Finite Group Databasebeta

← #7657350

Subgroups — #7657350

Order 512.

5088 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42497C212yesmaximal, complemented
2#42493C212yesmaximal, complemented
3#42491C212yesmaximal, complemented
4#42488C212yesmaximal, complemented
5#40618C214yesmaximal, complemented
6#40614C214yesmaximal, complemented
7#40613C214yesmaximal, complemented
8#40610C214yesmaximal, complemented
9#39498C211yesmaximal, characteristic, complemented
10#39369C211yesmaximal, characteristic, complemented
11#38967C211yesmaximal, characteristic, complemented
12#38964C211yesmaximal, characteristic, complemented
13#38101C212yesmaximal, complemented
14#38098C212yesmaximal, complemented
15#37875C212yesmaximal, complemented
16#37686C212yesmaximal, complemented
17#37642C211yesmaximal, characteristic, complemented
18#37624C211yesmaximal, characteristic, complemented
19#37477C212yesmaximal, complemented
20#37476C212yesmaximal, complemented
21#36290C211yesmaximal, characteristic, complemented
22#36261C211yesmaximal, characteristic, complemented
23#36165C211yesmaximal, characteristic, complemented
24D4×C4⋊Q8C211yesmaximal, characteristic, complemented
25#35961C212yesmaximal, complemented
26#35928C212yesmaximal, complemented
27#35836C212yesmaximal
28#35702C212yesmaximal
29#35294C211yesmaximal, characteristic, complemented
30#35253C212yesmaximal, complemented
31#34625C211yesmaximal, characteristic, complemented
32C2×#2628C212yesmaximal, complemented
33#34194C211yesmaximal, characteristic
34#34181C211yesmaximal, characteristic
35D4×#117C211yesmaximal, characteristic
36C2×#554C2212yes—
37C2×D4×Q8C2212yes—
38C2×#544C2212yescomplemented
39C22×C4⋊Q8C2212yescomplemented
40C2×#518C2212yes—
41C22×C4×D4C2211yescharacteristic
42C22×#117C2212yes—
43#2868C2211yescharacteristic, complemented
44#2859C2211yescharacteristic, complemented
45#2859C2211yescharacteristic, complemented
46#2859C2211yescharacteristic, complemented
47#2857C2212yescomplemented
48#2857C2212yescomplemented
49#2851C2212yescomplemented
50#2851C2212yescomplemented
51#2844C2214yescomplemented
52#2841C2214yes—
53#2841C2214yes—
54#2841C2214yes—
55#2841C2214yescomplemented
56#2841C2214yescomplemented
57#2807C2214yescomplemented
58#2807C2214yescomplemented
59#2805C2214yescomplemented
60#2802C2214yescomplemented
61#2792C2214yescomplemented
62#2788C2214yescomplemented
63#2788C2214yescomplemented
64#2774C2214yescomplemented
65#2774C2214yescomplemented
66#2768C2214yescomplemented
67#2768C2214yescomplemented
68#2763C2214yescomplemented
69#2763C2214yescomplemented
70#2755C2214yescomplemented
71#2742C2214yescomplemented
72#2742C2214yescomplemented
73#2734C2214yescomplemented
74#2729C2214yescomplemented
75#2729C2214yescomplemented
76#2720C2214yescomplemented
77#2720C2214yescomplemented
78#2713C2214yescomplemented
79#2677C2214yescomplemented
80#2677C2214yescomplemented
81#2667C2212yes—
82#2667C2214yes—
83#2666C2212yescomplemented
84#2666C2212yescomplemented
85#2666C2214yescomplemented
86#2665C2212yes—
87#2665C2214yes—
88#2660C2212yescomplemented
89#2660C2211yescharacteristic, complemented
90#2660C2211yescharacteristic, complemented
91#2659C2214yescomplemented
92#2659C2214yescomplemented
93#2647C2211yescharacteristic, complemented
94#2647C2211yescharacteristic, complemented
95#2647C2212yescomplemented
96#2646C2214yescomplemented
97#2646C2214yescomplemented
98#2629C2211yescharacteristic
99#2629C2211yescharacteristic
100#2629C2212yes—
101#2629C2212yes—
102#2628C2212yes—
103#2628C2212yes—
104#2628C2212yes—
