Finite Group Databasebeta

← #8467060

Subgroups — #8467060

Order 512.

4493 conjugacy classes of subgroups.

The subgroup lattice has 1686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59646C211yesmaximal, characteristic, complemented
2#59078C211yesmaximal, characteristic, complemented
3#59057C211yesmaximal, characteristic, complemented
4#57361C214yesmaximal, complemented
5#57132C214yesmaximal, complemented
6#55339C214yesmaximal, complemented
7#53134C212yesmaximal, complemented
8#53066C212yesmaximal, complemented
9#49603C214yesmaximal, complemented
10#46105C212yesmaximal, complemented
11#46083C212yesmaximal, complemented
12#44998C212yesmaximal, complemented
13#44944C212yesmaximal, complemented
14#42860C212yesmaximal, complemented
15#42778C212yesmaximal, complemented
16#42750C212yesmaximal, complemented
17#42715C212yesmaximal, complemented
18#39737C211yesmaximal, characteristic, complemented
19#39599C211yesmaximal, characteristic, complemented
20#39197C212yesmaximal, complemented
21#39173C211yesmaximal, characteristic, complemented
22#39002C212yesmaximal, complemented
23#38987C212yesmaximal, complemented
24#38921C211yesmaximal, characteristic, complemented
25#38289C212yesmaximal, complemented
26#37640C211yesmaximal, characteristic, complemented
27#37355C212yesmaximal, complemented
28#37329C212yesmaximal, complemented
29#36556C211yesmaximal, characteristic, complemented
30#36287C211yesmaximal, characteristic, complemented
31#36149C211yesmaximal, characteristic, complemented
32#35191C211yesmaximal, characteristic, complemented
33#35186C211yesmaximal, characteristic, complemented
34#34919C211yesmaximal, characteristic, complemented
35#34793C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C2×#532C2211yescharacteristic
40C2×#532C2211yescharacteristic
41C2×#529C2211yescharacteristic
42#2864C2212yes—
43#2862C2211yescharacteristic
44#2861C2212yes—
45#2861C2212yes—
46#2860C2212yes—
47#2859C2212yes—
48#2858C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2836C2214yes—
52#2829C2214yes—
53#2829C2214yes—
54#2828C2214yes—
55#2827C2214yes—
56#2827C2214yes—
57#2820C2214yes—
58#2813C2214yes—
59#2803C2214yes—
60#2803C2214yes—
61#2803C2214yes—
62#2800C2214yes—
63#2800C2214yes—
64#2797C2214yes—
65#2795C2214yes—
66#2786C2214yes—
67#2786C2214yes—
68#2783C2214yes—
69#2781C2214yes—
70#2781C2214yes—
71#2780C2214yes—
72#2780C2214yes—
73#2779C2214yes—
74#2773C2214yes—
75#2773C2214yes—
76#2772C2214yes—
77#2771C2214yes—
78#2768C2214yes—
79#2765C2214yes—
80#2761C2214yes—
81#2753C2214yes—
82#2752C2214yes—
83#2746C2214yes—
84#2744C2214yes—
85#2741C2214yes—
86#2741C2214yes—
87#2740C2214yes—
88#2740C2214yes—
89#2730C2214yes—
90#2730C2214yes—
91#2726C2214yes—
92#2721C2214yes—
93#2720C2214yes—
94#2711C2214yes—
95#2711C2214yes—
96#2707C2214yes—
97#2706C2214yes—
98#2705C2214yes—
99#2704C2214yes—
100#2701C2214yes—
101#2698C2214yes—
102#2698C2214yes—
103#2691C2214yes—
104#2690C2214yes—
105#2690C2214yes—
106#2690C2214yes—
107#2680C2214yes—
108#2661C2214yes—
109#2652C2214yes—
110#2651C2214yes—
111#2651C2214yes—
112#2649C2214yes—
113#2646C2214yes—
114#2644C2214yes—
115#2642C2212yes—
116#2629C2212yes—
117#2625C2212yes—
118#2624C2212yes—
119#2624C2212yes—
120#2620C2212yes—
121#2620C2212yes—
122#2620C2212yes—
