Finite Group Databasebeta

← #8425255

Subgroups — #8425255

Order 512.

4885 conjugacy classes of subgroups.

The subgroup lattice has 1759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59581C212yesmaximal, complemented
2#59450C211yesmaximal, characteristic, complemented
3#59081C211yesmaximal, characteristic, complemented
4#59066C211yesmaximal, characteristic, complemented
5#59034C212yesmaximal, complemented
6#55021C214yesmaximal, complemented
7#54964C214yesmaximal, complemented
8#53071C212yesmaximal, complemented
9#53046C212yesmaximal, complemented
10#53025C212yesmaximal, complemented
11#52995C212yesmaximal, complemented
12#52553C214yesmaximal, complemented
13#42992C212yesmaximal, complemented
14#42860C212yesmaximal, complemented
15#42759C212yesmaximal, complemented
16#42500C212yesmaximal, complemented
17#40911C214yesmaximal, complemented
18#39789C212yesmaximal, complemented
19#39608C211yesmaximal, characteristic, complemented
20#39341C211yesmaximal, characteristic, complemented
21#39222C212yesmaximal, complemented
22#39125C211yesmaximal, characteristic, complemented
23#38941C211yesmaximal, characteristic, complemented
24#38286C212yesmaximal, complemented
25#37781C212yesmaximal, complemented
26#37634C211yesmaximal, characteristic, complemented
27#37616C211yesmaximal, characteristic, complemented
28#37593C212yesmaximal, complemented
29#37516C212yesmaximal, complemented
30#36463C211yesmaximal, characteristic, complemented
31#36457C211yesmaximal, characteristic, complemented
32#36150C211yesmaximal, characteristic, complemented
33#34929C211yesmaximal, characteristic, complemented
34#34898C211yesmaximal, characteristic, complemented
35#34889C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×#547C2212yes—
39C2×#537C2212yes—
40C2×#533C2211yescharacteristic
41C2×#533C2212yes—
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C2×#529C2211yescharacteristic
45#2858C2211yescharacteristic
46#2858C2212yes—
47#2857C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2841C2214yes—
51#2832C2214yes—
52#2832C2214yes—
53#2831C2214yes—
54#2829C2214yes—
55#2828C2214yes—
56#2826C2214yes—
57#2824C2214yes—
58#2824C2214yes—
59#2819C2214yes—
60#2816C2214yes—
61#2816C2214yes—
62#2813C2214yes—
63#2813C2214yes—
64#2803C2214yes—
65#2800C2214yes—
66#2797C2214yes—
67#2788C2214yes—
68#2781C2214yes—
69#2771C2214yes—
70#2768C2214yes—
71#2763C2214yes—
72#2763C2214yes—
73#2753C2214yes—
74#2743C2214yes—
75#2741C2214yes—
76#2737C2214yes—
77#2733C2214yes—
78#2729C2214yes—
79#2716C2214yes—
80#2712C2214yes—
81#2711C2214yes—
82#2710C2214yes—
83#2708C2214yes—
84#2704C2214yes—
85#2701C2214yes—
86#2701C2214yes—
87#2700C2214yes—
88#2699C2214yes—
89#2699C2214yes—
90#2696C2214yes—
91#2696C2214yes—
92#2692C2214yes—
93#2686C2214yes—
94#2686C2214yes—
95#2681C2214yes—
96#2676C2214yes—
97#2675C2214yes—
98#2674C2214yes—
99#2672C2214yes—
100#2671C2214yes—
101#2665C2214yes—
102#2663C2214yes—
103#2662C2214yes—
104#2660C2212yes—
105#2652C2214yes—
106#2651C2214yes—
107#2651C2214yes—
108#2650C2214yes—
109#2648C2214yes—
110#2641C2212yes—
111#2640C2212yes—
112#2636C2214yes—
113#2632C2214yes—
114#2628C2212yes—
115#2628C2212yes—
116#2627C2214yes—
117#2620C2212yes—
118#2620C2212yes—
119#2620C2212yes—
120#2619C2212yes—
121#2616C2212yes—
122#2616C2212yes—
123#2615C2212yes—
124#2597C2214yes—
125#2591C2214yes—
126#2578C2214yes—
127#2577C2212yes—
128#2575C2214yes—
129#2575C2212yes—
130#2571C2212yes—
131#2570C2211yescharacteristic
132#2568C2211yescharacteristic
133#2566C2212yes—
134#2565C2211yescharacteristic
135#2563C2211yescharacteristic
136#2563C2211yescharacteristic
137#2563C2212yes—
138#2563C2212yes—
139#2563C2212yes—
140#2562C2211yescharacteristic
