Finite Group Databasebeta

← #8463254

Subgroups — #8463254

Order 512.

5063 conjugacy classes of subgroups.

The subgroup lattice has 1739 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59654C211yesmaximal, characteristic, complemented
3#59652C211yesmaximal, characteristic, complemented
4#54282C214yesmaximal, complemented
5#53721C214yesmaximal, complemented
6#53492C214yesmaximal, complemented
7#53095C212yesmaximal, complemented
8#53001C212yesmaximal, complemented
9#50779C214yesmaximal, complemented
10#46019C212yesmaximal, complemented
11#45677C212yesmaximal, complemented
12#45248C212yesmaximal, complemented
13#44940C212yesmaximal, complemented
14#42807C212yesmaximal, complemented
15#42739C212yesmaximal, complemented
16#42668C212yesmaximal, complemented
17#42472C212yesmaximal, complemented
18#40152C212yesmaximal, complemented
19#39618C211yesmaximal, characteristic, complemented
20#39491C211yesmaximal, characteristic, complemented
21#39360C211yesmaximal, characteristic, complemented
22#39282C212yesmaximal, complemented
23#39166C212yesmaximal, complemented
24#38958C211yesmaximal, characteristic, complemented
25#38027C212yesmaximal, complemented
26#37628C211yesmaximal, characteristic, complemented
27#37379C212yesmaximal, complemented
28#37312C212yesmaximal, complemented
29#36598C211yesmaximal, characteristic, complemented
30Q8×#127C211yesmaximal, characteristic, complemented
31#36276C211yesmaximal, characteristic, complemented
32#35196C211yesmaximal, characteristic, complemented
33#35185C211yesmaximal, characteristic, complemented
34#34934C211yesmaximal, characteristic, complemented
35#34902C211yesmaximal, characteristic, complemented
36C2×#555C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic
40C2×D4×Q8C2212yes—
41C2×D4×Q8C2212yes—
42C2×D4×Q8C2212yes—
43C2×D4×Q8C2211yescharacteristic
44C2×#548C2212yes—
45C2×#547C2211yescharacteristic
46C2×#536C2212yes—
47C2×#529C2212yes—
48#2868C2212yes—
49#2868C2211yescharacteristic
50#2864C2212yes—
51#2862C2211yescharacteristic
52#2862C2211yescharacteristic
53#2860C2212yes—
54#2857C2212yes—
55#2855C2212yes—
56#2850C2212yes—
57#2838C2214yes—
58#2836C2214yes—
59#2836C2214yes—
60#2829C2214yes—
61#2827C2214yes—
62#2826C2214yes—
63#2823C2214yes—
64#2817C2214yes—
65#2797C2214yes—
66#2796C2214yes—
67#2793C2214yes—
68#2792C2214yes—
69#2791C2214yes—
70#2790C2214yes—
71#2786C2214yes—
72#2780C2214yes—
73#2746C2214yes—
74#2742C2214yes—
75#2737C2214yes—
76#2734C2214yes—
77#2731C2214yes—
78#2730C2214yes—
79#2730C2214yes—
80#2729C2214yes—
81#2729C2214yes—
82#2729C2214yes—
83#2728C2214yes—
84#2728C2214yes—
85#2723C2214yes—
86#2720C2214yes—
87#2718C2214yes—
88#2716C2214yes—
89#2714C2214yes—
90#2713C2214yes—
91#2710C2214yes—
92#2710C2214yes—
93#2710C2214yes—
94#2706C2214yes—
95#2703C2214yes—
96#2700C2214yes—
97#2700C2214yes—
98#2700C2214yes—
99#2698C2214yes—
100#2696C2214yes—
101#2692C2214yes—
102#2692C2214yes—
103#2692C2214yes—
104#2691C2214yes—
105#2691C2214yes—
106#2683C2214yes—
107#2683C2214yes—
108#2681C2214yes—
109#2681C2214yes—
110#2680C2214yes—
111#2680C2214yes—
112#2677C2214yes—
113#2674C2214yes—
114#2660C2212yes—
115#2654C2214yes—
116#2651C2214yes—
117#2650C2214yes—
118#2649C2214yes—
119#2649C2214yes—
120#2647C2212yes—
121#2644C2212yes—
