Finite Group Databasebeta

← #7681152

Subgroups — #7681152

Order 512.

5084 conjugacy classes of subgroups.

The subgroup lattice has 1717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59922C212yesmaximal, complemented
2#59918C212yesmaximal, complemented
3#59569C212yesmaximal, complemented
4#59455C214yesmaximal, complemented
5#59455C212yesmaximal, complemented
6#59453C214yesmaximal, complemented
7#45360C212yesmaximal, complemented
8#45359C212yesmaximal, complemented
9#45180C212yesmaximal, complemented
10#45025C212yesmaximal, complemented
11#43555C214yesmaximal, complemented
12#43127C214yesmaximal, complemented
13#39693C212yesmaximal, complemented
14#39691C212yesmaximal, complemented
15#39690C212yesmaximal, complemented
16#39688C212yesmaximal, complemented
17#39606C212yesmaximal, complemented
18#39603C212yesmaximal, complemented
19#36570C212yesmaximal, complemented
20#36564C212yesmaximal, complemented
21#35585C211yesmaximal, characteristic, complemented
22#35575C211yesmaximal, characteristic, complemented
23#35566C211yesmaximal, characteristic, complemented
24#35532C211yesmaximal, characteristic, complemented
25#35280C211yesmaximal, characteristic, complemented
26#35257C211yesmaximal, characteristic, complemented
27#35257C211yesmaximal, characteristic, complemented
28C2×#2507C211yesmaximal, characteristic, complemented
29#34745C211yesmaximal, characteristic, complemented
30#34271C211yesmaximal, characteristic, complemented
31#34267C211yesmaximal, characteristic
32#34267C211yesmaximal, characteristic
33#34250C211yesmaximal, characteristic, complemented
34C4⋊C4×#41C211yesmaximal, characteristic, complemented
35C4×#537C211yesmaximal, characteristic
36C2×#544C2211yescharacteristic
37C2×#544C2211yescharacteristic
38C2×#537C2211yescharacteristic
39C2×#533C2211yescharacteristic
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C2×C4×#41C2211yescharacteristic
46#2857C2212yes—
47#2857C2212yes—
48#2857C2212yes—
49#2857C2212yes—
50#2851C2212yes—
51#2851C2212yes—
52#2807C2214yes—
53#2806C2214yes—
54#2802C2214yes—
55#2792C2214yes—
56#2791C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2790C2214yes—
60#2788C2214yes—
61#2788C2214yes—
62#2788C2214yes—
63#2784C2214yes—
64#2780C2214yes—
65#2774C2214yes—
66#2768C2214yes—
67#2768C2214yes—
68#2768C2214yes—
69#2768C2214yes—
70#2748C2214yes—
71#2748C2214yes—
72#2732C2214yes—
73#2729C2214yes—
74#2704C2214yes—
75#2692C2214yes—
76#2629C2212yes—
77#2629C2212yes—
78#2629C2212yes—
79#2629C2212yes—
80#2628C2212yes—
81#2628C2212yes—
82#2590C2214yes—
83#2589C2214yes—
84#2587C2214yes—
85#2587C2214yes—
86#2587C2214yes—
87#2587C2214yes—
88#2586C2214yes—
89#2586C2214yes—
90#2585C2214yes—
91#2584C2214yes—
92#2584C2212yes—
93#2584C2212yes—
94#2583C2214yes—
95#2582C2212yes—
96#2582C2212yes—
97#2579C2214yes—
98#2574C2214yes—
99#2574C2214yes—
100#2569C2214yes—
101#2567C2212yes—
102#2567C2212yes—
103#2566C2212yes—
104#2565C2212yes—
105#2564C2214yes—
106#2556C2214yes—
107#2552C2212yes—
108#2551C2212yes—
109#2550C2212yes—
110#2550C2212yes—
111#2549C2214yes—
112#2549C2214yes—
113#2549C2214yes—
114#2549C2214yes—
115#2546C2212yes—
116#2542C2212yes—
117#2538C2212yes—
118#2538C2214yes—
119#2538C2212yes—
120#2522C2214yes—
121#2522C2214yes—
122#2520C2214yes—
123#2509C2212yes—
124#2509C2212yes—
125#2508C2212yes—
126#2508C2212yes—
127#2508C2214yes—
128#2507C2212yes—
129#2507C2212yes—
130#2507C2212yes—
131#2507C2212yes—
132#2507C2214yes—
133#2507C2212yes—
134#2507C2212yes—
135#2507C2214yes—
136#2507C2212yes—
137#2507C2212yes—
138#2507C2212yes—
139#2507C2212yes—
140#2506C2212yes—
141#2506C2212yes—
142#2502C2214yes—
