Finite Group Databasebeta

← #7647425

Subgroups — #7647425

Order 512.

4680 conjugacy classes of subgroups.

The subgroup lattice has 1642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42490C212yesmaximal
2#42489C212yesmaximal, complemented
3#42488C212yesmaximal, complemented
4#42486C212yesmaximal
5#40626C214yesmaximal, complemented
6#40623C214yesmaximal, complemented
7#39498C211yesmaximal, characteristic, complemented
8#39497C211yesmaximal, characteristic, complemented
9#39494C212yesmaximal, complemented
10#39370C211yesmaximal, characteristic, complemented
11#39369C211yesmaximal, characteristic, complemented
12#39365C212yesmaximal, complemented
13#38966C211yesmaximal, characteristic, complemented
14#38966C211yesmaximal, characteristic, complemented
15#38965C211yesmaximal, characteristic, complemented
16#38965C211yesmaximal, characteristic, complemented
17#38961C212yesmaximal, complemented
18#38960C212yesmaximal, complemented
19#37481C212yesmaximal, complemented
20#37476C212yesmaximal, complemented
21#36756C214yesmaximal, complemented
22#36754C214yesmaximal, complemented
23#35612C212yesmaximal, complemented
24#35581C212yesmaximal, complemented
25#35294C211yesmaximal, characteristic, complemented
26#35253C212yesmaximal, complemented
27#35202C211yesmaximal, characteristic, complemented
28#35176C212yesmaximal, complemented
29#35175C212yesmaximal, complemented
30#35151C212yesmaximal, complemented
31#34978C211yesmaximal, characteristic, complemented
32#34912C211yesmaximal, characteristic, complemented
33#34194C211yesmaximal, characteristic
34D4×#117C211yesmaximal, characteristic
35#34058C211yesmaximal, characteristic
36C2×#544C2212yescomplemented
37C2×#544C2212yescomplemented
38C22×C4×D4C2211yescharacteristic
39C22×#117C2212yes—
40#2868C2211yescharacteristic, complemented
41#2864C2212yescomplemented
42#2859C2211yescharacteristic, complemented
43#2859C2211yescharacteristic, complemented
44#2859C2212yescomplemented
45#2859C2211yescharacteristic, complemented
46#2857C2214yescomplemented
47#2855C2214yescomplemented
48#2855C2214yescomplemented
49#2851C2214yescomplemented
50#2842C2214yes—
51#2842C2214yes—
52#2841C2214yes—
53#2841C2214yes—
54#2807C2214yescomplemented
55#2802C2214yescomplemented
56#2802C2214yescomplemented
57#2792C2214yescomplemented
58#2791C2214yescomplemented
59#2790C2214yescomplemented
60#2790C2214yescomplemented
61#2790C2214yescomplemented
62#2788C2214yescomplemented
63#2784C2214yes—
64#2780C2214yes—
65#2780C2214yes—
66#2780C2214yes—
67#2774C2214yescomplemented
68#2768C2214yescomplemented
69#2768C2214yescomplemented
70#2768C2214yescomplemented
71#2768C2214yescomplemented
72#2755C2214yescomplemented
73#2748C2214yes—
74#2734C2214yescomplemented
75#2732C2214yes—
76#2729C2214yescomplemented
77#2729C2214yescomplemented
78#2726C2214yescomplemented
79#2720C2214yescomplemented
80#2704C2214yescomplemented
81#2704C2214yescomplemented
82#2704C2214yescomplemented
83#2692C2214yes—
84#2683C2214yes—
85#2677C2214yescomplemented
86#2667C2214yes—
87#2667C2214yes—
88#2667C2214yes—
89#2667C2214yescomplemented
90#2667C2214yescomplemented
91#2667C2214yescomplemented
92#2665C2214yescomplemented
93#2629C2214yes—
94#2629C2212yes—
95#2629C2212yescomplemented
96#2629C2212yescomplemented
97#2629C2212yescomplemented
98#2629C2212yescomplemented
99#2629C2212yescomplemented
100#2629C2212yescomplemented
101#2628C2214yes—
102#2628C2212yes—
103#2628C2212yescomplemented
104#2628C2212yescomplemented
105#2626C2214yes—
106#2626C2214yes—
107#2626C2214yes—
108#2626C2214yes—
109#2612C2214yescomplemented
110#2608C2212yes—
111#2608C2214yescomplemented
112#2608C2214yescomplemented
113#2607C2212yes—
