Finite Group Databasebeta

← #8429509

Subgroups — #8429509

Order 512.

4651 conjugacy classes of subgroups.

The subgroup lattice has 1117 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C212yesmaximal, complemented
2#59817C211yesmaximal, characteristic, complemented
3#59459C212yesmaximal, complemented
4#59243C212yesmaximal, complemented
5#53827C218yesmaximal, complemented
6#53136C214yesmaximal, complemented
7#53126C214yesmaximal, complemented
8#52983C214yesmaximal, complemented
9#42937C214yesmaximal, complemented
10#42837C214yesmaximal, complemented
11#42762C214yesmaximal, complemented
12#39771C212yesmaximal, complemented
13#39596C212yesmaximal, complemented
14#39202C212yesmaximal
15#39167C212yesmaximal, complemented
16#38954C212yesmaximal, complemented
17#38911C212yesmaximal, complemented
18#37631C212yesmaximal, complemented
19#37631C212yesmaximal, complemented
20#37622C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36594C211yesmaximal, characteristic, complemented
23#36188C211yesmaximal, characteristic, complemented
24#34951C211yesmaximal, characteristic, complemented
25#34934C211yesmaximal, characteristic
26#34929C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#556C2212yes—
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×#533C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2858C2212yes—
36#2857C2212yes—
37#2838C2218yes—
38#2838C2218yes—
39#2838C2218yes—
40#2832C2218yes—
41#2830C2218yes—
42#2827C2218yes—
43#2814C2218yes—
44#2797C2218yes—
45#2796C2218yes—
46#2792C2218yes—
47#2790C2218yes—
48#2786C2218yes—
49#2771C2218yes—
50#2752C2218yes—
51#2751C2218yes—
52#2751C2218yes—
53#2727C2218yes—
54#2723C2218yes—
55#2723C2218yes—
56#2720C2218yes—
57#2698C2218yes—
58#2698C2218yes—
59#2692C2218yes—
60#2689C2218yes—
61#2687C2218yes—
62#2683C2214yes—
63#2664C2218yes—
64#2650C2218yes—
65#2650C2218yes—
66#2650C2218yes—
67#2645C2214yes—
68#2640C2214yes—
69#2640C2214yes—
70#2628C2214yes—
71#2628C2214yes—
72#2625C2214yes—
73#2625C2214yes—
74#2624C2214yes—
75#2621C2214yes—
76#2594C2218yes—
77#2592C2214yes—
78#2586C2218yes—
79#2585C2214yes—
80#2584C2214yes—
81#2582C2211yescharacteristic
82#2582C2212yes—
83#2580C2214yes—
84#2571C2212yes—
85#2570C2214yes—
86#2568C2212yes—
87#2568C2212yes—
88#2568C2211yescharacteristic
89#2567C2214yes—
90#2567C2214yes—
91#2556C2214yes—
92#2554C2214yes—
93#2552C2211yescharacteristic
94#2552C2211yescharacteristic
95#2551C2212yes—
96#2551C2211yescharacteristic
97#2550C2214yes—
98#2548C2214yes—
99#2548C2211yescharacteristic
100#2547C2212yes—
101#2547C2212yes—
102#2547C2212yes—
103#2546C2211yescharacteristic
104#2546C2211yescharacteristic
105#2545C2214yes—
106#2544C2214yes—
107#2542C2211yescharacteristic
108#2542C2214yes—
109#2541C2211yescharacteristic
110#2538C2212yes—
111#2538C2211yescharacteristic
112#2538C2211yescharacteristic
113#2538C2212yes—
114#2538C2212yes—
115#2538C2212yes—
116#2513C2214yes—
117#2512C2218yes—
118#2512C2214yes—
119#2512C2214yes—
120#2512C2212yes—
121#2511C2212yes—
122#2511C2214yes—
123#2509C2212yes—
124#2506C2212yes—
125#2499C2214yes—
126#2499C2214yes—
127#2496C2214yes—
128#2496C2214yes—
129#2494C2214yes—
130#2494C2214yes—
131#2492C2214yes—
132#2492C2212yes—
133#2492C2214yes—
134#2490C2214yes—
135#2490C2212yes—
136#2453C2212yes—
137#2452C2214yes—
138#2452C2214yes—
139#2452C2212yes—
140#2451C2214yes—
141#2451C2214yes—
142#2451C2214yes—
143#2448C2214yes—
144#2448C2214yes—
145#2448C2214yes—
146#2447C2214yes—
147#2447C2214yes—
148#2447C2214yes—
149#2446C2214yes—
150#2446C2212yes—
151#2445C2212yes—
152#2434C2214yes—
153#2429C2212yes—
154#2426C2212yes—
155#2420C2214yes—
156#2415C2214yes—
157#2415C2214yes—
158#2415C2214yes—
159#2415C2214yes—
160#2409C2214yes—
161#2409C2214yes—
162#2409C2214yes—
163#2402C2214yes—
164#2396C2214yes—
165#2392C2214yes—
166#2370C2214yes—
167#2366C2212yes—
168#2365C2212yes—
169#2365C2212yes—
170#2365C2212yes—
171#2355C2212yes—
172#2355C2212yes—
173#2354C2214yes—
174#2354C2212yes—
175#2354C2212yes—
176Q8×C4⋊C4C2214yes—
177#2326C2214yes—
178#2324C2214yes—
179#2310C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2212yes—
186C4×#127C2211yescharacteristic
187C4×#127C2212yes—
188C4×#125C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191#2295C2212yes—
192#2295C2212yes—
193#2293C2212yes—
194#2293C2212yes—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×Q8C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#556—48no—
201#556—48no—
202D4×Q8—48no—
203D4×Q8—48no—
204#533—48no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2312yes—
216C2×#127C2311yescharacteristic
217C2×#127C2312yes—
218#529—48no—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#126C2318yes—
222C2×#125C2312yes—
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#124C2314yes—
226C2×#124C2312yes—