141#2559C2212yes—
142#2557C2212yes—
143#2557C2214yes—
144#2556C2214yes—
145#2555C2214yes—
146#2551C2211yescharacteristic
147#2550C2211yescharacteristic
148#2550C2212yes—
149#2550C2212yes—
150#2548C2212yes—
151#2548C2211yescharacteristic
152#2547C2212yes—
153#2546C2211yescharacteristic
154#2544C2211yescharacteristic
155#2544C2212yes—
156#2542C2211yescharacteristic
157#2542C2211yescharacteristic
158#2541C2212yes—
159#2541C2211yescharacteristic
160#2540C2211yescharacteristic
161#2540C2212yes—
162#2538C2211yescharacteristic
163#2536C2212yes—
164#2536C2212yes—
165#2536C2211yescharacteristic
166#2536C2212yes—
167#2535C2211yescharacteristic
168#2524C2212yes—
169#2521C2212yes—
170#2513C2212yes—
171#2513C2212yes—
172#2511C2212yes—
173#2508C2212yes—
174#2506C2212yes—
175#2503C2212yes—
176#2500C2212yes—
177#2500C2212yes—
178#2497C2212yes—
179#2496C2211yescharacteristic
180#2495C2211yescharacteristic
181#2492C2212yes—
182#2492C2212yes—
183#2492C2211yescharacteristic
184#2491C2212yes—
185#2491C2212yes—
186#2491C2212yes—
187#2491C2212yes—
188#2491C2214yes—
189#2491C2212yes—
190#2491C2214yes—
191#2490C2214yes—
192#2490C2212yes—
193#2490C2212yes—
194#2490C2211yescharacteristic
195#2489C2212yes—
196#2487C2212yes—
197#2476C2214yes—
198#2476C2214yes—
199#2468C2212yes—
200#2467C2214yes—
201#2465C2214yes—
202#2464C2212yes—
203#2459C2214yes—
204#2459C2214yes—
205#2458C2214yes—
206#2458C2214yes—
207#2454C2212yes—
208#2453C2212yes—
209#2452C2212yes—
210#2452C2212yes—
211#2452C2212yes—
212#2451C2212yes—
213#2448C2212yes—
214#2448C2212yes—
215#2447C2212yes—
216#2446C2214yes—
217#2445C2212yes—
218#2445C2212yes—
219#2443C2214yes—
220#2442C2214yes—
221#2440C2212yes—
222#2439C2212yes—
223#2432C2212yes—
224#2429C2212yes—
225#2429C2212yes—
226#2428C2212yes—
227#2428C2212yes—
228#2428C2211yescharacteristic
229#2428C2212yes—
230#2427C2212yes—
231#2427C2212yes—
232#2427C2212yes—
233#2427C2211yescharacteristic
234#2426C2212yes—
235#2426C2212yes—
236#2426C2214yes—
237#2423C2211yescharacteristic
238#2422C2212yes—
239#2421C2212yes—
240#2421C2212yes—
241#2421C2211yescharacteristic
242#2420C2212yes—
243#2420C2212yes—
244#2416C2212yes—
245#2414C2212yes—
246#2414C2214yes—
247#2407C2212yes—
248#2407C2212yes—
249#2407C2212yes—
250#2407C2212yes—
251#2407C2212yes—
252#2402C2212yes—
253#2396C2214yes—
254#2395C2212yes—
255#2395C2212yes—
256#2388C2212yes—
257#2369C2211yescharacteristic
258#2367C2212yes—
259#2366C2211yescharacteristic
260#2366C2212yes—
261#2365C2212yes—
262#2363C2212yes—
263#2362C2212yes—
264#2360C2212yes—
265#2357C2212yes—
266#2357C2212yes—
267#2355C2211yescharacteristic
268#2352C2214yes—
269D4×C4⋊C4C2212yes—
270D4×C4⋊C4C2211yescharacteristic
271#2341C2212yes—
272#2341C2212yes—
273#2341C2212yes—
274#2337C2214yes—
275#2324C2212yes—
276#2323C2212yes—
277#2319C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2212yes—
280C4×#125C2211yescharacteristic
281C4×#126C2212yes—
282C4×#124C2211yescharacteristic
283C4×#124C2212yes—
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2212yes—
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×#121C2212yes—
289C4×#121C2211yescharacteristic
290C4×#121C2212yes—
291#2298C2212yes—
292#2297C2212yes—
293#2293C2212yes—
294#2285C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×Q8C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301C22×#41C2312yes—
302Q82—44no—
303#550—44no—
304#547—48no—
305#537—48no—
306#533—44no—
307#533—48no—
308#532—44no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2314yes—
319C2×#127C2311yescharacteristic
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2311yescharacteristic
323#529—44no—
324C2×#126C2312yes—
325C2×#126C2312yes—