123#2616C2214yes—
124#2612C2214yes—
125#2603C2214yes—
126#2602C2214yes—
127#2597C2214yes—
128#2593C2214yes—
129#2588C2214yes—
130#2584C2212yes—
131#2582C2212yes—
132#2582C2211yescharacteristic
133#2567C2211yescharacteristic
134#2567C2211yescharacteristic
135#2565C2212yes—
136#2564C2214yes—
137#2562C2212yes—
138#2560C2212yes—
139#2558C2212yes—
140#2556C2214yes—
141#2552C2212yes—
142#2552C2211yescharacteristic
143#2550C2211yescharacteristic
144#2548C2211yescharacteristic
145#2548C2211yescharacteristic
146#2548C2212yes—
147#2548C2211yescharacteristic
148#2547C2211yescharacteristic
149#2547C2212yes—
150#2547C2212yes—
151#2546C2212yes—
152#2546C2211yescharacteristic
153#2545C2211yescharacteristic
154#2545C2212yes—
155#2542C2212yes—
156#2541C2211yescharacteristic
157#2540C2212yes—
158#2540C2211yescharacteristic
159#2538C2212yes—
160#2538C2212yes—
161#2536C2211yescharacteristic
162#2535C2212yes—
163#2530C2212yes—
164#2529C2214yes—
165#2528C2212yes—
166#2526C2214yes—
167#2520C2214yes—
168#2519C2212yes—
169#2517C2212yes—
170#2516C2214yes—
171#2513C2212yes—
172#2513C2214yes—
173#2512C2212yes—
174#2511C2212yes—
175#2511C2212yes—
176#2511C2211yescharacteristic
177#2509C2212yes—
178#2508C2212yes—
179#2506C2211yescharacteristic
180#2506C2212yes—
181#2505C2214yes—
182#2500C2212yes—
183#2499C2211yescharacteristic
184#2497C2214yes—
185#2497C2212yes—
186#2497C2212yes—
187#2494C2211yescharacteristic
188#2491C2211yescharacteristic
189#2490C2212yes—
190#2490C2212yes—
191#2490C2212yes—
192#2489C2212yes—
193#2489C2211yescharacteristic
194#2489C2211yescharacteristic
195#2488C2214yes—
196#2486C2212yes—
197#2485C2212yes—
198#2485C2211yescharacteristic
199#2468C2214yes—
200#2461C2212yes—
201#2461C2214yes—
202#2460C2214yes—
203#2460C2212yes—
204#2454C2212yes—
205#2454C2214yes—
206#2454C2212yes—
207#2454C2212yes—
208#2451C2212yes—
209#2448C2212yes—
210#2448C2212yes—
211#2448C2212yes—
212#2447C2212yes—
213#2447C2212yes—
214#2447C2212yes—
215#2447C2212yes—
216#2446C2212yes—
217#2445C2212yes—
218#2442C2212yes—
219#2442C2212yes—
220#2441C2212yes—
221#2441C2212yes—
222#2441C2211yescharacteristic
223#2432C2212yes—
224#2432C2212yes—
225#2431C2212yes—
226#2429C2212yes—
227#2429C2211yescharacteristic
228#2429C2212yes—
229#2428C2212yes—
230#2427C2212yes—
231#2427C2212yes—
232#2427C2212yes—
233#2426C2212yes—
234#2426C2211yescharacteristic
235#2423C2212yes—
236#2422C2212yes—
237#2422C2212yes—
238#2421C2212yes—
239#2421C2212yes—
240#2420C2212yes—
241#2420C2212yes—
242#2416C2212yes—
243#2415C2212yes—
244#2415C2211yescharacteristic
245#2414C2212yes—
246#2414C2212yes—
247#2407C2212yes—
248#2407C2214yes—
249#2407C2212yes—
250#2401C2212yes—
251#2396C2212yes—
252#2395C2212yes—
253#2392C2212yes—
254#2378C2214yes—
255#2370C2212yes—
256#2369C2211yescharacteristic
257#2367C2212yes—
258#2367C2212yes—
259#2366C2212yes—
260#2365C2211yescharacteristic
261#2365C2212yes—
262#2363C2212yes—
263#2361C2212yes—
264#2355C2212yes—
265#2354C2211yescharacteristic
266Q8×C4⋊C4C2211yescharacteristic
267#2349C2212yes—
268#2346C2212yes—
269#2341C2212yes—
270#2339C2212yes—
271#2339C2212yes—
272#2326C2212yes—
273#2326C2212yes—
274#2324C2212yes—
275#2324C2212yes—
276#2323C2212yes—
277#2323C2212yes—
278#2319C2214yes—
279#2319C2212yes—
280#2317C2212yes—
281C4×#127C2211yescharacteristic
