Finite Group Databasebeta

← #8096653

Subgroups — #8096653

Order 512.

6492 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53080C212yesmaximal, complemented
2#53046C212yesmaximal, complemented
3#52990C211yesmaximal, characteristic, complemented
4#52958C211yesmaximal, characteristic, complemented
5#52530C212yesmaximal, complemented
6#52395C214yesmaximal, complemented
7#52367C214yesmaximal, complemented
8#52310C212yesmaximal, complemented
9#52294C211yesmaximal, characteristic, complemented
10C2×#2712C212yesmaximal, complemented
11#46099C214yesmaximal, complemented
12#46054C212yesmaximal, complemented
13#46043C212yesmaximal, complemented
14#46031C214yesmaximal, complemented
15#46016C212yesmaximal, complemented
16#45977C214yesmaximal, complemented
17#45601C212yesmaximal, complemented
18#45568C214yesmaximal, complemented
19#45539C212yesmaximal, complemented
20#45479C211yesmaximal, characteristic, complemented
21#36303C212yesmaximal, complemented
22#36238C212yesmaximal, complemented
23#36213C211yesmaximal, characteristic, complemented
24#36212C212yesmaximal, complemented
25D4×#124C212yesmaximal, complemented
26#35939C212yesmaximal, complemented
27#35847C211yesmaximal, characteristic, complemented
28#35750C212yesmaximal, complemented
29#35680C211yesmaximal, characteristic, complemented
30C22×H(5,𝔽2)C2211yescharacteristic, complemented
31C23×#41C2211yescharacteristic, complemented
32C2×H(3,𝔽4)C2212yescomplemented
33C2×#554C2211yescharacteristic, complemented
34C2×D4×Q8C2212yescomplemented
35C2×#547C2212yes—
36C2×#546C2211yescharacteristic
37C2×#546C2212yes—
38C2×#546C2212yes—
39C2×D42C2212yes—
40C22×#124C2214yescomplemented
41#2862C2212yescomplemented
42#2861C2212yescomplemented
43#2858C2212yescomplemented
44#2850C2214yescomplemented
45#2850C2214yescomplemented
46#2850C2214yescomplemented
47#2849C2212yescomplemented
48#2849C2214yescomplemented
49#2848C2211yescharacteristic, complemented
50#2847C2212yescomplemented
51#2840C2212yescomplemented
52#2835C2212yescomplemented
53#2832C2214yescomplemented
54#2832C2214yescomplemented
55#2832C2212yescomplemented
56#2832C2214yescomplemented
57#2832C2214yescomplemented
58#2828C2214yescomplemented
59#2828C2214yescomplemented
60#2828C2214yescomplemented
61#2824C2214yescomplemented
62#2824C2214yescomplemented
63#2824C2214yescomplemented
64#2824C2214yescomplemented
65#2824C2212yescomplemented
66#2819C2214yescomplemented
67#2819C2214yescomplemented
68#2819C2214yescomplemented
69#2812C2212yescomplemented
70#2811C2212yescomplemented
71#2804C2214yescomplemented
72#2804C2214yescomplemented
73#2804C2214yescomplemented
74#2785C2214yescomplemented
75#2782C2214yescomplemented
76#2782C2214yescomplemented
77#2782C2214yescomplemented
78#2763C2212yescomplemented
79#2763C2214yescomplemented
80#2763C2214yescomplemented
81#2763C2214yescomplemented
82#2763C2211yescharacteristic, complemented
83#2753C2212yescomplemented
84#2753C2214yescomplemented
85#2753C2214yescomplemented
86#2753C2214yescomplemented
87#2753C2214yescomplemented
88#2753C2214yescomplemented
89#2753C2212yescomplemented
90#2753C2212yescomplemented
91#2753C2214yescomplemented
92#2736C2211yescharacteristic, complemented
93#2736C2212yescomplemented
94#2733C2214yescomplemented
95#2733C2214yescomplemented
96#2733C2214yescomplemented
97#2712C2214yescomplemented
98#2712C2214yescomplemented
99#2712C2214yescomplemented
100#2712C2214yescomplemented
