Finite Group Databasebeta

← #8093195

Subgroups — #8093195

Order 512.

4410 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46325C214yesmaximal, complemented
2#46163C212yesmaximal, complemented
3#46162C212yesmaximal, complemented
4#46156C214yesmaximal, complemented
5#46155C212yesmaximal, complemented
6#46154C212yesmaximal, complemented
7#46146C214yesmaximal, complemented
8#46144C211yesmaximal, characteristic, complemented
9#45989C212yesmaximal, complemented
10#45988C211yesmaximal, characteristic
11#45839C214yesmaximal, complemented
12#45837C214yesmaximal, complemented
13#45827C214yesmaximal, complemented
14#45825C214yesmaximal, complemented
15#45735C214yesmaximal, complemented
16#45734C214yesmaximal, complemented
17#36638C212yesmaximal, complemented
18C2×#2862C211yesmaximal, characteristic, complemented
19#35459C214yesmaximal, complemented
20#35398C214yesmaximal, complemented
21#35387C214yesmaximal, complemented
22C2×#563C2214yes—
23C22×C4⋊Q8C2212yes—
24#2866C2214yes—
25#2865C2214yes—
26#2864C2212yes—
27#2863C2212yes—
28#2862C2214yes—
29#2862C2212yes—
30#2862C2212yes—
31#2862C2214yes—
32#2862C2212yes—
33#2862C2212yes—
34#2861C2212yes—
35#2860C2212yes—
36#2855C2212yes—
37#2854C2212yes—
38#2853C2214yes—
39#2852C2214yes—
40#2851C2212yes—
41#2850C2212yes—
42#2845C2211yescharacteristic
43#2845C2211yescharacteristic
44#2844C2212yes—
45#2833C2214yes—
46#2832C2214yes—
47#2831C2214yes—
48#2831C2214yes—
49#2822C2211yescharacteristic
50#2821C2214yes—
51#2821C2214yes—
52#2820C2212yes—
53#2819C2211yescharacteristic
54#2806C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2798C2214yes—
58#2798C2214yes—
59#2789C2214yes—
60#2788C2214yes—
61#2781C2214yes—
62#2775C2214yes—
63#2774C2214yes—
64#2773C2214yes—
65#2767C2214yes—
66#2767C2214yes—
67#2765C2214yes—
68#2762C2214yes—
69#2759C2214yes—
70#2759C2214yes—
71#2758C2214yes—
72#2755C2214yes—
73#2754C2214yes—
74#2754C2214yes—
75#2751C2214yes—
76#2734C2214yes—
77#2731C2214yes—
78#2730C2214yes—
79#2729C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2723C2214yes—
83#2719C2214yes—
84#2716C2214yes—
85#2716C2214yes—
86#2716C2214yes—
87#2713C2214yes—
88#2713C2214yes—
89#2713C2214yes—
90#2710C2214yes—
91#2706C2214yes—
92#2700C2214yes—
93#2698C2214yes—
94#2692C2214yes—
95#2690C2214yes—
96#2689C2214yes—
97#2687C2214yes—
98#2677C2214yes—
99#2677C2214yes—
100#2674C2214yes—
101#2674C2214yes—
102#2612C2214yes—
103#2607C2214yes—
104#2605C2214yes—
105#2605C2214yes—
106#2589C2214yes—
107#2589C2214yes—
108#2588C2214yes—
109#2588C2214yes—
110#2586C2214yes—
111#2576C2214yes—
112#2575C2214yes—
113#2574C2214yes—
114#2569C2214yes—
115#2564C2214yes—
116#2560C2214yes—
117#2557C2214yes—
118#2556C2214yes—
119#2553C2214yes—
120#2550C2214yes—
121#2549C2214yes—
122#2549C2214yes—
123#2543C2214yes—
124#2532C2214yes—
125#2532C2214yes—
126#2529C2214yes—
127#2528C2214yes—
128#2527C2214yes—
129#2527C2214yes—
130#2524C2214yes—
131#2523C2214yes—
132#2521C2214yes—
133#2520C2214yes—
134#2520C2214yes—
135#2520C2214yes—
136#2519C2214yes—
137#2518C2214yes—
138#2517C2214yes—
139#2515C2214yes—
140#2510C2214yes—
141#2508C2214yes—
142#2505C2214yes—
143#2505C2214yes—
144#2493C2214yes—
145#2492C2214yes—
146#2489C2214yes—
147#2488C2214yes—
148#2488C2214yes—
149#2488C2214yes—