227C2×#124C2314yes—
228C2×#124C2314yes—
229C2×#123C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2318yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2312yes—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2314yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×D4C2312yes—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2311yescharacteristic
265C2×#117C2314yes—
266C2×#117C2314yes—
267C2×#117C2314yes—
268C2×#117C2314yes—
269C22×C42C2312yes—
270#401C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2314yes—
281#400C2314yes—
282#399C2318yes—
283#399C2318yes—
284#399C2318yes—
285#399C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2314yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#396C2314yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#396C2318yes—
317#396C2314yes—
318#396C2314yes—
319#396C2318yes—
320#395C2318yes—
321#395C2318yes—
322#395C2318yes—
323#395C2318yes—
324#395C2318yes—
325#395C2314yes—
326#395C2318yes—
327#394C2314yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2314yes—
334#393C2318yes—
335#393C2318yes—
336#393C2314yes—
337#393C2318yes—
338#393C2318yes—
339#393C2318yes—
340#392C2314yes—
341#391C2312yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2314yes—
350#391C2318yes—
351#391C2314yes—
352#391C2318yes—
353#391C2318yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2312yes—
360#391C2312yes—
361#391C2312yes—
362#391C2314yes—
363#391C2312yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2314yes—
368#390C2312yes—
369#390C2312yes—
370#390C2314yes—
371#390C2318yes—
372#390C2314yes—
373#390C2312yes—
374#390C2314yes—
375#390C2314yes—
376#390C2314yes—
377#390C2314yes—
378#390C2318yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2312yes—
388#389C2314yes—
389#389C2314yes—
390#389C2314yes—
391#389C2312yes—
392#389C2314yes—
393#389C2314yes—
394#389C2312yes—
395#389C2314yes—
396#389C2312yes—
397#389C2312yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2318yes—
402#389C2318yes—
403#389C2314yes—
404#389C2312yes—
405#389C2312yes—
406#389C2318yes—
407#389C2314yes—
408#389C2318yes—
409#389C2314yes—
410#389C2314yes—
411#389C2312yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2312yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2314yes—
424#388C2314yes—
425#388C2318yes—
426#388C2314yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2318yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2314yes—
440#387C2314yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#387C2318yes—
445#387C2318yes—
446#387C2314yes—
447#387C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2314yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2314yes—
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2311yescharacteristic
463#384C2312yes—
464#384C2318yes—
465#384C2312yes—
466#384C2312yes—
467#384C2312yes—
468#384C2312yes—
469#382C2312yes—
470#382C2314yes—
471#382C2314yes—
472#382C2314yes—
473#382C2314yes—
474#381C2318yes—
475#381C2318yes—
476#380C2314yes—
477#380C2314yes—
478#380C2312yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2314yes—
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2312yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2311yescharacteristic
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521#376C2314yes—
522C43C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2411yescharacteristic
530C22×Q8C2414yes—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2418yes—
535C22×D4C2412yes—
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C23×C4C2412yes—
542C23×C4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2418yes—
546C4⋊Q8—24no—
547C4⋊Q8—24no—
548C4⋊Q8—28no—
549C4⋊Q8—28no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557#127—24no—
558#127—44no—
559#126—48no—
560#126—416no—
561#126—416no—
562#125—28no—
563#125—44no—
564#125—48no—
565#124—48no—
566#124—44no—
567#124—48no—
568#124—48no—
569#123—48no—
570C22⋊Q8—416no—
571C22⋊Q8—416no—
572C22⋊Q8—48no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581#121—28no—
582#121—44no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—28no—
587C4×Q8—28no—
588C4×Q8—24no—
589C4×Q8—24no—
590C4×Q8—48no—
591C4×Q8—42no—
592C4×Q8—48no—
593C4×Q8—48no—
594C4×Q8—48no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—42no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—44no—
603C4×D4—48no—
604C4×D4—48no—
605#117—48no—
606#117—48no—
607#117—48no—
608#117—48no—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C42—28no—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2411yescharacteristic
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2411yescharacteristic
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2412yes—
715C2×C42C2418yes—
716C2×C42C2411yescharacteristic