105#2628C2214yes—
106#2628C2212yes—
107#2628C2211yescharacteristic
108#2628C2212yes—
109#2628C2214yes—
110#2628C2214yes—
111#2628C2212yes—
112#2628C2211yescharacteristic
113#2628C2214yescomplemented
114#2628C2212yescomplemented
115#2628C2212yescomplemented
116#2628C2212yescomplemented
117#2628C2214yescomplemented
118#2628C2212yescomplemented
119#2626C2214yes—
120#2626C2214yes—
121#2584C2212yescomplemented
122#2584C2212yescomplemented
123#2583C2214yescomplemented
124#2583C2214yescomplemented
125#2580C2212yes—
126#2580C2212yes—
127#2571C2211yescharacteristic, complemented
128#2571C2211yescharacteristic, complemented
129#2571C2212yescomplemented
130#2571C2212yescomplemented
131#2571C2211yescharacteristic, complemented
132#2570C2212yescomplemented
133#2570C2212yescomplemented
134#2570C2212yescomplemented
135#2569C2214yescomplemented
136#2567C2212yescomplemented
137#2564C2214yes—
138#2564C2214yes—
139#2563C2212yes—
140#2552C2211yescharacteristic, complemented
141#2552C2211yescharacteristic, complemented
142#2551C2212yescomplemented
143#2551C2212yescomplemented
144#2551C2211yescharacteristic, complemented
145#2551C2212yescomplemented
146#2551C2211yescharacteristic, complemented
147#2551C2211yescharacteristic, complemented
148#2551C2212yescomplemented
149#2550C2212yescomplemented
150#2550C2212yescomplemented
151#2550C2212yescomplemented
152#2550C2212yescomplemented
153#2550C2212yescomplemented
154#2549C2214yescomplemented
155#2549C2214yescomplemented
156#2549C2214yescomplemented
157#2546C2212yescomplemented
158#2542C2212yes—
159#2509C2212yescomplemented
160#2509C2212yescomplemented
161#2509C2212yescomplemented
162#2508C2212yescomplemented
163#2508C2212yescomplemented
164#2508C2212yescomplemented
165#2507C2212yescomplemented
166#2506C2212yescomplemented
167#2505C2214yescomplemented
168#2505C2214yescomplemented
169#2505C2214yescomplemented
170#2505C2214yescomplemented
171#2505C2214yescomplemented
172#2505C2214yescomplemented
173#2487C2214yes—
174#2473C2214yescomplemented
175#2473C2214yescomplemented
176#2454C2212yes—
177#2454C2212yes—
178#2452C2212yes—
179#2452C2212yes—
180#2450C2214yes—
181#2450C2214yes—
182#2449C2214yes—
183#2449C2214yes—
184#2442C2212yescomplemented
185#2442C2212yescomplemented
186#2442C2212yescomplemented
187#2442C2212yescomplemented
188#2442C2212yescomplemented
189#2442C2212yescomplemented
190#2442C2214yescomplemented
191#2441C2212yes—
192#2441C2214yes—
193#2441C2212yes—
194#2441C2212yes—
195#2441C2212yescomplemented
196#2441C2212yescomplemented
197#2440C2212yescomplemented
198#2440C2212yescomplemented
199#2440C2214yescomplemented
200#2440C2212yescomplemented
201#2440C2212yescomplemented
202#2440C2214yescomplemented
203#2440C2214yescomplemented
204#2440C2212yescomplemented
205#2440C2212yescomplemented
206#2439C2212yes—
207#2439C2212yes—
208#2439C2212yes—
209#2439C2214yes—
210#2439C2212yescomplemented
211#2439C2212yescomplemented
212#2438C2214yescomplemented
213#2438C2214yescomplemented
214#2437C2214yes—
215#2437C2214yes—
216#2437C2214yes—
217#2437C2214yes—
218#2434C2214yescomplemented
219#2434C2214yescomplemented
220#2409C2214yes—
221#2402C2212yescomplemented
222#2399C2212yescomplemented
223#2396C2212yes—
224#2396C2212yes—
225C2×#400C2214yescomplemented
226C2×#399C2214yes—
227C2×#395C2214yescomplemented
228C2×#393C2214yes—
229#2354C2211yescharacteristic
230#2354C2211yescharacteristic
231#2354C2211yescharacteristic
232#2354C2211yescharacteristic
233#2352C2212yes—
234#2352C2212yes—
235#2352C2212yes—
236#2352C2212yes—
237#2349C2212yes—
238#2349C2212yes—
