Finite Group Databasebeta

← #7681137

Subgroups — #7681137

Order 512.

5274 conjugacy classes of subgroups.

The subgroup lattice has 1791 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59677C214yesmaximal, complemented
2#59675C214yesmaximal, complemented
3#59403C212yesmaximal, complemented
4#59398C212yesmaximal, complemented
5#59396C212yesmaximal, complemented
6#59393C212yesmaximal, complemented
7#45314C212yesmaximal, complemented
8#45309C212yesmaximal, complemented
9#45224C212yesmaximal, complemented
10#45046C212yesmaximal, complemented
11#43579C214yesmaximal, complemented
12#43155C214yesmaximal, complemented
13#39056C212yesmaximal, complemented
14#39054C212yesmaximal, complemented
15#38218C212yesmaximal, complemented
16#38213C212yesmaximal, complemented
17#38128C212yesmaximal, complemented
18#38123C212yesmaximal, complemented
19#36369C212yesmaximal, complemented
20#36278C212yesmaximal, complemented
21#35564C211yesmaximal, characteristic, complemented
22#35564C211yesmaximal, characteristic, complemented
23#35564C211yesmaximal, characteristic, complemented
24#35557C211yesmaximal, characteristic, complemented
25#35273C211yesmaximal, characteristic, complemented
26#35267C211yesmaximal, characteristic, complemented
27#35255C211yesmaximal, characteristic, complemented
28C2×#2507C211yesmaximal, characteristic, complemented
29#34744C211yesmaximal, characteristic, complemented
30#34274C211yesmaximal, characteristic, complemented
31#34267C211yesmaximal, characteristic, complemented
32#34253C211yesmaximal, characteristic, complemented
33#34250C211yesmaximal, characteristic, complemented
34#34141C211yesmaximal, characteristic, complemented
35C4×#537C211yesmaximal, characteristic, complemented
36C2×#537C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#537C2211yescharacteristic
40C2×#532C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#520C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47C2×C4×#41C2211yescharacteristic
48#2863C2212yes—
49#2860C2212yes—
50#2857C2212yes—
51#2856C2212yes—
52#2855C2212yes—
53#2854C2212yes—
54#2803C2214yes—
55#2800C2214yes—
56#2800C2214yes—
57#2797C2214yes—
58#2790C2214yes—
59#2787C2214yes—
60#2786C2214yes—
61#2783C2214yes—
62#2781C2214yes—
63#2780C2214yes—
64#2779C2214yes—
65#2779C2214yes—
66#2777C2214yes—
67#2772C2214yes—
68#2770C2214yes—
69#2761C2214yes—
70#2757C2214yes—
71#2756C2214yes—
72#2746C2214yes—
73#2741C2214yes—
74#2718C2214yes—
75#2708C2214yes—
76#2701C2214yes—
77#2691C2214yes—
78#2645C2212yes—
79#2644C2212yes—
80#2625C2212yes—
81#2624C2212yes—
82#2620C2212yes—
83#2620C2212yes—
84#2608C2214yes—
85#2608C2214yes—
86#2606C2214yes—
87#2603C2214yes—
88#2601C2214yes—
89#2597C2214yes—
90#2594C2214yes—
91#2593C2214yes—
92#2590C2214yes—
93#2587C2214yes—
94#2585C2214yes—
95#2579C2214yes—
96#2578C2214yes—
97#2576C2214yes—
98#2569C2214yes—
99#2559C2214yes—
100#2559C2214yes—
101#2554C2214yes—
102#2543C2214yes—
103#2543C2214yes—
104#2543C2214yes—
105#2543C2214yes—
106#2538C2212yes—
107#2538C2212yes—
108#2537C2212yes—
109#2537C2212yes—
110#2529C2214yes—
111#2525C2214yes—
112#2522C2214yes—
113#2512C2212yes—
114#2512C2214yes—
115#2512C2212yes—
116#2511C2212yes—
117#2511C2212yes—
118#2510C2214yes—
119#2509C2214yes—
120#2507C2212yes—
121#2507C2212yes—
122#2507C2212yes—
123#2507C2212yes—
124#2507C2212yes—
125#2507C2212yes—
126#2507C2212yes—
127#2507C2212yes—
128#2497C2214yes—
129#2497C2212yes—
130#2497C2212yes—
131#2497C2212yes—
132#2496C2212yes—
133#2496C2212yes—
134#2496C2212yes—
135#2495C2212yes—
136#2494C2212yes—
137#2485C2214yes—
138#2481C2214yes—
139#2481C2214yes—
140#2481C2214yes—
141#2476C2214yes—
142#2468C2214yes—
143#2467C2214yes—
144#2466C2214yes—
145#2464C2214yes—
146#2456C2214yes—
147#2448C2211yescharacteristic
148#2448C2211yescharacteristic
149#2447C2211yescharacteristic
150#2447C2211yescharacteristic
151#2446C2211yescharacteristic
152#2446C2211yescharacteristic
