Finite Group Databasebeta

← #7898320

Subgroups — #7898320

Order 512.

4835 conjugacy classes of subgroups.

The subgroup lattice has 1447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59127C212yesmaximal, complemented
3#52267C211yesmaximal, characteristic, complemented
4#51083C214yesmaximal, complemented
5#50907C214yesmaximal, complemented
6#47965C214yesmaximal, complemented
7#47725C214yesmaximal, complemented
8#45792C212yesmaximal, complemented
9#45281C212yesmaximal, complemented
10#44940C212yesmaximal, complemented
11#44939C212yesmaximal, complemented
12#44934C214yesmaximal, complemented
13#42933C212yesmaximal, complemented
14#42497C212yesmaximal, complemented
15#42008C214yesmaximal, complemented
16#39987C212yesmaximal, complemented
17#39694C212yesmaximal, complemented
18#39621C211yesmaximal, characteristic, complemented
19#39615C212yesmaximal, complemented
20#39493C211yesmaximal, characteristic, complemented
21#38446C212yesmaximal, complemented
22#37686C212yesmaximal, complemented
23#37308C212yesmaximal, complemented
24#36276C211yesmaximal, characteristic, complemented
25#35815C212yesmaximal, complemented
26#35576C212yesmaximal, complemented
27#35177C211yesmaximal, characteristic, complemented
28#34467C212yesmaximal
29#34321C211yesmaximal, characteristic
30C2×Q82C2212yes—
31C2×#555C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C2×D4×Q8C2214yes—
34C2×D4×Q8C2211yescharacteristic
35C2×#544C2212yes—
36C22×C4⋊Q8C2212yes—
37#2862C2211yescharacteristic
38#2857C2212yes—
39#2857C2212yes—
40#2855C2212yes—
41#2851C2212yes—
42#2843C2214yes—
43#2841C2214yes—
44#2811C2212yes—
45#2809C2214yes—
46#2807C2212yes—
47#2807C2214yes—
48#2806C2212yes—
49#2806C2211yescharacteristic
50#2806C2212yes—
51#2806C2212yes—
52#2805C2211yescharacteristic
53#2805C2212yes—
54#2805C2214yes—
55#2804C2214yes—
56#2804C2211yescharacteristic
57#2804C2212yes—
58#2802C2212yes—
59#2799C2214yes—
60#2790C2212yes—
61#2790C2214yes—
62#2788C2214yes—
63#2788C2212yes—
64#2788C2214yes—
65#2780C2212yes—
66#2780C2214yes—
67#2768C2214yes—
68#2763C2214yes—
69#2755C2214yes—
70#2748C2214yes—
71#2742C2214yes—
72#2742C2214yes—
73#2742C2214yes—
74#2734C2214yes—
75#2734C2212yes—
76#2734C2212yes—
77#2734C2212yes—
78#2732C2211yescharacteristic
79#2732C2212yes—
80#2729C2214yes—
81#2729C2214yes—
82#2729C2212yes—
83#2729C2214yes—
84#2729C2214yes—
85#2729C2214yes—
86#2729C2214yes—
87#2713C2214yes—
88#2704C2214yes—
89#2692C2214yes—
90#2692C2214yes—
91#2692C2214yes—
92#2677C2214yes—
93#2677C2214yes—
94#2677C2214yes—
95#2677C2214yes—
96#2677C2214yes—
97#2677C2214yes—
98#2666C2214yes—
99#2666C2214yes—
100#2666C2214yes—
101#2666C2214yes—
102#2665C2214yes—
103#2660C2212yes—
104#2659C2214yes—
105#2628C2214yes—
106#2628C2212yes—
107#2628C2212yes—
108#2605C2214yes—
109#2605C2214yes—
110#2589C2214yes—
111#2589C2214yes—
112#2586C2214yes—
113#2585C2214yes—
114#2583C2214yes—
115#2583C2214yes—
116#2582C2212yes—
117#2581C2214yes—
118#2580C2214yes—
119#2574C2214yes—
120#2570C2212yes—
121#2570C2214yes—
122#2570C2214yes—
123#2567C2211yescharacteristic
124#2567C2211yescharacteristic
125#2564C2214yes—
126#2564C2214yes—
127#2563C2212yes—
128#2563C2211yescharacteristic
129#2551C2212yes—
130#2551C2212yes—
131#2551C2214yes—
132#2551C2211yescharacteristic
133#2551C2214yes—
134#2551C2214yes—
135#2551C2212yes—
136#2551C2212yes—
137#2551C2212yes—
138#2550C2212yes—
139#2550C2212yes—
140#2550C2214yes—
141#2550C2214yes—
142#2550C2212yes—
143#2550C2212yes—
144#2550C2212yes—
145#2550C2212yes—
146#2549C2214yes—
147#2549C2214yes—
148#2549C2214yes—
149#2546C2212yes—
150#2546C2212yes—
151#2546C2211yescharacteristic
152#2542C2212yes—
153#2538C2211yescharacteristic
154#2522C2214yes—
155#2509C2212yes—
156#2509C2212yes—
157#2509C2212yes—
158#2508C2212yes—
159#2508C2212yes—
160#2507C2212yes—
161#2507C2212yes—
162#2505C2214yes—
163#2502C2212yes—
164#2497C2212yes—
165#2492C2214yes—
166#2492C2212yes—
