Finite Group Databasebeta

← #7986678

Subgroups — #7986678

Order 512.

4693 conjugacy classes of subgroups.

The subgroup lattice has 1109 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C211yesmaximal, characteristic, complemented
2#59437C212yesmaximal, complemented
3#59427C212yesmaximal, complemented
4#59078C212yesmaximal, complemented
5#49244C218yesmaximal, complemented
6#45662C214yesmaximal, complemented
7#45391C214yesmaximal, complemented
8#44919C214yesmaximal, complemented
9#42718C214yesmaximal, complemented
10#42696C214yesmaximal, complemented
11#39905C214yesmaximal, complemented
12#39724C212yesmaximal, complemented
13#39515C212yesmaximal, complemented
14#38967C212yesmaximal, complemented
15#38955C212yesmaximal, complemented
16#36598C211yesmaximal, characteristic, complemented
17#36560C211yesmaximal, characteristic, complemented
18#36177C212yesmaximal, complemented
19#36174C212yesmaximal, complemented
20#36127C211yesmaximal, characteristic
21#35196C212yesmaximal, complemented
22#35180C212yesmaximal, complemented
23#34954C211yesmaximal, characteristic, complemented
24#34929C211yesmaximal, characteristic, complemented
25#34480C212yesmaximal, complemented
26C4×#554C211yesmaximal, characteristic, complemented
27C2×#557C2212yes—
28C2×#554C2211yescharacteristic
29C2×#547C2212yes—
30C2×#533C2212yes—
31C2×#532C2212yes—
32#2868C2211yescharacteristic
33#2862C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2850C2214yes—
38#2850C2214yes—
39#2827C2218yes—
40#2808C2214yes—
41#2798C2218yes—
42#2788C2218yes—
43#2787C2218yes—
44#2783C2218yes—
45#2770C2218yes—
46#2768C2218yes—
47#2759C2218yes—
48#2747C2218yes—
49#2742C2218yes—
50#2740C2218yes—
51#2737C2218yes—
52#2719C2218yes—
53#2711C2218yes—
54#2690C2218yes—
55#2687C2218yes—
56#2687C2218yes—
57#2653C2218yes—
58#2649C2218yes—
59#2639C2218yes—
60#2628C2214yes—
61#2621C2214yes—
62#2593C2214yes—
63#2592C2214yes—
64#2592C2214yes—
65#2592C2214yes—
66#2582C2211yescharacteristic
67#2582C2212yes—
68#2581C2214yes—
69#2577C2218yes—
70#2571C2212yes—
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2568C2214yes—
74#2568C2212yes—
75#2568C2212yes—
76#2565C2214yes—
77#2563C2212yes—
78#2563C2214yes—
79#2562C2218yes—
80#2556C2214yes—
81#2551C2211yescharacteristic
82#2550C2214yes—
83#2548C2211yescharacteristic
84#2548C2212yes—
85#2548C2211yescharacteristic
86#2547C2212yes—
87#2547C2214yes—
88#2547C2212yes—
89#2546C2212yes—
90#2546C2211yescharacteristic
91#2546C2212yes—
92#2545C2214yes—
93#2542C2211yescharacteristic
94#2538C2211yescharacteristic
95#2537C2212yes—
96#2537C2212yes—
97#2533C2218yes—
98#2532C2218yes—
99#2530C2218yes—
100#2526C2218yes—
101#2518C2218yes—
102#2516C2218yes—
103#2514C2214yes—
104#2514C2214yes—
105#2513C2212yes—
106#2513C2214yes—
107#2513C2212yes—
108#2511C2214yes—
109#2509C2214yes—
110#2506C2214yes—
111#2506C2212yes—
112#2506C2214yes—
113#2503C2214yes—
114#2497C2214yes—
115#2495C2214yes—
116#2495C2214yes—
117#2494C2214yes—
118#2493C2218yes—
119#2492C2212yes—
120#2490C2214yes—
121#2489C2214yes—
122#2485C2214yes—
123#2460C2218yes—
124#2454C2214yes—
125#2452C2212yes—
126#2448C2214yes—
127#2448C2212yes—
128#2448C2212yes—
129#2446C2214yes—
130#2446C2214yes—
131#2442C2214yes—
132#2442C2214yes—
133#2439C2214yes—
134#2432C2214yes—
135#2432C2214yes—
136#2429C2212yes—
137#2426C2214yes—
138#2422C2214yes—
139#2422C2214yes—
140#2421C2214yes—
141#2420C2214yes—
142#2420C2214yes—
143#2396C2214yes—
144#2395C2214yes—
145#2376C2218yes—
146#2370C2212yes—
147#2369C2211yescharacteristic
148#2368C2214yes—
149#2367C2214yes—
150#2365C2212yes—
151#2365C2212yes—
152#2365C2212yes—
153#2363C2214yes—
154#2360C2214yes—
155#2360C2212yes—