282C4×#125C2212yes—
283C4×#125C2212yes—
284C4×#125C2211yescharacteristic
285C4×#124C2212yes—
286C4×#124C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×C22⋊Q8C2211yescharacteristic
289C4×C22⋊Q8C2211yescharacteristic
290C4×#121C2211yescharacteristic
291#2298C2212yes—
292#2295C2211yescharacteristic
293#2295C2212yes—
294#2293C2212yes—
295#2285C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301#557—44no—
302#554—44no—
303#533—44no—
304#532—44no—
305#532—44no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2311yescharacteristic
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×#127C2311yescharacteristic
313C2×#127C2312yes—
314#529—44no—
315C2×#126C2312yes—
316C2×#126C2314yes—
317C2×#125C2311yescharacteristic
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2311yescharacteristic
324C2×#125C2314yes—
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2311yescharacteristic
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2311yescharacteristic
335C2×#123C2312yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2311yescharacteristic
359C2×#121C2314yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C42C2311yescharacteristic
393C22×C42C2311yescharacteristic
394#401C2312yes—
395#400C2314yes—
396#400C2312yes—
397#400C2312yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2312yes—
410#400C2312yes—
411#399C2314yes—
412#399C2314yes—
413#399C2314yes—
414#399C2312yes—
415#399C2314yes—
416#399C2314yes—
417#399C2314yes—
418#399C2312yes—
419#399C2314yes—
420#398C2312yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2312yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2312yes—
438#397C2312yes—
439#397C2314yes—
440#397C2314yes—
441#397C2312yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2312yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2312yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2312yes—
459#397C2312yes—
460#397C2314yes—
461#397C2312yes—
462#397C2314yes—
463#397C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2312yes—
477#396C2314yes—
478#396C2312yes—
479#396C2312yes—
480#396C2312yes—
481#396C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2312yes—
486#394C2312yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2312yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2312yes—
500#394C2312yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#393C2312yes—
514#392C2312yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2312yes—
528#391C2311yescharacteristic
529#391C2314yes—
530#391C2312yes—
531#391C2314yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#391C2311yescharacteristic
536#391C2312yes—
537#391C2312yes—
538#391C2311yescharacteristic
539#391C2311yescharacteristic
540#391C2311yescharacteristic
541#391C2311yescharacteristic
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2314yes—
547#390C2312yes—
548#390C2314yes—
549#390C2312yes—
550#390C2314yes—
551#390C2314yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2312yes—
557#390C2311yescharacteristic
558#390C2312yes—
559#390C2314yes—
560#390C2312yes—
561#390C2314yes—
562#390C2314yes—
563#390C2312yes—
564#390C2312yes—
565#390C2312yes—
566#390C2312yes—
567#390C2311yescharacteristic
568#390C2314yes—
569#390C2312yes—
570#390C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2311yescharacteristic
