Finite Group Databasebeta

← #7650806

Subgroups — #7650806

Order 512.

4775 conjugacy classes of subgroups.

The subgroup lattice has 1736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42740C212yesmaximal, complemented
2#42720C212yesmaximal, complemented
3#42694C212yesmaximal, complemented
4#42691C212yesmaximal, complemented
5#42628C212yesmaximal, complemented
6#42604C212yesmaximal, complemented
7#42515C212yesmaximal, complemented
8#42512C212yesmaximal, complemented
9#40761C214yesmaximal, complemented
10#40734C214yesmaximal, complemented
11#40171C212yesmaximal, complemented
12#40102C212yesmaximal, complemented
13#40002C212yesmaximal, complemented
14#40001C212yesmaximal, complemented
15#39784C212yesmaximal, complemented
16#39193C212yesmaximal, complemented
17#38999C212yesmaximal, complemented
18#38978C212yesmaximal, complemented
19#38578C214yesmaximal, complemented
20#37915C214yesmaximal, complemented
21#35618C211yesmaximal, characteristic, complemented
22#35575C211yesmaximal, characteristic, complemented
23#35545C211yesmaximal, characteristic, complemented
24#35542C211yesmaximal, characteristic, complemented
25#35519C211yesmaximal, characteristic, complemented
26#35518C211yesmaximal, characteristic
27#35330C211yesmaximal, characteristic, complemented
28#35253C211yesmaximal, characteristic, complemented
29#35158C211yesmaximal, characteristic, complemented
30#34813C211yesmaximal, characteristic, complemented
31#34810C211yesmaximal, characteristic, complemented
32C2×#2495C211yesmaximal, characteristic, complemented
33#34253C211yesmaximal, characteristic, complemented
34#34213C211yesmaximal, characteristic, complemented
35#34202C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#544C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#533C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2862C2212yescomplemented
46#2859C2212yescomplemented
47#2857C2212yes—
48#2851C2212yes—
49#2850C2214yes—
50#2839C2214yescomplemented
51#2837C2214yescomplemented
52#2831C2214yes—
53#2829C2214yes—
54#2799C2214yescomplemented
55#2779C2214yes—
56#2779C2214yescomplemented
57#2777C2214yes—
58#2777C2214yescomplemented
59#2772C2214yes—
60#2772C2214yescomplemented
61#2770C2214yes—
62#2767C2214yescomplemented
63#2764C2214yescomplemented
64#2763C2214yes—
65#2762C2214yescomplemented
66#2761C2214yes—
67#2759C2214yescomplemented
68#2758C2214yescomplemented
69#2757C2214yes—
70#2757C2214yescomplemented
71#2754C2214yescomplemented
72#2751C2214yes—
73#2742C2214yescomplemented
74#2741C2214yes—
75#2738C2214yescomplemented
76#2737C2214yes—
77#2737C2214yescomplemented
78#2730C2214yes—
79#2712C2214yes—
80#2702C2214yescomplemented
81#2701C2214yes—
82#2700C2214yes—
83#2700C2214yes—
84#2698C2214yescomplemented
85#2672C2214yes—
86#2666C2214yescomplemented
87#2665C2214yescomplemented
88#2663C2214yes—
89#2662C2214yes—
90#2660C2212yescomplemented
91#2660C2212yescomplemented
92#2653C2214yes—
93#2650C2214yes—
94#2650C2214yescomplemented
95#2650C2214yescomplemented
96#2644C2214yes—
97#2639C2214yes—
98#2638C2214yes—
99#2632C2214yescomplemented
100#2629C2212yes—
101#2628C2212yes—
102#2625C2214yescomplemented
103#2582C2212yescomplemented
104#2581C2212yescomplemented
105#2580C2212yescomplemented
106#2564C2214yes—
107#2563C2212yes—
108#2562C2212yes—
109#2562C2212yes—
110#2550C2212yescomplemented
111#2550C2212yescomplemented
112#2550C2212yescomplemented
113#2550C2212yescomplemented
114#2549C2214yes—
115#2549C2214yes—
116#2547C2212yes—
117#2538C2212yes—
118#2538C2212yescomplemented
