Finite Group Databasebeta

← #7681097

Subgroups — #7681097

Order 512.

5551 conjugacy classes of subgroups.

The subgroup lattice has 1783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59943C214yesmaximal, complemented
2#59941C214yesmaximal, complemented
3#59281C212yesmaximal, complemented
4#59275C212yesmaximal, complemented
5#59274C212yesmaximal, complemented
6#59239C212yesmaximal, complemented
7#45290C212yesmaximal, complemented
8#45116C212yesmaximal, complemented
9#45003C212yesmaximal, complemented
10#44988C212yesmaximal, complemented
11#43643C214yesmaximal, complemented
12#43620C214yesmaximal, complemented
13#39044C212yesmaximal, complemented
14#39043C212yesmaximal, complemented
15#38207C212yesmaximal, complemented
16#38200C212yesmaximal, complemented
17#38116C212yesmaximal, complemented
18#38111C212yesmaximal, complemented
19#36368C212yesmaximal, complemented
20#36277C212yesmaximal, complemented
21#35659C211yesmaximal, characteristic
22#35630C211yesmaximal, characteristic, complemented
23#35574C211yesmaximal, characteristic, complemented
24#35516C211yesmaximal, characteristic, complemented
25#35313C211yesmaximal, characteristic, complemented
26#35311C211yesmaximal, characteristic, complemented
27#35279C211yesmaximal, characteristic, complemented
28C2×#2492C211yesmaximal, characteristic, complemented
29#34742C211yesmaximal, characteristic, complemented
30#34259C211yesmaximal, characteristic, complemented
31#34259C211yesmaximal, characteristic, complemented
32#34252C211yesmaximal, characteristic, complemented
33#34202C211yesmaximal, characteristic, complemented
34#34136C211yesmaximal, characteristic, complemented
35#34060C211yesmaximal, characteristic, complemented
36C22×2−1+4C2211yescharacteristic
37C22×C4⋊Q8C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C22×#117C2211yescharacteristic
46#2863C2212yescomplemented
47#2863C2212yescomplemented
48#2857C2212yescomplemented
49#2857C2212yescomplemented
50#2855C2212yes—
51#2855C2212yes—
52#2799C2214yescomplemented
53#2798C2214yes—
54#2778C2214yes—
55#2763C2214yes—
56#2762C2214yescomplemented
57#2760C2214yes—
58#2759C2214yes—
59#2759C2214yes—
60#2758C2214yescomplemented
61#2755C2214yescomplemented
62#2750C2214yescomplemented
63#2746C2214yes—
64#2746C2214yescomplemented
65#2745C2214yescomplemented
66#2745C2214yescomplemented
67#2743C2214yes—
68#2743C2214yescomplemented
69#2739C2214yescomplemented
70#2738C2214yescomplemented
71#2737C2214yes—
72#2737C2214yes—
73#2728C2214yescomplemented
74#2696C2214yes—
75#2696C2214yes—
76#2645C2212yescomplemented
77#2645C2212yescomplemented
78#2628C2212yescomplemented
79#2628C2212yescomplemented
80#2625C2212yes—
81#2625C2212yes—
82#2607C2214yes—
83#2605C2214yescomplemented
84#2605C2214yescomplemented
85#2598C2214yes—
86#2589C2214yes—
87#2588C2214yescomplemented
88#2586C2214yescomplemented
89#2579C2214yes—
90#2578C2214yescomplemented
91#2575C2214yescomplemented
92#2573C2214yescomplemented
93#2572C2214yes—
94#2572C2214yes—
95#2572C2214yescomplemented
96#2569C2214yescomplemented
97#2568C2212yescomplemented
98#2567C2212yescomplemented
99#2564C2214yes—
100#2564C2214yes—
101#2563C2212yescomplemented
102#2542C2212yescomplemented
103#2532C2214yes—
104#2527C2214yes—
105#2527C2214yescomplemented
106#2527C2214yescomplemented
107#2526C2214yes—
108#2516C2214yes—
109#2514C2212yescomplemented
110#2514C2212yescomplemented
111#2514C2212yescomplemented
112#2514C2212yescomplemented
113#2514C2212yescomplemented
114#2514C2212yescomplemented
115#2511C2212yescomplemented
