Finite Group Databasebeta

← #7979513

Subgroups — #7979513

Order 512.

4899 conjugacy classes of subgroups.

The subgroup lattice has 1695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59921C212yesmaximal, complemented
2#59828C211yesmaximal, characteristic, complemented
3#59413C212yesmaximal, complemented
4#59127C211yesmaximal, characteristic, complemented
5#59052C211yesmaximal, characteristic, complemented
6#51604C214yesmaximal, complemented
7#48841C214yesmaximal, complemented
8#46005C212yesmaximal, complemented
9#45497C212yesmaximal, complemented
10#44950C212yesmaximal, complemented
11#44944C212yesmaximal, complemented
12#44403C214yesmaximal, complemented
13#42972C212yesmaximal, complemented
14#42494C212yesmaximal, complemented
15#42006C214yesmaximal, complemented
16#39983C212yesmaximal, complemented
17#39654C212yesmaximal, complemented
18#39643C211yesmaximal, characteristic, complemented
19#39616C212yesmaximal, complemented
20#39615C212yesmaximal, complemented
21#39598C211yesmaximal, characteristic, complemented
22#38104C212yesmaximal, complemented
23Q8×#121C211yesmaximal, characteristic, complemented
24#36481C211yesmaximal, characteristic, complemented
25#36287C211yesmaximal, characteristic, complemented
26#36279C212yesmaximal, complemented
27#36276C211yesmaximal, characteristic, complemented
28#36129C211yesmaximal, characteristic, complemented
29#35284C212yesmaximal, complemented
30#35281C211yesmaximal, characteristic, complemented
31#35176C211yesmaximal, characteristic, complemented
32#34953C211yesmaximal, characteristic, complemented
33#34691C211yesmaximal, characteristic, complemented
34#34467C212yesmaximal
35C4×#555C211yesmaximal, characteristic
36C2×#557C2212yes—
37C2×#555C2211yescharacteristic
38C2×#554C2211yescharacteristic
39C2×D4×Q8C2212yes—
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2212yes—
42C2×#533C2211yescharacteristic
43C2×#533C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46#2868C2212yes—
47#2863C2212yes—
48#2862C2211yescharacteristic
49#2862C2212yes—
50#2859C2212yes—
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2855C2212yes—
57#2845C2214yes—
58#2841C2214yes—
59#2806C2214yes—
60#2806C2214yes—
61#2799C2214yes—
62#2792C2214yes—
63#2790C2214yes—
64#2788C2214yes—
65#2784C2214yes—
66#2780C2214yes—
67#2780C2214yes—
68#2780C2214yes—
69#2768C2214yes—
70#2768C2214yes—
71#2768C2214yes—
72#2755C2214yes—
73#2742C2214yes—
74#2734C2214yes—
75#2732C2214yes—
76#2732C2214yes—
77#2732C2214yes—
78#2729C2214yes—
79#2729C2214yes—
80#2726C2214yes—
81#2720C2214yes—
82#2720C2214yes—
83#2720C2214yes—
84#2720C2214yes—
85#2704C2214yes—
86#2704C2214yes—
87#2704C2214yes—
88#2704C2214yes—
89#2704C2214yes—
90#2683C2214yes—
91#2677C2214yes—
92#2667C2214yes—
93#2666C2214yes—
94#2660C2214yes—
95#2660C2214yes—
96#2659C2214yes—
97#2647C2214yes—
98#2647C2212yes—
99#2629C2212yes—
100#2629C2214yes—
101#2612C2214yes—
102#2612C2214yes—
103#2606C2214yes—
104#2605C2214yes—
105#2587C2214yes—
106#2586C2214yes—
107#2584C2212yes—
108#2584C2212yes—
109#2584C2212yes—
110#2583C2214yes—
111#2582C2212yes—
112#2582C2212yes—
113#2574C2214yes—
114#2568C2212yes—
115#2567C2212yes—
116#2567C2212yes—
117#2567C2214yes—
118#2567C2211yescharacteristic
119#2567C2211yescharacteristic
120#2566C2214yes—
121#2564C2214yes—
122#2564C2214yes—
123#2556C2214yes—
124#2556C2214yes—
125#2556C2214yes—
126#2552C2211yescharacteristic
127#2552C2212yes—
128#2552C2212yes—
129#2551C2212yes—
130#2550C2214yes—
131#2550C2212yes—
132#2550C2212yes—
133#2550C2212yes—
134#2549C2214yes—
135#2549C2214yes—
136#2546C2211yescharacteristic
137#2546C2211yescharacteristic
138#2546C2211yescharacteristic
139#2546C2212yes—
140#2546C2211yescharacteristic
141#2546C2211yescharacteristic
142#2542C2211yescharacteristic
