Finite Group Databasebeta

← #7979687

Subgroups — #7979687

Order 512.

4801 conjugacy classes of subgroups.

The subgroup lattice has 1703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59435C211yesmaximal, characteristic, complemented
2#59379C212yesmaximal, complemented
3#59282C212yesmaximal, complemented
4#59151C211yesmaximal, characteristic, complemented
5#59036C211yesmaximal, characteristic, complemented
6#50471C214yesmaximal, complemented
7#50277C214yesmaximal, complemented
8#46056C212yesmaximal, complemented
9#46049C212yesmaximal, complemented
10#45113C212yesmaximal, complemented
11#45078C212yesmaximal, complemented
12#44155C214yesmaximal, complemented
13#42991C212yesmaximal, complemented
14#42862C212yesmaximal, complemented
15#42114C214yesmaximal, complemented
16#40078C212yesmaximal, complemented
17#39978C212yesmaximal, complemented
18#39912C212yesmaximal, complemented
19#39561C212yesmaximal, complemented
20#39343C211yesmaximal, characteristic, complemented
21#39226C212yesmaximal, complemented
22#39203C211yesmaximal, characteristic, complemented
23Q8×#124C211yesmaximal, characteristic, complemented
24#36456C211yesmaximal, characteristic, complemented
25#36399C212yesmaximal, complemented
26#36314C211yesmaximal, characteristic, complemented
27#36176C211yesmaximal, characteristic, complemented
28#36129C211yesmaximal, characteristic, complemented
29#35289C211yesmaximal, characteristic, complemented
30#35192C212yesmaximal, complemented
31#35185C211yesmaximal, characteristic, complemented
32#34947C211yesmaximal, characteristic, complemented
33#34715C211yesmaximal, characteristic
34#34412C212yesmaximal, complemented
35C4×#552C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#552C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#536C2212yes—
40C2×#533C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C22×C4⋊Q8C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2864C2212yes—
45#2864C2212yes—
46#2862C2211yescharacteristic
47#2862C2212yes—
48#2862C2212yes—
49#2860C2212yes—
50#2858C2212yes—
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2854C2212yes—
55#2831C2214yes—
56#2830C2214yes—
57#2806C2214yes—
58#2798C2214yes—
59#2796C2214yes—
60#2783C2214yes—
61#2781C2214yes—
62#2775C2214yes—
63#2775C2214yes—
64#2774C2214yes—
65#2773C2214yes—
66#2764C2214yes—
67#2755C2214yes—
68#2754C2214yes—
69#2751C2214yes—
70#2749C2214yes—
71#2737C2214yes—
72#2734C2214yes—
73#2731C2214yes—
74#2728C2214yes—
75#2723C2214yes—
76#2717C2214yes—
77#2715C2214yes—
78#2715C2214yes—
79#2713C2214yes—
80#2707C2214yes—
81#2702C2214yes—
82#2698C2214yes—
83#2696C2214yes—
84#2695C2214yes—
85#2693C2214yes—
86#2692C2214yes—
87#2674C2214yes—
88#2674C2214yes—
89#2672C2214yes—
90#2666C2214yes—
91#2665C2214yes—
92#2665C2214yes—
93#2652C2214yes—
94#2650C2214yes—
95#2650C2214yes—
96#2640C2214yes—
97#2625C2212yes—
98#2616C2212yes—
99#2612C2214yes—
100#2610C2214yes—
101#2605C2214yes—
102#2605C2214yes—
103#2605C2214yes—
104#2604C2214yes—
105#2578C2214yes—
106#2577C2214yes—
107#2577C2214yes—
108#2571C2212yes—
109#2571C2212yes—
110#2571C2211yescharacteristic
111#2570C2212yes—
112#2568C2212yes—
113#2568C2211yescharacteristic
114#2567C2211yescharacteristic
115#2567C2211yescharacteristic
116#2566C2212yes—
117#2565C2212yes—
118#2564C2214yes—
119#2563C2212yes—
120#2563C2211yescharacteristic
121#2563C2211yescharacteristic
122#2563C2211yescharacteristic
123#2563C2211yescharacteristic
124#2563C2212yes—
125#2560C2214yes—
126#2557C2214yes—
127#2557C2214yes—
128#2554C2214yes—
