Finite Group Databasebeta

← #7682787

Subgroups — #7682787

Order 512.

5110 conjugacy classes of subgroups.

The subgroup lattice has 1693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59503C212yesmaximal, complemented
2#59502C212yesmaximal, complemented
3#59499C212yesmaximal, complemented
4#59498C212yesmaximal, complemented
5#59295C212yesmaximal, complemented
6#59294C212yesmaximal, complemented
7#59291C212yesmaximal, complemented
8#59290C212yesmaximal, complemented
9#59252C214yesmaximal, complemented
10#59027C214yesmaximal, complemented
11#45331C212yesmaximal, complemented
12#45252C212yesmaximal, complemented
13#45210C212yesmaximal, complemented
14#45055C212yesmaximal, complemented
15#45027C212yesmaximal, complemented
16#45005C212yesmaximal, complemented
17#44999C212yesmaximal, complemented
18#44917C212yesmaximal, complemented
19#43082C214yesmaximal, complemented
20#43057C214yesmaximal, complemented
21#35585C211yesmaximal, characteristic, complemented
22#35574C211yesmaximal, characteristic, complemented
23#35555C211yesmaximal, characteristic, complemented
24#35544C211yesmaximal, characteristic, complemented
25#35543C211yesmaximal, characteristic, complemented
26#35516C211yesmaximal, characteristic
27#34814C211yesmaximal, characteristic, complemented
28#34742C211yesmaximal, characteristic
29C2×#2440C211yesmaximal, characteristic, complemented
30#34253C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32#34216C211yesmaximal, characteristic, complemented
33#34200C211yesmaximal, characteristic
34#34188C211yesmaximal, characteristic, complemented
35#34178C211yesmaximal, characteristic, complemented
36C2×#552C2214yes—
37C22×C4⋊Q8C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C22×C22⋊Q8C2212yes—
40C2×#520C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×C4×#41C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44#2794C2214yescomplemented
45#2791C2214yescomplemented
46#2787C2214yescomplemented
47#2774C2214yescomplemented
48#2774C2214yescomplemented
49#2770C2214yes—
50#2770C2214yescomplemented
51#2768C2214yes—
52#2766C2214yescomplemented
53#2765C2214yescomplemented
54#2762C2214yescomplemented
55#2762C2214yescomplemented
56#2750C2214yes—
57#2745C2214yescomplemented
58#2745C2214yescomplemented
59#2739C2214yescomplemented
60#2719C2214yescomplemented
61#2698C2214yes—
62#2698C2214yes—
63#2695C2214yes—
64#2690C2214yescomplemented
65#2690C2214yescomplemented
66#2687C2214yes—
67#2687C2214yes—
68#2611C2214yes—
69#2609C2214yes—
70#2606C2214yescomplemented
71#2599C2214yescomplemented
72#2599C2214yescomplemented
73#2590C2214yescomplemented
74#2579C2214yes—
75#2575C2214yes—
76#2571C2212yescomplemented
77#2570C2212yescomplemented
78#2570C2212yescomplemented
79#2570C2212yescomplemented
80#2570C2212yescomplemented
81#2569C2214yes—
82#2556C2214yes—
83#2556C2214yes—
84#2552C2212yescomplemented
85#2552C2212yescomplemented
86#2552C2212yescomplemented
87#2536C2214yes—
88#2528C2214yescomplemented
89#2524C2214yescomplemented
90#2520C2214yescomplemented
91#2520C2214yescomplemented
92#2517C2214yes—
93#2515C2214yes—
94#2515C2214yescomplemented
95#2509C2212yescomplemented
96#2509C2212yescomplemented
97#2509C2212yescomplemented
98#2508C2212yescomplemented
99#2508C2212yescomplemented
100#2508C2212yescomplemented
101#2507C2212yescomplemented