143#2542C2212yes—
144#2538C2212yes—
145#2538C2212yes—
146#2538C2211yescharacteristic
147#2538C2212yes—
148#2522C2214yes—
149#2522C2214yes—
150#2520C2214yes—
151#2511C2212yes—
152#2509C2212yes—
153#2508C2212yes—
154#2507C2214yes—
155#2507C2212yes—
156#2507C2212yes—
157#2507C2214yes—
158#2506C2212yes—
159#2506C2212yes—
160#2506C2212yes—
161#2505C2214yes—
162#2502C2214yes—
163#2502C2212yes—
164#2502C2212yes—
165#2497C2214yes—
166#2497C2214yes—
167#2497C2212yes—
168#2492C2212yes—
169#2473C2212yes—
170#2465C2212yes—
171#2462C2212yes—
172#2454C2212yes—
173#2454C2214yes—
174#2454C2212yes—
175#2453C2214yes—
176#2452C2212yes—
177#2451C2214yes—
178#2451C2212yes—
179#2451C2211yescharacteristic
180#2449C2214yes—
181#2449C2212yes—
182#2446C2212yes—
183#2446C2211yescharacteristic
184#2446C2212yes—
185#2446C2212yes—
186#2446C2212yes—
187#2442C2212yes—
188#2441C2212yes—
189#2441C2212yes—
190#2441C2212yes—
191#2440C2211yescharacteristic
192#2440C2212yes—
193#2440C2212yes—
194#2439C2212yes—
195#2438C2214yes—
196#2434C2212yes—
197#2434C2212yes—
198#2434C2211yescharacteristic
199#2434C2212yes—
200#2434C2212yes—
201#2434C2212yes—
202#2429C2211yescharacteristic
203#2429C2212yes—
204#2429C2214yes—
205#2429C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2429C2212yes—
209#2429C2212yes—
210#2429C2212yes—
211#2423C2212yes—
212#2423C2212yes—
213#2423C2214yes—
214#2423C2212yes—
215#2423C2211yescharacteristic
216#2417C2212yes—
217#2417C2211yescharacteristic
218#2417C2214yes—
219#2417C2212yes—
220#2417C2212yes—
221#2417C2212yes—
222#2409C2212yes—
223#2409C2211yescharacteristic
224#2409C2212yes—
225#2399C2214yes—
226#2399C2212yes—
227#2396C2212yes—
228#2379C2214yes—
229#2377C2214yes—
230#2372C2212yes—
231#2372C2212yes—
232#2370C2212yes—
233#2370C2212yes—
234#2369C2211yescharacteristic
235#2369C2211yescharacteristic
236#2368C2214yes—
237#2367C2214yes—
238#2365C2211yescharacteristic
239#2365C2212yes—
240#2363C2211yescharacteristic
241#2363C2212yes—
242#2363C2211yescharacteristic
243#2363C2212yes—
244#2361C2212yes—
245#2360C2212yes—
246#2360C2212yes—
247#2354C2211yescharacteristic
248#2354C2211yescharacteristic
249#2352C2212yes—
250Q8×C4⋊C4C2211yescharacteristic
251Q8×C4⋊C4C2211yescharacteristic
252#2349C2212yes—
253#2349C2212yes—
254#2347C2212yes—
255#2346C2212yes—
256#2346C2211yescharacteristic
257#2346C2211yescharacteristic
258#2346C2212yes—
259#2343C2214yes—
260Q8×C22⋊C4C2212yes—
261Q8×C22⋊C4C2212yes—
262#2337C2214yes—
263#2331C2212yes—
264#2330C2214yes—
265#2330C2212yes—
266#2326C2214yes—
267#2325C2214yes—
268#2324C2212yes—
269#2319C2212yes—
270#2317C2212yes—
271#2317C2212yes—
272#2314C2214yes—
273C4×C4⋊Q8C2212yes—
274C4×C4⋊Q8C2212yes—
275C4×C4⋊Q8C2211yescharacteristic
276C4×C4⋊Q8C2211yescharacteristic
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2212yes—
279C4×#124C2212yes—
280C4×#124C2212yes—
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2212yes—
288#2296C2212yes—
289#2296C2212yes—
290#2295C2211yescharacteristic
291#2295C2212yes—
292C2×#391C2212yes—
293#2290C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2212yes—
298C4×#117C2211yescharacteristic
299C23×Q8C2312yes—
300C23×Q8C2311yescharacteristic
301C23×Q8C2312yes—
302#557—48no—
303#555Q8116yescomplemented
304#554—44no—
305D4×Q8—44no—
306D4×Q8—48no—
307D4×Q8—48no—
308#533—44no—
309#533—44no—
310C2×C4⋊Q8—44no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2314yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2312yes—
324C2×C4⋊Q8C2311yescharacteristic
325C2×C4⋊Q8C2312yes—
326C2×C4⋊Q8C2312yes—
327C2×C4⋊Q8C2314yes—
328C2×C4⋊Q8C2311yescharacteristic
329C2×#125C2312yes—
330C2×#125C2314yes—
331C2×#125C2312yes—
332C2×#125C2312yes—
333C2×#125C2314yes—
334C2×#125C2312yes—
335C2×#125C2314yes—