101#2712C2214yescomplemented
102#2712C2214yescomplemented
103#2712C2212yescomplemented
104#2712C2214yescomplemented
105#2712C2211yescharacteristic, complemented
106#2712C2212yescomplemented
107#2712C2212yescomplemented
108#2712C2214yescomplemented
109#2712C2214yescomplemented
110#2712C2212yescomplemented
111#2712C2214yescomplemented
112#2684C2212yescomplemented
113#2684C2214yescomplemented
114#2684C2214yescomplemented
115#2684C2214yescomplemented
116#2684C2214yescomplemented
117#2670C2214yescomplemented
118#2670C2211yescharacteristic, complemented
119#2670C2212yescomplemented
120#2670C2214yescomplemented
121#2670C2214yescomplemented
122#2640C2211yescharacteristic, complemented
123#2640C2212yescomplemented
124#2639C2212yescomplemented
125#2639C2214yescomplemented
126#2616C2212yescomplemented
127#2615C2211yescharacteristic, complemented
128#2613C2214yescomplemented
129#2613C2212yescomplemented
130#2592C2211yescharacteristic, complemented
131#2592C2212yescomplemented
132#2592C2212yescomplemented
133#2591C2214yescomplemented
134#2568C2212yescomplemented
135#2563C2212yescomplemented
136#2562C2212yescomplemented
137#2561C2214yescomplemented
138#2561C2214yescomplemented
139#2561C2212yescomplemented
140#2548C2212yescomplemented
141#2547C2211yescharacteristic, complemented
142#2547C2212yescomplemented
143#2547C2212yescomplemented
144#2504C2212yescomplemented
145#2503C2214yescomplemented
146#2492C2212yescomplemented
147#2492C2212yescomplemented
148#2492C2212yescomplemented
149#2492C2212yescomplemented
150#2492C2212yescomplemented
151#2492C2212yescomplemented
152#2492C2212yescomplemented
153#2491C2212yescomplemented
154#2491C2212yescomplemented
155#2491C2212yescomplemented
156#2491C2212yescomplemented
157#2491C2212yescomplemented
158#2491C2212yescomplemented
159#2491C2212yescomplemented
160#2490C2212yescomplemented
161#2490C2212yescomplemented
162#2489C2212yescomplemented
163#2489C2212yescomplemented
164#2488C2214yescomplemented
165#2488C2214yescomplemented
166#2488C2214yescomplemented
167#2488C2214yescomplemented
168#2488C2214yescomplemented
169#2488C2214yescomplemented
170#2488C2214yescomplemented
171#2488C2214yescomplemented
172#2488C2214yescomplemented
173#2472C2214yescomplemented
174#2472C2214yescomplemented
175#2472C2214yescomplemented
176#2472C2214yescomplemented
177#2472C2214yescomplemented
178#2472C2214yescomplemented
179#2472C2214yescomplemented
180#2472C2214yescomplemented
181#2472C2214yescomplemented
182#2436C2214yescomplemented
183#2436C2214yescomplemented
184#2436C2212yescomplemented
185#2436C2214yescomplemented
186#2435C2214yescomplemented
187#2435C2212yescomplemented
188#2434C2211yescharacteristic, complemented
189#2433C2211yescharacteristic, complemented
190#2432C2212yescomplemented
191#2432C2212yescomplemented
192#2432C2212yescomplemented
193#2431C2212yescomplemented
194#2431C2212yescomplemented
195#2431C2212yescomplemented
196#2430C2212yescomplemented
197#2430C2214yescomplemented
198#2430C2214yescomplemented
199#2430C2214yescomplemented
200#2430C2214yescomplemented
201#2410C2214yescomplemented
202#2410C2214yescomplemented
203#2410C2212yescomplemented
204#2410C2214yescomplemented
205#2410C2214yescomplemented
206#2409C2212yescomplemented
207#2409C2211yescharacteristic, complemented
208#2408C2211yescharacteristic
209#2408C2212yescomplemented
210#2407C2212yes—
211#2407C2212yescomplemented
212#2407C2212yescomplemented
