Finite Group Databasebeta

← #7688373

Subgroups — #7688373

Order 512.

5181 conjugacy classes of subgroups.

The subgroup lattice has 1738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59769C212yesmaximal, complemented
2#59550C212yesmaximal, complemented
3#59544C212yesmaximal, complemented
4#59489C212yesmaximal, complemented
5#59462C212yesmaximal, complemented
6#59451C211yesmaximal, characteristic, complemented
7#59104C212yesmaximal, complemented
8#59081C211yesmaximal, characteristic, complemented
9#59066C211yesmaximal, characteristic, complemented
10#44749C214yesmaximal, complemented
11#44388C214yesmaximal, complemented
12#44057C214yesmaximal, complemented
13#40214C212yesmaximal, complemented
14#40050C212yesmaximal, complemented
15#40007C212yesmaximal, complemented
16#39912C212yesmaximal, complemented
17#39243C212yesmaximal, complemented
18#39029C212yesmaximal, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36459C211yesmaximal, characteristic, complemented
21#36457C211yesmaximal, characteristic, complemented
22#36410C211yesmaximal, characteristic, complemented
23#36399C212yesmaximal, complemented
24#36381C212yesmaximal, complemented
25#36300C211yesmaximal, characteristic, complemented
26#36150C211yesmaximal, characteristic, complemented
27#36117C211yesmaximal, characteristic, complemented
28#35896C214yesmaximal, complemented
29#34955C211yesmaximal, characteristic, complemented
30#34951C211yesmaximal, characteristic, complemented
31#34947C211yesmaximal, characteristic, complemented
32#34316C212yesmaximal, complemented
33#34242C212yesmaximal, complemented
34C4×#552C211yesmaximal, characteristic, complemented
35C4×#548C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#552C2211yescharacteristic
38C2×#550C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#547C2212yes—
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#529C2212yes—
44C2×C4×#41C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46#2860C2212yes—
47#2860C2212yes—
48#2858C2212yes—
49#2858C2211yescharacteristic
50#2857C2212yes—
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2854C2212yes—
54#2854C2212yes—
55#2796C2214yes—
56#2795C2214yes—
57#2773C2214yes—
58#2768C2214yes—
59#2757C2214yes—
60#2754C2214yes—
61#2742C2214yes—
62#2741C2214yes—
63#2737C2214yes—
64#2730C2214yes—
65#2729C2214yes—
66#2727C2214yes—
67#2718C2214yes—
68#2717C2214yes—
69#2710C2214yes—
70#2703C2214yes—
71#2696C2214yes—
72#2695C2214yes—
73#2693C2214yes—
74#2691C2214yes—
75#2671C2214yes—
76#2651C2214yes—
77#2650C2214yes—
78#2649C2214yes—
79#2610C2214yes—
80#2596C2214yes—
81#2592C2212yes—
82#2592C2212yes—
83#2591C2214yes—
84#2589C2214yes—
85#2589C2214yes—
86#2585C2214yes—
87#2582C2212yes—
88#2582C2211yescharacteristic
89#2577C2214yes—
90#2574C2214yes—
91#2574C2214yes—
92#2570C2212yes—
93#2568C2211yescharacteristic
94#2568C2211yescharacteristic
95#2567C2212yes—
96#2567C2211yescharacteristic
97#2566C2212yes—
98#2565C2212yes—
99#2564C2214yes—
100#2563C2212yes—
101#2563C2211yescharacteristic
102#2560C2214yes—
103#2560C2214yes—
104#2560C2214yes—
105#2558C2214yes—
106#2557C2214yes—
107#2554C2214yes—
108#2553C2214yes—
109#2553C2214yes—
110#2552C2211yescharacteristic
111#2550C2212yes—
112#2548C2211yescharacteristic
113#2548C2211yescharacteristic
114#2548C2212yes—
115#2546C2211yescharacteristic
116#2542C2211yescharacteristic
117#2540C2212yes—
118#2532C2214yes—
119#2532C2214yes—
120#2531C2214yes—
121#2531C2214yes—
122#2523C2214yes—
