Finite Group Databasebeta

← #8094777

Subgroups — #8094777

Order 512.

4712 conjugacy classes of subgroups.

The subgroup lattice has 1693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53133C212yesmaximal, complemented
2#53119C212yesmaximal, complemented
3#53040C212yesmaximal, complemented
4#53038C212yesmaximal, complemented
5#53031C212yesmaximal, complemented
6#53001C212yesmaximal, complemented
7#52999C212yesmaximal, complemented
8#52987C212yesmaximal, complemented
9#52349C214yesmaximal, complemented
10#52322C214yesmaximal, complemented
11#46180C212yesmaximal, complemented
12#46174C212yesmaximal, complemented
13#46152C212yesmaximal, complemented
14#46147C212yesmaximal, complemented
15#46060C212yesmaximal, complemented
16#46049C212yesmaximal, complemented
17#46001C212yesmaximal, complemented
18#45993C212yesmaximal, complemented
19#45531C214yesmaximal, complemented
20#45446C214yesmaximal, complemented
21#35574C211yesmaximal, characteristic, complemented
22#35566C211yesmaximal, characteristic, complemented
23#35545C211yesmaximal, characteristic, complemented
24#35544C211yesmaximal, characteristic, complemented
25#35532C211yesmaximal, characteristic, complemented
26#35516C211yesmaximal, characteristic
27#35286C211yesmaximal, characteristic, complemented
28#35281C211yesmaximal, characteristic, complemented
29#35267C211yesmaximal, characteristic, complemented
30#35265C211yesmaximal, characteristic, complemented
31#35227C211yesmaximal, characteristic
32#35224C211yesmaximal, characteristic, complemented
33#34814C211yesmaximal, characteristic, complemented
34#34813C211yesmaximal, characteristic
35C2×#2440C211yesmaximal, characteristic, complemented
36C2×#563C2214yes—
37C2×#544C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×C22⋊Q8C2212yes—
42C2×#520C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44#2868C2212yescomplemented
45#2864C2212yescomplemented
46#2863C2212yescomplemented
47#2862C2212yescomplemented
48#2860C2212yescomplemented
49#2859C2212yescomplemented
50#2859C2212yescomplemented
51#2859C2212yescomplemented
52#2849C2214yes—
53#2848C2214yes—
54#2844C2214yescomplemented
55#2843C2214yescomplemented
56#2843C2214yescomplemented
57#2839C2214yescomplemented
58#2838C2214yescomplemented
59#2838C2214yescomplemented
60#2836C2214yescomplemented
61#2836C2214yescomplemented
62#2834C2214yes—
63#2834C2214yescomplemented
64#2833C2214yescomplemented
65#2833C2214yescomplemented
66#2833C2214yescomplemented
67#2831C2214yescomplemented
68#2827C2214yes—
69#2822C2214yescomplemented
70#2821C2214yescomplemented
71#2817C2214yes—
72#2817C2214yescomplemented
73#2814C2214yes—
74#2809C2214yescomplemented
75#2791C2214yescomplemented
76#2775C2214yescomplemented
77#2774C2214yescomplemented
78#2770C2214yes—
79#2766C2214yescomplemented
80#2765C2214yes—
81#2764C2214yes—
82#2764C2214yescomplemented
83#2762C2214yescomplemented
84#2758C2214yescomplemented
85#2745C2214yes—
86#2734C2214yescomplemented
87#2729C2214yes—
88#2728C2214yes—
89#2728C2214yes—
90#2724C2214yes—
91#2723C2214yes—
92#2721C2214yescomplemented
93#2720C2214yes—
94#2720C2214yes—
95#2720C2214yescomplemented
96#2720C2214yescomplemented
97#2718C2214yes—
98#2715C2214yes—
99#2713C2214yescomplemented
100#2707C2214yes—
101#2702C2214yes—
102#2698C2214yes—
103#2698C2214yes—
104#2698C2214yescomplemented
105#2698C2214yescomplemented
106#2690C2214yes—
107#2689C2214yes—
108#2683C2214yes—
109#2680C2214yes—
110#2680C2214yes—
111#2677C2214yes—
112#2677C2214yescomplemented
113#2674C2214yes—
114#2660C2212yescomplemented
115#2660C2212yescomplemented
116#2647C2212yescomplemented
