Finite Group Databasebeta

← #8095320

Subgroups — #8095320

Order 512.

4784 conjugacy classes of subgroups.

The subgroup lattice has 1743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53140C212yesmaximal, complemented
2#53108C212yesmaximal, complemented
3#53070C212yesmaximal, complemented
4#53056C212yesmaximal, complemented
5#53027C212yesmaximal, complemented
6#53025C212yesmaximal, complemented
7#53021C212yesmaximal, complemented
8#53010C212yesmaximal, complemented
9#52376C214yesmaximal, complemented
10#52321C214yesmaximal, complemented
11#45734C214yesmaximal, complemented
12#45718C212yesmaximal, complemented
13#45675C212yesmaximal, complemented
14#45670C212yesmaximal, complemented
15#45619C212yesmaximal, complemented
16#45603C212yesmaximal, complemented
17#45586C214yesmaximal, complemented
18#45525C212yesmaximal, complemented
19#45501C212yesmaximal, complemented
20#45500C212yesmaximal, complemented
21#35628C211yesmaximal, characteristic, complemented
22#35619C211yesmaximal, characteristic, complemented
23#35592C211yesmaximal, characteristic, complemented
24#35564C211yesmaximal, characteristic
25#35543C211yesmaximal, characteristic, complemented
26#35519C211yesmaximal, characteristic, complemented
27#35308C211yesmaximal, characteristic, complemented
28#35308C211yesmaximal, characteristic, complemented
29#35279C211yesmaximal, characteristic, complemented
30#35255C211yesmaximal, characteristic, complemented
31#35182C211yesmaximal, characteristic, complemented
32#35178C211yesmaximal, characteristic, complemented
33#34947C211yesmaximal, characteristic, complemented
34#34744C211yesmaximal, characteristic, complemented
35C2×#2451C211yesmaximal, characteristic, complemented
36C2×#537C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C2×#536C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C22×C4⋊Q8C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C22×C4×Q8C2211yescharacteristic
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2855C2212yes—
53#2854C2214yes—
54#2854C2212yes—
55#2853C2214yes—
56#2850C2212yes—
57#2850C2212yes—
58#2841C2214yes—
59#2841C2214yes—
60#2841C2214yes—
61#2839C2214yes—
62#2839C2214yes—
63#2837C2214yes—
64#2837C2214yes—
65#2836C2214yes—
66#2832C2214yes—
67#2832C2214yes—
68#2831C2214yes—
69#2831C2214yes—
70#2831C2214yes—
71#2831C2214yes—
72#2830C2214yes—
73#2829C2214yes—
74#2827C2214yes—
75#2820C2214yes—
76#2816C2214yes—
77#2814C2214yes—
78#2806C2214yes—
79#2806C2214yes—
80#2802C2214yes—
81#2802C2214yes—
82#2798C2214yes—
83#2798C2214yes—
84#2798C2214yes—
85#2788C2214yes—
86#2788C2214yes—
87#2783C2214yes—
88#2781C2214yes—
89#2779C2214yes—
90#2772C2214yes—
91#2768C2214yes—
92#2755C2214yes—
93#2755C2214yes—
94#2754C2214yes—
95#2754C2214yes—
96#2751C2214yes—
97#2747C2214yes—
98#2744C2214yes—
99#2743C2214yes—
100#2741C2214yes—
101#2741C2214yes—
102#2740C2214yes—
103#2740C2214yes—
104#2730C2214yes—
105#2710C2214yes—
106#2708C2214yes—
107#2704C2214yes—
108#2704C2214yes—
109#2700C2214yes—
110#2700C2214yes—
111#2696C2214yes—
112#2694C2214yes—
113#2692C2214yes—
114#2692C2214yes—
115#2687C2214yes—
116#2686C2214yes—
117#2672C2214yes—
118#2628C2212yes—
119#2628C2212yes—
120#2625C2212yes—
121#2624C2212yes—
122#2623C2214yes—
123#2621C2212yes—
124#2621C2212yes—
125#2620C2212yes—
126#2620C2212yes—
127#2618C2214yes—
128#2592C2212yes—
129#2592C2212yes—
130#2591C2214yes—
131#2582C2212yes—
132#2581C2212yes—
133#2580C2212yes—
134#2571C2212yes—
135#2570C2212yes—
136#2570C2212yes—
137#2568C2212yes—
138#2568C2212yes—
139#2568C2212yes—
140#2568C2211yescharacteristic
141#2567C2212yes—
142#2567C2211yescharacteristic
143#2566C2211yescharacteristic
144#2566C2211yescharacteristic
145#2565C2211yescharacteristic
146#2565C2211yescharacteristic
147#2564C2212yes—
148#2564C2212yes—
149#2563C2211yescharacteristic
150#2563C2212yes—
151#2552C2212yes—