575#389C2312yes—
576#389C2311yescharacteristic
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#389C2312yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2312yes—
589#389C2314yes—
590#389C2312yes—
591#389C2314yes—
592#389C2311yescharacteristic
593#389C2314yes—
594#389C2314yes—
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2314yes—
599#389C2311yescharacteristic
600#389C2312yes—
601#389C2312yes—
602#389C2314yes—
603#389C2311yescharacteristic
604#389C2312yes—
605#389C2312yes—
606#389C2314yes—
607#389C2311yescharacteristic
608#389C2312yes—
609#389C2311yescharacteristic
610#389C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2312yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2312yes—
649#388C2312yes—
650#388C2312yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#388C2312yes—
656#388C2312yes—
657#388C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2312yes—
661#387C2314yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2314yes—
666#387C2312yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2312yes—
684#387C2312yes—
685#387C2312yes—
686#387C2312yes—
687#387C2312yes—
688#387C2312yes—
689#387C2314yes—
690#387C2312yes—
691#387C2312yes—
692#386C2312yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2312yes—
717#385C2312yes—
718#385C2314yes—
719#385C2312yes—
720#384C2311yescharacteristic
721#384C2312yes—
722#384C2312yes—
723#384C2314yes—
724#384C2312yes—
725#384C2312yes—
726#384C2311yescharacteristic
727#384C2311yescharacteristic
728#382C2312yes—
729#382C2311yescharacteristic
730#382C2312yes—
731#382C2312yes—
732#382C2311yescharacteristic
733#382C2314yes—
734#382C2314yes—
735#382C2312yes—
736#382C2314yes—
737#382C2312yes—
738#381C2314yes—
739#381C2314yes—
740#381C2314yes—
741#381C2314yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2311yescharacteristic
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2311yescharacteristic
755#380C2312yes—
756#380C2314yes—
757#380C2312yes—
758#380C2314yes—
759#380C2311yescharacteristic
760#380C2311yescharacteristic
761#380C2314yes—
762#380C2314yes—
763#380C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809#376C2312yes—
810#376C2314yes—
811#376C2312yes—
812C2×#95C2314yes—
813C43C2311yescharacteristic
814C43C2312yes—
815C43C2312yes—
816C2×#41—44no—
817C2×#41—44no—
818C2×#41—44no—
819C2×#41—44no—
820C2×#41—44no—
821C2×#41—82no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2411yescharacteristic
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×D4C2412yes—
829C22×D4C2411yescharacteristic
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2414yes—
833C22×D4C2411yescharacteristic
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2414yes—
837C22×D4C2414yes—
838C22×D4C2414yes—
839C23×C4C2412yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2414yes—
846C23×C4C2411yescharacteristic
847C23×C4C2414yes—
848C23×C4C2414yes—
849C23×C4C2414yes—
850C4⋊Q8—24no—
851C4⋊Q8—24no—
852C4⋊Q8—42no—
853C4⋊Q8—44no—
854C4⋊Q8—42no—
855C4⋊Q8—44no—
856#127—24no—
857#127—44no—
858#126—44no—
859#126—84no—
860#125—24no—
861#125—44no—
862#125—42no—
863#125—44no—
864#125—44no—
865#125—44no—
866#125—44no—
867#125—48no—
868#125—84no—
869#124—44no—
870#124—44no—
871#124—44no—
872#124—42no—
