Finite Group Databasebeta

← #7657360

Subgroups — #7657360

Order 512.

4684 conjugacy classes of subgroups.

The subgroup lattice has 1652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42499C212yesmaximal, complemented
2#42495C212yesmaximal, complemented
3#42486C212yesmaximal
4#42486C212yesmaximal
5#40636C214yesmaximal, complemented
6#40632C214yesmaximal, complemented
7#40626C214yesmaximal, complemented
8#40622C214yesmaximal, complemented
9#39498C211yesmaximal, characteristic, complemented
10#39369C211yesmaximal, characteristic, complemented
11#38966C211yesmaximal, characteristic, complemented
12#38965C211yesmaximal, characteristic, complemented
13#38107C212yesmaximal, complemented
14#38104C212yesmaximal, complemented
15#37878C212yesmaximal, complemented
16#37691C212yesmaximal, complemented
17#37643C211yesmaximal, characteristic, complemented
18#37624C211yesmaximal, characteristic, complemented
19#37481C212yesmaximal, complemented
20#37476C212yesmaximal, complemented
21#36416C211yesmaximal, characteristic, complemented
22#36407C211yesmaximal, characteristic, complemented
23#36192C211yesmaximal, characteristic, complemented
24#36134C211yesmaximal, characteristic, complemented
25#35963C212yesmaximal, complemented
26#35934C212yesmaximal, complemented
27#35843C212yesmaximal, complemented
28#35708C212yesmaximal, complemented
29#35294C211yesmaximal, characteristic, complemented
30#35253C212yesmaximal, complemented
31#34634C212yesmaximal, complemented
32#34625C211yesmaximal, characteristic, complemented
33#34194C211yesmaximal, characteristic
34#34186C211yesmaximal, characteristic
35D4×#117C211yesmaximal, characteristic
36C2×#544C2212yescomplemented
37C2×#533C2212yescomplemented
38C22×C4×D4C2211yescharacteristic
39C22×#117C2212yes—
40#2868C2211yescharacteristic, complemented
41#2859C2211yescharacteristic, complemented
42#2859C2211yescharacteristic, complemented
43#2859C2211yescharacteristic, complemented
44#2857C2212yescomplemented
45#2857C2212yescomplemented
46#2851C2212yescomplemented
47#2851C2212yescomplemented
48#2845C2214yescomplemented
49#2842C2214yes—
50#2842C2214yes—
51#2841C2214yes—
52#2841C2214yescomplemented
53#2841C2214yescomplemented
54#2807C2214yescomplemented
55#2807C2214yescomplemented
56#2790C2214yescomplemented
57#2790C2214yescomplemented
58#2788C2214yescomplemented
59#2780C2214yes—
60#2780C2214yes—
61#2768C2214yescomplemented
62#2768C2214yescomplemented
63#2768C2214yescomplemented
64#2748C2214yes—
65#2748C2214yes—
66#2742C2214yescomplemented
67#2732C2214yes—
68#2732C2214yes—
69#2729C2214yescomplemented
70#2720C2214yescomplemented
71#2720C2214yescomplemented
72#2720C2214yescomplemented
73#2704C2214yescomplemented
74#2704C2214yescomplemented
75#2692C2214yes—
76#2692C2214yes—
77#2677C2214yescomplemented
78#2667C2212yes—
79#2667C2214yes—
80#2667C2214yescomplemented
81#2667C2214yescomplemented
82#2667C2214yescomplemented
83#2667C2214yescomplemented
84#2666C2212yescomplemented
85#2666C2212yescomplemented
86#2666C2214yescomplemented
87#2665C2214yes—
88#2665C2212yes—
89#2660C2212yescomplemented
90#2660C2211yescharacteristic, complemented
91#2660C2211yescharacteristic, complemented
92#2647C2211yescharacteristic, complemented
93#2647C2211yescharacteristic, complemented
94#2647C2212yescomplemented
95#2629C2212yes—
96#2629C2212yes—
97#2629C2212yes—
98#2629C2212yes—
99#2629C2214yes—
100#2629C2211yescharacteristic
101#2629C2211yescharacteristic
102#2629C2212yes—
103#2629C2212yes—
104#2629C2212yescomplemented
105#2629C2212yescomplemented
106#2628C2211yescharacteristic
107#2628C2211yescharacteristic
108#2628C2212yes—
109#2628C2212yes—
110#2628C2212yescomplemented
111#2628C2212yescomplemented
112#2627C2214yescomplemented
113#2627C2214yescomplemented