152#2548C2212yes—
153#2546C2212yes—
154#2545C2212yes—
155#2545C2212yes—
156#2543C2214yes—
157#2542C2211yescharacteristic
158#2542C2212yes—
159#2538C2212yes—
160#2538C2212yes—
161#2538C2212yes—
162#2536C2212yes—
163#2536C2212yes—
164#2509C2212yes—
165#2508C2212yes—
166#2507C2212yes—
167#2506C2212yes—
168#2505C2214yes—
169#2503C2212yes—
170#2502C2212yes—
171#2499C2212yes—
172#2499C2212yes—
173#2492C2212yes—
174#2492C2212yes—
175#2492C2212yes—
176#2492C2212yes—
177#2492C2212yes—
178#2492C2212yes—
179#2491C2212yes—
180#2491C2212yes—
181#2491C2212yes—
182#2491C2212yes—
183#2489C2212yes—
184#2489C2212yes—
185#2488C2214yes—
186#2488C2214yes—
187#2487C2214yes—
188#2473C2214yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2451C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2450C2214yes—
198#2449C2214yes—
199#2448C2211yescharacteristic
200#2448C2212yes—
201#2448C2211yescharacteristic
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2447C2211yescharacteristic
206#2447C2211yescharacteristic
207#2446C2212yes—
208#2446C2212yes—
209#2446C2212yes—
210#2446C2212yes—
211#2446C2211yescharacteristic
212#2446C2211yescharacteristic
213#2445C2211yescharacteristic
214#2445C2211yescharacteristic
215#2444C2214yes—
216#2444C2212yes—
217#2444C2212yes—
218#2443C2212yes—
219#2443C2212yes—
220#2443C2214yes—
221#2442C2212yes—
222#2441C2212yes—
223#2440C2212yes—
224#2439C2212yes—
225#2436C2214yes—
226#2429C2212yes—
227#2429C2212yes—
228#2429C2212yes—
229#2429C2212yes—
230#2429C2212yes—
231#2428C2212yes—
232#2427C2212yes—
233#2427C2212yes—
234#2427C2212yes—
235#2427C2212yes—
236#2427C2212yes—
237#2426C2212yes—
238#2425C2214yes—
239#2425C2214yes—
240#2425C2214yes—
241#2425C2214yes—
242#2423C2212yes—
243#2423C2212yes—
244#2423C2212yes—
245#2422C2212yes—
246#2421C2212yes—
247#2421C2212yes—
248#2421C2212yes—
249#2420C2212yes—
250#2419C2214yes—
251#2419C2214yes—
252#2417C2212yes—
253#2417C2212yes—
254#2417C2212yes—
255#2416C2212yes—
256#2416C2214yes—
257#2415C2212yes—
258#2414C2212yes—
259#2409C2214yes—
260#2396C2212yes—
261#2396C2212yes—
262#2395C2212yes—
263#2395C2212yes—
264C2×#398C2212yes—
265C2×#395C2212yes—
266#2379C2214yes—
267#2378C2214yes—
268#2378C2214yes—
269#2376C2214yes—
270#2317C2211yescharacteristic
271#2317C2211yescharacteristic
272#2317C2211yescharacteristic
273#2317C2211yescharacteristic
274#2311C2211yescharacteristic
275#2311C2211yescharacteristic
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278#2310C2211yescharacteristic
279C4×C22⋊Q8C2212yes—
280C4×C22⋊Q8C2212yes—
281C4×#123C2212yes—
282C4×#123C2212yes—
283#2297C2211yescharacteristic
284#2297C2211yescharacteristic
285#2297C2211yescharacteristic
286#2297C2211yescharacteristic
287#2297C2211yescharacteristic
288#2296C2211yescharacteristic
289C2×#391C2211yescharacteristic
290C2×#391C2211yescharacteristic
291C2×#391C2212yes—
292C2×#389C2211yescharacteristic
293C2×#389C2211yescharacteristic
294C2×#387C2212yes—
295#2285C2211yescharacteristic
296#2285C2211yescharacteristic
297#2274C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2311yescharacteristic
302C23×Q8C2311yescharacteristic
303C23×Q8C2312yes—
304#537—44no—
305#537—44no—
306#536—44no—
307#536—44no—
308#536—44no—
309#533—44no—
310#532—44no—
311C2×C4⋊Q8—44no—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#125C2311yescharacteristic
324C2×#125C2311yescharacteristic
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2312yes—
329C2×#124C2314yes—
330C2×#124C2311yescharacteristic
331C2×#124C2311yescharacteristic
332C2×#124C2314yes—
333C2×#123C2312yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2314yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2314yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2314yes—
365#520—44no—
366C4×#41—44no—
367C4×#41—44no—
368C2×C4×Q8—44no—
369C2×C4×Q8C2311yescharacteristic