239#2349C2212yes—
240#2349C2212yes—
241#2349C2212yes—
242#2349C2212yes—
243#2349C2214yes—
244D4×C4⋊C4C2212yes—
245D4×C4⋊C4C2211yescharacteristic
246D4×C4⋊C4C2211yescharacteristic
247D4×C4⋊C4C2211yescharacteristic
248D4×C4⋊C4C2212yes—
249D4×C4⋊C4C2211yescharacteristic
250D4×C4⋊C4C2211yescharacteristic
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2211yescharacteristic
253D4×C4⋊C4C2211yescharacteristic
254D4×C4⋊C4C2212yes—
255D4×C4⋊C4C2212yes—
256#2345C2212yes—
257#2344C2211yescharacteristic
258#2344C2211yescharacteristic
259#2342C2212yes—
260#2342C2212yes—
261#2342C2214yes—
262D4×C22⋊C4C2211yescharacteristic
263D4×C22⋊C4C2211yescharacteristic
264D4×C22⋊C4C2212yes—
265#2331C2212yescomplemented
266#2330C2212yescomplemented
267#2319C2212yes—
268#2318C2214yes—
269#2317C2212yescomplemented
270#2317C2212yescomplemented
271#2316C2212yes—
272#2316C2212yescomplemented
273#2315C2214yes—
274C4×C4⋊Q8C2211yescharacteristic, complemented
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×#125C2211yescharacteristic, complemented
277C4×#125C2211yescharacteristic, complemented
278#2293C2211yescharacteristic
279#2293C2211yescharacteristic
280C2×#389C2212yescomplemented
281C2×#389C2212yescomplemented
282#2290C2212yes—
283#2290C2212yes—
284#2285C2211yescharacteristic
285#2285C2211yescharacteristic
286#2285C2211yescharacteristic
287#2285C2211yescharacteristic
288#2283C2211yescharacteristic
289C2×#382C2212yescomplemented
290#2280C2212yes—
291#2280C2212yes—
292C2×#380C2212yes—
293C2×#380C2212yes—
294C2×#380C2212yes—
295#2275C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C23×Q8C2314yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#554—48no—
303D4×Q8—48no—
304#544—48no—
305C2×C4⋊Q8—48no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2314yes—
314C2×C4⋊Q8C2314yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2314yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2314yes—
321C2×#125C2311yescharacteristic
322C2×#125C2311yescharacteristic
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#125C2314yes—
328C2×#125C2312yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339#518—48no—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×D4Q8116yescomplemented
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2312yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×#117—48no—
362C2×#117C2312yes—
363C2×#117C2311yescharacteristic
364C2×#117C2312yes—
365C2×#117C2312yes—
366C2×#117C2312yes—
367C2×#117C2312yes—
368C2×#117C2312yes—
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2311yescharacteristic
375C2×#117C2312yes—
376C22×C4⋊C4C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2314yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2314yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2311yescharacteristic
388C22×C22⋊C4C2314yes—
389C22×C22⋊C4C2314yes—
390C22×C22⋊C4C2312yes—
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2314yes—
393C22×C22⋊C4C2312yes—
394C22×C42C2312yes—
395C22×C42C2312yes—
396C22×C42C2311yescharacteristic
397#400C2312yes—
398#400C2314yes—
399#400C2312yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#400C2312yes—
422#400C2312yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#399C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2312yes—
430#399C2314yes—
431#399C2312yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2312yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#398C2312yes—
458#398C2312yes—
459#398C2312yes—
460#398C2312yes—
461#398C2312yes—
462#398C2312yes—
463#398C2312yes—