114#2626C2214yes—
115#2626C2214yes—
116#2626C2214yes—
117#2626C2214yes—
118#2608C2214yes—
119#2608C2214yes—
120#2590C2214yescomplemented
121#2590C2214yescomplemented
122#2589C2214yescomplemented
123#2589C2214yescomplemented
124#2587C2214yescomplemented
125#2587C2214yescomplemented
126#2586C2214yescomplemented
127#2585C2214yescomplemented
128#2584C2212yescomplemented
129#2584C2212yescomplemented
130#2580C2212yes—
131#2580C2212yes—
132#2574C2214yescomplemented
133#2571C2211yescharacteristic, complemented
134#2570C2212yescomplemented
135#2570C2212yescomplemented
136#2570C2212yescomplemented
137#2569C2214yescomplemented
138#2566C2212yes—
139#2566C2212yes—
140#2556C2214yescomplemented
141#2556C2214yescomplemented
142#2556C2214yescomplemented
143#2552C2212yescomplemented
144#2552C2212yescomplemented
145#2552C2211yescharacteristic, complemented
146#2552C2211yescharacteristic, complemented
147#2552C2211yescharacteristic, complemented
148#2552C2212yescomplemented
149#2552C2211yescharacteristic, complemented
150#2552C2212yescomplemented
151#2552C2212yescomplemented
152#2552C2211yescharacteristic, complemented
153#2552C2211yescharacteristic, complemented
154#2551C2212yescomplemented
155#2551C2211yescharacteristic, complemented
156#2550C2212yescomplemented
157#2550C2212yescomplemented
158#2550C2212yescomplemented
159#2549C2214yescomplemented
160#2542C2212yes—
161#2542C2212yes—
162#2538C2212yes—
163#2538C2212yes—
164#2522C2214yescomplemented
165#2522C2214yescomplemented
166#2522C2214yescomplemented
167#2520C2214yescomplemented
168#2509C2212yescomplemented
169#2508C2212yescomplemented
170#2507C2212yescomplemented
171#2507C2214yescomplemented
172#2506C2212yescomplemented
173#2497C2214yescomplemented
174#2465C2214yescomplemented
175#2462C2214yescomplemented
176#2454C2212yes—
177#2454C2212yes—
178#2454C2212yes—
179#2454C2212yes—
180#2454C2212yes—
181#2454C2212yes—
182#2452C2212yes—
183#2452C2212yes—
184#2446C2214yescomplemented
185#2442C2212yescomplemented
186#2442C2212yescomplemented
187#2442C2214yescomplemented
188#2441C2214yes—
189#2441C2212yes—
190#2441C2212yes—
191#2441C2212yes—
192#2441C2212yescomplemented
193#2441C2212yescomplemented
194#2441C2212yescomplemented
195#2441C2212yescomplemented
196#2441C2212yescomplemented
197#2441C2212yescomplemented
198#2441C2212yescomplemented
199#2441C2212yescomplemented
200#2441C2212yescomplemented
201#2441C2212yescomplemented
202#2440C2214yescomplemented
203#2440C2212yescomplemented
204#2440C2212yescomplemented
205#2439C2214yes—
206#2439C2212yes—
207#2439C2212yes—
208#2439C2212yes—
209#2439C2212yescomplemented
210#2439C2212yescomplemented
211#2438C2214yescomplemented
212#2438C2214yescomplemented
213#2437C2214yes—
214#2437C2214yes—
215#2429C2214yescomplemented
216#2423C2214yescomplemented
217#2423C2214yescomplemented
218#2402C2212yescomplemented
219#2399C2212yescomplemented
220#2396C2212yes—
221#2396C2214yes—
222#2396C2212yes—
223#2396C2214yes—
224#2396C2214yescomplemented
225#2396C2214yescomplemented
226#2370C2212yescomplemented
227#2370C2212yescomplemented
228#2370C2212yescomplemented
229#2370C2212yescomplemented
230#2369C2212yescomplemented
231#2365C2212yescomplemented
232#2357C2212yes—
233#2357C2212yes—
234#2357C2214yes—
235#2355C2212yescomplemented
236#2354C2211yescharacteristic
237#2354C2211yescharacteristic
238#2354C2211yescharacteristic
239#2354C2211yescharacteristic
240#2354C2211yescharacteristic
241#2354C2212yes—
242#2354C2211yescharacteristic
243#2354C2211yescharacteristic
244#2354C2211yescharacteristic
245#2354C2212yes—
246#2352C2212yes—
247#2352C2212yes—
248#2352C2212yes—
249#2352C2212yes—
250Q8×C4⋊C4C2212yescomplemented
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2211yescharacteristic