129#2553C2214yes—
130#2551C2212yes—
131#2551C2212yes—
132#2551C2212yes—
133#2550C2212yes—
134#2550C2212yes—
135#2547C2212yes—
136#2547C2212yes—
137#2542C2211yescharacteristic
138#2538C2212yes—
139#2538C2212yes—
140#2538C2211yescharacteristic
141#2533C2214yes—
142#2532C2214yes—
143#2531C2214yes—
144#2530C2214yes—
145#2530C2214yes—
146#2526C2214yes—
147#2523C2214yes—
148#2521C2214yes—
149#2513C2212yes—
150#2513C2212yes—
151#2513C2212yes—
152#2513C2212yes—
153#2512C2212yes—
154#2511C2212yes—
155#2509C2212yes—
156#2508C2212yes—
157#2504C2212yes—
158#2504C2212yes—
159#2499C2212yes—
160#2496C2212yes—
161#2496C2212yes—
162#2495C2212yes—
163#2495C2212yes—
164#2495C2212yes—
165#2492C2212yes—
166#2492C2212yes—
167#2492C2214yes—
168#2492C2214yes—
169#2492C2212yes—
170#2491C2212yes—
171#2489C2212yes—
172#2488C2214yes—
173#2486C2212yes—
174#2476C2212yes—
175#2474C2212yes—
176#2471C2214yes—
177#2469C2214yes—
178#2465C2214yes—
179#2459C2212yes—
180#2456C2212yes—
181#2454C2212yes—
182#2452C2214yes—
183#2452C2212yes—
184#2451C2212yes—
185#2451C2212yes—
186#2451C2212yes—
187#2451C2211yescharacteristic
188#2448C2212yes—
189#2446C2212yes—
190#2445C2212yes—
191#2445C2211yescharacteristic
192#2442C2212yes—
193#2441C2212yes—
194#2440C2212yes—
195#2440C2212yes—
196#2439C2214yes—
197#2439C2212yes—
198#2439C2214yes—
199#2439C2212yes—
200#2439C2214yes—
201#2439C2211yescharacteristic
202#2439C2212yes—
203#2436C2214yes—
204#2434C2214yes—
205#2431C2211yescharacteristic
206#2429C2212yes—
207#2426C2211yescharacteristic
208#2423C2212yes—
209#2422C2212yes—
210#2421C2212yes—
211#2421C2212yes—
212#2421C2212yes—
213#2420C2211yescharacteristic
214#2417C2212yes—
215#2417C2212yes—
216#2417C2212yes—
217#2415C2212yes—
218#2414C2211yescharacteristic
219#2409C2212yes—
220#2409C2212yes—
221#2409C2212yes—
222#2407C2211yescharacteristic
223#2396C2214yes—
224#2392C2212yes—
225#2388C2212yes—
226#2379C2214yes—
227#2376C2214yes—
228#2374C2214yes—
229#2373C2212yes—
230#2372C2214yes—
231#2372C2214yes—
232#2371C2212yes—
233#2370C2211yescharacteristic
234#2369C2211yescharacteristic
235#2365C2211yescharacteristic
236#2363C2212yes—
237#2362C2211yescharacteristic
238#2362C2212yes—
239#2360C2212yes—
240#2360C2212yes—
241#2360C2212yes—
242#2360C2211yescharacteristic
243#2359C2212yes—
244#2356C2212yes—
245#2356C2212yes—
246#2356C2211yescharacteristic
247#2354C2211yescharacteristic
248#2352C2212yes—
249#2352C2212yes—
250#2352C2211yescharacteristic
251#2351C2212yes—
252Q8×C4⋊C4C2211yescharacteristic
253#2346C2212yes—
254#2346C2212yes—
255#2346C2211yescharacteristic
256#2344C2211yescharacteristic
257#2343C2212yes—
258#2341C2212yes—
259Q8×C22⋊C4C2212yes—
260Q8×C22⋊C4C2212yes—
261Q8×C22⋊C4C2212yes—
262Q8×C22⋊C4C2212yes—
263#2335C2214yes—
264#2335C2214yes—
265#2331C2214yes—
266#2331C2214yes—
267#2331C2214yes—
268#2323C2212yes—
269#2323C2212yes—
270#2314C2212yes—
271#2311C2212yes—
272#2311C2212yes—
273C4×C4⋊Q8C2211yescharacteristic
274C4×#125C2211yescharacteristic
275C4×#125C2212yes—
276C4×#126C2212yes—
277C4×#124C2211yescharacteristic
278C4×#124C2212yes—
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2212yes—
284C4×C22⋊Q8C2212yes—
285C4×#123C2212yes—
286C4×#123C2212yes—
287C4×#121C2211yescharacteristic
288#2297C2212yes—
289#2297C2212yes—
290#2295C2212yes—
291#2293C2211yescharacteristic
292#2285C2212yes—
293#2283C2212yes—
294C42×Q8C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C4×#117C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C23×Q8C2312yes—
302C23×Q8C2312yes—
303Q82—44no—
304#552—28no—