116#2511C2212yescomplemented
117#2511C2212yescomplemented
118#2511C2212yescomplemented
119#2511C2212yescomplemented
120#2511C2212yescomplemented
121#2510C2214yes—
122#2505C2214yescomplemented
123#2503C2212yes—
124#2502C2212yes—
125#2499C2212yes—
126#2499C2212yes—
127#2498C2214yes—
128#2493C2214yes—
129#2493C2214yes—
130#2493C2214yes—
131#2493C2214yes—
132#2493C2214yescomplemented
133#2493C2214yescomplemented
134#2492C2212yes—
135#2492C2212yes—
136#2492C2212yes—
137#2492C2212yes—
138#2492C2212yes—
139#2492C2212yes—
140#2492C2212yes—
141#2492C2212yes—
142#2488C2214yes—
143#2488C2214yes—
144#2487C2214yes—
145#2487C2212yes—
146#2486C2212yes—
147#2485C2212yes—
148#2485C2212yes—
149#2484C2214yes—
150#2483C2214yes—
151#2477C2214yescomplemented
152#2477C2214yescomplemented
153#2471C2214yes—
154#2463C2214yes—
155#2457C2214yes—
156#2452C2212yescomplemented
157#2452C2212yescomplemented
158#2451C2212yescomplemented
159#2451C2212yescomplemented
160#2440C2212yescomplemented
161#2440C2212yescomplemented
162#2439C2212yescomplemented
163#2439C2212yescomplemented
164#2438C2214yescomplemented
165#2438C2214yescomplemented
166#2423C2212yes—
167#2423C2211yescharacteristic
168#2423C2211yescharacteristic
169#2422C2211yescharacteristic
170#2422C2212yes—
171#2422C2211yescharacteristic
172#2421C2211yescharacteristic
173#2421C2212yes—
174#2421C2211yescharacteristic
175#2420C2211yescharacteristic
176#2420C2211yescharacteristic
177#2420C2212yes—
178#2419C2212yes—
179#2419C2214yes—
180#2419C2212yes—
181#2418C2212yes—
182#2418C2214yes—
183#2418C2212yes—
184#2409C2214yes—
185#2409C2214yes—
186#2409C2212yes—
187#2409C2212yes—
188#2409C2212yes—
189#2409C2212yes—
190#2407C2212yes—
191#2407C2212yes—
192#2407C2212yes—
193#2407C2212yes—
194#2406C2214yes—
195#2404C2214yes—
196#2395C2212yes—
197#2395C2212yes—
198C2×#400C2212yes—
199C2×#393C2212yes—
200#2368C2214yescomplemented
201#2368C2214yescomplemented
202#2363C2211yescharacteristic
203#2363C2211yescharacteristic
204#2362C2211yescharacteristic
205#2362C2211yescharacteristic
206#2361C2211yescharacteristic
207#2361C2211yescharacteristic
208#2360C2211yescharacteristic
209#2360C2211yescharacteristic
210#2359C2214yes—
211#2359C2212yes—
212#2359C2214yes—
213#2359C2212yes—
214#2358C2212yes—
215#2358C2214yes—
216#2358C2212yes—
217#2357C2212yescomplemented
218#2356C2212yescomplemented
219#2355C2212yescomplemented
220#2354C2212yes—
221#2354C2212yescomplemented
222#2353C2214yes—
223#2352C2212yes—
224#2352C2212yes—
225D4×C4⋊C4C2212yes—
226#2347C2212yescomplemented
227#2346C2212yescomplemented
228#2345C2212yescomplemented
229#2344C2212yescomplemented
230Q8×C22⋊C4C2212yescomplemented
231Q8×C22⋊C4C2212yescomplemented
232Q8×C22⋊C4C2212yescomplemented
233Q8×C22⋊C4C2212yescomplemented
234#2339C2214yes—
235#2339C2214yes—
236#2339C2214yes—
237#2339C2214yes—
238#2339C2212yescomplemented
239#2339C2212yescomplemented
240#2339C2212yescomplemented
241#2339C2212yescomplemented
242#2324C2212yes—
243#2323C2212yes—
244#2320C2212yescomplemented
245#2319C2212yescomplemented
246#2318C2214yes—
247#2318C2214yes—
248#2317C2211yescharacteristic
249#2317C2211yescharacteristic
250#2317C2211yescharacteristic
251#2317C2211yescharacteristic
252#2316C2211yescharacteristic
253#2314C2212yescomplemented
254#2314C2212yescomplemented
255#2311C2211yescharacteristic
256#2311C2211yescharacteristic
257#2311C2211yescharacteristic
258#2311C2211yescharacteristic
259#2311C2212yescomplemented
260#2311C2212yescomplemented
261#2310C2211yescharacteristic
262#2310C2211yescharacteristic
263#2310C2211yescharacteristic