253D4×C4⋊C4C2211yescharacteristic
254D4×C4⋊C4C2211yescharacteristic
255#2345C2212yes—
256#2344C2211yescharacteristic
257#2344C2211yescharacteristic
258#2342C2212yes—
259#2342C2212yes—
260#2342C2214yes—
261D4×C22⋊C4C2211yescharacteristic
262D4×C22⋊C4C2211yescharacteristic
263D4×C22⋊C4C2212yes—
264#2331C2212yescomplemented
265#2330C2212yescomplemented
266#2319C2212yes—
267#2318C2214yes—
268#2317C2212yescomplemented
269#2317C2212yescomplemented
270#2316C2212yescomplemented
271#2312C2214yes—
272#2309C2212yes—
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×C4⋊Q8C2211yescharacteristic, complemented
275C4×#125C2211yescharacteristic, complemented
276C4×#125C2211yescharacteristic, complemented
277#2296C2212yescomplemented
278#2296C2212yescomplemented
279#2293C2211yescharacteristic
280#2293C2211yescharacteristic
281#2290C2212yes—
282#2290C2212yes—
283#2285C2211yescharacteristic
284#2285C2211yescharacteristic
285#2285C2211yescharacteristic
286#2285C2211yescharacteristic
287#2285C2212yescomplemented
288#2283C2211yescharacteristic
289#2280C2212yes—
290#2280C2212yes—
291#2280C2212yes—
292#2280C2212yes—
293C2×#380C2212yes—
294#2275C2212yes—
295#2274C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C23×D4C2311yescharacteristic
300C24×C4C2312yes—
301#544—48no—
302#533—48no—
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2312yes—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2314yes—
310C2×C4⋊Q8C2312yes—
311C2×#125C2311yescharacteristic
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#125C2314yes—
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2314yes—
335C2×C4×Q8C2314yes—
336C2×C4×D4Q8116yescomplemented
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2312yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2312yes—
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2312yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2311yescharacteristic
349C2×#117—48no—
350C2×#117C2312yes—
351C2×#117C2311yescharacteristic
352C2×#117C2312yes—
353C2×#117C2312yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2312yes—
364C2×#117C2312yes—
365C2×#117C2312yes—
366C2×#117C2311yescharacteristic
367C2×#117C2312yes—
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2312yes—
371C22×C4⋊C4C2312yes—
372C22×C4⋊C4C2311yescharacteristic
373C22×C22⋊C4C2312yes—
374C22×C22⋊C4C2312yes—
375C22×C22⋊C4C2314yes—
376C22×C22⋊C4C2312yes—
377C22×C42C2312yes—
378C22×C42C2312yes—
379C22×C42C2311yescharacteristic
380#400C2312yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2312yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2314yes—
390#400C2312yes—
391#400C2314yes—
392#400C2312yes—
393#400C2312yes—
394#399C2314yes—
395#399C2314yes—
396#399C2314yes—
397#399C2314yes—
398#399C2314yes—
399#399C2314yes—
400#399C2314yes—
401#399C2314yes—
402#399C2314yes—
403#399C2314yes—
404#399C2314yes—
405#399C2312yes—
406#399C2312yes—
407#399C2314yes—
408#399C2314yes—
409#399C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2312yes—
436#398C2312yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2312yes—
443#398C2312yes—
444#398C2312yes—
445#398C2312yes—
446#398C2312yes—
447#398C2312yes—
448#398C2312yes—
449#398C2312yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2312yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2312yes—
477#396C2312yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2312yes—
483#395C2314yes—
484#395C2314yes—
485#395C2312yes—
486#395C2314yes—
487#395C2312yes—
488#395C2314yes—
489#395C2312yes—
490#395C2312yes—
491#395C2312yes—
492#393C2314yes—
493#393C2314yes—
494#393C2314yes—
495#393C2314yes—
496#393C2314yes—
497#393C2312yes—
498#393C2312yes—
499#393C2314yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2312yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2311yescharacteristic