150#2481C2214yes—
151#2481C2214yes—
152#2477C2214yes—
153#2474C2214yes—
154#2473C2214yes—
155#2473C2214yes—
156#2465C2214yes—
157#2459C2214yes—
158#2451C2214yes—
159#2450C2214yes—
160#2450C2214yes—
161#2449C2214yes—
162#2449C2214yes—
163#2444C2214yes—
164#2443C2214yes—
165#2443C2214yes—
166#2439C2214yes—
167#2438C2214yes—
168#2436C2214yes—
169#2434C2214yes—
170#2425C2214yes—
171#2419C2214yes—
172#2409C2214yes—
173#2409C2214yes—
174#2382C2212yes—
175#2382C2212yes—
176#2381C2214yes—
177#2381C2214yes—
178#2379C2214yes—
179#2379C2212yes—
180#2379C2212yes—
181#2378C2214yes—
182#2378C2214yes—
183#2329C2214yes—
184#2325C2214yes—
185#2318C2214yes—
186C4×#125C2212yes—
187C4×#126C2214yes—
188C4×#124C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#123C2214yes—
191C4×#121C2212yes—
192#2298C2214yes—
193#2295C2212yes—
194C2×#391C2214yes—
195C2×#391C2214yes—
196#2293C2212yes—
197#2290C2214yes—
198C2×#382C2211yescharacteristic
199C2×#382C2212yes—
200C2×#382C2211yescharacteristic
201#2275C2214yes—
202C2×C43C2211yescharacteristic
203C23×Q8C2314yes—
204#563—416no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×#126C2314yes—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#125C2312yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2314yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×#117C2314yes—
242C22×C4⋊C4C2312yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248C22×C42C2312yes—
249C22×C42C2312yes—
250#401C2314yes—
251#401C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#400C2314yes—
271#400C2314yes—
272#400C2314yes—
273#399C2314yes—
274#399C2314yes—
275#399C2314yes—
276#399C2314yes—
277#399C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#398C2314yes—
286#398C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2314yes—
295#398C2314yes—
296#398C2314yes—
297#397C2314yes—
298#397C2314yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2314yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2314yes—
310#396C2314yes—
311#396C2314yes—
312#396C2314yes—
313#396C2314yes—
314#396C2314yes—
315#396C2314yes—
316#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#395C2314yes—
320#395C2314yes—
321#395C2314yes—
322#395C2314yes—
323#395C2314yes—
324#395C2314yes—
325#395C2314yes—
326#395C2314yes—
327#395C2314yes—
328#395C2314yes—
329#394C2314yes—
330#394C2314yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#393C2314yes—
335#393C2314yes—
336#393C2314yes—
337#393C2314yes—
338#393C2314yes—
339#393C2314yes—
340#393C2314yes—
341#393C2314yes—
342#393C2314yes—
343#393C2314yes—
344#393C2314yes—
345#392C2314yes—
346#391C2314yes—
347#391C2314yes—
348#391C2314yes—
349#391C2314yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2314yes—
354#391C2314yes—
355#391C2314yes—
356#391C2314yes—
357#391C2314yes—
358#391C2314yes—
359#391C2314yes—
360#391C2312yes—
361#391C2312yes—
362#391C2312yes—
363#391C2312yes—
364#391C2314yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2314yes—
370#391C2314yes—
371#391C2314yes—
372#391C2314yes—
373#391C2314yes—
374#391C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2314yes—
378#391C2314yes—
379#391C2314yes—
380#390C2312yes—
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2312yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2314yes—