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2312yes—
379C2×C4×Q8C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2314yes—
392C2×#117C2311yescharacteristic
393C2×#117C2311yescharacteristic
394C2×#117C2311yescharacteristic
395C2×#117C2311yescharacteristic
396C2×#117C2311yescharacteristic
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C22×C4⋊C4C2311yescharacteristic
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2311yescharacteristic
403C22×C4⋊C4C2311yescharacteristic
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2311yescharacteristic
407C22×C4⋊C4C2312yes—
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C42C2311yescharacteristic
411C22×C42C2311yescharacteristic
412C22×C42C2311yescharacteristic
413C22×C42C2312yes—
414C22×C42C2312yes—
415C22×C42C2312yes—
416#400C2312yes—
417#400C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2312yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2312yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#399C2312yes—
442#399C2312yes—
443#399C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2312yes—
448#398C2314yes—
449#398C2314yes—
450#398C2312yes—
451#398C2312yes—
452#398C2312yes—
453#398C2312yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#398C2314yes—
469#398C2314yes—
470#398C2312yes—
471#398C2314yes—
472#398C2314yes—
473#398C2312yes—
474#398C2314yes—
475#398C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2312yes—
479#397C2314yes—
480#397C2314yes—
481#397C2314yes—
482#397C2312yes—
483#397C2314yes—
484#397C2314yes—
485#397C2312yes—
486#397C2314yes—
487#397C2314yes—
488#397C2314yes—
489#397C2314yes—
490#397C2314yes—
491#397C2312yes—
492#397C2312yes—
493#397C2314yes—
494#397C2314yes—
495#397C2314yes—
496#397C2312yes—
497#397C2314yes—
498#396C2312yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2312yes—
503#396C2312yes—
504#396C2312yes—
505#396C2314yes—
506#396C2314yes—
507#396C2314yes—
508#396C2314yes—
509#396C2314yes—
510#396C2314yes—
511#396C2314yes—
512#396C2314yes—
513#396C2314yes—
514#395C2312yes—
515#395C2312yes—
516#395C2314yes—
517#395C2314yes—
518#395C2314yes—
519#395C2314yes—
520#395C2314yes—
521#395C2314yes—
522#395C2314yes—
523#394C2312yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2312yes—
532#394C2314yes—
533#394C2314yes—
534#394C2312yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2312yes—
540#393C2312yes—
541#393C2314yes—
542#393C2312yes—
543#393C2314yes—
544#393C2314yes—
545#393C2314yes—
546#393C2314yes—
547#393C2314yes—
548#393C2314yes—
549#393C2314yes—
550#393C2314yes—
551#392C2314yes—
552#391C2311yescharacteristic
553#391C2311yescharacteristic
554#391C2311yescharacteristic
555#391C2311yescharacteristic
556#391C2312yes—
557#391C2312yes—
558#391C2312yes—
559#391C2312yes—
560#391C2312yes—
561#391C2312yes—
562#391C2312yes—
563#391C2312yes—
564#391C2311yescharacteristic
565#391C2311yescharacteristic
566#391C2314yes—
567#391C2314yes—
568#391C2312yes—
569#391C2312yes—
570#391C2312yes—
571#391C2314yes—
572#391C2314yes—
573#391C2312yes—
574#391C2314yes—
575#391C2314yes—
576#391C2311yescharacteristic
577#391C2311yescharacteristic
578#391C2314yes—
579#391C2312yes—
580#391C2312yes—
581#391C2314yes—
582#391C2314yes—
583#391C2312yes—
584#391C2312yes—
585#391C2312yes—
586#391C2312yes—
587#391C2314yes—
588#391C2311yescharacteristic
589#391C2311yescharacteristic
590#391C2314yes—
591#390C2311yescharacteristic
592#390C2311yescharacteristic
593#390C2312yes—
594#390C2312yes—
595#390C2311yescharacteristic
596#390C2311yescharacteristic
597#390C2312yes—
598#390C2312yes—
599#390C2314yes—
600#390C2314yes—
601#390C2311yescharacteristic
602#390C2311yescharacteristic
603#390C2311yescharacteristic
604#390C2314yes—
605#390C2311yescharacteristic
606#390C2311yescharacteristic
607#390C2311yescharacteristic
608#389C2314yes—
609#389C2314yes—
610#389C2312yes—