143#2465C2214yes—
144#2454C2211yescharacteristic
145#2454C2214yes—
146#2454C2212yes—
147#2454C2212yes—
148#2454C2211yescharacteristic
149#2454C2212yes—
150#2453C2212yes—
151#2453C2211yescharacteristic
152#2453C2212yes—
153#2453C2212yes—
154#2453C2211yescharacteristic
155#2452C2211yescharacteristic
156#2452C2212yes—
157#2452C2214yes—
158#2452C2212yes—
159#2452C2212yes—
160#2452C2211yescharacteristic
161#2451C2211yescharacteristic
162#2451C2212yes—
163#2451C2212yes—
164#2451C2212yes—
165#2451C2211yescharacteristic
166#2450C2214yes—
167#2450C2212yes—
168#2450C2214yes—
169#2450C2214yes—
170#2450C2214yes—
171#2450C2212yes—
172#2449C2214yes—
173#2449C2214yes—
174#2449C2214yes—
175#2449C2214yes—
176#2449C2212yes—
177#2449C2214yes—
178#2449C2214yes—
179#2449C2212yes—
180#2442C2214yes—
181#2442C2212yes—
182#2441C2212yes—
183#2441C2212yes—
184#2441C2212yes—
185#2440C2212yes—
186#2440C2212yes—
187#2440C2214yes—
188#2440C2214yes—
189#2440C2212yes—
190#2439C2212yes—
191#2423C2214yes—
192#2417C2214yes—
193#2417C2214yes—
194#2417C2214yes—
195#2417C2214yes—
196#2396C2212yes—
197#2396C2212yes—
198C2×#398C2212yes—
199C2×#398C2212yes—
200#2370C2212yes—
201#2370C2212yes—
202#2370C2212yes—
203#2370C2212yes—
204#2369C2212yes—
205#2369C2212yes—
206#2369C2214yes—
207#2368C2214yes—
208#2365C2212yes—
209#2365C2212yes—
210#2364C2214yes—
211#2364C2214yes—
212#2363C2212yes—
213#2363C2212yes—
214#2362C2212yes—
215#2362C2212yes—
216#2361C2214yes—
217#2361C2212yes—
218#2361C2212yes—
219#2361C2214yes—
220#2360C2212yes—
221#2360C2212yes—
222#2351C2212yes—
223#2351C2211yescharacteristic
224#2351C2211yescharacteristic
225Q8×C4⋊C4C2212yes—
226Q8×C4⋊C4C2211yescharacteristic
227Q8×C4⋊C4C2211yescharacteristic
228#2349C2212yes—
229#2349C2212yes—
230#2349C2211yescharacteristic
231#2349C2214yes—
232#2349C2212yes—
233#2349C2211yescharacteristic
234#2349C2214yes—
235D4×C4⋊C4C2212yes—
236D4×C4⋊C4C2214yes—
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2212yes—
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241#2345C2214yes—
242#2329C2214yes—
243#2325C2214yes—
244#2324C2212yes—
245#2324C2212yes—
246#2324C2212yes—
247#2324C2212yes—
248#2323C2212yes—
249#2323C2212yes—
250#2323C2212yes—
251#2323C2212yes—
252#2317C2211yescharacteristic
253#2317C2212yes—
254#2317C2211yescharacteristic
255#2316C2211yescharacteristic
256#2316C2211yescharacteristic
257#2316C2212yes—
258#2316C2211yescharacteristic
259#2311C2211yescharacteristic
260#2311C2211yescharacteristic
261#2311C2211yescharacteristic
262#2311C2211yescharacteristic
263C4×C22⋊Q8C2212yes—
264C4×C22⋊Q8C2212yes—
265C4×C22⋊Q8C2212yes—
266C4×C22⋊Q8C2212yes—
267C4×C22⋊Q8C2212yes—
268C4×C22⋊Q8C2214yes—
269C4×C22⋊Q8C2212yes—
270C4×#121C2212yes—
271C4×#121C2212yes—
272C4×#121C2214yes—
273C4×#121C2212yes—
274C4×#121C2212yes—
275#2297C2211yescharacteristic
276#2297C2211yescharacteristic
277#2296C2211yescharacteristic
278#2296C2212yes—
279#2296C2212yes—
280#2296C2212yes—
281#2296C2211yescharacteristic
282#2296C2211yescharacteristic
283#2296C2211yescharacteristic
284C2×#389C2211yescharacteristic
285C2×#389C2212yes—
286C2×#389C2212yes—
287C2×#389C2211yescharacteristic
288C2×#389C2211yescharacteristic
289C2×#389C2211yescharacteristic
290C2×#387C2212yes—
291#2285C2211yescharacteristic
292#2285C2212yes—
293C2×#384C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296C2×C4×C4⋊C4C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301#544—28no—
302#544—44no—
303#537Q8116yescomplemented
304#533—44no—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2314yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2311yescharacteristic