264#2310C2212yescomplemented
265#2310C2212yescomplemented
266C4×C22⋊Q8C2212yes—
267C4×#123C2212yes—
268C4×#123C2212yes—
269C4×#121C2212yes—
270#2297C2211yescharacteristic
271#2297C2211yescharacteristic
272#2297C2212yescomplemented
273#2297C2212yescomplemented
274#2296C2211yescharacteristic
275#2296C2211yescharacteristic
276#2295C2212yescomplemented
277C2×#391C2212yes—
278C2×#391C2211yescharacteristic
279C2×#391C2211yescharacteristic
280C2×#391C2212yescomplemented
281C2×#391C2212yescomplemented
282#2293C2212yes—
283#2293C2212yescomplemented
284#2290C2214yes—
285#2290C2214yes—
286#2290C2212yes—
287#2290C2212yes—
288C2×#388C2212yes—
289#2285C2211yescharacteristic
290#2285C2212yescomplemented
291#2283C2212yescomplemented
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295C42×D4C2212yes—
296C4×#117C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C2×2−1+4—28no—
300C2×2−1+4—28no—
301C2×2−1+4—44no—
302C22×#41C2312yes—
303C22×#41C2312yes—
304C22×#41C2314yes—
305C22×#41C2311yescharacteristic
306C22×#41C2311yescharacteristic
307C23×Q8C2311yescharacteristic
308C23×Q8C2312yes—
309C23×Q8C2312yes—
310C23×Q8C2312yes—
311C24×C4C2311yescharacteristic
312C2×C4⋊Q8—44no—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317#525—28no—
318#525—28no—
319C2×#123C2312yes—
320C2×#123C2312yes—
321C2×#123C2312yes—
322C2×#123C2312yes—
323C2×#123C2314yes—
324C2×C22⋊Q8—44no—
325C2×C22⋊Q8C2311yescharacteristic
326C2×C22⋊Q8C2311yescharacteristic
327C2×C22⋊Q8C2311yescharacteristic
328C2×C22⋊Q8C2311yescharacteristic
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×#121C2311yescharacteristic
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#121C2311yescharacteristic
341C2×#120C2312yes—
342C2×#120C2312yes—
343#520—28no—
344#520—44no—
345C4×#41—28no—
346C4×#41—44no—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2312yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2314yes—
372C2×#117—44no—
373C2×#117C2311yescharacteristic
374C2×#117C2311yescharacteristic
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C2×#117C2311yescharacteristic
386C2×#117C2312yes—
387C2×#117C2314yes—
388C2×#117C2314yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C22⋊C4C2311yescharacteristic
399C22×C22⋊C4C2312yes—
400C22×C22⋊C4C2311yescharacteristic
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2312yes—
403C22×C42C2311yescharacteristic
404C22×C42C2311yescharacteristic
405C22×C42C2312yes—
406C22×C42C2312yes—
407C22×C42C2312yes—
408C22×C42C2312yes—
409#401C2314yes—
410#401C2314yes—
411#401C2314yes—
412#401C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2312yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2312yes—
434#400C2314yes—
435#400C2314yes—
436#399C2312yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#398C2312yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2312yes—
447#398C2314yes—
448#397C2312yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2312yes—
455#397C2312yes—
456#397C2312yes—
457#397C2312yes—
458#397C2312yes—
459#397C2314yes—
460#397C2314yes—
461#396C2314yes—
462#396C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#395C2314yes—
468#395C2314yes—
469#394C2312yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2312yes—
474#394C2312yes—
475#394C2312yes—
476#394C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#392C2314yes—
488#392C2314yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2311yescharacteristic
502#391C2311yescharacteristic
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#391C2314yes—
511#391C2312yes—
