Finite Group Databasebeta

← #8429501

Subgroups — #8429501

Order 512.

4591 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59421C212yesmaximal
3#59214C212yesmaximal, complemented
4#59144C212yesmaximal, complemented
5#53760C218yesmaximal, complemented
6#53091C214yesmaximal, complemented
7#53041C214yesmaximal, complemented
8#52978C214yesmaximal, complemented
9#42859C214yesmaximal, complemented
10#42853C214yesmaximal, complemented
11#42622C214yesmaximal, complemented
12#39744C212yesmaximal, complemented
13#39616C212yesmaximal, complemented
14#39609C212yesmaximal, complemented
15#39149C212yesmaximal, complemented
16#39146C212yesmaximal, complemented
17#39127C212yesmaximal, complemented
18#37630C212yesmaximal, complemented
19#37624C212yesmaximal, complemented
20#37617C212yesmaximal, complemented
21#36593C211yesmaximal, characteristic, complemented
22#36188C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34945C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic
27C2×#557C2212yes—
28C2×#557C2212yes—
29C2×#556C2212yes—
30C2×D4×Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2868C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2841C2218yes—
38#2839C2218yes—
39#2838C2218yes—
40#2838C2218yes—
41#2833C2218yes—
42#2827C2218yes—
43#2821C2218yes—
44#2805C2218yes—
45#2796C2218yes—
46#2787C2218yes—
47#2780C2218yes—
48#2776C2218yes—
49#2774C2218yes—
50#2770C2218yes—
51#2746C2218yes—
52#2742C2218yes—
53#2739C2218yes—
54#2726C2214yes—
55#2725C2218yes—
56#2721C2218yes—
57#2721C2218yes—
58#2720C2218yes—
59#2720C2218yes—
60#2713C2218yes—
61#2707C2218yes—
62#2702C2218yes—
63#2666C2218yes—
64#2660C2214yes—
65#2658C2214yes—
66#2655C2218yes—
67#2652C2218yes—
68#2647C2214yes—
69#2645C2214yes—
70#2645C2214yes—
71#2642C2214yes—
72#2629C2214yes—
73#2628C2214yes—
74#2628C2214yes—
75#2623C2218yes—
76#2587C2218yes—
77#2582C2212yes—
78#2573C2214yes—
79#2573C2214yes—
80#2571C2211yescharacteristic
81#2571C2211yescharacteristic
82#2570C2214yes—
83#2568C2211yescharacteristic
84#2568C2212yes—
85#2568C2211yescharacteristic
86#2567C2214yes—
87#2566C2214yes—
88#2562C2214yes—
89#2560C2218yes—
90#2553C2214yes—
91#2552C2214yes—
92#2552C2212yes—
93#2552C2214yes—
94#2552C2211yescharacteristic
95#2552C2212yes—
96#2552C2212yes—
97#2551C2212yes—
98#2551C2212yes—
99#2550C2214yes—
100#2547C2212yes—
101#2547C2211yescharacteristic
102#2547C2212yes—
103#2547C2211yescharacteristic
104#2547C2211yescharacteristic
105#2546C2214yes—
106#2546C2212yes—
107#2546C2212yes—
108#2546C2214yes—
109#2546C2212yes—
110#2545C2214yes—
111#2542C2211yescharacteristic
112#2538C2211yescharacteristic
113#2538C2214yes—
114#2538C2211yescharacteristic
115#2537C2211yescharacteristic
116#2514C2212yes—
117#2514C2212yes—
118#2511C2214yes—
119#2509C2214yes—
120#2509C2214yes—
121#2506C2214yes—
122#2499C2214yes—
123#2497C2214yes—
124#2496C2214yes—
125#2496C2214yes—
126#2496C2212yes—
127#2494C2214yes—
128#2494C2212yes—
129#2494C2212yes—
130#2492C2214yes—
131#2489C2212yes—
132#2487C2214yes—
133#2487C2214yes—
134#2473C2218yes—
135#2453C2214yes—
136#2453C2214yes—
137#2451C2214yes—
138#2447C2212yes—
139#2447C2212yes—
140#2446C2214yes—
141#2446C2214yes—
142#2442C2214yes—
143#2441C2214yes—
144#2441C2214yes—
145#2440C2214yes—
146#2440C2214yes—
147#2439C2214yes—
148#2436C2214yes—
149#2434C2214yes—
150#2434C2214yes—
151#2434C2214yes—
152#2429C2214yes—
153#2429C2214yes—
154#2427C2214yes—
155#2427C2212yes—
156#2426C2214yes—
157#2423C2214yes—
158#2423C2214yes—
159#2422C2212yes—
160#2421C2214yes—
161#2421C2212yes—
162#2421C2212yes—
163#2401C2214yes—
164#2401C2214yes—
165#2395C2214yes—
166#2365C2212yes—
167#2365C2212yes—
168#2365C2212yes—
169#2363C2214yes—
170#2360C2214yes—
171Q8×C4⋊C4C2212yes—
172Q8×C4⋊C4C2212yes—
173Q8×C4⋊C4C2212yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176Q8×C22⋊C4C2214yes—
177#2327C2214yes—
178#2326C2214yes—
179#2323C2214yes—
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2211yescharacteristic
184C4×#124C2212yes—
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2295C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194#2283C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#557—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⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218#529—48no—
219C2×#126C2318yes—
220C2×#126C2314yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2312yes—