305D4×Q8—44no—
306#536—216no—
307#533—44no—
308#532—44no—
309C2×C4⋊Q8—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2314yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2314yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2311yescharacteristic
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2314yes—
323C2×#127C2311yescharacteristic
324C2×#126C2312yes—
325C2×#126C2314yes—
326C2×#126C2314yes—
327C2×#125C2311yescharacteristic
328C2×#125C2312yes—
329C2×#125C2312yes—
330C2×#124C2314yes—
331C2×#124C2311yescharacteristic
332C2×#124C2314yes—
333C2×#124C2312yes—
334C2×#124C2314yes—
335C2×#123C2314yes—
336C2×#123C2312yes—
337C2×#123C2314yes—
338C2×#123C2312yes—
339C2×#123C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×#121C2311yescharacteristic
355C2×#121C2311yescharacteristic
356C2×#121C2311yescharacteristic
357C2×#121C2312yes—
358C4×#41—44no—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×#117C2311yescharacteristic
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C42C2312yes—
396C22×C42C2311yescharacteristic
397C22×C42C2311yescharacteristic
398C22×C42C2312yes—
399#400C2314yes—
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#399C2314yes—
415#399C2314yes—
416#399C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#398C2314yes—
426#398C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2312yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2312yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2314yes—
467#394C2314yes—
468#394C2312yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2312yes—
473#394C2312yes—
474#394C2312yes—
475#394C2312yes—
476#394C2312yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2312yes—
488#393C2314yes—
489#392C2312yes—
490#392C2312yes—
491#392C2312yes—
492#392C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2311yescharacteristic
501#391C2314yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2314yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2311yescharacteristic
515#391C2312yes—
516#391C2314yes—
517#391C2312yes—
518#391C2312yes—
519#391C2314yes—
520#391C2312yes—
521#391C2314yes—
522#391C2314yes—
523#391C2314yes—
524#391C2312yes—
525#391C2311yescharacteristic
526#391C2312yes—
527#391C2314yes—
528#391C2311yescharacteristic
529#390C2312yes—
530#390C2312yes—
531#390C2311yescharacteristic
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2312yes—
536#390C2312yes—
537#390C2314yes—
538#390C2314yes—
539#390C2312yes—
540#390C2312yes—
541#390C2314yes—
542#390C2312yes—
543#390C2311yescharacteristic
544#390C2314yes—
545#390C2311yescharacteristic
546#390C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2311yescharacteristic
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2311yescharacteristic
558#389C2312yes—
559#389C2311yescharacteristic
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2311yescharacteristic
571#389C2312yes—
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2314yes—
580#389C2311yescharacteristic
581#389C2314yes—
582#389C2314yes—
583#389C2312yes—
584#389C2311yescharacteristic
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2312yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2312yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2314yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2312yes—
662#387C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2312yes—
670#386C2314yes—
671#386C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2314yes—
676#386C2312yes—
677#386C2312yes—
678#386C2312yes—