114#2606C2212yescomplemented
115#2606C2214yescomplemented
116#2605C2212yescomplemented
117#2589C2214yescomplemented
118#2587C2214yescomplemented
119#2587C2214yescomplemented
120#2587C2214yescomplemented
121#2584C2212yescomplemented
122#2584C2212yescomplemented
123#2584C2212yescomplemented
124#2580C2212yes—
125#2574C2214yescomplemented
126#2574C2214yescomplemented
127#2571C2211yescharacteristic, complemented
128#2570C2212yescomplemented
129#2570C2211yescharacteristic, complemented
130#2570C2211yescharacteristic, complemented
131#2570C2212yescomplemented
132#2569C2214yescomplemented
133#2566C2212yes—
134#2566C2212yes—
135#2566C2212yes—
136#2556C2214yescomplemented
137#2556C2214yescomplemented
138#2552C2212yescomplemented
139#2552C2211yescharacteristic, complemented
140#2552C2211yescharacteristic, complemented
141#2552C2211yescharacteristic, complemented
142#2552C2211yescharacteristic, complemented
143#2552C2211yescharacteristic, complemented
144#2552C2212yescomplemented
145#2552C2211yescharacteristic, complemented
146#2551C2211yescharacteristic, complemented
147#2551C2212yescomplemented
148#2550C2211yescharacteristic, complemented
149#2550C2212yescomplemented
150#2550C2212yescomplemented
151#2550C2211yescharacteristic, complemented
152#2550C2212yescomplemented
153#2549C2214yescomplemented
154#2546C2212yescomplemented
155#2542C2212yes—
156#2538C2212yes—
157#2538C2212yes—
158#2538C2212yes—
159#2522C2214yescomplemented
160#2522C2214yescomplemented
161#2522C2214yescomplemented
162#2509C2212yescomplemented
163#2508C2212yescomplemented
164#2508C2212yescomplemented
165#2507C2212yescomplemented
166#2507C2212yescomplemented
167#2507C2212yescomplemented
168#2506C2212yescomplemented
169#2506C2212yescomplemented
170#2497C2214yescomplemented
171#2465C2214yescomplemented
172#2454C2212yes—
173#2454C2212yes—
174#2454C2212yes—
175#2454C2212yes—
176#2454C2212yes—
177#2452C2212yes—
178#2452C2212yes—
179#2452C2212yes—
180#2442C2212yescomplemented
181#2442C2212yescomplemented
182#2442C2212yescomplemented
183#2442C2212yescomplemented
184#2441C2211yescharacteristic
185#2441C2212yes—
186#2441C2214yes—
187#2441C2211yescharacteristic
188#2441C2212yes—
189#2441C2212yes—
190#2441C2212yes—
191#2441C2212yes—
192#2441C2212yes—
193#2441C2212yes—
194#2441C2212yes—
195#2441C2214yescomplemented
196#2441C2212yescomplemented
197#2441C2212yescomplemented
198#2441C2212yescomplemented
199#2441C2212yescomplemented
200#2441C2212yescomplemented
201#2441C2212yescomplemented
202#2440C2212yescomplemented
203#2440C2212yescomplemented
204#2440C2212yescomplemented
205#2440C2212yescomplemented
206#2439C2212yes—
207#2439C2212yes—
208#2439C2214yes—
209#2439C2211yescharacteristic
210#2439C2211yescharacteristic
211#2439C2212yes—
212#2439C2212yes—
213#2439C2212yescomplemented
214#2439C2212yescomplemented
215#2439C2214yescomplemented
216#2438C2214yescomplemented
217#2438C2214yescomplemented
218#2437C2214yes—
219#2437C2214yes—
220#2429C2214yescomplemented
221#2429C2214yescomplemented
222#2423C2214yescomplemented
223#2396C2212yes—
224#2396C2212yes—
225#2396C2214yes—
226#2354C2211yescharacteristic
227#2354C2211yescharacteristic
228#2354C2211yescharacteristic
229#2354C2211yescharacteristic
230#2352C2212yes—
231#2352C2212yes—
232#2352C2212yes—
233#2352C2212yes—
234D4×C4⋊C4C2211yescharacteristic
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237D4×C4⋊C4C2211yescharacteristic
238#2345C2212yes—
239#2344C2212yes—
240#2342C2214yes—
241#2342C2214yes—
242D4×C22⋊C4C2212yes—
243D4×C22⋊C4C2212yes—
244#2331C2212yescomplemented
245#2330C2212yescomplemented
246#2330C2212yescomplemented
247#2330C2212yescomplemented
248#2319C2211yescharacteristic