122#2639C2214yes—
123#2638C2214yes—
124#2638C2214yes—
125#2625C2212yes—
126#2621C2212yes—
127#2621C2212yes—
128#2620C2212yes—
129#2619C2212yes—
130#2600C2214yes—
131#2596C2212yes—
132#2594C2212yes—
133#2592C2211yescharacteristic
134#2582C2212yes—
135#2581C2211yescharacteristic
136#2571C2212yes—
137#2571C2211yescharacteristic
138#2570C2211yescharacteristic
139#2570C2212yes—
140#2570C2212yes—
141#2568C2212yes—
142#2567C2211yescharacteristic
143#2566C2212yes—
144#2564C2214yes—
145#2563C2211yescharacteristic
146#2563C2212yes—
147#2554C2212yes—
148#2554C2212yes—
149#2552C2211yescharacteristic
150#2551C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2549C2214yes—
154#2549C2214yes—
155#2549C2214yes—
156#2548C2211yescharacteristic
157#2547C2211yescharacteristic
158#2546C2211yescharacteristic
159#2545C2211yescharacteristic
160#2543C2214yes—
161#2542C2212yes—
162#2542C2212yes—
163#2542C2214yes—
164#2542C2211yescharacteristic
165#2542C2214yes—
166#2542C2212yes—
167#2542C2211yescharacteristic
168#2542C2212yes—
169#2541C2211yescharacteristic
170#2540C2212yes—
171#2538C2211yescharacteristic
172#2538C2211yescharacteristic
173#2538C2212yes—
174#2538C2211yescharacteristic
175#2537C2211yescharacteristic
176#2536C2212yes—
177#2525C2212yes—
178#2522C2214yes—
179#2516C2214yes—
180#2514C2211yescharacteristic
181#2513C2212yes—
182#2513C2212yes—
183#2512C2211yescharacteristic
184#2512C2211yescharacteristic
185#2512C2211yescharacteristic
186#2511C2212yes—
187#2511C2212yes—
188#2509C2212yes—
189#2507C2212yes—
190#2504C2212yes—
191#2502C2212yes—
192#2500C2212yes—
193#2499C2212yes—
194#2497C2212yes—
195#2496C2212yes—
196#2491C2212yes—
197#2490C2212yes—
198#2490C2212yes—
199#2488C2214yes—
200#2469C2212yes—
201#2469C2214yes—
202#2463C2214yes—
203#2461C2214yes—
204#2461C2214yes—
205#2456C2214yes—
206#2452C2212yes—
207#2452C2214yes—
208#2452C2214yes—
209#2452C2212yes—
210#2448C2211yescharacteristic
211#2446C2211yescharacteristic
212#2446C2212yes—
213#2446C2212yes—
214#2445C2211yescharacteristic
215#2445C2211yescharacteristic
216#2444C2214yes—
217#2441C2212yes—
218#2440C2212yes—
219#2440C2212yes—
220#2440C2212yes—
221#2439C2212yes—
222#2439C2212yes—
223#2436C2212yes—
224#2434C2212yes—
225#2434C2212yes—
226#2432C2212yes—
227#2429C2212yes—
228#2428C2212yes—
229#2428C2212yes—
230#2426C2214yes—
231#2426C2212yes—
232#2426C2212yes—
233#2422C2212yes—
234#2422C2212yes—
235#2421C2212yes—
236#2421C2212yes—
237#2421C2212yes—
238#2420C2212yes—
239#2420C2212yes—
240#2420C2212yes—
241#2419C2214yes—
242#2417C2212yes—
243#2417C2212yes—
244#2416C2212yes—
245#2415C2212yes—
246#2415C2212yes—
247#2415C2212yes—
248#2409C2212yes—
249#2409C2212yes—
250#2409C2212yes—
251#2409C2212yes—
252#2409C2212yes—
253#2407C2212yes—
254#2407C2212yes—
255#2407C2212yes—
256#2401C2212yes—
257#2396C2212yes—
258#2392C2212yes—
259#2392C2212yes—
260#2383C2214yes—
261#2366C2212yes—
262#2365C2212yes—
263#2363C2212yes—
264#2361C2212yes—
265#2355C2212yes—
266#2355C2212yes—
267#2352C2212yes—
268#2349C2212yes—
269#2349C2212yes—
270#2328C2212yes—
271#2325C2214yes—
272#2324C2212yes—
273#2323C2212yes—
274#2317C2212yes—
275#2314C2212yes—
276#2314C2212yes—
277#2310C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×#127C2211yescharacteristic
