Finite Group Databasebeta

← #7688608

Subgroups — #7688608

Order 512.

5213 conjugacy classes of subgroups.

The subgroup lattice has 1689 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59712C212yesmaximal, complemented
2#59669C212yesmaximal, complemented
3#59459C211yesmaximal, characteristic, complemented
4#59305C211yesmaximal, characteristic, complemented
5#59230C211yesmaximal, characteristic, complemented
6#59153C212yesmaximal, complemented
7#59136C212yesmaximal, complemented
8#59136C212yesmaximal, complemented
9#59113C212yesmaximal, complemented
10#44369C214yesmaximal, complemented
11#43561C214yesmaximal, complemented
12#43551C214yesmaximal, complemented
13#39983C212yesmaximal, complemented
14#39977C212yesmaximal, complemented
15#39751C212yesmaximal, complemented
16#39660C212yesmaximal, complemented
17#39657C212yesmaximal, complemented
18#39614C212yesmaximal, complemented
19#36599C211yesmaximal, characteristic, complemented
20#36565C211yesmaximal, characteristic, complemented
21#36561C211yesmaximal, characteristic, complemented
22#36561C211yesmaximal, characteristic, complemented
23#36288C211yesmaximal, characteristic, complemented
24#36261C211yesmaximal, characteristic, complemented
25#36189C211yesmaximal, characteristic, complemented
26#36129C212yesmaximal, complemented
27#36129C212yesmaximal, complemented
28#35931C214yesmaximal, complemented
29#34938C211yesmaximal, characteristic, complemented
30#34929C211yesmaximal, characteristic, complemented
31C2×#2551C211yesmaximal, characteristic, complemented
32#34332C212yesmaximal, complemented
33#34323C212yesmaximal
34C4×#554C211yesmaximal, characteristic, complemented
35C4×#553C211yesmaximal, characteristic
36C2×#554C2212yes—
37C2×#554C2211yescharacteristic
38C2×#554C2212yes—
39C2×#554C2212yes—
40C2×#553C2211yescharacteristic
41C2×#533C2212yes—
42C2×#533C2212yes—
43C22×C4⋊Q8C2212yes—
44C22×C4⋊Q8C2212yes—
45#2862C2212yes—
46#2862C2212yes—
47#2859C2211yescharacteristic
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2211yescharacteristic
53#2857C2211yescharacteristic
54#2805C2214yes—
55#2792C2214yes—
56#2790C2214yes—
57#2788C2214yes—
58#2784C2214yes—
59#2774C2214yes—
60#2763C2214yes—
61#2755C2214yes—
62#2755C2214yes—
63#2742C2214yes—
64#2729C2214yes—
65#2729C2214yes—
66#2729C2214yes—
67#2729C2214yes—
68#2726C2214yes—
69#2726C2214yes—
70#2720C2214yes—
71#2704C2214yes—
72#2704C2214yes—
73#2692C2214yes—
74#2683C2214yes—
75#2666C2214yes—
76#2665C2214yes—
77#2659C2214yes—
78#2612C2214yes—
79#2605C2214yes—
80#2588C2214yes—
81#2586C2214yes—
82#2586C2214yes—
83#2586C2214yes—
84#2585C2214yes—
85#2584C2212yes—
86#2584C2212yes—
87#2583C2214yes—
88#2579C2214yes—
89#2574C2214yes—
90#2574C2214yes—
91#2570C2212yes—
92#2569C2214yes—
93#2567C2212yes—
94#2567C2212yes—
95#2566C2212yes—
96#2564C2214yes—
97#2564C2214yes—
98#2563C2212yes—
99#2563C2212yes—
100#2556C2214yes—
101#2556C2214yes—
102#2556C2214yes—
103#2552C2211yescharacteristic
104#2552C2211yescharacteristic
105#2551C2212yes—
106#2551C2212yes—
107#2551C2214yes—
108#2551C2212yes—
109#2551C2211yescharacteristic
110#2551C2211yescharacteristic
111#2551C2211yescharacteristic
112#2551C2211yescharacteristic
113#2551C2212yes—