317C2×#125C2311yescharacteristic
318C2×#125C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2314yes—
337#520—28no—
338#520—44no—
339C4×#41—28no—
340C4×#41—44no—
341C4×#41—44no—
342C4×#41—44no—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2314yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2312yes—
407C22×C4⋊C4C2311yescharacteristic
408C22×C42C2312yes—
409C22×C42C2311yescharacteristic
410C22×C42C2311yescharacteristic
411C22×C42C2311yescharacteristic
412C22×C42C2312yes—
413C22×C42C2312yes—
414C22×C42C2312yes—
415C22×C42C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2312yes—
424#400C2312yes—
425#399C2314yes—
426#399C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2312yes—
430#399C2312yes—
431#399C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2312yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2312yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2312yes—
459#398C2312yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2312yes—
468#396C2312yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2312yes—
478#396C2312yes—
479#396C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2314yes—
483#395C2314yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2312yes—
490#395C2312yes—
491#393C2314yes—
492#393C2312yes—
493#393C2314yes—
494#393C2314yes—
495#393C2312yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2311yescharacteristic
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2312yes—
513#391C2314yes—
514#391C2312yes—
515#391C2311yescharacteristic
516#390C2311yescharacteristic
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2311yescharacteristic
522#390C2314yes—
523#390C2311yescharacteristic
524#390C2314yes—
525#390C2314yes—
526#390C2311yescharacteristic
527#389C2311yescharacteristic
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2311yescharacteristic
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2312yes—
554#389C2312yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2312yes—
560#389C2314yes—
561#389C2314yes—
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2312yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#389C2312yes—
575#389C2314yes—
576#389C2314yes—
577#389C2314yes—
578#389C2312yes—
579#389C2314yes—
580#389C2314yes—
581#389C2312yes—
582#389C2311yescharacteristic
583#389C2311yescharacteristic
584#389C2312yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2312yes—
591#389C2311yescharacteristic
592#389C2314yes—
593#389C2312yes—
594#389C2311yescharacteristic
595#389C2312yes—
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2311yescharacteristic
600#389C2314yes—
601#389C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2312yes—
604#389C2311yescharacteristic
605#389C2312yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2314yes—
611#389C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2312yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#387C2314yes—
651#387C2312yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2312yes—
656#386C2312yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#386C2314yes—
669#386C2312yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2312yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2312yes—
686#385C2312yes—
687#385C2312yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#385C2312yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2312yes—
702#385C2312yes—
703#385C2312yes—
704#385C2312yes—
705#385C2314yes—
706#385C2314yes—
707#385C2312yes—
708#385C2312yes—
709#385C2312yes—
710#384C2312yes—
711#384C2312yes—
712#384C2312yes—
713#384C2314yes—
714#384C2312yes—
715#384C2314yes—
716#384C2312yes—