123#2522C2214yes—
124#2521C2214yes—
125#2521C2214yes—
126#2513C2212yes—
127#2513C2212yes—
128#2512C2212yes—
129#2512C2212yes—
130#2511C2212yes—
131#2509C2212yes—
132#2504C2212yes—
133#2501C2212yes—
134#2499C2212yes—
135#2496C2212yes—
136#2495C2212yes—
137#2492C2212yes—
138#2491C2214yes—
139#2491C2212yes—
140#2491C2214yes—
141#2491C2212yes—
142#2490C2212yes—
143#2490C2212yes—
144#2489C2212yes—
145#2485C2212yes—
146#2479C2214yes—
147#2477C2214yes—
148#2476C2214yes—
149#2474C2214yes—
150#2474C2214yes—
151#2473C2214yes—
152#2471C2214yes—
153#2467C2214yes—
154#2464C2214yes—
155#2464C2214yes—
156#2461C2214yes—
157#2459C2214yes—
158#2454C2212yes—
159#2454C2212yes—
160#2454C2212yes—
161#2453C2212yes—
162#2453C2212yes—
163#2451C2212yes—
164#2451C2212yes—
165#2451C2214yes—
166#2448C2212yes—
167#2448C2212yes—
168#2448C2212yes—
169#2448C2212yes—
170#2446C2214yes—
171#2446C2212yes—
172#2445C2212yes—
173#2445C2212yes—
174#2443C2214yes—
175#2440C2214yes—
176#2440C2212yes—
177#2439C2212yes—
178#2436C2212yes—
179#2432C2212yes—
180#2431C2212yes—
181#2429C2212yes—
182#2428C2212yes—
183#2427C2212yes—
184#2427C2212yes—
185#2426C2212yes—
186#2426C2212yes—
187#2425C2214yes—
188#2423C2212yes—
189#2422C2212yes—
190#2417C2212yes—
191#2417C2212yes—
192#2414C2212yes—
193#2414C2212yes—
194#2407C2212yes—
195#2407C2212yes—
196#2407C2212yes—
197#2402C2214yes—
198#2398C2214yes—
199#2396C2214yes—
200#2374C2214yes—
201#2374C2214yes—
202#2373C2212yes—
203#2373C2214yes—
204#2373C2214yes—
205#2372C2214yes—
206#2371C2212yes—
207#2370C2211yescharacteristic
208#2369C2211yescharacteristic
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2367C2211yescharacteristic
213#2367C2212yes—
214#2366C2211yescharacteristic
215#2365C2212yes—
216#2363C2214yes—
217#2363C2212yes—
218#2363C2212yes—
219#2362C2211yescharacteristic
220#2362C2212yes—
221#2362C2212yes—
222#2362C2211yescharacteristic
223#2362C2212yes—
224#2361C2212yes—
225#2361C2211yescharacteristic
226#2361C2212yes—
227#2360C2211yescharacteristic
228#2359C2212yes—
229#2356C2211yescharacteristic
230#2355C2212yes—
231#2354C2212yes—
232#2354C2212yes—
233#2354C2211yescharacteristic
234#2354C2212yes—
235#2354C2214yes—
236#2352C2212yes—
237#2352C2211yescharacteristic
238#2352C2214yes—
239#2352C2211yescharacteristic
240#2351C2211yescharacteristic
241Q8×C4⋊C4C2211yescharacteristic
242Q8×C4⋊C4C2212yes—
243D4×C4⋊C4C2212yes—
244#2347C2212yes—
245#2346C2211yescharacteristic
246#2345C2214yes—
247#2344C2211yescharacteristic
248#2343C2212yes—
249#2341C2212yes—
250#2341C2212yes—
251#2341C2211yescharacteristic
252#2341C2212yes—
253Q8×C22⋊C4C2211yescharacteristic
254Q8×C22⋊C4C2212yes—
255#2335C2214yes—
256#2335C2214yes—
257#2335C2214yes—
258#2335C2214yes—
259#2324C2214yes—
260#2314C2214yes—
261C4×C4⋊Q8C2212yes—
262C4×C4⋊Q8C2211yescharacteristic
263C4×#125C2211yescharacteristic
264C4×#125C2212yes—
265C4×#125C2212yes—
266C4×#125C2212yes—
267C4×#126C2212yes—
268C4×#124C2212yes—
269C4×#124C2212yes—
270C4×#124C2211yescharacteristic
271C4×#124C2212yes—
272C4×#124C2212yes—
273C4×C22⋊Q8C2212yes—
274C4×C22⋊Q8C2212yes—
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2212yes—
277C4×C22⋊Q8C2211yescharacteristic
278C4×C22⋊Q8C2212yes—
279C4×C22⋊Q8C2211yescharacteristic
280C4×#123C2212yes—
281C4×#121C2212yes—
282C4×#121C2211yescharacteristic
283#2297C2212yes—
284#2297C2212yes—
285#2297C2212yes—
286#2297C2212yes—
287#2295C2212yes—
288#2295C2212yes—
289#2293C2212yes—
290#2285C2212yes—