119#2537C2212yes—
120#2536C2212yes—
121#2535C2212yes—
122#2532C2214yescomplemented
123#2527C2214yes—
124#2525C2214yescomplemented
125#2515C2214yescomplemented
126#2514C2212yescomplemented
127#2513C2212yescomplemented
128#2512C2212yescomplemented
129#2511C2212yescomplemented
130#2510C2214yes—
131#2509C2214yescomplemented
132#2504C2211yescharacteristic
133#2504C2212yescomplemented
134#2503C2211yescharacteristic
135#2503C2212yescomplemented
136#2502C2211yescharacteristic
137#2501C2211yescharacteristic
138#2500C2211yescharacteristic
139#2500C2211yescharacteristic
140#2500C2212yescomplemented
141#2499C2211yescharacteristic
142#2499C2211yescharacteristic
143#2499C2212yescomplemented
144#2498C2212yes—
145#2498C2212yes—
146#2497C2212yescomplemented
147#2496C2212yescomplemented
148#2495C2212yes—
149#2495C2212yes—
150#2495C2212yes—
151#2495C2212yes—
152#2495C2212yes—
153#2495C2212yes—
154#2495C2212yes—
155#2495C2212yes—
156#2495C2214yescomplemented
157#2495C2212yescomplemented
158#2494C2212yescomplemented
159#2492C2212yes—
160#2492C2211yescharacteristic
161#2492C2211yescharacteristic
162#2492C2212yescomplemented
163#2492C2212yescomplemented
164#2491C2212yes—
165#2491C2211yescharacteristic
166#2491C2211yescharacteristic
167#2491C2212yescomplemented
168#2491C2212yescomplemented
169#2490C2212yes—
170#2490C2211yescharacteristic
171#2490C2211yescharacteristic
172#2490C2212yescomplemented
173#2490C2212yescomplemented
174#2489C2212yes—
175#2489C2211yescharacteristic
176#2489C2211yescharacteristic
177#2489C2212yescomplemented
178#2489C2212yescomplemented
179#2488C2212yes—
180#2488C2214yes—
181#2488C2212yes—
182#2481C2214yes—
183#2477C2214yescomplemented
184#2474C2214yes—
185#2472C2212yes—
186#2472C2214yes—
187#2472C2212yes—
188#2468C2214yes—
189#2458C2214yes—
190#2454C2212yescomplemented
191#2453C2212yescomplemented
192#2452C2212yescomplemented
193#2451C2212yescomplemented
194#2450C2214yes—
195#2449C2214yes—
196#2448C2214yes—
197#2444C2214yes—
198#2444C2214yes—
199#2442C2212yes—
200#2442C2212yescomplemented
201#2442C2212yescomplemented
202#2441C2212yes—
203#2441C2212yescomplemented
204#2441C2212yescomplemented
205#2440C2212yes—
206#2440C2212yescomplemented
207#2440C2212yescomplemented
208#2439C2212yes—
209#2439C2212yescomplemented
210#2439C2212yescomplemented
211#2438C2214yes—
212#2437C2214yes—
213#2427C2214yes—
214#2425C2214yes—
215#2424C2214yes—
216#2421C2212yescomplemented
217#2421C2212yescomplemented
218#2420C2212yescomplemented
219#2420C2212yescomplemented
220#2417C2214yes—
221#2417C2212yes—
222#2416C2212yes—
223#2415C2212yes—
224#2414C2212yes—
225#2412C2212yes—
226#2412C2212yes—
227#2398C2212yes—
228#2398C2212yes—
229#2395C2212yes—
230#2395C2212yes—
231C2×#400C2212yes—
232C2×#397C2212yes—
233#2370C2212yescomplemented
234#2370C2212yescomplemented
235#2369C2212yescomplemented
236#2365C2212yescomplemented
237#2359C2214yes—
238#2358C2214yes—
239#2355C2212yescomplemented
240#2355C2212yescomplemented
241#2355C2212yescomplemented
242#2354C2212yes—
243#2353C2214yes—
244#2352C2212yes—
245#2352C2214yes—
246#2352C2212yes—
247Q8×C4⋊C4C2212yescomplemented
248D4×C4⋊C4C2212yes—
249#2347C2212yescomplemented
250#2346C2212yescomplemented
251#2345C2212yescomplemented
252#2344C2212yescomplemented
253#2337C2214yescomplemented
254#2332C2214yes—
255#2329C2214yes—
256#2324C2214yes—
257#2324C2212yes—
258#2323C2212yes—
259#2320C2212yescomplemented
260#2320C2214yescomplemented
261#2319C2212yescomplemented
262#2317C2211yescharacteristic
263#2317C2211yescharacteristic