249#2319C2211yescharacteristic
250#2319C2211yescharacteristic
251#2319C2212yes—
252#2319C2212yes—
253#2319C2211yescharacteristic
254#2319C2212yes—
255#2318C2214yes—
256#2317C2212yescomplemented
257#2317C2212yescomplemented
258#2317C2212yescomplemented
259#2317C2212yescomplemented
260#2316C2211yescharacteristic
261#2316C2211yescharacteristic
262#2316C2212yescomplemented
263#2316C2212yescomplemented
264#2312C2212yes—
265#2312C2212yes—
266#2309C2211yescharacteristic
267#2309C2211yescharacteristic
268C4×C4⋊Q8C2212yescomplemented
269C4×C4⋊Q8C2211yescharacteristic, complemented
270C4×C4⋊Q8C2211yescharacteristic, complemented
271C4×C4⋊Q8C2212yescomplemented
272C4×#125C2212yescomplemented
273C4×#125C2212yescomplemented
274C4×#125C2211yescharacteristic, complemented
275C4×#125C2211yescharacteristic, complemented
276#2295C2212yescomplemented
277#2295C2212yescomplemented
278#2293C2212yes—
279#2293C2212yes—
280#2293C2211yescharacteristic
281#2293C2211yescharacteristic
282#2293C2211yescharacteristic
283#2293C2211yescharacteristic
284#2293C2212yes—
285#2290C2214yes—
286#2285C2211yescharacteristic
287#2285C2211yescharacteristic
288#2283C2211yescharacteristic
289#2280C2212yes—
290#2280C2212yes—
291#2280C2212yes—
292#2280C2212yes—
293C2×#380C2212yes—
294#2275C2212yes—
295C42×D4C2212yes—
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C23×D4C2311yescharacteristic
300C24×C4C2312yes—
301#544—48no—
302#544—48no—
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2314yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2314yes—
311C2×C4⋊Q8C2312yes—
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2311yescharacteristic
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#125C2314yes—
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2314yes—
324C2×#125C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2314yes—
336C2×C4×D4Q8116yescomplemented
337C2×C4×D4C2312yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2312yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×#117—48no—
348C2×#117C2312yes—
349C2×#117C2311yescharacteristic
350C2×#117C2311yescharacteristic
351C2×#117C2311yescharacteristic
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C2×#117C2312yes—
358C2×#117C2312yes—
359C2×#117C2312yes—
360C2×#117C2312yes—
361C2×#117C2314yes—
362C2×#117C2314yes—
363C2×#117C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2312yes—
366C22×C4⋊C4C2312yes—
367C22×C4⋊C4C2312yes—
368C22×C4⋊C4C2312yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2311yescharacteristic
371C22×C22⋊C4C2314yes—
372C22×C22⋊C4C2314yes—
373C22×C22⋊C4C2312yes—
374C22×C42C2314yes—
375C22×C42C2311yescharacteristic
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2312yes—
380#400C2312yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2312yes—
390#399C2314yes—
391#399C2314yes—
392#399C2314yes—
393#399C2314yes—
394#399C2314yes—
395#399C2312yes—
396#399C2314yes—
397#399C2314yes—
398#399C2314yes—
399#399C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2312yes—
419#398C2312yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2312yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2312yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2312yes—
458#396C2312yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2312yes—
468#395C2312yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2312yes—
475#393C2314yes—
476#393C2314yes—
477#393C2312yes—
478#393C2314yes—
479#393C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2312yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#390C2311yescharacteristic
493#390C2311yescharacteristic
494#390C2311yescharacteristic
495#390C2311yescharacteristic