291#2274C2214yes—
292C42×Q8C2211yescharacteristic
293C42×Q8C2211yescharacteristic
294C42×D4C2212yes—
295C42×D4C2211yescharacteristic
296C4×#117C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×Q8C2311yescharacteristic
303Q82—44no—
304#552—28no—
305#550—44no—
306#548—28no—
307#547—216no—
308#533—44no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2314yes—
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318#529—216no—
319C2×#126C2312yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#125C2311yescharacteristic
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2314yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2312yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2311yescharacteristic
351C2×C22⋊Q8C2311yescharacteristic
352C2×#121C2314yes—
353C2×#121C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2314yes—
361C2×#121C2312yes—
362C4×#41—44no—
363C2×C4×Q8—44no—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2312yes—
381C2×C4×Q8C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2314yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×#117C2314yes—
399C2×#117C2312yes—
400C2×#117C2311yescharacteristic
401C2×#117C2314yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2311yescharacteristic
405C2×#117C2311yescharacteristic
406C2×#117C2312yes—
407C2×#117C2312yes—
408C22×C4⋊C4C2311yescharacteristic
409C22×C4⋊C4C2314yes—
410C22×C4⋊C4C2312yes—
411C22×C4⋊C4C2311yescharacteristic
412C22×C4⋊C4C2311yescharacteristic
413C22×C42C2312yes—
414C22×C42C2311yescharacteristic
415C22×C42C2311yescharacteristic
416C22×C42C2312yes—
417C22×C42C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#399C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2314yes—
487#392C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2311yescharacteristic
504#391C2312yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2311yescharacteristic
508#391C2312yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2312yes—
512#390C2314yes—
513#390C2314yes—
514#390C2314yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2311yescharacteristic
531#390C2312yes—
532#390C2314yes—
533#390C2311yescharacteristic
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2311yescharacteristic
546#389C2312yes—
547#389C2311yescharacteristic
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2314yes—
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2314yes—
565#389C2314yes—
566#389C2314yes—
567#389C2311yescharacteristic
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2312yes—
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#388C2312yes—
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2314yes—
622#388C2312yes—
623#388C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2314yes—
640#387C2314yes—
641#387C2312yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2312yes—
654#387C2314yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#386C2312yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#386C2312yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#384C2311yescharacteristic
694#384C2312yes—
695#384C2312yes—
696#384C2312yes—
697#384C2314yes—
698#384C2312yes—
699#383C2312yes—
700#383C2314yes—
701#382C2312yes—
702#382C2312yes—
703#382C2312yes—
704#382C2311yescharacteristic
705#382C2311yescharacteristic
706#382C2312yes—
707#382C2314yes—
708#382C2312yes—
709#381C2312yes—
710#380C2314yes—
711#380C2314yes—
712#380C2312yes—
713#380C2312yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2314yes—
