073C2—44no—
1074C2—82no—
1075C2C2×#355511yescharacteristic
1076C2C2×#350711yescharacteristic
1077C2C2×#351511yescharacteristic
1078C2#6292911yescharacteristic
1079C2#6296211yescharacteristic
1080C2#6299411yescharacteristic
1081C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2537C22
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. #59672C2semidirect
3. #59256C2semidirect
4. #59243C2semidirect
5. #49132C2semidirect
6. #45640C2semidirect
7. #45218C2semidirect
8. #44990C2semidirect
9. #42750C2semidirect
10. #42655C2semidirect
11. #39928C2semidirect
12. #39480C2semidirect
13. #39480C2semidirect
14. #39203C2semidirect
15. #38921C2semidirect
16. #36598C2semidirect
17. #36194C2semidirect
18. #36194C2semidirect
19. #36176C2semidirect
20. #36175C2semidirect
22. #35181C2semidirect
23. #34941C2semidirect
25. #34383C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#596722
#592562
#592432
#491322
#456402
#452182
#449902
#427502
#426552
#399282
#394802
#392032
#389212
#365982
#361942
#361762
#361752
#352072
#351812
#349412
#349322
#343832
C4×#5542