Finite Group Databasebeta

← #7739321

Subgroups — #7739321

Order 512.

4876 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59864C212yesmaximal, complemented
2#59442C212yesmaximal, complemented
3#59436C212yesmaximal, complemented
4#59426C212yesmaximal, complemented
5#51615C218yesmaximal, complemented
6#45368C214yesmaximal, complemented
7#45254C214yesmaximal, complemented
8#45251C214yesmaximal, complemented
9#45250C214yesmaximal, complemented
10#39771C212yesmaximal, complemented
11#39146C212yesmaximal, complemented
12#38986C212yesmaximal, complemented
13#38940C212yesmaximal, complemented
14#37414C214yesmaximal, complemented
15#36586C212yesmaximal, complemented
16#36476C212yesmaximal, complemented
17#36116C212yesmaximal, complemented
18#36115C212yesmaximal, complemented
19#35664C214yesmaximal, complemented
20#35289C211yesmaximal, characteristic, complemented
21#35279C211yesmaximal, characteristic, complemented
22#34978C211yesmaximal, characteristic, complemented
23#34977C211yesmaximal, characteristic
24#34368C211yesmaximal, characteristic, complemented
25#34209C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#532C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C2×#529C2214yes—
30C2×#519C2212yes—
31C2×C4×#41C2211yescharacteristic
32#2862C2212yes—
33#2858C2212yes—
34#2857C2212yes—
35#2857C2212yes—
36#2855C2214yes—
37#2850C2214yes—
38#2804C2218yes—
39#2796C2218yes—
40#2789C2218yes—
41#2775C2218yes—
42#2770C2218yes—
43#2760C2218yes—
44#2759C2218yes—
45#2758C2218yes—
46#2751C2218yes—
47#2751C2218yes—
48#2751C2218yes—
49#2750C2218yes—
50#2749C2218yes—
51#2746C2218yes—
52#2745C2218yes—
53#2737C2218yes—
54#2645C2214yes—
55#2640C2214yes—
56#2640C2214yes—
57#2628C2214yes—
58#2612C2214yes—
59#2610C2214yes—
60#2609C2218yes—
61#2607C2218yes—
62#2599C2218yes—
63#2598C2218yes—
64#2596C2218yes—
65#2592C2214yes—
66#2589C2218yes—
67#2580C2214yes—
68#2580C2218yes—
69#2580C2214yes—
70#2571C2214yes—
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2570C2214yes—
74#2568C2212yes—
75#2567C2212yes—
76#2567C2211yescharacteristic
77#2563C2214yes—
78#2563C2212yes—
79#2563C2212yes—
80#2563C2212yes—
81#2563C2211yescharacteristic
82#2562C2214yes—
83#2552C2211yescharacteristic
84#2552C2211yescharacteristic
85#2551C2211yescharacteristic
86#2548C2211yescharacteristic
87#2547C2212yes—
88#2547C2212yes—
89#2542C2212yes—
90#2541C2211yescharacteristic
91#2514C2214yes—
92#2514C2214yes—
93#2514C2214yes—
94#2513C2214yes—
95#2512C2214yes—
96#2510C2218yes—
97#2504C2214yes—
98#2500C2212yes—
99#2496C2214yes—
100#2495C2214yes—
101#2494C2214yes—
102#2494C2214yes—
103#2492C2214yes—
104#2487C2214yes—
105#2487C2214yes—
106#2487C2214yes—
107#2486C2214yes—
108#2485C2214yes—
109#2479C2218yes—
110#2478C2218yes—
111#2471C2218yes—
112#2471C2218yes—
113#2469C2218yes—
114#2467C2218yes—
115#2458C2218yes—
116#2453C2214yes—
117#2448C2214yes—
118#2447C2214yes—
119#2447C2214yes—
120#2445C2214yes—
121#2442C2214yes—
122#2441C2212yes—
123#2441C2212yes—
124#2439C2214yes—
125#2439C2212yes—
126#2439C2212yes—
127#2436C2214yes—
128#2431C2212yes—
129#2427C2214yes—
130#2426C2214yes—
131#2423C2214yes—
132#2419C2218yes—
133#2414C2212yes—
134#2414C2212yes—
135#2409C2214yes—
136#2396C2214yes—
137#2388C2214yes—
138#2379C2214yes—
139#2369C2212yes—
140#2366C2214yes—
141#2366C2212yes—
142#2365C2212yes—
143#2365C2212yes—
144#2365C2212yes—
145#2365C2212yes—
146#2357C2214yes—
147#2355C2211yescharacteristic
148#2355C2214yes—
149#2355C2211yescharacteristic
150#2354C2214yes—
151#2354C2212yes—
152#2354C2212yes—
153#2352C2214yes—
154#2352C2212yes—
155#2352C2212yes—
156D4×C4⋊C4C2212yes—
157D4×C4⋊C4C2214yes—
158D4×C4⋊C4C2212yes—
159D4×C4⋊C4C2211yescharacteristic
160D4×C4⋊C4C2211yescharacteristic
161#2347C2214yes—
162#2347C2212yes—
163#2344C2214yes—
164#2344C2214yes—
165#2344C2214yes—
166#2343C2214yes—
167#2339C2212yes—
168#2327C2214yes—
169#2326C2214yes—
170#2324C2214yes—
171#2324C2214yes—
172#2320C2214yes—
173#2317C2212yes—
174#2311C2212yes—
175#2311C2214yes—
176#2311C2212yes—
177#2311C2212yes—
178#2310C2212yes—
179C4×C4⋊Q8C2212yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×#127C2212yes—
184C4×#125C2212yes—
185C4×#125C2212yes—
186C4×#124C2212yes—
187C4×C22⋊Q8C2214yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2290C2214yes—
192#2285C2211yescharacteristic
193#2285C2211yescharacteristic
194#2283C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×Q8C2312yes—
202#532—28no—
203C2×C4⋊Q8—28no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2312yes—
212C2×#127C2311yescharacteristic
213#529—416no—
214C2×#126C2318yes—
215C2×#125C2312yes—
216C2×#125C2312yes—
217C2×#124C2312yes—
218C2×#124C2314yes—
219C2×#124C2312yes—
220C2×#124C2314yes—
221C2×#123C2318yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×#121C2312yes—
225C2×#121C2312yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228#519—48no—