283C4×#127C2211yescharacteristic
284C4×#127C2211yescharacteristic
285C4×#127C2212yes—
286C4×#126C2212yes—
287C4×#124C2211yescharacteristic
288C4×#124C2211yescharacteristic
289C4×#121C2212yes—
290#2298C2212yes—
291#2295C2211yescharacteristic
292C2×#391C2212yes—
293#2293C2211yescharacteristic
294#2293C2211yescharacteristic
295#2293C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C23×Q8C2312yes—
301C23×Q8C2312yes—
302C23×Q8C2312yes—
303#555—44no—
304#554—44no—
305D4×Q8—48no—
306D4×Q8—44no—
307D4×Q8—44no—
308D4×Q8—44no—
309D4×Q8—48no—
310D4×Q8—48no—
311#548—48no—
312#547—44no—
313#536—48no—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2314yes—
322C2×C4⋊Q8C2312yes—
323C2×C4⋊Q8C2312yes—
324C2×C4⋊Q8C2312yes—
325C2×C4⋊Q8C2314yes—
326C2×C4⋊Q8C2314yes—
327C2×#127C2311yescharacteristic
328C2×#127C2311yescharacteristic
329C2×#127C2311yescharacteristic
330#529—48no—
331C2×#126C2312yes—
332C2×#126C2314yes—
333C2×#126C2312yes—
334C2×#126C2312yes—
335C2×#125C2312yes—
336C2×#125C2312yes—
337C2×#124C2311yescharacteristic
338C2×#124C2311yescharacteristic
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#123C2312yes—
344C2×#123C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×C22⋊Q8C2312yes—
362C2×C22⋊Q8C2312yes—
363C2×C22⋊Q8C2314yes—
364C2×C22⋊Q8C2314yes—
365C2×C22⋊Q8C2314yes—
366C2×C22⋊Q8C2314yes—
367C2×C22⋊Q8C2314yes—
368C2×C22⋊Q8C2314yes—
369C2×C22⋊Q8C2314yes—
370C2×C22⋊Q8C2314yes—
371C2×C22⋊Q8C2314yes—
372C2×C22⋊Q8C2314yes—
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2312yes—
377C2×#121C2312yes—
378C2×#121C2312yes—
379C2×#121C2314yes—
380C2×#121C2312yes—
381C2×#121C2312yes—
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2311yescharacteristic
384C2×C4×Q8C2311yescharacteristic
385C2×C4×Q8C2311yescharacteristic
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2311yescharacteristic
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2312yes—
390C2×C4×Q8C2312yes—
391C2×C4×Q8C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2314yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2314yes—
412C2×#117C2312yes—
413C2×#117C2312yes—
414C2×#117C2312yes—
415C2×#117C2312yes—
416C2×#117C2312yes—
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2312yes—
419C22×C42C2312yes—
420#401C2312yes—
421#400C2312yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2312yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2312yes—
434#400C2312yes—
435#399C2312yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2312yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#398C2314yes—
458#398C2314yes—
459#398C2312yes—
460#398C2312yes—
461#397C2312yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2312yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2312yes—
474#397C2312yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2312yes—
480#397C2314yes—
481#397C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2312yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2312yes—
493#396C2314yes—
494#396C2314yes—
495#396C2312yes—
496#396C2312yes—
497#396C2314yes—
498#396C2312yes—
499#396C2312yes—
500#395C2314yes—
501#395C2314yes—
502#395C2314yes—
503#395C2314yes—
504#395C2314yes—
505#395C2314yes—
506#395C2312yes—
507#395C2314yes—
508#395C2314yes—
509#395C2314yes—