114#2551C2211yescharacteristic
115#2550C2214yes—
116#2550C2212yes—
117#2550C2212yes—
118#2550C2212yes—
119#2550C2212yes—
120#2550C2212yes—
121#2550C2214yes—
122#2550C2212yes—
123#2549C2214yes—
124#2549C2214yes—
125#2546C2211yescharacteristic
126#2542C2211yescharacteristic
127#2538C2211yescharacteristic
128#2520C2214yes—
129#2511C2212yes—
130#2511C2212yes—
131#2509C2212yes—
132#2508C2212yes—
133#2508C2212yes—
134#2507C2212yes—
135#2507C2212yes—
136#2506C2212yes—
137#2506C2212yes—
138#2506C2212yes—
139#2502C2212yes—
140#2497C2212yes—
141#2497C2212yes—
142#2492C2214yes—
143#2492C2212yes—
144#2492C2212yes—
145#2492C2214yes—
146#2492C2212yes—
147#2492C2212yes—
148#2492C2212yes—
149#2487C2212yes—
150#2465C2214yes—
151#2465C2214yes—
152#2462C2214yes—
153#2452C2214yes—
154#2452C2212yes—
155#2452C2212yes—
156#2452C2212yes—
157#2451C2212yes—
158#2451C2214yes—
159#2451C2212yes—
160#2451C2212yes—
161#2451C2212yes—
162#2449C2214yes—
163#2446C2214yes—
164#2446C2214yes—
165#2446C2212yes—
166#2442C2212yes—
167#2442C2214yes—
168#2442C2212yes—
169#2442C2214yes—
170#2442C2212yes—
171#2441C2212yes—
172#2440C2214yes—
173#2440C2212yes—
174#2440C2212yes—
175#2440C2212yes—
176#2440C2212yes—
177#2439C2212yes—
178#2439C2214yes—
179#2439C2212yes—
180#2438C2214yes—
181#2429C2214yes—
182#2429C2214yes—
183#2429C2212yes—
184#2429C2212yes—
185#2423C2212yes—
186#2417C2212yes—
187#2417C2214yes—
188#2417C2212yes—
189#2417C2214yes—
190#2417C2212yes—
191#2417C2212yes—
192#2417C2212yes—
193#2409C2214yes—
194#2409C2214yes—
195#2409C2214yes—
196#2399C2214yes—
197#2396C2214yes—
198C2×#395C2214yes—
199#2374C2212yes—
200#2373C2214yes—
201#2373C2212yes—
202#2370C2212yes—
203#2370C2212yes—
204#2370C2211yescharacteristic
205#2370C2214yes—
206#2370C2212yes—
207#2369C2212yes—
208#2369C2212yes—
209#2369C2212yes—
210#2369C2211yescharacteristic
211#2368C2212yes—
212#2368C2212yes—
213#2365C2211yescharacteristic
214#2365C2211yescharacteristic
215#2364C2212yes—
216#2363C2211yescharacteristic
217#2363C2212yes—
218#2361C2211yescharacteristic
219#2361C2214yes—
220#2361C2212yes—
221#2360C2214yes—
222#2360C2214yes—
223#2360C2212yes—
224#2360C2212yes—
225#2360C2211yescharacteristic
226#2360C2212yes—
227#2360C2211yescharacteristic
228#2359C2214yes—
229#2357C2211yescharacteristic
230#2355C2211yescharacteristic
231#2355C2211yescharacteristic
232#2355C2211yescharacteristic
233#2353C2212yes—
234#2352C2214yes—
235#2352C2212yes—
236#2352C2211yescharacteristic
237Q8×C4⋊C4C2212yes—
238#2349C2212yes—
239#2349C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241D4×C4⋊C4C2214yes—
242D4×C4⋊C4C2212yes—
243D4×C4⋊C4C2211yescharacteristic
244D4×C4⋊C4C2211yescharacteristic
245#2347C2211yescharacteristic
246#2346C2212yes—
247#2345C2212yes—
248#2345C2211yescharacteristic
249#2345C2212yes—
250#2345C2211yescharacteristic
251#2345C2212yes—
252#2345C2211yescharacteristic
253Q8×C22⋊C4C2214yes—
254#2335C2214yes—
255#2334C2214yes—
256#2330C2214yes—
257#2329C2214yes—
258#2329C2214yes—
259#2325C2214yes—
260C4×C4⋊Q8C2212yes—
261C4×C4⋊Q8C2212yes—
262C4×C4⋊Q8C2212yes—
263C4×C4⋊Q8C2211yescharacteristic
264C4×C4⋊Q8C2211yescharacteristic
265C4×#125C2212yes—
266C4×#125C2212yes—
267C4×#125C2211yescharacteristic