224C2×#125C2318yes—
225C2×#125C2318yes—
226C2×#124C2312yes—
227C2×#124C2312yes—
228C2×#124C2312yes—
229C2×#124C2314yes—
230C2×#123C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2314yes—
249C2×C4×Q8C2314yes—
250C2×C4×Q8C2314yes—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2314yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2311yescharacteristic
259C2×#117C2314yes—
260C2×#117C2314yes—
261C22×C4⋊C4C2314yes—
262C22×C4⋊C4C2314yes—
263C22×C42C2312yes—
264C22×C42C2312yes—
265#401C2314yes—
266#401C2314yes—
267#401C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2314yes—
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#399C2318yes—
288#399C2318yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2318yes—
312#397C2314yes—
313#397C2314yes—
314#397C2314yes—
315#397C2314yes—
316#397C2314yes—
317#397C2314yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2314yes—
322#396C2314yes—
323#396C2318yes—
324#396C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#395C2318yes—
329#395C2318yes—
330#395C2318yes—
331#394C2314yes—
332#394C2318yes—
333#394C2314yes—
334#393C2318yes—
335#393C2318yes—
336#391C2318yes—
337#391C2314yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#391C2314yes—
343#391C2312yes—
344#391C2312yes—
345#391C2312yes—
346#391C2314yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2318yes—
351#391C2314yes—
352#391C2314yes—
353#391C2312yes—
354#391C2314yes—
355#391C2312yes—
356#391C2312yes—
357#390C2318yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2314yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2312yes—
394#389C2318yes—
395#389C2312yes—
396#389C2312yes—
397#388C2314yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2314yes—
427#386C2318yes—
428#386C2318yes—
429#386C2314yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2314yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2314yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#384C2312yes—
447#384C2312yes—
448#384C2312yes—
449#384C2314yes—
450#384C2312yes—
451#384C2314yes—
452#384C2312yes—
453#383C2314yes—
454#383C2314yes—
455#382C2314yes—
456#382C2312yes—
457#382C2312yes—
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#382C2312yes—
462#382C2314yes—
463#381C2314yes—
464#381C2314yes—
465#380C2312yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2318yes—
473#380C2314yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2312yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2314yes—
521#376C2314yes—
522#376C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2418yes—
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2414yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2418yes—
544C4⋊Q8—24no—
545C4⋊Q8—28no—
546C4⋊Q8—28no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—48no—
552C4⋊Q8—48no—
553C4⋊Q8—44no—
554C4⋊Q8—48no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557#126—48no—
558#126—416no—
559#125—44no—
560#125—48no—
561#125—48no—
562#125—416no—
563#125—416no—
564#124—28no—
565#124—44no—
566#124—44no—
567#124—48no—
568#123—48no—
569C22⋊Q8—28no—
570C22⋊Q8—28no—
571C22⋊Q8—416no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—28no—
577#121—44no—
578C4×Q8—24no—
579C4×Q8—28no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—24no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×Q8—48no—
588C4×Q8—48no—
589C4×D4—24no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—24no—
593C4×D4—24no—
594C4×D4—42no—
595C4×D4—48no—
596C4×D4—48no—
597#117—48no—
598#117—48no—
599C2×C4⋊C4—48no—
600C2×C4⋊C4—48no—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2412yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C42—28no—
683C2×C42—28no—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2411yescharacteristic
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2418yes—
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2414yes—
710#95C2414yes—
711#95C2414yes—
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2418yes—
740#95C2418yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759C24C2512yes—
760C24C2512yes—
761C2×Q8—22no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—28no—
767C2×Q8—28no—
768C2×Q8—24no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—28no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—48no—
778C2×Q8—832no—
779C2×Q82−1+414yes—