156#2356C2214yes—
157#2355C2211yescharacteristic
158#2355C2212yes—
159#2355C2212yes—
160#2355C2212yes—
161#2354C2212yes—
162#2354C2212yes—
163#2349C2212yes—
164D4×C4⋊C4C2212yes—
165D4×C4⋊C4C2212yes—
166D4×C4⋊C4C2211yescharacteristic
167#2346C2214yes—
168#2345C2214yes—
169#2345C2212yes—
170#2341C2214yes—
171#2335C2218yes—
172#2324C2214yes—
173#2323C2214yes—
174#2316C2214yes—
175#2314C2214yes—
176#2311C2214yes—
177#2311C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2211yescharacteristic
184C4×#125C2212yes—
185C4×#124C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2214yes—
190#2293C2212yes—
191#2293C2212yes—
192#2293C2212yes—
193#2283C2214yes—
194C42×Q8C2211yescharacteristic
195C42×Q8C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2314yes—
200#557—48no—
201#554—28no—
202#547—216no—
203#533—48no—
204#532—48no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2311yescharacteristic
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2314yes—
220C2×#124C2314yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2314yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117C2314yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2314yes—
261C22×C4⋊C4C2312yes—
262C22×C42C2312yes—
263C22×C42C2314yes—
264#401C2318yes—
265#400C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2314yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#399C2314yes—
277#399C2318yes—
278#399C2314yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2314yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#397C2318yes—
297#397C2318yes—
298#396C2314yes—
299#396C2318yes—
300#396C2318yes—
301#396C2314yes—
302#395C2318yes—
303#395C2314yes—
304#394C2314yes—
305#394C2318yes—
306#394C2318yes—
307#394C2318yes—
308#394C2314yes—
309#394C2318yes—
310#394C2318yes—
311#393C2318yes—
312#393C2318yes—
313#393C2318yes—
314#393C2314yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2314yes—
326#391C2314yes—
327#391C2318yes—
328#391C2314yes—
329#391C2312yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2312yes—
334#391C2314yes—
335#390C2312yes—
336#390C2312yes—
337#390C2312yes—
338#390C2312yes—
339#390C2314yes—
340#390C2314yes—
341#390C2312yes—
342#390C2312yes—
343#390C2314yes—
344#390C2312yes—
345#390C2318yes—
346#390C2318yes—
347#390C2312yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2312yes—
357#389C2312yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2314yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2318yes—
369#389C2314yes—
370#389C2318yes—
371#389C2312yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2314yes—
419#387C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2314yes—
423#387C2314yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#385C2314yes—
429#385C2318yes—
430#385C2318yes—
431#385C2314yes—
432#385C2318yes—
433#385C2314yes—
434#385C2318yes—
435#385C2318yes—
436#385C2314yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2312yes—
441#384C2311yescharacteristic
442#384C2312yes—
443#384C2312yes—
444#384C2312yes—
445#383C2318yes—
446#383C2318yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2318yes—
452#382C2314yes—
453#382C2314yes—
454#382C2312yes—
455#382C2312yes—
456#381C2318yes—
457#381C2318yes—
458#380C2318yes—
459#380C2318yes—
460#380C2318yes—
461#380C2318yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2318yes—
466#380C2312yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2314yes—
472#380C2312yes—
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2312yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519#376C2318yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2311yescharacteristic
523C43C2312yes—