512#391C2312yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2314yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2314yes—
526#391C2314yes—
527#391C2314yes—
528#391C2311yescharacteristic
529#391C2311yescharacteristic
530#391C2314yes—
531#391C2312yes—
532#391C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2311yescharacteristic
538#390C2311yescharacteristic
539#390C2314yes—
540#390C2311yescharacteristic
541#390C2312yes—
542#390C2312yes—
543#390C2311yescharacteristic
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2314yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2311yescharacteristic
568#389C2311yescharacteristic
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2314yes—
595#388C2312yes—
596#388C2312yes—
597#388C2314yes—
598#388C2314yes—
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#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2312yes—
629#387C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2314yes—
636#387C2312yes—
637#386C2312yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2312yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2314yes—
654#386C2312yes—
655#386C2314yes—
656#386C2312yes—
657#386C2312yes—
658#386C2314yes—
659#386C2314yes—
660#386C2312yes—
661#386C2312yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2312yes—
666#385C2314yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2312yes—
677#385C2314yes—
678#385C2312yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2312yes—
683#385C2312yes—
684#385C2312yes—
685#385C2312yes—
686#385C2312yes—
687#385C2314yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#384C2312yes—
692#384C2312yes—
693#384C2312yes—
694#384C2312yes—
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#383C2314yes—
698#383C2314yes—
699#383C2314yes—
700#383C2314yes—
701#383C2314yes—
702#383C2314yes—
703#382C2312yes—
704#382C2312yes—
705#382C2312yes—
706#382C2312yes—
707#382C2314yes—
708#382C2314yes—
709#382C2311yescharacteristic
710#382C2311yescharacteristic
711#381C2314yes—
712#381C2314yes—
713#381C2314yes—
714#381C2314yes—
715#381C2314yes—
716#381C2314yes—
717#381C2314yes—
718#381C2314yes—
719#381C2312yes—
720#381C2314yes—
721#381C2314yes—
722#381C2314yes—
723#381C2314yes—
724#381C2312yes—
725#381C2312yes—
726#380C2314yes—
727#380C2314yes—
728#380C2314yes—
729#380C2314yes—
730#380C2314yes—
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#380C2312yes—
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2312yes—
748#380C2311yescharacteristic
749#380C2311yescharacteristic
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#379C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
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⋊C4C2312yes—
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806#376C2312yes—
807#376C2314yes—
808#376C2314yes—
809C2×#95C2314yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2312yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2314yes—
818C2×#95C2311yescharacteristic
819C2×#95C2312yes—
820C2×#95C2311yescharacteristic
821C43C2312yes—
822C25C2411yescharacteristic
8232−1+4—464no—
824C2×#41—28no—
825C2×#41—28no—
826C2×#41—216no—
827C2×#41—216no—
828C2×#41—24no—
829C2×#41—24no—
830C2×#41—28no—
831C2×#41—28no—
832C2×#41—24no—
833C2×#41—24no—
834C2×#41—48no—
835C2×#41—44no—
836C2×#41—44no—
837C2×#41#4118yes—
838C2×#41#4118yes—
839C22×Q8—28no—
840C22×Q8—28no—
841C22×Q8—28no—
842C22×Q8—28no—
843C22×Q8—24no—
844C22×Q8—24no—
845C22×Q8—24no—
846C22×Q8—44no—
847C22×Q8—44no—
848C22×Q8—44no—
849C22×Q8—44no—