213#2407C2212yescomplemented
214#2407C2212yescomplemented
215#2407C2212yescomplemented
216#2406C2214yescomplemented
217#2406C2214yescomplemented
218#2405C2214yescomplemented
219#2405C2214yescomplemented
220#2405C2212yescomplemented
221#2404C2212yes—
222#2404C2214yescomplemented
223#2404C2214yescomplemented
224#2403C2214yes—
225#2403C2214yescomplemented
226#2398C2211yescharacteristic, complemented
227#2398C2212yescomplemented
228C2×#397C2212yescomplemented
229#2388C2211yescharacteristic
230#2388C2212yescomplemented
231C2×#394C2214yescomplemented
232C2×#393C2214yescomplemented
233C2×#392C2212yes—
234#2379C2214yescomplemented
235#2379C2214yescomplemented
236#2379C2214yescomplemented
237#2375C2214yescomplemented
238#2339C2212yescomplemented
239#2339C2211yescharacteristic, complemented
240#2339C2212yescomplemented
241#2339C2212yescomplemented
242#2339C2212yescomplemented
243D4×C22⋊C4C2212yescomplemented
244D4×C22⋊C4C2211yescharacteristic, complemented
245D4×C22⋊C4C2212yescomplemented
246D4×C22⋊C4C2212yescomplemented
247D4×C22⋊C4C2212yescomplemented
248C4×#124C2212yescomplemented
249C4×#124C2212yescomplemented
250C4×#124C2212yescomplemented
251C4×#120C2212yescomplemented
252C4×#120C2211yescharacteristic, complemented
253C2×#391C2214yescomplemented
254C2×#388C2214yescomplemented
255C2×#386C2214yescomplemented
256C2×#385C2212yescomplemented
257#2275C2211yescharacteristic, complemented
258C42×D4C2212yescomplemented
259C2×H(5,𝔽2)—48no—
260C2×H(5,𝔽2)—44no—
261C22×#41—48no—
262C22×#41—44no—
263C22×#41C2312yes—
264C22×#41C2311yescharacteristic
265C22×#41C2314yes—
266C22×#41C2312yes—
267C22×#41C2311yescharacteristic
268C22×#41C2312yes—
269C22×#41C2312yes—
270C23×Q8C2311yescharacteristic
271C23×Q8C2314yes—
272C23×D4C2311yescharacteristic
273C23×D4C2312yes—
274C23×D4C2312yes—
275C23×D4C2312yes—
276C23×D4C2314yes—
277C23×D4C2311yescharacteristic
278C23×D4C2314yes—
279C24×C4C2311yescharacteristic
280C24×C4C2312yes—
281H(3,𝔽4)—48no—
282#554—44no—
283D4×Q8—48no—
284#547—48no—
285#546—48no—
286#546—44no—
287#546—48no—
288D42—48no—
289C2×C4⋊Q8C2312yes—
290C2×C4⋊Q8C2312yes—
291C2×C4⋊Q8C2312yes—
292C2×C4⋊Q8C2312yes—
293C2×C4⋊Q8C2311yescharacteristic
294C2×#127C2312yes—
295C2×#125C2312yes—
296C2×#124—416no—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2314yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#124C2314yes—
304C2×#124C2312yes—
305C2×#124C2311yescharacteristic
306C2×#124C2312yes—
307C2×#124C2314yes—
308C2×#124C2314yes—
309C2×#124C2314yes—
310C2×#124C2314yes—
311C2×#124C2314yes—
312C2×#124C2314yes—
313C2×#124C2312yes—
314C2×#124C2312yes—
315C2×#124C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2312yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2311yescharacteristic
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×#121C2314yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2312yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2312yes—
338C2×#121C2311yescharacteristic
339C2×#121C2314yes—
340C2×#121C2312yes—
341C2×#120C2311yescharacteristic
342C2×#120C2314yes—
343C2×#120C2312yes—
344C2×#120C2314yes—
345C2×#120C2314yes—
346C2×#120C2314yes—
347C2×#120C2314yes—
348C2×#120C2314yes—
349C2×#120C2312yes—
350C2×#120C2312yes—
351C2×#120C2314yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C22×C4⋊C4C2312yes—
365C22×C4⋊C4C2314yes—
366C22×C22⋊C4C2312yes—
367C22×C22⋊C4C2312yes—
368C22×C22⋊C4C2314yes—
369C22×C22⋊C4C2314yes—