611#389C2312yes—
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2314yes—
617#389C2312yes—
618#389C2312yes—
619#389C2312yes—
620#389C2312yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2314yes—
625#389C2312yes—
626#389C2314yes—
627#389C2314yes—
628#389C2314yes—
629#389C2314yes—
630#389C2314yes—
631#389C2314yes—
632#389C2314yes—
633#389C2314yes—
634#389C2312yes—
635#389C2311yescharacteristic
636#389C2311yescharacteristic
637#389C2312yes—
638#389C2311yescharacteristic
639#389C2311yescharacteristic
640#389C2312yes—
641#389C2312yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2312yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2314yes—
662#388C2314yes—
663#388C2314yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2312yes—
668#388C2312yes—
669#388C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2312yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2314yes—
691#387C2312yes—
692#387C2314yes—
693#387C2314yes—
694#387C2312yes—
695#387C2312yes—
696#387C2314yes—
697#387C2314yes—
698#386C2312yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2312yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2312yes—
715#386C2312yes—
716#386C2312yes—
717#386C2312yes—
718#386C2312yes—
719#386C2312yes—
720#386C2312yes—
721#385C2312yes—
722#385C2312yes—
723#385C2312yes—
724#385C2312yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2314yes—
732#385C2312yes—
733#385C2312yes—
734#385C2314yes—
735#385C2314yes—
736#385C2312yes—
737#385C2312yes—
738#384C2311yescharacteristic
739#384C2311yescharacteristic
740#384C2311yescharacteristic
741#384C2311yescharacteristic
742#384C2312yes—
743#384C2312yes—
744#384C2312yes—
745#384C2312yes—
746#382C2311yescharacteristic
747#382C2311yescharacteristic
748#382C2312yes—
749#382C2312yes—
750#382C2314yes—
751#382C2311yescharacteristic
752#382C2311yescharacteristic
753#382C2314yes—
754#382C2312yes—
755#382C2312yes—
756#382C2314yes—
757#381C2314yes—
758#381C2314yes—
759#381C2312yes—
760#381C2314yes—
761#381C2314yes—
762#381C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2314yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2312yes—
773#380C2312yes—
774#380C2312yes—
775#380C2312yes—
776#380C2312yes—
777#380C2312yes—
778#380C2312yes—
779#380C2314yes—
780#380C2314yes—
781#380C2314yes—
782#380C2314yes—
783#380C2314yes—
784#380C2314yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2312yes—
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2311yescharacteristic
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C2×#95C2311yescharacteristic
815C2×#95C2311yescharacteristic
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C2×#95C2312yes—
821C2×#95C2312yes—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—24no—
827C2×#41—24no—
828C2×#41—24no—
829C2×#41—24no—
830C2×#41—24no—
831C22×Q8—24no—
832C22×Q8—24no—
833C22×Q8—24no—
834C22×Q8—44no—
835C22×Q8—44no—
836C22×Q8—82no—
837C22×Q8C2412yes—
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2411yescharacteristic
841C22×Q8C2411yescharacteristic
842C22×Q8C2412yes—
843C22×Q8C2414yes—
844C22×Q8C2412yes—
845C22×Q8C2414yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2411yescharacteristic
850C22×D4C2411yescharacteristic
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2411yescharacteristic
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C23×C4C2411yescharacteristic
875C4⋊Q8—44no—
876C4⋊Q8—44no—
877C4⋊Q8—44no—
878C4⋊Q8—44no—
879C4⋊Q8—42no—
880C4⋊Q8—42no—
881C4⋊Q8—42no—
882C4⋊Q8—44no—
883C4⋊Q8—44no—
884C4⋊Q8—44no—
885#127—42no—
886#125—42no—
887#125—42no—
888#125—84no—
889#124—42no—
890#124—42no—
891#124—44no—
892#124—44no—
893#124—44no—
894#124—48no—
895#124—84no—
896#123—28no—
897#123—44no—
898#123—48no—
899#123—48no—
900#123—48no—
901#123—84no—
902C22⋊Q8—28no—
903C22⋊Q8—44no—
904C22⋊Q8—44no—
905C22⋊Q8—44no—