102#2507C2212yescomplemented
103#2507C2212yescomplemented
104#2507C2212yescomplemented
105#2507C2212yescomplemented
106#2506C2212yescomplemented
107#2506C2212yescomplemented
108#2506C2212yescomplemented
109#2506C2212yescomplemented
110#2506C2212yescomplemented
111#2505C2214yes—
112#2499C2214yes—
113#2497C2212yes—
114#2497C2212yes—
115#2497C2211yescharacteristic
116#2497C2211yescharacteristic
117#2496C2212yes—
118#2496C2212yes—
119#2496C2211yescharacteristic
120#2496C2211yescharacteristic
121#2495C2212yes—
122#2495C2211yescharacteristic
123#2495C2212yes—
124#2495C2211yescharacteristic
125#2494C2211yescharacteristic
126#2494C2212yes—
127#2494C2212yes—
128#2494C2211yescharacteristic
129#2493C2212yes—
130#2493C2214yes—
131#2493C2212yes—
132#2489C2214yes—
133#2487C2212yes—
134#2486C2212yes—
135#2485C2212yes—
136#2485C2212yes—
137#2484C2214yescomplemented
138#2480C2212yes—
139#2480C2214yes—
140#2480C2212yes—
141#2478C2214yes—
142#2477C2214yes—
143#2477C2214yes—
144#2475C2214yescomplemented
145#2473C2214yes—
146#2473C2214yes—
147#2473C2214yes—
148#2473C2214yescomplemented
149#2470C2214yes—
150#2468C2214yes—
151#2462C2214yescomplemented
152#2462C2214yescomplemented
153#2460C2214yes—
154#2452C2212yescomplemented
155#2452C2212yescomplemented
156#2451C2212yescomplemented
157#2451C2212yescomplemented
158#2442C2214yes—
159#2440C2212yes—
160#2440C2212yes—
161#2440C2212yes—
162#2440C2212yes—
163#2440C2212yes—
164#2440C2212yes—
165#2440C2212yes—
166#2440C2212yes—
167#2440C2212yescomplemented
168#2440C2212yescomplemented
169#2439C2212yescomplemented
170#2439C2212yescomplemented
171#2438C2214yescomplemented
172#2438C2214yescomplemented
173#2423C2211yescharacteristic
174#2423C2214yes—
175#2423C2212yes—
176#2423C2211yescharacteristic
177#2422C2211yescharacteristic
178#2422C2212yes—
179#2422C2211yescharacteristic
180#2421C2212yes—
181#2421C2211yescharacteristic
182#2421C2211yescharacteristic
183#2420C2212yes—
184#2420C2211yescharacteristic
185#2420C2211yescharacteristic
186#2419C2212yes—
187#2419C2214yes—
188#2419C2212yes—
189#2419C2214yes—
190#2418C2212yes—
191#2418C2214yes—
192#2418C2212yes—
193#2417C2214yes—
194#2415C2214yes—
195#2409C2214yes—
196#2401C2212yes—
197#2401C2212yes—
198#2395C2212yes—
199#2395C2212yes—
200C2×#398C2212yes—
201C2×#395C2212yes—
202#2373C2214yes—
203#2369C2212yescomplemented
204#2369C2212yescomplemented
205#2365C2212yescomplemented
206#2365C2212yescomplemented
207#2362C2214yes—
208#2361C2212yes—
209#2361C2212yes—
210#2360C2212yes—
211#2360C2212yes—
212#2359C2214yes—
213#2355C2212yescomplemented
214#2355C2212yescomplemented
215#2354C2212yescomplemented
216#2354C2212yescomplemented
217#2353C2214yes—
218#2352C2214yes—
219#2352C2214yes—
220#2352C2214yes—
221#2352C2212yes—
222#2352C2212yes—
223#2351C2212yescomplemented
224Q8×C4⋊C4C2212yescomplemented
225#2349C2214yes—
226#2349C2212yescomplemented
227D4×C4⋊C4C2212yes—
228D4×C4⋊C4C2214yes—
229D4×C4⋊C4C2212yes—
230D4×C4⋊C4C2212yescomplemented
231#2347C2212yescomplemented
232#2346C2212yescomplemented
233#2345C2212yes—
234#2345C2214yes—
235#2345C2212yes—
236#2345C2212yes—
237#2345C2212yes—
238#2345C2212yescomplemented
239#2344C2212yes—
240#2344C2212yes—
241#2344C2212yes—
242#2344C2212yes—
243#2344C2212yescomplemented
244Q8×C22⋊C4C2214yes—
245#2331C2212yescomplemented
246#2331C2212yescomplemented
