Finite Group Databasebeta

← #7682783

Subgroups — #7682783

Order 512.

5064 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#59716C212yesmaximal, complemented
2#59715C212yesmaximal, complemented
3#59712C212yesmaximal, complemented
4#59711C212yesmaximal, complemented
5#59431C212yesmaximal, complemented
6#59430C212yesmaximal, complemented
7#59429C212yesmaximal, complemented
8#59428C212yesmaximal, complemented
9#59238C214yesmaximal, complemented
10#59025C214yesmaximal, complemented
11#45341C212yesmaximal, complemented
12#45311C212yesmaximal, complemented
13#45212C212yesmaximal, complemented
14#45058C212yesmaximal, complemented
15#45032C212yesmaximal, complemented
16#45014C212yesmaximal, complemented
17#44984C212yesmaximal, complemented
18#44984C212yesmaximal, complemented
19#43085C214yesmaximal, complemented
20#43058C214yesmaximal, complemented
21#35574C211yesmaximal, characteristic, complemented
22#35566C211yesmaximal, characteristic, complemented
23#35557C211yesmaximal, characteristic, complemented
24#35545C211yesmaximal, characteristic, complemented
25#35544C211yesmaximal, characteristic, complemented
26#35542C211yesmaximal, characteristic
27#34814C211yesmaximal, characteristic, complemented
28#34813C211yesmaximal, characteristic
29C2×#2440C211yesmaximal, characteristic, complemented
30#34272C211yesmaximal, characteristic, complemented
31#34253C211yesmaximal, characteristic, complemented
32#34216C211yesmaximal, characteristic, complemented
33#34214C211yesmaximal, characteristic, complemented
34#34200C211yesmaximal, characteristic
35#34178C211yesmaximal, characteristic, complemented
36C2×#556C2214yes—
37C2×#544C2211yescharacteristic
38C2×#533C2211yescharacteristic
39C22×C4⋊Q8C2211yescharacteristic
40C2×#525C2211yescharacteristic
41C22×C22⋊Q8C2212yes—
42C2×#520C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44#2805C2214yescomplemented
45#2805C2214yescomplemented
46#2793C2214yescomplemented
47#2789C2214yescomplemented
48#2788C2214yes—
49#2788C2214yescomplemented
50#2787C2214yes—
51#2787C2214yescomplemented
52#2786C2214yes—
53#2776C2214yescomplemented
54#2776C2214yescomplemented
55#2767C2214yescomplemented
56#2762C2214yescomplemented
57#2762C2214yescomplemented
58#2759C2214yescomplemented
59#2759C2214yescomplemented
60#2716C2214yescomplemented
61#2715C2214yes—
62#2700C2214yes—
63#2700C2214yes—
64#2689C2214yes—
65#2689C2214yes—
66#2689C2214yescomplemented
67#2689C2214yescomplemented
68#2605C2214yescomplemented
69#2605C2214yescomplemented
70#2601C2214yes—
71#2599C2214yes—
72#2599C2214yescomplemented
73#2594C2214yescomplemented
74#2588C2214yescomplemented
75#2584C2212yescomplemented
76#2584C2212yescomplemented
77#2581C2214yescomplemented
78#2581C2214yescomplemented
79#2579C2214yes—
80#2573C2214yes—
81#2570C2214yescomplemented
82#2567C2212yescomplemented
83#2563C2212yes—
84#2562C2212yes—
85#2562C2212yes—
86#2560C2214yes—
87#2560C2214yes—
88#2552C2212yescomplemented
89#2551C2212yescomplemented
90#2550C2212yescomplemented
91#2550C2212yescomplemented
92#2549C2214yes—
93#2547C2212yes—
94#2546C2212yescomplemented
95#2538C2214yes—
96#2527C2214yes—
97#2525C2214yescomplemented
98#2524C2214yescomplemented
99#2523C2214yes—
100#2514C2212yescomplemented
101#2513C2212yescomplemented
102#2512C2212yescomplemented
103#2512C2212yescomplemented
104#2512C2212yescomplemented
105#2511C2212yescomplemented
106#2511C2212yescomplemented
107#2511C2212yescomplemented
108#2510C2214yes—
109#2499C2214yes—
110#2497C2211yescharacteristic
111#2497C2212yes—
112#2497C2211yescharacteristic
113#2497C2212yes—
114#2497C2212yescomplemented
115#2497C2212yescomplemented
116#2497C2212yescomplemented
117#2496C2211yescharacteristic
118#2496C2212yes—
119#2496C2211yescharacteristic