510#395C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2312yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2312yes—
525#394C2314yes—
526#394C2312yes—
527#394C2312yes—
528#394C2312yes—
529#394C2314yes—
530#394C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2312yes—
537#393C2314yes—
538#393C2314yes—
539#393C2314yes—
540#392C2314yes—
541#392C2314yes—
542#392C2312yes—
543#392C2314yes—
544#392C2312yes—
545#392C2314yes—
546#391C2312yes—
547#391C2312yes—
548#391C2311yescharacteristic
549#391C2311yescharacteristic
550#391C2312yes—
551#391C2311yescharacteristic
552#391C2312yes—
553#391C2312yes—
554#391C2312yes—
555#391C2314yes—
556#391C2314yes—
557#391C2314yes—
558#391C2312yes—
559#391C2312yes—
560#391C2312yes—
561#391C2311yescharacteristic
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2312yes—
567#391C2311yescharacteristic
568#391C2311yescharacteristic
569#391C2314yes—
570#391C2314yes—
571#390C2311yescharacteristic
572#390C2312yes—
573#390C2311yescharacteristic
574#390C2311yescharacteristic
575#390C2312yes—
576#390C2312yes—
577#390C2312yes—
578#390C2312yes—
579#390C2314yes—
580#390C2312yes—
581#390C2314yes—
582#390C2311yescharacteristic
583#390C2311yescharacteristic
584#390C2312yes—
585#390C2312yes—
586#390C2311yescharacteristic
587#390C2312yes—
588#390C2314yes—
589#390C2314yes—
590#390C2311yescharacteristic
591#390C2311yescharacteristic
592#390C2311yescharacteristic
593#390C2312yes—
594#390C2314yes—
595#390C2312yes—
596#390C2311yescharacteristic
597#390C2311yescharacteristic
598#390C2311yescharacteristic
599#390C2311yescharacteristic
600#390C2311yescharacteristic
601#390C2314yes—
602#390C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2311yescharacteristic
614#389C2311yescharacteristic
615#389C2312yes—
616#389C2312yes—
617#389C2314yes—
618#389C2314yes—
619#389C2314yes—
620#389C2314yes—
621#389C2311yescharacteristic
622#389C2311yescharacteristic
623#389C2314yes—
624#389C2314yes—
625#389C2312yes—
626#389C2312yes—
627#389C2311yescharacteristic
628#389C2312yes—
629#389C2312yes—
630#389C2314yes—
631#389C2314yes—
632#389C2311yescharacteristic
633#389C2312yes—
634#389C2311yescharacteristic
635#389C2311yescharacteristic
636#389C2314yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2312yes—
648#388C2314yes—
649#388C2314yes—
650#388C2312yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#388C2312yes—
656#388C2314yes—
657#388C2312yes—
658#388C2312yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2312yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2312yes—
667#388C2312yes—
668#388C2314yes—
669#388C2312yes—
670#388C2312yes—
671#388C2312yes—
672#388C2312yes—
673#387C2312yes—
674#387C2312yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2312yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2312yes—
690#387C2314yes—
691#387C2312yes—
692#387C2314yes—
693#387C2312yes—
694#387C2312yes—
695#387C2314yes—
696#387C2314yes—
697#387C2314yes—
698#387C2314yes—
699#387C2312yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2314yes—
715#386C2314yes—
716#386C2312yes—
717#386C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2314yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#384C2312yes—
736#384C2311yescharacteristic
737#384C2311yescharacteristic