679#386C2312yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2312yes—
693#384C2311yescharacteristic
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#384C2312yes—
698#383C2312yes—
699#383C2314yes—
700#383C2314yes—
701#383C2314yes—
702#382C2312yes—
703#382C2311yescharacteristic
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2314yes—
711#382C2312yes—
712#382C2311yescharacteristic
713#382C2314yes—
714#382C2314yes—
715#382C2312yes—
716#382C2312yes—
717#382C2314yes—
718#381C2312yes—
719#381C2314yes—
720#381C2312yes—
721#380C2312yes—
722#380C2311yescharacteristic
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2314yes—
733#380C2312yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2314yes—
740#380C2312yes—
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808#376C2314yes—
809#376C2314yes—
810#376C2312yes—
811#376C2312yes—
812#376C2312yes—
813#376C2314yes—
814C2×#95C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C2×#41—24no—
819C2×#41—28no—
820C2×#41—24no—
821C2×#41—44no—
822C2×#41—44no—
823C2×#41—42no—
824C22×Q8—28no—
825C22×Q8—44no—
826C22×Q8—44no—
827C22×Q8—44no—
828C22×Q8—44no—
829C22×Q8—82no—
830C22×Q8C2412yes—
831C22×Q8C2411yescharacteristic
832C22×Q8C2411yescharacteristic
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×Q8C2412yes—
836C22×Q8C2414yes—
837C22×Q8C2412yes—
838C22×Q8C2414yes—
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C4⋊Q8—216no—
863C4⋊Q8—24no—
864C4⋊Q8—24no—
865C4⋊Q8—24no—
866C4⋊Q8—44no—
867C4⋊Q8—44no—
868C4⋊Q8—42no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—48no—
874C4⋊Q8—48no—
875#127—42no—
876#126—28no—
877#126—84no—
878#126—84no—
879#125—28no—
880#125—24no—
881#125—44no—
882#124—24no—
883#124—216no—
884#124—44no—
885#124—48no—
886#124—84no—
887#123—216no—
888#123—216no—
889#123—28no—
890#123—44no—
891#123—84no—
892C22⋊Q8—28no—
893C22⋊Q8—24no—
894C22⋊Q8—24no—
895C22⋊Q8—28no—
896C22⋊Q8—28no—
897C22⋊Q8—48no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902C22⋊Q8—84no—
903C22⋊Q8—82no—
904C22⋊Q8—84no—
905C22⋊Q8#4118yescomplemented
906#121—24no—
907#121—44no—
908#121—42no—
909#121—42no—
910C4×Q8—24no—
911C4×Q8—28no—
912C4×Q8—24no—
913C4×Q8—24no—
914C4×Q8—42no—
915C4×Q8—44no—
916C4×Q8—42no—
917C4×Q8—44no—
918C4×Q8—44no—
919C4×Q8—44no—
920C4×Q8—44no—
921C4×Q8—82no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—24no—
925C4×D4—24no—
926C4×D4—42no—
927C4×D4—44no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—42no—
932C4×D4—44no—
933#117—24no—
934#117—28no—
935#117—28no—
936#117—44no—
937#117—44no—
938#117—44no—
939#117—42no—
940#117—42no—
941#117—44no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—42no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4—44no—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C22⋊C4C2411yescharacteristic
1014C2×C22⋊C4C2411yescharacteristic
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C42—28no—
1064C2×C42—24no—
1065C2×C42—24no—
1066C2×C42—44no—
1067C2×C42C2411yescharacteristic
1068C2×C42C2411yescharacteristic
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2414yes—
1074C2×C42C2411yescharacteristic
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2412yes—
1082C2×C42C2414yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2411yescharacteristic
1096C2×C42C2414yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2414yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2411yescharacteristic
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2411yescharacteristic
1110#95C2411yescharacteristic