229C4×#41—28no—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2312yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2318yes—
250C2×#117C2311yescharacteristic
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2312yes—
258C2×#117C2314yes—
259C2×#117C2318yes—
260C2×#117C2318yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C42C2312yes—
267C22×C42C2314yes—
268C22×C42C2311yescharacteristic
269#401C2318yes—
270#401C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2318yes—
280#399C2318yes—
281#399C2318yes—
282#399C2314yes—
283#398C2318yes—
284#398C2318yes—
285#398C2314yes—
286#398C2314yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#396C2314yes—
296#396C2318yes—
297#396C2314yes—
298#395C2318yes—
299#395C2314yes—
300#395C2314yes—
301#394C2318yes—
302#394C2318yes—
303#394C2314yes—
304#394C2314yes—
305#394C2314yes—
306#393C2318yes—
307#393C2318yes—
308#393C2318yes—
309#393C2318yes—
310#393C2314yes—
311#393C2318yes—
312#393C2318yes—
313#393C2314yes—
314#392C2314yes—
315#392C2314yes—
316#392C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2318yes—
326#391C2314yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2318yes—
335#390C2312yes—
336#390C2314yes—
337#390C2312yes—
338#390C2314yes—
339#390C2314yes—
340#390C2314yes—
341#390C2318yes—
342#390C2314yes—
343#390C2318yes—
344#390C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2312yes—
349#390C2312yes—
350#390C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2312yes—
354#389C2312yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2314yes—
360#389C2314yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2312yes—
366#389C2314yes—
367#389C2314yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2314yes—
386#388C2318yes—
387#388C2314yes—
388#388C2318yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2314yes—
408#387C2314yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2318yes—
417#386C2318yes—
418#386C2318yes—
419#386C2318yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2314yes—
424#386C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2314yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#384C2312yes—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2312yes—
439#384C2312yes—
440#384C2314yes—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#383C2318yes—
444#383C2314yes—
445#383C2318yes—
446#382C2312yes—
447#382C2312yes—
448#382C2314yes—
449#382C2314yes—
450#382C2312yes—
451#382C2318yes—
452#382C2314yes—
453#382C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2312yes—
457#381C2318yes—
458#381C2314yes—
459#381C2318yes—
460#381C2318yes—
461#380C2312yes—
462#380C2314yes—
463#380C2314yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2312yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2314yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479#380C2318yes—
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2318yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2312yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2311yescharacteristic
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2318yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2314yes—
519#376C2312yes—
520#376C2312yes—
521C2×#95C2314yes—
522C43C2312yes—
523C43C2312yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—44no—
528C2×#41—44no—
529C2×#41—42no—
530C22×Q8—28no—
531C22×Q8—44no—
532C22×Q8—44no—
533C22×Q8C2414yes—
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2414yes—
538C22×D4C2412yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2412yes—
542C22×D4C2411yescharacteristic
543C22×D4C2414yes—
544C22×D4C2414yes—
545C22×D4C2412yes—
546C23×C4C2412yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2414yes—
554C23×C4C2414yes—
555C23×C4C2418yes—
556C23×C4C2414yes—
557C4⋊Q8—28no—
558C4⋊Q8—28no—
559C4⋊Q8—28no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564#127—28no—
565#127—24no—
566#126—416no—
567#125—28no—
568#125—44no—
569#124—28no—
570#124—44no—
571#124—48no—
572#124—48no—
573#123—416no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—44no—
580C4×Q8—216no—
581C4×Q8—24no—
582C4×Q8—24no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C4×D4—28no—
588C4×D4—28no—
589C4×D4—28no—
590C4×D4—24no—
591C4×D4—24no—
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—48no—
595C4×D4—44no—
596C4×D4—48no—
597C4×D4—416no—
598C4×D4—48no—
599C4×D4—48no—
600#117—24no—
601#117—24no—
602#117—28no—
603#117—44no—
604#117—44no—
605#117—416no—
606#117—416no—
607#117—42no—
608#117—42no—
609#117—48no—
610#117—42no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2411yescharacteristic
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C42—28no—
695C2×C42—48no—
696C2×C42#4118yes—
697C2×C42C2418yes—
698C2×C42C2412yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2414yes—