117#2647C2212yescomplemented
118#2647C2212yescomplemented
119#2647C2212yescomplemented
120#2645C2212yescomplemented
121#2644C2212yescomplemented
122#2627C2214yes—
123#2623C2214yes—
124#2584C2212yescomplemented
125#2584C2212yescomplemented
126#2579C2214yes—
127#2571C2212yescomplemented
128#2571C2212yescomplemented
129#2567C2212yescomplemented
130#2567C2212yescomplemented
131#2567C2212yescomplemented
132#2567C2212yescomplemented
133#2566C2212yescomplemented
134#2565C2212yescomplemented
135#2552C2212yescomplemented
136#2552C2212yescomplemented
137#2552C2212yescomplemented
138#2551C2212yescomplemented
139#2550C2212yescomplemented
140#2550C2212yescomplemented
141#2549C2214yes—
142#2546C2212yescomplemented
143#2546C2212yescomplemented
144#2546C2212yescomplemented
145#2542C2212yescomplemented
146#2514C2212yescomplemented
147#2513C2212yescomplemented
148#2512C2212yescomplemented
149#2511C2212yescomplemented
150#2510C2214yes—
151#2510C2214yes—
152#2509C2212yescomplemented
153#2508C2212yescomplemented
154#2507C2212yescomplemented
155#2506C2212yescomplemented
156#2505C2214yes—
157#2504C2212yes—
158#2503C2212yes—
159#2502C2212yes—
160#2502C2214yes—
161#2501C2212yes—
162#2497C2212yes—
163#2497C2211yescharacteristic
164#2497C2212yes—
165#2497C2211yescharacteristic
166#2497C2212yescomplemented
167#2497C2212yescomplemented
168#2496C2212yes—
169#2496C2211yescharacteristic
170#2496C2212yes—
171#2496C2211yescharacteristic
172#2496C2212yescomplemented
173#2496C2212yescomplemented
174#2495C2211yescharacteristic
175#2495C2212yes—
176#2495C2212yes—
177#2495C2211yescharacteristic
178#2495C2212yescomplemented
179#2495C2212yescomplemented
180#2494C2212yes—
181#2494C2212yes—
182#2494C2211yescharacteristic
183#2494C2211yescharacteristic
184#2494C2212yescomplemented
185#2494C2212yescomplemented
186#2493C2212yes—
187#2493C2214yes—
188#2493C2212yes—
189#2492C2211yescharacteristic
190#2492C2211yescharacteristic
191#2491C2211yescharacteristic
192#2491C2211yescharacteristic
193#2490C2211yescharacteristic
194#2490C2211yescharacteristic
195#2489C2211yescharacteristic
196#2489C2211yescharacteristic
197#2488C2212yes—
198#2488C2212yes—
199#2487C2212yes—
200#2487C2212yes—
201#2487C2212yes—
202#2486C2212yes—
203#2486C2212yes—
204#2486C2212yes—
205#2485C2212yes—
206#2485C2212yes—
207#2481C2214yes—
208#2481C2214yes—
209#2480C2212yes—
210#2480C2214yes—
211#2480C2212yes—
212#2473C2214yes—
213#2472C2212yes—
214#2472C2212yes—
215#2452C2212yescomplemented
216#2452C2212yescomplemented
217#2451C2212yescomplemented
218#2451C2212yescomplemented
219#2449C2214yes—
220#2449C2214yes—
221#2442C2212yes—
222#2442C2212yes—
223#2442C2212yes—
224#2442C2214yes—
225#2442C2212yes—
226#2442C2214yes—
227#2441C2212yescomplemented
228#2441C2212yescomplemented
229#2440C2212yes—
230#2440C2212yes—
231#2440C2212yes—
232#2440C2212yes—
233#2440C2212yes—
234#2440C2212yes—
235#2440C2212yes—
236#2440C2212yes—
237#2440C2212yes—
238#2440C2214yes—
239#2440C2212yes—
240#2440C2212yes—
241#2440C2212yes—
242#2440C2212yescomplemented
243#2440C2212yescomplemented
244#2440C2212yescomplemented
245#2440C2212yescomplemented
246#2439C2212yescomplemented
247#2439C2212yescomplemented
248#2434C2214yes—
249#2423C2212yes—
250#2422C2212yes—
251#2421C2212yes—
252#2420C2212yes—
253#2419C2214yes—
254#2418C2214yes—
255#2409C2214yes—
256#2401C2212yes—
257#2401C2212yes—
258#2398C2212yes—
259#2398C2212yes—
260C2×#398C2212yes—
261C2×#395C2212yes—
262#2383C2214yes—
263#2379C2214yes—
264#2378C2214yes—
265#2317C2211yescharacteristic
266#2317C2211yescharacteristic
267#2317C2211yescharacteristic
268#2317C2211yescharacteristic