268C4×#126C2212yes—
269C4×C22⋊Q8C2212yes—
270C4×C22⋊Q8C2212yes—
271C4×C22⋊Q8C2212yes—
272C4×C22⋊Q8C2212yes—
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×#123C2212yes—
276C4×#121C2212yes—
277C4×#121C2212yes—
278C4×#121C2212yes—
279C4×#121C2211yescharacteristic
280C4×#121C2211yescharacteristic
281#2296C2212yes—
282#2295C2212yes—
283#2293C2212yes—
284C2×#389C2212yes—
285C2×#389C2212yes—
286C2×#389C2212yes—
287#2285C2211yescharacteristic
288C2×#384C2211yescharacteristic
289#2275C2214yes—
290C42×Q8C2211yescharacteristic
291C42×D4C2212yes—
292C42×D4C2212yes—
293C42×D4C2211yescharacteristic
294C42×D4C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C2×C4×C4⋊C4C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C23×Q8C2314yes—
300#554—216no—
301#554—28no—
302#554—48no—
303#554—48no—
304#553Q8116yescomplemented
305#533—48no—
306#533—48no—
307C2×C4⋊Q8—48no—
308C2×C4⋊Q8—48no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2312yes—
322C2×C4⋊Q8C2314yes—
323C2×C4⋊Q8C2314yes—
324C2×C4⋊Q8C2314yes—
325C2×C4⋊Q8C2314yes—
326C2×#126C2312yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#125C2312yes—
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#125C2314yes—
333C2×#125C2314yes—
334C2×#125C2311yescharacteristic
335C2×#123C2312yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2311yescharacteristic
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2314yes—
355C2×#121C2312yes—
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2314yes—
364C2×C4×Q8C2314yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2314yes—
367C2×C4×Q8C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2311yescharacteristic
385C2×#117C2311yescharacteristic
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2314yes—
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2314yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2314yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2311yescharacteristic
403C22×C42C2311yescharacteristic
404C22×C42C2311yescharacteristic
405C22×C42C2312yes—
406C22×C42C2312yes—
407C22×C42C2312yes—
408C22×C42C2312yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#399C2314yes—
421#399C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#391C2314yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2311yescharacteristic
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#390C2311yescharacteristic
511#390C2312yes—
512#390C2314yes—
513#390C2311yescharacteristic
514#390C2312yes—
515#390C2312yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2311yescharacteristic
569#389C2311yescharacteristic
570#389C2312yes—
571#389C2314yes—
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2314yes—
578#389C2312yes—
579#389C2314yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2312yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2312yes—
596#388C2312yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2314yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2312yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2312yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2314yes—
644#386C2312yes—
645#386C2312yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2312yes—
652#386C2312yes—