247#2322C2214yes—
248#2320C2212yescomplemented
249#2319C2212yescomplemented
250#2317C2211yescharacteristic
251#2317C2211yescharacteristic
252#2317C2211yescharacteristic
253#2317C2211yescharacteristic
254#2317C2212yescomplemented
255#2316C2211yescharacteristic
256#2316C2211yescharacteristic
257#2316C2211yescharacteristic
258#2316C2211yescharacteristic
259#2316C2212yescomplemented
260#2314C2212yescomplemented
261#2314C2212yescomplemented
262#2313C2214yes—
263#2311C2211yescharacteristic
264#2311C2211yescharacteristic
265C4×C4⋊Q8C2212yescomplemented
266C4×C4⋊Q8C2212yescomplemented
267C4×#126C2212yes—
268C4×#126C2212yes—
269C4×#123C2212yes—
270C4×#123C2212yes—
271C4×#120C2214yes—
272#2297C2211yescharacteristic
273#2296C2211yescharacteristic
274#2296C2211yescharacteristic
275#2296C2211yescharacteristic
276#2296C2212yescomplemented
277#2295C2212yescomplemented
278#2293C2212yescomplemented
279C2×#389C2211yescharacteristic
280C2×#389C2211yescharacteristic
281C2×#389C2212yescomplemented
282C2×#385C2212yes—
283#2285C2211yescharacteristic
284#2285C2211yescharacteristic
285#2285C2212yescomplemented
286#2285C2212yescomplemented
287C2×#384C2211yescharacteristic
288#2280C2214yes—
289#2280C2211yescharacteristic
290#2280C2211yescharacteristic
291#2280C2211yescharacteristic
292C2×#380C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2312yes—
301C24×C4C2311yescharacteristic
302C24×C4C2312yes—
303#552—416no—
304C2×C4⋊Q8—28no—
305C2×C4⋊Q8C2312yes—
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×#126C2312yes—
310C2×#126C2312yes—
311C2×#126C2314yes—
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316#525—28no—
317C2×#123C2312yes—
318C2×#123C2312yes—
319C2×#123C2312yes—
320C2×#123C2314yes—
321C2×C22⋊Q8—48no—
322C2×C22⋊Q8C2311yescharacteristic
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×#121C2311yescharacteristic
331C2×#121C2311yescharacteristic
332C2×#120C2312yes—
333#520—28no—
334#520—28no—
335C4×#41—28no—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2314yes—
341C2×C4×Q8C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2314yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×#117C2311yescharacteristic
355C2×#117C2311yescharacteristic
356C2×#117C2312yes—
357C2×#117C2311yescharacteristic
358C2×#117C2311yescharacteristic
359C2×#117C2311yescharacteristic
360C2×#117C2311yescharacteristic
361C2×#117C2312yes—
362C2×#117C2311yescharacteristic
363C2×#117C2312yes—
364C2×#117C2314yes—
365C2×#117C2314yes—
366C2×#117C2314yes—
367C2×#117C2314yes—
368C2×#117C2314yes—
369C22×C4⋊C4—28no—
370C22×C4⋊C4C2311yescharacteristic
371C22×C4⋊C4C2311yescharacteristic
372C22×C4⋊C4C2312yes—
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2312yes—
375C22×C4⋊C4C2312yes—
376C22×C4⋊C4C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2312yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2314yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2311yescharacteristic
387C22×C22⋊C4C2311yescharacteristic
388C22×C22⋊C4C2311yescharacteristic
389C22×C22⋊C4C2312yes—
390C22×C42C2311yescharacteristic
391C22×C42C2312yes—
392C22×C42C2311yescharacteristic
393#401C2312yes—
394#401C2312yes—
395#401C2314yes—
396#400C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2312yes—
406#400C2312yes—
407#400C2312yes—
408#400C2312yes—
409#400C2312yes—
410#400C2312yes—