264#2317C2211yescharacteristic
265#2317C2211yescharacteristic
266#2316C2211yescharacteristic
267#2311C2211yescharacteristic
268#2311C2211yescharacteristic
269#2311C2211yescharacteristic
270#2311C2211yescharacteristic
271C4×#124C2212yes—
272C4×#124C2212yes—
273C4×C22⋊Q8C2214yes—
274C4×C22⋊Q8C2212yes—
275C4×#123C2212yes—
276C4×#123C2212yes—
277C4×#121C2212yes—
278#2297C2211yescharacteristic
279#2297C2211yescharacteristic
280#2297C2211yescharacteristic
281#2297C2211yescharacteristic
282#2295C2212yescomplemented
283#2293C2212yescomplemented
284C2×#389C2211yescharacteristic
285C2×#389C2211yescharacteristic
286C2×#388C2212yes—
287#2285C2211yescharacteristic
288#2285C2211yescharacteristic
289C2×#383C2212yes—
290C2×#382C2211yescharacteristic
291#2280C2211yescharacteristic
292C2×#380C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C24×C4C2311yescharacteristic
302#544—44no—
303#544—44no—
304#537—44no—
305#533—28no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×#126C2314yes—
313C2×#125C2311yescharacteristic
314C2×#125C2311yescharacteristic
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#124C2314yes—
320C2×#124C2312yes—
321C2×#124C2312yes—
322C2×#124C2314yes—
323#525—28no—
324#525—44no—
325C2×#123C2312yes—
326C2×#123C2312yes—
327C2×#123C2312yes—
328C2×#123C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×#121C2311yescharacteristic
343C2×#121C2311yescharacteristic
344C2×#121C2314yes—
345C2×#121C2314yes—
346C2×#121C2311yescharacteristic
347C2×#121C2311yescharacteristic
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#120C2312yes—
351C2×#120C2312yes—
352#520—28no—
353#520—44no—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2314yes—
358C2×C4×Q8C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×#117—44no—
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2311yescharacteristic
372C2×#117C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2311yescharacteristic
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2312yes—
380C2×#117C2314yes—
381C2×#117C2311yescharacteristic
382C22×C4⋊C4C2311yescharacteristic
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2311yescharacteristic
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C22⋊C4C2312yes—
393C22×C22⋊C4C2311yescharacteristic
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2311yescharacteristic
396C22×C22⋊C4C2312yes—
397C22×C42C2311yescharacteristic
398C22×C42C2311yescharacteristic
399C22×C42C2312yes—
400C22×C42C2312yes—
401#401C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2312yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2312yes—
420#400C2312yes—
421#400C2312yes—
422#400C2312yes—
423#400C2312yes—
424#399C2314yes—
425#399C2314yes—
426#399C2314yes—
427#399C2312yes—
428#399C2312yes—
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#397C2314yes—
443#397C2314yes—
444#397C2312yes—
445#397C2314yes—
446#397C2312yes—
447#397C2314yes—
448#397C2312yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2312yes—
459#397C2312yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2312yes—
465#397C2314yes—
466#397C2312yes—
467#397C2312yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#395C2314yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2312yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2312yes—
494#394C2314yes—
495#394C2312yes—
496#394C2312yes—
497#394C2312yes—
498#394C2312yes—
499#394C2312yes—
500#394C2314yes—
501#393C2314yes—
502#393C2314yes—
503#393C2314yes—
504#393C2312yes—
505#393C2314yes—
506#393C2314yes—
507#393C2312yes—
508#393C2314yes—