738#384C2311yescharacteristic
739#384C2311yescharacteristic
740#384C2311yescharacteristic
741#384C2312yes—
742#384C2312yes—
743#384C2314yes—
744#384C2312yes—
745#384C2312yes—
746#384C2312yes—
747#384C2312yes—
748#384C2314yes—
749#383C2312yes—
750#382C2312yes—
751#382C2312yes—
752#382C2314yes—
753#382C2312yes—
754#382C2312yes—
755#382C2312yes—
756#382C2312yes—
757#382C2312yes—
758#382C2311yescharacteristic
759#382C2311yescharacteristic
760#381C2314yes—
761#381C2314yes—
762#381C2314yes—
763#380C2314yes—
764#380C2312yes—
765#380C2312yes—
766#380C2314yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#380C2314yes—
774#380C2314yes—
775#380C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2314yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2311yescharacteristic
803C4×C4⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815#376C2312yes—
816C2×#95C2314yes—
817C2×#95C2314yes—
818C43C2312yes—
819C43C2311yescharacteristic
820C43C2311yescharacteristic
821C43C2311yescharacteristic
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—44no—
825C22×Q8—28no—
826C22×Q8—28no—
827C22×Q8—44no—
828C22×Q8—44no—
829C22×Q8—44no—
830C22×Q8—44no—
831C22×Q8—44no—
832C22×Q8—44no—
833C22×Q8—44no—
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×Q8C2412yes—
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2414yes—
841C22×Q8C2414yes—
842C22×Q8C2414yes—
843C22×D4C2411yescharacteristic
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2411yescharacteristic
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2414yes—
865C23×C4C2414yes—
866C23×C4C2414yes—
867C4⋊Q8—24no—
868C4⋊Q8—28no—
869C4⋊Q8—24no—
870C4⋊Q8—24no—
871C4⋊Q8—24no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—48no—
876C4⋊Q8—44no—
877C4⋊Q8—44no—
878C4⋊Q8—48no—
879C4⋊Q8—48no—
880#127—24no—
881#127—24no—
882#127—24no—
883#126—44no—
884#126—48no—
885#126—44no—
886#126—44no—
887#125—44no—
888#125—44no—
889#124—24no—
890#124—24no—
891#124—44no—
892#124—44no—
893#124—48no—
894#124—48no—
895#123—44no—
896#123—48no—
897#123—48no—
898#123—48no—
899#123—44no—
900C22⋊Q8—28no—
901C22⋊Q8—48no—
902C22⋊Q8—48no—
903C22⋊Q8—48no—
904C22⋊Q8—48no—
905C22⋊Q8—48no—
906C22⋊Q8—48no—
907C22⋊Q8—48no—
908C22⋊Q8—44no—
909C22⋊Q8—48no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912C22⋊Q8—48no—
913C22⋊Q8—44no—
914C22⋊Q8—44no—
915C22⋊Q8—44no—
916C22⋊Q8—44no—
917C22⋊Q8—44no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—48no—
922C22⋊Q8—48no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925#121—28no—
926#121—48no—
927#121—48no—
928#121—44no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934C4×Q8—24no—
935C4×Q8—24no—
936C4×Q8—24no—
937C4×Q8—24no—
938C4×Q8—24no—
939C4×Q8—24no—
940C4×Q8—42no—
941C4×Q8—44no—
942C4×Q8—44no—
943C4×Q8—44no—
944C4×D4—24no—
945C4×D4—28no—
946C4×D4—24no—
947C4×D4—24no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—24no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—48no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—48no—
961C4×D4—44no—
962C4×D4—48no—
963C4×D4—48no—
964#117—28no—
965#117—28no—
966#117—44no—
967#117—44no—
968#117—44no—
969C2×C4⋊C4—44no—
970C2×C4⋊C4—44no—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2414yes—
1104C2×C42—44no—
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2412yes—