719#380C2314yes—
720#380C2312yes—
721#380C2314yes—
722#380C2311yescharacteristic
723#380C2312yes—
724#380C2311yescharacteristic
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2314yes—
734C4×C4⋊C4C2314yes—
735C4×C4⋊C4C2314yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C22⋊C4C2311yescharacteristic
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2314yes—
811#376C2312yes—
812#376C2312yes—
813#376C2314yes—
814#376C2312yes—
815C2×#95C2312yes—
816C43C2312yes—
817C43C2312yes—
818C43C2311yescharacteristic
819C43C2312yes—
820C2×#41—28no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—28no—
824C2×#41—42no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C22×Q8—24no—
830C22×Q8—24no—
831C22×Q8—42no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×Q8C2414yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2414yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C4⋊Q8—28no—
867C4⋊Q8—24no—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—48no—
872#127—24no—
873#127—44no—
874#126—216no—
875#126—28no—
876#126—84no—
877#126—84no—
878#125—28no—
879#125—28no—
880#125—24no—
881#125—44no—
882#124—28no—
883#124—24no—
884#124—28no—
885#124—28no—
886#124—48no—
887#124—44no—
888#124—44no—
889#124—84no—
890#124—82no—
891#123—216no—
892#123—216no—
893#123—216no—
894#123—28no—
895#123—84no—
896#123—84no—
897C22⋊Q8—24no—
898C22⋊Q8—28no—
899C22⋊Q8—28no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902C22⋊Q8—44no—
903C22⋊Q8—82no—
904C22⋊Q8—84no—
905C22⋊Q8#4118yescomplemented
906C22⋊Q8#4118yescomplemented
907#121—28no—
908#121—24no—
909#121—216no—
910#121—28no—
911#121—48no—
912#121—44no—
913#121—44no—
914#121—44no—
915#121—44no—
916#121—82no—
917C4×Q8—28no—
918C4×Q8—24no—
919C4×Q8—24no—
920C4×Q8—24no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—24no—
924C4×Q8—44no—
925C4×Q8—44no—
926C4×Q8—42no—
927C4×Q8—42no—
928C4×Q8—42no—
929C4×Q8—44no—
930C4×Q8—42no—
931C4×Q8—44no—
932C4×Q8—44no—
933C4×Q8—44no—
934C4×Q8—44no—
935C4×D4—28no—
936C4×D4—24no—
937C4×D4—24no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—28no—
941C4×D4—216no—
942C4×D4—24no—
943C4×D4—44no—
944C4×D4—42no—
945C4×D4—42no—
946C4×D4—44no—
947C4×D4—44no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—44no—
951#117—24no—
952#117—216no—
953#117—28no—
954#117—48no—
955#117—44no—
956#117—44no—
957#117—42no—
958#117—44no—
959#117—42no—
960#117—44no—
961C2×C4⋊C4—216no—
962C2×C4⋊C4—24no—
963C2×C4⋊C4—42no—
964C2×C4⋊C4—42no—
965C2×C4⋊C4—44no—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2411yescharacteristic
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2411yescharacteristic
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C42—28no—
1086C2×C42—24no—
1087C2×C42—24no—
1088C2×C42—44no—
1089C2×C42—44no—
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2414yes—
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2412yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2412yes—
1124C2×C42C2414yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2414yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2411yescharacteristic
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2411yescharacteristic
1161#95C2411yescharacteristic
1162#95C2412yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2411yescharacteristic
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200C24C2514yes—
1201C24C2512yes—
1202C24C2511yescharacteristic
1203C24C2511yescharacteristic