653#386C2312yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2312yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2314yes—
675#385C2312yes—
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2312yes—
679#384C2312yes—
680#384C2311yescharacteristic
681#384C2312yes—
682#384C2314yes—
683#384C2311yescharacteristic
684#384C2311yescharacteristic
685#384C2312yes—
686#384C2312yes—
687#383C2312yes—
688#382C2312yes—
689#382C2312yes—
690#382C2311yescharacteristic
691#382C2312yes—
692#382C2314yes—
693#382C2312yes—
694#382C2312yes—
695#382C2314yes—
696#382C2314yes—
697#381C2312yes—
698#380C2311yescharacteristic
699#380C2314yes—
700#380C2314yes—
701#380C2312yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2314yes—
707#380C2314yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#380C2312yes—
712#380C2314yes—
713#380C2312yes—
714#380C2311yescharacteristic
715#380C2311yescharacteristic
716#380C2312yes—
717#380C2312yes—
718#380C2314yes—
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2312yes—
722#380C2312yes—
723C4×C4⋊C4C2311yescharacteristic
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2312yes—
726C4×C4⋊C4C2311yescharacteristic
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2314yes—
731C4×C4⋊C4C2314yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2311yescharacteristic
736C4×C4⋊C4C2311yescharacteristic
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809#376C2314yes—
810#376C2312yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C43C2312yes—
817C43C2312yes—
818C43C2311yescharacteristic
819C22×Q8—48no—
820C22×Q8—48no—
821C22×Q8—48no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2414yes—
825C22×Q8C2412yes—
826C22×Q8C2414yes—
827C22×Q8C2414yes—
828C22×Q8C2414yes—
829C22×Q8C2414yes—
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C23×C4C2412yes—
835C23×C4C2411yescharacteristic
836C23×C4C2412yes—
837C23×C4C2412yes—
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2414yes—
843C23×C4C2412yes—
844C23×C4C2414yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2414yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C4⋊Q8—24no—
853C4⋊Q8—28no—
854C4⋊Q8—28no—
855C4⋊Q8—28no—
856C4⋊Q8—28no—
857C4⋊Q8—28no—
858C4⋊Q8—24no—
859C4⋊Q8—44no—
860C4⋊Q8—44no—
861C4⋊Q8—44no—
862C4⋊Q8—44no—
863C4⋊Q8—44no—
864C4⋊Q8—44no—
865C4⋊Q8—48no—
866C4⋊Q8—48no—
867C4⋊Q8—48no—
868C4⋊Q8—48no—
869#126C2×Q8116yescomplemented
870#125—28no—
871#125—216no—
872#125—28no—
873#125—44no—
874#125—44no—
875#125—48no—
876#125—48no—
877#125C2×Q818yescomplemented
878#123C2×Q8116yescomplemented
879C22⋊Q8—216no—
880C22⋊Q8—28no—
881C22⋊Q8—24no—
882C22⋊Q8—28no—
883C22⋊Q8—216no—
884C22⋊Q8—28no—
885C22⋊Q8—24no—
886C22⋊Q8—28no—
887C22⋊Q8—28no—
888C22⋊Q8—48no—
889C22⋊Q8—48no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—48no—
893C22⋊Q8—48no—
894C22⋊Q8—44no—
895C22⋊Q8—44no—
896C22⋊Q8—48no—
897C22⋊Q8—48no—
898#121C2×Q8116yes—
899#121C2×Q818yes—
900#121C2×Q818yescomplemented
901C4×Q8—28no—
902C4×Q8—24no—
903C4×Q8—24no—
904C4×Q8—24no—
905C4×Q8—44no—
906C4×Q8—48no—
907C4×Q8—44no—
908C4×Q8—48no—
909C4×Q8—48no—
910C4×Q8—44no—
911C4×D4—216no—
912C4×D4—28no—
913C4×D4—24no—
914C4×D4—28no—
915C4×D4—24no—
916C4×D4—24no—
