Finite Group Databasebeta

← #7677816

Subgroups — #7677816

Order 512.

5263 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59815C211yesmaximal, characteristic, complemented
3#59764C212yesmaximal, complemented
4#59696C212yesmaximal, complemented
5#59504C212yesmaximal, complemented
6#59457C211yesmaximal, characteristic, complemented
7#59446C212yesmaximal, complemented
8#59442C211yesmaximal, characteristic, complemented
9#59214C211yesmaximal, characteristic, complemented
10#59211C211yesmaximal, characteristic, complemented
11#59039C211yesmaximal, characteristic, complemented
12#59039C211yesmaximal, characteristic, complemented
13#45406C212yesmaximal, complemented
14#45243C212yesmaximal, complemented
15#45035C212yesmaximal, complemented
16#45022C212yesmaximal, complemented
17#44267C214yesmaximal, complemented
18#44152C214yesmaximal, complemented
19#40393C214yesmaximal, complemented
20#40177C212yesmaximal, complemented
21#40141C212yesmaximal, complemented
22#38505C214yesmaximal, complemented
23#36462C212yesmaximal, complemented
24#36239C212yesmaximal, complemented
25#35551C212yesmaximal, complemented
26#35520C212yesmaximal, complemented
27#35189C212yesmaximal, complemented
28#35185C211yesmaximal, characteristic, complemented
29#34941C211yesmaximal, characteristic, complemented
30#34914C211yesmaximal, characteristic, complemented
31#34313C211yesmaximal, characteristic, complemented
32#34289C212yesmaximal, complemented
33#34226C211yesmaximal, characteristic, complemented
34C4×#550C211yesmaximal, characteristic, complemented
35C4×#541C211yesmaximal, characteristic, complemented
36C2×#550C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#547C2212yes—
39C2×#541C2211yescharacteristic
40C2×#532C2211yescharacteristic
41C2×#529C2212yes—
42C2×#520C2212yes—
43C2×C4×#41C2212yes—
44#2864C2212yes—
45#2860C2212yes—
46#2851C2214yes—
47#2850C2214yes—
48#2806C2214yes—
49#2780C2214yes—
50#2780C2214yes—
51#2779C2214yes—
52#2779C2214yes—
53#2761C2214yes—
54#2757C2214yes—
55#2756C2214yes—
56#2751C2214yes—
57#2751C2214yes—
58#2741C2214yes—
59#2740C2214yes—
60#2738C2214yes—
61#2714C2214yes—
62#2711C2214yes—
63#2711C2214yes—
64#2707C2214yes—
65#2706C2214yes—
66#2705C2214yes—
67#2705C2214yes—
68#2691C2214yes—
69#2686C2214yes—
70#2686C2214yes—
71#2682C2214yes—
72#2650C2214yes—
73#2630C2214yes—
74#2630C2214yes—
75#2602C2214yes—
76#2601C2214yes—
77#2601C2214yes—
78#2587C2214yes—
79#2584C2214yes—
80#2582C2212yes—
81#2582C2212yes—
82#2580C2212yes—
83#2577C2214yes—
84#2574C2214yes—
85#2573C2214yes—
86#2572C2214yes—
87#2571C2211yescharacteristic
88#2570C2212yes—
89#2570C2212yes—
90#2569C2214yes—
91#2569C2214yes—
92#2567C2211yescharacteristic
93#2567C2211yescharacteristic
94#2566C2212yes—
95#2566C2212yes—
96#2566C2212yes—
97#2563C2211yescharacteristic
98#2563C2211yescharacteristic
99#2562C2212yes—
100#2560C2214yes—
101#2560C2212yes—
102#2559C2212yes—
103#2559C2214yes—
104#2558C2214yes—
105#2558C2212yes—
106#2558C2214yes—
107#2557C2212yes—
108#2554C2214yes—
109#2552C2212yes—
110#2552C2211yescharacteristic
111#2552C2212yes—
112#2543C2214yes—
113#2541C2212yes—
114#2538C2212yes—
115#2538C2211yescharacteristic
116#2538C2211yescharacteristic
117#2538C2212yes—
118#2537C2212yes—
119#2537C2212yes—
120#2537C2212yes—
121#2536C2212yes—
122#2525C2214yes—
123#2518C2214yes—
124#2513C2212yes—
125#2513C2212yes—
126#2513C2212yes—
127#2512C2211yescharacteristic