153#2445C2211yescharacteristic
154#2445C2211yescharacteristic
155#2444C2214yes—
156#2444C2214yes—
157#2444C2212yes—
158#2444C2212yes—
159#2443C2214yes—
160#2443C2212yes—
161#2443C2214yes—
162#2443C2212yes—
163#2429C2212yes—
164#2429C2212yes—
165#2429C2212yes—
166#2428C2212yes—
167#2428C2212yes—
168#2428C2212yes—
169#2427C2212yes—
170#2427C2212yes—
171#2427C2212yes—
172#2426C2212yes—
173#2426C2212yes—
174#2426C2212yes—
175#2423C2212yes—
176#2422C2212yes—
177#2421C2212yes—
178#2420C2212yes—
179#2420C2214yes—
180#2417C2212yes—
181#2417C2212yes—
182#2417C2212yes—
183#2416C2212yes—
184#2416C2214yes—
185#2416C2214yes—
186#2416C2214yes—
187#2416C2214yes—
188#2416C2214yes—
189#2416C2214yes—
190#2416C2212yes—
191#2416C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2415C2212yes—
195#2414C2212yes—
196#2414C2212yes—
197#2414C2212yes—
198#2395C2212yes—
199#2395C2212yes—
200C2×#398C2212yes—
201C2×#398C2212yes—
202#2374C2214yes—
203#2367C2211yescharacteristic
204#2367C2211yescharacteristic
205#2367C2211yescharacteristic
206#2367C2211yescharacteristic
207#2366C2211yescharacteristic
208#2366C2211yescharacteristic
209#2365C2211yescharacteristic
210#2365C2211yescharacteristic
211#2364C2214yes—
212#2364C2212yes—
213#2364C2212yes—
214#2363C2214yes—
215#2363C2212yes—
216#2363C2212yes—
217#2363C2212yes—
218#2362C2212yes—
219#2362C2212yes—
220#2362C2212yes—
221#2361C2212yes—
222#2361C2214yes—
223#2361C2212yes—
224#2361C2212yes—
225#2361C2212yes—
226#2361C2212yes—
227#2360C2212yes—
228#2360C2212yes—
229#2360C2212yes—
230#2353C2214yes—
231#2353C2214yes—
232#2352C2214yes—
233#2351C2212yes—
234Q8×C4⋊C4C2212yes—
235#2349C2212yes—
236#2349C2214yes—
237D4×C4⋊C4C2212yes—
238D4×C4⋊C4C2214yes—
239#2347C2212yes—
240#2346C2212yes—
241#2345C2212yes—
242#2345C2214yes—
243#2344C2212yes—
244#2325C2214yes—
245#2325C2214yes—
246#2324C2212yes—
247#2324C2212yes—
248#2324C2212yes—
249#2323C2212yes—
250#2323C2212yes—
251#2323C2212yes—
252#2320C2212yes—
253#2319C2212yes—
254#2317C2212yes—
255#2317C2211yescharacteristic
256#2316C2211yescharacteristic
257#2316C2212yes—
258#2316C2211yescharacteristic
259#2311C2211yescharacteristic
260#2311C2211yescharacteristic
261#2311C2211yescharacteristic
262#2311C2211yescharacteristic
263#2311C2211yescharacteristic
264C4×C22⋊Q8C2212yes—
265C4×C22⋊Q8C2212yes—
266C4×C22⋊Q8C2212yes—
267C4×#123C2212yes—
268C4×#123C2212yes—
269C4×#121C2212yes—
270C4×#121C2212yes—
271C4×#121C2212yes—
272C4×#121C2214yes—
273C4×#121C2214yes—
274#2297C2211yescharacteristic
275#2297C2211yescharacteristic
276#2297C2211yescharacteristic
277#2297C2211yescharacteristic
278#2297C2211yescharacteristic
279#2296C2212yes—
280#2296C2211yescharacteristic
281#2295C2212yes—
282#2293C2212yes—
283#2293C2212yes—
284C2×#389C2212yes—
285C2×#389C2212yes—
286C2×#389C2211yescharacteristic
287C2×#389C2211yescharacteristic
288C2×#389C2211yescharacteristic
289C2×#389C2211yescharacteristic
290#2290C2212yes—
291#2290C2212yes—
292C2×#387C2212yes—
293C2×#384C2211yescharacteristic
294#2274C2211yescharacteristic
295C42×D4C2212yes—
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2311yescharacteristic
302C22×#41C2311yescharacteristic
303#537—28no—
304#537—28no—
305#537—28no—
306#537—44no—
307#532—28no—
308#532—44no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×#127C2311yescharacteristic
312C2×#127C2311yescharacteristic
313C2×#126C2314yes—
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#124C2311yescharacteristic
317C2×#124C2311yescharacteristic
318C2×#124C2311yescharacteristic
319C2×#124C2311yescharacteristic
320C2×#123C2312yes—
321C2×#123C2312yes—
322C2×#123C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2312yes—
340C2×#121C2314yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2312yes—
345C2×#121C2312yes—
346C2×#121C2312yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2314yes—
352#520—28no—
353#520—28no—
354#520—44no—
355C4×#41—44no—
356C4×#41—44no—