873#124—44no—
874#124—42no—
875#124—44no—
876#124—44no—
877#124—44no—
878#123—44no—
879#123—84no—
880#123—84no—
881C22⋊Q8—24no—
882C22⋊Q8—48no—
883C22⋊Q8—44no—
884C22⋊Q8—42no—
885C22⋊Q8—44no—
886C22⋊Q8—42no—
887C22⋊Q8—48no—
888C22⋊Q8—42no—
889C22⋊Q8—42no—
890C22⋊Q8—42no—
891C22⋊Q8—44no—
892C22⋊Q8—82no—
893C22⋊Q8—84no—
894#121—28no—
895#121—44no—
896#121—42no—
897#121—42no—
898#121—44no—
899#121—44no—
900#121—44no—
901#121—44no—
902#121—84no—
903C4×Q8—24no—
904C4×Q8—24no—
905C4×Q8—24no—
906C4×Q8—44no—
907C4×Q8—44no—
908C4×Q8—42no—
909C4×Q8—42no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—44no—
913C4×D4—24no—
914C4×D4—44no—
915C4×D4—44no—
916C4×D4—44no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—42no—
922C4×D4—42no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—48no—
926C4×D4—42no—
927C4×D4—82no—
928#117—24no—
929#117—44no—
930#117—44no—
931#117—44no—
932#117—44no—
933#117—42no—
934C2×C4⋊C4—44no—
935C2×C4⋊C4C2411yescharacteristic
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2411yescharacteristic
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C42—24no—
1068C2×C42—24no—
1069C2×C42C2411yescharacteristic
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2414yes—
1092C2×C42C2414yes—
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2411yescharacteristic
1121#95C2412yes—
1122#95C2411yescharacteristic
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2411yescharacteristic
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172C24C2512yes—
1173C24C2511yescharacteristic
1174C24C2514yes—
1175C24C2511yescharacteristic
1176#41—816no—
1177#41—816no—
1178C2×Q8—22no—
1179C2×Q8—22no—
1180C2×Q8—22no—
1181C2×Q8—24no—
1182C2×Q8—24no—
1183C2×Q8—22no—
1184C2×Q8—22no—
1185C2×Q8—22no—
1186C2×Q8—24no—
1187C2×Q8—22no—
1188C2×Q8—22no—
1189C2×Q8—24no—
1190C2×Q8—22no—
1191C2×Q8—24no—
1192C2×Q8—42no—
1193C2×Q8—42no—
1194C2×Q8—42no—
1195C2×Q8—42no—
1196C2×D4—22no—
1197C2×D4—24no—
1198C2×D4—24no—
1199C2×D4—24no—
1200C2×D4—24no—
1201C2×D4—28no—
1202C2×D4—24no—
1203C2×D4—24no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—24no—
1207C2×D4—41no—
1208C2×D4—41no—
1209C2×D4—41no—
1210C2×D4—42no—
1211C2×D4—42no—
1212C2×D4—42no—
1213C2×D4—44no—
1214C2×D4—42no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—42no—
1218C2×D4—42no—
1219C2×D4—44no—
1220C2×D4—42no—
1221C2×D4—42no—
1222C2×D4—44no—
1223C2×D4—44no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—44no—
1228C2×D4—44no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—24no—
1235C22×C4—22no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—28no—
1248C22×C4—41no—
1249C22×C4—44no—
1250C22×C4—44no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—44no—
1254C22×C4—44no—
1255C22×C4—44no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4C2511yescharacteristic
1263C22×C4C2511yescharacteristic
1264C22×C4C2511yescharacteristic
1265C22×C4C2511yescharacteristic
1266C22×C4C2511yescharacteristic
1267C22×C4C2512yes—
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2511yescharacteristic
1271C22×C4C2512yes—
1272C22×C4C2511yescharacteristic
1273C22×C4C2512yes—
1274C22×C4C2514yes—
1275C22×C4C2514yes—
1276C22×C4C2512yes—
1277C22×C4C2512yes—
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2514yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2512yes—