411#400C2312yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#399C2312yes—
419#399C2312yes—
420#399C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2312yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2312yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#397C2314yes—
445#397C2312yes—
446#397C2314yes—
447#397C2314yes—
448#397C2312yes—
449#397C2312yes—
450#397C2312yes—
451#397C2312yes—
452#397C2312yes—
453#397C2312yes—
454#397C2312yes—
455#397C2312yes—
456#397C2312yes—
457#397C2312yes—
458#397C2312yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2312yes—
465#396C2312yes—
466#396C2314yes—
467#395C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2314yes—
473#394C2314yes—
474#394C2312yes—
475#394C2312yes—
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#393C2314yes—
480#393C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2312yes—
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2311yescharacteristic
493#390C2312yes—
494#390C2312yes—
495#390C2311yescharacteristic
496#390C2311yescharacteristic
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2311yescharacteristic
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2311yescharacteristic
546#389C2311yescharacteristic
547#389C2311yescharacteristic
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2311yescharacteristic
553#389C2311yescharacteristic
554#389C2311yescharacteristic
555#388C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2312yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2312yes—
630#387C2312yes—
631#386C2314yes—
632#386C2314yes—
633#386C2312yes—
634#386C2312yes—
635#386C2314yes—
636#386C2314yes—
637#386C2312yes—
638#386C2314yes—
639#386C2312yes—
640#385C2312yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2312yes—
651#385C2314yes—
652#385C2314yes—
653#385C2312yes—
654#385C2314yes—
655#385C2314yes—
656#385C2312yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#385C2314yes—
667#384C2311yescharacteristic
668#384C2311yescharacteristic
669#384C2312yes—
670#384C2312yes—
671#384C2312yes—
672#384C2312yes—
673#384C2312yes—
674#384C2312yes—
675#384C2314yes—
676#384C2312yes—
677#384C2312yes—
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#383C2312yes—
681#383C2312yes—
682#383C2314yes—
683#383C2314yes—
684#382C2311yescharacteristic
685#382C2311yescharacteristic
686#382C2312yes—
687#382C2312yes—
688#382C2312yes—
689#382C2311yescharacteristic
690#382C2312yes—
691#382C2311yescharacteristic
692#382C2314yes—
693#382C2314yes—
694#382C2314yes—
695#382C2314yes—
696#382C2314yes—
697#382C2314yes—
698#381C2312yes—
699#381C2312yes—
700#381C2314yes—
701#381C2314yes—
702#381C2312yes—
703#381C2314yes—
704#381C2312yes—
705#381C2314yes—
706#381C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2314yes—
713#380C2312yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2314yes—
719#380C2312yes—
720#380C2311yescharacteristic
721#380C2311yescharacteristic
722#380C2311yescharacteristic
723#380C2311yescharacteristic
724#380C2314yes—
725#380C2312yes—
726#380C2311yescharacteristic
727#380C2311yescharacteristic
728#380C2314yes—
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#380C2311yescharacteristic
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2311yescharacteristic
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#379C2312yes—
