Finite Group Databasebeta

← #8467091

Subgroups — #8467091

Order 512.

5298 conjugacy classes of subgroups.

The subgroup lattice has 1837 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59429C211yesmaximal, characteristic, complemented
2#59135C211yesmaximal, characteristic, complemented
3#59039C211yesmaximal, characteristic, complemented
4#55375C214yesmaximal, complemented
5#55342C214yesmaximal, complemented
6#53666C214yesmaximal, complemented
7#53057C212yesmaximal, complemented
8#52957C212yesmaximal, complemented
9#47937C214yesmaximal, complemented
10#45486C212yesmaximal, complemented
11#45484C212yesmaximal, complemented
12#45035C212yesmaximal, complemented
13#44889C212yesmaximal, complemented
14#42989C212yesmaximal, complemented
15#42907C212yesmaximal, complemented
16#42608C212yesmaximal, complemented
17#42465C212yesmaximal, complemented
18#40077C212yesmaximal, complemented
19#39984C212yesmaximal, complemented
20#39607C211yesmaximal, characteristic, complemented
21#39562C212yesmaximal, complemented
22#39469C211yesmaximal, characteristic, complemented
23#39352C211yesmaximal, characteristic, complemented
24#39201C211yesmaximal, characteristic, complemented
25#38033C212yesmaximal, complemented
26#37639C211yesmaximal, characteristic, complemented
27#37316C212yesmaximal, complemented
28#37276C212yesmaximal, complemented
29#36455C211yesmaximal, characteristic, complemented
30#36412C211yesmaximal, characteristic, complemented
31#36122C211yesmaximal, characteristic, complemented
32#35279C211yesmaximal, characteristic, complemented
33#35207C211yesmaximal, characteristic, complemented
34#34932C211yesmaximal, characteristic, complemented
35#34715C211yesmaximal, characteristic, complemented
36C2×#562C2214yes—
37C2×#555C2211yescharacteristic
38C2×#550C2211yescharacteristic
39C2×#550C2212yes—
40C2×#548C2212yes—
41C2×#540C2212yes—
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C22×C4⋊Q8C2211yescharacteristic
45C2×#529C2212yes—
46C2×C4×#41C2211yescharacteristic
47#2858C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2212yes—
50#2857C2212yes—
51#2856C2211yescharacteristic
52#2856C2212yes—
53#2856C2212yes—
54#2854C2212yes—
55#2851C2212yes—
56#2829C2214yes—
57#2829C2214yes—
58#2828C2214yes—
59#2824C2214yes—
60#2819C2214yes—
61#2816C2214yes—
62#2813C2214yes—
63#2813C2214yes—
64#2808C2214yes—
65#2804C2214yes—
66#2798C2214yes—
67#2788C2214yes—
68#2787C2214yes—
69#2784C2214yes—
70#2780C2214yes—
71#2779C2214yes—
72#2778C2214yes—
73#2755C2214yes—
74#2741C2214yes—
75#2733C2214yes—
76#2731C2214yes—
77#2730C2214yes—
78#2730C2214yes—
79#2712C2214yes—
80#2712C2214yes—
81#2711C2214yes—
82#2710C2214yes—
83#2710C2214yes—
84#2709C2214yes—
85#2707C2214yes—
86#2706C2214yes—
87#2705C2214yes—
88#2704C2214yes—
89#2703C2214yes—
90#2703C2214yes—
91#2696C2214yes—
92#2694C2214yes—
93#2692C2214yes—
94#2691C2214yes—
95#2688C2214yes—
96#2687C2214yes—
97#2686C2214yes—
98#2682C2214yes—
99#2681C2214yes—
100#2681C2214yes—
101#2676C2214yes—
102#2676C2214yes—
103#2676C2214yes—
104#2676C2214yes—
105#2675C2214yes—
106#2673C2214yes—
107#2673C2214yes—
108#2672C2214yes—
109#2671C2214yes—
110#2671C2214yes—
111#2671C2214yes—
112#2671C2214yes—
113#2665C2214yes—
114#2653C2214yes—
115#2653C2214yes—
116#2653C2214yes—
117#2648C2214yes—
118#2630C2214yes—
119#2629C2212yes—
120#2628C2214yes—
121#2624C2212yes—
122#2624C2212yes—
123#2619C2212yes—
124#2619C2212yes—
125#2615C2214yes—
126#2615C2212yes—
127#2615C2212yes—
128#2615C2212yes—
129#2607C2214yes—
130#2581C2212yes—
131#2580C2212yes—
132#2570C2212yes—
133#2569C2214yes—
134#2568C2212yes—
135#2567C2211yescharacteristic