509#393C2314yes—
510#393C2312yes—
511#393C2312yes—
512#392C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2314yes—
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#391C2314yes—
524#391C2314yes—
525#391C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2312yes—
532#391C2314yes—
533#391C2314yes—
534#391C2311yescharacteristic
535#391C2311yescharacteristic
536#391C2311yescharacteristic
537#391C2311yescharacteristic
538#391C2311yescharacteristic
539#390C2314yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2311yescharacteristic
546#390C2312yes—
547#390C2314yes—
548#390C2311yescharacteristic
549#390C2312yes—
550#390C2314yes—
551#390C2311yescharacteristic
552#390C2311yescharacteristic
553#390C2311yescharacteristic
554#390C2311yescharacteristic
555#390C2311yescharacteristic
556#390C2311yescharacteristic
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2314yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2312yes—
603#388C2312yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
626#388C2312yes—
627#388C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2314yes—
653#387C2312yes—
654#387C2312yes—
655#386C2312yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2312yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2312yes—
666#386C2312yes—
667#386C2314yes—
668#386C2312yes—
669#386C2312yes—
670#386C2312yes—
671#386C2314yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2312yes—
688#385C2312yes—
689#384C2312yes—
690#384C2312yes—
691#384C2312yes—
692#384C2312yes—
693#384C2311yescharacteristic
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#383C2314yes—
701#383C2314yes—
702#383C2314yes—
703#382C2314yes—
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2312yes—
708#382C2314yes—
709#382C2314yes—
710#382C2311yescharacteristic
711#382C2312yes—
712#382C2311yescharacteristic
713#382C2311yescharacteristic
714#382C2311yescharacteristic
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#381C2314yes—
721#381C2312yes—
722#381C2314yes—
723#381C2314yes—
724#381C2312yes—
725#381C2312yes—
726#380C2312yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2311yescharacteristic
734#380C2312yes—
735#380C2312yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2314yes—
743#380C2312yes—
744#380C2312yes—
745#380C2314yes—
746#380C2312yes—
747#380C2312yes—
748#380C2314yes—
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2314yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#379C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807#376C2312yes—
808#376C2314yes—
809C2×#95C2312yes—
810C2×#95C2312yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2311yescharacteristic
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2311yescharacteristic
818C43C2312yes—
819C25C2411yescharacteristic
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2412yes—
830C22×Q8C2414yes—
831C22×Q8C2414yes—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2412yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2414yes—
841C23×C4—24no—
842C23×C4—24no—
843C23×C4—24no—
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C23×C4C2414yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2411yescharacteristic
864C4⋊Q8—24no—
865C4⋊Q8—24no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870#126—84no—
871#125—24no—
872#125—24no—
873#125—44no—
874#125—44no—
875#125—44no—
876#125—44no—
877#124—48no—
878#124—44no—
879#124—44no—
880#124—84no—
881#123—28no—
882#123—44no—
883#123—44no—
884#123—44no—
885C22⋊Q8—24no—