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2412yes—
727#95C2412yes—
728#95C2412yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764C24C2512yes—
765C24C2514yes—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—28no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—28no—
777C2×Q8—28no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—44no—
782C2×Q8—48no—
783C2×Q8—48no—
784C2×Q8—44no—
785C2×Q8—48no—
786C2×Q8—44no—
787C2×Q8—832no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—44no—
800C2×D4—42no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—42no—
805C2×D4—44no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—48no—
821C22×C4C2512yes—
822C22×C4C2512yes—
823C22×C4C2512yes—
824C22×C4C2511yescharacteristic
825C22×C4C2512yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2514yes—
829C22×C4C2518yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2514yes—
833C22×C4C2514yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C22×C4C2511yescharacteristic
841C22×C4C2512yes—
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C4⋊C4—22no—
846C4⋊C4—24no—
847C4⋊C4—28no—
848C4⋊C4—22no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—22no—
854C4⋊C4—28no—
855C4⋊C4—24no—
856C4⋊C4—24no—
857C4⋊C4—28no—
858C4⋊C4—22no—
859C4⋊C4—24no—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—28no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—22no—
874C4⋊C4—24no—
875C4⋊C4—22no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—44no—
887C4⋊C4—42no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C42−1+414yes—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—24no—
906C22⋊C4—24no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—42no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—28no—
936C42—28no—
937C42—24no—
938C42—22no—
939C42—24no—
940C42—24no—
941C42—24no—
942C42—22no—
943C42—24no—
944C42—22no—
945C42—24no—
946C42—24no—
947C42—41no—
948C42—42no—
949C42—42no—
950C42—48no—
951C42—48no—
952C42—48no—
953C42—42no—
954C42H(5,𝔽2)14yes—
955C42H(5,𝔽2)14yes—
956C422−1+414yes—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—24no—
970C23—22no—
971C23C2611yescharacteristic
972Q8—44no—
973Q8—48no—
974Q8—48no—
975Q8—44no—
976Q8—416no—
977Q8—88no—
978Q8—816no—
979D4—48no—
980D4—48no—
981D4—44no—
982D4—88no—
983D4—84no—
984D4—88no—
985C2×C4—21no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—24no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—22no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—28no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—48no—
1045C2×C4—416no—
1046C2×C4—48no—
1047C2×C4—84no—
1048C2×C4—816no—
1049C2×C4C2×H(5,𝔽2)12yes—
1050C2×C4C2×H(5,𝔽2)12yes—
1051C2×C4C2×H(5,𝔽2)12yes—
1052C2×C4C2×H(5,𝔽2)12yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×H(5,𝔽2)12yes—
1055C2×C4C2×2−1+414yes—
1056C2×C4C2×2−1+412yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4C2×2−1+412yes—
1059C2×C4C2×2−1+412yes—
1060C2×C4#58512yes—
1061C2×C4#58512yes—
1062C22—42no—
1063C22—44no—
1064C22—44no—
1065C22—42no—
1066C22—42no—
1067C22—44no—
1068C22—42no—
1069C22—44no—
1070C22—44no—
1071C22—42no—
1072C22—42no—
1073C22—44no—
1074C22—42no—
1075C22—44no—
1076C22C22×H(5,𝔽2)11yescharacteristic
1077C22C22×H(5,𝔽2)11yescharacteristic
1078C22C22×2−1+411yescharacteristic
1079C22C22×2−1+411yescharacteristic
1080C22C2×#58511yescharacteristic
1081C22C2×#58511yescharacteristic
1082C222−1+611yescharacteristic
1083C4—24no—
1084C4—22no—
1085C4—22no—
1086C4—22no—
1087C4—48no—
1088C4—42no—
1089C4—44no—
1090C4—44no—
1091C4—44no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—41no—
1096C4—42no—
1097C4—42no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—42no—
1102C4—44no—
1103C4—42no—
1104C4#354614yes—
1105C4#355014yes—
1106C4#355414yes—
1107C2—84no—
1108C2—82no—
1109C2C2×#355411yescharacteristic
1110C2C2×#354611yescharacteristic
1111C2C2×#355011yescharacteristic
1112C2#6293211yescharacteristic
1113C2#6294611yescharacteristic
1114C2#6296011yescharacteristic
1115C2#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. #59821C2semidirect
2. #59817C2semidirect
3. #59459C2semidirect
4. #59243C2semidirect
5. #53827C2semidirect
6. #53136C2semidirect
7. #53126C2semidirect
8. #52983C2semidirect
9. #42937C2semidirect
10. #42837C2semidirect
11. #42762C2semidirect
12. #39771C2semidirect
13. #39596C2semidirect
15. #39167C2semidirect
16. #38954C2semidirect
17. #38911C2semidirect
18. #37631C2semidirect
19. #37631C2semidirect
20. #37622C2semidirect
21. #36598C2semidirect
22. #36594C2semidirect
23. #36188C2semidirect
24. #34951C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#598172
#594592
#592432
#538272
#531362
#531262
#529832
#429372
#428372
#427622
#397712
#395962
#392022
#391672
#389542
#389112
#376312
#376222
#365982
#365942
#361882
#349512
#349342
#349292