464#398C2312yes—
465#398C2312yes—
466#398C2312yes—
467#396C2312yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2312yes—
479#395C2312yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2312yes—
492#395C2314yes—
493#395C2314yes—
494#395C2314yes—
495#395C2314yes—
496#395C2314yes—
497#395C2312yes—
498#395C2314yes—
499#395C2314yes—
500#395C2314yes—
501#395C2314yes—
502#395C2312yes—
503#395C2312yes—
504#395C2312yes—
505#393C2314yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#393C2314yes—
511#393C2312yes—
512#393C2314yes—
513#393C2312yes—
514#393C2314yes—
515#393C2314yes—
516#393C2314yes—
517#391C2312yes—
518#391C2312yes—
519#391C2314yes—
520#391C2314yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#390C2311yescharacteristic
527#390C2312yes—
528#390C2312yes—
529#390C2311yescharacteristic
530#390C2311yescharacteristic
531#390C2311yescharacteristic
532#389C2311yescharacteristic
533#389C2311yescharacteristic
534#389C2311yescharacteristic
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2312yes—
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2314yes—
569#389C2312yes—
570#389C2314yes—
571#389C2314yes—
572#389C2312yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2311yescharacteristic
585#389C2314yes—
586#389C2314yes—
587#389C2312yes—
588#389C2312yes—
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2314yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2314yes—
596#389C2314yes—
597#389C2314yes—
598#389C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2314yes—
639#386C2312yes—
640#386C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2312yes—
669#385C2312yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#384C2311yescharacteristic
676#384C2311yescharacteristic
677#384C2314yes—
678#384C2312yes—
679#384C2312yes—
680#384C2312yes—
681#384C2311yescharacteristic
682#384C2311yescharacteristic
683#384C2311yescharacteristic
684#384C2311yescharacteristic
685#384C2312yes—
686#384C2311yescharacteristic
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#384C2311yescharacteristic
690#384C2312yes—
691#383C2312yes—
692#382C2311yescharacteristic
693#382C2311yescharacteristic
694#382C2312yes—
695#382C2312yes—
696#382C2311yescharacteristic
697#382C2312yes—
698#382C2312yes—
699#382C2312yes—
700#382C2312yes—
701#382C2312yes—
702#382C2312yes—
703#382C2312yes—
704#382C2312yes—
705#382C2314yes—
706#382C2312yes—
707#382C2314yes—
708#382C2312yes—
709#382C2312yes—
710#382C2311yescharacteristic
711#382C2314yes—
712#382C2314yes—
713#381C2314yes—
714#381C2312yes—
715#381C2312yes—
716#381C2312yes—
717#380C2314yes—
718#380C2314yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2312yes—
724#380C2314yes—
725#380C2314yes—
726#380C2312yes—
727#380C2312yes—
728#380C2314yes—
729#380C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2312yes—
733#380C2314yes—
734#380C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2311yescharacteristic
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2311yescharacteristic
752#380C2312yes—
753#380C2311yescharacteristic
754#380C2312yes—
755#380C2311yescharacteristic
756#380C2314yes—
757#379C2312yes—
758#379C2312yes—
759#379C2314yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805#376C2312yes—
806#376C2311yescharacteristic
807#376C2311yescharacteristic
808C2×#95C2314yes—
809C2×#95C2314yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2314yes—
814C2×#95C2314yes—
815C43C2311yescharacteristic
816C43C2311yescharacteristic
817C25C2412yes—
818C22×Q8—48no—
819C22×Q8—48no—
820C22×Q8—84no—
821C22×Q8C2412yes—