906C22⋊Q8—48no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—44no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—44no—
915C22⋊Q8—44no—
916C22⋊Q8—44no—
917C22⋊Q8—84no—
918C22⋊Q8—84no—
919#121—44no—
920#121—44no—
921#121—44no—
922#121—44no—
923#121—44no—
924#121—44no—
925#121—48no—
926#121—48no—
927#121—84no—
928C4×Q8—44no—
929C4×Q8—44no—
930C4×Q8—44no—
931C4×Q8—44no—
932C4×Q8—44no—
933C4×Q8—44no—
934C4×Q8—42no—
935C4×Q8—42no—
936C4×Q8—42no—
937C4×Q8—42no—
938C4×Q8—44no—
939C4×D4—42no—
940C4×D4—42no—
941C4×D4—42no—
942C4×D4—42no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—44no—
947C4×D4—44no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—48no—
951#117—24no—
952#117—24no—
953#117—24no—
954#117—24no—
955#117—24no—
956#117—44no—
957#117—44no—
958#117—44no—
959C2×C4⋊C4—24no—
960C2×C4⋊C4—24no—
961C2×C4⋊C4—24no—
962C2×C4⋊C4—24no—
963C2×C4⋊C4—42no—
964C2×C4⋊C4—44no—
965C2×C4⋊C4—44no—
966C2×C4⋊C4—44no—
967C2×C4⋊C4—82no—
968C2×C4⋊C4—82no—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C42—24no—
1095C2×C42—24no—
1096C2×C42—24no—
1097C2×C42—44no—
1098C2×C42—44no—
1099C2×C42—44no—
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2414yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
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#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
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—
1200C24C2512yes—
1201C24C2512yes—
1202C24C2512yes—
1203C24C2511yescharacteristic
1204#41—416no—
1205#41—416no—
1206#41—416no—
1207C2×Q8—24no—
1208C2×Q8—22no—
1209C2×Q8—24no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—22no—
1214C2×Q8—22no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—24no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—24no—
1223C2×Q8—28no—
1224C2×Q8—42no—
1225C2×Q8—42no—
1226C2×Q8—42no—
1227C2×Q8—42no—
1228C2×Q8—44no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—44no—
1232C2×Q8—44no—
1233C2×Q8—42no—
1234C2×Q8—416no—
1235C2×Q8—816no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—24no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—42no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—22no—
1275C22×C4—22no—
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—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—22no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—24no—
1294C22×C4—41no—
1295C22×C4—42no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—42no—
1299C22×C4—41no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—42no—
1310C22×C4—42no—
1311C22×C4—42no—
1312C22×C4—42no—
1313C22×C4—41no—
1314C22×C4—42no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—44no—
1318C22×C4—44no—
1319C22×C4—44no—
1320C22×C4H(5,𝔽2)14yes—
1321C22×C4H(5,𝔽2)14yes—
1322C22×C42−1+414yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2512yes—
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2511yescharacteristic
1333C22×C4C2512yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2514yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2514yes—
1340C22×C4C2512yes—
1341C22×C4C2514yes—
1342C22×C4C2514yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2512yes—
1345C22×C4C2512yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—24no—
1379C4⋊C4—41no—
1380C4⋊C4—41no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—44no—
1418C4⋊C4—42no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C42−1+414yes—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—44no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—44no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—22no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—22no—
1489C42—22no—
1490C42—22no—
1491C42—24no—
1492C42—24no—
1493C42—24no—
1494C42—24no—
1495C42—24no—
1496C42—42no—
1497C42—42no—
1498C42—42no—
1499C42—42no—
1500C42—44no—
1501C42—44no—
1502C42—44no—