128#2509C2212yes—
129#2509C2212yes—
130#2508C2212yes—
131#2507C2212yes—
132#2507C2212yes—
133#2506C2211yescharacteristic
134#2505C2214yes—
135#2505C2214yes—
136#2500C2212yes—
137#2497C2212yes—
138#2497C2212yes—
139#2496C2212yes—
140#2496C2211yescharacteristic
141#2495C2212yes—
142#2491C2211yescharacteristic
143#2488C2214yes—
144#2487C2212yes—
145#2486C2212yes—
146#2485C2212yes—
147#2485C2212yes—
148#2481C2214yes—
149#2479C2214yes—
150#2477C2214yes—
151#2476C2214yes—
152#2473C2214yes—
153#2473C2214yes—
154#2470C2214yes—
155#2469C2214yes—
156#2468C2214yes—
157#2464C2214yes—
158#2460C2214yes—
159#2460C2214yes—
160#2459C2214yes—
161#2458C2214yes—
162#2455C2214yes—
163#2454C2212yes—
164#2454C2212yes—
165#2452C2212yes—
166#2452C2211yescharacteristic
167#2450C2214yes—
168#2445C2212yes—
169#2445C2212yes—
170#2445C2212yes—
171#2445C2211yescharacteristic
172#2445C2212yes—
173#2445C2212yes—
174#2443C2214yes—
175#2441C2212yes—
176#2430C2214yes—
177#2430C2214yes—
178#2428C2211yescharacteristic
179#2428C2212yes—
180#2428C2212yes—
181#2425C2214yes—
182#2423C2212yes—
183#2422C2212yes—
184#2422C2211yescharacteristic
185#2422C2212yes—
186#2421C2212yes—
187#2420C2212yes—
188#2420C2212yes—
189#2419C2214yes—
190#2416C2214yes—
191#2415C2214yes—
192#2414C2214yes—
193#2407C2212yes—
194#2407C2212yes—
195#2407C2212yes—
196#2407C2212yes—
197#2398C2212yes—
198#2396C2214yes—
199#2392C2212yes—
200#2369C2212yes—
201#2367C2212yes—
202#2367C2212yes—
203#2366C2211yescharacteristic
204#2366C2212yes—
205#2366C2212yes—
206#2366C2211yescharacteristic
207#2365C2212yes—
208#2364C2214yes—
209#2363C2212yes—
210#2363C2212yes—
211#2363C2212yes—
212#2363C2212yes—
213#2363C2214yes—
214#2362C2212yes—
215#2361C2214yes—
216#2361C2212yes—
217#2360C2212yes—
218#2359C2214yes—
219#2359C2214yes—
220#2357C2212yes—
221#2357C2212yes—
222#2354C2211yescharacteristic
223#2354C2212yes—
224#2352C2212yes—
225Q8×C4⋊C4C2211yescharacteristic
226Q8×C4⋊C4C2211yescharacteristic
227#2349C2212yes—
228#2349C2212yes—
229#2349C2212yes—
230#2349C2212yes—
231#2349C2212yes—
232D4×C4⋊C4C2211yescharacteristic
233D4×C4⋊C4C2212yes—
234D4×C4⋊C4C2212yes—
235#2347C2212yes—
236#2344C2214yes—
237#2341C2212yes—
238#2341C2212yes—
239#2341C2212yes—
240#2339C2212yes—
241#2339C2212yes—
242#2339C2212yes—
243#2336C2212yes—
244#2336C2212yes—
245#2334C2212yes—
246#2334C2212yes—
247#2330C2211yescharacteristic
248#2327C2211yescharacteristic
249#2325C2214yes—
250#2324C2212yes—
251#2324C2214yes—
252#2324C2212yes—
253#2324C2212yes—
254#2323C2211yescharacteristic
255#2323C2211yescharacteristic
256#2323C2212yes—
257#2322C2214yes—
258#2320C2211yescharacteristic
259#2320C2211yescharacteristic
260#2319C2212yes—
261#2314C2211yescharacteristic
262#2314C2212yes—
263C4×C4⋊Q8C2211yescharacteristic
264C4×C4⋊Q8C2211yescharacteristic
265C4×C4⋊Q8C2211yescharacteristic
266C4×C4⋊Q8C2211yescharacteristic
267C4×#127C2212yes—
268C4×#127C2211yescharacteristic
269C4×#127C2211yescharacteristic
270C4×#127C2211yescharacteristic
271C4×#127C2212yes—
272C4×#125C2211yescharacteristic
273C4×#125C2212yes—
274C4×#125C2212yes—
275C4×#125C2212yes—
276C4×#126C2212yes—
277C4×#126C2212yes—
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2212yes—
281C4×#123C2214yes—
282C4×#121C2211yescharacteristic
283C4×#121C2211yescharacteristic
284C4×#121C2214yes—
285C4×#121C2212yes—
286#2293C2211yescharacteristic
287#2293C2212yes—
288#2293C2212yes—
289#2290C2212yes—