269#2317C2211yescharacteristic
270#2317C2211yescharacteristic
271#2317C2211yescharacteristic
272#2316C2211yescharacteristic
273#2316C2211yescharacteristic
274#2316C2211yescharacteristic
275#2311C2211yescharacteristic
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278C4×#126C2212yes—
279C4×#126C2212yes—
280C4×#124C2212yes—
281C4×#124C2212yes—
282#2297C2211yescharacteristic
283#2297C2211yescharacteristic
284#2296C2211yescharacteristic
285#2296C2211yescharacteristic
286C2×#389C2211yescharacteristic
287C2×#389C2211yescharacteristic
288C2×#385C2212yes—
289#2285C2211yescharacteristic
290C2×#384C2211yescharacteristic
291#2280C2211yescharacteristic
292#2280C2211yescharacteristic
293#2280C2211yescharacteristic
294C2×#380C2211yescharacteristic
295#2274C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2312yes—
301C24×C4C2311yescharacteristic
302C24×C4C2312yes—
303#563—416no—
304#544—44no—
305#533—44no—
306C2×C4⋊Q8—44no—
307C2×C4⋊Q8C2314yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2314yes—
317C2×C4⋊Q8C2314yes—
318C2×#126C2312yes—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#125C2314yes—
325C2×#125C2314yes—
326C2×#125C2312yes—
327C2×#125C2311yescharacteristic
328C2×#125C2311yescharacteristic
329C2×#125C2314yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332#525—44no—
333C2×#123C2314yes—
334C2×#123C2312yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×C22⋊Q8—48no—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2314yes—
353C2×#121C2311yescharacteristic
354C2×#121C2311yescharacteristic
355C2×#120C2312yes—
356#520—44no—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2311yescharacteristic
368C2×#117C2311yescharacteristic
369C2×#117C2311yescharacteristic
370C2×#117C2311yescharacteristic
371C2×#117C2312yes—
372C22×C4⋊C4—44no—
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2311yescharacteristic
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2312yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2312yes—
388C22×C22⋊C4C2311yescharacteristic
389C22×C22⋊C4C2311yescharacteristic
390C22×C22⋊C4C2312yes—
391C22×C42C2311yescharacteristic
392C22×C42C2311yescharacteristic
393#401C2314yes—
394#401C2312yes—
395#401C2312yes—
396#401C2314yes—
397#401C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2312yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2312yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2312yes—
417#400C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#400C2314yes—
422#400C2312yes—
423#400C2312yes—
424#400C2314yes—
425#400C2312yes—
426#400C2314yes—
427#400C2312yes—
428#400C2312yes—
429#400C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
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#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#397C2312yes—
467#397C2312yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2312yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2312yes—
482#397C2314yes—
483#397C2312yes—
484#397C2314yes—
485#397C2314yes—
486#397C2312yes—
487#397C2312yes—
488#397C2312yes—
489#397C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2314yes—
495#396C2314yes—
496#396C2314yes—
497#396C2312yes—
498#396C2312yes—
499#395C2314yes—
500#395C2314yes—
501#395C2314yes—
502#395C2314yes—
503#395C2314yes—
504#395C2314yes—
505#395C2314yes—
506#395C2314yes—
507#395C2314yes—
508#395C2314yes—
509#395C2314yes—
510#395C2314yes—
511#395C2314yes—
512#395C2314yes—
513#395C2314yes—
514#395C2314yes—
515#395C2314yes—
516#395C2314yes—
517#394C2312yes—
518#394C2314yes—
519#394C2312yes—
520#394C2312yes—
521#394C2312yes—
522#394C2314yes—