401#389C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#386C2314yes—
487#386C2314yes—
488#386C2314yes—
489#386C2314yes—
490#386C2314yes—
491#386C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#385C2314yes—
517#385C2314yes—
518#383C2314yes—
519#383C2314yes—
520#383C2314yes—
521#383C2314yes—
522#382C2312yes—
523#382C2311yescharacteristic
524#382C2312yes—
525#382C2311yescharacteristic
526#382C2314yes—
527#382C2312yes—
528#382C2314yes—
529#382C2312yes—
530#382C2312yes—
531#382C2314yes—
532#382C2314yes—
533#382C2314yes—
534#382C2312yes—
535#382C2311yescharacteristic
536#382C2312yes—
537#382C2312yes—
538#382C2311yescharacteristic
539#382C2314yes—
540#382C2314yes—
541#381C2314yes—
542#381C2314yes—
543#381C2314yes—
544#381C2314yes—
545#380C2312yes—
546#380C2314yes—
547#380C2314yes—
548#380C2312yes—
549#380C2314yes—
550#380C2314yes—
551#380C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2314yes—
554C4×C4⋊C4C2314yes—
555C4×C4⋊C4C2312yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2312yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C22⋊C4C2314yes—
562C4×C22⋊C4C2314yes—
563C4×C22⋊C4C2314yes—
564C4×C22⋊C4C2314yes—
565C4×C22⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571#376C2314yes—
572#376C2314yes—
573C2×#95C2314yes—
574C2×#95C2314yes—
575C2×#95C2314yes—
576C2×#95C2314yes—
577C2×#95C2314yes—
578C43C2312yes—
579C43C2312yes—
580C43C2312yes—
581C43C2312yes—
582C22×Q8—48no—
583C22×Q8—48no—
584C22×Q8—48no—
585C22×Q8C2412yes—
586C22×Q8C2414yes—
587C22×Q8C2414yes—
588C22×Q8C2414yes—
589C22×Q8C2414yes—
590C22×Q8C2414yes—
591C22×D4C2414yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C23×C4C2411yescharacteristic
595C23×C4C2412yes—
596C23×C4C2411yescharacteristic
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2414yes—
601C23×C4C2414yes—
602C23×C4C2414yes—
603C23×C4C2411yescharacteristic
604C4⋊Q8—216no—
605C4⋊Q8—44no—
606C4⋊Q8—48no—
607C4⋊Q8—44no—
608C4⋊Q8—44no—
609C4⋊Q8—44no—
610C4⋊Q8—48no—
611C4⋊Q8—48no—
612#126—216no—
613#126—48no—
614#126—48no—
615#125—28no—
616#125—48no—
617#125—48no—
618#124—28no—
619#124—48no—
620#124—48no—
621#123—48no—
622#123—48no—
623#123—48no—
624C22⋊Q8—44no—
625C22⋊Q8—48no—
626C22⋊Q8—48no—
627C22⋊Q8—48no—
628C22⋊Q8—48no—
629C22⋊Q8—48no—
630C22⋊Q8—48no—
631C22⋊Q8—48no—
632#121—44no—
633#121—48no—
634C4×Q8—44no—
635C4×D4—216no—
636C4×D4—44no—
637C4×D4—48no—
638C4×D4—48no—
639#117—48no—
640C2×C4⋊C4—44no—
641C2×C4⋊C4—48no—
642C2×C4⋊C4—44no—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C42—24no—
717C2×C42—24no—
718C2×C42—24no—
719C2×C42—44no—
720C2×C42—44no—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2414yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2411yescharacteristic
729C2×C42C2412yes—
730C2×C42C2414yes—
731C2×C42C2414yes—
732C2×C42C2414yes—
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2412yes—
741C2×C42C2412yes—
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810C24C2514yes—
811C24C2511yescharacteristic
812C2×Q8—28no—
813C2×Q8—28no—
814C2×Q8—24no—
815C2×Q8—28no—
816C2×Q8—28no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×Q8—44no—
824C2×Q8—44no—
825C2×Q8—44no—
826C2×Q8—44no—
827C2×Q8—44no—
828C2×Q8—44no—
829C2×Q8—44no—