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2414yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2411yescharacteristic
1169#95C2411yescharacteristic
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2411yescharacteristic
1173#95C2412yes—
1174#95C2412yes—
1175#95C2411yescharacteristic
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202C24C2512yes—
1203C24C2512yes—
1204C24C2512yes—
1205C24C2512yes—
1206#41—816no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—24no—
1212C2×Q8—24no—
1213C2×Q8—22no—
1214C2×Q8—24no—
1215C2×Q8—24no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—22no—
1219C2×Q8—24no—
1220C2×Q8—28no—
1221C2×Q8—28no—
1222C2×Q8—22no—
1223C2×Q8—41no—
1224C2×Q8—42no—
1225C2×Q8—44no—
1226C2×Q8—44no—
1227C2×Q8—44no—
1228C2×Q8—44no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—44no—
1232C2×Q8—42no—
1233C2×Q8—816no—
1234C2×Q8—816no—
1235C2×Q8—816no—
1236C2×Q8H(5,𝔽2)14yes—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—28no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—24no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—42no—
1268C2×D4—44no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D42−1+414yes—
1276C22×C4—24no—
1277C22×C4—24no—
1278C22×C4—24no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—28no—
1290C22×C4—28no—
1291C22×C4—24no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—44no—
1302C22×C4—42no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2514yes—
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2511yescharacteristic
1318C22×C4C2511yescharacteristic
1319C22×C4C2514yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2514yes—
1327C22×C4C2514yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—28no—
1354C4⋊C4—28no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—28no—
1369C4⋊C4—24no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—24no—
1378C4⋊C4—22no—
1379C4⋊C4—28no—
1380C4⋊C4—22no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—42no—
1394C4⋊C4—41no—
1395C4⋊C4—42no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—44no—
1412C4⋊C4—42no—
1413C4⋊C4—44no—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—28no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—42no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C42—22no—
1474C42—24no—
1475C42—22no—
1476C42—24no—
1477C42—24no—
1478C42—22no—
1479C42—24no—
1480C42—24no—
1481C42—22no—
1482C42—22no—
1483C42—24no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—22no—
1489C42—22no—
1490C42—24no—
1491C42—42no—
1492C42—42no—
1493C42—41no—
1494C42—42no—
1495C42—41no—
1496C42—41no—
1497C42—44no—
1498C42—44no—
1499C42—44no—
1500C42—44no—
1501C42—41no—
1502C42—41no—
1503C42H(5,𝔽2)14yes—
1504C42H(5,𝔽2)14yes—
1505C422−1+414yes—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—22no—
1517C23—22no—
1518C23—22no—
1519C23—22no—
1520C23—22no—
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23C2×2−1+414yes—
1534C23C2611yescharacteristic
1535Q8—28no—
1536Q8—44no—
1537Q8—44no—
1538Q8—48no—
1539Q8—48no—
1540Q8—84no—
1541Q8—88no—
1542Q8—88no—
1543Q8—88no—
1544D4—28no—
1545D4—48no—
1546D4—48no—
1547D4—48no—
1548D4—44no—
1549D4—44no—
1550D4—44no—
1551D4—84no—
1552D4—88no—
1553D4—84no—
1554D4—84no—