523#393C2312yes—
524#393C2314yes—
525#393C2312yes—
526#393C2314yes—
527#393C2312yes—
528#393C2312yes—
529#391C2311yescharacteristic
530#391C2312yes—
531#391C2312yes—
532#391C2312yes—
533#391C2311yescharacteristic
534#391C2314yes—
535#391C2314yes—
536#391C2314yes—
537#391C2314yes—
538#391C2314yes—
539#391C2314yes—
540#391C2314yes—
541#391C2311yescharacteristic
542#391C2314yes—
543#391C2311yescharacteristic
544#391C2312yes—
545#391C2312yes—
546#390C2311yescharacteristic
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#390C2312yes—
553#390C2312yes—
554#390C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2314yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2314yes—
588#389C2314yes—
589#389C2314yes—
590#389C2311yescharacteristic
591#389C2311yescharacteristic
592#389C2314yes—
593#389C2314yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2314yes—
598#389C2314yes—
599#389C2314yes—
600#389C2312yes—
601#389C2311yescharacteristic
602#389C2312yes—
603#389C2312yes—
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2312yes—
607#389C2312yes—
608#389C2311yescharacteristic
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2312yes—
633#388C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2312yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2312yes—
691#385C2314yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#384C2314yes—
699#384C2314yes—
700#384C2314yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2311yescharacteristic
709#384C2311yescharacteristic
710#384C2312yes—
711#383C2312yes—
712#383C2312yes—
713#383C2314yes—
714#383C2314yes—
715#383C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2314yes—
721#382C2314yes—
722#382C2312yes—
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2314yes—
728#382C2311yescharacteristic
729#382C2311yescharacteristic
730#381C2314yes—
731#381C2314yes—
732#381C2314yes—
733#381C2312yes—
734#381C2312yes—
735#381C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2314yes—
743#380C2314yes—
744#380C2314yes—
745#380C2314yes—
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2311yescharacteristic
752#380C2311yescharacteristic
753#380C2311yescharacteristic
754#380C2311yescharacteristic
755#380C2312yes—
756#380C2312yes—
757#380C2311yescharacteristic
758#380C2311yescharacteristic
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2311yescharacteristic
762#380C2311yescharacteristic
763#380C2311yescharacteristic
764#380C2311yescharacteristic
765#379C2312yes—
766#379C2312yes—
767#379C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C22⋊C4C2311yescharacteristic
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809#376C2312yes—
810#376C2312yes—
811C2×#95C2311yescharacteristic
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2311yescharacteristic
815C2×#95C2312yes—
816C43C2312yes—
817C43C2312yes—
818C25C2411yescharacteristic
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—24no—
822C22×Q8—44no—
823C22×Q8—44no—
824C22×Q8—82no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×Q8C2414yes—
830C22×Q8C2414yes—
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2412yes—
835C23×C4—24no—
836C23×C4—24no—
837C23×C4—24no—
838C23×C4—44no—
839C23×C4—44no—
840C23×C4—82no—
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2414yes—
858C23×C4C2411yescharacteristic
859C4⋊Q8—44no—
860C4⋊Q8—44no—
861C4⋊Q8—44no—
862C4⋊Q8—44no—
863C4⋊Q8—42no—
864C4⋊Q8—42no—
865C4⋊Q8—44no—
866C4⋊Q8—44no—
867C4⋊Q8—48no—
868C4⋊Q8—48no—
869C4⋊Q8—84no—
870#126—28no—
871#126—28no—
872#126—48no—
873#126—48no—
874#126—48no—
875#125—42no—
876#125—42no—
877#125—44no—
878#125—44no—
