Finite Group Databasebeta

← #7699868

Subgroups — #7699868

Order 512.

5442 conjugacy classes of subgroups.

The subgroup lattice has 1721 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59857C212yesmaximal, complemented
2#59849C214yesmaximal, complemented
3#59695C212yesmaximal, complemented
4#59686C214yesmaximal, complemented
5#59681C211yesmaximal, characteristic, complemented
6#59402C212yesmaximal, complemented
7#59389C214yesmaximal, complemented
8#59289C212yesmaximal, complemented
9#59243C211yesmaximal, characteristic, complemented
10#59218C211yesmaximal, characteristic, complemented
11#59209C212yesmaximal, complemented
12#59139C212yesmaximal, complemented
13#36599C211yesmaximal, characteristic, complemented
14#36588C212yesmaximal, complemented
15#36488C212yesmaximal, complemented
16#36486C212yesmaximal, complemented
17#36481C211yesmaximal, characteristic, complemented
18#36477C211yesmaximal, characteristic, complemented
19#36382C212yesmaximal, complemented
20#36353C214yesmaximal, complemented
21#36259C212yesmaximal, complemented
22#36259C211yesmaximal, characteristic, complemented
23#36259C211yesmaximal, characteristic, complemented
24#36241C212yesmaximal, complemented
25#36217C212yesmaximal, complemented
26#36210C211yesmaximal, characteristic, complemented
27#36200C212yesmaximal, complemented
28D4×#125C211yesmaximal, characteristic, complemented
29C4×#553C211yesmaximal, characteristic, complemented
30C4×#547C211yesmaximal, characteristic, complemented
31C4×#547C211yesmaximal, characteristic, complemented
32C4×#547C212yesmaximal, complemented
33C2×#2370C212yesmaximal, complemented
34#34127C211yesmaximal, characteristic, complemented
35C4⋊C4×#41C211yesmaximal, characteristic, complemented
36C2×#553C2211yescharacteristic
37C2×#547C2212yes—
38C2×#547C2211yescharacteristic
39C2×#547C2211yescharacteristic
40C2×#547C2212yes—
41C22×#125C2212yes—
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2212yes—
45C2×C4×#41C2212yes—
46#2863C2212yes—
47#2859C2211yescharacteristic
48#2857C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2854C2214yes—
53#2854C2212yes—
54#2854C2212yes—
55#2853C2214yes—
56#2852C2214yes—
57#2851C2212yes—
58#2802C2214yes—
59#2786C2214yes—
60#2783C2214yes—
61#2776C2214yes—
62#2772C2214yes—
63#2770C2214yes—
64#2766C2214yes—
65#2725C2214yes—
66#2711C2214yes—
67#2608C2214yes—
68#2606C2214yes—
69#2606C2214yes—
70#2601C2214yes—
71#2597C2214yes—
72#2596C2214yes—
73#2595C2214yes—
74#2595C2214yes—
75#2594C2214yes—
76#2594C2214yes—
77#2594C2214yes—
78#2593C2214yes—
79#2590C2214yes—
80#2590C2214yes—
81#2587C2214yes—
82#2587C2214yes—
83#2585C2214yes—
84#2585C2214yes—
85#2577C2214yes—
86#2573C2214yes—
87#2570C2212yes—
88#2570C2212yes—
89#2569C2214yes—
90#2566C2212yes—
91#2562C2212yes—
92#2558C2214yes—
93#2552C2211yescharacteristic
94#2552C2211yescharacteristic
95#2546C2212yes—
96#2546C2211yescharacteristic
97#2546C2211yescharacteristic
98#2538C2212yes—
99#2538C2211yescharacteristic
100#2538C2211yescharacteristic
101#2530C2214yes—
102#2529C2214yes—
103#2525C2214yes—
104#2525C2214yes—
105#2522C2214yes—
106#2515C2214yes—
107#2514C2212yes—
108#2513C2212yes—
109#2512C2212yes—
110#2511C2212yes—
111#2511C2212yes—
112#2510C2214yes—
113#2509C2212yes—
114#2509C2212yes—
115#2509C2212yes—
116#2507C2212yes—
117#2507C2212yes—
118#2506C2212yes—
119#2506C2212yes—
120#2499C2212yes—
121#2498C2214yes—
122#2497C2212yes—
123#2497C2212yes—
124#2496C2212yes—
125#2495C2212yes—
126#2494C2212yes—
127#2494C2212yes—
128#2494C2212yes—
129#2494C2212yes—
130#2493C2214yes—
131#2493C2214yes—
132#2493C2214yes—
133#2490C2212yes—
134#2490C2212yes—
135#2486C2212yes—
136#2486C2214yes—
137#2486C2212yes—
138#2485C2212yes—
139#2485C2212yes—