1204#41—416no—
1205#41—816no—
1206#41—816no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—22no—
1218C2×Q8—24no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×Q8—42no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×Q8—416no—
1226C2×Q8C2×#4114yes—
1227C2×Q8C2×#4114yes—
1228C2×Q82−1+414yes—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—24no—
1233C2×D4—28no—
1234C2×D4—28no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—22no—
1239C2×D4—28no—
1240C2×D4—22no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—24no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—41no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—28no—
1270C22×C4—22no—
1271C22×C4—28no—
1272C22×C4—24no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—28no—
1285C22×C4—28no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4C2×#4114yes—
1309C22×C4C2×#4114yes—
1310C22×C4C2511yescharacteristic
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2512yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2512yes—
1319C22×C4C2514yes—
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2514yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2514yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2511yescharacteristic
1337C22×C4C2512yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C4⋊C4—24no—
1342C4⋊C4—22no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—28no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—28no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—28no—
1356C4⋊C4—24no—
1357C4⋊C4—28no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—22no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—41no—
1386C4⋊C4—42no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4C2×#4118yes—
1403C4⋊C4C2×#4114yes—
1404C4⋊C4C2×#4118yes—
1405C4⋊C4C2×#4114yes—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—28no—
1412C22⋊C4—24no—
1413C22⋊C4—28no—
1414C22⋊C4—22no—
1415C22⋊C4—24no—
1416C22⋊C4—28no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—28no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—28no—
1425C22⋊C4—28no—
1426C22⋊C4—22no—
1427C22⋊C4—28no—
1428C22⋊C4—22no—
1429C22⋊C4—24no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—42no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4C2×#4118yes—
1459C22⋊C4C2×#4118yes—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—28no—
1466C42—24no—
1467C42—24no—
1468C42—24no—
1469C42—22no—
1470C42—22no—
1471C42—22no—
1472C42—22no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—24no—
1478C42—24no—
1479C42—24no—
1480C42—24no—
1481C42—22no—
1482C42—24no—
1483C42—24no—
1484C42—24no—
1485C42—22no—
1486C42—22no—
1487C42—42no—
1488C42—42no—
1489C42—42no—
1490C42—42no—
1491C42—44no—
1492C42—42no—
1493C42—42no—
1494C42—44no—
1495C42—44no—
1496C42—42no—
1497C42—44no—
1498C42—44no—
1499C42—41no—
1500C42—42no—
1501C42—42no—
1502C42—42no—
1503C42H(5,𝔽2)14yes—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—24no—
1517C23—22no—
1518C23—22no—
1519C23—24no—
1520C23—22no—
1521C23—24no—
1522C23—24no—
1523C23—22no—
1524C23—24no—
1525C23—22no—
1526C23—22no—
1527C23—24no—
1528C23—22no—
1529C23—24no—
1530C23C22×#4112yes—
1531C23C22×#4112yes—
1532C23C2611yescharacteristic
1533Q8—28no—
1534Q8—28no—
1535Q8—28no—
1536Q8—48no—
1537Q8—48no—
1538Q8—84no—
1539Q8—164no—
1540D4—48no—
1541D4—48no—
1542D4—44no—
1543D4—48no—
1544D4—48no—
1545D4—44no—
1546D4—84no—
1547D4—88no—
1548D4—88no—
1549D4—88no—