830C2×Q8—832no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—24no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C22×C4—22no—
841C22×C4—24no—
842C22×C4—22no—
843C22×C4—24no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—24no—
852C22×C4—28no—
853C22×C4—42no—
854C22×C4—42no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C42−1+414yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2514yes—
872C22×C4C2514yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2514yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2514yes—
880C22×C4C2514yes—
881C22×C4C2511yescharacteristic
882C22×C4C2512yes—
883C22×C4C2512yes—
884C22×C4C2512yes—
885C22×C4C2511yescharacteristic
886C22×C4C2512yes—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—42no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—44no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—44no—
960C42—24no—
961C42—22no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—22no—
966C42—28no—
967C42—24no—
968C42—24no—
969C42—42no—
970C42—42no—
971C42—42no—
972C42—42no—
973C42—42no—
974C42—42no—
975C42—44no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42H(5,𝔽2)14yes—
984C422−1+414yes—
985C23—21no—
986C23—21no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23C2×2−1+412yes—
996C23#58514yes—
997C23C2611yescharacteristic
998Q8—84no—
999Q8—88no—
1000Q8—88no—
1001Q8—88no—
1002Q8—88no—
1003Q8—164no—
1004D4—416no—
1005D4—84no—
1006D4—164no—
1007C2×C4—28no—
1008C2×C4—216no—
1009C2×C4—21no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—44no—
1061C2×C4—48no—
1062C2×C4—44no—
1063C2×C4—88no—
1064C2×C4—88no—
1065C2×C4—88no—
1066C2×C4—164no—
1067C2×C4—164no—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)14yes—
1070C2×C4C2×2−1+414yes—
1071C2×C4C2×2−1+412yes—
1072C2×C4C2×2−1+414yes—
1073C2×C4#58514yes—
1074C22—22no—
1075C22—24no—
1076C22—24no—
1077C22—22no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22—44no—
1085C22#353114yes—
1086C22C22×H(5,𝔽2)11yescharacteristic
1087C22C22×2−1+411yescharacteristic
1088C22C22×2−1+411yescharacteristic
1089C22C2×#58512yes—
1090C22C2×#58512yes—
1091C4—24no—
1092C4—24no—
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—22no—
1097C4—44no—
1098C4—44no—
1099C4—44no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4—42no—
1109C4—44no—
1110C2—24no—
1111C2—84no—
1112C2C2×#353111yescharacteristic
1113C2#6282311yescharacteristic
1114C2#6282412yes—
1115C2#6283112yes—
1116C2#6283311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#45988C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #46325C2semidirect
2. #46163C2semidirect
3. #46162C2semidirect
4. #46156C2semidirect
5. #46155C2semidirect
6. #46154C2semidirect
7. #46146C2semidirect
8. #46144C2semidirect
9. #45989C2semidirect
11. #45839C2semidirect
12. #45837C2semidirect
13. #45827C2semidirect
14. #45825C2semidirect
15. #45735C2semidirect
16. #45734C2semidirect
17. #36638C2semidirect
18. C2×#2862C2semidirect
19. #35459C2semidirect
20. #35398C2semidirect
21. #35387C2semidirect

Maximal subgroups

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

subgroupindex
#463252
#461632
#461622
#461562
#461552
#461542
#461462
#461442
#459892
#459882
#458392
#458372
#458272
#458252
#457352
#457342
#366382
C2×#28622
#354592
#353982
#353872