336C2×#125C2314yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×C22⋊Q8C2311yescharacteristic
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2311yescharacteristic
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2312yes—
361C2×#121C2311yescharacteristic
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×C4×Q8—44no—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2314yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×Q8C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2314yes—
384C2×C4×D4C2314yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×#117C2311yescharacteristic
394C2×#117C2311yescharacteristic
395C2×#117C2312yes—
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2311yescharacteristic
400C2×#117C2311yescharacteristic
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2311yescharacteristic
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409C22×C42C2312yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2312yes—
419#400C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2312yes—
424#399C2314yes—
425#399C2314yes—
426#399C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2314yes—
454#398C2312yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2312yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2312yes—
479#396C2314yes—
480#396C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2312yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2314yes—
492#395C2314yes—
493#395C2314yes—
494#395C2312yes—
495#395C2314yes—
496#395C2312yes—
497#395C2312yes—
498#395C2312yes—
499#395C2314yes—
500#395C2314yes—
501#393C2312yes—
502#393C2314yes—
503#393C2314yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2311yescharacteristic
519#391C2312yes—
520#391C2312yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2311yescharacteristic
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2314yes—
539#391C2312yes—
540#391C2311yescharacteristic
541#390C2312yes—
542#390C2314yes—
543#390C2312yes—
544#390C2312yes—
545#390C2314yes—
546#390C2311yescharacteristic
547#390C2311yescharacteristic
548#390C2312yes—
549#390C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2311yescharacteristic
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2314yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2314yes—
592#389C2314yes—
593#389C2314yes—
594#389C2314yes—
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
599#389C2311yescharacteristic
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2314yes—
605#389C2312yes—
606#389C2311yescharacteristic
607#389C2311yescharacteristic
608#389C2314yes—
609#389C2314yes—
610#389C2314yes—
611#389C2314yes—
612#389C2311yescharacteristic
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2312yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2312yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2312yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2312yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2312yes—
671#387C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2314yes—
675#386C2314yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2314yes—
683#385C2312yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2312yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2312yes—
706#385C2312yes—
707#385C2312yes—
708#384C2312yes—
709#384C2312yes—
710#384C2311yescharacteristic
711#384C2311yescharacteristic
712#384C2312yes—
713#384C2311yescharacteristic
714#384C2314yes—
715#384C2314yes—
716#384C2314yes—
717#384C2314yes—
718#384C2314yes—
719#384C2312yes—
720#384C2312yes—
721#384C2312yes—
722#383C2314yes—
723#382C2314yes—
724#382C2314yes—
725#382C2314yes—
726#382C2314yes—
727#382C2312yes—
728#382C2312yes—
729#382C2312yes—
730#382C2312yes—
731#381C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2314yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2314yes—