743#379C2312yes—
744#379C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809#376C2312yes—
810#376C2314yes—
811C2×#95C2312yes—
812C2×#95C2314yes—
813C2×#95C2312yes—
814C2×#95C2311yescharacteristic
815C2×#95C2312yes—
816C2×#95C2311yescharacteristic
817C43C2312yes—
818C25C2411yescharacteristic
819C2×#41—24no—
820C2×#41—24no—
821C2×#41#4118yes—
822C22×Q8—28no—
823C22×Q8—44no—
824C22×Q8—82no—
825C22×Q8C2414yes—
826C22×Q8C2411yescharacteristic
827C22×Q8C2414yes—
828C22×D4C2412yes—
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C23×C4—24no—
833C23×C4—24no—
834C23×C4—24no—
835C23×C4—28no—
836C23×C4—44no—
837C23×C4—82no—
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2412yes—
848C23×C4C2414yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C4⋊Q8—28no—
860C4⋊Q8—28no—
861C4⋊Q8—28no—
862C4⋊Q8—28no—
863#126—28no—
864#126—28no—
865#126—48no—
866#125—48no—
867#125—48no—
868#125—48no—
869#125—84no—
870#123—28no—
871#123—28no—
872#123—28no—
873#123—48no—
874C22⋊Q8—24no—
875C22⋊Q8—24no—
876C22⋊Q8—216no—
877C22⋊Q8—48no—
878C22⋊Q8—48no—
879C22⋊Q8—48no—
880C22⋊Q8—48no—
881C22⋊Q8—84no—
882#121—24no—
883#121—24no—
884#120—28no—
885C4×Q8—24no—
886C4×Q8—24no—
887C4×Q8—28no—
888C4×Q8—28no—
889C4×Q8—48no—
890C4×Q8—84no—
891C4×D4—28no—
892C4×D4—28no—
893C4×D4—24no—
894C4×D4—24no—
895C4×D4—216no—
896C4×D4—28no—
897C4×D4—216no—
898C4×D4—28no—
899C4×D4—28no—
900C4×D4—28no—
901C4×D4—48no—
902C4×D4—84no—
903#117—28no—
904#117—24no—
905#117—28no—
906#117—24no—
907#117—24no—
908#117—24no—
909#117—24no—
910#117—24no—
911#117—24no—
912#117—28no—
913#117—48no—
914#117—48no—
915#117—48no—
916#117—84no—
917#117—84no—
918C2×C4⋊C4—28no—
919C2×C4⋊C4—24no—
920C2×C4⋊C4—28no—
921C2×C4⋊C4—24no—
922C2×C4⋊C4—28no—
923C2×C4⋊C4—24no—
924C2×C4⋊C4—28no—
925C2×C4⋊C4—28no—
926C2×C4⋊C4—28no—
927C2×C4⋊C4—28no—
928C2×C4⋊C4—28no—
929C2×C4⋊C4—44no—
930C2×C4⋊C4—44no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4—48no—
933C2×C4⋊C4—82no—
934C2×C4⋊C4#4118yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2411yescharacteristic
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C22⋊C4—24no—
1012C2×C22⋊C4—24no—
1013C2×C22⋊C4—44no—
1014C2×C22⋊C4C2411yescharacteristic
1015C2×C22⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2411yescharacteristic
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2411yescharacteristic
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C42—28no—
1060C2×C42—24no—
1061C2×C42—24no—
1062C2×C42C2412yes—
1063C2×C42C2412yes—
1064C2×C42C2411yescharacteristic
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2414yes—
1068C2×C42C2412yes—
1069C2×C42C2414yes—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2411yescharacteristic
1074C2×C42C2411yescharacteristic
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2414yes—
1084C2×C42C2414yes—
1085C2×C42C2414yes—
1086C2×C42C2414yes—
1087C2×C42C2414yes—
1088C2×C42C2414yes—
1089C2×C42C2414yes—
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093#95C2414yes—
1094#95C2412yes—
1095#95C2414yes—
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2411yescharacteristic
1103#95C2411yescharacteristic
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2414yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175C24—22no—
1176C24—22no—
1177C24—22no—
1178C24—22no—
1179C24—22no—
1180C24—41no—
1181C24—41no—