167#2473C2214yes—
168#2473C2214yes—
169#2465C2214yes—
170#2465C2214yes—
171#2465C2214yes—
172#2465C2214yes—
173#2454C2212yes—
174#2452C2212yes—
175#2452C2214yes—
176#2452C2212yes—
177#2452C2214yes—
178#2451C2214yes—
179#2451C2214yes—
180#2451C2214yes—
181#2451C2214yes—
182#2449C2214yes—
183#2449C2214yes—
184#2449C2214yes—
185#2446C2214yes—
186#2442C2212yes—
187#2440C2212yes—
188#2440C2212yes—
189#2440C2212yes—
190#2439C2212yes—
191#2439C2212yes—
192#2438C2214yes—
193#2434C2214yes—
194#2434C2214yes—
195#2434C2214yes—
196#2434C2214yes—
197#2434C2212yes—
198#2429C2214yes—
199#2423C2214yes—
200#2417C2214yes—
201#2409C2214yes—
202#2409C2214yes—
203#2402C2212yes—
204#2399C2214yes—
205#2396C2212yes—
206#2396C2212yes—
207#2379C2214yes—
208#2377C2214yes—
209#2370C2212yes—
210#2369C2211yescharacteristic
211#2367C2214yes—
212#2367C2214yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2363C2212yes—
217#2363C2212yes—
218#2361C2212yes—
219#2361C2212yes—
220#2355C2212yes—
221#2354C2211yescharacteristic
222#2352C2212yes—
223#2349C2212yes—
224#2349C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226#2347C2212yes—
227#2347C2212yes—
228#2347C2212yes—
229#2346C2212yes—
230#2343C2214yes—
231#2337C2214yes—
232#2337C2214yes—
233#2331C2214yes—
234#2331C2212yes—
235#2331C2212yes—
236#2326C2214yes—
237#2325C2214yes—
238#2324C2212yes—
239#2324C2212yes—
240#2319C2212yes—
241#2317C2212yes—
242#2317C2212yes—
243#2314C2214yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2211yescharacteristic
246C4×C4⋊Q8C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#121C2212yes—
249C4×#121C2212yes—
250#2296C2212yes—
251#2296C2212yes—
252#2296C2212yes—
253#2295C2211yescharacteristic
254C2×#391C2212yes—
255#2293C2211yescharacteristic
256#2290C2212yes—
257#2274C2212yes—
258C42×D4C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2314yes—
261Q82—48no—
262#555Q8116yescomplemented
263#554—44no—
264D4×Q8—44no—
265D4×Q8—416no—
266#544—48no—
267C2×C4⋊Q8—48no—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×C4⋊Q8C2312yes—
287C2×C4⋊Q8C2312yes—
288C2×C4⋊Q8C2314yes—
289C2×C4⋊Q8C2311yescharacteristic
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#124C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2314yes—
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×C4×D4C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2312yes—
339C22×C42C2312yes—
340C22×C42C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2312yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#399C2312yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#399C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2312yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#396C2312yes—
399#396C2314yes—
400#396C2314yes—
401#396C2312yes—
402#396C2312yes—
403#396C2312yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2312yes—
443#393C2314yes—
444#393C2314yes—
445#393C2312yes—
446#393C2314yes—
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2311yescharacteristic
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2314yes—
468#391C2314yes—
469#391C2311yescharacteristic
470#391C2312yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2311yescharacteristic
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2311yescharacteristic
487#390C2311yescharacteristic
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2311yescharacteristic
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2312yes—
604#386C2314yes—
605#385C2312yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2312yes—
624#385C2312yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2314yes—
635#385C2312yes—
636#385C2312yes—
637#384C2311yescharacteristic
638#384C2311yescharacteristic
639#384C2311yescharacteristic
640#384C2312yes—
641#384C2312yes—
642#384C2314yes—
643#384C2312yes—
644#384C2312yes—
645#383C2314yes—
646#383C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2314yes—