822C22×Q8C2414yes—
823C22×Q8C2412yes—
824C22×Q8C2414yes—
825C22×Q8C2414yes—
826C22×Q8C2414yes—
827C22×D4—24no—
828C22×D4—24no—
829C22×D4C2×Q818yes—
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C23×C4—44no—
834C23×C4—44no—
835C23×C4C2×Q8116yescomplemented
836C23×C4C2412yes—
837C23×C4C2412yes—
838C23×C4C2412yes—
839C23×C4C2412yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2414yes—
844C23×C4C2414yes—
845C23×C4C2414yes—
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2414yes—
849C23×C4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C4⋊Q8—24no—
855C4⋊Q8—28no—
856C4⋊Q8—44no—
857C4⋊Q8—44no—
858C4⋊Q8—48no—
859C4⋊Q8—42no—
860C4⋊Q8—44no—
861C4⋊Q8—44no—
862C4⋊Q8—44no—
863C4⋊Q8—44no—
864C4⋊Q8—44no—
865C4⋊Q8—48no—
866C4⋊Q8—48no—
867C4⋊Q8—84no—
868C4⋊Q8—82no—
869#125—24no—
870#125—44no—
871#125—42no—
872#125—44no—
873#125—44no—
874#125—44no—
875#125—48no—
876#125—82no—
877C22⋊Q8—48no—
878C22⋊Q8—48no—
879C22⋊Q8—48no—
880C22⋊Q8—48no—
881C22⋊Q8—48no—
882C22⋊Q8—48no—
883C22⋊Q8—48no—
884C22⋊Q8—48no—
885C22⋊Q8—84no—
886C22⋊Q8—84no—
887C4×Q8—44no—
888C4×Q8—44no—
889C4×D4—28no—
890C4×D4—28no—
891C4×D4—24no—
892C4×D4—28no—
893C4×D4—24no—
894C4×D4—24no—
895C4×D4—28no—
896C4×D4—24no—
897C4×D4—44no—
898C4×D4—44no—
899C4×D4—48no—
900C4×D4—48no—
901C4×D4C2×Q818yes—
902C4×D4C2×Q818yes—
903C4×D4C2×Q818yescomplemented
904C4×D4C2×Q818yescomplemented
905C4×D4C2×Q8116yescomplemented
906C4×D4C2×Q8116yescomplemented
907#117—24no—
908#117—28no—
909#117—44no—
910#117—44no—
911#117—42no—
912#117—44no—
913#117—44no—
914#117—44no—
915#117—44no—
916#117—44no—
917#117—44no—
918#117—44no—
919#117—44no—
920#117—82no—
921C2×C4⋊C4—44no—
922C2×C4⋊C4—44no—
923C2×C4⋊C4—44no—
924C2×C4⋊C4—44no—
925C2×C4⋊C4—44no—
926C2×C4⋊C4—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4—48no—
929C2×C4⋊C4—44no—
930C2×C4⋊C4—48no—
931C2×C4⋊C4—84no—
932C2×C4⋊C4C2×Q818yescomplemented
933C2×C4⋊C4C2411yescharacteristic
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C22⋊C4—44no—
1025C2×C22⋊C4—44no—
1026C2×C22⋊C4—48no—
1027C2×C22⋊C4—48no—
1028C2×C22⋊C4—84no—
1029C2×C22⋊C4C2×Q8116yescomplemented
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C42—28no—
1069C2×C42—44no—
1070C2×C42C2×Q818yescomplemented
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2412yes—
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2412yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2414yes—
1090C2×C42C2414yes—
1091C2×C42C2414yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101#95C2412yes—
1102#95C2412yes—
1103#95C2414yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177C24—24no—
1178C24—24no—
1179C24—42no—
1180C24—42no—
1181C24—42no—
1182C24—42no—
1183C24C22×Q818yes—
1184C24C2511yescharacteristic
1185C24C2512yes—
1186C24C2512yes—
1187C2×Q8—24no—
1188C2×Q8—28no—
1189C2×Q8—42no—
1190C2×Q8—42no—
1191C2×Q8—42no—
1192C2×Q8—44no—
1193C2×Q8—44no—
1194C2×Q8—44no—
1195C2×Q8—44no—
1196C2×Q8—44no—
1197C2×Q8—44no—
1198C2×Q8—42no—
1199C2×Q8—44no—
1200C2×Q8—44no—
1201C2×Q8—42no—
1202C2×Q8—44no—
1203C2×Q8—44no—
1204C2×Q8—44no—
1205C2×Q8—832no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—232no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4C22×Q818yes—
1212C2×D4C22×Q814yes—
1213C2×D4C22×Q814yes—
1214C2×D4H(5,𝔽2)14yes—
1215C2×D42−1+414yes—
1216C22×C4—24no—
1217C22×C4—24no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—24no—
1222C22×C4—24no—
1223C22×C4—22no—
1224C22×C4—24no—
1225C22×C4—24no—
1226C22×C4—28no—
1227C22×C4—28no—
1228C22×C4—24no—
1229C22×C4—28no—
1230C22×C4—28no—