1182C24C2512yes—
1183C24C2511yescharacteristic
1184C24C2511yescharacteristic
1185C24C2511yescharacteristic
1186#41—232no—
1187C2×Q8—22no—
1188C2×Q8—28no—
1189C2×Q8—28no—
1190C2×Q8—28no—
1191C2×Q8—22no—
1192C2×Q8—44no—
1193C2×Q8—44no—
1194C2×Q8—44no—
1195C2×Q8—816no—
1196C2×Q8C2×#4114yes—
1197C2×D4—24no—
1198C2×D4—24no—
1199C2×D4—24no—
1200C2×D4—24no—
1201C2×D4—24no—
1202C2×D4—24no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—42no—
1206C2×D4—42no—
1207C2×D4C2×#4118yes—
1208C2×D4C2×#4114yes—
1209C22×C4—24no—
1210C22×C4—24no—
1211C22×C4—22no—
1212C22×C4—24no—
1213C22×C4—24no—
1214C22×C4—22no—
1215C22×C4—22no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—28no—
1220C22×C4—22no—
1221C22×C4—24no—
1222C22×C4—24no—
1223C22×C4—28no—
1224C22×C4—24no—
1225C22×C4—28no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—28no—
1245C22×C4—28no—
1246C22×C4—42no—
1247C22×C4—41no—
1248C22×C4—42no—
1249C22×C4—44no—
1250C22×C4—42no—
1251C22×C4—41no—
1252C22×C4—42no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—42no—
1256C22×C4—42no—
1257C22×C4—42no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4—44no—
1266C22×C4—42no—
1267C22×C4—416no—
1268C22×C4—816no—
1269C22×C4C2×#4118yes—
1270C22×C4C2×#4118yes—
1271C22×C4C2×#4114yes—
1272C22×C4C2×#4114yes—
1273C22×C42−1+414yes—
1274C22×C4C2511yescharacteristic
1275C22×C4C2511yescharacteristic
1276C22×C4C2511yescharacteristic
1277C22×C4C2512yes—
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2514yes—
1291C22×C4C2512yes—
1292C22×C4C2514yes—
1293C22×C4C2512yes—
1294C22×C4C2511yescharacteristic
1295C22×C4C2514yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2514yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2511yescharacteristic
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C4⋊C4—28no—
1306C4⋊C4—28no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—22no—
1312C4⋊C4—28no—
1313C4⋊C4—28no—
1314C4⋊C4—24no—
1315C4⋊C4—28no—
1316C4⋊C4—28no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—22no—
1320C4⋊C4—22no—
1321C4⋊C4—24no—
1322C4⋊C4—24no—
1323C4⋊C4—22no—
1324C4⋊C4—22no—
1325C4⋊C4—22no—
1326C4⋊C4—22no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—28no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—44no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4C2×#4118yes—
1380C4⋊C4C2×#4118yes—
1381C22⋊C4—28no—
1382C22⋊C4—24no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—22no—
1391C22⋊C4—28no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—22no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—28no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—22no—
1406C22⋊C4—22no—
1407C22⋊C4—24no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—24no—
1411C22⋊C4—44no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—42no—
1415C22⋊C4—42no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4H(5,𝔽2)14yes—
1425C22⋊C42−1+414yes—
1426C42—22no—
1427C42—24no—
1428C42—22no—
1429C42—24no—
1430C42—24no—
1431C42—22no—
1432C42—22no—
1433C42—22no—
1434C42—22no—
1435C42—22no—
1436C42—22no—
1437C42—24no—
1438C42—28no—
1439C42—28no—
1440C42—24no—
1441C42—24no—
1442C42—24no—
1443C42—24no—
1444C42—24no—
1445C42—24no—
1446C42—24no—
1447C42—42no—
1448C42—44no—
1449C42—44no—
1450C42—44no—
1451C42—44no—
1452C42—44no—
1453C42—44no—
1454C42—44no—
1455C42—44no—
