Finite Group Databasebeta

← #8429487

Subgroups — #8429487

Order 512.

4665 conjugacy classes of subgroups.

The subgroup lattice has 1111 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic, complemented
2#59678C212yesmaximal, complemented
3#59413C212yesmaximal, complemented
4#59134C212yesmaximal, complemented
5#53724C218yesmaximal, complemented
6#53041C214yesmaximal, complemented
7#53035C214yesmaximal, complemented
8#52982C214yesmaximal, complemented
9#42934C214yesmaximal, complemented
10#42834C214yesmaximal, complemented
11#42567C214yesmaximal, complemented
12#39746C212yesmaximal, complemented
13#39634C212yesmaximal, complemented
14#39171C212yesmaximal
15#39146C212yesmaximal, complemented
16#38967C212yesmaximal, complemented
17#38923C212yesmaximal, complemented
18#37631C212yesmaximal, complemented
19#37630C212yesmaximal, complemented
20#37617C212yesmaximal, complemented
21#36594C211yesmaximal, characteristic, complemented
22#36560C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34951C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34934C211yesmaximal, characteristic
27C2×#559C2212yes—
28C2×#557C2212yes—
29C2×#556C2212yes—
30C2×D4×Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2859C2212yes—
35#2858C2212yes—
36#2857C2212yes—
37#2841C2218yes—
38#2839C2218yes—
39#2838C2218yes—
40#2838C2218yes—
41#2831C2218yes—
42#2827C2218yes—
43#2821C2218yes—
44#2796C2218yes—
45#2788C2218yes—
46#2780C2218yes—
47#2780C2218yes—
48#2770C2218yes—
49#2750C2218yes—
50#2746C2218yes—
51#2746C2218yes—
52#2745C2218yes—
53#2742C2218yes—
54#2724C2214yes—
55#2722C2218yes—
56#2716C2218yes—
57#2704C2218yes—
58#2696C2218yes—
59#2696C2218yes—
60#2695C2218yes—
61#2694C2218yes—
62#2694C2218yes—
63#2658C2214yes—
64#2655C2218yes—
65#2650C2218yes—
66#2649C2218yes—
67#2647C2214yes—
68#2645C2214yes—
69#2645C2214yes—
70#2642C2214yes—
71#2640C2214yes—
72#2628C2214yes—
73#2628C2214yes—
74#2625C2214yes—
75#2623C2218yes—
76#2597C2218yes—
77#2585C2214yes—
78#2582C2211yescharacteristic
79#2582C2212yes—
80#2573C2214yes—
81#2571C2211yescharacteristic
82#2568C2212yes—
83#2568C2211yescharacteristic
84#2568C2211yescharacteristic
85#2565C2214yes—
86#2563C2214yes—
87#2562C2214yes—
88#2556C2218yes—
89#2554C2214yes—
90#2552C2211yescharacteristic
91#2552C2211yescharacteristic
92#2551C2212yes—
93#2551C2212yes—
94#2550C2214yes—
95#2548C2211yescharacteristic
96#2547C2214yes—
97#2547C2211yescharacteristic
98#2547C2212yes—
99#2547C2212yes—
100#2547C2212yes—
101#2546C2212yes—
102#2546C2212yes—
103#2546C2212yes—
104#2546C2211yescharacteristic
105#2545C2214yes—
106#2545C2214yes—
107#2544C2214yes—
108#2541C2211yescharacteristic
109#2538C2211yescharacteristic
110#2538C2211yescharacteristic
111#2538C2212yes—
112#2538C2212yes—
113#2514C2212yes—
114#2512C2212yes—
115#2512C2214yes—
116#2512C2214yes—
117#2511C2214yes—
118#2511C2212yes—
119#2509C2214yes—
120#2509C2212yes—
121#2506C2214yes—
122#2506C2214yes—
123#2494C2212yes—
124#2494C2214yes—
125#2492C2214yes—
126#2490C2212yes—
127#2487C2214yes—
128#2487C2214yes—
129#2487C2214yes—
130#2486C2214yes—
131#2485C2214yes—
132#2481C2218yes—
133#2454C2214yes—
134#2454C2214yes—
135#2454C2214yes—
136#2453C2214yes—
137#2453C2212yes—
138#2451C2214yes—
139#2448C2214yes—
140#2448C2214yes—
141#2447C2214yes—
142#2447C2214yes—
143#2447C2212yes—
144#2446C2212yes—
145#2446C2214yes—
146#2445C2212yes—
147#2442C2214yes—
148#2440C2214yes—
149#2440C2214yes—
150#2439C2214yes—
151#2436C2214yes—
152#2436C2214yes—
153#2434C2214yes—
154#2434C2214yes—
155#2429C2214yes—
156#2427C2214yes—
157#2427C2214yes—
158#2426C2212yes—
159#2423C2214yes—
160#2421C2212yes—
161#2417C2214yes—
162#2417C2214yes—
163#2402C2214yes—
164#2401C2214yes—
165#2392C2214yes—
166#2367C2214yes—
167#2365C2212yes—
168#2365C2212yes—
169#2354C2212yes—
170#2354C2212yes—
171#2352C2214yes—
172D4×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176Q8×C22⋊C4C2214yes—
177#2328C2214yes—
178#2326C2214yes—
179#2316C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2212yes—
184C4×C4⋊Q8C2211yescharacteristic
185C4×#127C2212yes—
186C4×#127C2211yescharacteristic
187C4×#125C2212yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2295C2212yes—
194#2293C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#559—48no—
201#557—48no—
202#556—48no—
203D4×Q8—48no—
204C2×C4⋊Q8—48no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×#127C2312yes—
217C2×#127C2311yescharacteristic
218#529—48no—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#125C2314yes—
223C2×#125C2312yes—
224C2×#125C2318yes—
225C2×#124C2312yes—