496#390C2312yes—
497#390C2312yes—
498#390C2311yescharacteristic
499#390C2311yescharacteristic
500#390C2311yescharacteristic
501#390C2311yescharacteristic
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2311yescharacteristic
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2311yescharacteristic
533#389C2311yescharacteristic
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2312yes—
576#389C2314yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2314yes—
581#389C2314yes—
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2314yes—
624#387C2314yes—
625#387C2312yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2312yes—
630#387C2312yes—
631#387C2312yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2312yes—
640#387C2312yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#384C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2312yes—
680#384C2312yes—
681#384C2312yes—
682#384C2312yes—
683#384C2312yes—
684#384C2311yescharacteristic
685#384C2314yes—
686#384C2312yes—
687#384C2312yes—
688#384C2314yes—
689#384C2312yes—
690#384C2311yescharacteristic
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#383C2312yes—
694#382C2312yes—
695#382C2311yescharacteristic
696#382C2311yescharacteristic
697#382C2312yes—
698#382C2312yes—
699#382C2312yes—
700#382C2312yes—
701#382C2311yescharacteristic
702#382C2312yes—
703#382C2312yes—
704#382C2311yescharacteristic
705#382C2314yes—
706#382C2314yes—
707#381C2314yes—
708#381C2312yes—
709#381C2312yes—
710#381C2312yes—
711#381C2312yes—
712#381C2314yes—
713#381C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2314yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2314yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2314yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2312yes—
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2311yescharacteristic
746#379C2312yes—
747#379C2312yes—
748#379C2312yes—
749#379C2312yes—
750#379C2314yes—
751#379C2314yes—
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2311yescharacteristic
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804#376C2311yescharacteristic
805#376C2311yescharacteristic
806#376C2312yes—
807#376C2312yes—
808#376C2312yes—
809C2×#95C2314yes—
810C43C2311yescharacteristic
811C43C2312yes—
812C43C2312yes—
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×C4C2412yes—
830C23×C4C2411yescharacteristic
831C23×C4C2411yescharacteristic
832C23×C4C2414yes—
833C23×C4C2414yes—
834C23×C4C2414yes—
835C23×C4C2414yes—
836C23×C4C2411yescharacteristic
837C23×C4C2412yes—
838C23×C4C2412yes—
839C23×C4C2412yes—
840C4⋊Q8—24no—
841C4⋊Q8—28no—
842C4⋊Q8—42no—
843C4⋊Q8—44no—
844C4⋊Q8—44no—
845C4⋊Q8—44no—
846C4⋊Q8—48no—
847C4⋊Q8—48no—
848C4⋊Q8—82no—
849#125—24no—
850#125—44no—
851#125—42no—
852#125—44no—
853#125—44no—
854#125—44no—
855#125—44no—
856#125—48no—
857#125—44no—
858#125—44no—
859#125—44no—
860#125—48no—
861#125—82no—
862C22⋊Q8—48no—
863C22⋊Q8—48no—
864C22⋊Q8—48no—
865C22⋊Q8—48no—
866C22⋊Q8—84no—
867C22⋊Q8—84no—
868C22⋊Q8—84no—
869C22⋊Q8—84no—
870C4×Q8—44no—
871C4×Q8—44no—
872C4×Q8—84no—
873C4×D4—44no—
874C4×D4—44no—
875C4×D4—44no—
876C4×D4—44no—
877C4×D4C2×Q818yes—
878C4×D4C2×Q818yes—
879C4×D4C2×Q8116yes—
880C4×D4C2×Q818yes—
881C4×D4C2×Q818yes—
882C4×D4C2×Q8116yes—
883#117—24no—
884#117—28no—
885#117—44no—
886#117—44no—
887#117—42no—
888#117—42no—
889#117—44no—
890#117—44no—
891#117—48no—
892#117—48no—
893#117—44no—
894#117—44no—
895#117—44no—
896#117—42no—
897#117—42no—
898#117—42no—
899#117—44no—
900#117—82no—
901C2×C4⋊C4—28no—
902C2×C4⋊C4—44no—
903C2×C4⋊C4—44no—
904C2×C4⋊C4—44no—
905C2×C4⋊C4C2×Q818yes—
906C2×C4⋊C4C2411yescharacteristic
907C2×C4⋊C4C2411yescharacteristic