879#125—48no—
880#125—48no—
881#125—84no—
882#124—28no—
883#124—28no—
884#123—48no—
885#123—44no—
886#123—48no—
887#123—84no—
888C22⋊Q8—216no—
889C22⋊Q8—48no—
890C22⋊Q8—44no—
891C22⋊Q8—44no—
892C22⋊Q8—48no—
893C22⋊Q8—48no—
894C22⋊Q8—48no—
895C22⋊Q8—48no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898C22⋊Q8—42no—
899C22⋊Q8—42no—
900C22⋊Q8—84no—
901C22⋊Q8—84no—
902C22⋊Q8—84no—
903#121—42no—
904#121—42no—
905#120—44no—
906C4×Q8—44no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×D4—44no—
910C4×D4—44no—
911C4×D4—44no—
912C4×D4—48no—
913#117—24no—
914#117—24no—
915#117—24no—
916#117—24no—
917#117—24no—
918#117—24no—
919#117—24no—
920#117—44no—
921C2×C4⋊C4—24no—
922C2×C4⋊C4—24no—
923C2×C4⋊C4—24no—
924C2×C4⋊C4—24no—
925C2×C4⋊C4—44no—
926C2×C4⋊C4—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4—44no—
929C2×C4⋊C4—44no—
930C2×C4⋊C4—44no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4—44no—
933C2×C4⋊C4—44no—
934C2×C4⋊C4—44no—
935C2×C4⋊C4—82no—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
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⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C22⋊C4—24no—
1015C2×C22⋊C4—24no—
1016C2×C22⋊C4—44no—
1017C2×C22⋊C4C2411yescharacteristic
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2411yescharacteristic
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⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2411yescharacteristic
1065C2×C42—24no—
1066C2×C42—24no—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2414yes—
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2414yes—
1093#95C2411yescharacteristic
1094#95C2411yescharacteristic
1095#95C2411yescharacteristic
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175C24—22no—
1176C24—22no—
1177C24—22no—
1178C24—22no—
1179C24—22no—
1180C24—41no—
1181C24—41no—
1182C24C2512yes—
1183C24C2511yescharacteristic
1184C24C2511yescharacteristic
1185C24C2511yescharacteristic
1186#41—416no—
1187C2×Q8—22no—
1188C2×Q8—28no—
1189C2×Q8—24no—
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—24no—
1193C2×Q8—42no—
1194C2×Q8—42no—
1195C2×Q8—44no—
1196C2×Q8—44no—
1197C2×Q8—44no—
1198C2×Q8—44no—
1199C2×Q8—42no—
1200C2×Q8—44no—
1201C2×Q8—42no—
1202C2×Q8—44no—
1203C2×Q8—44no—
1204C2×Q8—44no—
1205C2×Q8—816no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—42no—
1215C2×D4—42no—
1216C2×D4—42no—
1217C2×D4—42no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—24no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—24no—
1227C22×C4—24no—
1228C22×C4—28no—
1229C22×C4—24no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—42no—
1250C22×C4—41no—
1251C22×C4—42no—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—42no—
1256C22×C4—42no—
1257C22×C4—42no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4—42no—
1266C22×C4—44no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—416no—
1270C22×C4—816no—
1271C22×C4H(5,𝔽2)14yes—
1272C22×C42−1+414yes—
1273C22×C42−1+414yes—
1274C22×C4C2512yes—
1275C22×C4C2511yescharacteristic
1276C22×C4C2511yescharacteristic
1277C22×C4C2511yescharacteristic
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2514yes—
1289C22×C4C2511yescharacteristic
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2511yescharacteristic
1293C22×C4C2514yes—
1294C22×C4C2512yes—
1295C22×C4C2514yes—
1296C22×C4C2514yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C4⋊C4—24no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—24no—
1311C4⋊C4—22no—
1312C4⋊C4—28no—
1313C4⋊C4—28no—
1314C4⋊C4—28no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—22no—