326C2×#125C2311yescharacteristic
327C2×#125C2311yescharacteristic
328C2×#125C2312yes—
329C2×#125C2314yes—
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2311yescharacteristic
336C2×#124C2311yescharacteristic
337C2×#124C2314yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#123C2314yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2312yes—
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C2×#121C2314yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2311yescharacteristic
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2312yes—
373C2×#121C2314yes—
374C2×#121C2311yescharacteristic
375C2×#121C2311yescharacteristic
376C2×#121C2314yes—
377C2×#121C2314yes—
378C2×#121C2314yes—
379C2×#121C2312yes—
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2314yes—
385C2×C4×Q8C2311yescharacteristic
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2311yescharacteristic
406C2×C4×D4C2311yescharacteristic
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2314yes—
410C2×#117C2312yes—
411C22×C4⋊C4C2314yes—
412C22×C4⋊C4C2312yes—
413C22×C42C2311yescharacteristic
414C22×C42C2311yescharacteristic
415C22×C42C2312yes—
416#400C2312yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2312yes—
422#400C2312yes—
423#400C2314yes—
424#400C2314yes—
425#400C2312yes—
426#400C2312yes—
427#400C2312yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2314yes—
436#399C2312yes—
437#399C2314yes—
438#399C2312yes—
439#398C2312yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2312yes—
444#398C2312yes—
445#398C2312yes—
446#398C2312yes—
447#398C2314yes—
448#398C2312yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2312yes—
466#397C2312yes—
467#397C2314yes—
468#397C2312yes—
469#397C2312yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2312yes—
486#395C2314yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2312yes—
499#394C2314yes—
500#394C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2312yes—
516#394C2314yes—
517#394C2314yes—
518#394C2312yes—
519#394C2312yes—
520#394C2312yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#393C2314yes—
525#393C2314yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2312yes—
537#393C2314yes—
538#392C2312yes—
539#392C2314yes—
540#392C2314yes—
541#392C2314yes—
542#392C2314yes—
543#392C2312yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2312yes—
550#391C2314yes—
551#391C2312yes—
552#391C2311yescharacteristic
553#391C2311yescharacteristic
554#391C2312yes—
555#391C2312yes—
556#391C2312yes—
557#391C2314yes—
558#391C2314yes—
559#391C2312yes—
560#391C2312yes—
561#391C2314yes—
562#391C2311yescharacteristic
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2314yes—
567#391C2311yescharacteristic
568#390C2312yes—
569#390C2314yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2314yes—
577#390C2312yes—
578#390C2312yes—
579#390C2312yes—
580#390C2314yes—
581#390C2314yes—
582#390C2312yes—
583#390C2314yes—
584#390C2314yes—
585#390C2314yes—
586#390C2314yes—
587#390C2312yes—
588#390C2312yes—
589#390C2311yescharacteristic
590#390C2312yes—
591#390C2312yes—
592#390C2314yes—
593#390C2312yes—
594#390C2312yes—
595#390C2312yes—
596#390C2312yes—
597#390C2312yes—
598#390C2311yescharacteristic
599#390C2312yes—
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#389C2312yes—
603#389C2314yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2311yescharacteristic
608#389C2311yescharacteristic
609#389C2312yes—
610#389C2314yes—
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2314yes—
615#389C2312yes—
616#389C2312yes—
617#389C2311yescharacteristic
618#389C2312yes—
619#389C2314yes—
620#389C2312yes—
621#389C2314yes—
622#389C2312yes—
623#389C2312yes—