908C2×C4⋊C4C2411yescharacteristic
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2411yescharacteristic
915C2×C4⋊C4C2411yescharacteristic
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2412yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2414yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2411yescharacteristic
997C2×C22⋊C4—48no—
998C2×C22⋊C4—84no—
999C2×C22⋊C4C2×Q8116yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2412yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2414yes—
1007C2×C22⋊C4C2414yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2411yescharacteristic
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2411yescharacteristic
1017C2×C22⋊C4C2411yescharacteristic
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C42—48no—
1045C2×C42C2×Q818yes—
1046C2×C42C2412yes—
1047C2×C42C2411yescharacteristic
1048C2×C42C2412yes—
1049C2×C42C2411yescharacteristic
1050C2×C42C2414yes—
1051C2×C42C2412yes—
1052C2×C42C2411yescharacteristic
1053C2×C42C2411yescharacteristic
1054C2×C42C2411yescharacteristic
1055C2×C42C2411yescharacteristic
1056C2×C42C2411yescharacteristic
1057C2×C42C2411yescharacteristic
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2412yes—
1062C2×C42C2414yes—
1063C2×C42C2414yes—
1064C2×C42C2414yes—
1065C2×C42C2414yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2414yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2411yescharacteristic
1073C2×C42C2411yescharacteristic
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082#95C2412yes—
1083#95C2414yes—
1084#95C2414yes—
1085#95C2414yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2411yescharacteristic
1090#95C2411yescharacteristic
1091#95C2412yes—
1092#95C2411yescharacteristic
1093#95C2412yes—
1094#95C2411yescharacteristic
1095#95C2412yes—
1096#95C2412yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2412yes—
1104#95C2412yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2414yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154C24—42no—
1155C24—42no—
1156C24—42no—
1157C24—42no—
1158C24—42no—
1159C24—42no—
1160C24C22×Q818yes—
1161C24C2511yescharacteristic
1162C24C2512yes—
1163C24C2512yes—
1164C2×Q8—28no—
1165C2×Q8—24no—
1166C2×Q8—42no—
1167C2×Q8—42no—
1168C2×Q8—44no—
1169C2×Q8—42no—
1170C2×Q8—42no—
1171C2×Q8—44no—
1172C2×Q8—42no—
1173C2×Q8—44no—
1174C2×Q8—44no—
1175C2×Q8—44no—
1176C2×D4—22no—
1177C2×D4—22no—
1178C2×D4—22no—
1179C2×D4—22no—
1180C2×D4—416no—
1181C2×D4—42no—
1182C2×D4—42no—
1183C2×D4C22×Q814yes—
1184C2×D4C22×Q814yes—
1185C2×D4C22×Q818yes—
1186C22×C4—24no—
1187C22×C4—24no—
1188C22×C4—22no—
1189C22×C4—24no—
1190C22×C4—24no—
1191C22×C4—22no—
1192C22×C4—22no—
1193C22×C4—22no—
1194C22×C4—28no—
1195C22×C4—432no—
1196C22×C4—42no—
1197C22×C4—42no—
1198C22×C4—42no—
1199C22×C4—41no—
1200C22×C4—42no—
1201C22×C4—42no—
1202C22×C4—42no—
1203C22×C4—41no—
1204C22×C4—44no—
1205C22×C4—44no—
1206C22×C4—44no—
1207C22×C4—44no—
1208C22×C4—44no—
1209C22×C4—44no—
1210C22×C4—44no—
1211C22×C4—44no—
1212C22×C4—44no—
1213C22×C4—44no—
1214C22×C4—44no—
1215C22×C4C22×Q814yes—
1216C22×C4C22×Q814yes—
1217C22×C4C22×Q818yes—
1218C22×C4C22×Q818yes—
1219C22×C4C22×Q814yes—
1220C22×C4C22×Q818yes—
1221C22×C4C22×Q818yes—
1222C22×C4C22×Q818yes—
1223C22×C4C2512yes—
1224C22×C4C2512yes—
1225C22×C4C2511yescharacteristic
1226C22×C4C2511yescharacteristic
1227C22×C4C2512yes—
1228C22×C4C2512yes—
1229C22×C4C2512yes—
1230C22×C4C2511yescharacteristic
1231C22×C4C2511yescharacteristic
1232C22×C4C2512yes—
1233C22×C4C2514yes—
1234C22×C4C2514yes—
1235C22×C4C2514yes—
1236C22×C4C2512yes—
1237C22×C4C2511yescharacteristic
1238C22×C4C2511yescharacteristic
1239C22×C4C2512yes—
1240C22×C4C2512yes—