1456C42—42no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—28no—
1462C23—22no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—22no—
1469C23—21no—
1470C23—22no—
1471C23—21no—
1472C23—21no—
1473C23—22no—
1474C23—22no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—22no—
1480C23—44no—
1481C23—44no—
1482C23—44no—
1483C23—44no—
1484C23—44no—
1485C23—44no—
1486C23C22×#4114yes—
1487C23C22×#4112yes—
1488C23C22×#4112yes—
1489C23C2×H(5,𝔽2)12yes—
1490C23C2×2−1+412yes—
1491C23C2×2−1+412yes—
1492C23C2611yescharacteristic
1493Q8—28no—
1494Q8—416no—
1495Q8—88no—
1496D4—216no—
1497D4—28no—
1498D4—48no—
1499D4—48no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—22no—
1504C2×C4—21no—
1505C2×C4—24no—
1506C2×C4—22no—
1507C2×C4—21no—
1508C2×C4—24no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—216no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—21no—
1517C2×C4—22no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—24no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—24no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—24no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—24no—
1538C2×C4—22no—
1539C2×C4—24no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—24no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—24no—
1582C2×C4—48no—
1583C2×C4—44no—
1584C2×C4—48no—
1585C2×C4—44no—
1586C2×C4—44no—
1587C2×C4—48no—
1588C2×C4—416no—
1589C2×C4—44no—
1590C2×C4—44no—
1591C2×C4—44no—
1592C2×C4—44no—
1593C2×C4—44no—
1594C2×C4—44no—
1595C2×C4—88no—
1596C2×C4—88no—
1597C2×C4—84no—
1598C2×C4—88no—
1599C2×C4—84no—
1600C2×C4—84no—
1601C2×C4#552116yescomplemented
1602C2×C4C22×#4114yes—
1603C2×C4C22×#4118yes—
1604C2×C4C22×#4112yes—
1605C2×C4C22×#4112yes—
1606C2×C4C22×#4112yes—
1607C2×C4C22×#4112yes—
1608C2×C4C2×H(5,𝔽2)12yes—
1609C2×C4C2×H(5,𝔽2)12yes—
1610C2×C4C2×2−1+412yes—
1611C2×C4C2×2−1+412yes—
1612C2×C4C2×2−1+412yes—
1613C2×C4C2×2−1+412yes—
1614C22—22no—
1615C22—22no—
1616C22—22no—
1617C22—22no—
1618C22—22no—
1619C22—22no—
1620C22—22no—
1621C22—24no—
1622C22—22no—
1623C22—22no—
1624C22—24no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—24no—
1629C22—416no—
1630C22—41no—
1631C22—42no—
1632C22—41no—
1633C22—42no—
1634C22—41no—
1635C22—41no—
1636C22—42no—
1637C22—42no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22C2×#55214yes—
1643C22C23×#4111yescharacteristic
1644C22C23×#4111yescharacteristic
1645C22C22×H(5,𝔽2)11yescharacteristic
1646C22C22×2−1+411yescharacteristic
1647C22C22×2−1+411yescharacteristic
1648C22H(7,𝔽2)11yescharacteristic
1649C222−1+611yescharacteristic
1650C4—28no—
1651C4—22no—
1652C4—22no—
1653C4—22no—
1654C4—22no—
1655C4—24no—
1656C4—44no—
1657C4—41no—
1658C4—42no—
1659C4—44no—
1660C4—42no—
1661C4—41no—
1662C4—42no—
1663C4—44no—
1664C4—42no—
1665C4—42no—
1666C4—41no—
1667C4—42no—
1668C4—41no—
1669C4—42no—
1670C4—42no—
1671C4—42no—
1672C4—42no—
1673C4—42no—
1674C4—42no—
1675C4—42no—
1676C4—42no—
1677C4—41no—
1678C4—41no—
1679C4C2×#55214yes—
1680C4C2×#55214yes—
1681C2—24no—
1682C2—44no—
1683C2—42no—
1684C2—42no—
1685C2C22×#55211yescharacteristic
1686C2#6283311yescharacteristic
1687C2#6287711yescharacteristic
1688C2#6298311yescharacteristic
1689C2#6298511yescharacteristic
1690C2#6299811yescharacteristic
1691C2#6300011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59503C2semidirect
2. #59502C2semidirect