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2414yes—
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2412yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181C24C2512yes—
1182C24C2512yes—
1183C24C2511yescharacteristic
1184C24C2511yescharacteristic
1185#41—416no—
1186#41—816no—
1187C2×Q8—24no—
1188C2×Q8—28no—
1189C2×Q8—24no—
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—24no—
1193C2×Q8—24no—
1194C2×Q8—24no—
1195C2×Q8—22no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—28no—
1199C2×Q8—42no—
1200C2×Q8—42no—
1201C2×Q8—44no—
1202C2×Q8—42no—
1203C2×Q8—42no—
1204C2×Q8—44no—
1205C2×Q8—44no—
1206C2×Q8—44no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—44no—
1212C2×Q8—816no—
1213C2×Q8—816no—
1214C2×Q8C2×#4114yes—
1215C2×Q82−1+414yes—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—24no—
1231C2×D4—42no—
1232C2×D4—41no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—42no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—24no—
1250C22×C4—22no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—28no—
1267C22×C4—22no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—41no—
1271C22×C4—42no—
1272C22×C4—44no—
1273C22×C4—42no—
1274C22×C4—44no—
1275C22×C4—41no—
1276C22×C4—41no—
1277C22×C4—42no—
1278C22×C4—44no—
1279C22×C4—42no—
1280C22×C4—42no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4C2×#4114yes—
1284C22×C42−1+414yes—
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2511yescharacteristic
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2511yescharacteristic
1296C22×C4C2511yescharacteristic
1297C22×C4C2514yes—
1298C22×C4C2512yes—
1299C22×C4C2514yes—
1300C22×C4C2514yes—
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2512yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2512yes—
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—28no—
1324C4⋊C4—28no—
1325C4⋊C4—28no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—22no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—24no—
1336C4⋊C4—22no—
1337C4⋊C4—24no—
1338C4⋊C4—22no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—28no—
1342C4⋊C4—24no—
1343C4⋊C4—22no—
1344C4⋊C4—22no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—22no—
1351C4⋊C4—24no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—42no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4C2×#4114yes—
1382C4⋊C4C2×#4118yes—
1383C22⋊C4—24no—
1384C22⋊C4—22no—
1385C22⋊C4—28no—
1386C22⋊C4—22no—
1387C22⋊C4—22no—
1388C22⋊C4—24no—
1389C22⋊C4—28no—
1390C22⋊C4—28no—
1391C22⋊C4—28no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—22no—
1395C22⋊C4—24no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—44no—
1407C22⋊C4—42no—
1408C22⋊C4—42no—
1409C22⋊C4—41no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4C2×#4118yes—
1433C42—24no—
1434C42—24no—
1435C42—28no—
1436C42—22no—
1437C42—22no—
1438C42—22no—
1439C42—22no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—24no—
1444C42—24no—
1445C42—24no—
1446C42—24no—
1447C42—24no—
1448C42—24no—
1449C42—22no—
1450C42—28no—
1451C42—24no—
1452C42—22no—
1453C42—22no—
1454C42—24no—
1455C42—24no—
1456C42—42no—
1457C42—42no—
1458C42—42no—
1459C42—42no—
1460C42—44no—
1461C42—41no—
1462C42—42no—
1463C42—44no—
1464C42—44no—
1465C42—41no—
1466C42—44no—
1467C42—42no—
1468C42—42no—
1469C42—44no—
1470C42H(5,𝔽2)14yes—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—22no—
1484C23—22no—
1485C23—22no—
1486C23—22no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—22no—
1495C23—22no—
1496C23—22no—
1497C23C22×#4112yes—
1498C23C2×2−1+412yes—