136#2567C2211yescharacteristic
137#2563C2211yescharacteristic
138#2563C2212yes—
139#2563C2211yescharacteristic
140#2563C2211yescharacteristic
141#2563C2211yescharacteristic
142#2559C2214yes—
143#2557C2214yes—
144#2555C2214yes—
145#2555C2214yes—
146#2555C2214yes—
147#2553C2212yes—
148#2553C2212yes—
149#2552C2211yescharacteristic
150#2552C2211yescharacteristic
151#2552C2212yes—
152#2548C2212yes—
153#2547C2211yescharacteristic
154#2545C2212yes—
155#2543C2214yes—
156#2542C2212yes—
157#2542C2211yescharacteristic
158#2541C2211yescharacteristic
159#2541C2211yescharacteristic
160#2541C2212yes—
161#2541C2212yes—
162#2538C2212yes—
163#2537C2212yes—
164#2537C2212yes—
165#2537C2211yescharacteristic
166#2537C2212yes—
167#2537C2212yes—
168#2537C2211yescharacteristic
169#2537C2212yes—
170#2535C2212yes—
171#2513C2212yes—
172#2507C2212yes—
173#2506C2212yes—
174#2501C2212yes—
175#2500C2212yes—
176#2497C2212yes—
177#2497C2212yes—
178#2497C2212yes—
179#2497C2212yes—
180#2496C2211yescharacteristic
181#2496C2211yescharacteristic
182#2494C2212yes—
183#2494C2212yes—
184#2491C2212yes—
185#2491C2212yes—
186#2491C2212yes—
187#2491C2212yes—
188#2491C2212yes—
189#2490C2212yes—
190#2489C2212yes—
191#2487C2212yes—
192#2487C2212yes—
193#2485C2212yes—
194#2476C2212yes—
195#2474C2212yes—
196#2467C2214yes—
197#2465C2214yes—
198#2460C2214yes—
199#2460C2214yes—
200#2459C2212yes—
201#2458C2214yes—
202#2457C2214yes—
203#2456C2212yes—
204#2454C2212yes—
205#2453C2212yes—
206#2452C2212yes—
207#2452C2212yes—
208#2451C2211yescharacteristic
209#2445C2212yes—
210#2445C2212yes—
211#2445C2211yescharacteristic
212#2445C2212yes—
213#2440C2212yes—
214#2439C2212yes—
215#2439C2212yes—
216#2439C2212yes—
217#2439C2211yescharacteristic
218#2436C2212yes—
219#2436C2214yes—
220#2432C2212yes—
221#2431C2212yes—
222#2431C2211yescharacteristic
223#2430C2214yes—
224#2428C2212yes—
225#2428C2212yes—
226#2428C2212yes—
227#2428C2214yes—
228#2428C2214yes—
229#2428C2212yes—
230#2428C2212yes—
231#2427C2212yes—
232#2426C2211yescharacteristic
233#2425C2214yes—
234#2422C2212yes—
235#2422C2211yescharacteristic
236#2422C2211yescharacteristic
237#2422C2212yes—
238#2422C2212yes—
239#2422C2212yes—
240#2420C2211yescharacteristic
241#2420C2212yes—
242#2416C2212yes—
243#2416C2212yes—
244#2416C2212yes—
245#2416C2212yes—
246#2416C2212yes—
247#2416C2212yes—
248#2414C2212yes—
249#2414C2214yes—
250#2414C2212yes—
251#2414C2211yescharacteristic
252#2409C2214yes—
253#2407C2211yescharacteristic
254#2407C2212yes—
255#2395C2212yes—
256#2395C2212yes—
257#2392C2212yes—
258#2388C2212yes—
259#2369C2211yescharacteristic
260#2367C2212yes—
261#2366C2211yescharacteristic
262#2363C2212yes—
263#2363C2212yes—
264#2361C2212yes—
265#2361C2212yes—
266#2352C2212yes—
267#2352C2212yes—
268Q8×C4⋊C4C2211yescharacteristic
269#2349C2212yes—
270D4×C4⋊C4C2211yescharacteristic
271#2345C2212yes—
272#2341C2212yes—
273#2339C2212yes—
274#2329C2214yes—
275#2324C2212yes—
276#2324C2212yes—
277#2323C2212yes—
278#2317C2212yes—
279#2314C2212yes—
280#2311C2212yes—
281#2311C2212yes—
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2211yescharacteristic
284C4×#124C2211yescharacteristic
285C4×C22⋊Q8C2212yes—
286C4×C22⋊Q8C2211yescharacteristic
287C4×#123C2212yes—
288C4×#121C2211yescharacteristic
289C4×#121C2211yescharacteristic
290C4×#121C2212yes—
291C4×#121C2211yescharacteristic
292#2297C2212yes—
293#2297C2212yes—
294#2293C2211yescharacteristic
295#2285C2211yescharacteristic
296#2285C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303C23×Q8C2312yes—
304#562—416no—
305#555—44no—
306#550—44no—
307#550—48no—
308#548—48no—
309#540—48no—
310#532—44no—