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—44no—
1337C4⋊C4—44no—
1338C4⋊C4—44no—
1339C4⋊C4—44no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—42no—
1350C4⋊C4—44no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—42no—
1368C4⋊C4—44no—
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—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—44no—
1383C22⋊C4—22no—
1384C22⋊C4—28no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—22no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—44no—
1408C22⋊C4—42no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—44no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
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—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4H(5,𝔽2)14yes—
1430C22⋊C42−1+414yes—
1431C42—22no—
1432C42—22no—
1433C42—22no—
1434C42—22no—
1435C42—24no—
1436C42—24no—
1437C42—24no—
1438C42—24no—
1439C42—24no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—24no—
1445C42—24no—
1446C42—24no—
1447C42—24no—
1448C42—24no—
1449C42—24no—
1450C42—42no—
1451C42—42no—
1452C42—44no—
1453C42—44no—
1454C42—42no—
1455C42—44no—
1456C42—42no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—28no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—44no—
1482C23—44no—
1483C23—44no—
1484C23—44no—
1485C23—44no—
1486C23—44no—
1487C23C2×H(5,𝔽2)12yes—
1488C23C2×H(5,𝔽2)12yes—
1489C23C2×2−1+412yes—
1490C23C2×2−1+412yes—
1491C23C2×2−1+412yes—
1492C23C2611yescharacteristic
1493Q8—44no—
1494Q8—84no—
1495Q8—84no—
1496Q8—88no—
1497Q8—88no—
1498Q8—164no—
1499D4—48no—
1500D4—44no—
1501D4—84no—
1502D4—84no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—24no—
1527C2×C4—24no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—24no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—24no—
1535C2×C4—24no—
1536C2×C4—24no—
1537C2×C4—24no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—24no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—24no—
1575C2×C4—24no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—44no—
1587C2×C4—44no—
1588C2×C4—44no—
1589C2×C4—44no—
1590C2×C4—48no—
1591C2×C4—44no—
1592C2×C4—44no—
1593C2×C4—44no—
1594C2×C4—44no—
1595C2×C4—44no—
1596C2×C4—48no—
1597C2×C4—84no—
1598C2×C4—88no—
1599C2×C4—84no—
1600C2×C4—84no—
1601C2×C4—88no—
1602C2×C4—164no—
1603C2×C4#563116yescomplemented
1604C2×C4C2×H(5,𝔽2)12yes—
1605C2×C4C2×H(5,𝔽2)12yes—
1606C2×C4C2×H(5,𝔽2)12yes—
1607C2×C4C2×H(5,𝔽2)12yes—
1608C2×C4C2×2−1+412yes—
1609C2×C4C2×2−1+412yes—
1610C2×C4C2×2−1+412yes—
1611C2×C4C2×2−1+412yes—
1612C2×C4C2×2−1+412yes—
1613C2×C4C2×2−1+412yes—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—416no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—42no—
1636C22—42no—
1637C22—42no—
1638C22—42no—
1639C22—42no—
1640C22—42no—
1641C22—42no—
1642C22C2×#56314yes—
1643C22C22×H(5,𝔽2)11yescharacteristic
1644C22C22×H(5,𝔽2)11yescharacteristic
1645C22C22×2−1+411yescharacteristic
1646C22C22×2−1+411yescharacteristic
1647C22C22×2−1+411yescharacteristic
1648C22H(7,𝔽2)11yescharacteristic
1649C222−1+611yescharacteristic
1650C4—22no—
1651C4—22no—
1652C4—22no—
1653C4—22no—
1654C4—42no—
1655C4—42no—
1656C4—42no—
1657C4—42no—
1658C4—42no—
1659C4—42no—
1660C4—44no—
1661C4—41no—
1662C4—44no—
1663C4—44no—
1664C4—42no—
1665C4—42no—
1666C4—42no—
1667C4—42no—
1668C4—41no—
1669C4—44no—
1670C4—42no—
1671C4—41no—
1672C4—42no—
1673C4—42no—
1674C4—42no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—42no—
1679C4C2×#56314yes—
1680C4C2×#56314yes—
1681C2—24no—
1682C2—42no—
1683C2—42no—
1684C2—82no—
1685C2C22×#56311yescharacteristic
1686C2#6283311yescharacteristic