746#380C2312yes—
747#380C2314yes—
748#380C2311yescharacteristic
749#380C2311yescharacteristic
750#380C2311yescharacteristic
751#380C2312yes—
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809#376C2312yes—
810#376C2314yes—
811#376C2312yes—
812#376C2312yes—
813#376C2312yes—
814#376C2312yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C43C2311yescharacteristic
818C43C2312yes—
819C43C2312yes—
820C22×Q8—24no—
821C22×Q8—28no—
822C22×Q8—42no—
823C22×Q8—42no—
824C22×Q8—44no—
825C22×Q8—44no—
826C22×Q8—44no—
827C22×Q8—44no—
828C22×Q8—44no—
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2412yes—
832C22×Q8C2412yes—
833C22×Q8C2411yescharacteristic
834C22×Q8C2412yes—
835C22×Q8C2412yes—
836C22×Q8C2412yes—
837C22×Q8C2414yes—
838C22×Q8C2414yes—
839C22×Q8C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2414yes—
853C23×C4C2412yes—
854C23×C4C2414yes—
855C23×C4C2412yes—
856C23×C4C2414yes—
857C23×C4C2412yes—
858C4⋊Q8—28no—
859C4⋊Q8—24no—
860C4⋊Q8—24no—
861C4⋊Q8—24no—
862C4⋊Q8—24no—
863C4⋊Q8—44no—
864C4⋊Q8—44no—
865C4⋊Q8—42no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—42no—
871C4⋊Q8—48no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—48no—
875C4⋊Q8C2×Q818yescomplemented
876#125—28no—
877#125—48no—
878#125—44no—
879#125—44no—
880#125—44no—
881#125—48no—
882#125—48no—
883#125—48no—
884#124C2×Q8116yescomplemented
885#124C2×Q8116yescomplemented
886C22⋊Q8—24no—
887C22⋊Q8—48no—
888C22⋊Q8—48no—
889C22⋊Q8—44no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—48no—
895C22⋊Q8—44no—
896C22⋊Q8—42no—
897C22⋊Q8—42no—
898C22⋊Q8—42no—
899C22⋊Q8—44no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904C22⋊Q8—48no—
905C22⋊Q8—48no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908#121C2×Q818yescomplemented
909#121C2×Q818yescomplemented
910#121C2×Q8116yescomplemented
911C4×Q8—28no—
912C4×Q8—24no—
913C4×Q8—24no—
914C4×Q8—24no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—48no—
920C4×Q8—42no—
921C4×Q8—42no—
922C4×Q8—44no—
923C4×Q8—44no—
924C4×Q8—44no—
925C4×Q8—44no—
926C4×Q8—44no—
927C4×D4—24no—
928C4×D4—24no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—42no—
932C4×D4—48no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—42no—
936C4×D4—48no—
937C4×D4C2×Q818yescomplemented
938C4×D4C2×Q818yescomplemented
939#117—24no—
940#117—24no—
941#117—44no—
942#117—44no—
943#117—44no—
944#117C2×Q818yescomplemented
945#117C2×Q818yescomplemented
946#117C2×Q8116yescomplemented
947C2×C4⋊C4—44no—
948C2×C4⋊C4—42no—
949C2×C4⋊C4—44no—
950C2×C4⋊C4—44no—
951C2×C4⋊C4—44no—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2411yescharacteristic
1037C2×C4⋊C4C2411yescharacteristic
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2411yescharacteristic
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C42—24no—
1077C2×C42—24no—
1078C2×C42—44no—
1079C2×C42—44no—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2412yes—
1086C2×C42C2414yes—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2412yes—
1100C2×C42C2414yes—
1101C2×C42C2412yes—
1102C2×C42C2414yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2414yes—
1105C2×C42C2414yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2414yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118#95C2412yes—
1119#95C2412yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2411yescharacteristic
1127#95C2412yes—
1128#95C2411yescharacteristic
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2411yescharacteristic
1151#95C2411yescharacteristic
1152#95C2412yes—
1153#95C2412yes—
1154#95C2411yescharacteristic
1155#95C2411yescharacteristic
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190C24C2511yescharacteristic
1191C24C2512yes—
1192C24C2511yescharacteristic
1193C2×Q8—22no—