357C4×#41—44no—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2314yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2314yes—
392C2×C4×D4C2314yes—
393C2×C4×D4C2314yes—
394C2×#117C2311yescharacteristic
395C2×#117C2311yescharacteristic
396C2×#117C2311yescharacteristic
397C2×#117C2311yescharacteristic
398C2×#117C2312yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2314yes—
405C22×C4⋊C4C2311yescharacteristic
406C22×C4⋊C4C2311yescharacteristic
407C22×C4⋊C4C2311yescharacteristic
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C4⋊C4C2311yescharacteristic
411C22×C4⋊C4C2312yes—
412C22×C4⋊C4C2314yes—
413C22×C4⋊C4C2312yes—
414C22×C4⋊C4C2311yescharacteristic
415C22×C4⋊C4C2312yes—
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2312yes—
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2311yescharacteristic
421C22×C42C2311yescharacteristic
422C22×C42C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2312yes—
425C22×C42C2312yes—
426C22×C42C2312yes—
427C22×C42C2312yes—
428#401C2314yes—
429#400C2312yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2312yes—
438#400C2314yes—
439#399C2314yes—
440#399C2312yes—
441#399C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2312yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2312yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2312yes—
467#397C2312yes—
468#397C2312yes—
469#397C2312yes—
470#397C2312yes—
471#397C2312yes—
472#397C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2312yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2312yes—
496#394C2312yes—
497#394C2312yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2312yes—
511#391C2312yes—
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2311yescharacteristic
515#391C2311yescharacteristic
516#391C2311yescharacteristic
517#391C2311yescharacteristic
518#391C2311yescharacteristic
519#391C2311yescharacteristic
520#391C2311yescharacteristic
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2311yescharacteristic
529#390C2311yescharacteristic
530#390C2314yes—
531#390C2314yes—
532#390C2314yes—
533#390C2314yes—
534#390C2311yescharacteristic
535#390C2314yes—
536#390C2314yes—
537#390C2312yes—
538#390C2314yes—
539#390C2311yescharacteristic
540#390C2311yescharacteristic
541#390C2312yes—
542#390C2311yescharacteristic
543#390C2314yes—
544#390C2311yescharacteristic
545#390C2311yescharacteristic
546#390C2311yescharacteristic
547#390C2311yescharacteristic
548#389C2312yes—
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2311yescharacteristic
563#389C2312yes—
564#389C2314yes—
565#389C2312yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2314yes—
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2314yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2311yescharacteristic
594#389C2311yescharacteristic
595#389C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2314yes—
600#388C2312yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2312yes—
623#388C2312yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2312yes—
631#388C2312yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2312yes—
636#388C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2314yes—
655#387C2314yes—
656#387C2312yes—
657#387C2314yes—
658#387C2312yes—
659#387C2314yes—
660#387C2312yes—
661#387C2314yes—
662#387C2312yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2312yes—
683#386C2312yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2312yes—
688#386C2312yes—
689#386C2312yes—
690#386C2312yes—
691#386C2312yes—
692#386C2312yes—
693#386C2312yes—
694#386C2312yes—
695#386C2312yes—
696#386C2312yes—
697#386C2314yes—
698#386C2312yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2312yes—
708#385C2312yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2312yes—
714#385C2312yes—
715#385C2314yes—
716#385C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#384C2312yes—
723#384C2314yes—
724#384C2312yes—
725#384C2312yes—
726#384C2312yes—