1231C22×C4—24no—
1232C22×C4—24no—
1233C22×C4—24no—
1234C22×C4—432no—
1235C22×C4—42no—
1236C22×C4—42no—
1237C22×C4—42no—
1238C22×C4—41no—
1239C22×C4—42no—
1240C22×C4—42no—
1241C22×C4—42no—
1242C22×C4—41no—
1243C22×C4—42no—
1244C22×C4—42no—
1245C22×C4—42no—
1246C22×C4—42no—
1247C22×C4—44no—
1248C22×C4—44no—
1249C22×C4—44no—
1250C22×C4—44no—
1251C22×C4—44no—
1252C22×C4—44no—
1253C22×C4—42no—
1254C22×C4—44no—
1255C22×C4—42no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4C22×Q814yes—
1264C22×C4C22×Q814yes—
1265C22×C4C22×Q818yes—
1266C22×C4C22×Q818yes—
1267C22×C4C22×Q814yes—
1268C22×C4C22×Q818yes—
1269C22×C4C22×Q818yes—
1270C22×C4C22×Q818yes—
1271C22×C4C2511yescharacteristic
1272C22×C4C2512yes—
1273C22×C4C2512yes—
1274C22×C4C2512yes—
1275C22×C4C2514yes—
1276C22×C4C2512yes—
1277C22×C4C2512yes—
1278C22×C4C2511yescharacteristic
1279C22×C4C2511yescharacteristic
1280C22×C4C2511yescharacteristic
1281C22×C4C2512yes—
1282C22×C4C2514yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2514yes—
1289C22×C4C2512yes—
1290C22×C4C2514yes—
1291C22×C4C2512yes—
1292C22×C4C2511yescharacteristic
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2511yescharacteristic
1296C22×C4C2511yescharacteristic
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—24no—
1312C4⋊C4—24no—
1313C4⋊C4—28no—
1314C4⋊C4—22no—
1315C4⋊C4—24no—
1316C4⋊C4—24no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—22no—
1323C4⋊C4—22no—
1324C4⋊C4—24no—
1325C4⋊C4—22no—
1326C4⋊C4—24no—
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—22no—
1331C4⋊C4—42no—
1332C4⋊C4—44no—
1333C4⋊C4—44no—
1334C4⋊C4—44no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4—42no—
1338C4⋊C4—42no—
1339C4⋊C4—44no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—41no—
1360C4⋊C4—41no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4C22×Q814yes—
1392C4⋊C4C22×Q814yes—
1393C4⋊C4C22×Q818yes—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—24no—
1397C22⋊C4—28no—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—42no—
1407C22⋊C4—42no—
1408C22⋊C4—44no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—44no—
1414C22⋊C4—44no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—41no—
1423C22⋊C4—41no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4C22×Q818yes—
1429C22⋊C4C22×Q818yes—
1430C22⋊C4C22×Q818yes—
1431C22⋊C4C22×Q818yes—
1432C42—24no—
1433C42—24no—
1434C42—24no—
1435C42—22no—
1436C42—24no—
1437C42—24no—
1438C42—24no—
1439C42—22no—
1440C42—24no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—24no—
1445C42—22no—
1446C42—22no—
1447C42—42no—
1448C42—42no—
1449C42—41no—
1450C42—41no—
1451C42—44no—
1452C42—44no—
1453C42—44no—
1454C42—44no—
1455C42—41no—
1456C42—41no—
1457C42C22×Q814yes—
1458C42C22×Q814yes—
1459C42C22×Q814yes—
1460C42C22×Q814yes—
1461C42H(5,𝔽2)14yes—
1462C23—22no—
1463C23—22no—
1464C23—22no—
1465C23—22no—
1466C23—22no—
1467C23—21no—
1468C23—21no—
1469C23—22no—
1470C23—21no—
1471C23—22no—
1472C23—22no—
1473C23—21no—
1474C23—22no—
1475C23—21no—
1476C23—22no—
1477C23—21no—
1478C23—216no—
1479C23—48no—
1480C23—48no—
1481C23—84no—
1482C23—84no—
1483C23—84no—
1484C23—84no—
1485C23C23×Q814yes—
1486C23C23×Q812yes—
1487C23C23×Q814yes—
1488C23C2×H(5,𝔽2)14yes—
1489C23C2×2−1+414yes—
1490C23C2611yescharacteristic
1491Q8—48no—
1492Q8—88no—
1493Q8—84no—
1494Q8—88no—
1495Q8—88no—
1496Q8—164no—
1497D4—216no—
1498D4—28no—
1499D4#544116yescomplemented
1500C2×C4—22no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—22no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—28no—
1517C2×C4—28no—