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—24no—
1200C2×Q8—24no—
1201C2×Q8—22no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—28no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—24no—
1208C2×Q8—22no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—42no—
1212C2×Q8—42no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—44no—
1222C2×Q8—42no—
1223C2×Q8—42no—
1224C2×Q8—416no—
1225C2×Q8—816no—
1226C2×Q8—816no—
1227C2×Q8C22×Q818yes—
1228C2×Q8H(5,𝔽2)14yes—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4C22×Q814yes—
1238C2×D4C22×Q814yes—
1239C2×D4C22×Q818yes—
1240C2×D4C22×Q818yes—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—22no—
1252C22×C4—24no—
1253C22×C4—24no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—28no—
1259C22×C4—24no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—42no—
1263C22×C4—41no—
1264C22×C4—42no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—41no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—41no—
1274C22×C4—42no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—44no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4C22×Q814yes—
1281C22×C4C22×Q814yes—
1282C22×C4C22×Q818yes—
1283C22×C4C2511yescharacteristic
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2514yes—
1288C22×C4C2511yescharacteristic
1289C22×C4C2514yes—
1290C22×C4C2511yescharacteristic
1291C22×C4C2514yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2511yescharacteristic
1298C22×C4C2512yes—
1299C22×C4C2514yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C4⋊C4—22no—
1316C4⋊C4—24no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—22no—
1327C4⋊C4—28no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—28no—
1331C4⋊C4—22no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—28no—
1335C4⋊C4—24no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—28no—
1339C4⋊C4—28no—
1340C4⋊C4—24no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—28no—
1344C4⋊C4—24no—
1345C4⋊C4—42no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—41no—
1360C4⋊C4—44no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4C22×Q814yes—
1398C4⋊C4C22×Q814yes—
1399C4⋊C4C22×Q818yes—
1400C4⋊C4C22×Q814yes—
1401C4⋊C4C22×Q814yes—
1402C4⋊C42−1+414yes—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—22no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—41no—
1416C22⋊C4—41no—
1417C22⋊C4—41no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4C22×Q818yes—
1433C22⋊C4C22×Q818yes—
1434C22⋊C4C22×Q818yes—
1435C22⋊C4C22×Q818yes—
1436C22⋊C4C22×Q814yes—
1437C22⋊C4C22×Q814yes—
1438C22⋊C4C22×Q818yes—
1439C42—22no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—22no—
1445C42—24no—
1446C42—24no—
1447C42—24no—
1448C42—28no—
1449C42—24no—
1450C42—24no—
1451C42—22no—
1452C42—24no—
1453C42—24no—
1454C42—22no—
1455C42—24no—
1456C42—22no—
1457C42—24no—
1458C42—24no—
1459C42—42no—
1460C42—42no—
1461C42—42no—
1462C42—42no—
1463C42—42no—
1464C42—44no—
1465C42—42no—
1466C42—41no—
1467C42—42no—
1468C42—44no—
1469C42—41no—
1470C42—44no—
1471C42—44no—
1472C42—44no—
1473C42C22×Q818yes—
1474C42C22×Q818yes—
1475C42C22×Q814yes—
1476C42H(5,𝔽2)14yes—
1477C23—21no—
1478C23—22no—
1479C23—21no—
1480C23—22no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—22no—
1486C23—22no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—22no—
1491C23—21no—
1492C23—21no—
1493C23—22no—
1494C23—21no—
1495C23C23×Q812yes—
1496C23C23×Q812yes—
1497C23C23×Q814yes—
1498C23C2611yescharacteristic
1499Q8—28no—
1500Q8—48no—
1501Q8—48no—
1502Q8—44no—
1503Q8—44no—
1504Q8—48no—
1505Q8—48no—
1506Q8—84no—
1507Q8—84no—
1508Q8—88no—
1509Q8—88no—
1510D4—28no—
1511D4—48no—
1512D4—48no—
1513D4—44no—
1514C2×C4—22no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—21no—