1499C23C2611yescharacteristic
1500Q8—28no—
1501Q8—28no—
1502Q8—48no—
1503Q8—48no—
1504Q8—88no—
1505Q8—84no—
1506Q8—88no—
1507Q8—84no—
1508Q8—164no—
1509D4—48no—
1510D4—44no—
1511D4—44no—
1512D4—44no—
1513D4—84no—
1514D4—84no—
1515D4—84no—
1516D4—84no—
1517D4—84no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—28no—
1533C2×C4—28no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—24no—
1538C2×C4—22no—
1539C2×C4—21no—
1540C2×C4—24no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—24no—
1550C2×C4—24no—
1551C2×C4—24no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—24no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—44no—
1601C2×C4—48no—
1602C2×C4—48no—
1603C2×C4—44no—
1604C2×C4—48no—
1605C2×C4—48no—
1606C2×C4—44no—
1607C2×C4—82no—
1608C2×C4—88no—
1609C2×C4—84no—
1610C2×C4—84no—
1611C2×C4—88no—
1612C2×C4C22×#4114yes—
1613C2×C4C22×#4112yes—
1614C2×C4C22×#4114yes—
1615C2×C4C22×#4112yes—
1616C2×C4C2×H(5,𝔽2)12yes—
1617C2×C4C2×H(5,𝔽2)12yes—
1618C2×C4C2×H(5,𝔽2)12yes—
1619C2×C4C2×2−1+412yes—
1620C2×C4C2×2−1+414yes—
1621C2×C4C2×2−1+412yes—
1622C2×C4C2×2−1+412yes—
1623C2×C4#58512yes—
1624C2×C4#58512yes—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—42no—
1640C22—42no—
1641C22—42no—
1642C22—42no—
1643C22—42no—
1644C22—42no—
1645C22—42no—
1646C22—42no—
1647C22—42no—
1648C22—42no—
1649C22—42no—
1650C22—42no—
1651C22—42no—
1652C22—42no—
1653C22C23×#4111yescharacteristic
1654C22C22×H(5,𝔽2)11yescharacteristic
1655C22C22×2−1+411yescharacteristic
1656C22C22×2−1+411yescharacteristic
1657C22C2×#58511yescharacteristic
1658C22C2×#58511yescharacteristic
1659C22H(7,𝔽2)11yescharacteristic
1660C4—22no—
1661C4—24no—
1662C4—22no—
1663C4—24no—
1664C4—24no—
1665C4—22no—
1666C4—22no—
1667C4—41no—
1668C4—41no—
1669C4—44no—
1670C4—42no—
1671C4—41no—
1672C4—42no—
1673C4—42no—
1674C4—44no—
1675C4—42no—
1676C4—41no—
1677C4—42no—
1678C4—42no—
1679C4—41no—
1680C4—41no—
1681C4—44no—
1682C4—44no—
1683C4—42no—
1684C4—42no—
1685C4—41no—
1686C4—42no—
1687C4—42no—
1688C4—42no—
1689C4#351414yes—
1690C4#353814yes—
1691C2—42no—
1692C2—42no—
1693C2—82no—
1694C2—82no—
1695C2C2×#353811yescharacteristic
1696C2C2×#351411yescharacteristic
1697C2#6280511yescharacteristic
1698C2#6292411yescharacteristic
1699C2#6292911yescharacteristic
1700C2#6299911yescharacteristic
1701C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34715C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59435C2semidirect
2. #59379C2semidirect
3. #59282C2semidirect
4. #59151C2semidirect
5. #59036C2semidirect
6. #50471C2semidirect
7. #50277C2semidirect
8. #46056C2semidirect
9. #46049C2semidirect
10. #45113C2semidirect
11. #45078C2semidirect
12. #44155C2semidirect
13. #42991C2semidirect
14. #42862C2semidirect
15. #42114C2semidirect
16. #40078C2semidirect
17. #39978C2semidirect
18. #39912C2semidirect
19. #39561C2semidirect
20. #39343C2semidirect
21. #39226C2semidirect
22. #39203C2semidirect
23. Q8×#124C2semidirect
24. #36456C2semidirect
25. #36399C2semidirect
26. #36314C2semidirect
27. #36176C2semidirect
28. #36129C2semidirect
29. #35289C2semidirect
30. #35192C2semidirect
31. #35185C2semidirect
32. #34947C2semidirect
34. #34412C2semidirect
35. C4×#552C2semidirect
905. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#594352
#593792
#592822
#591512
#590362
#504712
#502772
#460562
#460492
#451132
#450782
#441552
#429912
#428622
#421142
#400782
#399782
#399122
#395612
#393432
#392262
#392032
Q8×#1242
#364562
#363992
#363142
#361762
#361292
#352892
#351922
#351852
#349472
#347152
#344122
C4×#5522