850C22×Q8—82no—
851C22×Q8C2412yes—
852C22×Q8C2412yes—
853C22×Q8C2414yes—
854C22×Q8C2411yescharacteristic
855C22×Q8C2411yescharacteristic
856C22×Q8C2414yes—
857C22×Q8C2414yes—
858C22×D4C2412yes—
859C22×D4C2412yes—
860C22×D4C2414yes—
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2411yescharacteristic
864C22×D4C2411yescharacteristic
865C22×D4C2412yes—
866C22×D4C2412yes—
867C23×C4—24no—
868C23×C4—24no—
869C23×C4—24no—
870C23×C4C2412yes—
871C23×C4C2411yescharacteristic
872C23×C4C2411yescharacteristic
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2411yescharacteristic
879C23×C4C2412yes—
880C23×C4C2414yes—
881C23×C4C2414yes—
882C23×C4C2412yes—
883C23×C4C2412yes—
884C23×C4C2412yes—
885C23×C4C2412yes—
886C23×C4C2412yes—
887C23×C4C2412yes—
888C23×C4C2411yescharacteristic
889C23×C4C2414yes—
890C23×C4C2412yes—
891C23×C4C2412yes—
892C23×C4C2412yes—
893C23×C4C2412yes—
894C23×C4C2414yes—
895C23×C4C2411yescharacteristic
896C4⋊Q8—44no—
897C4⋊Q8—44no—
898C4⋊Q8—44no—
899C4⋊Q8—44no—
900#123—28no—
901#123—28no—
902#123—28no—
903#123—44no—
904#123—84no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—24no—
908C22⋊Q8—24no—
909C22⋊Q8—48no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—48no—
915C22⋊Q8—84no—
916C22⋊Q8—84no—
917#121—24no—
918#121—24no—
919#121—24no—
920#121—24no—
921#120—28no—
922#120—28no—
923C4×Q8—24no—
924C4×Q8—24no—
925C4×Q8—28no—
926C4×Q8—42no—
927C4×Q8—42no—
928C4×Q8—44no—
929C4×D4—28no—
930C4×D4—24no—
931C4×D4—28no—
932C4×D4—24no—
933C4×D4—216no—
934C4×D4—28no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—42no—
941C4×D4—42no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—48no—
947C4×D4—84no—
948#117—28no—
949#117—24no—
950#117—28no—
951#117—24no—
952#117—24no—
953#117—24no—
954#117—24no—
955#117—24no—
956#117—44no—
957#117—44no—
958#117—44no—
959#117—42no—
960#117—42no—
961#117—44no—
962#117—84no—
963#117—84no—
964C2×C4⋊C4—28no—
965C2×C4⋊C4—24no—
966C2×C4⋊C4—24no—
967C2×C4⋊C4—24no—
968C2×C4⋊C4—42no—
969C2×C4⋊C4—42no—
970C2×C4⋊C4—44no—
971C2×C4⋊C4—44no—
972C2×C4⋊C4—44no—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C22⋊C4—24no—
1030C2×C22⋊C4—42no—
1031C2×C22⋊C4—44no—
1032C2×C22⋊C4—44no—
1033C2×C22⋊C4—82no—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2411yescharacteristic
1040C2×C22⋊C4C2411yescharacteristic
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2411yescharacteristic
1088C2×C42—28no—
1089C2×C42—24no—
1090C2×C42—24no—
1091C2×C42—44no—
1092C2×C42—44no—
1093C2×C42—82no—
1094C2×C42C2412yes—
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2414yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2412yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2414yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204C24—22no—
1205C24—22no—
1206C24—22no—
1207C24—22no—
1208C24—41no—
1209C24—41no—
1210C24—41no—
1211C24C2511yescharacteristic
1212C24C2512yes—
1213C24C2512yes—
1214C24C2511yescharacteristic
1215C24C2511yescharacteristic
1216#41—232no—
1217#41—232no—
1218#41—432no—
1219#41—432no—
1220#41—464no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—28no—
1224C2×Q8—28no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—24no—
1228C2×Q8—24no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—24no—
1232C2×Q8—24no—
1233C2×Q8—28no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×Q8—44no—
1237C2×Q8—44no—
1238C2×Q8—44no—
1239C2×Q8—44no—
1240C2×Q8—432no—
1241C2×Q8—432no—
1242C2×Q8—416no—
1243C2×Q8—816no—
1244C2×Q8C2×#4114yes—