1241C22×C4C2511yescharacteristic
1242C22×C4C2512yes—
1243C22×C4C2511yescharacteristic
1244C22×C4C2512yes—
1245C22×C4C2514yes—
1246C22×C4C2511yescharacteristic
1247C22×C4C2511yescharacteristic
1248C22×C4C2511yescharacteristic
1249C22×C4C2511yescharacteristic
1250C22×C4C2512yes—
1251C22×C4C2512yes—
1252C22×C4C2512yes—
1253C22×C4C2511yescharacteristic
1254C22×C4C2511yescharacteristic
1255C4⋊C4—28no—
1256C4⋊C4—24no—
1257C4⋊C4—22no—
1258C4⋊C4—22no—
1259C4⋊C4—24no—
1260C4⋊C4—24no—
1261C4⋊C4—22no—
1262C4⋊C4—24no—
1263C4⋊C4—24no—
1264C4⋊C4—28no—
1265C4⋊C4—24no—
1266C4⋊C4—22no—
1267C4⋊C4—24no—
1268C4⋊C4—22no—
1269C4⋊C4—22no—
1270C4⋊C4—22no—
1271C4⋊C4—22no—
1272C4⋊C4—22no—
1273C4⋊C4—22no—
1274C4⋊C4—22no—
1275C4⋊C4—24no—
1276C4⋊C4—24no—
1277C4⋊C4—24no—
1278C4⋊C4—24no—
1279C4⋊C4—44no—
1280C4⋊C4—44no—
1281C4⋊C4—44no—
1282C4⋊C4—42no—
1283C4⋊C4—42no—
1284C4⋊C4—42no—
1285C4⋊C4—42no—
1286C4⋊C4—42no—
1287C4⋊C4—44no—
1288C4⋊C4—44no—
1289C4⋊C4—42no—
1290C4⋊C4—42no—
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—41no—
1294C4⋊C4—41no—
1295C4⋊C4—42no—
1296C4⋊C4—42no—
1297C4⋊C4—42no—
1298C4⋊C4—42no—
1299C4⋊C4—42no—
1300C4⋊C4—42no—
1301C4⋊C4—42no—
1302C4⋊C4—42no—
1303C4⋊C4—42no—
1304C4⋊C4—42no—
1305C4⋊C4—42no—
1306C4⋊C4—42no—
1307C4⋊C4—42no—
1308C4⋊C4—42no—
1309C4⋊C4—44no—
1310C4⋊C4—44no—
1311C4⋊C4—44no—
1312C4⋊C4—44no—
1313C4⋊C4—44no—
1314C4⋊C4—44no—
1315C4⋊C4—44no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—42no—
1320C4⋊C4—44no—
1321C4⋊C4—42no—
1322C4⋊C4—44no—
1323C4⋊C4—44no—
1324C4⋊C4—44no—
1325C4⋊C4—44no—
1326C4⋊C4—42no—
1327C4⋊C4—42no—
1328C4⋊C4—44no—
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—42no—
1339C4⋊C4—42no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4C22×Q818yes—
1343C4⋊C4C22×Q814yes—
1344C4⋊C4C22×Q814yes—
1345C4⋊C4H(5,𝔽2)14yes—
1346C22⋊C4—24no—
1347C22⋊C4—28no—
1348C22⋊C4—44no—
1349C22⋊C4—44no—
1350C22⋊C4—42no—
1351C22⋊C4—44no—
1352C22⋊C4—44no—
1353C22⋊C4—44no—
1354C22⋊C4—42no—
1355C22⋊C4—42no—
1356C22⋊C4—42no—
1357C22⋊C4—42no—
1358C22⋊C4—44no—
1359C22⋊C4—42no—
1360C22⋊C4—42no—
1361C22⋊C4—42no—
1362C22⋊C4—42no—
1363C22⋊C4—42no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—44no—
1369C22⋊C4—42no—
1370C22⋊C4—42no—
1371C22⋊C4—42no—
1372C22⋊C4—42no—
1373C22⋊C4—42no—
1374C22⋊C4—42no—
1375C22⋊C4—42no—
1376C22⋊C4—44no—
1377C22⋊C4—44no—
1378C22⋊C4—44no—
1379C22⋊C4—44no—
1380C22⋊C4—44no—
1381C22⋊C4—42no—
1382C22⋊C4—42no—
1383C22⋊C4—42no—
1384C22⋊C4—44no—
1385C22⋊C4—42no—
1386C22⋊C4C22×Q818yes—
1387C22⋊C4C22×Q818yes—
1388C22⋊C4C22×Q818yes—
1389C22⋊C4C22×Q818yes—
1390C42—24no—
1391C42—28no—
1392C42—22no—
1393C42—22no—
1394C42—24no—
1395C42—24no—
1396C42—22no—
1397C42—22no—
1398C42—22no—
1399C42—22no—
1400C42—22no—
1401C42—22no—
1402C42—24no—
1403C42—24no—
1404C42—24no—
1405C42—24no—
1406C42—44no—
1407C42—44no—
1408C42—42no—
1409C42—42no—
1410C42—41no—
1411C42—41no—
1412C42—44no—
1413C42—42no—
1414C42—42no—
1415C42—42no—
1416C42—44no—
1417C42—44no—
1418C42—42no—
1419C42—42no—
1420C42—41no—
1421C42—41no—
1422C42C22×Q814yes—
1423C42C22×Q814yes—
1424C42C22×Q814yes—
1425C42C22×Q814yes—
1426C23—22no—
1427C23—21no—
1428C23—22no—
1429C23—22no—
1430C23—21no—
1431C23—21no—
1432C23—22no—
1433C23—21no—
1434C23—22no—
1435C23—22no—
1436C23—22no—
1437C23—22no—
1438C23—22no—
1439C23—21no—
1440C23—22no—
1441C23—22no—
1442C23—22no—
1443C23—21no—
1444C23—48no—
1445C23—48no—
1446C23—48no—
1447C23—84no—
1448C23—84no—
1449C23—84no—
1450C23—84no—
1451C23C23×Q814yes—
1452C23C23×Q814yes—
1453C23C23×Q812yes—
1454C23C2611yescharacteristic
1455Q8—84no—
1456Q8—88no—
1457Q8—84no—
1458Q8—164no—
1459D4—28no—
1460D4—28no—
1461D4—48no—
1462C2×C4—21no—
1463C2×C4—22no—
1464C2×C4—22no—