311#532—44no—
312C2×C4⋊Q8—44no—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×#127C2311yescharacteristic
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2314yes—
325C2×#127C2311yescharacteristic
326#529—48no—
327C2×#126C2312yes—
328C2×#126C2312yes—
329C2×#125C2312yes—
330C2×#125C2312yes—
331C2×#125C2314yes—
332C2×#124C2311yescharacteristic
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2314yes—
339C2×#124C2314yes—
340C2×#124C2314yes—
341C2×#124C2312yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2312yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2312yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2314yes—
359C2×#121C2312yes—
360C2×#121C2311yescharacteristic
361C2×#121C2314yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2314yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2311yescharacteristic
374C2×#121C2312yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×#121C2311yescharacteristic
380C2×#121C2312yes—
381C2×#121C2311yescharacteristic
382C2×#121C2314yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2314yes—
386C2×#121C2312yes—
387C2×#121C2314yes—
388C2×#121C2311yescharacteristic
389C2×#121C2314yes—
390C2×#121C2314yes—
391C2×#121C2314yes—
392C2×#121C2314yes—
393C2×#121C2314yes—
394C4×#41—44no—
395C2×C4×Q8C2311yescharacteristic
396C2×C4×Q8C2312yes—
397C2×C4×Q8C2312yes—
398C2×C4×Q8C2311yescharacteristic
399C2×C4×Q8C2312yes—
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2311yescharacteristic
403C2×C4×D4C2312yes—
404C2×C4×D4C2311yescharacteristic
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2312yes—
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2314yes—
415C2×C4×D4C2311yescharacteristic
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2314yes—
422C2×C4×D4C2311yescharacteristic
423C2×#117C2312yes—
424C2×#117C2312yes—
425C2×#117C2312yes—
426C2×#117C2311yescharacteristic
427C2×#117C2312yes—
428C2×#117C2312yes—
429C2×#117C2312yes—
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2312yes—
433C22×C42C2311yescharacteristic
434C22×C42C2311yescharacteristic
435C22×C42C2312yes—
436C22×C42C2312yes—
437#401C2314yes—
438#400C2314yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2312yes—
444#400C2312yes—
445#400C2314yes—
446#399C2312yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2312yes—
453#398C2314yes—
454#398C2314yes—
455#398C2312yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2312yes—
461#398C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2312yes—
465#397C2312yes—
466#397C2312yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2312yes—
472#397C2312yes—
473#397C2312yes—
474#397C2314yes—
475#397C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2312yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2312yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2312yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2312yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2312yes—
517#394C2312yes—
518#394C2312yes—
519#394C2312yes—
520#394C2312yes—
521#394C2314yes—
522#394C2312yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2314yes—
537#393C2314yes—
538#393C2312yes—
539#393C2314yes—
540#393C2314yes—
541#393C2314yes—
542#393C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2314yes—
552#392C2314yes—
553#392C2314yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2312yes—
559#392C2312yes—
560#392C2312yes—
561#392C2312yes—
562#392C2314yes—
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2312yes—
567#391C2314yes—
568#391C2314yes—
569#391C2314yes—
570#391C2311yescharacteristic
571#391C2314yes—
572#391C2311yescharacteristic