713C2×C42C2418yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723#95C2412yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2412yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2412yes—
733#95C2412yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767C24C2514yes—
768C24C2511yescharacteristic
769C24C2512yes—
770#41—416no—
771#41—816no—
772C2×Q8—22no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—24no—
776C2×Q8—28no—
777C2×Q8—22no—
778C2×Q8—28no—
779C2×Q8—22no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—432no—
788C2×D4—24no—
789C2×D4—28no—
790C2×D4—24no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—22no—
794C2×D4—24no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—28no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—44no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D42−1+414yes—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—28no—
829C22×C4—28no—
830C22×C4—24no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—42no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—44no—
842C22×C4C2×#4114yes—
843C22×C4C2×#4114yes—
844C22×C4C2×#4114yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2518yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2512yes—
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—28no—
880C4⋊C4—216no—
881C4⋊C4—24no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—22no—
893C4⋊C4—22no—
894C4⋊C4—24no—
895C4⋊C4—24no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4H(5,𝔽2)14yes—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—44no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—28no—
951C42—24no—
952C42—216no—
953C42—24no—
954C42—24no—
955C42—28no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—44no—
962C42—44no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—48no—
967C42—48no—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C42C2×#4114yes—
971C42C2×#4114yes—
972C23—22no—
973C23—21no—
974C23—22no—
975C23—21no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—21no—
982C23—21no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23C22×#4112yes—
992C23C2×2−1+414yes—
993C23C2611yescharacteristic
994Q8—416no—
995Q8—44no—
996Q8—416no—
997Q8—84no—
998Q8—88no—
999D4—28no—
1000D4—416no—
1001D4—48no—
1002D4—48no—
1003D4—48no—
1004D4—84no—
1005D4—88no—
1006D4—88no—
1007C2×C4—21no—
1008C2×C4—22no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—28no—
1016C2×C4—28no—
1017C2×C4—28no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—28no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—28no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—48no—
1067C2×C4—416no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—416no—
1071C2×C4—88no—
1072C2×C4—88no—
1073C2×C4—816no—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C2×H(5,𝔽2)14yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4#58512yes—
1084C2×C4#58512yes—
1085C2×C4#58512yes—
1086C2×C4#58512yes—
1087C22—24no—
1088C22—22no—
1089C22—24no—
1090C22—22no—
1091C22—24no—
1092C22—22no—
1093C22—41no—
1094C22—42no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—42no—
1100C22—42no—
1101C22—44no—
1102C22—44no—
1103C22—44no—
1104C22—44no—
1105C22—44no—
1106C22—44no—
1107C22—44no—
1108C22C23×#4111yescharacteristic
1109C22C22×H(5,𝔽2)11yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C22C2×#58511yescharacteristic
1114C22C2×#58511yescharacteristic
1115C4—24no—
1116C4—22no—
1117C4—22no—
1118C4—22no—
1119C4—44no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—48no—
1127C4—42no—
1128C4—42no—
1129C4—44no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—44no—
1135C4#349514yes—
1136C4#350614yes—
1137C4#351014yes—
1138C2—44no—
1139C2—42no—
1140C2—84no—
1141C2C2×#350611yescharacteristic
1142C2C2×#349511yescharacteristic
1143C2C2×#351011yescharacteristic
1144C2#6301311yescharacteristic
1145C2#6302211yescharacteristic
1146C2#6302511yescharacteristic
1147C2#6303111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59864C2semidirect
2. #59442C2semidirect
3. #59436C2semidirect
4. #59426C2semidirect
5. #51615C2semidirect
6. #45368C2semidirect
7. #45254C2semidirect
8. #45251C2semidirect
9. #45250C2semidirect
10. #39771C2semidirect
11. #39146C2semidirect
12. #38986C2semidirect
13. #38940C2semidirect
14. #37414C2semidirect
15. #36586C2semidirect
16. #36476C2semidirect
17. #36116C2semidirect
18. #36115C2semidirect
19. #35664C2semidirect
20. #35289C2semidirect
21. #35279C2semidirect
22. #34978C2semidirect
24. #34368C2semidirect
25. #34209C2semidirect
26. #34127C2semidirect

Maximal subgroups

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

subgroupindex
#598642
#594422
#594362
#594262
#516152
#453682
#452542
#452512
#452502
#397712
#391462
#389862
#389402
#374142
#365862
#364762
#361162
#361152
#356642
#352892
#352792
#349782
#349772
#343682
#342092
#341272