1503C42—44no—
1504C42—44no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
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—
1530C23C2×H(5,𝔽2)12yes—
1531C23C2×H(5,𝔽2)12yes—
1532C23C2×2−1+412yes—
1533C23C2611yescharacteristic
1534Q8—48no—
1535Q8—48no—
1536Q8—44no—
1537Q8—44no—
1538Q8—44no—
1539Q8—84no—
1540Q8—88no—
1541Q8—84no—
1542Q8—88no—
1543D4—48no—
1544D4—48no—
1545D4—48no—
1546D4—44no—
1547D4—44no—
1548D4—44no—
1549D4—84no—
1550D4—84no—
1551D4—164no—
1552D4—164no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—24no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—24no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—24no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—24no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—24no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—24no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—24no—
1636C2×C4—44no—
1637C2×C4—44no—
1638C2×C4—44no—
1639C2×C4—44no—
1640C2×C4—48no—
1641C2×C4—48no—
1642C2×C4—48no—
1643C2×C4—48no—
1644C2×C4—48no—
1645C2×C4—84no—
1646C2×C4—84no—
1647C2×C4—84no—
1648C2×C4—82no—
1649C2×C4—84no—
1650C2×C4—82no—
1651C2×C4—84no—
1652C2×C4—84no—
1653C2×C4—164no—
1654C2×C4#562116yes—
1655C2×C4C2×H(5,𝔽2)12yes—
1656C2×C4C2×H(5,𝔽2)12yes—
1657C2×C4C2×H(5,𝔽2)12yes—
1658C2×C4C2×H(5,𝔽2)12yes—
1659C2×C4C2×2−1+412yes—
1660C2×C4C2×2−1+412yes—
1661C2×C4C2×2−1+412yes—
1662C2×C4C2×2−1+412yes—
1663C2×C4C2×2−1+412yes—
1664C2×C4#58512yes—
1665C22—22no—
1666C22—22no—
1667C22—22no—
1668C22—22no—
1669C22—22no—
1670C22—22no—
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—
1689C22—42no—
1690C22—42no—
1691C22—42no—
1692C22C2×#56214yes—
1693C22C22×H(5,𝔽2)11yescharacteristic
1694C22C22×H(5,𝔽2)11yescharacteristic
1695C22C22×2−1+411yescharacteristic
1696C22C22×2−1+411yescharacteristic
1697C22C2×#58511yescharacteristic
1698C22H(7,𝔽2)11yescharacteristic
1699C222−1+611yescharacteristic
1700C4—22no—
1701C4—22no—
1702C4—22no—
1703C4—22no—
1704C4—41no—
1705C4—42no—
1706C4—42no—
1707C4—42no—
1708C4—42no—
1709C4—41no—
1710C4—44no—
1711C4—41no—
1712C4—42no—
1713C4—42no—
1714C4—44no—
1715C4—41no—
1716C4—41no—
1717C4—42no—
1718C4—41no—
1719C4—44no—
1720C4—41no—
1721C4—41no—
1722C4—42no—
1723C4—42no—
1724C4—42no—
1725C4—42no—
1726C4—42no—
1727C4—44no—
1728C4—42no—
1729C4C2×#56214yes—
1730C4C2×#56214yes—
1731C2—24no—
1732C2—82no—
1733C2—82no—
1734C2—82no—
1735C2C22×#56211yescharacteristic
1736C2#6283511yescharacteristic
1737C2#6287811yescharacteristic
1738C2#6292411yescharacteristic
1739C2#6294211yescharacteristic
1740C2#6294311yescharacteristic
1741C2#6295611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35564C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53140C2semidirect
2. #53108C2semidirect
3. #53070C2semidirect
4. #53056C2semidirect
5. #53027C2semidirect
6. #53025C2semidirect
7. #53021C2semidirect
8. #53010C2semidirect
9. #52376C2semidirect
10. #52321C2semidirect
11. #45734C2semidirect
12. #45718C2semidirect
13. #45675C2semidirect
14. #45670C2semidirect
15. #45619C2semidirect
16. #45603C2semidirect
17. #45586C2semidirect
18. #45525C2semidirect
19. #45501C2semidirect
20. #45500C2semidirect
21. #35628C2semidirect
22. #35619C2semidirect
23. #35592C2semidirect
25. #35543C2semidirect
26. #35519C2semidirect
27. #35308C2semidirect
28. #35308C2semidirect
29. #35279C2semidirect
30. #35255C2semidirect
31. #35182C2semidirect
32. #35178C2semidirect
33. #34947C2semidirect
34. #34744C2semidirect
35. C2×#2451C2semidirect

Maximal subgroups

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

subgroupindex
#531402
#531082
#530702
#530562
#530272
#530252
#530212
#530102
#523762
#523212
#457342
#457182
#456752
#456702
#456192
#456032
#455862
#455252
#455012
#455002
#356282
#356192
#355922
#355642
#355432
#355192
#353082
#352792
#352552
#351822
#351782
#349472
#347442
C2×#24512