717#384C2312yes—
718#384C2312yes—
719#384C2311yescharacteristic
720#384C2311yescharacteristic
721#384C2312yes—
722#382C2312yes—
723#382C2314yes—
724#382C2312yes—
725#382C2314yes—
726#382C2311yescharacteristic
727#382C2311yescharacteristic
728#382C2312yes—
729#382C2312yes—
730#380C2312yes—
731#380C2314yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2314yes—
741#380C2314yes—
742#380C2314yes—
743#380C2314yes—
744#380C2312yes—
745#380C2314yes—
746#380C2314yes—
747#380C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2314yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C2×#95C2312yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2314yes—
815C2×#95C2311yescharacteristic
816C2×#95C2311yescharacteristic
817C2×#95C2312yes—
818C2×#95C2312yes—
819C2×#95C2312yes—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41C2×Q818yes—
825C2×#41C2×Q818yes—
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2414yes—
830C22×Q8C2412yes—
831C22×Q8C2414yes—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2414yes—
837C23×C4C2411yescharacteristic
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2412yes—
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2412yes—
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2412yes—
858C23×C4C2412yes—
859C23×C4C2411yescharacteristic
860C4⋊Q8—28no—
861C4⋊Q8—28no—
862C4⋊Q8—42no—
863C4⋊Q8—42no—
864C4⋊Q8—44no—
865C4⋊Q8—44no—
866C4⋊Q8—48no—
867#125—28no—
868#125—28no—
869#125—42no—
870#125—42no—
871#125—44no—
872#125—44no—
873#125—84no—
874C22⋊Q8—28no—
875C22⋊Q8—216no—
876C22⋊Q8—44no—
877C22⋊Q8—44no—
878C22⋊Q8—48no—
879C22⋊Q8—44no—
880C22⋊Q8—84no—
881C22⋊Q8—84no—
882C22⋊Q8—84no—
883C22⋊Q8—84no—
884C22⋊Q8—84no—
885C22⋊Q8—84no—
886C22⋊Q8—84no—
887C22⋊Q8C2×Q8116yes—
888C22⋊Q8C2×Q8116yes—
889#121C2×Q8116yes—
890#121C2×Q8116yes—
891#121C2×Q8132yes—
892C4×Q8—24no—
893C4×Q8—24no—
894C4×Q8—28no—
895C4×Q8—44no—
896C4×Q8—44no—
897C4×Q8—42no—
898C4×Q8—42no—
899C4×Q8—42no—
900C4×Q8—42no—
901C4×Q8—42no—
902C4×Q8—42no—
903C4×Q8—44no—
904C4×Q8—84no—
905C4×D4—24no—
906C4×D4—24no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—216no—
910C4×D4—28no—
911C4×D4—42no—
912C4×D4—42no—
913C4×D4—42no—
914C4×D4—42no—
915C4×D4—42no—
916C4×D4—42no—
917C4×D4—44no—
918C4×D4—48no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—48no—
926C4×D4—84no—
927C4×D4—84no—
928#117—24no—
929#117—24no—
930#117—24no—
931#117—24no—
932#117—24no—
933#117—28no—
934#117—28no—
935#117—44no—
936#117—44no—
937#117—44no—
938#117—44no—
939#117#4118yes—
940C2×C4⋊C4—24no—
941C2×C4⋊C4—24no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—28no—
944C2×C4⋊C4—24no—
945C2×C4⋊C4—28no—
946C2×C4⋊C4—42no—
947C2×C4⋊C4—44no—
948C2×C4⋊C4—44no—
949C2×C4⋊C4—44no—
950C2×C4⋊C4—82no—
951C2×C4⋊C4—84no—
952C2×C4⋊C4—82no—
953C2×C4⋊C4—82no—
954C2×C4⋊C4—82no—
955C2×C4⋊C4—82no—
956C2×C4⋊C4C2×Q818yes—
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2414yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2411yescharacteristic
1048C2×C4⋊C4C2411yescharacteristic
1049C2×C4⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C42—24no—
1085C2×C42—24no—
1086C2×C42—24no—
1087C2×C42—28no—
1088C2×C42—44no—
1089C2×C42—44no—
1090C2×C42—44no—
1091C2×C42—82no—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2412yes—
1098C2×C42C2411yescharacteristic
1099C2×C42C2414yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2414yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2412yes—
1126#95C2411yescharacteristic
1127#95C2412yes—
1128#95C2411yescharacteristic
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2412yes—
1136#95C2411yescharacteristic