1687C2#6287711yescharacteristic
1688C2#6291211yescharacteristic
1689C2#6291511yescharacteristic
1690C2#6294211yescharacteristic
1691C2#6294511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53133C2semidirect
2. #53119C2semidirect
3. #53040C2semidirect
4. #53038C2semidirect
5. #53031C2semidirect
6. #53001C2semidirect
7. #52999C2semidirect
8. #52987C2semidirect
9. #52349C2semidirect
10. #52322C2semidirect
11. #46180C2semidirect
12. #46174C2semidirect
13. #46152C2semidirect
14. #46147C2semidirect
15. #46060C2semidirect
16. #46049C2semidirect
17. #46001C2semidirect
18. #45993C2semidirect
19. #45531C2semidirect
20. #45446C2semidirect
21. #35574C2semidirect
22. #35566C2semidirect
23. #35545C2semidirect
24. #35544C2semidirect
25. #35532C2semidirect
27. #35286C2semidirect
28. #35281C2semidirect
29. #35267C2semidirect
30. #35265C2semidirect
32. #35224C2semidirect
33. #34814C2semidirect
35. C2×#2440C2semidirect
44. #2868C22semidirect
45. #2864C22semidirect
46. #2863C22semidirect
47. #2862C22semidirect
48. #2860C22semidirect
49. #2859C22semidirect
50. #2859C22semidirect
51. #2859C22semidirect
54. #2844C22semidirect
55. #2843C22semidirect
56. #2843C22semidirect
57. #2839C22semidirect
58. #2838C22semidirect
59. #2838C22semidirect
60. #2836C22semidirect
61. #2836C22semidirect
63. #2834C22semidirect
64. #2833C22semidirect
65. #2833C22semidirect
66. #2833C22semidirect
67. #2831C22semidirect
69. #2822C22semidirect
70. #2821C22semidirect
72. #2817C22semidirect
74. #2809C22semidirect
75. #2791C22semidirect
76. #2775C22semidirect
77. #2774C22semidirect
79. #2766C22semidirect
82. #2764C22semidirect
83. #2762C22semidirect
84. #2758C22semidirect
86. #2734C22semidirect
92. #2721C22semidirect
95. #2720C22semidirect
96. #2720C22semidirect
99. #2713C22semidirect
104. #2698C22semidirect
105. #2698C22semidirect
112. #2677C22semidirect
114. #2660C22semidirect
115. #2660C22semidirect
116. #2647C22semidirect
117. #2647C22semidirect
118. #2647C22semidirect
119. #2647C22semidirect
120. #2645C22semidirect
121. #2644C22semidirect
124. #2584C22semidirect
125. #2584C22semidirect
127. #2571C22semidirect
128. #2571C22semidirect
129. #2567C22semidirect
130. #2567C22semidirect
131. #2567C22semidirect
132. #2567C22semidirect
133. #2566C22semidirect
134. #2565C22semidirect
135. #2552C22semidirect
136. #2552C22semidirect
137. #2552C22semidirect
138. #2551C22semidirect
139. #2550C22semidirect
140. #2550C22semidirect
142. #2546C22semidirect
143. #2546C22semidirect
144. #2546C22semidirect
145. #2542C22semidirect
146. #2514C22semidirect
147. #2513C22semidirect
148. #2512C22semidirect
149. #2511C22semidirect
152. #2509C22semidirect
153. #2508C22semidirect
154. #2507C22semidirect
155. #2506C22semidirect
166. #2497C22semidirect
167. #2497C22semidirect
172. #2496C22semidirect
173. #2496C22semidirect
178. #2495C22semidirect
179. #2495C22semidirect
184. #2494C22semidirect
185. #2494C22semidirect
215. #2452C22semidirect
216. #2452C22semidirect
217. #2451C22semidirect
218. #2451C22semidirect
227. #2441C22semidirect
228. #2441C22semidirect
242. #2440C22semidirect
243. #2440C22semidirect
244. #2440C22semidirect
245. #2440C22semidirect
246. #2439C22semidirect
247. #2439C22semidirect
1603. C2×C4#563semidirect

Maximal subgroups

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

subgroupindex
#531332
#531192
#530402
#530382
#530312
#530012
#529992
#529872
#523492
#523222
#461802
#461742
#461522
#461472
#460602
#460492
#460012
#459932
#455312
#454462
#355742
#355662
#355452
#355442
#355322
#355162
#352862
#352812
#352672
#352652
#352272
#352242
#348142
#348132
C2×#24402