624#388C2312yes—
625#388C2312yes—
626#388C2312yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2312yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2312yes—
657#388C2312yes—
658#388C2314yes—
659#388C2312yes—
660#388C2314yes—
661#388C2312yes—
662#388C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2312yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#386C2312yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2312yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2312yes—
710#385C2312yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2312yes—
719#384C2312yes—
720#384C2311yescharacteristic
721#384C2311yescharacteristic
722#384C2311yescharacteristic
723#384C2312yes—
724#383C2312yes—
725#383C2312yes—
726#382C2311yescharacteristic
727#382C2311yescharacteristic
728#382C2311yescharacteristic
729#382C2312yes—
730#382C2314yes—
731#382C2312yes—
732#382C2312yes—
733#382C2314yes—
734#382C2311yescharacteristic
735#382C2312yes—
736#382C2312yes—
737#381C2312yes—
738#381C2314yes—
739#381C2314yes—
740#381C2314yes—
741#381C2314yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2314yes—
753#380C2312yes—
754#380C2314yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2314yes—
760#380C2314yes—
761#380C2312yes—
762#380C2311yescharacteristic
763#380C2311yescharacteristic
764#380C2311yescharacteristic
765#380C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2314yes—
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⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2312yes—
816#376C2312yes—
817C43C2312yes—
818C43C2311yescharacteristic
819C2×#41—28no—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C22×Q8C2411yescharacteristic
829C22×Q8C2412yes—
830C22×Q8C2411yescharacteristic
831C22×Q8C2412yes—
832C22×Q8C2414yes—
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2414yes—
861C23×C4C2414yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2414yes—
865C23×C4C2414yes—
866C23×C4C2412yes—
867C4⋊Q8—28no—
868C4⋊Q8—24no—
869C4⋊Q8—24no—
870C4⋊Q8—44no—
871C4⋊Q8—42no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—48no—
876#127—24no—
877#127—44no—
878#127—42no—
879#127—44no—
880#126—44no—
881#126—44no—
882#125—42no—
883#125—42no—
884#125—44no—
885#125—48no—
886#124—44no—
887#124—48no—
888#124—44no—
889#124—44no—
890#124—42no—
891#124—42no—
892#124—44no—
893#124—84no—
894#124—84no—
895#124—82no—
896#124—84no—
897#123—44no—
898#123—48no—
899#123—48no—
900#123—84no—
901C22⋊Q8—28no—
902C22⋊Q8—24no—
903C22⋊Q8—24no—
904C22⋊Q8—24no—
905C22⋊Q8—48no—
906C22⋊Q8—48no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—42no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—84no—
915C22⋊Q8—82no—
916#121—24no—
917#121—44no—
918#121—44no—
919#121—48no—
920#121—48no—
921#121—48no—
922#121—48no—
923#121—48no—
924#121—44no—
925#121—44no—
926#121—42no—
927#121—44no—
928#121—42no—
929#121—42no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—44no—
934#121—82no—
935#121—84no—
936C4×Q8—24no—
937C4×Q8—24no—
938C4×Q8—24no—
939C4×Q8—48no—
940C4×Q8—42no—
941C4×Q8—44no—
942C4×Q8—44no—
943C4×Q8—44no—
944C4×Q8—44no—
945C4×Q8—44no—
946C4×D4—24no—
947C4×D4—28no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—42no—
951C4×D4—44no—
952C4×D4—42no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—42no—
958C4×D4—42no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—48no—
963#117—44no—
964#117—44no—
965#117—48no—
966#117—44no—
967C2×C4⋊C4—44no—
968C2×C4⋊C4—48no—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C42—24no—
1098C2×C42—24no—
1099C2×C42—44no—
1100C2×C42C2412yes—
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2412yes—