573#391C2312yes—
574#391C2312yes—
575#391C2314yes—
576#391C2312yes—
577#391C2312yes—
578#390C2312yes—
579#390C2312yes—
580#390C2312yes—
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2314yes—
585#390C2314yes—
586#390C2314yes—
587#390C2312yes—
588#390C2314yes—
589#390C2312yes—
590#390C2314yes—
591#390C2312yes—
592#390C2311yescharacteristic
593#390C2311yescharacteristic
594#390C2312yes—
595#390C2311yescharacteristic
596#390C2314yes—
597#390C2314yes—
598#390C2314yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2312yes—
603#390C2312yes—
604#390C2312yes—
605#390C2311yescharacteristic
606#390C2311yescharacteristic
607#390C2311yescharacteristic
608#390C2312yes—
609#389C2311yescharacteristic
610#389C2312yes—
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2312yes—
617#389C2312yes—
618#389C2312yes—
619#389C2312yes—
620#389C2314yes—
621#389C2314yes—
622#389C2312yes—
623#389C2314yes—
624#389C2312yes—
625#389C2311yescharacteristic
626#389C2312yes—
627#389C2312yes—
628#389C2314yes—
629#389C2312yes—
630#389C2312yes—
631#389C2311yescharacteristic
632#389C2314yes—
633#389C2312yes—
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#389C2311yescharacteristic
637#389C2311yescharacteristic
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2312yes—
654#388C2312yes—
655#388C2314yes—
656#388C2314yes—
657#388C2312yes—
658#388C2312yes—
659#388C2314yes—
660#388C2312yes—
661#388C2312yes—
662#388C2312yes—
663#388C2312yes—
664#388C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2312yes—
676#387C2314yes—
677#387C2312yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#386C2314yes—
705#386C2312yes—
706#386C2312yes—
707#386C2312yes—
708#386C2314yes—
709#386C2312yes—
710#386C2314yes—
711#386C2312yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2312yes—
726#385C2312yes—
727#385C2312yes—
728#385C2312yes—
729#384C2311yescharacteristic
730#384C2311yescharacteristic
731#384C2312yes—
732#384C2312yes—
733#384C2312yes—
734#384C2312yes—
735#384C2311yescharacteristic
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2311yescharacteristic
739#382C2312yes—
740#382C2312yes—
741#382C2312yes—
742#382C2312yes—
743#382C2312yes—
744#382C2311yescharacteristic
745#382C2312yes—
746#381C2312yes—
747#381C2314yes—
748#380C2312yes—
749#380C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2314yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2311yescharacteristic
759#380C2312yes—
760#380C2312yes—
761#380C2314yes—
762#380C2314yes—
763#380C2314yes—
764#380C2314yes—
765#380C2312yes—
766#380C2312yes—
767#380C2314yes—
768#380C2312yes—
769#380C2314yes—
770#380C2311yescharacteristic
771#380C2311yescharacteristic
772#380C2311yescharacteristic
773#380C2312yes—
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2312yes—
777#380C2311yescharacteristic
778#380C2311yescharacteristic
779#380C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2311yescharacteristic
818C4×C22⋊C4C2311yescharacteristic
819C2×#95C2314yes—
820C43C2311yescharacteristic
821C2×#41—24no—
822C2×#41—28no—
823C2×#41—24no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—42no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—82no—
833C22×Q8—44no—
834C22×Q8—44no—
835C22×Q8—82no—
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×Q8C2412yes—
839C22×Q8C2414yes—
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2414yes—
861C22×D4C2414yes—
862C22×D4C2414yes—
863C22×D4C2414yes—
864C22×D4C2412yes—
865C22×D4C2412yes—
866C22×D4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2412yes—
869C23×C4C2411yescharacteristic
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2411yescharacteristic