226C2×#124C2314yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#123C2314yes—
232C2×#123C2318yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2318yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2314yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2314yes—
264C22×C4⋊C4C2314yes—
265C22×C4⋊C4C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C42C2312yes—
268#401C2314yes—
269#401C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2314yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2314yes—
295#398C2314yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2314yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2314yes—
317#396C2318yes—
318#396C2318yes—
319#396C2314yes—
320#396C2318yes—
321#396C2314yes—
322#396C2318yes—
323#396C2314yes—
324#396C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#394C2318yes—
330#394C2314yes—
331#394C2318yes—
332#394C2314yes—
333#394C2314yes—
334#393C2318yes—
335#393C2318yes—
336#393C2318yes—
337#393C2318yes—
338#392C2314yes—
339#391C2312yes—
340#391C2314yes—
341#391C2312yes—
342#391C2312yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2314yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2318yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2312yes—
357#391C2318yes—
358#391C2312yes—
359#391C2312yes—
360#390C2314yes—
361#390C2312yes—
362#390C2312yes—
363#390C2314yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2312yes—
368#390C2314yes—
369#390C2312yes—
370#390C2312yes—
371#390C2314yes—
372#390C2314yes—
373#390C2314yes—
374#390C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2314yes—
379#389C2314yes—
380#389C2312yes—
381#389C2314yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2312yes—
386#389C2312yes—
387#389C2312yes—
388#389C2312yes—
389#389C2318yes—
390#389C2314yes—
391#389C2314yes—
392#389C2318yes—
393#389C2314yes—
394#389C2314yes—
395#389C2312yes—
396#389C2314yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#389C2312yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2312yes—
407#389C2312yes—
408#389C2312yes—
409#388C2318yes—
410#388C2318yes—
411#388C2314yes—
412#388C2314yes—
413#388C2318yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#388C2318yes—
421#388C2314yes—
422#387C2314yes—
423#387C2314yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#387C2314yes—
428#387C2314yes—
429#387C2314yes—
430#387C2318yes—
431#387C2314yes—
432#387C2314yes—
433#387C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#386C2318yes—
443#386C2314yes—
444#385C2318yes—
445#385C2318yes—
446#385C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2312yes—
457#384C2311yescharacteristic
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#384C2312yes—
462#383C2314yes—
463#382C2312yes—
464#382C2312yes—
465#382C2314yes—
466#382C2312yes—
467#382C2312yes—
468#381C2314yes—
469#381C2318yes—
470#380C2312yes—
471#380C2314yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#380C2318yes—
477#380C2318yes—
478#380C2312yes—
479#380C2318yes—
480#380C2314yes—
481#380C2314yes—
482#380C2312yes—
483#380C2314yes—
484#380C2314yes—
485#380C2312yes—
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2318yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520#376C2314yes—
521#376C2314yes—
522C43C2312yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2412yes—
533C22×Q8C2418yes—
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2418yes—
545C23×C4C2418yes—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—48no—
551C4⋊Q8—48no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—48no—
557#127—28no—
558#127—24no—
559#126—48no—
560#126—416no—
561#125—44no—
562#125—44no—
563#125—48no—
564#125—416no—
565#124—28no—
566#124—48no—
567#124—44no—
568#124—48no—
569#124—48no—
570#124—48no—
571#123—48no—
572#123—416no—
573C22⋊Q8—416no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578#121—44no—
579#121—44no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—28no—
585C4×Q8—24no—
586C4×Q8—42no—
587C4×Q8—42no—
588C4×Q8—48no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×D4—24no—
592C4×D4—28no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—28no—
596C4×D4—48no—
597C4×D4—48no—
598C4×D4—48no—
599C4×D4—44no—
600C4×D4—48no—
601C4×D4—48no—
602#117—48no—
603#117—48no—
604C2×C4⋊C4—48no—
605C2×C4⋊C4—48no—
606C2×C4⋊C4—48no—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2418yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C42—28no—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2414yes—
693C2×C42C2411yescharacteristic
694C2×C42C2412yes—
695C2×C42C2414yes—
696C2×C42C2411yescharacteristic