727#384C2312yes—
728#383C2314yes—
729#383C2314yes—
730#382C2314yes—
731#382C2312yes—
732#382C2314yes—
733#381C2314yes—
734#381C2314yes—
735#381C2312yes—
736#381C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2314yes—
751#380C2314yes—
752#380C2314yes—
753#380C2314yes—
754#380C2314yes—
755#380C2314yes—
756#380C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811#376C2312yes—
812#376C2314yes—
813C2×#95C2314yes—
814C2×#95C2312yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2311yescharacteristic
818C2×#95C2311yescharacteristic
819C2×#95C2312yes—
820C2×#95C2312yes—
821C43C2312yes—
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—
831C2×#41—24no—
832C2×#41—24no—
833C2×#41#4118yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×Q8C2411yescharacteristic
837C22×Q8C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2411yescharacteristic
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2411yescharacteristic
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2412yes—
850C22×D4C2412yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2414yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2411yescharacteristic
878C4⋊Q8—24no—
879C4⋊Q8—42no—
880#127—24no—
881#127—42no—
882#126—84no—
883#126—84no—
884#126—84no—
885#124—24no—
886#124—24no—
887#124—42no—
888#124—42no—
889#123—28no—
890#123—44no—
891#123—84no—
892C22⋊Q8—28no—
893C22⋊Q8—28no—
894C22⋊Q8—28no—
895C22⋊Q8—28no—
896C22⋊Q8—28no—
897C22⋊Q8—28no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900#121—28no—
901#121—28no—
902#121—28no—
903#121—28no—
904#121—216no—
905#121—216no—
906#121—28no—
907#121—28no—
908#121—216no—
909#121—28no—
910#121—28no—
911#121—48no—
912#121—44no—
913#121—44no—
914#121—44no—
915#121—44no—
916#121—48no—
917#121—84no—
918#121—84no—
919#121—84no—
920#121—84no—
921C4×Q8—28no—
922C4×Q8—28no—
923C4×Q8—42no—
924C4×Q8—42no—
925C4×Q8—42no—
926C4×Q8—42no—
927C4×Q8—42no—
928C4×Q8—42no—
929C4×Q8—44no—
930C4×D4—216no—
931C4×D4—216no—
932C4×D4—28no—
933C4×D4—28no—
934C4×D4—28no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—42no—
938C4×D4—42no—
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—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—48no—
954C4×D4—84no—
955C4×D4—84no—
956C4×D4—84no—
957#117—24no—
958#117—24no—
959#117—24no—
960#117—24no—
961#117—28no—
962#117—28no—
963#117—44no—
964#117—44no—
965#117—44no—
966#117—44no—
967#117—84no—
968C2×C4⋊C4—24no—
969C2×C4⋊C4—24no—
970C2×C4⋊C4—24no—
971C2×C4⋊C4—28no—
972C2×C4⋊C4—28no—
973C2×C4⋊C4—24no—
974C2×C4⋊C4—44no—
975C2×C4⋊C4—48no—
976C2×C4⋊C4—42no—
977C2×C4⋊C4—44no—
978C2×C4⋊C4—82no—
979C2×C4⋊C4—82no—
980C2×C4⋊C4—82no—
981C2×C4⋊C4—82no—
982C2×C4⋊C4—82no—
983C2×C4⋊C4#4118yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
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⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2412yes—
1106C2×C42—24no—
1107C2×C42—24no—
1108C2×C42—24no—
1109C2×C42—44no—
1110C2×C42—44no—
1111C2×C42—44no—
1112C2×C42—82no—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2414yes—
1120C2×C42C2412yes—
1121C2×C42C2414yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2412yes—
1133C2×C42C2414yes—
1134C2×C42C2414yes—
1135C2×C42C2412yes—
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2414yes—
1142C2×C42C2412yes—
1143C2×C42C2414yes—
1144C2×C42C2414yes—
1145C2×C42C2412yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2411yescharacteristic
1151#95C2411yescharacteristic
1152#95C2414yes—
1153#95C2411yescharacteristic
1154#95C2411yescharacteristic
1155#95C2414yes—
1156#95C2414yes—
1157#95C2411yescharacteristic
1158#95C2411yescharacteristic
1159#95C2411yescharacteristic
1160#95C2411yescharacteristic
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24C2512yes—
1211C24C2512yes—
1212C24C2512yes—
1213C24C2512yes—
1214C24C2511yescharacteristic
1215#41—232no—
1216#41—416no—
1217#41—416no—