1288C22×C4C2511yescharacteristic
1289C22×C4C2512yes—
1290C22×C4C2511yescharacteristic
1291C22×C4C2511yescharacteristic
1292C22×C4C2511yescharacteristic
1293C4⋊C4—22no—
1294C4⋊C4—24no—
1295C4⋊C4—22no—
1296C4⋊C4—24no—
1297C4⋊C4—24no—
1298C4⋊C4—24no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—24no—
1302C4⋊C4—24no—
1303C4⋊C4—24no—
1304C4⋊C4—22no—
1305C4⋊C4—24no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—22no—
1312C4⋊C4—22no—
1313C4⋊C4—24no—
1314C4⋊C4—24no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—44no—
1320C4⋊C4—42no—
1321C4⋊C4—42no—
1322C4⋊C4—42no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—42no—
1326C4⋊C4—41no—
1327C4⋊C4—42no—
1328C4⋊C4—41no—
1329C4⋊C4—42no—
1330C4⋊C4—42no—
1331C4⋊C4—44no—
1332C4⋊C4—42no—
1333C4⋊C4—44no—
1334C4⋊C4—42no—
1335C4⋊C4—42no—
1336C4⋊C4—42no—
1337C4⋊C4—42no—
1338C4⋊C4—44no—
1339C4⋊C4—44no—
1340C4⋊C4—44no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—44no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—42no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—42no—
1361C4⋊C4—44no—
1362C4⋊C4—42no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C42−1+414yes—
1366C22⋊C4—24no—
1367C22⋊C4—24no—
1368C22⋊C4—28no—
1369C22⋊C4—24no—
1370C22⋊C4—24no—
1371C22⋊C4—22no—
1372C22⋊C4—42no—
1373C22⋊C4—42no—
1374C22⋊C4—44no—
1375C22⋊C4—42no—
1376C22⋊C4—42no—
1377C22⋊C4—42no—
1378C22⋊C4—42no—
1379C22⋊C4—42no—
1380C22⋊C4—44no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—42no—
1384C22⋊C4—42no—
1385C22⋊C4—44no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—44no—
1390C22⋊C4—44no—
1391C22⋊C4—44no—
1392C22⋊C4—44no—
1393C22⋊C4—44no—
1394C22⋊C4—44no—
1395C22⋊C4—42no—
1396C22⋊C4—42no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—44no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—44no—
1405C22⋊C4—44no—
1406C22⋊C4—44no—
1407C22⋊C4—44no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—44no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C42—22no—
1426C42—22no—
1427C42—22no—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—24no—
1432C42—24no—
1433C42—24no—
1434C42—24no—
1435C42—22no—
1436C42—24no—
1437C42—24no—
1438C42—22no—
1439C42—22no—
1440C42—22no—
1441C42—24no—
1442C42—24no—
1443C42—44no—
1444C42—42no—
1445C42—44no—
1446C42—41no—
1447C42—41no—
1448C42—44no—
1449C42—42no—
1450C42—42no—
1451C42—44no—
1452C42—44no—
1453C42—42no—
1454C42—42no—
1455C42—42no—
1456C42—42no—
1457C42H(5,𝔽2)14yes—
1458C23—22no—
1459C23—21no—
1460C23—24no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—24no—
1465C23—22no—
1466C23—21no—
1467C23—22no—
1468C23—22no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—24no—
1473C23—24no—
1474C23—21no—
1475C23—22no—
1476C23—24no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—24no—
1481C23—22no—
1482C23—21no—
1483C23—24no—
1484C23—22no—
1485C23—21no—
1486C23C2611yescharacteristic
1487Q8—44no—
1488Q8—44no—
1489Q8—48no—
1490Q8—44no—
1491Q8—84no—
1492Q8—84no—
1493D4—48no—
1494D4—44no—
1495D4—44no—
1496D4—48no—
1497D4—48no—
1498D4—88no—
1499D4—84no—
1500D4—84no—
1501D4—88no—
1502D4—88no—
1503D4—164no—
1504C2×C4—21no—
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—24no—
1522C2×C4—22no—