290C2×#387C2214yes—
291#2285C2211yescharacteristic
292#2285C2212yes—
293#2275C2212yes—
294C42×Q8C2211yescharacteristic
295C42×Q8C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C42×D4C2212yes—
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301C22×#41C2312yes—
302#550—28no—
303#550—28no—
304#547—216no—
305#541—28no—
306#532—28no—
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×#127C2312yes—
311C2×#127C2312yes—
312C2×#127C2311yescharacteristic
313C2×#127C2311yescharacteristic
314#529—48no—
315C2×#126C2312yes—
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2312yes—
319C2×#126C2314yes—
320C2×#125C2311yescharacteristic
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2312yes—
324C2×#125C2312yes—
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#123C2314yes—
329C2×#123C2314yes—
330C2×#123C2312yes—
331C2×#123C2312yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2314yes—
345C2×#121C2312yes—
346C2×#121C2311yescharacteristic
347C2×#121C2312yes—
348C2×#121C2314yes—
349C2×#121C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2314yes—
352C2×#121C2314yes—
353C2×#121C2314yes—
354#520—48no—
355C4×#41—48no—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2312yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2314yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2314yes—
396C2×#117C2312yes—
397C2×#117C2311yescharacteristic
398C2×#117C2311yescharacteristic
399C2×#117C2314yes—
400C2×#117C2314yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2314yes—
404C22×C4⋊C4C2314yes—
405C22×C4⋊C4C2314yes—
406C22×C4⋊C4C2312yes—
407C22×C42C2312yes—
408C22×C42C2311yescharacteristic
409C22×C42C2314yes—
410#400C2314yes—
411#400C2312yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2312yes—
418#400C2314yes—
419#400C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#398C2312yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#397C2314yes—
435#397C2312yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2312yes—
441#397C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2312yes—
455#396C2312yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#394C2312yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#393C2312yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2312yes—
485#392C2314yes—
486#392C2314yes—
487#392C2312yes—
488#392C2314yes—
489#392C2314yes—
490#391C2312yes—
491#391C2314yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2311yescharacteristic
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2311yescharacteristic
500#391C2311yescharacteristic
501#390C2312yes—
502#390C2314yes—
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2312yes—
515#390C2311yescharacteristic
516#390C2314yes—
517#390C2311yescharacteristic
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2311yescharacteristic
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2311yescharacteristic
530#390C2312yes—
531#390C2311yescharacteristic
532#390C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2311yescharacteristic
559#389C2311yescharacteristic
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2312yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2311yescharacteristic
572#389C2312yes—
573#389C2311yescharacteristic
574#389C2312yes—
575#389C2311yescharacteristic
576#388C2312yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2312yes—
581#388C2312yes—