520#390C2311yescharacteristic
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2311yescharacteristic
526#389C2312yes—
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2311yescharacteristic
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2312yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2311yescharacteristic
553#389C2311yescharacteristic
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2311yescharacteristic
572#389C2311yescharacteristic
573#389C2312yes—
574#389C2312yes—
575#389C2312yes—
576#389C2314yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#389C2312yes—
584#389C2314yes—
585#389C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2312yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2312yes—
641#386C2312yes—
642#386C2312yes—
643#386C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2312yes—
662#385C2312yes—
663#385C2312yes—
664#385C2312yes—
665#385C2314yes—
666#384C2311yescharacteristic
667#384C2311yescharacteristic
668#384C2312yes—
669#384C2312yes—
670#384C2312yes—
671#384C2312yes—
672#384C2312yes—
673#384C2311yescharacteristic
674#384C2312yes—
675#384C2314yes—
676#384C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#384C2311yescharacteristic
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2311yescharacteristic
684#384C2311yescharacteristic
685#384C2312yes—
686#384C2314yes—
687#383C2312yes—
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2312yes—
691#382C2312yes—
692#382C2311yescharacteristic
693#382C2312yes—
694#382C2312yes—
695#382C2312yes—
696#382C2312yes—
697#382C2312yes—
698#382C2314yes—
699#382C2312yes—
700#382C2312yes—
701#382C2311yescharacteristic
702#381C2314yes—
703#381C2312yes—
704#381C2314yes—
705#381C2312yes—
706#381C2312yes—
707#381C2314yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2314yes—
713#380C2314yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2314yes—
727#380C2312yes—
728#380C2314yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2314yes—
735#380C2314yes—
736#380C2311yescharacteristic
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#379C2314yes—
743#379C2314yes—
744#379C2312yes—
745#379C2312yes—
746#379C2314yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808#376C2312yes—
809#376C2311yescharacteristic
810#376C2311yescharacteristic
811C2×#95C2314yes—
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C25C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2414yes—
817C22×Q8C2412yes—
818C22×Q8C2414yes—
819C22×D4—42no—
820C22×D4—42no—
821C22×D4C2×Q818yes—
822C22×D4C2411yescharacteristic
823C22×D4C2411yescharacteristic
824C22×D4C2412yes—
825C23×C4—44no—
826C23×C4—44no—
827C23×C4C2×Q8116yes—
828C23×C4C2412yes—
829C23×C4C2411yescharacteristic
830C23×C4C2412yes—
831C23×C4C2411yescharacteristic
832C23×C4C2412yes—
833C23×C4C2412yes—
834C23×C4C2414yes—
835C23×C4C2412yes—
836C23×C4C2414yes—
837C23×C4C2412yes—
838C23×C4C2411yescharacteristic
839C23×C4C2412yes—
840C23×C4C2412yes—
841C23×C4C2412yes—
842C4⋊Q8—24no—
843C4⋊Q8—28no—
844C4⋊Q8—42no—
845C4⋊Q8—44no—
846C4⋊Q8—44no—
847C4⋊Q8—44no—
848C4⋊Q8—48no—
849C4⋊Q8—82no—
850#125—24no—
851#125—44no—
852#125—44no—
853#125—44no—
854#125—42no—
855#125—44no—
856#125—44no—
857#125—44no—
858#125—44no—
859#125—44no—
860#125—48no—
861#125—84no—
862#125—82no—
863C22⋊Q8—48no—
864C22⋊Q8—48no—
865C22⋊Q8—48no—
866C22⋊Q8—48no—
867C22⋊Q8—84no—
868C22⋊Q8—84no—
869C22⋊Q8—84no—
870C22⋊Q8—84no—
871C4×Q8—44no—
872C4×Q8—44no—
873C4×Q8—48no—
874C4×Q8—48no—
875C4×D4—42no—
876C4×D4—42no—
877C4×D4—44no—
878C4×D4—42no—
879C4×D4—44no—
880C4×D4—42no—
881C4×D4C2×Q818yes—
882C4×D4C2×Q818yes—
883C4×D4C2×Q8116yes—
884C4×D4C2×Q818yes—
885C4×D4C2×Q818yes—
886C4×D4C2×Q8116yes—
887#117—24no—