140#2484C2214yes—
141#2481C2214yes—
142#2481C2214yes—
143#2473C2214yes—
144#2473C2214yes—
145#2468C2214yes—
146#2460C2214yes—
147#2446C2212yes—
148#2446C2212yes—
149#2444C2214yes—
150#2443C2214yes—
151#2442C2212yes—
152#2442C2212yes—
153#2442C2212yes—
154#2441C2212yes—
155#2429C2212yes—
156#2429C2212yes—
157#2429C2212yes—
158#2429C2212yes—
159#2425C2214yes—
160#2425C2214yes—
161#2425C2214yes—
162#2425C2214yes—
163#2423C2212yes—
164#2421C2212yes—
165#2419C2214yes—
166#2419C2214yes—
167#2416C2214yes—
168#2416C2212yes—
169#2416C2212yes—
170#2415C2212yes—
171#2415C2212yes—
172#2415C2212yes—
173#2415C2212yes—
174#2413C2214yes—
175#2413C2214yes—
176#2413C2214yes—
177#2413C2214yes—
178#2374C2212yes—
179#2373C2214yes—
180#2373C2212yes—
181#2370C2214yes—
182#2370C2212yes—
183#2370C2214yes—
184#2370C2214yes—
185#2370C2212yes—
186#2370C2211yescharacteristic
187#2370C2212yes—
188#2370C2212yes—
189#2370C2212yes—
190#2370C2212yes—
191#2370C2214yes—
192#2370C2212yes—
193#2365C2212yes—
194#2365C2211yescharacteristic
195#2365C2211yescharacteristic
196#2364C2212yes—
197#2363C2211yescharacteristic
198#2362C2211yescharacteristic
199#2362C2211yescharacteristic
200#2362C2212yes—
201#2362C2212yes—
202#2362C2212yes—
203#2361C2214yes—
204#2361C2212yes—
205#2361C2212yes—
206#2361C2211yescharacteristic
207#2359C2212yes—
208#2359C2214yes—
209#2359C2214yes—
210#2359C2214yes—
211#2359C2212yes—
212#2357C2211yescharacteristic
213#2357C2212yes—
214#2355C2211yescharacteristic
215#2355C2211yescharacteristic
216#2354C2211yescharacteristic
217#2354C2212yes—
218#2354C2211yescharacteristic
219#2353C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222#2352C2211yescharacteristic
223#2351C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225Q8×C4⋊C4C2211yescharacteristic
226#2349C2214yes—
227#2349C2212yes—
228D4×C4⋊C4C2212yes—
229D4×C4⋊C4C2211yescharacteristic
230D4×C4⋊C4C2211yescharacteristic
231D4×C4⋊C4C2212yes—
232D4×C4⋊C4C2212yes—
233D4×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236#2347C2212yes—
237#2347C2212yes—
238#2347C2211yescharacteristic
239#2347C2212yes—
240#2345C2211yescharacteristic
241#2345C2212yes—
242#2344C2212yes—
243#2344C2214yes—
244#2344C2212yes—
245#2343C2214yes—
246#2339C2212yes—
247#2339C2211yescharacteristic
248#2339C2211yescharacteristic
249#2339C2212yes—
250#2339C2212yes—
251#2339C2212yes—
252C4×C4⋊Q8C2211yescharacteristic
253C4×C4⋊Q8C2211yescharacteristic
254C4×C4⋊Q8C2212yes—
255C4×#125C2211yescharacteristic
256C4×#126C2212yes—
257C4×C22⋊Q8C2212yes—
258C4×C22⋊Q8C2212yes—
259C4×C22⋊Q8C2211yescharacteristic
260C4×C22⋊Q8C2211yescharacteristic
261C4×C22⋊Q8C2212yes—
262C4×#123C2214yes—
263C4×#123C2212yes—
264C4×#123C2212yes—
265C4×#123C2214yes—
266C4×#123C2212yes—
267C4×#123C2214yes—
268C4×#121C2212yes—
269C4×#121C2212yes—
270C4×#121C2214yes—
271C4×#121C2211yescharacteristic
272C4×#121C2211yescharacteristic
273C4×#121C2212yes—
274#2296C2214yes—
275#2296C2212yes—
276#2295C2212yes—
277C2×#389C2212yes—
278C2×#389C2212yes—
279C2×#389C2214yes—
280#2290C2214yes—
281C2×#387C2214yes—
282C2×#387C2214yes—
283#2285C2212yes—
284#2285C2211yescharacteristic
285#2285C2211yescharacteristic
286#2283C2212yes—
287C42×D4C2211yescharacteristic
288C42×D4C2212yes—
289C42×D4C2212yes—
290C42×D4C2211yescharacteristic
291C42×D4C2211yescharacteristic
292C4×#117C2211yescharacteristic
293C2×C4×C4⋊C4C2214yes—
294C2×C4×C4⋊C4C2212yes—
295C2×C4×C4⋊C4C2211yescharacteristic
296C2×C4×C4⋊C4C2212yes—
297C2×C4×C4⋊C4C2212yes—
298C2×C4×C4⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2311yescharacteristic
302#553—28no—
303#547—216no—
304#547—28no—
305#547—28no—
306#547—48no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×#126C2312yes—