917C4×D4—44no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—48no—
921C4×D4—42no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—48no—
925C4×D4C2×Q8116yes—
926C4×D4C2×Q818yes—
927C4×D4C2×Q818yescomplemented
928#117—24no—
929#117—48no—
930#117—44no—
931#117C2×Q818yescomplemented
932C2×C4⋊C4—28no—
933C2×C4⋊C4—24no—
934C2×C4⋊C4—24no—
935C2×C4⋊C4—24no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—48no—
939C2×C4⋊C4—44no—
940C2×C4⋊C4—48no—
941C2×C4⋊C4—44no—
942C2×C4⋊C4—48no—
943C2×C4⋊C4—44no—
944C2×C4⋊C4C2×Q818yes—
945C2×C4⋊C4#4118yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2412yes—
1063C2×C42—24no—
1064C2×C42—24no—
1065C2×C42—44no—
1066C2×C42—44no—
1067C2×C42—44no—
1068C2×C42—44no—
1069C2×C42C2412yes—
1070C2×C42C2412yes—
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2414yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2414yes—
1090C2×C42C2414yes—
1091C2×C42C2414yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2414yes—
1108C2×C42C2412yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111#95C2414yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2411yescharacteristic
1141#95C2412yes—
1142#95C2412yes—
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2411yescharacteristic
1151#95C2414yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185C24C2511yescharacteristic
1186C24C2512yes—
1187C24C2511yescharacteristic
1188C2×Q8—22no—
1189C2×Q8—24no—
1190C2×Q8—24no—
1191C2×Q8—28no—
1192C2×Q8—22no—
1193C2×Q8—24no—
1194C2×Q8—28no—
1195C2×Q8—28no—
1196C2×Q8—28no—
1197C2×Q8—28no—
1198C2×Q8—22no—
1199C2×Q8—24no—
1200C2×Q8—44no—
1201C2×Q8—42no—
1202C2×Q8—44no—
1203C2×Q8—44no—
1204C2×Q8—44no—
1205C2×Q8—44no—
1206C2×Q8—44no—
1207C2×Q8—44no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×Q8—44no—
1211C2×Q8—42no—
1212C2×Q8—832no—
1213C2×D4—24no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—24no—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—42no—
1220C2×D4—42no—
1221C2×D4C22×Q818yes—
1222C2×D4C22×Q814yes—
1223C2×D4C22×Q814yes—
1224C2×D4C22×Q818yes—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—24no—
1233C22×C4—24no—
1234C22×C4—28no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—24no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—24no—
1244C22×C4—28no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—22no—
1249C22×C4—42no—
1250C22×C4—42no—
1251C22×C4—42no—
1252C22×C4—42no—
1253C22×C4—42no—
1254C22×C4—42no—
1255C22×C4—42no—
1256C22×C4—41no—
1257C22×C4—42no—
1258C22×C4—42no—
1259C22×C4—42no—
1260C22×C4—42no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—41no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—41no—
1268C22×C4—42no—
1269C22×C4—44no—
1270C22×C4—44no—
1271C22×C4—44no—
1272C22×C4—44no—
1273C22×C4C22×Q814yes—
1274C22×C4C22×Q814yes—
1275C22×C4C22×Q818yes—
1276C22×C4C22×Q818yes—
1277C22×C4C2×#4114yes—
1278C22×C4C2×#4118yes—
1279C22×C4C2511yescharacteristic
1280C22×C4C2511yescharacteristic
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2514yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2514yes—
1290C22×C4C2512yes—
1291C22×C4C2512yes—
1292C22×C4C2514yes—
1293C22×C4C2512yes—
1294C22×C4C2514yes—
1295C22×C4C2511yescharacteristic
1296C22×C4C2511yescharacteristic