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2414yes—
1194C24C2512yes—
1195C24C2512yes—
1196C24C2511yescharacteristic
1197#41—232no—
1198#41—232no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—28no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—24no—
1205C2×Q8—24no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—44no—
1209C2×Q8—42no—
1210C2×Q8—44no—
1211C2×Q8—42no—
1212C2×Q8—44no—
1213C2×Q8—44no—
1214C2×Q8—44no—
1215C2×Q8C22×Q814yes—
1216C2×Q8C22×Q814yes—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4C22×Q818yes—
1228C2×D4C22×Q818yes—
1229C2×D4C22×Q814yes—
1230C2×D4C22×Q814yes—
1231C2×D4C22×Q8116yes—
1232C22×C4—24no—
1233C22×C4—24no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—22no—
1244C22×C4—24no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—24no—
1252C22×C4—28no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—41no—
1258C22×C4—42no—
1259C22×C4—42no—
1260C22×C4—42no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—42no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—42no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—42no—
1271C22×C4—42no—
1272C22×C4—41no—
1273C22×C4—42no—
1274C22×C4—41no—
1275C22×C4—42no—
1276C22×C4—42no—
1277C22×C4—41no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—42no—
1281C22×C4—41no—
1282C22×C4—44no—
1283C22×C4—42no—
1284C22×C4—42no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4C22×Q818yes—
1296C22×C4C22×Q818yes—
1297C22×C4C22×Q818yes—
1298C22×C4C22×Q814yes—
1299C22×C4C2×#4114yes—
1300C22×C4H(5,𝔽2)14yes—
1301C22×C4C2511yescharacteristic
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2511yescharacteristic
1314C22×C4C2512yes—
1315C22×C4C2514yes—
1316C22×C4C2512yes—
1317C22×C4C2514yes—
1318C22×C4C2514yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2514yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C4⋊C4—24no—
1334C4⋊C4—28no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—28no—
1343C4⋊C4—28no—
1344C4⋊C4—28no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—28no—
1365C4⋊C4—22no—
1366C4⋊C4—24no—
1367C4⋊C4—42no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—41no—
1371C4⋊C4—41no—
1372C4⋊C4—44no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
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⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—44no—
1393C4⋊C4—42no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—42no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—42no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4C22×Q818yes—
1421C4⋊C4C22×Q818yes—
1422C4⋊C4C22×Q8116yes—
1423C4⋊C4C2×#4114yes—
1424C4⋊C4C2×#4114yes—
1425C4⋊C42−1+414yes—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—28no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4C22×Q8116yes—
1458C22⋊C4C22×Q8116yes—
1459C22⋊C4C2×#4118yes—
1460C42—22no—
1461C42—22no—
1462C42—24no—
1463C42—22no—
1464C42—24no—
1465C42—22no—
1466C42—28no—
1467C42—24no—
1468C42—22no—
1469C42—22no—
1470C42—22no—
1471C42—22no—
1472C42—22no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—24no—
1477C42—24no—
1478C42—24no—
1479C42—24no—
1480C42—42no—
1481C42—42no—
1482C42—42no—
1483C42—42no—
1484C42—42no—
1485C42—42no—
1486C42—44no—
1487C42—44no—
1488C42—44no—
1489C42—44no—
1490C42—44no—
1491C42—44no—
1492C42—44no—
1493C42C2×#4118yes—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—22no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23C23×Q814yes—
1511C23C23×Q814yes—
1512C23C23×Q812yes—
1513C23C22×#4112yes—
1514C23C2×H(5,𝔽2)12yes—
1515C23C2611yescharacteristic
1516Q8—28no—
1517Q8—28no—
1518Q8—88no—
1519Q8—84no—
1520Q8—84no—