582#388C2314yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2312yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2312yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2312yes—
651#386C2314yes—
652#386C2312yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2312yes—
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#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#385C2312yes—
690#385C2312yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2312yes—
700#384C2311yescharacteristic
701#384C2312yes—
702#384C2311yescharacteristic
703#384C2311yescharacteristic
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#383C2312yes—
708#383C2312yes—
709#383C2314yes—
710#382C2312yes—
711#382C2311yescharacteristic
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2312yes—
716#382C2312yes—
717#382C2312yes—
718#382C2314yes—
719#381C2314yes—
720#381C2314yes—
721#381C2314yes—
722#381C2314yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2314yes—
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2311yescharacteristic
736#380C2311yescharacteristic
737#380C2312yes—
738#380C2314yes—
739#380C2312yes—
740#380C2314yes—
741#380C2312yes—
742#380C2314yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808#376C2311yescharacteristic
809#376C2311yescharacteristic
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C2×#41—28no—
819C2×#41—28no—
820C2×#41—28no—
821C2×#41—28no—
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—82no—
826C2×#41—82no—
827C22×Q8C2411yescharacteristic
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2414yes—
834C22×D4C2414yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2414yes—
850C23×C4C2414yes—
851C23×C4C2412yes—
852C23×C4C2414yes—
853C23×C4C2414yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2411yescharacteristic
858C23×C4C2414yes—
859C23×C4C2414yes—
860C4⋊Q8—24no—
861C4⋊Q8—24no—
862C4⋊Q8#4118yescomplemented
863#127—28no—
864#127—28no—
865#127—42no—
866#127#4118yes—
867#126—28no—
868#126—28no—
869#126—44no—
870#126—44no—
871#126—84no—
872#125—28no—
873#125—28no—
874#125—24no—
875#125—44no—
876#125—44no—
877#125—84no—
878#124—28no—
879#124—44no—
880#123—216no—
881#123—216no—
882#123—44no—
883#123—44no—
884#123—84no—
885#123—84no—
886#123—84no—
887C22⋊Q8—24no—
888C22⋊Q8—24no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—44no—
892C22⋊Q8—84no—
893#121—28no—
894#121—28no—
895#121—28no—
896#121—28no—
897#121—216no—
898#121—216no—
899#121—216no—
900#121—24no—
901#121—44no—
902#121—42no—
903#121—84no—
904#121—84no—
905#121—84no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—24no—
911C4×Q8—24no—
912C4×Q8—44no—
913C4×Q8—44no—
914C4×Q8—44no—
915C4×Q8—82no—
916C4×Q8—82no—
917C4×D4—28no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—28no—
921C4×D4—24no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—28no—
925C4×D4—24no—
926C4×D4—24no—
927C4×D4—28no—
928C4×D4—48no—
929C4×D4—44no—
930C4×D4—42no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—44no—
935C4×D4—44no—
936C4×D4—48no—
937C4×D4—44no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—48no—
941C4×D4—48no—
942C4×D4—82no—
943C4×D4—84no—
944C4×D4—82no—
945C4×D4—84no—
946#117—24no—
947#117—28no—
948#117—24no—
949#117—48no—
950#117—48no—
951#117—44no—
952#117—44no—
953#117—84no—
954C2×C4⋊C4—216no—
955C2×C4⋊C4—48no—
956C2×C4⋊C4—44no—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C42—24no—
1084C2×C42—28no—
1085C2×C42—48no—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2412yes—