312C2×#126C2314yes—
313C2×#125—216no—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#125C2314yes—
319C2×#125C2311yescharacteristic
320C2×#123C2312yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×#123C2312yes—
325C2×#123C2312yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×C22⋊Q8C2311yescharacteristic
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×#121C2312yes—
336C2×#121C2314yes—
337C2×#121C2312yes—
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#121C2312yes—
341C2×#121C2314yes—
342C4×#41—28no—
343C4×#41—28no—
344C4×#41—48no—
345C4×#41—48no—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2311yescharacteristic
383C2×#117C2311yescharacteristic
384C2×#117C2311yescharacteristic
385C2×#117C2311yescharacteristic
386C2×#117C2314yes—
387C2×#117C2314yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C22×C4⋊C4C2314yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2311yescharacteristic
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2314yes—
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2314yes—
403C22×C42C2312yes—
404C22×C42C2312yes—
405C22×C42C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2314yes—
409C22×C42C2314yes—
410C22×C42C2314yes—
411C22×C42C2312yes—
412C22×C42C2312yes—
413#401C2314yes—
414#401C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#399C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#391C2311yescharacteristic
468#391C2311yescharacteristic
469#391C2312yes—
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2311yescharacteristic
486#390C2311yescharacteristic
487#390C2312yes—
488#389C2311yescharacteristic
489#389C2311yescharacteristic
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2311yescharacteristic
531#389C2312yes—
532#389C2312yes—
533#389C2311yescharacteristic
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#388C2312yes—
545#388C2312yes—
546#388C2312yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2312yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2312yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2314yes—
624#387C2312yes—
625#387C2314yes—
626#387C2312yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2312yes—
641#386C2312yes—
642#386C2314yes—
643#386C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2312yes—
647#386C2312yes—
648#386C2312yes—
649#386C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2312yes—
657#385C2314yes—
658#385C2314yes—
659#385C2312yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2312yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2312yes—
670#384C2311yescharacteristic
671#384C2312yes—
672#384C2311yescharacteristic
673#384C2312yes—
674#384C2312yes—
675#384C2311yescharacteristic
676#384C2311yescharacteristic
677#384C2312yes—
678#383C2312yes—
679#383C2314yes—
680#383C2314yes—
681#383C2314yes—
682#382C2311yescharacteristic
683#382C2312yes—
684#382C2312yes—
685#382C2312yes—
686#382C2312yes—
687#382C2312yes—
688#382C2314yes—
689#381C2314yes—
690#381C2314yes—
691#381C2314yes—
692#381C2312yes—
693#381C2314yes—
694#381C2314yes—
695#381C2312yes—
696#381C2312yes—
697#380C2312yes—
698#380C2312yes—
699#380C2312yes—
700#380C2312yes—
701#380C2312yes—
702#380C2314yes—
703#380C2314yes—
704#380C2312yes—
705#380C2312yes—
706#380C2311yescharacteristic
707#380C2312yes—
708#380C2312yes—
709#380C2311yescharacteristic
710#380C2312yes—
711#380C2312yes—
712#380C2314yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2311yescharacteristic
717#380C2312yes—
718#380C2312yes—
719#380C2311yescharacteristic
720#380C2314yes—
721#380C2312yes—
722C4×C4⋊C4C2311yescharacteristic
723C4×C4⋊C4C2312yes—
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2311yescharacteristic
726C4×C4⋊C4C2311yescharacteristic