1465C2×C4—22no—
1466C2×C4—22no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—22no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—22no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—28no—
1477C2×C4—28no—
1478C2×C4—216no—
1479C2×C4—216no—
1480C2×C4—22no—
1481C2×C4—24no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—22no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—22no—
1488C2×C4—22no—
1489C2×C4—24no—
1490C2×C4—24no—
1491C2×C4—22no—
1492C2×C4—22no—
1493C2×C4—21no—
1494C2×C4—22no—
1495C2×C4—21no—
1496C2×C4—22no—
1497C2×C4—21no—
1498C2×C4—22no—
1499C2×C4—22no—
1500C2×C4—22no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—22no—
1511C2×C4—22no—
1512C2×C4—22no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—24no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—24no—
1522C2×C4—24no—
1523C2×C4—24no—
1524C2×C4—24no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—21no—
1528C2×C4—24no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—24no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—24no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—24no—
1549C2×C4—48no—
1550C2×C4—48no—
1551C2×C4—48no—
1552C2×C4—44no—
1553C2×C4—88no—
1554C2×C4—88no—
1555C2×C4—164no—
1556C2×C4—164no—
1557C2×C4C23×Q812yes—
1558C2×C4C23×Q812yes—
1559C2×C4C23×Q812yes—
1560C2×C4C23×Q812yes—
1561C2×C4C23×Q814yes—
1562C2×C4C23×Q814yes—
1563C2×C4C23×Q812yes—
1564C2×C4C23×Q812yes—
1565C2×C4C2×H(5,𝔽2)14yes—
1566C2×C4C2×H(5,𝔽2)12yes—
1567C2×C4#58512yes—
1568C2×C4#58512yes—
1569C2×C4#58512yes—
1570C22—22no—
1571C22—24no—
1572C22—24no—
1573C22—22no—
1574C22—24no—
1575C22—24no—
1576C22—22no—
1577C22—24no—
1578C22—24no—
1579C22—42no—
1580C22—42no—
1581C22—41no—
1582C22—42no—
1583C22—42no—
1584C22—41no—
1585C22—42no—
1586C22—42no—
1587C22—41no—
1588C22—42no—
1589C22—42no—
1590C22—41no—
1591C22—816no—
1592C22C24×Q811yescharacteristic
1593C22C22×H(5,𝔽2)11yescharacteristic
1594C22C2×#58511yescharacteristic
1595C22C2×#58511yescharacteristic
1596C22C2×#58511yescharacteristic
1597C22H(7,𝔽2)11yescharacteristic
1598C222−1+611yescharacteristic
1599C4—22no—
1600C4—24no—
1601C4—24no—
1602C4—22no—
1603C4—22no—
1604C4—24no—
1605C4—22no—
1606C4—44no—
1607C4—42no—
1608C4—44no—
1609C4—41no—
1610C4—42no—
1611C4—41no—
1612C4—41no—
1613C4—41no—
1614C4—42no—
1615C4—42no—
1616C4—44no—
1617C4—42no—
1618C4—41no—
1619C4—42no—
1620C4—44no—
1621C4—42no—
1622C4—42no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—42no—
1627C4—42no—
1628C4—42no—
1629C4#345814yes—
1630C4#350114yes—
1631C2—44no—
1632C2—44no—
1633C2—42no—
1634C2C2×#345811yescharacteristic
1635C2C2×#350111yescharacteristic
1636C2#6285411yescharacteristic
1637C2#6292011yescharacteristic
1638C2#6292211yescharacteristic
1639C2#6293711yescharacteristic
1640C2#6293911yescharacteristic
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
2. #42489C2semidirect
3. #42488C2semidirect
5. #40626C2semidirect
6. #40623C2semidirect
7. #39498C2semidirect
8. #39497C2semidirect
9. #39494C2semidirect
10. #39370C2semidirect
11. #39369C2semidirect
12. #39365C2semidirect
13. #38966C2semidirect
14. #38966C2semidirect
15. #38965C2semidirect
16. #38965C2semidirect
17. #38961C2semidirect
18. #38960C2semidirect
19. #37481C2semidirect
20. #37476C2semidirect
21. #36756C2semidirect
22. #36754C2semidirect
23. #35612C2semidirect
24. #35581C2semidirect
25. #35294C2semidirect
26. #35253C2semidirect
27. #35202C2semidirect
28. #35176C2semidirect
29. #35175C2semidirect
30. #35151C2semidirect
31. #34978C2semidirect
32. #34912C2semidirect
36. C2×#544C22semidirect
37. C2×#544C22semidirect
40. #2868C22semidirect
41. #2864C22semidirect
42. #2859C22semidirect