888#117—28no—
889#117—44no—
890#117—44no—
891#117—44no—
892#117—42no—
893#117—44no—
894#117—44no—
895#117—44no—
896#117—44no—
897#117—44no—
898#117—44no—
899#117—44no—
900#117—44no—
901#117—44no—
902#117—44no—
903#117—44no—
904#117—82no—
905C2×C4⋊C4—44no—
906C2×C4⋊C4—44no—
907C2×C4⋊C4—44no—
908C2×C4⋊C4—44no—
909C2×C4⋊C4C2×Q818yes—
910C2×C4⋊C4C2411yescharacteristic
911C2×C4⋊C4C2411yescharacteristic
912C2×C4⋊C4C2411yescharacteristic
913C2×C4⋊C4C2411yescharacteristic
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2411yescharacteristic
924C2×C4⋊C4C2411yescharacteristic
925C2×C4⋊C4C2411yescharacteristic
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2411yescharacteristic
929C2×C4⋊C4C2411yescharacteristic
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2411yescharacteristic
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2411yescharacteristic
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2414yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C22⋊C4—44no—
1004C2×C22⋊C4—44no—
1005C2×C22⋊C4—84no—
1006C2×C22⋊C4C2×Q8116yes—
1007C2×C22⋊C4C2411yescharacteristic
1008C2×C22⋊C4C2411yescharacteristic
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2411yescharacteristic
1026C2×C22⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C42—28no—
1050C2×C42—44no—
1051C2×C42C2×Q818yes—
1052C2×C42C2411yescharacteristic
1053C2×C42C2412yes—
1054C2×C42C2412yes—
1055C2×C42C2412yes—
1056C2×C42C2412yes—
1057C2×C42C2412yes—
1058C2×C42C2412yes—
1059C2×C42C2411yescharacteristic
1060C2×C42C2411yescharacteristic
1061C2×C42C2411yescharacteristic
1062C2×C42C2411yescharacteristic
1063C2×C42C2412yes—
1064C2×C42C2411yescharacteristic
1065C2×C42C2412yes—
1066C2×C42C2411yescharacteristic
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2414yes—
1070C2×C42C2414yes—
1071C2×C42C2414yes—
1072C2×C42C2414yes—
1073C2×C42C2414yes—
1074C2×C42C2414yes—
1075C2×C42C2414yes—
1076C2×C42C2414yes—
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086#95C2412yes—
1087#95C2414yes—
1088#95C2414yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2412yes—
1092#95C2412yes—
1093#95C2411yescharacteristic
1094#95C2411yescharacteristic
1095#95C2411yescharacteristic
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2414yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2412yes—
1134#95C2414yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158C24—42no—
1159C24—42no—
1160C24—42no—
1161C24—42no—
1162C24—42no—
1163C24—42no—
1164C24C22×Q818yes—
1165C24C2511yescharacteristic
1166C24C2512yes—
1167C24C2512yes—
1168C2×Q8—24no—
1169C2×Q8—28no—
1170C2×Q8—42no—
1171C2×Q8—42no—
1172C2×Q8—42no—
1173C2×Q8—42no—
1174C2×Q8—44no—
1175C2×Q8—44no—
1176C2×Q8—42no—
1177C2×Q8—44no—
1178C2×Q8—44no—
1179C2×Q8—44no—
1180C2×D4—22no—
1181C2×D4—22no—
1182C2×D4—22no—
1183C2×D4—22no—
1184C2×D4—416no—
1185C2×D4—42no—
1186C2×D4—42no—
1187C2×D4C22×Q814yes—
1188C2×D4C22×Q814yes—
1189C2×D4C22×Q818yes—
1190C22×C4—24no—
1191C22×C4—24no—
1192C22×C4—22no—
1193C22×C4—24no—
1194C22×C4—24no—
1195C22×C4—22no—
1196C22×C4—22no—
1197C22×C4—22no—
1198C22×C4—24no—
1199C22×C4—24no—
1200C22×C4—432no—
1201C22×C4—42no—
1202C22×C4—42no—
1203C22×C4—42no—
1204C22×C4—41no—
1205C22×C4—42no—
1206C22×C4—42no—
1207C22×C4—42no—
1208C22×C4—41no—
1209C22×C4—42no—
1210C22×C4—42no—
1211C22×C4—42no—
1212C22×C4—42no—
1213C22×C4—42no—
1214C22×C4—42no—
1215C22×C4—42no—
1216C22×C4—42no—
1217C22×C4—42no—
1218C22×C4—42no—
1219C22×C4—44no—
1220C22×C4—44no—
1221C22×C4—44no—
1222C22×C4—44no—
1223C22×C4—44no—
1224C22×C4—44no—
1225C22×C4C22×Q814yes—
1226C22×C4C22×Q814yes—
1227C22×C4C22×Q818yes—
1228C22×C4C22×Q818yes—
1229C22×C4C22×Q814yes—
1230C22×C4C22×Q818yes—
1231C22×C4C22×Q818yes—
1232C22×C4C22×Q818yes—
1233C22×C4C2512yes—