873C23×C4C2412yes—
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2414yes—
878C23×C4C2412yes—
879C23×C4C2414yes—
880C23×C4C2412yes—
881C23×C4C2414yes—
882C23×C4C2414yes—
883C23×C4C2414yes—
884C23×C4C2412yes—
885C4⋊Q8—24no—
886C4⋊Q8—24no—
887C4⋊Q8—44no—
888C4⋊Q8—44no—
889C4⋊Q8—42no—
890C4⋊Q8—42no—
891C4⋊Q8—44no—
892#127—24no—
893#127—42no—
894#127—44no—
895#127—44no—
896#127—44no—
897#127—48no—
898#126—44no—
899#126—44no—
900#125—44no—
901#125—44no—
902#125—48no—
903#124—24no—
904#124—44no—
905#124—44no—
906#124—44no—
907#124—44no—
908#124—48no—
909#124—48no—
910#124—48no—
911#124—48no—
912#124—82no—
913#123—28no—
914#123—44no—
915#123—48no—
916#123—48no—
917#123—48no—
918#123—44no—
919#123—48no—
920#123—48no—
921#123—84no—
922C22⋊Q8—24no—
923C22⋊Q8—216no—
924C22⋊Q8—28no—
925C22⋊Q8—44no—
926C22⋊Q8—48no—
927C22⋊Q8—44no—
928C22⋊Q8—48no—
929C22⋊Q8—84no—
930#121—24no—
931#121—28no—
932#121—44no—
933#121—44no—
934#121—48no—
935#121—48no—
936#121—48no—
937#121—48no—
938#121—48no—
939#121—48no—
940#121—44no—
941#121—48no—
942#121—48no—
943#121—48no—
944#121—44no—
945#121—44no—
946#121—42no—
947#121—44no—
948#121—44no—
949#121—44no—
950#121—42no—
951#121—44no—
952#121—44no—
953#121—44no—
954#121—42no—
955#121—42no—
956#121—44no—
957#121—44no—
958#121—44no—
959#121—44no—
960#121—48no—
961#121—84no—
962#121—84no—
963#121—84no—
964#121—84no—
965C4×Q8—24no—
966C4×Q8—44no—
967C4×Q8—44no—
968C4×Q8—42no—
969C4×Q8—44no—
970C4×D4—24no—
971C4×D4—28no—
972C4×D4—24no—
973C4×D4—24no—
974C4×D4—24no—
975C4×D4—24no—
976C4×D4—42no—
977C4×D4—44no—
978C4×D4—42no—
979C4×D4—42no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—44no—
986C4×D4—42no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—44no—
991C4×D4—48no—
992C4×D4—48no—
993#117—28no—
994#117—44no—
995#117—44no—
996#117—44no—
997#117—42no—
998#117—44no—
999#117—44no—
1000C2×C4⋊C4—44no—
1001C2×C4⋊C4—44no—
1002C2×C4⋊C4—44no—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2411yescharacteristic
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2414yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2412yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2411yescharacteristic
1073C2×C22⋊C4C2411yescharacteristic
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C22⋊C4C2411yescharacteristic
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2411yescharacteristic
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2412yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2412yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2412yes—
1134C2×C22⋊C4C2414yes—
1135C2×C42—24no—
1136C2×C42—24no—
1137C2×C42—44no—
1138C2×C42—44no—
1139C2×C42C2411yescharacteristic
1140C2×C42C2412yes—
1141C2×C42C2411yescharacteristic
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2412yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2411yescharacteristic
1151C2×C42C2411yescharacteristic
1152C2×C42C2411yescharacteristic
1153C2×C42C2411yescharacteristic
1154C2×C42C2411yescharacteristic
1155C2×C42C2414yes—
1156C2×C42C2412yes—
1157C2×C42C2414yes—
1158C2×C42C2414yes—
1159C2×C42C2412yes—
1160C2×C42C2414yes—
1161C2×C42C2411yescharacteristic
1162C2×C42C2412yes—
1163C2×C42C2412yes—
1164C2×C42C2411yescharacteristic
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2411yescharacteristic
1174#95C2411yescharacteristic
1175#95C2411yescharacteristic
1176#95C2411yescharacteristic
1177#95C2412yes—
1178#95C2411yescharacteristic
1179#95C2412yes—
1180#95C2412yes—
1181#95C2411yescharacteristic
1182#95C2414yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2412yes—
1209#95C2414yes—