1245C2×Q8C2×#4114yes—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—24no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—28no—
1253C2×D4—28no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—22no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4C2×#4118yes—
1270C2×D4C2×#4118yes—
1271C2×D4C2×#4114yes—
1272C2×D4C2×#4114yes—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—28no—
1282C22×C4—28no—
1283C22×C4—24no—
1284C22×C4—24no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—22no—
1290C22×C4—24no—
1291C22×C4—22no—
1292C22×C4—28no—
1293C22×C4—24no—
1294C22×C4—24no—
1295C22×C4—24no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—28no—
1305C22×C4—28no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—24no—
1313C22×C4—22no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—41no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—41no—
1320C22×C4—42no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—41no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—41no—
1330C22×C4—42no—
1331C22×C4—44no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—41no—
1339C22×C4—42no—
1340C22×C4—44no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—44no—
1346C22×C4—416no—
1347C22×C4C2×#4118yes—
1348C22×C4C2×#4118yes—
1349C22×C4C2×#4114yes—
1350C22×C4C2×#4114yes—
1351C22×C4H(5,𝔽2)14yes—
1352C22×C4C2514yes—
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2512yes—
1359C22×C4C2514yes—
1360C22×C4C2512yes—
1361C22×C4C2512yes—
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2512yes—
1365C22×C4C2511yescharacteristic
1366C22×C4C2511yescharacteristic
1367C22×C4C2512yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2512yes—
1370C22×C4C2514yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2512yes—
1373C22×C4C2514yes—
1374C22×C4C2512yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2511yescharacteristic
1378C22×C4C2511yescharacteristic
1379C22×C4C2511yescharacteristic
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C4⋊C4—24no—
1383C4⋊C4—22no—
1384C4⋊C4—28no—
1385C4⋊C4—24no—
1386C4⋊C4—22no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—24no—
1396C4⋊C4—24no—
1397C4⋊C4—24no—
1398C4⋊C4—24no—
1399C4⋊C4—24no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—24no—
1403C4⋊C4—22no—
1404C4⋊C4—22no—
1405C4⋊C4—22no—
1406C4⋊C4—22no—
1407C4⋊C4—24no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—24no—
1411C4⋊C4—24no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—44no—
1418C4⋊C4—44no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—44no—
1423C4⋊C4—42no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—44no—
1437C4⋊C4—42no—
1438C22⋊C4—28no—
1439C22⋊C4—24no—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—24no—
1444C22⋊C4—24no—
1445C22⋊C4—24no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—22no—
1452C22⋊C4—24no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—22no—
1458C22⋊C4—22no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—22no—
1462C22⋊C4—22no—
1463C22⋊C4—24no—
1464C22⋊C4—41no—
1465C22⋊C4—41no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—42no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—42no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C42−1+414yescomplemented
1492C42—22no—
1493C42—22no—
1494C42—24no—
1495C42—24no—
1496C42—22no—
1497C42—24no—
1498C42—22no—
1499C42—24no—
1500C42—24no—
1501C42—28no—
1502C42—24no—
1503C42—22no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—24no—
1508C42—24no—
1509C42—24no—
1510C42—42no—
1511C42—42no—
1512C42—42no—
1513C42—42no—
1514C42—44no—
1515C42—44no—
1516C42—44no—
1517C42—42no—