1234C22×C4C2511yescharacteristic
1235C22×C4C2511yescharacteristic
1236C22×C4C2511yescharacteristic
1237C22×C4C2512yes—
1238C22×C4C2514yes—
1239C22×C4C2511yescharacteristic
1240C22×C4C2512yes—
1241C22×C4C2512yes—
1242C22×C4C2512yes—
1243C22×C4C2512yes—
1244C22×C4C2512yes—
1245C22×C4C2512yes—
1246C22×C4C2514yes—
1247C22×C4C2512yes—
1248C22×C4C2511yescharacteristic
1249C22×C4C2512yes—
1250C22×C4C2511yescharacteristic
1251C22×C4C2512yes—
1252C22×C4C2514yes—
1253C22×C4C2514yes—
1254C22×C4C2512yes—
1255C22×C4C2511yescharacteristic
1256C22×C4C2511yescharacteristic
1257C22×C4C2512yes—
1258C22×C4C2511yescharacteristic
1259C22×C4C2511yescharacteristic
1260C22×C4C2512yes—
1261C22×C4C2511yescharacteristic
1262C22×C4C2511yescharacteristic
1263C22×C4C2511yescharacteristic
1264C22×C4C2511yescharacteristic
1265C4⋊C4—22no—
1266C4⋊C4—22no—
1267C4⋊C4—22no—
1268C4⋊C4—24no—
1269C4⋊C4—24no—
1270C4⋊C4—24no—
1271C4⋊C4—22no—
1272C4⋊C4—22no—
1273C4⋊C4—22no—
1274C4⋊C4—24no—
1275C4⋊C4—24no—
1276C4⋊C4—28no—
1277C4⋊C4—24no—
1278C4⋊C4—24no—
1279C4⋊C4—22no—
1280C4⋊C4—24no—
1281C4⋊C4—24no—
1282C4⋊C4—22no—
1283C4⋊C4—22no—
1284C4⋊C4—22no—
1285C4⋊C4—24no—
1286C4⋊C4—24no—
1287C4⋊C4—22no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—22no—
1291C4⋊C4—24no—
1292C4⋊C4—22no—
1293C4⋊C4—44no—
1294C4⋊C4—42no—
1295C4⋊C4—42no—
1296C4⋊C4—42no—
1297C4⋊C4—42no—
1298C4⋊C4—44no—
1299C4⋊C4—42no—
1300C4⋊C4—42no—
1301C4⋊C4—42no—
1302C4⋊C4—42no—
1303C4⋊C4—42no—
1304C4⋊C4—42no—
1305C4⋊C4—44no—
1306C4⋊C4—44no—
1307C4⋊C4—42no—
1308C4⋊C4—42no—
1309C4⋊C4—41no—
1310C4⋊C4—41no—
1311C4⋊C4—42no—
1312C4⋊C4—42no—
1313C4⋊C4—42no—
1314C4⋊C4—42no—
1315C4⋊C4—42no—
1316C4⋊C4—42no—
1317C4⋊C4—42no—
1318C4⋊C4—42no—
1319C4⋊C4—44no—
1320C4⋊C4—44no—
1321C4⋊C4—44no—
1322C4⋊C4—44no—
1323C4⋊C4—44no—
1324C4⋊C4—44no—
1325C4⋊C4—44no—
1326C4⋊C4—42no—
1327C4⋊C4—42no—
1328C4⋊C4—42no—
1329C4⋊C4—44no—
1330C4⋊C4—44no—
1331C4⋊C4—44no—
1332C4⋊C4—44no—
1333C4⋊C4—44no—
1334C4⋊C4—44no—
1335C4⋊C4—44no—
1336C4⋊C4—44no—
1337C4⋊C4—44no—
1338C4⋊C4—44no—
1339C4⋊C4—42no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4—44no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4C22×Q818yes—
1356C4⋊C4C22×Q814yes—
1357C4⋊C4C22×Q814yes—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—24no—
1361C22⋊C4—24no—
1362C22⋊C4—42no—
1363C22⋊C4—42no—
1364C22⋊C4—42no—
1365C22⋊C4—42no—
1366C22⋊C4—42no—
1367C22⋊C4—44no—
1368C22⋊C4—44no—
1369C22⋊C4—44no—
1370C22⋊C4—42no—
1371C22⋊C4—42no—
1372C22⋊C4—44no—
1373C22⋊C4—44no—
1374C22⋊C4—42no—
1375C22⋊C4—42no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—42no—
1379C22⋊C4—44no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—44no—
1383C22⋊C4—44no—
1384C22⋊C4—44no—
1385C22⋊C4—44no—
1386C22⋊C4—42no—
1387C22⋊C4—42no—
1388C22⋊C4—44no—
1389C22⋊C4—42no—
1390C22⋊C4—44no—
1391C22⋊C4—42no—
1392C22⋊C4—42no—
1393C22⋊C4—42no—
1394C22⋊C4—44no—
1395C22⋊C4—44no—
1396C22⋊C4C22×Q818yes—
1397C22⋊C4C22×Q818yes—
1398C22⋊C4C22×Q818yes—
1399C22⋊C4C22×Q818yes—
1400C42—24no—
1401C42—24no—
1402C42—24no—
1403C42—22no—
1404C42—24no—
1405C42—24no—
1406C42—24no—
1407C42—22no—
1408C42—22no—
1409C42—22no—
1410C42—24no—
1411C42—22no—
1412C42—22no—
1413C42—24no—
1414C42—22no—
1415C42—42no—
1416C42—42no—
1417C42—41no—
1418C42—41no—
1419C42—44no—
1420C42—44no—
1421C42—44no—
1422C42—44no—
1423C42—44no—
1424C42—44no—
1425C42—44no—
1426C42—44no—
1427C42—41no—
1428C42—41no—
1429C42C22×Q814yes—
1430C42C22×Q814yes—
1431C42C22×Q814yes—
1432C42C22×Q814yes—
1433C42H(5,𝔽2)14yes—
1434C23—22no—
1435C23—21no—
1436C23—22no—
1437C23—22no—
1438C23—21no—
1439C23—21no—
1440C23—22no—
1441C23—21no—
1442C23—22no—
1443C23—22no—
1444C23—22no—
1445C23—22no—
1446C23—22no—
1447C23—21no—
1448C23—22no—
1449C23—22no—
1450C23—22no—
1451C23—21no—
1452C23—48no—