1210#95C2412yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221C24C2512yes—
1222C24C2514yes—
1223C24C2512yes—
1224C24C2511yescharacteristic
1225C24C2512yes—
1226C24C2511yescharacteristic
1227#41—416no—
1228#41—816no—
1229#41—816no—
1230#41—816no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—28no—
1236C2×Q8—24no—
1237C2×Q8—42no—
1238C2×Q8—42no—
1239C2×Q8—42no—
1240C2×Q8—42no—
1241C2×Q8—44no—
1242C2×Q8—42no—
1243C2×Q8—42no—
1244C2×Q8—44no—
1245C2×Q8—42no—
1246C2×Q8—42no—
1247C2×Q8—42no—
1248C2×Q8—816no—
1249C2×Q82−1+414yes—
1250C2×D4—22no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—28no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—22no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—22no—
1267C2×D4—24no—
1268C2×D4—22no—
1269C2×D4—24no—
1270C2×D4—28no—
1271C2×D4—22no—
1272C2×D4—24no—
1273C2×D4—22no—
1274C2×D4—24no—
1275C2×D4—42no—
1276C2×D4—41no—
1277C2×D4—44no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—44no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—42no—
1290C2×D4—42no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—42no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—42no—
1300C2×D4—42no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—42no—
1305C2×D4—42no—
1306C2×D4—42no—
1307C2×D4—44no—
1308C2×D4—44no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—44no—
1313C2×D4—44no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—44no—
1319C2×D4—44no—
1320C2×D4—44no—
1321C2×D4—44no—
1322C2×D4—44no—
1323C2×D4—44no—
1324C2×D4—44no—
1325C22×C4—22no—
1326C22×C4—22no—
1327C22×C4—22no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—22no—
1332C22×C4—24no—
1333C22×C4—24no—
1334C22×C4—22no—
1335C22×C4—24no—
1336C22×C4—24no—
1337C22×C4—22no—
1338C22×C4—22no—
1339C22×C4—24no—
1340C22×C4—22no—
1341C22×C4—24no—
1342C22×C4—24no—
1343C22×C4—24no—
1344C22×C4—24no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—24no—
1348C22×C4—22no—
1349C22×C4—24no—
1350C22×C4—22no—
1351C22×C4—28no—
1352C22×C4—24no—
1353C22×C4—24no—
1354C22×C4—28no—
1355C22×C4—42no—
1356C22×C4—41no—
1357C22×C4—41no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—44no—
1364C22×C4—44no—
1365C22×C4—44no—
1366C22×C4—42no—
1367C22×C4—42no—
1368C22×C4—42no—
1369C22×C4—44no—
1370C22×C4—44no—
1371C22×C4—42no—
1372C22×C4—44no—
1373C22×C4—44no—
1374C22×C4—44no—
1375C22×C4—44no—
1376C22×C4—44no—
1377C22×C4—44no—
1378C22×C4H(5,𝔽2)14yes—
1379C22×C4C2511yescharacteristic
1380C22×C4C2512yes—
1381C22×C4C2511yescharacteristic
1382C22×C4C2512yes—
1383C22×C4C2512yes—
1384C22×C4C2511yescharacteristic
1385C22×C4C2512yes—
1386C22×C4C2512yes—
1387C22×C4C2512yes—
1388C22×C4C2512yes—
1389C22×C4C2512yes—
1390C22×C4C2514yes—
1391C22×C4C2511yescharacteristic
1392C22×C4C2512yes—
1393C22×C4C2511yescharacteristic
1394C22×C4C2511yescharacteristic
1395C22×C4C2514yes—
1396C22×C4C2512yes—
1397C22×C4C2514yes—
1398C22×C4C2512yes—
1399C22×C4C2512yes—
1400C22×C4C2511yescharacteristic
1401C22×C4C2511yescharacteristic
1402C22×C4C2511yescharacteristic
1403C22×C4C2511yescharacteristic
1404C22×C4C2511yescharacteristic
1405C22×C4C2512yes—
1406C22×C4C2511yescharacteristic
1407C22×C4C2511yescharacteristic
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—24no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—24no—
1414C4⋊C4—22no—
1415C4⋊C4—22no—
1416C4⋊C4—22no—
1417C4⋊C4—24no—
1418C4⋊C4—22no—
1419C4⋊C4—24no—
1420C4⋊C4—22no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—28no—
1424C4⋊C4—28no—
1425C4⋊C4—24no—
1426C4⋊C4—24no—
1427C4⋊C4—24no—
1428C4⋊C4—22no—
1429C4⋊C4—24no—
1430C4⋊C4—22no—
1431C4⋊C4—24no—
1432C4⋊C4—22no—