886C22⋊Q8—24no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—48no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—42no—
893C22⋊Q8—42no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—84no—
897C22⋊Q8—84no—
898#121—24no—
899#121—24no—
900#121—48no—
901#121—42no—
902#121—42no—
903#121—44no—
904#121—44no—
905#121—48no—
906#120—28no—
907#120—44no—
908C4×Q8—28no—
909C4×Q8—28no—
910C4×Q8—28no—
911C4×Q8—48no—
912C4×Q8—44no—
913C4×D4—216no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—28no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—48no—
921C4×D4—84no—
922#117—24no—
923#117—24no—
924#117—24no—
925#117—24no—
926#117—24no—
927#117—28no—
928#117—44no—
929#117—44no—
930#117—42no—
931#117—42no—
932#117—44no—
933#117—84no—
934#117#4118yes—
935C2×C4⋊C4—24no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—24no—
938C2×C4⋊C4—24no—
939C2×C4⋊C4—28no—
940C2×C4⋊C4—42no—
941C2×C4⋊C4—42no—
942C2×C4⋊C4—44no—
943C2×C4⋊C4—82no—
944C2×C4⋊C4—82no—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C22⋊C4—42no—
1009C2×C22⋊C4—44no—
1010C2×C22⋊C4—42no—
1011C2×C22⋊C4—44no—
1012C2×C22⋊C4—82no—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2411yescharacteristic
1017C2×C22⋊C4C2411yescharacteristic
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C42—24no—
1074C2×C42—24no—
1075C2×C42—44no—
1076C2×C42—44no—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2414yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2414yes—
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2414yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2412yes—
1105#95C2414yes—
1106#95C2411yescharacteristic
1107#95C2411yescharacteristic
1108#95C2411yescharacteristic
1109#95C2411yescharacteristic
1110#95C2411yescharacteristic
1111#95C2411yescharacteristic
1112#95C2411yescharacteristic
1113#95C2411yescharacteristic
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#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181C24—22no—
1182C24—22no—
1183C24—22no—
1184C24—22no—
1185C24—41no—
1186C24—41no—
1187C24—41no—
1188C24C2511yescharacteristic
1189C24C2512yes—
1190C24C2512yes—
1191C24C2511yescharacteristic
1192C24C2511yescharacteristic
1193#41—416no—
1194#41—416no—
1195C2×Q8—22no—
1196C2×Q8—24no—
1197C2×Q8—22no—
1198C2×Q8—24no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—22no—
1202C2×Q8—22no—
1203C2×Q8—24no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8—44no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—44no—
1212C2×Q8—44no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—24no—
1216C2×D4—24no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—24no—
1223C2×D4—22no—
1224C2×D4—24no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—42no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—44no—
1238C2×D4—44no—
1239C2×D4—44no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—28no—
1272C22×C4—41no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—42no—
1276C22×C4—42no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—42no—
1281C22×C4—42no—
1282C22×C4—42no—
1283C22×C4—42no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—42no—
1287C22×C4—44no—
1288C22×C4—42no—
1289C22×C4—44no—
1290C22×C4—42no—
1291C22×C4—41no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—416no—
1298C22×C4C2×#4114yes—
1299C22×C4H(5,𝔽2)14yes—
1300C22×C42−1+414yes—
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2514yes—
1317C22×C4C2514yes—
1318C22×C4C2514yes—
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C4⋊C4—24no—