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2314yes—
733C4×C4⋊C4C2314yes—
734C4×C4⋊C4C2311yescharacteristic
735C4×C4⋊C4C2314yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2314yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2314yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2311yescharacteristic
790C4×C22⋊C4C2311yescharacteristic
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808#376C2312yes—
809#376C2314yes—
810C2×#95C2312yes—
811C2×#95C2314yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C2×#95C2314yes—
818C43C2312yes—
819C43C2311yescharacteristic
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—28no—
824C2×#41—28no—
825C2×#41—24no—
826C2×#41—28no—
827C2×#41—24no—
828C2×#41#4118yes—
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×Q8C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2414yes—
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2414yes—
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2414yes—
849C23×C4C2412yes—
850C23×C4C2414yes—
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2411yescharacteristic
862C4⋊Q8—24no—
863C4⋊Q8—28no—
864C4⋊Q8—24no—
865C4⋊Q8—44no—
866#126—28no—
867#126—48no—
868#125—28no—
869#125—28no—
870#125—216no—
871#125—216no—
872#125—28no—
873#125#4118yescomplemented
874#123—216no—
875#123—28no—
876#123—28no—
877#123—216no—
878#123—28no—
879#123—216no—
880#123—48no—
881#123—48no—
882C22⋊Q8—24no—
883C22⋊Q8—28no—
884C22⋊Q8—24no—
885C22⋊Q8—28no—
886C22⋊Q8—28no—
887C22⋊Q8—44no—
888C22⋊Q8—44no—
889#121—216no—
890#121—28no—
891#121—28no—
892#121—28no—
893#121—24no—
894#121—24no—
895#121—48no—
896C4×Q8—24no—
897C4×Q8—24no—
898C4×Q8—24no—
899C4×Q8—24no—
900C4×Q8—44no—
901C4×Q8—44no—
902C4×Q8—44no—
903C4×Q8—44no—
904C4×D4—24no—
905C4×D4—24no—
906C4×D4—28no—
907C4×D4—24no—
908C4×D4—24no—
909C4×D4—28no—
910C4×D4—28no—
911C4×D4—28no—
912C4×D4—28no—
913C4×D4—28no—
914C4×D4—24no—
915C4×D4—28no—
916C4×D4—24no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—24no—
920C4×D4—24no—
921C4×D4—24no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—42no—
925C4×D4—48no—
926C4×D4—48no—
927C4×D4—48no—
928C4×D4—48no—
929C4×D4#4118yes—
930#117—24no—
931#117—24no—
932#117—24no—
933#117—24no—
934#117—28no—
935#117—28no—
936#117—44no—
937#117—48no—
938#117—48no—
939#117—44no—
940#117—44no—
941C2×C4⋊C4—216no—
942C2×C4⋊C4—28no—
943C2×C4⋊C4—28no—
944C2×C4⋊C4—28no—
945C2×C4⋊C4—28no—
946C2×C4⋊C4—216no—
947C2×C4⋊C4—216no—
948C2×C4⋊C4—24no—
949C2×C4⋊C4—28no—
950C2×C4⋊C4—24no—
951C2×C4⋊C4—44no—
952C2×C4⋊C4—48no—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C42—28no—
1070C2×C42—28no—
1071C2×C42—24no—
1072C2×C42—24no—
1073C2×C42—28no—
1074C2×C42—44no—
1075C2×C42—44no—
1076C2×C42—48no—
1077C2×C42—48no—
1078C2×C42—48no—
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2414yes—
1085C2×C42C2412yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2414yes—
1107C2×C42C2414yes—
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2414yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2414yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121#95C2412yes—
1122#95C2412yes—
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2411yescharacteristic
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2411yescharacteristic
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2411yescharacteristic
1168#95C2411yescharacteristic
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193C24C2512yes—
1194C24C2511yescharacteristic
1195C24C2511yescharacteristic
1196C24C2512yes—
1197#41—232no—
1198#41—416no—
1199#41—432no—
1200C2×Q8—22no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—22no—
1206C2×Q8—24no—
1207C2×Q8—22no—