1433C4⋊C4—22no—
1434C4⋊C4—22no—
1435C4⋊C4—22no—
1436C4⋊C4—22no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—42no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4—42no—
1445C4⋊C4—41no—
1446C4⋊C4—42no—
1447C4⋊C4—42no—
1448C4⋊C4—42no—
1449C4⋊C4—44no—
1450C4⋊C4—42no—
1451C4⋊C4—42no—
1452C4⋊C4—42no—
1453C4⋊C4—42no—
1454C4⋊C4—44no—
1455C4⋊C4—44no—
1456C4⋊C4—44no—
1457C4⋊C4—44no—
1458C4⋊C4—42no—
1459C4⋊C4—44no—
1460C4⋊C4—44no—
1461C4⋊C4—44no—
1462C4⋊C4—44no—
1463C4⋊C4—42no—
1464C4⋊C4—44no—
1465C4⋊C4—42no—
1466C4⋊C4—42no—
1467C4⋊C4H(5,𝔽2)14yes—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—24no—
1471C22⋊C4—22no—
1472C22⋊C4—24no—
1473C22⋊C4—22no—
1474C22⋊C4—24no—
1475C22⋊C4—24no—
1476C22⋊C4—24no—
1477C22⋊C4—22no—
1478C22⋊C4—22no—
1479C22⋊C4—28no—
1480C22⋊C4—24no—
1481C22⋊C4—24no—
1482C22⋊C4—28no—
1483C22⋊C4—24no—
1484C22⋊C4—28no—
1485C22⋊C4—24no—
1486C22⋊C4—24no—
1487C22⋊C4—24no—
1488C22⋊C4—24no—
1489C22⋊C4—24no—
1490C22⋊C4—24no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—42no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—41no—
1503C22⋊C4—42no—
1504C22⋊C4—42no—
1505C22⋊C4—41no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—42no—
1515C22⋊C4—44no—
1516C22⋊C4—42no—
1517C22⋊C4—44no—
1518C22⋊C4—42no—
1519C22⋊C4—44no—
1520C22⋊C4—44no—
1521C22⋊C4—42no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C22⋊C4—44no—
1525C22⋊C4—44no—
1526C22⋊C4—44no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C22⋊C4—42no—
1530C22⋊C4—44no—
1531C22⋊C4—42no—
1532C22⋊C4—44no—
1533C22⋊C4—44no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—42no—
1539C22⋊C4—44no—
1540C42—22no—
1541C42—22no—
1542C42—22no—
1543C42—22no—
1544C42—22no—
1545C42—22no—
1546C42—22no—
1547C42—24no—
1548C42—24no—
1549C42—24no—
1550C42—24no—
1551C42—22no—
1552C42—22no—
1553C42—22no—
1554C42—24no—
1555C42—22no—
1556C42—42no—
1557C42—42no—
1558C42—42no—
1559C42—42no—
1560C42—44no—
1561C42—44no—
1562C42—44no—
1563C42—44no—
1564C42—41no—
1565C42H(5,𝔽2)14yes—
1566C23—21no—
1567C23—21no—
1568C23—21no—
1569C23—21no—
1570C23—21no—
1571C23—21no—
1572C23—22no—
1573C23—24no—
1574C23—22no—
1575C23—21no—
1576C23—21no—
1577C23—22no—
1578C23—22no—
1579C23—22no—
1580C23—22no—
1581C23—22no—
1582C23—22no—
1583C23—24no—
1584C23—24no—
1585C23—22no—
1586C23—21no—
1587C23—21no—
1588C23—22no—
1589C23—22no—
1590C23—22no—
1591C23—24no—
1592C23—22no—
1593C23—24no—
1594C23—22no—
1595C23—24no—
1596C23—22no—
1597C23—21no—
1598C23—22no—
1599C23—22no—
1600C23—21no—
1601C23—22no—
1602C23—22no—
1603C23—22no—
1604C23—24no—
1605C23—21no—
1606C23—22no—
1607C23C2×H(5,𝔽2)12yes—
1608C23C2611yescharacteristic
1609Q8—28no—
1610Q8—48no—
1611Q8—84no—
1612Q8—84no—
1613Q8—88no—
1614Q8—84no—
1615D4—44no—
1616D4—48no—
1617D4—44no—
1618D4—44no—
1619D4—48no—
1620D4—44no—
1621D4—48no—
1622D4—84no—
1623D4—88no—
1624D4—84no—
1625D4—88no—
1626D4—84no—
1627D4—84no—
1628D4—84no—
1629D4—88no—
1630D4—84no—
1631D4—84no—
1632D4—84no—
1633D4—88no—
1634D4—164no—
1635D4—164no—
1636D4—164no—
1637D4—164no—
1638D4—164no—
1639D4—164no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—22no—
1645C2×C4—21no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—28no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—24no—
1672C2×C4—24no—
1673C2×C4—24no—
1674C2×C4—24no—
1675C2×C4—24no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—24no—
1682C2×C4—21no—
1683C2×C4—21no—
1684C2×C4—22no—
1685C2×C4—21no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—21no—
1691C2×C4—22no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—22no—
1695C2×C4—22no—
1696C2×C4—22no—
1697C2×C4—22no—
1698C2×C4—22no—