1332C4⋊C4—28no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—44no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4C2×#4114yes—
1393C4⋊C4C2×#4114yes—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—41no—
1413C22⋊C4—41no—
1414C22⋊C4—41no—
1415C22⋊C4—41no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4C2×#4118yes—
1454C42—22no—
1455C42—22no—
1456C42—22no—
1457C42—22no—
1458C42—28no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—22no—
1468C42—28no—
1469C42—44no—
1470C42—42no—
1471C42—42no—
1472C42—42no—
1473C42—44no—
1474C42—42no—
1475C42—44no—
1476C42—44no—
1477C42—44no—
1478C42—42no—
1479C42—42no—
1480C42—44no—
1481C42C2×#4118yes—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—22no—
1493C23—21no—
1494C23—22no—
1495C23—21no—
1496C23—22no—
1497C23—22no—
1498C23—21no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—21no—
1504C23—21no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—21no—
1510C23—22no—
1511C23—22no—
1512C23—21no—
1513C23—44no—
1514C23—44no—
1515C23—44no—
1516C23—44no—
1517C23—82no—
1518C23—82no—
1519C23—82no—
1520C23C22×#4112yes—
1521C23C2×H(5,𝔽2)12yes—
1522C23C2×2−1+412yes—
1523C23#58512yes—
1524C23C2611yescharacteristic
1525Q8—48no—
1526Q8—44no—
1527Q8—44no—
1528Q8—84no—
1529Q8—164no—
1530Q8—164no—
1531D4—48no—
1532D4—48no—
1533D4—48no—
1534D4—44no—
1535D4—44no—
1536D4—84no—
1537D4—84no—
1538D4—84no—
1539D4—164no—
1540C2×C4—21no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—24no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—24no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—24no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—44no—
1622C2×C4—44no—
1623C2×C4—44no—
1624C2×C4—44no—
1625C2×C4—44no—
1626C2×C4—44no—
1627C2×C4—48no—
1628C2×C4—48no—
1629C2×C4—88no—
1630C2×C4—82no—
1631C2×C4—84no—
1632C2×C4—84no—
1633C2×C4—84no—
1634C2×C4—84no—
1635C2×C4—82no—
1636C2×C4—82no—
1637C2×C4—84no—
1638C2×C4—84no—
1639C2×C4—164no—
1640C2×C4#542116yes—
1641C2×C4C22×#4114yes—
1642C2×C4C22×#4114yes—
1643C2×C4C22×#4112yes—
1644C2×C4C22×#4112yes—
1645C2×C4C2×H(5,𝔽2)12yes—
1646C2×C4C2×H(5,𝔽2)12yes—
1647C2×C4C2×2−1+412yes—
1648C2×C4C2×2−1+412yes—
1649C2×C4#58512yes—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—22no—
1656C22—22no—
1657C22—22no—
1658C22—22no—
1659C22—41no—
1660C22—41no—
1661C22—41no—
1662C22—41no—
1663C22—41no—
1664C22—42no—
1665C22—42no—
1666C22—42no—
1667C22—42no—
1668C22—41no—
1669C22—42no—
1670C22—42no—
1671C22—41no—
1672C22—42no—
1673C22—41no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—41no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—41no—
1682C22—42no—
1683C22—42no—
1684C22—88no—
1685C22C2×#54214yes—
1686C22C23×#4111yescharacteristic
1687C22C22×H(5,𝔽2)11yescharacteristic
1688C22C22×2−1+411yescharacteristic
1689C22C2×#58511yescharacteristic
1690C22C2×#58511yescharacteristic
1691C22H(7,𝔽2)11yescharacteristic
1692C222−1+611yescharacteristic
1693C4—22no—
1694C4—24no—
1695C4—24no—
1696C4—41no—
1697C4—42no—
1698C4—41no—
1699C4—44no—
1700C4—41no—
1701C4—42no—
1702C4—42no—
1703C4—44no—
1704C4—42no—
1705C4—42no—
1706C4—42no—
1707C4—42no—
1708C4—42no—
1709C4—44no—
1710C4—42no—
1711C4—42no—
1712C4—41no—
1713C4—41no—
1714C4—41no—
1715C4—41no—
1716C4—44no—
1717C4—41no—
1718C4—41no—
1719C4—42no—
1720C4—42no—
1721C4C2×#54214yes—
1722C4C2×#54214yes—
1723C2—24no—
1724C2—42no—
1725C2—82no—
1726C2—82no—
1727C2—81no—
1728C2C22×#54211yescharacteristic
1729C2#6283011yescharacteristic
1730C2#6287811yescharacteristic
1731C2#6292811yescharacteristic
1732C2#6292911yescharacteristic
1733C2#6299311yescharacteristic