120#2496C2212yes—
121#2496C2212yescomplemented
122#2496C2212yescomplemented
123#2496C2212yescomplemented
124#2495C2211yescharacteristic
125#2495C2212yes—
126#2495C2212yes—
127#2495C2211yescharacteristic
128#2495C2212yescomplemented
129#2494C2212yes—
130#2494C2212yes—
131#2494C2211yescharacteristic
132#2494C2211yescharacteristic
133#2494C2212yescomplemented
134#2493C2212yes—
135#2493C2214yes—
136#2493C2212yes—
137#2492C2212yes—
138#2492C2211yescharacteristic
139#2492C2214yes—
140#2492C2211yescharacteristic
141#2491C2211yescharacteristic
142#2491C2212yes—
143#2491C2211yescharacteristic
144#2490C2212yes—
145#2490C2211yescharacteristic
146#2490C2211yescharacteristic
147#2489C2211yescharacteristic
148#2489C2212yes—
149#2489C2211yescharacteristic
150#2488C2212yes—
151#2488C2214yes—
152#2488C2212yes—
153#2481C2214yes—
154#2481C2214yes—
155#2481C2214yes—
156#2480C2212yes—
157#2480C2214yes—
158#2480C2212yes—
159#2478C2214yes—
160#2478C2214yescomplemented
161#2474C2214yes—
162#2472C2212yes—
163#2472C2214yes—
164#2472C2212yes—
165#2469C2214yescomplemented
166#2469C2214yescomplemented
167#2466C2214yes—
168#2466C2214yes—
169#2465C2214yes—
170#2465C2214yes—
171#2465C2214yescomplemented
172#2465C2214yescomplemented
173#2452C2212yescomplemented
174#2452C2212yescomplemented
175#2451C2212yescomplemented
176#2451C2212yescomplemented
177#2447C2214yes—
178#2446C2214yescomplemented
179#2440C2212yes—
180#2440C2212yes—
181#2440C2212yes—
182#2440C2212yes—
183#2440C2214yes—
184#2440C2212yes—
185#2440C2212yes—
186#2440C2212yes—
187#2440C2212yes—
188#2440C2212yescomplemented
189#2440C2212yescomplemented
190#2439C2212yescomplemented
191#2439C2212yescomplemented
192#2421C2214yes—
193#2415C2214yes—
194#2415C2214yes—
195#2409C2214yes—
196#2401C2212yes—
197#2401C2212yes—
198#2398C2212yes—
199#2398C2212yes—
200C2×#398C2212yes—
201C2×#395C2212yes—
202#2373C2214yes—
203#2370C2212yescomplemented
204#2370C2212yescomplemented
205#2369C2212yescomplemented
206#2369C2212yescomplemented
207#2369C2212yescomplemented
208#2368C2214yes—
209#2367C2214yes—
210#2365C2212yescomplemented
211#2365C2212yescomplemented
212#2365C2212yescomplemented
213#2362C2214yes—
214#2361C2212yes—
215#2361C2212yes—
216#2360C2212yes—
217#2360C2214yes—
218#2360C2212yes—
219#2360C2214yes—
220#2360C2214yes—
221#2355C2212yescomplemented
222#2355C2212yescomplemented
223#2353C2214yes—
224#2352C2212yes—
225#2352C2212yes—
226#2352C2214yes—
227Q8×C4⋊C4C2212yescomplemented
228Q8×C4⋊C4C2212yescomplemented
229D4×C4⋊C4C2212yes—
230D4×C4⋊C4C2212yes—
231#2347C2212yescomplemented
232#2346C2212yescomplemented
233#2345C2212yes—
234#2345C2212yes—
235#2345C2212yes—
236#2345C2214yes—
237#2345C2212yes—
238#2345C2212yescomplemented
239#2344C2212yes—
240#2344C2212yes—
241#2344C2212yes—
242#2344C2212yes—
243#2344C2212yescomplemented
244Q8×C22⋊C4C2214yes—
245#2331C2212yescomplemented
246#2331C2212yescomplemented
247#2331C2212yescomplemented
248#2330C2212yescomplemented
249#2330C2212yescomplemented
250#2330C2212yescomplemented
251#2322C2214yes—
252#2320C2212yescomplemented
253#2319C2212yescomplemented
254#2317C2211yescharacteristic
255#2317C2211yescharacteristic
256#2317C2211yescharacteristic
257#2316C2211yescharacteristic
258#2316C2211yescharacteristic
259#2316C2211yescharacteristic
260#2313C2214yes—
261#2311C2211yescharacteristic
262#2311C2211yescharacteristic
263#2311C2211yescharacteristic
264C4×C4⋊Q8C2212yescomplemented
265C4×C4⋊Q8C2212yescomplemented
266C4×C4⋊Q8C2212yescomplemented
267C4×C4⋊Q8C2212yescomplemented
268C4×C4⋊Q8C2212yescomplemented
269C4×#125C2212yescomplemented
270C4×#126C2212yes—
271C4×#126C2212yes—
272C4×#124C2212yes—
273C4×#124C2212yes—
274C4×#120C2214yes—
275#2297C2211yescharacteristic