1218#41—416no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—22no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8C2×#4114yes—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
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—28no—
1245C2×D4—28no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—28no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—42no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—44no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4C2×#4118yes—
1278C2×D4C2×#4114yes—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—22no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—24no—
1294C22×C4—24no—
1295C22×C4—24no—
1296C22×C4—24no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—28no—
1304C22×C4—28no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—41no—
1310C22×C4—42no—
1311C22×C4—41no—
1312C22×C4—42no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—42no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—44no—
1323C22×C4—41no—
1324C22×C4—42no—
1325C22×C4—41no—
1326C22×C4—41no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—41no—
1331C22×C4—42no—
1332C22×C4—44no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—44no—
1338C22×C4—44no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—44no—
1346C22×C4C2×#4118yes—
1347C22×C4C2×#4118yes—
1348C22×C4C2×#4114yes—
1349C22×C4C2×#4114yes—
1350C22×C4H(5,𝔽2)14yes—
1351C22×C4C2511yescharacteristic
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2512yes—
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2511yescharacteristic
1360C22×C4C2512yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2512yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2512yes—
1366C22×C4C2511yescharacteristic
1367C22×C4C2514yes—
1368C22×C4C2514yes—
1369C22×C4C2514yes—
1370C22×C4C2511yescharacteristic
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2514yes—
1374C22×C4C2512yes—
1375C22×C4C2511yescharacteristic
1376C22×C4C2511yescharacteristic
1377C22×C4C2511yescharacteristic
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C4⋊C4—22no—
1382C4⋊C4—22no—
1383C4⋊C4—28no—
1384C4⋊C4—28no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—24no—
1392C4⋊C4—24no—
1393C4⋊C4—28no—
1394C4⋊C4—28no—
1395C4⋊C4—28no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—22no—
1399C4⋊C4—22no—
1400C4⋊C4—22no—
1401C4⋊C4—22no—
1402C4⋊C4—22no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—24no—
1406C4⋊C4—28no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—22no—
1410C4⋊C4—41no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—41no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—44no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—42no—
1431C4⋊C4—42no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—42no—
1440C4⋊C4—42no—
1441C4⋊C4C2×#4118yes—
1442C4⋊C4C2×#4118yes—
1443C4⋊C42−1+414yes—
1444C22⋊C4—24no—
1445C22⋊C4—24no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—28no—
1457C22⋊C4—28no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—44no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C42—22no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—28no—
1508C42—28no—
1509C42—24no—
1510C42—24no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—22no—
1519C42—24no—
1520C42—24no—
1521C42—24no—
1522C42—42no—
1523C42—42no—
1524C42—42no—
1525C42—42no—
1526C42—42no—
1527C42—42no—
1528C42—44no—
1529C42—44no—
1530C42—44no—
1531C42—42no—
1532C42—44no—
1533C42—42no—
1534C42—44no—
1535C42—42no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—22no—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—22no—
1562C23—22no—
1563C23—22no—
1564C23—22no—
1565C23—22no—
1566C23—22no—
1567C23C22×#4114yes—
1568C23C22×#4112yes—
1569C23C22×#4112yes—
1570C23C2×H(5,𝔽2)12yes—
1571C23C2611yescharacteristic
1572Q8—28no—
1573Q8—44no—
1574Q8—44no—
1575Q8—44no—
1576D4—216no—
1577D4—28no—
1578D4—48no—
1579D4—48no—
1580D4—48no—
1581D4—48no—
1582D4—44no—
1583D4—44no—
1584D4—44no—