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2418yes—
707C2×C42C2418yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2411yescharacteristic
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24C2514yes—
763C24C2512yes—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—24no—
768C2×Q8—22no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—28no—
778C2×Q8—24no—
779C2×Q8—48no—
780C2×Q8—48no—
781C2×Q8—48no—
782C2×Q8—832no—
783C2×D4—28no—
784C2×D4—28no—
785C2×D4—22no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—44no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—42no—
799C2×D4—44no—
800C2×D42−1+414yes—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—42no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2511yescharacteristic
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2514yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2518yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—22no—
848C4⋊C4—24no—
849C4⋊C4—22no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—28no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—22no—
862C4⋊C4—22no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—48no—
873C4⋊C4—48no—
874C4⋊C4—48no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—42no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—48no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C22⋊C4—24no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—24no—
903C22⋊C4—28no—
904C22⋊C4—24no—
905C22⋊C4—28no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—28no—
931C42—24no—
932C42—24no—
933C42—22no—
934C42—24no—
935C42—24no—
936C42—24no—
937C42—22no—
938C42—24no—
939C42—22no—
940C42—24no—
941C42—41no—
942C42—42no—
943C42—42no—
944C42—48no—
945C42—42no—
946C42—42no—
947C42—48no—
948C42H(5,𝔽2)14yes—
949C42H(5,𝔽2)14yes—
950C422−1+414yes—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23C2×2−1+414yes—
965C23C2611yescharacteristic
966Q8—44no—
967Q8—416no—
968Q8—48no—
969Q8—48no—
970Q8—44no—
971Q8—816no—
972D4—28no—
973D4—48no—
974D4—48no—
975D4—84no—
976D4—88no—
977D4—88no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—22no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—28no—
999C2×C4—28no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—21no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—24no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—28no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—48no—
1039C2×C4—48no—
1040C2×C4—48no—
1041C2×C4—416no—
1042C2×C4—816no—
1043C2×C4—168no—
1044C2×C4C2×H(5,𝔽2)12yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×H(5,𝔽2)12yes—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4C2×2−1+412yes—
1052C2×C4C2×2−1+412yes—
1053C2×C4C2×2−1+412yes—
1054C2×C4#58512yes—
1055C2×C4#58512yes—
1056C22—24no—
1057C22—24no—
1058C22—24no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22—44no—
1069C22—44no—
1070C22C22×H(5,𝔽2)11yescharacteristic
1071C22C22×H(5,𝔽2)11yescharacteristic
1072C22C22×2−1+411yescharacteristic
1073C22C22×2−1+411yescharacteristic
1074C22C2×#58511yescharacteristic
1075C22C2×#58511yescharacteristic
1076C222−1+611yescharacteristic
1077C4—22no—
1078C4—22no—
1079C4—22no—
1080C4—44no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—48no—
1087C4—42no—
1088C4—41no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—44no—
1093C4—44no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—42no—
1098C4#354614yes—
1099C4#355214yes—
1100C4#355414yes—
1101C2—44no—
1102C2—84no—
1103C2C2×#355211yescharacteristic
1104C2C2×#355411yescharacteristic
1105C2C2×#354611yescharacteristic
1106C2#6293111yescharacteristic
1107C2#6294211yescharacteristic
1108C2#6295611yescharacteristic
1109C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2541C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59827C2semidirect
2. #59678C2semidirect
3. #59413C2semidirect
4. #59134C2semidirect
5. #53724C2semidirect
6. #53041C2semidirect
7. #53035C2semidirect
8. #52982C2semidirect
9. #42934C2semidirect
10. #42834C2semidirect
11. #42567C2semidirect
12. #39746C2semidirect
13. #39634C2semidirect
15. #39146C2semidirect
16. #38967C2semidirect
17. #38923C2semidirect
18. #37631C2semidirect
19. #37630C2semidirect
20. #37617C2semidirect
21. #36594C2semidirect
22. #36560C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34951C2semidirect
25. #34945C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#596782
#594132
#591342
#537242
#530412
#530352
#529822
#429342
#428342
#425672
#397462
#396342
#391712
#391462
#389672
#389232
#376312
#376302
#376172
#365942
#365602
D4×C4⋊Q82
#349512
#349452
#349342