524C2×#41—216no—
525C2×#41—48no—
526C2×#41—48no—
527C22×Q8C2411yescharacteristic
528C22×Q8C2412yes—
529C22×Q8C2411yescharacteristic
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×D4C2412yes—
534C22×D4C2412yes—
535C22×D4C2411yescharacteristic
536C22×D4C2412yes—
537C22×D4C2418yes—
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2418yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C4⋊Q8—28no—
546C4⋊Q8—24no—
547C4⋊Q8—28no—
548C4⋊Q8—24no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—48no—
554#127—24no—
555#125—28no—
556#125—48no—
557#125—48no—
558#125—416no—
559#124—44no—
560#124—48no—
561#124—44no—
562#124—48no—
563#123—232no—
564C22⋊Q8—216no—
565C22⋊Q8—28no—
566C22⋊Q8—216no—
567C22⋊Q8—48no—
568C22⋊Q8—44no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571#121—216no—
572#121—48no—
573#121—48no—
574C4×Q8—24no—
575C4×Q8—24no—
576C4×Q8—28no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—44no—
580C4×Q8—48no—
581C4×Q8—42no—
582C4×Q8—48no—
583C4×Q8—42no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×D4—28no—
587C4×D4—28no—
588C4×D4—24no—
589C4×D4—28no—
590C4×D4—44no—
591C4×D4—42no—
592C4×D4—48no—
593C4×D4—48no—
594C4×D4—44no—
595C4×D4#4118yes—
596#117—48no—
597#117—48no—
598#117—48no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—216no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2412yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2418yes—
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⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2411yescharacteristic
656C2×C22⋊C4C2414yes—
657C2×C22⋊C4C2414yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2412yes—
683C2×C42—28no—
684C2×C42—48no—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2414yes—
689C2×C42C2411yescharacteristic
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2411yescharacteristic
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2418yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#95C2412yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2418yes—
721#95C2418yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2414yes—
729#95C2414yes—
730#95C2412yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758C24C2514yes—
759C24C2512yes—
760#41—832no—
761C2×Q8—22no—
762C2×Q8—28no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—28no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—28no—
773C2×Q8—24no—
774C2×Q8—44no—
775C2×Q8—42no—
776C2×Q8—44no—
777C2×Q8—42no—
778C2×Q8—44no—
779C2×D4—216no—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—24no—
783C2×D4—24no—
784C2×D4—22no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4C2×#4114yes—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—24no—
799C22×C4—28no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—28no—
803C22×C4—216no—
804C22×C4—24no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—48no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—42no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4C2×#4118yes—
815C22×C4C2512yes—
816C22×C4C2512yes—
817C22×C4C2514yes—
818C22×C4C2514yes—
819C22×C4C2512yes—
820C22×C4C2512yes—
821C22×C4C2512yes—
822C22×C4C2514yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2518yes—
827C22×C4C2511yescharacteristic
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2511yescharacteristic
833C22×C4C2512yes—
834C22×C4C2511yescharacteristic
835C22×C4C2511yescharacteristic
836C22×C4C2511yescharacteristic
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C4⋊C4—22no—
840C4⋊C4—28no—
841C4⋊C4—216no—
842C4⋊C4—28no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—22no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—22no—