1106C2×C42C2411yescharacteristic
1107C2×C42C2412yes—
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2414yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2412yes—
1116C2×C42C2414yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2414yes—
1120C2×C42C2412yes—
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2411yescharacteristic
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190C24C2511yescharacteristic
1191C24C2512yes—
1192C24C2512yes—
1193C24C2514yes—
1194#41—432no—
1195#41—432no—
1196#41—816no—
1197C2×Q8—22no—
1198C2×Q8—22no—
1199C2×Q8—24no—
1200C2×Q8—22no—
1201C2×Q8—22no—
1202C2×Q8—24no—
1203C2×Q8—42no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8C2×#4114yes—
1208C2×Q8C2×#4114yes—
1209C2×D4—28no—
1210C2×D4—28no—
1211C2×D4—28no—
1212C2×D4—28no—
1213C2×D4—28no—
1214C2×D4—24no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—28no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—44no—
1229C2×D4—44no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—44no—
1236C2×D4—44no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—44no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4C2×#4118yes—
1249C2×D4C2×#4118yes—
1250C2×D4C2×#4118yes—
1251C22×C4—28no—
1252C22×C4—28no—
1253C22×C4—28no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—28no—
1258C22×C4—28no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—24no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—28no—
1272C22×C4—24no—
1273C22×C4—28no—
1274C22×C4—28no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4—42no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—42no—
1283C22×C4—44no—
1284C22×C4—44no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4C2511yescharacteristic
1297C22×C4C2511yescharacteristic
1298C22×C4C2511yescharacteristic
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2514yes—
1310C22×C4C2512yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2514yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2511yescharacteristic
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C4⋊C4—24no—
1328C4⋊C4—28no—
1329C4⋊C4—28no—
1330C4⋊C4—22no—
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—42no—
1394C4⋊C4C2×#4118yes—
1395C4⋊C4C2×#4118yes—
1396C4⋊C42−1+414yes—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—28no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—28no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C42—22no—
1454C42—22no—
1455C42—22no—
1456C42—22no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—24no—
1466C42—22no—
1467C42—24no—
1468C42—22no—
1469C42—24no—
1470C42—22no—
1471C42—22no—
1472C42—24no—
1473C42—22no—
1474C42—44no—
1475C42—44no—
1476C42—44no—
1477C42—44no—
1478C42—42no—
1479C42—44no—
1480C42—41no—
1481C42—42no—
1482C42—41no—
1483C42—42no—
1484C42—41no—
1485C42—41no—
1486C42—44no—
1487C42—42no—
1488C42C2×#4114yes—
1489C42C2×#4114yes—
1490C42H(5,𝔽2)14yes—
1491C23—24no—
1492C23—24no—
1493C23—24no—
1494C23—24no—
1495C23—24no—
1496C23—24no—
1497C23—21no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—21no—
1503C23—21no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—21no—
1509C23—21no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—21no—
1517C23—21no—
1518C23C22×#4118yes—
1519C23C2611yescharacteristic
1520Q8—28no—
1521Q8—28no—
1522Q8—48no—
1523Q8—84no—
1524D4—216no—
1525D4—216no—
1526D4—48no—
1527D4—416no—
1528D4—416no—