1453C23—48no—
1454C23—48no—
1455C23—84no—
1456C23—84no—
1457C23—84no—
1458C23—84no—
1459C23C23×Q814yes—
1460C23C23×Q814yes—
1461C23C23×Q812yes—
1462C23C2611yescharacteristic
1463Q8—48no—
1464Q8—88no—
1465Q8—84no—
1466Q8—164no—
1467D4—28no—
1468D4—28no—
1469D4—48no—
1470C2×C4—22no—
1471C2×C4—22no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—22no—
1476C2×C4—21no—
1477C2×C4—22no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—28no—
1487C2×C4—28no—
1488C2×C4—216no—
1489C2×C4—216no—
1490C2×C4—22no—
1491C2×C4—22no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—22no—
1495C2×C4—22no—
1496C2×C4—22no—
1497C2×C4—22no—
1498C2×C4—22no—
1499C2×C4—24no—
1500C2×C4—24no—
1501C2×C4—22no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—22no—
1505C2×C4—21no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—22no—
1509C2×C4—21no—
1510C2×C4—22no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—24no—
1523C2×C4—22no—
1524C2×C4—24no—
1525C2×C4—24no—
1526C2×C4—24no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—22no—
1531C2×C4—24no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—24no—
1536C2×C4—24no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—22no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—48no—
1557C2×C4—48no—
1558C2×C4—48no—
1559C2×C4—44no—
1560C2×C4—84no—
1561C2×C4—84no—
1562C2×C4—84no—
1563C2×C4—84no—
1564C2×C4—164no—
1565C2×C4—164no—
1566C2×C4C23×Q812yes—
1567C2×C4C23×Q812yes—
1568C2×C4C23×Q812yes—
1569C2×C4C23×Q812yes—
1570C2×C4C23×Q814yes—
1571C2×C4C23×Q814yes—
1572C2×C4C23×Q812yes—
1573C2×C4C23×Q812yes—
1574C2×C4C2×H(5,𝔽2)12yes—
1575C2×C4C2×H(5,𝔽2)12yes—
1576C2×C4C2×H(5,𝔽2)12yes—
1577C2×C4#58512yes—
1578C2×C4#58512yes—
1579C2×C4#58512yes—
1580C22—22no—
1581C22—24no—
1582C22—24no—
1583C22—22no—
1584C22—24no—
1585C22—24no—
1586C22—22no—
1587C22—24no—
1588C22—24no—
1589C22—42no—
1590C22—42no—
1591C22—41no—
1592C22—42no—
1593C22—42no—
1594C22—41no—
1595C22—42no—
1596C22—42no—
1597C22—41no—
1598C22—42no—
1599C22—42no—
1600C22—41no—
1601C22—816no—
1602C22C24×Q811yescharacteristic
1603C22C22×H(5,𝔽2)11yescharacteristic
1604C22C2×#58511yescharacteristic
1605C22C2×#58511yescharacteristic
1606C22C2×#58511yescharacteristic
1607C22H(7,𝔽2)11yescharacteristic
1608C222−1+611yescharacteristic
1609C4—22no—
1610C4—24no—
1611C4—24no—
1612C4—22no—
1613C4—22no—
1614C4—22no—
1615C4—22no—
1616C4—22no—
1617C4—42no—
1618C4—42no—
1619C4—42no—
1620C4—41no—
1621C4—42no—
1622C4—42no—
1623C4—41no—
1624C4—42no—
1625C4—44no—
1626C4—42no—
1627C4—42no—
1628C4—41no—
1629C4—42no—
1630C4—41no—
1631C4—42no—
1632C4—42no—
1633C4—44no—
1634C4—44no—
1635C4—41no—
1636C4—41no—
1637C4—42no—
1638C4—44no—
1639C4#345814yes—
1640C4#350114yes—
1641C2—44no—
1642C2—44no—
1643C2—42no—
1644C2C2×#345811yescharacteristic
1645C2C2×#350111yescharacteristic
1646C2#6285411yescharacteristic
1647C2#6292511yescharacteristic
1648C2#6293711yescharacteristic
1649C2#6295511yescharacteristic
1650C2#6296711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42499C2semidirect
2. #42495C2semidirect
5. #40636C2semidirect
6. #40632C2semidirect
7. #40626C2semidirect
8. #40622C2semidirect
9. #39498C2semidirect
10. #39369C2semidirect
11. #38966C2semidirect
12. #38965C2semidirect
13. #38107C2semidirect
14. #38104C2semidirect
15. #37878C2semidirect
16. #37691C2semidirect
17. #37643C2semidirect
18. #37624C2semidirect
19. #37481C2semidirect
20. #37476C2semidirect
21. #36416C2semidirect
22. #36407C2semidirect
23. #36192C2semidirect
24. #36134C2semidirect
25. #35963C2semidirect
26. #35934C2semidirect
27. #35843C2semidirect
28. #35708C2semidirect
29. #35294C2semidirect
30. #35253C2semidirect
31. #34634C2semidirect
32. #34625C2semidirect
36. C2×#544C22semidirect
37. C2×#533C22semidirect