3. #59499C2semidirect
4. #59498C2semidirect
5. #59295C2semidirect
6. #59294C2semidirect
7. #59291C2semidirect
8. #59290C2semidirect
9. #59252C2semidirect
10. #59027C2semidirect
11. #45331C2semidirect
12. #45252C2semidirect
13. #45210C2semidirect
14. #45055C2semidirect
15. #45027C2semidirect
16. #45005C2semidirect
17. #44999C2semidirect
18. #44917C2semidirect
19. #43082C2semidirect
20. #43057C2semidirect
21. #35585C2semidirect
22. #35574C2semidirect
23. #35555C2semidirect
24. #35544C2semidirect
25. #35543C2semidirect
27. #34814C2semidirect
29. C2×#2440C2semidirect
30. #34253C2semidirect
31. #34250C2semidirect
32. #34216C2semidirect
34. #34188C2semidirect
35. #34178C2semidirect
44. #2794C22semidirect
45. #2791C22semidirect
46. #2787C22semidirect
47. #2774C22semidirect
48. #2774C22semidirect
50. #2770C22semidirect
52. #2766C22semidirect
53. #2765C22semidirect
54. #2762C22semidirect
55. #2762C22semidirect
57. #2745C22semidirect
58. #2745C22semidirect
59. #2739C22semidirect
60. #2719C22semidirect
64. #2690C22semidirect
65. #2690C22semidirect
70. #2606C22semidirect
71. #2599C22semidirect
72. #2599C22semidirect
73. #2590C22semidirect
76. #2571C22semidirect
77. #2570C22semidirect
78. #2570C22semidirect
79. #2570C22semidirect
80. #2570C22semidirect
84. #2552C22semidirect
85. #2552C22semidirect
86. #2552C22semidirect
88. #2528C22semidirect
89. #2524C22semidirect
90. #2520C22semidirect
91. #2520C22semidirect
94. #2515C22semidirect
95. #2509C22semidirect
96. #2509C22semidirect
97. #2509C22semidirect
98. #2508C22semidirect
99. #2508C22semidirect
100. #2508C22semidirect
101. #2507C22semidirect
102. #2507C22semidirect
103. #2507C22semidirect
104. #2507C22semidirect
105. #2507C22semidirect
106. #2506C22semidirect
107. #2506C22semidirect
108. #2506C22semidirect
109. #2506C22semidirect
110. #2506C22semidirect
137. #2484C22semidirect
144. #2475C22semidirect
148. #2473C22semidirect
151. #2462C22semidirect
152. #2462C22semidirect
154. #2452C22semidirect
155. #2452C22semidirect
156. #2451C22semidirect
157. #2451C22semidirect
167. #2440C22semidirect
168. #2440C22semidirect
169. #2439C22semidirect
170. #2439C22semidirect
171. #2438C22semidirect
172. #2438C22semidirect
203. #2369C22semidirect
204. #2369C22semidirect
205. #2365C22semidirect
206. #2365C22semidirect
213. #2355C22semidirect
214. #2355C22semidirect
215. #2354C22semidirect
216. #2354C22semidirect
223. #2351C22semidirect
224. Q8×C4⋊C4C22semidirect
226. #2349C22semidirect
230. D4×C4⋊C4C22semidirect
231. #2347C22semidirect
232. #2346C22semidirect
238. #2345C22semidirect
243. #2344C22semidirect
245. #2331C22semidirect
246. #2331C22semidirect
248. #2320C22semidirect
249. #2319C22semidirect
254. #2317C22semidirect
259. #2316C22semidirect
260. #2314C22semidirect
261. #2314C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
276. #2296C22semidirect
277. #2295C22semidirect
278. #2293C22semidirect
281. C2×#389C22semidirect
285. #2285C22semidirect
286. #2285C22semidirect
1601. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
#595032
#595022
#594992
#594982
#592952
#592942
#592912
#592902
#592522
#590272
#453312
#452522
#452102
#450552
#450272
#450052
#449992
#449172
#430822
#430572
#355852
#355742
#355552
#355442
#355432
#355162
#348142
#347422
C2×#24402
#342532
#342502
#342162
#342002
#341882
#341782