1208C2×Q8C2×#4114yes—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—22no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—28no—
1216C2×D4—28no—
1217C2×D4—28no—
1218C2×D4—24no—
1219C2×D4—22no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—24no—
1224C2×D4—22no—
1225C2×D4—42no—
1226C2×D4—41no—
1227C2×D4—42no—
1228C2×D4—42no—
1229C2×D4C2×#4118yes—
1230C2×D4C2×#4114yes—
1231C2×D4C2×#4114yes—
1232C2×D4H(5,𝔽2)14yes—
1233C22×C4—24no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—24no—
1241C22×C4—24no—
1242C22×C4—28no—
1243C22×C4—24no—
1244C22×C4—28no—
1245C22×C4—28no—
1246C22×C4—24no—
1247C22×C4—28no—
1248C22×C4—28no—
1249C22×C4—28no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—24no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—28no—
1259C22×C4—28no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—28no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—44no—
1278C22×C4—44no—
1279C22×C4—42no—
1280C22×C4—41no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—44no—
1284C22×C4—42no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4C2×#4118yes—
1297C22×C4C2×#4118yes—
1298C22×C4C2×#4114yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2514yes—
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2514yes—
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2514yes—
1316C22×C4C2512yes—
1317C22×C4C2514yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C4⋊C4—24no—
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—24no—
1335C4⋊C4—28no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—24no—
1339C4⋊C4—28no—
1340C4⋊C4—24no—
1341C4⋊C4—28no—
1342C4⋊C4—24no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—28no—
1346C4⋊C4—28no—
1347C4⋊C4—28no—
1348C4⋊C4—28no—
1349C4⋊C4—28no—
1350C4⋊C4—28no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—22no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—24no—
1363C4⋊C4—28no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—28no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—24no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4C2×#4114yes—
1397C4⋊C4C2×#4114yes—
1398C4⋊C4C2×#4118yes—
1399C4⋊C4C2×#4118yes—
1400C4⋊C4C2×#4114yes—
1401C4⋊C42−1+414yes—
1402C22⋊C4—24no—
1403C22⋊C4—24no—
1404C22⋊C4—28no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—22no—
1408C22⋊C4—28no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—28no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—22no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—24no—
1423C22⋊C4—28no—
1424C22⋊C4—24no—
1425C22⋊C4—28no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—22no—
1430C22⋊C4—24no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—41no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4C2×#4118yes—
1446C42—22no—
1447C42—22no—
1448C42—24no—
1449C42—22no—
1450C42—24no—
1451C42—22no—
1452C42—22no—
1453C42—24no—
1454C42—24no—
1455C42—24no—
1456C42—22no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—22no—
1464C42—22no—
1465C42—24no—
1466C42—24no—
1467C42—24no—
1468C42—22no—
1469C42—24no—
1470C42—28no—
1471C42—42no—
1472C42—42no—
1473C42—44no—
1474C42—44no—
1475C42—42no—
1476C42—44no—
1477C42—42no—
1478C42—44no—
1479C42—44no—
1480C42—44no—
1481C42—44no—
1482C42—44no—
1483C42—42no—
1484C42—41no—
1485C42—41no—
1486C42C2×#4114yes—
1487C42C2×#4114yes—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—22no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—22no—
1499C23—21no—
1500C23—22no—
1501C23—21no—
1502C23—22no—
1503C23—21no—
1504C23—21no—
1505C23—22no—
1506C23—21no—
1507C23—22no—
1508C23—22no—
1509C23—21no—
1510C23—22no—
1511C23—21no—
1512C23C22×#4112yes—
1513C23C22×#4114yes—
1514C23C22×#4114yes—
1515C23C2×H(5,𝔽2)14yes—