1518C42—44no—
1519C42—42no—
1520C42—44no—
1521C42—42no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—21no—
1526C23—21no—
1527C23—21no—
1528C23—22no—
1529C23—22no—
1530C23—21no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23—22no—
1536C23—21no—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—21no—
1541C23—22no—
1542C23—21no—
1543C23—22no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—44no—
1552C23—44no—
1553C23—44no—
1554C23—44no—
1555C23—82no—
1556C23—82no—
1557C23—82no—
1558C23C22×#4114yes—
1559C23C22×#4114yes—
1560C23C22×#4112yes—
1561C23C22×#4112yes—
1562C23C2×H(5,𝔽2)12yes—
1563C23C2×2−1+412yes—
1564C23C2611yescharacteristic
1565Q8—28no—
1566Q8—28no—
1567Q8—416no—
1568Q8—48no—
1569Q8—48no—
1570Q8—88no—
1571Q8—88no—
1572D4—216no—
1573D4—216no—
1574D4—28no—
1575D4—28no—
1576D4—48no—
1577D4—48no—
1578D4—416no—
1579D4—84no—
1580D4—84no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—216no—
1592C2×C4—216no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—21no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—24no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—24no—
1610C2×C4—24no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—24no—
1619C2×C4—24no—
1620C2×C4—24no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—24no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—24no—
1641C2×C4—21no—
1642C2×C4—24no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—21no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—24no—
1657C2×C4—22no—
1658C2×C4—21no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—22no—
1662C2×C4—44no—
1663C2×C4—48no—
1664C2×C4—44no—
1665C2×C4—416no—
1666C2×C4—416no—
1667C2×C4—44no—
1668C2×C4—48no—
1669C2×C4—44no—
1670C2×C4—48no—
1671C2×C4—44no—
1672C2×C4—44no—
1673C2×C4—44no—
1674C2×C4—44no—
1675C2×C4—84no—
1676C2×C4—84no—
1677C2×C4—82no—
1678C2×C4—84no—
1679C2×C4—84no—
1680C2×C4—88no—
1681C2×C4—84no—
1682C2×C4—84no—
1683C2×C4—84no—
1684C2×C4—164no—
1685C2×C4#551116yes—
1686C2×C4C22×#4114yes—
1687C2×C4C22×#4114yes—
1688C2×C4C22×#4112yes—
1689C2×C4C22×#4112yes—
1690C2×C4C22×#4112yes—
1691C2×C4C22×#4112yes—
1692C2×C4C2×H(5,𝔽2)12yes—
1693C2×C4C2×H(5,𝔽2)12yes—
1694C2×C4C2×2−1+412yes—
1695C2×C4C2×2−1+412yes—
1696C2×C4#58512yes—
1697C22—22no—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—24no—
1704C22—22no—
1705C22—24no—
1706C22—22no—
1707C22—24no—
1708C22—24no—
1709C22—22no—
1710C22—24no—
1711C22—24no—
1712C22—42no—
1713C22—42no—
1714C22—41no—
1715C22—42no—
1716C22—42no—
1717C22—41no—
1718C22—41no—
1719C22—42no—
1720C22—42no—
1721C22—42no—
1722C22—42no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—88no—
1732C22C2×#55114yes—
1733C22C23×#4111yescharacteristic
1734C22C23×#4111yescharacteristic
1735C22C22×H(5,𝔽2)11yescharacteristic
1736C22C22×2−1+411yescharacteristic
1737C22C2×#58511yescharacteristic
1738C22H(7,𝔽2)11yescharacteristic
1739C222−1+611yescharacteristic
1740C4—22no—
1741C4—22no—
1742C4—22no—
1743C4—24no—
1744C4—24no—
1745C4—41no—
1746C4—42no—
1747C4—42no—
1748C4—41no—
1749C4—42no—
1750C4—41no—
1751C4—42no—
1752C4—42no—
1753C4—42no—
1754C4—44no—
1755C4—42no—
1756C4—42no—
1757C4—44no—
1758C4—41no—
1759C4—42no—
1760C4—42no—
1761C4—44no—
1762C4—41no—
1763C4—42no—
1764C4—42no—
1765C4—41no—
1766C4—41no—
1767C4—44no—
1768C4C2×#55114yes—
1769C4C2×#55114yes—
1770C2—24no—
1771C2—44no—
1772C2—44no—
1773C2—42no—
1774C2—81no—
1775C2C22×#55111yescharacteristic
1776C2#6280511yescharacteristic
1777C2#6285711yescharacteristic
1778C2#6292411yescharacteristic
1779C2#6294211yescharacteristic