1518C2×C4—216no—
1519C2×C4—216no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—21no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—24no—
1537C2×C4—24no—
1538C2×C4—24no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—22no—
1559C2×C4—24no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—24no—
1567C2×C4—24no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—24no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—48no—
1587C2×C4—48no—
1588C2×C4—48no—
1589C2×C4—44no—
1590C2×C4—48no—
1591C2×C4—48no—
1592C2×C4—84no—
1593C2×C4—88no—
1594C2×C4—84no—
1595C2×C4—88no—
1596C2×C4—88no—
1597C2×C4—88no—
1598C2×C4—164no—
1599C2×C4—164no—
1600C2×C4C23×Q812yes—
1601C2×C4C23×Q812yes—
1602C2×C4C23×Q812yes—
1603C2×C4C23×Q812yes—
1604C2×C4C23×Q814yes—
1605C2×C4C23×Q814yes—
1606C2×C4C23×Q812yes—
1607C2×C4C23×Q812yes—
1608C2×C4C2×H(5,𝔽2)12yes—
1609C2×C4C2×H(5,𝔽2)12yes—
1610C2×C4C2×H(5,𝔽2)12yes—
1611C2×C4C2×H(5,𝔽2)12yes—
1612C2×C4C2×2−1+412yes—
1613C2×C4#58512yes—
1614C22—24no—
1615C22—24no—
1616C22—24no—
1617C22—24no—
1618C22—24no—
1619C22—24no—
1620C22—22no—
1621C22—24no—
1622C22—22no—
1623C22—24no—
1624C22—22no—
1625C22—24no—
1626C22—42no—
1627C22—41no—
1628C22—42no—
1629C22—41no—
1630C22—42no—
1631C22—41no—
1632C22—42no—
1633C22—41no—
1634C22—816no—
1635C22C2×#54418yes—
1636C22C24×Q811yescharacteristic
1637C22C22×H(5,𝔽2)11yescharacteristic
1638C22C22×H(5,𝔽2)11yescharacteristic
1639C22C22×2−1+411yescharacteristic
1640C22C2×#58511yescharacteristic
1641C22H(7,𝔽2)11yescharacteristic
1642C222−1+611yescharacteristic
1643C4—22no—
1644C4—24no—
1645C4—24no—
1646C4—22no—
1647C4—22no—
1648C4—22no—
1649C4—22no—
1650C4—22no—
1651C4—42no—
1652C4—41no—
1653C4—42no—
1654C4—42no—
1655C4—44no—
1656C4—44no—
1657C4—42no—
1658C4—42no—
1659C4—41no—
1660C4—42no—
1661C4—44no—
1662C4—42no—
1663C4—42no—
1664C4—41no—
1665C4—42no—
1666C4—42no—
1667C4—42no—
1668C4—41no—
1669C4—41no—
1670C4—41no—
1671C4—44no—
1672C4—42no—
1673C4C2×#54414yes—
1674C4#350114yes—
1675C2—28no—
1676C2—44no—
1677C2—42no—
1678C2C22×#54411yescharacteristic
1679C2C2×#350111yescharacteristic
1680C2#6285411yescharacteristic
1681C2#6291211yescharacteristic
1682C2#6292111yescharacteristic
1683C2#6294211yescharacteristic
1684C2#6295111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42497C2semidirect
2. #42493C2semidirect
3. #42491C2semidirect
4. #42488C2semidirect
5. #40618C2semidirect
6. #40614C2semidirect
7. #40613C2semidirect
8. #40610C2semidirect
9. #39498C2semidirect
10. #39369C2semidirect
11. #38967C2semidirect
12. #38964C2semidirect
13. #38101C2semidirect
14. #38098C2semidirect
15. #37875C2semidirect
16. #37686C2semidirect
17. #37642C2semidirect
18. #37624C2semidirect
19. #37477C2semidirect
20. #37476C2semidirect
21. #36290C2semidirect
22. #36261C2semidirect
23. #36165C2semidirect
24. D4×C4⋊Q8C2semidirect
25. #35961C2semidirect
26. #35928C2semidirect
29. #35294C2semidirect
30. #35253C2semidirect
31. #34625C2semidirect
32. C2×#2628C2semidirect
38. C2×#544C22semidirect
39. C22×C4⋊Q8C22semidirect
43. #2868C22semidirect
44. #2859C22semidirect
45. #2859C22semidirect
46. #2859C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
49. #2851C22semidirect
50. #2851C22semidirect
51. #2844C22semidirect
55. #2841C22semidirect
56. #2841C22semidirect
57. #2807C22semidirect
58. #2807C22semidirect
59. #2805C22semidirect
60. #2802C22semidirect
61. #2792C22semidirect
62. #2788C22semidirect
63. #2788C22semidirect
64. #2774C22semidirect
65. #2774C22semidirect
66. #2768C22semidirect
67. #2768C22semidirect