1516C23C2611yescharacteristic
1517Q8—28no—
1518Q8—44no—
1519Q8—48no—
1520D4—216no—
1521D4—48no—
1522D4—44no—
1523D4—48no—
1524D4—416no—
1525D4—44no—
1526D4—84no—
1527D4#553116yescomplemented
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—21no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—216no—
1549C2×C4—28no—
1550C2×C4—216no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—24no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—24no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—44no—
1609C2×C4—48no—
1610C2×C4—416no—
1611C2×C4—48no—
1612C2×C4—416no—
1613C2×C4—48no—
1614C2×C4—416no—
1615C2×C4—48no—
1616C2×C4—416no—
1617C2×C4—44no—
1618C2×C4—48no—
1619C2×C4—44no—
1620C2×C4—44no—
1621C2×C4—84no—
1622C2×C4—84no—
1623C2×C4—82no—
1624C2×C4—84no—
1625C2×C4—84no—
1626C2×C4—84no—
1627C2×C4C22×#4114yes—
1628C2×C4C22×#4112yes—
1629C2×C4C22×#4112yes—
1630C2×C4C22×#4112yes—
1631C2×C4C22×#4114yes—
1632C2×C4C22×#4112yes—
1633C2×C4C22×#4114yes—
1634C2×C4C22×#4114yes—
1635C2×C4C22×#4112yes—
1636C2×C4C22×#4112yes—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4112yes—
1639C2×C4C2×H(5,𝔽2)12yes—
1640C2×C4C2×2−1+414yes—
1641C2×C4C2×2−1+412yes—
1642C2×C4#58512yes—
1643C22—24no—
1644C22—24no—
1645C22—24no—
1646C22—24no—
1647C22—24no—
1648C22—24no—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—42no—
1657C22—41no—
1658C22—41no—
1659C22—42no—
1660C22—41no—
1661C22—42no—
1662C22—42no—
1663C22—41no—
1664C22—42no—
1665C22—41no—
1666C22—41no—
1667C22—42no—
1668C22—42no—
1669C22—41no—
1670C22C2×#55318yes—
1671C22C23×#4111yescharacteristic
1672C22C23×#4111yescharacteristic
1673C22C23×#4111yescharacteristic
1674C22C22×H(5,𝔽2)11yescharacteristic
1675C22C22×2−1+411yescharacteristic
1676C22C2×#58511yescharacteristic
1677C222−1+611yescharacteristic
1678C4—22no—
1679C4—24no—
1680C4—22no—
1681C4—22no—
1682C4—24no—
1683C4—22no—
1684C4—24no—
1685C4—24no—
1686C4—24no—
1687C4—22no—
1688C4—42no—
1689C4—44no—
1690C4—42no—
1691C4—42no—
1692C4—42no—
1693C4—41no—
1694C4—41no—
1695C4—42no—
1696C4—44no—
1697C4—42no—
1698C4—41no—
1699C4—41no—
1700C4—42no—
1701C4—42no—
1702C4—44no—
1703C4—41no—
1704C4—41no—
1705C4—42no—
1706C4—44no—
1707C4C2×#55314yes—
1708C4#348214yes—
1709C2—28no—
1710C2—42no—
1711C2—82no—
1712C2—81no—
1713C2C22×#55311yescharacteristic
1714C2C2×#348211yescharacteristic
1715C2#41211yescharacteristic
1716C2#6298511yescharacteristic
1717C2#6299311yescharacteristic
1718C2#6300111yescharacteristic
1719C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59857C2semidirect
2. #59849C2semidirect
3. #59695C2semidirect
4. #59686C2semidirect
5. #59681C2semidirect
6. #59402C2semidirect
7. #59389C2semidirect
8. #59289C2semidirect
9. #59243C2semidirect
10. #59218C2semidirect
11. #59209C2semidirect
12. #59139C2semidirect
13. #36599C2semidirect
14. #36588C2semidirect
15. #36488C2semidirect
16. #36486C2semidirect
17. #36481C2semidirect
18. #36477C2semidirect
19. #36382C2semidirect
20. #36353C2semidirect
21. #36259C2semidirect
22. #36259C2semidirect
23. #36259C2semidirect
24. #36241C2semidirect
25. #36217C2semidirect
26. #36210C2semidirect
27. #36200C2semidirect
28. D4×#125C2semidirect
29. C4×#553C2semidirect
30. C4×#547C2semidirect
31. C4×#547C2semidirect
32. C4×#547C2semidirect
33. C2×#2370C2semidirect
34. #34127C2semidirect
35. C4⋊C4×#41C2semidirect
873. #125#41semidirect
1527. D4#553semidirect

Maximal subgroups

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

subgroupindex
#598572
#598492
#596952
#596862
#596812
#594022
#593892
#592892
#592432
#592182
#592092
#591392
#365992
#365882
#364882
#364862
#364812
#364772
#363822
#363532
#362592
#362412
#362172
#362102
#362002
D4×#1252
C4×#5532
C4×#5472
C2×#23702
#341272
C4⋊C4×#412