276#2297C2211yescharacteristic
277#2296C2211yescharacteristic
278#2296C2211yescharacteristic
279#2295C2212yescomplemented
280#2293C2212yescomplemented
281C2×#389C2211yescharacteristic
282C2×#389C2211yescharacteristic
283C2×#385C2212yes—
284#2285C2211yescharacteristic
285C2×#384C2211yescharacteristic
286#2280C2214yes—
287#2280C2211yescharacteristic
288#2280C2211yescharacteristic
289#2280C2211yescharacteristic
290C2×#380C2211yescharacteristic
291#2274C2211yescharacteristic
292#2274C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2312yes—
301C24×C4C2311yescharacteristic
302C24×C4C2312yes—
303#556—416no—
304#544—28no—
305#533—28no—
306C2×C4⋊Q8—28no—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2314yes—
316C2×#126C2312yes—
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#125C2312yes—
323C2×#125C2311yescharacteristic
324C2×#125C2311yescharacteristic
325C2×#125C2312yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2314yes—
329#525—28no—
330C2×#123C2312yes—
331C2×C22⋊Q8—48no—
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2311yescharacteristic
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2314yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×#121C2311yescharacteristic
344C2×#121C2311yescharacteristic
345C2×#120C2312yes—
346#520—28no—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2314yes—
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2314yes—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2314yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×#117C2311yescharacteristic
362C2×#117C2311yescharacteristic
363C2×#117C2311yescharacteristic
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2312yes—
368C2×#117C2314yes—
369C2×#117C2314yes—
370C2×#117C2314yes—
371C2×#117C2311yescharacteristic
372C22×C4⋊C4—28no—
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2312yes—
377C22×C4⋊C4C2312yes—
378C22×C4⋊C4C2312yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2311yescharacteristic
388C22×C22⋊C4C2311yescharacteristic
389C22×C22⋊C4C2311yescharacteristic
390C22×C22⋊C4C2312yes—
391C22×C42C2311yescharacteristic
392C22×C42C2311yescharacteristic
393#401C2314yes—
394#401C2312yes—
395#401C2312yes—
396#401C2314yes—
397#400C2314yes—
398#400C2314yes—
399#400C2312yes—
400#400C2314yes—
401#400C2314yes—
402#400C2312yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2312yes—
407#400C2312yes—
408#400C2312yes—
409#400C2312yes—
410#400C2312yes—
411#400C2312yes—
412#400C2312yes—
413#400C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#397C2312yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2312yes—
436#397C2312yes—
437#397C2312yes—
438#397C2312yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#396C2312yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#394C2312yes—
468#394C2314yes—
469#394C2314yes—
470#394C2312yes—
471#394C2312yes—
472#394C2312yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2312yes—
478#393C2312yes—
479#393C2312yes—
480#393C2312yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#391C2314yes—
497#391C2314yes—
498#391C2314yes—
499#391C2314yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2311yescharacteristic
504#391C2311yescharacteristic
505#391C2311yescharacteristic
506#390C2312yes—
507#390C2314yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2311yescharacteristic
512#390C2312yes—
513#390C2311yescharacteristic
514#390C2311yescharacteristic
515#390C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2311yescharacteristic
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2314yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2314yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2311yescharacteristic