654#382C2312yes—
655#382C2314yes—
656#381C2314yes—
657#380C2312yes—
658#380C2314yes—
659#380C2312yes—
660#380C2314yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715#376C2314yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C43C2311yescharacteristic
719C22×Q8—28no—
720C22×Q8—48no—
721C22×Q8—44no—
722C22×Q8—48no—
723C22×Q8—82no—
724C22×Q8—84no—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×Q8C2414yes—
733C22×Q8C2412yes—
734C22×Q8C2414yes—
735C22×Q8C2412yes—
736C22×Q8C2411yescharacteristic
737C22×D4C2411yescharacteristic
738C22×D4C2414yes—
739C22×D4C2411yescharacteristic
740C23×C4C2412yes—
741C23×C4C2412yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2412yes—
750C4⋊Q8—216no—
751C4⋊Q8—24no—
752C4⋊Q8—28no—
753C4⋊Q8—28no—
754C4⋊Q8—24no—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758C4⋊Q8—42no—
759C4⋊Q8—42no—
760C4⋊Q8—48no—
761C4⋊Q8—48no—
762C4⋊Q8—48no—
763C4⋊Q8—48no—
764C4⋊Q8—48no—
765C4⋊Q8—48no—
766C4⋊Q8—48no—
767C4⋊Q8—48no—
768C4⋊Q8—82no—
769C4⋊Q8—82no—
770C4⋊Q8—84no—
771C4⋊Q8C2×Q818yescomplemented
772#125—28no—
773#125—44no—
774#125—48no—
775#124C2×Q8132yescomplemented
776C22⋊Q8—28no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—48no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—44no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—84no—
789C22⋊Q8—84no—
790C22⋊Q8—82no—
791#121C2×Q8116yescomplemented
792#121C2×Q8116yescomplemented
793C4×Q8—24no—
794C4×Q8—42no—
795C4×Q8—42no—
796C4×Q8—48no—
797C4×Q8—48no—
798C4×Q8—44no—
799C4×Q8—44no—
800C4×Q8—48no—
801C4×D4—24no—
802C4×D4—24no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—48no—
806C4×D4—48no—
807C4×D4—48no—
808C4×D4—82no—
809C4×D4C2×Q818yescomplemented
810C4×D4C2×Q818yescomplemented
811#117—28no—
812#117—44no—
813#117—44no—
814#117—82no—
815#117C2×Q8116yescomplemented
816#117C2×Q8116yescomplemented
817C2×C4⋊C4—28no—
818C2×C4⋊C4—44no—
819C2×C4⋊C4—48no—
820C2×C4⋊C4—44no—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2411yescharacteristic
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C42—44no—
930C2×C42—82no—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2411yescharacteristic
936C2×C42C2412yes—
937C2×C42C2411yescharacteristic
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958#95C2412yes—
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2512yes—
1028C24C2512yes—
1029C2×Q8—28no—
1030C2×Q8—28no—
1031C2×Q8—24no—
1032C2×Q8—28no—
1033C2×Q8—28no—
1034C2×Q8—22no—
1035C2×Q8—24no—
1036C2×Q8—22no—
1037C2×Q8—42no—
1038C2×Q8—42no—
1039C2×Q8—41no—
1040C2×Q8—41no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—41no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—41no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—44no—
1052C2×Q8—41no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—41no—
1057C2×Q8—42no—
1058C2×Q8—44no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×Q8—42no—
1062C2×Q8—42no—
1063C2×Q8—816no—
1064C2×Q8—832no—
1065C2×Q8C22×Q818yes—
1066C2×Q8H(5,𝔽2)14yes—
1067C2×D4—22no—
1068C2×D4—22no—
1069C2×D4—44no—
1070C2×D4—41no—
1071C2×D4—44no—
1072C2×D4—41no—
1073C2×D4C22×Q814yes—
1074C2×D4C22×Q814yes—
1075C2×D4C22×Q8116yes—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—24no—
1081C22×C4—28no—
1082C22×C4—28no—
1083C22×C4—24no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—42no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4C22×Q818yes—
1105C22×C4C22×Q818yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2514yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2514yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—24no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—41no—
1181C4⋊C4—42no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—41no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—42no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—41no—
1207C4⋊C4—42no—
1208C4⋊C4C22×Q814yes—
1209C4⋊C4C22×Q814yes—