1520C2×C4—22no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—28no—
1537C2×C4—28no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—24no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—24no—
1553C2×C4—24no—
1554C2×C4—24no—
1555C2×C4—24no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—24no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—24no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—24no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—24no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—48no—
1596C2×C4—44no—
1597C2×C4—48no—
1598C2×C4—44no—
1599C2×C4—48no—
1600C2×C4—44no—
1601C2×C4—84no—
1602C2×C4—82no—
1603C2×C4—88no—
1604C2×C4—84no—
1605C2×C4—88no—
1606C2×C4—164no—
1607C2×C4C23×Q812yes—
1608C2×C4C23×Q812yes—
1609C2×C4C23×Q814yes—
1610C2×C4C23×Q812yes—
1611C2×C4C23×Q814yes—
1612C2×C4C23×Q814yes—
1613C2×C4C23×Q812yes—
1614C2×C4C23×Q812yes—
1615C2×C4C2×H(5,𝔽2)12yes—
1616C2×C4C2×H(5,𝔽2)14yes—
1617C2×C4C2×H(5,𝔽2)12yes—
1618C2×C4C2×H(5,𝔽2)12yes—
1619C2×C4C2×H(5,𝔽2)12yes—
1620C2×C4C2×2−1+414yes—
1621C2×C4C2×2−1+412yes—
1622C2×C4#58512yes—
1623C2×C4#58512yes—
1624C22—22no—
1625C22—22no—
1626C22—24no—
1627C22—22no—
1628C22—22no—
1629C22—24no—
1630C22—24no—
1631C22—22no—
1632C22—22no—
1633C22—41no—
1634C22—41no—
1635C22—42no—
1636C22—42no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—42no—
1642C22—41no—
1643C22—41no—
1644C22—42no—
1645C22C24×Q811yescharacteristic
1646C22C22×H(5,𝔽2)11yescharacteristic
1647C22C22×H(5,𝔽2)11yescharacteristic
1648C22C22×2−1+411yescharacteristic
1649C22C2×#58511yescharacteristic
1650C22C2×#58511yescharacteristic
1651C222−1+611yescharacteristic
1652C4—24no—
1653C4—24no—
1654C4—22no—
1655C4—22no—
1656C4—22no—
1657C4—22no—
1658C4—24no—
1659C4—24no—
1660C4—22no—
1661C4—22no—
1662C4—24no—
1663C4—44no—
1664C4—42no—
1665C4—42no—
1666C4—41no—
1667C4—42no—
1668C4—42no—
1669C4—41no—
1670C4—41no—
1671C4—42no—
1672C4—42no—
1673C4—42no—
1674C4—44no—
1675C4—41no—
1676C4—42no—
1677C4—42no—
1678C4—41no—
1679C4—44no—
1680C4—44no—
1681C4—42no—
1682C4#350314yes—
1683C4#354214yes—
1684C2—42no—
1685C2—42no—
1686C2—44no—
1687C2C2×#354211yescharacteristic
1688C2C2×#350311yescharacteristic
1689C2#6281311yescharacteristic
1690C2#6295011yescharacteristic
1691C2#6295411yescharacteristic
1692C2Q8×H(5,𝔽2)11yescharacteristic
1693C2#6303911yescharacteristic
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. #59921C2semidirect
2. #59828C2semidirect
3. #59413C2semidirect
4. #59127C2semidirect
5. #59052C2semidirect
6. #51604C2semidirect
7. #48841C2semidirect
8. #46005C2semidirect
9. #45497C2semidirect
10. #44950C2semidirect
11. #44944C2semidirect
12. #44403C2semidirect
13. #42972C2semidirect
14. #42494C2semidirect
15. #42006C2semidirect
16. #39983C2semidirect
17. #39654C2semidirect
18. #39643C2semidirect
19. #39616C2semidirect
20. #39615C2semidirect
21. #39598C2semidirect
22. #38104C2semidirect
23. Q8×#121C2semidirect
24. #36481C2semidirect
25. #36287C2semidirect
26. #36279C2semidirect
27. #36276C2semidirect
28. #36129C2semidirect
29. #35284C2semidirect
30. #35281C2semidirect
31. #35176C2semidirect
32. #34953C2semidirect
33. #34691C2semidirect
303. #555Q8semidirect
875. C4⋊Q8C2×Q8semidirect
884. #124C2×Q8semidirect
885. #124C2×Q8semidirect
908. #121C2×Q8semidirect
909. #121C2×Q8semidirect
910. #121C2×Q8semidirect
937. C4×D4C2×Q8semidirect
938. C4×D4C2×Q8semidirect
944. #117C2×Q8semidirect
945. #117C2×Q8semidirect
946. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599212
#598282
#594132
#591272
#590522
#516042
#488412
#460052
#454972
#449502
#449442
#444032
#429722
#424942
#420062
#399832
#396542
#396432
#396162
#396152
#395982
#381042
Q8×#1212
#364812
#362872
#362792
#362762
#361292
#352842
#352812
#351762
#349532
#346912
#344672
C4×#5552