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2311yescharacteristic
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2311yescharacteristic
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2312yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2312yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
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#387C2314yes—
622#387C2314yes—
623#387C2314yes—
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#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2312yes—
650#386C2314yes—
651#386C2312yes—
652#386C2312yes—
653#386C2312yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2312yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2312yes—
667#385C2314yes—
668#385C2314yes—
669#385C2312yes—
670#385C2312yes—
671#384C2312yes—
672#384C2311yescharacteristic
673#384C2311yescharacteristic
674#384C2312yes—
675#384C2314yes—
676#384C2312yes—
677#384C2312yes—
678#384C2312yes—
679#384C2312yes—
680#384C2312yes—
681#383C2312yes—
682#383C2312yes—
683#383C2314yes—
684#383C2314yes—
685#383C2314yes—
686#382C2312yes—
687#382C2314yes—
688#382C2312yes—
689#382C2312yes—
690#382C2312yes—
691#382C2314yes—
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#381C2312yes—
696#381C2312yes—
697#381C2314yes—
698#381C2314yes—
699#381C2312yes—
700#381C2314yes—
701#380C2312yes—
702#380C2311yescharacteristic
703#380C2311yescharacteristic
704#380C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2312yes—
708#380C2311yescharacteristic
709#380C2312yes—
710#380C2312yes—
711#380C2312yes—
712#380C2314yes—
713#380C2314yes—
714#380C2314yes—
715#380C2314yes—
716#380C2312yes—
717#380C2311yescharacteristic
718#380C2311yescharacteristic
719#380C2311yescharacteristic
720#380C2314yes—
721#380C2312yes—
722#380C2311yescharacteristic
723#380C2311yescharacteristic
724#380C2314yes—
725#380C2311yescharacteristic
726#380C2311yescharacteristic
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2312yes—
730#380C2312yes—
731#379C2312yes—
732#379C2312yes—
733#379C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C22⋊C4C2311yescharacteristic
777C4×C22⋊C4C2311yescharacteristic
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808#376C2312yes—
809#376C2312yes—
810#376C2314yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2311yescharacteristic
814C2×#95C2312yes—
815C2×#95C2311yescharacteristic
816C43C2312yes—
817C43C2312yes—
818C25C2411yescharacteristic
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—24no—
822C22×Q8—28no—
823C22×Q8—44no—
824C22×Q8—82no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×Q8C2414yes—
830C22×Q8C2414yes—
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2412yes—
835C23×C4—24no—
836C23×C4—24no—
837C23×C4—24no—
838C23×C4—28no—
839C23×C4—44no—
840C23×C4—82no—
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2414yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C23×C4C2414yes—
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C4⋊Q8—28no—
860C4⋊Q8—28no—
861C4⋊Q8—28no—
862C4⋊Q8—28no—
863C4⋊Q8—24no—
864C4⋊Q8—24no—
865C4⋊Q8—28no—
866C4⋊Q8—28no—
867C4⋊Q8—48no—
868#126—28no—
869#126—28no—
870#126—48no—
871#126—48no—
872#126—48no—
873#126—84no—
874#125—24no—
875#125—24no—
876#125—28no—
877#125—28no—
878#124—28no—
879#124—28no—
880#124—48no—
881#123—28no—
882C22⋊Q8—24no—
883C22⋊Q8—24no—
884C22⋊Q8—28no—
885C22⋊Q8—28no—
886C22⋊Q8—216no—
887C22⋊Q8—216no—
888C22⋊Q8—48no—
889C22⋊Q8—48no—
890C22⋊Q8—48no—
891C22⋊Q8—48no—
892C22⋊Q8—84no—
893#121—24no—
894#121—24no—
895#120—28no—
896C4×Q8—28no—
897C4×Q8—28no—
898C4×Q8—28no—
899C4×Q8—48no—
900C4×Q8—48no—
901C4×Q8—48no—
902C4×Q8—84no—
903C4×Q8—84no—
904C4×D4—216no—
905C4×D4—28no—
906C4×D4—28no—
907C4×D4—28no—
908C4×D4—48no—
909C4×D4—84no—
910#117—24no—