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2414yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2411yescharacteristic
1126C2×C42C2412yes—
1127C2×C42C2414yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2411yescharacteristic
1135#95C2412yes—
1136#95C2412yes—
1137#95C2411yescharacteristic
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2411yescharacteristic
1142#95C2412yes—
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2411yescharacteristic
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196C24C2512yes—
1197C24C2511yescharacteristic
1198C24C2511yescharacteristic
1199C24C2512yes—
1200C24C2514yes—
1201#41—816no—
1202#41—816no—
1203#41—816no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—24no—
1207C2×Q8—24no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—24no—
1212C2×Q8—22no—
1213C2×Q8—44no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8—44no—
1217C2×Q8—42no—
1218C2×Q8—42no—
1219C2×Q8—44no—
1220C2×Q8—42no—
1221C2×Q8—44no—
1222C2×Q8—44no—
1223C2×Q8—44no—
1224C2×Q8H(5,𝔽2)14yes—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—24no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—28no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—22no—
1235C2×D4—24no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—44no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—42no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—44no—
1259C2×D4—42no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—42no—
1267C2×D4—44no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—24no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—28no—
1302C22×C4—28no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—41no—
1310C22×C4—41no—
1311C22×C4—44no—
1312C22×C4—42no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—42no—
1316C22×C4—44no—
1317C22×C4—44no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4—44no—
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2514yes—
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2512yes—
1341C22×C4C2514yes—
1342C22×C4C2512yes—
1343C22×C4C2514yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—28no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—22no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—28no—
1369C4⋊C4—28no—
1370C4⋊C4—24no—
1371C4⋊C4—24no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—44no—
1386C4⋊C4—41no—
1387C4⋊C4—41no—
1388C4⋊C4—41no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—44no—
1412C4⋊C42−1+414yes—
1413C22⋊C4—28no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—22no—
1423C22⋊C4—28no—
1424C22⋊C4—22no—
1425C22⋊C4—24no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—41no—
1433C22⋊C4—41no—
1434C22⋊C4—42no—
1435C22⋊C4—41no—
1436C22⋊C4—41no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—42no—
1445C22⋊C4—44no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—42no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—24no—
1487C42—24no—
1488C42—24no—
1489C42—24no—
1490C42—22no—
1491C42—24no—
1492C42—24no—
1493C42—24no—
1494C42—22no—
1495C42—22no—
1496C42—22no—
1497C42—24no—
1498C42—42no—
1499C42—42no—
1500C42—44no—
1501C42—44no—
1502C42—44no—
1503C42—42no—
1504C42—44no—
1505C42—41no—
1506C42—42no—
1507C42—44no—
1508C42H(5,𝔽2)14yes—
1509C23—22no—
1510C23—21no—
1511C23—21no—
1512C23—22no—
1513C23—22no—
1514C23—21no—
1515C23—22no—
1516C23—24no—
1517C23—24no—
1518C23—21no—
1519C23—21no—
1520C23—22no—
1521C23—24no—
1522C23—22no—
1523C23—21no—
1524C23—21no—
1525C23—24no—
1526C23—22no—
1527C23—21no—
1528C23—21no—
1529C23—22no—
1530C23—24no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—24no—
1538C23—22no—
1539C23—21no—
1540C23—24no—
1541C23—22no—
1542C23—22no—
1543C23—21no—
1544C23C2611yescharacteristic