1780C2#6300011yescharacteristic
1781C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35659C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59943C2semidirect
2. #59941C2semidirect
3. #59281C2semidirect
4. #59275C2semidirect
5. #59274C2semidirect
6. #59239C2semidirect
7. #45290C2semidirect
8. #45116C2semidirect
9. #45003C2semidirect
10. #44988C2semidirect
11. #43643C2semidirect
12. #43620C2semidirect
13. #39044C2semidirect
14. #39043C2semidirect
15. #38207C2semidirect
16. #38200C2semidirect
17. #38116C2semidirect
18. #38111C2semidirect
19. #36368C2semidirect
20. #36277C2semidirect
22. #35630C2semidirect
23. #35574C2semidirect
24. #35516C2semidirect
25. #35313C2semidirect
26. #35311C2semidirect
27. #35279C2semidirect
28. C2×#2492C2semidirect
29. #34742C2semidirect
30. #34259C2semidirect
31. #34259C2semidirect
32. #34252C2semidirect
33. #34202C2semidirect
34. #34136C2semidirect
35. #34060C2semidirect
46. #2863C22semidirect
47. #2863C22semidirect
48. #2857C22semidirect
49. #2857C22semidirect
52. #2799C22semidirect
56. #2762C22semidirect
60. #2758C22semidirect
61. #2755C22semidirect
62. #2750C22semidirect
64. #2746C22semidirect
65. #2745C22semidirect
66. #2745C22semidirect
68. #2743C22semidirect
69. #2739C22semidirect
70. #2738C22semidirect
73. #2728C22semidirect
76. #2645C22semidirect
77. #2645C22semidirect
78. #2628C22semidirect
79. #2628C22semidirect
83. #2605C22semidirect
84. #2605C22semidirect
87. #2588C22semidirect
88. #2586C22semidirect
90. #2578C22semidirect
91. #2575C22semidirect
92. #2573C22semidirect
95. #2572C22semidirect
96. #2569C22semidirect
97. #2568C22semidirect
98. #2567C22semidirect
101. #2563C22semidirect
102. #2542C22semidirect
105. #2527C22semidirect
106. #2527C22semidirect
109. #2514C22semidirect
110. #2514C22semidirect
111. #2514C22semidirect
112. #2514C22semidirect
113. #2514C22semidirect
114. #2514C22semidirect
115. #2511C22semidirect
116. #2511C22semidirect
117. #2511C22semidirect
118. #2511C22semidirect
119. #2511C22semidirect
120. #2511C22semidirect
122. #2505C22semidirect
132. #2493C22semidirect
133. #2493C22semidirect
151. #2477C22semidirect
152. #2477C22semidirect
156. #2452C22semidirect
157. #2452C22semidirect
158. #2451C22semidirect
159. #2451C22semidirect
160. #2440C22semidirect
161. #2440C22semidirect
162. #2439C22semidirect
163. #2439C22semidirect
164. #2438C22semidirect
165. #2438C22semidirect
200. #2368C22semidirect
201. #2368C22semidirect
217. #2357C22semidirect
218. #2356C22semidirect
219. #2355C22semidirect
221. #2354C22semidirect
226. #2347C22semidirect
227. #2346C22semidirect
228. #2345C22semidirect
229. #2344C22semidirect
230. Q8×C22⋊C4C22semidirect
231. Q8×C22⋊C4C22semidirect
232. Q8×C22⋊C4C22semidirect
233. Q8×C22⋊C4C22semidirect
238. #2339C22semidirect
239. #2339C22semidirect
240. #2339C22semidirect
241. #2339C22semidirect
244. #2320C22semidirect
245. #2319C22semidirect
253. #2314C22semidirect
254. #2314C22semidirect
259. #2311C22semidirect
260. #2311C22semidirect
264. #2310C22semidirect
265. #2310C22semidirect
272. #2297C22semidirect
273. #2297C22semidirect
276. #2295C22semidirect
280. C2×#391C22semidirect
281. C2×#391C22semidirect
283. #2293C22semidirect
290. #2285C22semidirect
291. #2283C22semidirect
1491. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#599432
#599412
#592812
#592752
#592742
#592392
#452902
#451162
#450032
#449882
#436432
#436202
#390442
#390432
#382072
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C2×#24922
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