911#117—24no—
912#117—24no—
913#117—24no—
914#117—24no—
915#117—24no—
916#117—28no—
917#117—48no—
918#117—48no—
919#117—84no—
920#117#4118yes—
921C2×C4⋊C4—28no—
922C2×C4⋊C4—24no—
923C2×C4⋊C4—28no—
924C2×C4⋊C4—24no—
925C2×C4⋊C4—24no—
926C2×C4⋊C4—28no—
927C2×C4⋊C4—28no—
928C2×C4⋊C4—28no—
929C2×C4⋊C4—28no—
930C2×C4⋊C4—28no—
931C2×C4⋊C4—44no—
932C2×C4⋊C4—44no—
933C2×C4⋊C4—44no—
934C2×C4⋊C4—82no—
935C2×C4⋊C4#4118yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2411yescharacteristic
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2414yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C22⋊C4—24no—
1007C2×C22⋊C4—24no—
1008C2×C22⋊C4—44no—
1009C2×C22⋊C4C2411yescharacteristic
1010C2×C22⋊C4C2411yescharacteristic
1011C2×C22⋊C4C2411yescharacteristic
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2411yescharacteristic
1014C2×C22⋊C4C2411yescharacteristic
1015C2×C22⋊C4C2411yescharacteristic
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C42—24no—
1058C2×C42—24no—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2414yes—
1062C2×C42C2412yes—
1063C2×C42C2412yes—
1064C2×C42C2412yes—
1065C2×C42C2412yes—
1066C2×C42C2412yes—
1067C2×C42C2412yes—
1068C2×C42C2411yescharacteristic
1069C2×C42C2411yescharacteristic
1070C2×C42C2412yes—
1071C2×C42C2411yescharacteristic
1072C2×C42C2412yes—
1073C2×C42C2411yescharacteristic
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2414yes—
1079C2×C42C2414yes—
1080C2×C42C2414yes—
1081C2×C42C2414yes—
1082C2×C42C2414yes—
1083C2×C42C2414yes—
1084C2×C42C2414yes—
1085C2×C42C2414yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2412yes—
1093#95C2414yes—
1094#95C2411yescharacteristic
1095#95C2411yescharacteristic
1096#95C2411yescharacteristic
1097#95C2411yescharacteristic
1098#95C2411yescharacteristic
1099#95C2411yescharacteristic
1100#95C2411yescharacteristic
1101#95C2411yescharacteristic
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2412yes—
1108#95C2412yes—
1109#95C2414yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
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—416no—
1187C2×Q8—22no—
1188C2×Q8—24no—
1189C2×Q8—24no—
1190C2×Q8—22no—
1191C2×Q8—28no—
1192C2×Q8—28no—
1193C2×Q8—28no—
1194C2×Q8—24no—
1195C2×Q8—28no—
1196C2×Q8—24no—
1197C2×Q8—22no—
1198C2×Q8—42no—
1199C2×Q8—44no—
1200C2×Q8—42no—
1201C2×Q8—44no—
1202C2×Q8—44no—
1203C2×Q8—44no—
1204C2×Q8—44no—
1205C2×Q8—816no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—22no—
1212C2×D4—24no—
1213C2×D4—24no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—42no—
1217C2×D4—42no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—28no—
1225C22×C4—22no—
1226C22×C4—24no—
1227C22×C4—24no—
1228C22×C4—24no—
1229C22×C4—28no—
1230C22×C4—22no—
1231C22×C4—22no—
1232C22×C4—22no—
1233C22×C4—22no—
1234C22×C4—24no—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—24no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—24no—
1249C22×C4—28no—
1250C22×C4—28no—
1251C22×C4—42no—
1252C22×C4—41no—
1253C22×C4—44no—
1254C22×C4—42no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—42no—
1259C22×C4—42no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—42no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4—44no—
1266C22×C4—44no—
1267C22×C4—42no—
1268C22×C4—416no—
1269C22×C4—816no—
1270C22×C4C2×#4118yes—
1271C22×C4C2×#4114yes—
1272C22×C4C2×#4114yes—
1273C22×C42−1+414yes—
1274C22×C4C2512yes—
1275C22×C4C2511yescharacteristic
1276C22×C4C2511yescharacteristic
1277C22×C4C2511yescharacteristic
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×C4C2514yes—
1292C22×C4C2512yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2514yes—
1295C22×C4C2512yes—
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—28no—
1311C4⋊C4—24no—
1312C4⋊C4—24no—