1555D4—88no—
1556D4—164no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—24no—
1590C2×C4—24no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—24no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—24no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—24no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—24no—
1637C2×C4—48no—
1638C2×C4—48no—
1639C2×C4—48no—
1640C2×C4—48no—
1641C2×C4—84no—
1642C2×C4—88no—
1643C2×C4—88no—
1644C2×C4—84no—
1645C2×C4—88no—
1646C2×C4—88no—
1647C2×C4—164no—
1648C2×C4C2×H(5,𝔽2)12yes—
1649C2×C4C2×H(5,𝔽2)14yes—
1650C2×C4C2×H(5,𝔽2)12yes—
1651C2×C4C2×H(5,𝔽2)12yes—
1652C2×C4C2×H(5,𝔽2)12yes—
1653C2×C4C2×H(5,𝔽2)12yes—
1654C2×C4C2×H(5,𝔽2)12yes—
1655C2×C4C2×H(5,𝔽2)12yes—
1656C2×C4C2×2−1+412yes—
1657C2×C4C2×2−1+412yes—
1658C2×C4C2×2−1+412yes—
1659C2×C4C2×2−1+412yes—
1660C2×C4#58512yes—
1661C22—24no—
1662C22—24no—
1663C22—24no—
1664C22—42no—
1665C22—42no—
1666C22—42no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—42no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—42no—
1682C22—42no—
1683C22—42no—
1684C22—42no—
1685C22—42no—
1686C22—42no—
1687C22—42no—
1688C22—42no—
1689C22C22×H(5,𝔽2)11yescharacteristic
1690C22C22×H(5,𝔽2)11yescharacteristic
1691C22C22×H(5,𝔽2)11yescharacteristic
1692C22C22×2−1+411yescharacteristic
1693C22C22×2−1+411yescharacteristic
1694C22C2×#58511yescharacteristic
1695C222−1+611yescharacteristic
1696C4—24no—
1697C4—22no—
1698C4—22no—
1699C4—22no—
1700C4—22no—
1701C4—22no—
1702C4—22no—
1703C4—42no—
1704C4—42no—
1705C4—42no—
1706C4—44no—
1707C4—42no—
1708C4—44no—
1709C4—42no—
1710C4—41no—
1711C4—44no—
1712C4—41no—
1713C4—42no—
1714C4—42no—
1715C4—41no—
1716C4—41no—
1717C4—42no—
1718C4—41no—
1719C4—42no—
1720C4—42no—
1721C4—44no—
1722C4—42no—
1723C4—41no—
1724C4—41no—
1725C4#354314yes—
1726C4#355214yes—
1727C2—44no—
1728C2—82no—
1729C2—82no—
1730C2—82no—
1731C2C2×#354311yescharacteristic
1732C2C2×#355211yescharacteristic
1733C2#6283511yescharacteristic
1734C2#6291311yescharacteristic
1735C2#6293111yescharacteristic
1736C2#6294211yescharacteristic
1737C2#6301511yescharacteristic
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. #59817C2semidirect
2. #59654C2semidirect
3. #59652C2semidirect
4. #54282C2semidirect
5. #53721C2semidirect
6. #53492C2semidirect
7. #53095C2semidirect
8. #53001C2semidirect
9. #50779C2semidirect
10. #46019C2semidirect
11. #45677C2semidirect
12. #45248C2semidirect
13. #44940C2semidirect
14. #42807C2semidirect
15. #42739C2semidirect
16. #42668C2semidirect
17. #42472C2semidirect
18. #40152C2semidirect
19. #39618C2semidirect
20. #39491C2semidirect
21. #39360C2semidirect
22. #39282C2semidirect
23. #39166C2semidirect
24. #38958C2semidirect
25. #38027C2semidirect
26. #37628C2semidirect
27. #37379C2semidirect
28. #37312C2semidirect
29. #36598C2semidirect
30. Q8×#127C2semidirect
31. #36276C2semidirect
32. #35196C2semidirect
33. #35185C2semidirect
34. #34934C2semidirect
35. #34902C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596542
#596522
#542822
#537212
#534922
#530952
#530012
#507792
#460192
#456772
#452482
#449402
#428072
#427392
#426682
#424722
#401522
#396182
#394912
#393602
#392822
#391662
#389582
#380272
#376282
#373792
#373122
#365982
Q8×#1272
#362762
#351962
#351852
#349342
#349022