780C2×D4—28no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—22no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D42−1+414yes—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—42no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—48no—
810C22×C4C2512yes—
811C22×C4C2511yescharacteristic
812C22×C4C2512yes—
813C22×C4C2512yes—
814C22×C4C2512yes—
815C22×C4C2514yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2514yes—
825C22×C4C2518yes—
826C22×C4C2514yes—
827C22×C4C2511yescharacteristic
828C22×C4C2511yescharacteristic
829C22×C4C2511yescharacteristic
830C22×C4C2512yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—28no—
837C4⋊C4—28no—
838C4⋊C4—24no—
839C4⋊C4—28no—
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—22no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—28no—
846C4⋊C4—28no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—28no—
850C4⋊C4—24no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—22no—
867C4⋊C4—48no—
868C4⋊C4—48no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—48no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C22⋊C4—24no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—42no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—28no—
919C42—28no—
920C42—28no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—22no—
926C42—24no—
927C42—22no—
928C42—24no—
929C42—24no—
930C42—22no—
931C42—24no—
932C42—41no—
933C42—42no—
934C42—48no—
935C42—48no—
936C42—48no—
937C42H(5,𝔽2)14yes—
938C42H(5,𝔽2)14yes—
939C422−1+414yes—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23C2×2−1+414yes—
954C23C2611yescharacteristic
955Q8—28no—
956Q8—48no—
957Q8—416no—
958Q8—48no—
959Q8—48no—
960Q8—816no—
961D4—28no—
962D4—44no—
963D4—88no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—24no—
976C2×C4—24no—
977C2×C4—24no—
978C2×C4—24no—
979C2×C4—24no—
980C2×C4—22no—
981C2×C4—24no—
982C2×C4—22no—
983C2×C4—24no—
984C2×C4—28no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—24no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—48no—
1024C2×C4—48no—
1025C2×C4—48no—
1026C2×C4—48no—
1027C2×C4—48no—
1028C2×C4—84no—
1029C2×C4—816no—
1030C2×C4C2×H(5,𝔽2)12yes—
1031C2×C4C2×H(5,𝔽2)12yes—
1032C2×C4C2×H(5,𝔽2)12yes—
1033C2×C4C2×H(5,𝔽2)12yes—
1034C2×C4C2×H(5,𝔽2)12yes—
1035C2×C4C2×H(5,𝔽2)12yes—
1036C2×C4C2×2−1+412yes—
1037C2×C4C2×2−1+414yes—
1038C2×C4C2×2−1+412yes—
1039C2×C4C2×2−1+412yes—
1040C2×C4C2×2−1+412yes—
1041C2×C4C2×2−1+412yes—
1042C2×C4#58512yes—
1043C22—24no—
1044C22—24no—
1045C22—24no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—42no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22C22×H(5,𝔽2)11yescharacteristic
1058C22C22×H(5,𝔽2)11yescharacteristic
1059C22C22×2−1+411yescharacteristic
1060C22C22×2−1+411yescharacteristic
1061C22C22×2−1+411yescharacteristic
1062C22C2×#58511yescharacteristic
1063C222−1+611yescharacteristic
1064C4—24no—
1065C4—22no—
1066C4—22no—
1067C4—22no—
1068C4—42no—
1069C4—42no—
1070C4—42no—
1071C4—44no—
1072C4—42no—
1073C4—44no—
1074C4—48no—
1075C4—44no—
1076C4—41no—
1077C4—42no—
1078C4—42no—
1079C4—42no—
1080C4—44no—
1081C4—44no—
1082C4—44no—
1083C4—42no—
1084C4—42no—
1085C4#354614yes—
1086C4#355214yes—
1087C4#355214yes—
1088C2—44no—
1089C2—82no—
1090C2C2×#355211yescharacteristic
1091C2C2×#355211yescharacteristic
1092C2C2×#354611yescharacteristic
1093C2#6294211yescharacteristic
1094C2#6294611yescharacteristic
1095C2#6295911yescharacteristic
1096C2#6303211yescharacteristic
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. #59828C2semidirect
3. #59214C2semidirect
4. #59144C2semidirect
5. #53760C2semidirect
6. #53091C2semidirect
7. #53041C2semidirect
8. #52978C2semidirect
9. #42859C2semidirect
10. #42853C2semidirect
11. #42622C2semidirect
12. #39744C2semidirect
13. #39616C2semidirect
14. #39609C2semidirect
15. #39149C2semidirect
16. #39146C2semidirect
17. #39127C2semidirect
18. #37630C2semidirect
19. #37624C2semidirect
20. #37617C2semidirect
21. #36593C2semidirect
22. #36188C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #34945C2semidirect
25. #34945C2semidirect

Maximal subgroups

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

subgroupindex
#598282
#594212
#592142
#591442
#537602
#530912
#530412
#529782
#428592
#428532
#426222
#397442
#396162
#396092
#391492
#391462
#391272
#376302
#376242
#376172
#365932
#361882
D4×C4⋊Q82
#349452
#349322