1313C4⋊C4—28no—
1314C4⋊C4—28no—
1315C4⋊C4—24no—
1316C4⋊C4—24no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—22no—
1320C4⋊C4—22no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—28no—
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—28no—
1334C4⋊C4—28no—
1335C4⋊C4—28no—
1336C4⋊C4—24no—
1337C4⋊C4—24no—
1338C4⋊C4—24no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—22no—
1344C4⋊C4—22no—
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—42no—
1354C4⋊C4—42no—
1355C4⋊C4—44no—
1356C4⋊C4—42no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4C2×#4118yes—
1372C4⋊C4C2×#4118yes—
1373C4⋊C4C2×#4114yes—
1374C4⋊C4C2×#4114yes—
1375C22⋊C4—24no—
1376C22⋊C4—24no—
1377C22⋊C4—24no—
1378C22⋊C4—22no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—22no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—28no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—22no—
1396C22⋊C4—22no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—44no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—42no—
1407C22⋊C4—44no—
1408C22⋊C4—42no—
1409C22⋊C4—42no—
1410C22⋊C4—44no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—44no—
1414C22⋊C4—42no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4C2×#4118yes—
1421C22⋊C4H(5,𝔽2)14yes—
1422C22⋊C42−1+414yes—
1423C42—22no—
1424C42—22no—
1425C42—22no—
1426C42—22no—
1427C42—22no—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—28no—
1432C42—24no—
1433C42—24no—
1434C42—24no—
1435C42—24no—
1436C42—24no—
1437C42—24no—
1438C42—24no—
1439C42—24no—
1440C42—24no—
1441C42—24no—
1442C42—42no—
1443C42—42no—
1444C42—44no—
1445C42—44no—
1446C42—44no—
1447C42—44no—
1448C42—44no—
1449C42—44no—
1450C42—44no—
1451C42—44no—
1452C42—44no—
1453C42—42no—
1454C42—44no—
1455C42—42no—
1456C42C2×#4118yes—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—28no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—44no—
1482C23—44no—
1483C23—44no—
1484C23—44no—
1485C23—44no—
1486C23—44no—
1487C23C22×#4112yes—
1488C23C22×#4112yes—
1489C23C2×H(5,𝔽2)12yes—
1490C23C2×2−1+412yes—
1491C23C2×2−1+412yes—
1492C23C2611yescharacteristic
1493Q8—48no—
1494Q8—48no—
1495Q8—416no—
1496Q8—44no—
1497Q8—88no—
1498Q8—88no—
1499D4—48no—
1500D4—48no—
1501D4—48no—
1502D4—44no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—22no—
1508C2×C4—24no—
1509C2×C4—22no—
1510C2×C4—22no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—24no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—22no—
1522C2×C4—21no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—22no—
1531C2×C4—24no—
1532C2×C4—24no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—24no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—24no—
1543C2×C4—24no—
1544C2×C4—24no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—22no—
1569C2×C4—24no—
1570C2×C4—22no—
1571C2×C4—24no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—48no—
1584C2×C4—44no—
1585C2×C4—44no—
1586C2×C4—44no—
1587C2×C4—416no—
1588C2×C4—44no—
1589C2×C4—44no—
1590C2×C4—44no—
1591C2×C4—44no—
1592C2×C4—44no—
1593C2×C4—44no—
1594C2×C4—48no—
1595C2×C4—88no—
1596C2×C4—88no—
1597C2×C4—84no—
1598C2×C4—84no—
1599C2×C4—84no—
1600C2×C4#556116yescomplemented
1601C2×C4C22×#4118yes—
1602C2×C4C22×#4114yes—
1603C2×C4C22×#4114yes—
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—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—416no—
1627C22—41no—
1628C22—41no—
1629C22—41no—
1630C22—41no—
1631C22—41no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—42no—
1636C22—42no—
1637C22—42no—
1638C22—42no—
1639C22—42no—
1640C22—42no—
1641C22—42no—
1642C22C2×#55614yes—
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—24no—
1654C4—22no—
1655C4—22no—
1656C4—24no—
1657C4—44no—
1658C4—41no—