1210C4⋊C4C22×Q818yes—
1211C4⋊C4C22×Q818yes—
1212C4⋊C4H(5,𝔽2)14yes—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—42no—
1220C22⋊C4—42no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—44no—
1237C22⋊C4C22×Q8116yes—
1238C22⋊C4C22×Q8116yes—
1239C22⋊C4C22×Q818yes—
1240C22⋊C4C22×Q818yes—
1241C42—24no—
1242C42—24no—
1243C42—24no—
1244C42—22no—
1245C42—28no—
1246C42—22no—
1247C42—24no—
1248C42—24no—
1249C42—42no—
1250C42—42no—
1251C42—41no—
1252C42—42no—
1253C42—42no—
1254C42—42no—
1255C42—44no—
1256C42—41no—
1257C42—41no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C42—44no—
1264C42—44no—
1265C42C22×Q8116yes—
1266C42C22×Q814yes—
1267C422−1+414yes—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23C23×Q814yes—
1281C23C23×Q814yes—
1282C23C2611yescharacteristic
1283Q8—44no—
1284Q8—48no—
1285Q8—416no—
1286Q8—48no—
1287Q8—82no—
1288Q8—82no—
1289Q8—84no—
1290Q8—88no—
1291Q8—88no—
1292Q8—88no—
1293Q8—162no—
1294Q8—164no—
1295D4—28no—
1296D4—416no—
1297D4—44no—
1298C2×C4—24no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—216no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—24no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—48no—
1368C2×C4—48no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—84no—
1372C2×C4—88no—
1373C2×C4—88no—
1374C2×C4—88no—
1375C2×C4—164no—
1376C2×C4C23×Q814yes—
1377C2×C4C23×Q814yes—
1378C2×C4C23×Q812yes—
1379C2×C4C23×Q818yes—
1380C2×C4C23×Q812yes—
1381C2×C4C23×Q812yes—
1382C2×C4C2×H(5,𝔽2)14yes—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4C2×H(5,𝔽2)14yes—
1385C2×C4C2×H(5,𝔽2)12yes—
1386C2×C4C2×2−1+412yes—
1387C2×C4C2×2−1+412yes—
1388C2×C4C2×2−1+412yes—
1389C22—24no—
1390C22—24no—
1391C22—24no—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—42no—
1396C22—42no—
1397C22—42no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—42no—
1402C22—42no—
1403C22C24×Q811yescharacteristic
1404C22C22×H(5,𝔽2)11yescharacteristic
1405C22C22×H(5,𝔽2)11yescharacteristic
1406C22C22×2−1+411yescharacteristic
1407C22H(7,𝔽2)11yescharacteristic
1408C222−1+611yescharacteristic
1409C222−1+611yescharacteristic
1410C4—28no—
1411C4—22no—
1412C4—24no—
1413C4—22no—
1414C4—24no—
1415C4—22no—
1416C4—22no—
1417C4—24no—
1418C4—24no—
1419C4—22no—
1420C4—42no—
1421C4—42no—
1422C4—42no—
1423C4—44no—
1424C4—41no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—44no—
1430C4—44no—
1431C4—44no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—44no—
1436C4#350314yes—
1437C2—44no—
1438C2—44no—
1439C2C2×#350311yescharacteristic
1440C2#6285411yescharacteristic
1441C2#6287911yescharacteristic
1442C2#6289211yescharacteristic
1443C2#6291311yescharacteristic
1444C2Q8×H(5,𝔽2)11yescharacteristic
1445C2#6304811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#555C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59832C2semidirect
2. #59127C2semidirect
3. #52267C2semidirect
4. #51083C2semidirect
5. #50907C2semidirect
6. #47965C2semidirect
7. #47725C2semidirect
8. #45792C2semidirect
9. #45281C2semidirect
10. #44940C2semidirect
11. #44939C2semidirect
12. #44934C2semidirect
13. #42933C2semidirect
14. #42497C2semidirect
15. #42008C2semidirect
16. #39987C2semidirect
17. #39694C2semidirect
18. #39621C2semidirect
19. #39615C2semidirect
20. #39493C2semidirect
21. #38446C2semidirect
22. #37686C2semidirect
23. #37308C2semidirect
24. #36276C2semidirect
25. #35815C2semidirect
26. #35576C2semidirect
27. #35177C2semidirect
262. #555Q8semidirect
771. C4⋊Q8C2×Q8semidirect
775. #124C2×Q8semidirect
791. #121C2×Q8semidirect
792. #121C2×Q8semidirect
809. C4×D4C2×Q8semidirect
810. C4×D4C2×Q8semidirect
815. #117C2×Q8semidirect
816. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598322
#591272
#522672
#510832
#509072
#479652
#477252
#457922
#452812
#449402
#449392
#449342
#429332
#424972
#420082
#399872
#396942
#396212
#396152
#394932
#384462
#376862
#373082
#362762
#358152
#355762
#351772
#344672
#343212