1297C22×C4C2511yescharacteristic
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2512yes—
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C4⋊C4—28no—
1312C4⋊C4—24no—
1313C4⋊C4—24no—
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—24no—
1317C4⋊C4—24no—
1318C4⋊C4—28no—
1319C4⋊C4—28no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—28no—
1323C4⋊C4—28no—
1324C4⋊C4—24no—
1325C4⋊C4—22no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—22no—
1331C4⋊C4—28no—
1332C4⋊C4—24no—
1333C4⋊C4—28no—
1334C4⋊C4—24no—
1335C4⋊C4—28no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—28no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—41no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4C22×Q814yes—
1385C4⋊C4C22×Q814yes—
1386C4⋊C4C22×Q818yes—
1387C4⋊C4C22×Q814yes—
1388C4⋊C4C22×Q818yes—
1389C4⋊C4C22×Q814yes—
1390C4⋊C4C22×Q818yes—
1391C4⋊C4C2×#4114yes—
1392C4⋊C4C2×#4114yes—
1393C4⋊C4C2×#4118yes—
1394C4⋊C4H(5,𝔽2)14yes—
1395C4⋊C4H(5,𝔽2)14yes—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—24no—
1401C22⋊C4—22no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—24no—
1405C22⋊C4—22no—
1406C22⋊C4—24no—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—42no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—41no—
1417C22⋊C4—44no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4C22×Q818yes—
1423C22⋊C4C22×Q814yes—
1424C22⋊C4C22×Q818yes—
1425C22⋊C4C22×Q814yes—
1426C22⋊C4C22×Q818yes—
1427C22⋊C4C22×Q818yes—
1428C42—28no—
1429C42—24no—
1430C42—24no—
1431C42—22no—
1432C42—22no—
1433C42—24no—
1434C42—24no—
1435C42—24no—
1436C42—24no—
1437C42—24no—
1438C42—24no—
1439C42—24no—
1440C42—22no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—24no—
1448C42—42no—
1449C42—42no—
1450C42—42no—
1451C42—42no—
1452C42—42no—
1453C42—42no—
1454C42—42no—
1455C42—42no—
1456C42—41no—
1457C42—42no—
1458C42—44no—
1459C42—42no—
1460C42—44no—
1461C42—44no—
1462C42—41no—
1463C42—42no—
1464C42—42no—
1465C42—44no—
1466C42—44no—
1467C42C22×Q818yes—
1468C42C22×Q814yes—
1469C422−1+414yes—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—22no—
1476C23—21no—
1477C23—22no—
1478C23—22no—
1479C23—21no—
1480C23—22no—
1481C23—21no—
1482C23—21no—
1483C23—22no—
1484C23—22no—
1485C23—21no—
1486C23C23×Q814yes—
1487C23C23×Q812yes—
1488C23C23×Q812yes—
1489C23C22×#4112yes—
1490C23#58512yes—
1491C23C2611yescharacteristic
1492Q8—416no—
1493Q8—44no—
1494Q8—48no—
1495Q8—84no—
1496Q8—88no—
1497Q8—88no—
1498Q8—88no—
1499Q8—88no—
1500D4—216no—
1501D4—28no—
1502D4—28no—
1503D4—48no—
1504C2×C4—22no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—22no—
1509C2×C4—22no—
1510C2×C4—22no—
1511C2×C4—22no—
1512C2×C4—22no—
1513C2×C4—22no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—22no—
1521C2×C4—21no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—28no—
1531C2×C4—28no—
1532C2×C4—28no—
1533C2×C4—22no—
1534C2×C4—24no—
1535C2×C4—21no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—24no—
1555C2×C4—24no—
1556C2×C4—21no—
1557C2×C4—24no—
1558C2×C4—24no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—24no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—21no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—48no—
1585C2×C4—48no—