1545Q8—28no—
1546Q8—44no—
1547Q8—48no—
1548Q8—84no—
1549Q8—88no—
1550Q8—84no—
1551Q8—164no—
1552D4—44no—
1553D4—44no—
1554D4—44no—
1555D4—48no—
1556D4—48no—
1557D4—84no—
1558D4—84no—
1559D4—88no—
1560D4—88no—
1561D4—84no—
1562D4—84no—
1563D4—84no—
1564D4—84no—
1565D4—84no—
1566D4—88no—
1567D4—164no—
1568D4—164no—
1569D4—164no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—24no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—22no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—21no—
1647C2×C4—22no—
1648C2×C4—21no—
1649C2×C4—22no—
1650C2×C4—48no—
1651C2×C4—44no—
1652C2×C4—44no—
1653C2×C4—48no—
1654C2×C4—44no—
1655C2×C4—48no—
1656C2×C4—44no—
1657C2×C4—88no—
1658C2×C4—82no—
1659C2×C4—82no—
1660C2×C4—88no—
1661C2×C4—84no—
1662C2×C4—88no—
1663C2×C4—164no—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×H(5,𝔽2)14yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×H(5,𝔽2)12yes—
1669C2×C4C2×2−1+414yes—
1670C2×C4C2×2−1+412yes—
1671C2×C4#58512yes—
1672C2×C4#58512yes—
1673C2×C4#58512yes—
1674C22—42no—
1675C22—41no—
1676C22—41no—
1677C22—42no—
1678C22—44no—
1679C22—41no—
1680C22—41no—
1681C22—42no—
1682C22—42no—
1683C22—44no—
1684C22—42no—
1685C22—44no—
1686C22—41no—
1687C22—42no—
1688C22—41no—
1689C22—41no—
1690C22—41no—
1691C22—42no—
1692C22—44no—
1693C22—42no—
1694C22—42no—
1695C22—42no—
1696C22—41no—
1697C22—44no—
1698C22—41no—
1699C22—41no—
1700C22—42no—
1701C22—44no—
1702C22—42no—
1703C22—41no—
1704C22—41no—
1705C22—41no—
1706C22—42no—
1707C22—42no—
1708C22—44no—
1709C22C22×H(5,𝔽2)11yescharacteristic
1710C22C22×H(5,𝔽2)11yescharacteristic
1711C22C22×2−1+411yescharacteristic
1712C22C2×#58511yescharacteristic
1713C22C2×#58511yescharacteristic
1714C22C2×#58511yescharacteristic
1715C22H(7,𝔽2)11yescharacteristic
1716C4—24no—
1717C4—22no—
1718C4—24no—
1719C4—22no—
1720C4—41no—
1721C4—42no—
1722C4—41no—
1723C4—42no—
1724C4—44no—
1725C4—41no—
1726C4—41no—
1727C4—42no—
1728C4—42no—
1729C4—42no—
1730C4—41no—
1731C4—42no—
1732C4—41no—
1733C4—42no—
1734C4—42no—
1735C4—44no—
1736C4—42no—
1737C4—41no—
1738C4—42no—
1739C4—41no—
1740C4—41no—
1741C4—42no—
1742C4—42no—
1743C4—44no—
1744C4#354714yes—
1745C4#355814yes—
1746C2—81no—
1747C2—81no—
1748C2—82no—
1749C2—82no—
1750C2—84no—
1751C2C2×#355811yescharacteristic
1752C2C2×#354711yescharacteristic
1753C2#6276211yescharacteristic
1754C2#6292311yescharacteristic
1755C2#6295211yescharacteristic
1756C2#6295511yescharacteristic
1757C2#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. #59581C2semidirect
2. #59450C2semidirect
3. #59081C2semidirect
4. #59066C2semidirect
5. #59034C2semidirect
6. #55021C2semidirect
7. #54964C2semidirect
8. #53071C2semidirect
9. #53046C2semidirect
10. #53025C2semidirect
11. #52995C2semidirect
12. #52553C2semidirect
13. #42992C2semidirect
14. #42860C2semidirect
15. #42759C2semidirect
16. #42500C2semidirect
17. #40911C2semidirect
18. #39789C2semidirect
19. #39608C2semidirect
20. #39341C2semidirect
21. #39222C2semidirect
22. #39125C2semidirect
23. #38941C2semidirect
24. #38286C2semidirect
25. #37781C2semidirect
26. #37634C2semidirect
27. #37616C2semidirect
28. #37593C2semidirect
29. #37516C2semidirect
30. #36463C2semidirect
31. #36457C2semidirect
32. #36150C2semidirect
33. #34929C2semidirect
34. #34898C2semidirect
35. #34889C2semidirect

Maximal subgroups

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

subgroupindex
#595812
#594502
#590812
#590662
#590342
#550212
#549642
#530712
#530462
#530252
#529952
#525532
#429922
#428602
#427592
#425002
#409112
#397892
#396082
#393412
#392222
#391252
#389412
#382862
#377812
#376342
#376162
#375932
#375162
#364632
#364572
#361502
#349292
#348982
#348892