1529D4—44no—
1530D4—44no—
1531D4—84no—
1532D4—84no—
1533D4—88no—
1534D4—88no—
1535D4—88no—
1536D4—84no—
1537D4—84no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—24no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—24no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—48no—
1618C2×C4—416no—
1619C2×C4—416no—
1620C2×C4—44no—
1621C2×C4—44no—
1622C2×C4—48no—
1623C2×C4—48no—
1624C2×C4—44no—
1625C2×C4—88no—
1626C2×C4—88no—
1627C2×C4—84no—
1628C2×C4—88no—
1629C2×C4—88no—
1630C2×C4—164no—
1631C2×C4—164no—
1632C2×C4C22×#4112yes—
1633C2×C4C22×#4114yes—
1634C2×C4C22×#4114yes—
1635C2×C4C22×#4112yes—
1636C2×C4C22×#4112yes—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4112yes—
1639C2×C4C22×#4112yes—
1640C2×C4C2×H(5,𝔽2)12yes—
1641C2×C4C2×H(5,𝔽2)12yes—
1642C2×C4C2×H(5,𝔽2)12yes—
1643C2×C4C2×2−1+414yes—
1644C2×C4C2×2−1+412yes—
1645C2×C4#58512yes—
1646C22—28no—
1647C22—28no—
1648C22—28no—
1649C22—44no—
1650C22—44no—
1651C22—44no—
1652C22—44no—
1653C22—41no—
1654C22—42no—
1655C22—42no—
1656C22—42no—
1657C22—42no—
1658C22—41no—
1659C22—41no—
1660C22—42no—
1661C22—42no—
1662C22—41no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22—41no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—41no—
1671C22—42no—
1672C22—42no—
1673C22—41no—
1674C22C23×#4111yescharacteristic
1675C22C23×#4111yescharacteristic
1676C22C22×H(5,𝔽2)11yescharacteristic
1677C22C22×2−1+411yescharacteristic
1678C22C2×#58511yescharacteristic
1679C22H(7,𝔽2)11yescharacteristic
1680C22H(7,𝔽2)11yescharacteristic
1681C4—22no—
1682C4—22no—
1683C4—22no—
1684C4—22no—
1685C4—24no—
1686C4—22no—
1687C4—24no—
1688C4—24no—
1689C4—41no—
1690C4—42no—
1691C4—41no—
1692C4—42no—
1693C4—44no—
1694C4—41no—
1695C4—41no—
1696C4—44no—
1697C4—42no—
1698C4—42no—
1699C4—42no—
1700C4—42no—
1701C4—41no—
1702C4—42no—
1703C4—44no—
1704C4—42no—
1705C4—42no—
1706C4—41no—
1707C4—41no—
1708C4—42no—
1709C4—42no—
1710C4#348114yes—
1711C4#351514yes—
1712C2—48no—
1713C2—82no—
1714C2—82no—
1715C2—81no—
1716C2C2×#348111yescharacteristic
1717C2C2×#351511yescharacteristic
1718C2#6284611yescharacteristic
1719C2#6294411yescharacteristic
1720C2#6295511yescharacteristic
1721C2#6299911yescharacteristic
1722C2#6300611yescharacteristic
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. #59871C2semidirect
2. #59815C2semidirect
3. #59764C2semidirect
4. #59696C2semidirect
5. #59504C2semidirect
6. #59457C2semidirect
7. #59446C2semidirect
8. #59442C2semidirect
9. #59214C2semidirect
10. #59211C2semidirect
11. #59039C2semidirect
12. #59039C2semidirect
13. #45406C2semidirect
14. #45243C2semidirect
15. #45035C2semidirect
16. #45022C2semidirect
17. #44267C2semidirect
18. #44152C2semidirect
19. #40393C2semidirect
20. #40177C2semidirect
21. #40141C2semidirect
22. #38505C2semidirect
23. #36462C2semidirect
24. #36239C2semidirect
25. #35551C2semidirect
26. #35520C2semidirect
27. #35189C2semidirect
28. #35185C2semidirect
29. #34941C2semidirect
30. #34914C2semidirect
31. #34313C2semidirect
32. #34289C2semidirect
33. #34226C2semidirect
34. C4×#550C2semidirect
35. C4×#541C2semidirect
862. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598712
#598152
#597642
#596962
#595042
#594572
#594462
#594422
#592142
#592112
#590392
#454062
#452432
#450352
#450222
#442672
#441522
#403932
#401772
#401412
#385052
#364622
#362392
#355512
#355202
#351892
#351852
#349412
#349142
#343132
#342892
#342262
C4×#5502
C4×#5412