1586C2×C4—48no—
1587C2×C4—44no—
1588C2×C4—48no—
1589C2×C4—48no—
1590C2×C4—48no—
1591C2×C4—44no—
1592C2×C4—88no—
1593C2×C4—84no—
1594C2×C4—84no—
1595C2×C4—84no—
1596C2×C4—82no—
1597C2×C4—88no—
1598C2×C4—164no—
1599C2×C4C23×Q812yes—
1600C2×C4C23×Q814yes—
1601C2×C4C23×Q812yes—
1602C2×C4C23×Q814yes—
1603C2×C4C23×Q812yes—
1604C2×C4C23×Q812yes—
1605C2×C4C23×Q814yes—
1606C2×C4C23×Q812yes—
1607C2×C4C22×#4114yes—
1608C2×C4C22×#4114yes—
1609C2×C4C22×#4112yes—
1610C2×C4C22×#4112yes—
1611C2×C4C2×H(5,𝔽2)14yes—
1612C2×C4C2×H(5,𝔽2)14yes—
1613C2×C4C2×H(5,𝔽2)12yes—
1614C2×C4C2×H(5,𝔽2)12yes—
1615C2×C4C2×2−1+412yes—
1616C2×C4C2×2−1+412yes—
1617C2×C4C2×2−1+412yes—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—24no—
1625C22—22no—
1626C22—22no—
1627C22—24no—
1628C22—24no—
1629C22—22no—
1630C22—41no—
1631C22—42no—
1632C22—41no—
1633C22—42no—
1634C22—42no—
1635C22—41no—
1636C22—41no—
1637C22—42no—
1638C22Q8×#4114yes—
1639C22C24×Q811yescharacteristic
1640C22C23×#4111yescharacteristic
1641C22C22×H(5,𝔽2)11yescharacteristic
1642C22C22×H(5,𝔽2)11yescharacteristic
1643C22C22×2−1+411yescharacteristic
1644C22C2×#58511yescharacteristic
1645C222−1+611yescharacteristic
1646C4—22no—
1647C4—24no—
1648C4—24no—
1649C4—24no—
1650C4—24no—
1651C4—24no—
1652C4—24no—
1653C4—22no—
1654C4—22no—
1655C4—22no—
1656C4—22no—
1657C4—24no—
1658C4—22no—
1659C4—42no—
1660C4—44no—
1661C4—41no—
1662C4—42no—
1663C4—42no—
1664C4—42no—
1665C4—41no—
1666C4—42no—
1667C4—44no—
1668C4—44no—
1669C4—42no—
1670C4—41no—
1671C4—42no—
1672C4—44no—
1673C4—42no—
1674C4—41no—
1675C4—41no—
1676C4#350314yes—
1677C4#351114yes—
1678C2—24no—
1679C2—44no—
1680C2—42no—
1681C2C2×Q8×#4111yescharacteristic
1682C2C2×#350311yescharacteristic
1683C2C2×#351111yescharacteristic
1684C2#6292811yescharacteristic
1685C2Q8×H(5,𝔽2)11yescharacteristic
1686C2#6298411yescharacteristic
1687C2#6301211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#553C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59712C2semidirect
2. #59669C2semidirect
3. #59459C2semidirect
4. #59305C2semidirect
5. #59230C2semidirect
6. #59153C2semidirect
7. #59136C2semidirect
8. #59136C2semidirect
9. #59113C2semidirect
10. #44369C2semidirect
11. #43561C2semidirect
12. #43551C2semidirect
13. #39983C2semidirect
14. #39977C2semidirect
15. #39751C2semidirect
16. #39660C2semidirect
17. #39657C2semidirect
18. #39614C2semidirect
19. #36599C2semidirect
20. #36565C2semidirect
21. #36561C2semidirect
22. #36561C2semidirect
23. #36288C2semidirect
24. #36261C2semidirect
25. #36189C2semidirect
26. #36129C2semidirect
27. #36129C2semidirect
28. #35931C2semidirect
29. #34938C2semidirect
30. #34929C2semidirect
31. C2×#2551C2semidirect
32. #34332C2semidirect
34. C4×#554C2semidirect
304. #553Q8semidirect
869. #126C2×Q8semidirect
877. #125C2×Q8semidirect
878. #123C2×Q8semidirect
900. #121C2×Q8semidirect
927. C4×D4C2×Q8semidirect
931. #117C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#597122
#596692
#594592
#593052
#592302
#591532
#591362
#591132
#443692
#435612
#435512
#399832
#399772
#397512
#396602
#396572
#396142
#365992
#365652
#365612
#362882
#362612
#361892
#361292
#359312
#349382
#349292
C2×#25512
#343322
#343232
C4×#5542
C4×#5532