858C4⋊C4—24no—
859C4⋊C4—22no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—44no—
870C4⋊C4—42no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—44no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—48no—
880C4⋊C4—42no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4C2×#4114yes—
893C22⋊C4—28no—
894C22⋊C4—216no—
895C22⋊C4—28no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—42no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4C2×#4118yes—
920C42—24no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—28no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—28no—
930C42—24no—
931C42—24no—
932C42—22no—
933C42—22no—
934C42—24no—
935C42—22no—
936C42—44no—
937C42—44no—
938C42—41no—
939C42—42no—
940C42—42no—
941C42—48no—
942C42—42no—
943C42—42no—
944C42—48no—
945C42—48no—
946C42C2×#4114yes—
947C42H(5,𝔽2)14yes—
948C422−1+414yes—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23C22×#4114yes—
963C23C2611yescharacteristic
964Q8—44no—
965Q8—416no—
966Q8—48no—
967Q8—44no—
968Q8—84no—
969Q8—88no—
970D4—28no—
971D4—48no—
972D4—48no—
973D4—48no—
974D4—816no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—216no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—28no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—24no—
996C2×C4—22no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—416no—
1036C2×C4—48no—
1037C2×C4—84no—
1038C2×C4—816no—
1039C2×C4—88no—
1040C2×C4—88no—
1041C2×C4C22×#4112yes—
1042C2×C4C22×#4114yes—
1043C2×C4C22×#4112yes—
1044C2×C4C22×#4112yes—
1045C2×C4C2×H(5,𝔽2)12yes—
1046C2×C4C2×H(5,𝔽2)12yes—
1047C2×C4C2×H(5,𝔽2)12yes—
1048C2×C4C2×2−1+412yes—
1049C2×C4C2×2−1+412yes—
1050C2×C4C2×2−1+412yes—
1051C2×C4#58512yes—
1052C2×C4#58512yes—
1053C2×C4#58512yes—
1054C22—24no—
1055C22—24no—
1056C22—24no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—44no—
1062C22—44no—
1063C22—44no—
1064C22—44no—
1065C22—44no—
1066C22—44no—
1067C22—44no—
1068C22C23×#4111yescharacteristic
1069C22C22×H(5,𝔽2)11yescharacteristic
1070C22C22×2−1+411yescharacteristic
1071C22C2×#58511yescharacteristic
1072C22C2×#58511yescharacteristic
1073C22C2×#58511yescharacteristic
1074C222−1+611yescharacteristic
1075C4—22no—
1076C4—24no—
1077C4—22no—
1078C4—22no—
1079C4—42no—
1080C4—44no—
1081C4—42no—
1082C4—44no—
1083C4—42no—
1084C4—41no—
1085C4—42no—
1086C4—44no—
1087C4—42no—
1088C4—44no—
1089C4—48no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—44no—
1094C4—42no—
1095C4—42no—
1096C4#350714yes—
1097C4#351414yes—
1098C4#354714yes—
1099C2—44no—
1100C2—84no—
1101C2C2×#354711yescharacteristic
1102C2C2×#350711yescharacteristic
1103C2C2×#351411yescharacteristic
1104C2#6292511yescharacteristic
1105C2#6295611yescharacteristic
1106C2#6299511yescharacteristic
1107C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59863C2semidirect
2. #59437C2semidirect
3. #59427C2semidirect
4. #59078C2semidirect
5. #49244C2semidirect
6. #45662C2semidirect
7. #45391C2semidirect
8. #44919C2semidirect
9. #42718C2semidirect
10. #42696C2semidirect
11. #39905C2semidirect
12. #39724C2semidirect
13. #39515C2semidirect
14. #38967C2semidirect
15. #38955C2semidirect
16. #36598C2semidirect
17. #36560C2semidirect
18. #36177C2semidirect
19. #36174C2semidirect
21. #35196C2semidirect
22. #35180C2semidirect
23. #34954C2semidirect
24. #34929C2semidirect
25. #34480C2semidirect
26. C4×#554C2semidirect

Maximal subgroups

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

subgroupindex
#598632
#594372
#594272
#590782
#492442
#456622
#453912
#449192
#427182
#426962
#399052
#397242
#395152
#389672
#389552
#365982
#365602
#361772
#361742
#361272
#351962
#351802
#349542
#349292
#344802
C4×#5542