43. #2859C22semidirect
44. #2859C22semidirect
45. #2859C22semidirect
46. #2857C22semidirect
47. #2855C22semidirect
48. #2855C22semidirect
49. #2851C22semidirect
54. #2807C22semidirect
55. #2802C22semidirect
56. #2802C22semidirect
57. #2792C22semidirect
58. #2791C22semidirect
59. #2790C22semidirect
60. #2790C22semidirect
61. #2790C22semidirect
62. #2788C22semidirect
67. #2774C22semidirect
68. #2768C22semidirect
69. #2768C22semidirect
70. #2768C22semidirect
71. #2768C22semidirect
72. #2755C22semidirect
74. #2734C22semidirect
76. #2729C22semidirect
77. #2729C22semidirect
78. #2726C22semidirect
79. #2720C22semidirect
80. #2704C22semidirect
81. #2704C22semidirect
82. #2704C22semidirect
85. #2677C22semidirect
89. #2667C22semidirect
90. #2667C22semidirect
91. #2667C22semidirect
92. #2665C22semidirect
95. #2629C22semidirect
96. #2629C22semidirect
97. #2629C22semidirect
98. #2629C22semidirect
99. #2629C22semidirect
100. #2629C22semidirect
103. #2628C22semidirect
104. #2628C22semidirect
109. #2612C22semidirect
111. #2608C22semidirect
112. #2608C22semidirect
114. #2606C22semidirect
115. #2606C22semidirect
116. #2605C22semidirect
117. #2589C22semidirect
118. #2587C22semidirect
119. #2587C22semidirect
120. #2587C22semidirect
121. #2584C22semidirect
122. #2584C22semidirect
123. #2584C22semidirect
125. #2574C22semidirect
126. #2574C22semidirect
127. #2571C22semidirect
128. #2570C22semidirect
129. #2570C22semidirect
130. #2570C22semidirect
131. #2570C22semidirect
132. #2569C22semidirect
136. #2556C22semidirect
137. #2556C22semidirect
138. #2552C22semidirect
139. #2552C22semidirect
140. #2552C22semidirect
141. #2552C22semidirect
142. #2552C22semidirect
143. #2552C22semidirect
144. #2552C22semidirect
145. #2552C22semidirect
146. #2551C22semidirect
147. #2551C22semidirect
148. #2550C22semidirect
149. #2550C22semidirect
150. #2550C22semidirect
151. #2550C22semidirect
152. #2550C22semidirect
153. #2549C22semidirect
154. #2546C22semidirect
159. #2522C22semidirect
160. #2522C22semidirect
161. #2522C22semidirect
162. #2509C22semidirect
163. #2508C22semidirect
164. #2508C22semidirect
165. #2507C22semidirect
166. #2507C22semidirect
167. #2507C22semidirect
168. #2506C22semidirect
169. #2506C22semidirect
170. #2497C22semidirect
171. #2465C22semidirect
180. #2442C22semidirect
181. #2442C22semidirect
182. #2442C22semidirect
183. #2442C22semidirect
195. #2441C22semidirect
196. #2441C22semidirect
197. #2441C22semidirect
198. #2441C22semidirect
199. #2441C22semidirect
200. #2441C22semidirect
201. #2441C22semidirect
202. #2440C22semidirect
203. #2440C22semidirect
204. #2440C22semidirect
205. #2440C22semidirect
213. #2439C22semidirect
214. #2439C22semidirect
215. #2439C22semidirect
216. #2438C22semidirect
217. #2438C22semidirect
220. #2429C22semidirect
221. #2429C22semidirect
222. #2423C22semidirect
244. #2331C22semidirect
245. #2330C22semidirect
246. #2330C22semidirect
247. #2330C22semidirect
256. #2317C22semidirect
257. #2317C22semidirect
258. #2317C22semidirect
259. #2317C22semidirect
262. #2316C22semidirect
263. #2316C22semidirect
268. C4×C4⋊Q8C22semidirect
269. C4×C4⋊Q8C22semidirect
270. C4×C4⋊Q8C22semidirect
271. C4×C4⋊Q8C22semidirect
272. C4×#125C22semidirect
273. C4×#125C22semidirect
274. C4×#125C22semidirect
275. C4×#125C22semidirect
276. #2295C22semidirect
277. #2295C22semidirect
336. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#424902
#424892
#424882
#424862
#406262
#406232
#394982
#394972
#394942
#393702
#393692
#393652
#389662
#389652
#389612
#389602
#374812
#374762
#367562
#367542
#356122
#355812
#352942
#352532
#352022
#351762
#351752
#351512
#349782
#349122
#341942
D4×#1172
#340582