1523C2×C4—24no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—21no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—24no—
1557C2×C4—24no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—24no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—24no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—24no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—24no—
1588C2×C4—44no—
1589C2×C4—44no—
1590C2×C4—44no—
1591C2×C4—44no—
1592C2×C4—44no—
1593C2×C4—48no—
1594C2×C4—82no—
1595C2×C4—88no—
1596C2×C4—88no—
1597C2×C4—164no—
1598C2×C4—164no—
1599C2×C4C2×H(5,𝔽2)12yes—
1600C2×C4C2×H(5,𝔽2)12yes—
1601C2×C4C2×H(5,𝔽2)12yes—
1602C2×C4C2×2−1+414yes—
1603C2×C4C2×2−1+412yes—
1604C2×C4#58512yes—
1605C2×C4#58512yes—
1606C2×C4#58512yes—
1607C2×C4#58512yes—
1608C22—41no—
1609C22—41no—
1610C22—44no—
1611C22—42no—
1612C22—42no—
1613C22—41no—
1614C22—41no—
1615C22—44no—
1616C22—42no—
1617C22—44no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—42no—
1623C22—44no—
1624C22—41no—
1625C22—44no—
1626C22—41no—
1627C22—42no—
1628C22—41no—
1629C22—41no—
1630C22—44no—
1631C22—42no—
1632C22—44no—
1633C22—41no—
1634C22—42no—
1635C22—41no—
1636C22C22×H(5,𝔽2)11yescharacteristic
1637C22C22×2−1+411yescharacteristic
1638C22C2×#58511yescharacteristic
1639C22C2×#58511yescharacteristic
1640C22C2×#58511yescharacteristic
1641C22C2×#58511yescharacteristic
1642C22H(7,𝔽2)11yescharacteristic
1643C4—24no—
1644C4—22no—
1645C4—22no—
1646C4—41no—
1647C4—41no—
1648C4—44no—
1649C4—42no—
1650C4—42no—
1651C4—41no—
1652C4—41no—
1653C4—42no—
1654C4—42no—
1655C4—41no—
1656C4—42no—
1657C4—42no—
1658C4—42no—
1659C4—41no—
1660C4—41no—
1661C4—44no—
1662C4—42no—
1663C4—42no—
1664C4—42no—
1665C4—42no—
1666C4—41no—
1667C4—42no—
1668C4—44no—
1669C4—41no—
1670C4—42no—
1671C4—42no—
1672C4#355114yes—
1673C4#355414yes—
1674C2—81no—
1675C2—81no—
1676C2—84no—
1677C2—82no—
1678C2C2×#355111yescharacteristic
1679C2C2×#355411yescharacteristic
1680C2#6284011yescharacteristic
1681C2#6292411yescharacteristic
1682C2#6295211yescharacteristic
1683C2#6296611yescharacteristic
1684C2#6302511yescharacteristic
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. #59646C2semidirect
2. #59078C2semidirect
3. #59057C2semidirect
4. #57361C2semidirect
5. #57132C2semidirect
6. #55339C2semidirect
7. #53134C2semidirect
8. #53066C2semidirect
9. #49603C2semidirect
10. #46105C2semidirect
11. #46083C2semidirect
12. #44998C2semidirect
13. #44944C2semidirect
14. #42860C2semidirect
15. #42778C2semidirect
16. #42750C2semidirect
17. #42715C2semidirect
18. #39737C2semidirect
19. #39599C2semidirect
20. #39197C2semidirect
21. #39173C2semidirect
22. #39002C2semidirect
23. #38987C2semidirect
24. #38921C2semidirect
25. #38289C2semidirect
26. #37640C2semidirect
27. #37355C2semidirect
28. #37329C2semidirect
29. #36556C2semidirect
30. #36287C2semidirect
31. #36149C2semidirect
32. #35191C2semidirect
33. #35186C2semidirect
34. #34919C2semidirect
35. #34793C2semidirect

Maximal subgroups

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

subgroupindex
#596462
#590782
#590572
#573612
#571322
#553392
#531342
#530662
#496032
#461052
#460832
#449982
#449442
#428602
#427782
#427502
#427152
#397372
#395992
#391972
#391732
#390022
#389872
#389212
#382892
#376402
#373552
#373292
#365562
#362872
#361492
#351912
#351862
#349192
#347932