1659C4—42no—
1660C4—44no—
1661C4—41no—
1662C4—44no—
1663C4—42no—
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—41no—
1677C4—41no—
1678C4—42no—
1679C4C2×#55614yes—
1680C4C2×#55614yes—
1681C2—24no—
1682C2—42no—
1683C2—42no—
1684C2—82no—
1685C2C22×#55611yescharacteristic
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. #59716C2semidirect
2. #59715C2semidirect
3. #59712C2semidirect
4. #59711C2semidirect
5. #59431C2semidirect
6. #59430C2semidirect
7. #59429C2semidirect
8. #59428C2semidirect
9. #59238C2semidirect
10. #59025C2semidirect
11. #45341C2semidirect
12. #45311C2semidirect
13. #45212C2semidirect
14. #45058C2semidirect
15. #45032C2semidirect
16. #45014C2semidirect
17. #44984C2semidirect
18. #44984C2semidirect
19. #43085C2semidirect
20. #43058C2semidirect
21. #35574C2semidirect
22. #35566C2semidirect
23. #35557C2semidirect
24. #35545C2semidirect
25. #35544C2semidirect
27. #34814C2semidirect
29. C2×#2440C2semidirect
30. #34272C2semidirect
31. #34253C2semidirect
32. #34216C2semidirect
33. #34214C2semidirect
35. #34178C2semidirect
44. #2805C22semidirect
45. #2805C22semidirect
46. #2793C22semidirect
47. #2789C22semidirect
49. #2788C22semidirect
51. #2787C22semidirect
53. #2776C22semidirect
54. #2776C22semidirect
55. #2767C22semidirect
56. #2762C22semidirect
57. #2762C22semidirect
58. #2759C22semidirect
59. #2759C22semidirect
60. #2716C22semidirect
66. #2689C22semidirect
67. #2689C22semidirect
68. #2605C22semidirect
69. #2605C22semidirect
72. #2599C22semidirect
73. #2594C22semidirect
74. #2588C22semidirect
75. #2584C22semidirect
76. #2584C22semidirect
77. #2581C22semidirect
78. #2581C22semidirect
81. #2570C22semidirect
82. #2567C22semidirect
88. #2552C22semidirect
89. #2551C22semidirect
90. #2550C22semidirect
91. #2550C22semidirect
94. #2546C22semidirect
97. #2525C22semidirect
98. #2524C22semidirect
100. #2514C22semidirect
101. #2513C22semidirect
102. #2512C22semidirect
103. #2512C22semidirect
104. #2512C22semidirect
105. #2511C22semidirect
106. #2511C22semidirect
107. #2511C22semidirect
114. #2497C22semidirect
115. #2497C22semidirect
116. #2497C22semidirect
121. #2496C22semidirect
122. #2496C22semidirect
123. #2496C22semidirect
128. #2495C22semidirect
133. #2494C22semidirect
160. #2478C22semidirect
165. #2469C22semidirect
166. #2469C22semidirect
171. #2465C22semidirect
172. #2465C22semidirect
173. #2452C22semidirect
174. #2452C22semidirect
175. #2451C22semidirect
176. #2451C22semidirect
178. #2446C22semidirect
188. #2440C22semidirect
189. #2440C22semidirect
190. #2439C22semidirect
191. #2439C22semidirect
203. #2370C22semidirect
204. #2370C22semidirect
205. #2369C22semidirect
206. #2369C22semidirect
207. #2369C22semidirect
210. #2365C22semidirect
211. #2365C22semidirect
212. #2365C22semidirect
221. #2355C22semidirect
222. #2355C22semidirect
227. Q8×C4⋊C4C22semidirect
228. Q8×C4⋊C4C22semidirect
231. #2347C22semidirect
232. #2346C22semidirect
238. #2345C22semidirect
243. #2344C22semidirect
245. #2331C22semidirect
246. #2331C22semidirect
247. #2331C22semidirect
248. #2330C22semidirect
249. #2330C22semidirect
250. #2330C22semidirect
252. #2320C22semidirect
253. #2319C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×C4⋊Q8C22semidirect
268. C4×C4⋊Q8C22semidirect
269. C4×#125C22semidirect
279. #2295C22semidirect
280. #2293C22semidirect
1600. C2×C4#556semidirect

Maximal subgroups

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

subgroupindex
#597162
#597152
#597122
#597112
#594312
#594302
#594292
#594282
#592382
#590252
#453412
#453112
#452122
#450582
#450322
#450142
#449842
#430852
#430582
#355742
#355662
#355572
#355452
#355442
#355422
#348142
#348132
C2×#24402
#342722
#342532
#342162
#342142
#342002
#341782