1734C2#6300811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35518C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42740C2semidirect
2. #42720C2semidirect
3. #42694C2semidirect
4. #42691C2semidirect
5. #42628C2semidirect
6. #42604C2semidirect
7. #42515C2semidirect
8. #42512C2semidirect
9. #40761C2semidirect
10. #40734C2semidirect
11. #40171C2semidirect
12. #40102C2semidirect
13. #40002C2semidirect
14. #40001C2semidirect
15. #39784C2semidirect
16. #39193C2semidirect
17. #38999C2semidirect
18. #38978C2semidirect
19. #38578C2semidirect
20. #37915C2semidirect
21. #35618C2semidirect
22. #35575C2semidirect
23. #35545C2semidirect
24. #35542C2semidirect
25. #35519C2semidirect
27. #35330C2semidirect
28. #35253C2semidirect
29. #35158C2semidirect
30. #34813C2semidirect
31. #34810C2semidirect
32. C2×#2495C2semidirect
33. #34253C2semidirect
34. #34213C2semidirect
35. #34202C2semidirect
45. #2862C22semidirect
46. #2859C22semidirect
50. #2839C22semidirect
51. #2837C22semidirect
54. #2799C22semidirect
56. #2779C22semidirect
58. #2777C22semidirect
60. #2772C22semidirect
62. #2767C22semidirect
63. #2764C22semidirect
65. #2762C22semidirect
67. #2759C22semidirect
68. #2758C22semidirect
70. #2757C22semidirect
71. #2754C22semidirect
73. #2742C22semidirect
75. #2738C22semidirect
77. #2737C22semidirect
80. #2702C22semidirect
84. #2698C22semidirect
86. #2666C22semidirect
87. #2665C22semidirect
90. #2660C22semidirect
91. #2660C22semidirect
94. #2650C22semidirect
95. #2650C22semidirect
99. #2632C22semidirect
102. #2625C22semidirect
103. #2582C22semidirect
104. #2581C22semidirect
105. #2580C22semidirect
110. #2550C22semidirect
111. #2550C22semidirect
112. #2550C22semidirect
113. #2550C22semidirect
118. #2538C22semidirect
122. #2532C22semidirect
124. #2525C22semidirect
125. #2515C22semidirect
126. #2514C22semidirect
127. #2513C22semidirect
128. #2512C22semidirect
129. #2511C22semidirect
131. #2509C22semidirect
133. #2504C22semidirect
135. #2503C22semidirect
140. #2500C22semidirect
143. #2499C22semidirect
146. #2497C22semidirect
147. #2496C22semidirect
156. #2495C22semidirect
157. #2495C22semidirect
158. #2494C22semidirect
162. #2492C22semidirect
163. #2492C22semidirect
167. #2491C22semidirect
168. #2491C22semidirect
172. #2490C22semidirect
173. #2490C22semidirect
177. #2489C22semidirect
178. #2489C22semidirect
183. #2477C22semidirect
190. #2454C22semidirect
191. #2453C22semidirect
192. #2452C22semidirect
193. #2451C22semidirect
200. #2442C22semidirect
201. #2442C22semidirect
203. #2441C22semidirect
204. #2441C22semidirect
206. #2440C22semidirect
207. #2440C22semidirect
209. #2439C22semidirect
210. #2439C22semidirect
216. #2421C22semidirect
217. #2421C22semidirect
218. #2420C22semidirect
219. #2420C22semidirect
233. #2370C22semidirect
234. #2370C22semidirect
235. #2369C22semidirect
236. #2365C22semidirect
239. #2355C22semidirect
240. #2355C22semidirect
241. #2355C22semidirect
247. Q8×C4⋊C4C22semidirect
249. #2347C22semidirect
250. #2346C22semidirect
251. #2345C22semidirect
252. #2344C22semidirect
253. #2337C22semidirect
259. #2320C22semidirect
260. #2320C22semidirect
261. #2319C22semidirect
282. #2295C22semidirect
283. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#427402
#427202
#426942
#426912
#426282
#426042
#425152
#425122
#407612
#407342
#401712
#401022
#400022
#400012
#397842
#391932
#389992
#389782
#385782
#379152
#356182
#355752
#355452
#355422
#355192
#355182
#353302
#352532
#351582
#348132
#348102
C2×#24952
#342532
#342132
#342022