1521Q8—164no—
1522D4—216no—
1523D4—216no—
1524D4—28no—
1525D4—28no—
1526D4—416no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—22no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—24no—
1538C2×C4—21no—
1539C2×C4—24no—
1540C2×C4—21no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—216no—
1546C2×C4—216no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—24no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—24no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—24no—
1603C2×C4—24no—
1604C2×C4—24no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—48no—
1611C2×C4—48no—
1612C2×C4—44no—
1613C2×C4—44no—
1614C2×C4—44no—
1615C2×C4—44no—
1616C2×C4—88no—
1617C2×C4—84no—
1618C2×C4—84no—
1619C2×C4—84no—
1620C2×C4—84no—
1621C2×C4—84no—
1622C2×C4—82no—
1623C2×C4—84no—
1624C2×C4—84no—
1625C2×C4—82no—
1626C2×C4—84no—
1627C2×C4—84no—
1628C2×C4—84no—
1629C2×C4—164no—
1630C2×C4#554116yes—
1631C2×C4C23×Q818yes—
1632C2×C4C23×Q814yes—
1633C2×C4C23×Q814yes—
1634C2×C4C23×Q812yes—
1635C2×C4C23×Q812yes—
1636C2×C4C22×#4114yes—
1637C2×C4C22×#4114yes—
1638C2×C4C22×#4112yes—
1639C2×C4C22×#4112yes—
1640C2×C4C2×H(5,𝔽2)12yes—
1641C2×C4C2×H(5,𝔽2)12yes—
1642C2×C4C2×2−1+412yes—
1643C2×C4C2×2−1+412yes—
1644C2×C4C2×2−1+412yes—
1645C2×C4#58512yes—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—24no—
1653C22—24no—
1654C22—24no—
1655C22—24no—
1656C22—24no—
1657C22—24no—
1658C22—42no—
1659C22—42no—
1660C22—42no—
1661C22—42no—
1662C22—42no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22C2×#55414yes—
1667C22C24×Q811yescharacteristic
1668C22C23×#4111yescharacteristic
1669C22C22×H(5,𝔽2)11yescharacteristic
1670C22C22×2−1+411yescharacteristic
1671C22C2×#58511yescharacteristic
1672C22H(7,𝔽2)11yescharacteristic
1673C22H(7,𝔽2)11yescharacteristic
1674C4—28no—
1675C4—22no—
1676C4—24no—
1677C4—24no—
1678C4—22no—
1679C4—22no—
1680C4—22no—
1681C4—24no—
1682C4—24no—
1683C4—42no—
1684C4—41no—
1685C4—41no—
1686C4—44no—
1687C4—41no—
1688C4—44no—
1689C4—42no—
1690C4—41no—
1691C4—41no—
1692C4—42no—
1693C4—42no—
1694C4—42no—
1695C4—42no—
1696C4—41no—
1697C4—41no—
1698C4—41no—
1699C4—42no—
1700C4—44no—
1701C4—42no—
1702C4—42no—
1703C4—42no—
1704C4C2×#55414yes—
1705C4C2×#55414yes—
1706C2—24no—
1707C2—44no—
1708C2—44no—
1709C2C22×#55411yescharacteristic
1710C2#6280511yescharacteristic
1711C2#6285811yescharacteristic
1712C2#6294411yescharacteristic
1713C2#6295711yescharacteristic
1714C2#6298911yescharacteristic
1715C2Q8×2−1+411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59922C2semidirect
2. #59918C2semidirect
3. #59569C2semidirect
4. #59455C2semidirect
5. #59455C2semidirect
6. #59453C2semidirect
7. #45360C2semidirect
8. #45359C2semidirect
9. #45180C2semidirect
10. #45025C2semidirect
11. #43555C2semidirect
12. #43127C2semidirect
13. #39693C2semidirect
14. #39691C2semidirect
15. #39690C2semidirect
16. #39688C2semidirect
17. #39606C2semidirect
18. #39603C2semidirect
19. #36570C2semidirect
20. #36564C2semidirect
21. #35585C2semidirect
22. #35575C2semidirect
23. #35566C2semidirect
24. #35532C2semidirect
25. #35280C2semidirect
26. #35257C2semidirect
27. #35257C2semidirect
28. C2×#2507C2semidirect
29. #34745C2semidirect
30. #34271C2semidirect
33. #34250C2semidirect
34. C4⋊C4×#41C2semidirect
303. #537Q8semidirect

Maximal subgroups

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

subgroupindex
#599222
#599182
#595692
#594552
#594532
#453602
#453592
#451802
#450252
#435552
#431272
#396932
#396912
#396902
#396882
#396062
#396032
#365702
#365642
#355852
#355752
#355662
#355322
#352802
#352572
C2×#25072
#347452
#342712
#342672
#342502
C4⋊C4×#412
C4×#5372