68. #2763C22semidirect
69. #2763C22semidirect
70. #2755C22semidirect
71. #2742C22semidirect
72. #2742C22semidirect
73. #2734C22semidirect
74. #2729C22semidirect
75. #2729C22semidirect
76. #2720C22semidirect
77. #2720C22semidirect
78. #2713C22semidirect
79. #2677C22semidirect
80. #2677C22semidirect
83. #2666C22semidirect
84. #2666C22semidirect
85. #2666C22semidirect
88. #2660C22semidirect
89. #2660C22semidirect
90. #2660C22semidirect
91. #2659C22semidirect
92. #2659C22semidirect
93. #2647C22semidirect
94. #2647C22semidirect
95. #2647C22semidirect
96. #2646C22semidirect
97. #2646C22semidirect
113. #2628C22semidirect
114. #2628C22semidirect
115. #2628C22semidirect
116. #2628C22semidirect
117. #2628C22semidirect
118. #2628C22semidirect
121. #2584C22semidirect
122. #2584C22semidirect
123. #2583C22semidirect
124. #2583C22semidirect
127. #2571C22semidirect
128. #2571C22semidirect
129. #2571C22semidirect
130. #2571C22semidirect
131. #2571C22semidirect
132. #2570C22semidirect
133. #2570C22semidirect
134. #2570C22semidirect
135. #2569C22semidirect
136. #2567C22semidirect
140. #2552C22semidirect
141. #2552C22semidirect
142. #2551C22semidirect
143. #2551C22semidirect
144. #2551C22semidirect
145. #2551C22semidirect
146. #2551C22semidirect
147. #2551C22semidirect
148. #2551C22semidirect
149. #2550C22semidirect
150. #2550C22semidirect
151. #2550C22semidirect
152. #2550C22semidirect
153. #2550C22semidirect
154. #2549C22semidirect
155. #2549C22semidirect
156. #2549C22semidirect
157. #2546C22semidirect
159. #2509C22semidirect
160. #2509C22semidirect
161. #2509C22semidirect
162. #2508C22semidirect
163. #2508C22semidirect
164. #2508C22semidirect
165. #2507C22semidirect
166. #2506C22semidirect
167. #2505C22semidirect
168. #2505C22semidirect
169. #2505C22semidirect
170. #2505C22semidirect
171. #2505C22semidirect
172. #2505C22semidirect
174. #2473C22semidirect
175. #2473C22semidirect
184. #2442C22semidirect
185. #2442C22semidirect
186. #2442C22semidirect
187. #2442C22semidirect
188. #2442C22semidirect
189. #2442C22semidirect
190. #2442C22semidirect
195. #2441C22semidirect
196. #2441C22semidirect
197. #2440C22semidirect
198. #2440C22semidirect
199. #2440C22semidirect
200. #2440C22semidirect
201. #2440C22semidirect
202. #2440C22semidirect
203. #2440C22semidirect
204. #2440C22semidirect
205. #2440C22semidirect
210. #2439C22semidirect
211. #2439C22semidirect
212. #2438C22semidirect
213. #2438C22semidirect
218. #2434C22semidirect
219. #2434C22semidirect
221. #2402C22semidirect
222. #2399C22semidirect
225. C2×#400C22semidirect
227. C2×#395C22semidirect
265. #2331C22semidirect
266. #2330C22semidirect
269. #2317C22semidirect
270. #2317C22semidirect
272. #2316C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×C4⋊Q8C22semidirect
276. C4×#125C22semidirect
277. C4×#125C22semidirect
280. C2×#389C22semidirect
281. C2×#389C22semidirect
289. C2×#382C22semidirect
342. C2×C4×D4Q8semidirect
835. C23×C4C2×Q8semidirect
903. C4×D4C2×Q8semidirect
904. C4×D4C2×Q8semidirect
905. C4×D4C2×Q8semidirect
906. C4×D4C2×Q8semidirect
932. C2×C4⋊C4C2×Q8semidirect
1029. C2×C22⋊C4C2×Q8semidirect
1070. C2×C42C2×Q8semidirect
1499. D4#544semidirect

Maximal subgroups

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

subgroupindex
#424972
#424932
#424912
#424882
#406182
#406142
#406132
#406102
#394982
#393692
#389672
#389642
#381012
#380982
#378752
#376862
#376422
#376242
#374772
#374762
#362902
#362612
#361652
D4×C4⋊Q82
#359612
#359282
#358362
#357022
#352942
#352532
#346252
C2×#26282
#341942
#341812
D4×#1172