1550D4—164no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—28no—
1570C2×C4—28no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—24no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—24no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—24no—
1613C2×C4—24no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—21no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—24no—
1631C2×C4—416no—
1632C2×C4—48no—
1633C2×C4—48no—
1634C2×C4—48no—
1635C2×C4—44no—
1636C2×C4—48no—
1637C2×C4—44no—
1638C2×C4—82no—
1639C2×C4—82no—
1640C2×C4—88no—
1641C2×C4—88no—
1642C2×C4—84no—
1643C2×C4—84no—
1644C2×C4—84no—
1645C2×C4C22×#4112yes—
1646C2×C4C22×#4114yes—
1647C2×C4C22×#4112yes—
1648C2×C4C22×#4114yes—
1649C2×C4C22×#4114yes—
1650C2×C4C22×#4114yes—
1651C2×C4C22×#4112yes—
1652C2×C4C22×#4112yes—
1653C2×C4C2×H(5,𝔽2)12yes—
1654C2×C4C2×H(5,𝔽2)12yes—
1655C2×C4C2×H(5,𝔽2)12yes—
1656C2×C4C2×2−1+414yes—
1657C2×C4C2×2−1+412yes—
1658C2×C4#58512yes—
1659C2×C4#58512yes—
1660C22—22no—
1661C22—22no—
1662C22—22no—
1663C22—22no—
1664C22—22no—
1665C22—22no—
1666C22—41no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—42no—
1675C22—44no—
1676C22—44no—
1677C22—42no—
1678C22—42no—
1679C22—44no—
1680C22—44no—
1681C22—42no—
1682C22—42no—
1683C22—44no—
1684C22—42no—
1685C22—44no—
1686C22—44no—
1687C22—42no—
1688C22C23×#4111yescharacteristic
1689C22C23×#4111yescharacteristic
1690C22C22×H(5,𝔽2)11yescharacteristic
1691C22C22×2−1+411yescharacteristic
1692C22C2×#58511yescharacteristic
1693C22C2×#58511yescharacteristic
1694C22H(7,𝔽2)11yescharacteristic
1695C4—22no—
1696C4—24no—
1697C4—24no—
1698C4—22no—
1699C4—22no—
1700C4—24no—
1701C4—22no—
1702C4—24no—
1703C4—24no—
1704C4—41no—
1705C4—42no—
1706C4—42no—
1707C4—41no—
1708C4—42no—
1709C4—42no—
1710C4—44no—
1711C4—41no—
1712C4—42no—
1713C4—41no—
1714C4—42no—
1715C4—44no—
1716C4—41no—
1717C4—42no—
1718C4—41no—
1719C4—42no—
1720C4—42no—
1721C4—44no—
1722C4—42no—
1723C4—41no—
1724C4#351414yes—
1725C4#352014yes—
1726C2—42no—
1727C2—42no—
1728C2—84no—
1729C2—82no—
1730C2#41211yescharacteristic
1731C2C2×#352011yescharacteristic
1732C2C2×#351411yescharacteristic
1733C2#6295511yescharacteristic
1734C2#6299911yescharacteristic
1735C2#6300611yescharacteristic
1736C2#6303311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59769C2semidirect
2. #59550C2semidirect
3. #59544C2semidirect
4. #59489C2semidirect
5. #59462C2semidirect
6. #59451C2semidirect
7. #59104C2semidirect
8. #59081C2semidirect
9. #59066C2semidirect
10. #44749C2semidirect
11. #44388C2semidirect
12. #44057C2semidirect
13. #40214C2semidirect
14. #40050C2semidirect
15. #40007C2semidirect
16. #39912C2semidirect
17. #39243C2semidirect
18. #39029C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36459C2semidirect
21. #36457C2semidirect
22. #36410C2semidirect
23. #36399C2semidirect
24. #36381C2semidirect
25. #36300C2semidirect
26. #36150C2semidirect
27. #36117C2semidirect
28. #35896C2semidirect
29. #34955C2semidirect
30. #34951C2semidirect
31. #34947C2semidirect
32. #34316C2semidirect
33. #34242C2semidirect
34. C4×#552C2semidirect
35. C4×#548C2semidirect
905. C22⋊Q8#41semidirect
906. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597692
#595502
#595442
#594892
#594622
#594512
#591042
#590812
#590662
#447492
#443882
#440572
#402142
#400502
#400072
#399122
#392432
#390292
Q8×C22⋊Q82
#364592
#364572
#364102
#363992
#363812
#363002
#361502
#361172
#358962
#349552
#349512
#349472
#343162
#342422
C4×#5522
C4×#5482