40. #2868C22semidirect
41. #2859C22semidirect
42. #2859C22semidirect
43. #2859C22semidirect
44. #2857C22semidirect
45. #2857C22semidirect
46. #2851C22semidirect
47. #2851C22semidirect
48. #2845C22semidirect
52. #2841C22semidirect
53. #2841C22semidirect
54. #2807C22semidirect
55. #2807C22semidirect
56. #2790C22semidirect
57. #2790C22semidirect
58. #2788C22semidirect
61. #2768C22semidirect
62. #2768C22semidirect
63. #2768C22semidirect
66. #2742C22semidirect
69. #2729C22semidirect
70. #2720C22semidirect
71. #2720C22semidirect
72. #2720C22semidirect
73. #2704C22semidirect
74. #2704C22semidirect
77. #2677C22semidirect
80. #2667C22semidirect
81. #2667C22semidirect
82. #2667C22semidirect
83. #2667C22semidirect
84. #2666C22semidirect
85. #2666C22semidirect
86. #2666C22semidirect
89. #2660C22semidirect
90. #2660C22semidirect
91. #2660C22semidirect
92. #2647C22semidirect
93. #2647C22semidirect
94. #2647C22semidirect
104. #2629C22semidirect
105. #2629C22semidirect
110. #2628C22semidirect
111. #2628C22semidirect
112. #2627C22semidirect
113. #2627C22semidirect
120. #2590C22semidirect
121. #2590C22semidirect
122. #2589C22semidirect
123. #2589C22semidirect
124. #2587C22semidirect
125. #2587C22semidirect
126. #2586C22semidirect
127. #2585C22semidirect
128. #2584C22semidirect
129. #2584C22semidirect
132. #2574C22semidirect
133. #2571C22semidirect
134. #2570C22semidirect
135. #2570C22semidirect
136. #2570C22semidirect
137. #2569C22semidirect
140. #2556C22semidirect
141. #2556C22semidirect
142. #2556C22semidirect
143. #2552C22semidirect
144. #2552C22semidirect
145. #2552C22semidirect
146. #2552C22semidirect
147. #2552C22semidirect
148. #2552C22semidirect
149. #2552C22semidirect
150. #2552C22semidirect
151. #2552C22semidirect
152. #2552C22semidirect
153. #2552C22semidirect
154. #2551C22semidirect
155. #2551C22semidirect
156. #2550C22semidirect
157. #2550C22semidirect
158. #2550C22semidirect
159. #2549C22semidirect
164. #2522C22semidirect
165. #2522C22semidirect
166. #2522C22semidirect
167. #2520C22semidirect
168. #2509C22semidirect
169. #2508C22semidirect
170. #2507C22semidirect
171. #2507C22semidirect
172. #2506C22semidirect
173. #2497C22semidirect
174. #2465C22semidirect
175. #2462C22semidirect
184. #2446C22semidirect
185. #2442C22semidirect
186. #2442C22semidirect
187. #2442C22semidirect
192. #2441C22semidirect
193. #2441C22semidirect
194. #2441C22semidirect
195. #2441C22semidirect
196. #2441C22semidirect
197. #2441C22semidirect
198. #2441C22semidirect
199. #2441C22semidirect
200. #2441C22semidirect
201. #2441C22semidirect
202. #2440C22semidirect
203. #2440C22semidirect
204. #2440C22semidirect
209. #2439C22semidirect
210. #2439C22semidirect
211. #2438C22semidirect
212. #2438C22semidirect
215. #2429C22semidirect
216. #2423C22semidirect
217. #2423C22semidirect
218. #2402C22semidirect
219. #2399C22semidirect
224. #2396C22semidirect
225. #2396C22semidirect
226. #2370C22semidirect
227. #2370C22semidirect
228. #2370C22semidirect
229. #2370C22semidirect
230. #2369C22semidirect
231. #2365C22semidirect
235. #2355C22semidirect
250. Q8×C4⋊C4C22semidirect
264. #2331C22semidirect
265. #2330C22semidirect
268. #2317C22semidirect
269. #2317C22semidirect
270. #2316C22semidirect
273. C4×C4⋊Q8C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×#125C22semidirect
276. C4×#125C22semidirect
277. #2296C22semidirect
278. #2296C22semidirect
287. #2285C22semidirect
336. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#424992
#424952
#424862
#406362
#406322
#406262
#406222
#394982
#393692
#389662
#389652
#381072
#381042
#378782
#376912
#376432
#376242
#374812
#374762
#364162
#364072
#361922
#361342
#359632
#359342
#358432
#357082
#352942
#352532
#346342
#346252
#341942
#341862
D4×#1172