1585D4—88no—
1586D4—84no—
1587D4—84no—
1588D4—88no—
1589D4—88no—
1590D4—84no—
1591D4—164no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—24no—
1600C2×C4—21no—
1601C2×C4—24no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—216no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—24no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—22no—
1647C2×C4—24no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—24no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—24no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—21no—
1665C2×C4—24no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—24no—
1671C2×C4—48no—
1672C2×C4—44no—
1673C2×C4—44no—
1674C2×C4—44no—
1675C2×C4—44no—
1676C2×C4—48no—
1677C2×C4—48no—
1678C2×C4—48no—
1679C2×C4—88no—
1680C2×C4—88no—
1681C2×C4—84no—
1682C2×C4—84no—
1683C2×C4—84no—
1684C2×C4—84no—
1685C2×C4—82no—
1686C2×C4—84no—
1687C2×C4—84no—
1688C2×C4—82no—
1689C2×C4—84no—
1690C2×C4—84no—
1691C2×C4—84no—
1692C2×C4—164no—
1693C2×C4#553116yes—
1694C2×C4C22×#4118yes—
1695C2×C4C22×#4114yes—
1696C2×C4C22×#4112yes—
1697C2×C4C22×#4112yes—
1698C2×C4C22×#4112yes—
1699C2×C4C22×#4112yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×H(5,𝔽2)12yes—
1702C2×C4C2×2−1+412yes—
1703C2×C4C2×2−1+412yes—
1704C2×C4C2×2−1+412yes—
1705C2×C4#58512yes—
1706C22—22no—
1707C22—22no—
1708C22—22no—
1709C22—22no—
1710C22—22no—
1711C22—22no—
1712C22—24no—
1713C22—24no—
1714C22—24no—
1715C22—42no—
1716C22—42no—
1717C22—42no—
1718C22—42no—
1719C22—42no—
1720C22—42no—
1721C22—42no—
1722C22—42no—
1723C22—42no—
1724C22—42no—
1725C22—42no—
1726C22—42no—
1727C22—42no—
1728C22—42no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—42no—
1736C22—42no—
1737C22—42no—
1738C22—42no—
1739C22—42no—
1740C22C2×#55314yes—
1741C22C23×#4111yescharacteristic
1742C22C23×#4111yescharacteristic
1743C22C22×H(5,𝔽2)11yescharacteristic
1744C22C22×2−1+411yescharacteristic
1745C22C2×#58511yescharacteristic
1746C22H(7,𝔽2)11yescharacteristic
1747C22H(7,𝔽2)11yescharacteristic
1748C4—28no—
1749C4—22no—
1750C4—22no—
1751C4—22no—
1752C4—22no—
1753C4—24no—
1754C4—42no—
1755C4—42no—
1756C4—42no—
1757C4—42no—
1758C4—41no—
1759C4—41no—
1760C4—44no—
1761C4—44no—
1762C4—41no—
1763C4—41no—
1764C4—41no—
1765C4—42no—
1766C4—42no—
1767C4—41no—
1768C4—42no—
1769C4—41no—
1770C4—41no—
1771C4—42no—
1772C4—44no—
1773C4—42no—
1774C4—42no—
1775C4—42no—
1776C4C2×#55314yes—
1777C4C2×#55314yes—
1778C2—24no—
1779C2—44no—
1780C2—82no—
1781C2—82no—
1782C2—82no—
1783C2C22×#55311yescharacteristic
1784C2#6280511yescharacteristic
1785C2#6285811yescharacteristic
1786C2#6294411yescharacteristic
1787C2#6295711yescharacteristic
1788C2#6299211yescharacteristic
1789C2#6299911yescharacteristic
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. #59677C2semidirect
2. #59675C2semidirect
3. #59403C2semidirect
4. #59398C2semidirect
5. #59396C2semidirect
6. #59393C2semidirect
7. #45314C2semidirect
8. #45309C2semidirect
9. #45224C2semidirect
10. #45046C2semidirect
11. #43579C2semidirect
12. #43155C2semidirect
13. #39056C2semidirect
14. #39054C2semidirect
15. #38218C2semidirect
16. #38213C2semidirect
17. #38128C2semidirect
18. #38123C2semidirect
19. #36369C2semidirect
20. #36278C2semidirect
21. #35564C2semidirect
22. #35564C2semidirect
23. #35564C2semidirect
24. #35557C2semidirect
25. #35273C2semidirect
26. #35267C2semidirect
27. #35255C2semidirect
28. C2×#2507C2semidirect
29. #34744C2semidirect
30. #34274C2semidirect
31. #34267C2semidirect
32. #34253C2semidirect
33. #34250C2semidirect
34. #34141C2semidirect
35. C4×#537C2semidirect

Maximal subgroups

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

subgroupindex
#596772
#596752
#594032
#593982
#593962
#593932
#453142
#453092
#452242
#450462
#435792
#431552
#390562
#390542
#382182
#382132
#381282
#381232
#363692
#362782
#355642
#355572
#352732
#352672
#352552
C2×#25072
#347442
#342742
#342672
#342532
#342502
#341412
C4×#5372