1699C2×C4—22no—
1700C2×C4—24no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—21no—
1705C2×C4—21no—
1706C2×C4—22no—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—22no—
1710C2×C4—24no—
1711C2×C4—24no—
1712C2×C4—22no—
1713C2×C4—22no—
1714C2×C4—22no—
1715C2×C4—22no—
1716C2×C4—44no—
1717C2×C4—48no—
1718C2×C4—44no—
1719C2×C4—44no—
1720C2×C4—48no—
1721C2×C4—44no—
1722C2×C4—48no—
1723C2×C4—48no—
1724C2×C4—44no—
1725C2×C4—84no—
1726C2×C4—84no—
1727C2×C4—88no—
1728C2×C4—88no—
1729C2×C4—84no—
1730C2×C4—88no—
1731C2×C4—164no—
1732C2×C4—164no—
1733C2×C4C2×H(5,𝔽2)12yes—
1734C2×C4C2×H(5,𝔽2)12yes—
1735C2×C4C2×H(5,𝔽2)12yes—
1736C2×C4C2×H(5,𝔽2)12yes—
1737C2×C4C2×H(5,𝔽2)12yes—
1738C2×C4C2×H(5,𝔽2)12yes—
1739C2×C4C2×H(5,𝔽2)12yes—
1740C2×C4C2×H(5,𝔽2)12yes—
1741C2×C4C2×2−1+414yes—
1742C2×C4C2×2−1+412yes—
1743C2×C4#58512yes—
1744C2×C4#58512yes—
1745C22—22no—
1746C22—22no—
1747C22—22no—
1748C22—41no—
1749C22—41no—
1750C22—41no—
1751C22—41no—
1752C22—42no—
1753C22—42no—
1754C22—41no—
1755C22—44no—
1756C22—42no—
1757C22—41no—
1758C22—42no—
1759C22—42no—
1760C22—42no—
1761C22—44no—
1762C22—42no—
1763C22—44no—
1764C22—42no—
1765C22—41no—
1766C22—42no—
1767C22—42no—
1768C22—42no—
1769C22—41no—
1770C22—44no—
1771C22—42no—
1772C22—41no—
1773C22—44no—
1774C22—42no—
1775C22—42no—
1776C22—42no—
1777C22—42no—
1778C22—44no—
1779C22—41no—
1780C22—42no—
1781C22—42no—
1782C22—41no—
1783C22—42no—
1784C22—42no—
1785C22—44no—
1786C22—42no—
1787C22C22×H(5,𝔽2)11yescharacteristic
1788C22C22×H(5,𝔽2)11yescharacteristic
1789C22C22×H(5,𝔽2)11yescharacteristic
1790C22C22×2−1+411yescharacteristic
1791C22C2×#58511yescharacteristic
1792C22C2×#58511yescharacteristic
1793C22H(7,𝔽2)11yescharacteristic
1794C4—22no—
1795C4—24no—
1796C4—22no—
1797C4—22no—
1798C4—22no—
1799C4—22no—
1800C4—41no—
1801C4—42no—
1802C4—41no—
1803C4—41no—
1804C4—42no—
1805C4—42no—
1806C4—41no—
1807C4—42no—
1808C4—42no—
1809C4—42no—
1810C4—44no—
1811C4—42no—
1812C4—44no—
1813C4—42no—
1814C4—44no—
1815C4—41no—
1816C4—42no—
1817C4—42no—
1818C4—42no—
1819C4—42no—
1820C4—41no—
1821C4#353614yes—
1822C4#356214yes—
1823C2—42no—
1824C2—82no—
1825C2—82no—
1826C2—81no—
1827C2—84no—
1828C2—82no—
1829C2C2×#353611yescharacteristic
1830C2C2×#356211yescharacteristic
1831C2#6283411yescharacteristic
1832C2#6291211yescharacteristic
1833C2#6293011yescharacteristic
1834C2#6295211yescharacteristic
1835C2#6303911yescharacteristic
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. #59429C2semidirect
2. #59135C2semidirect
3. #59039C2semidirect
4. #55375C2semidirect
5. #55342C2semidirect
6. #53666C2semidirect
7. #53057C2semidirect
8. #52957C2semidirect
9. #47937C2semidirect
10. #45486C2semidirect
11. #45484C2semidirect
12. #45035C2semidirect
13. #44889C2semidirect
14. #42989C2semidirect
15. #42907C2semidirect
16. #42608C2semidirect
17. #42465C2semidirect
18. #40077C2semidirect
19. #39984C2semidirect
20. #39607C2semidirect
21. #39562C2semidirect
22. #39469C2semidirect
23. #39352C2semidirect
24. #39201C2semidirect
25. #38033C2semidirect
26. #37639C2semidirect
27. #37316C2semidirect
28. #37276C2semidirect
29. #36455C2semidirect
30. #36412C2semidirect
31. #36122C2semidirect
32. #35279C2semidirect
33. #35207C2semidirect
34. #34932C2semidirect
35. #34715C2semidirect

Maximal subgroups

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

subgroupindex
#594292
#591352
#590392
#553752
#553422
#536662
#530572
#529572
#479372
#454862
#454842
#450352
#448892
#429892
#429072
#426082
#424652
#400772
#399842
#396072
#395622
#394692
#393522
#392012
#380332
#376392
#373162
#372762
#364552
#364122
#361222
#352792
#352072
#349322
#347152