370C22×C22⋊C4C2314yes—
371C22×C22⋊C4C2314yes—
372C22×C22⋊C4C2314yes—
373C22×C22⋊C4C2314yes—
374C22×C42C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2312yes—
386#400C2314yes—
387#400C2314yes—
388#400C2312yes—
389#400C2312yes—
390#397C2312yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2312yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2312yes—
408#397C2311yescharacteristic
409#397C2314yes—
410#397C2311yescharacteristic
411#395C2312yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2311yescharacteristic
416#395C2312yes—
417#394C2314yes—
418#394C2312yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2311yescharacteristic
446#394C2312yes—
447#394C2312yes—
448#394C2314yes—
449#394C2312yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2314yes—
456#393C2311yescharacteristic
457#393C2314yes—
458#393C2312yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2312yes—
477#393C2312yes—
478#393C2312yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2311yescharacteristic
483#393C2311yescharacteristic
484#393C2314yes—
485#393C2312yes—
486#393C2314yes—
487#393C2314yes—
488#393C2312yes—
489#392C2314yes—
490#392C2312yes—
491#392C2314yes—
492#392C2314yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#392C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2314yes—
500#392C2312yes—
501#392C2312yes—
502#392C2312yes—
503#392C2312yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2311yescharacteristic
508#392C2314yes—
509#392C2312yes—
510#392C2312yes—
511#392C2312yes—
512#391C2312yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2314yes—
528#391C2314yes—
529#391C2314yes—
530#391C2314yes—
531#391C2312yes—
532#391C2314yes—
533#391C2312yes—
534#391C2314yes—
535#391C2314yes—
536#391C2312yes—
537#390C2314yes—
538#390C2314yes—
539#390C2314yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2314yes—
551#390C2314yes—
552#390C2314yes—
553#390C2312yes—
554#390C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2312yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2314yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2314yes—
592#388C2312yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#386C2312yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2311yescharacteristic
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2312yes—
633#386C2314yes—
634#386C2314yes—
635#386C2312yes—
636#386C2314yes—
637#386C2312yes—
638#385C2312yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2312yes—
645#385C2312yes—
646#385C2312yes—
647#385C2314yes—
648#385C2312yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2312yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2311yescharacteristic
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#382C2312yes—
666#382C2314yes—
667#382C2312yes—
668#382C2314yes—
669#382C2312yes—
670#381C2314yes—
671#381C2314yes—
672#381C2314yes—
673#381C2314yes—
674#381C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2312yes—
680#380C2312yes—
681#380C2312yes—
682#380C2311yescharacteristic
683#380C2311yescharacteristic
684#380C2312yes—
685#379C2314yes—
686#379C2314yes—
687#379C2314yes—
688#379C2314yes—
689#379C2314yes—
690#379C2312yes—
691#379C2312yes—
692#379C2312yes—
693#379C2314yes—
694#379C2314yes—
695#379C2311yescharacteristic
696#379C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2311yescharacteristic
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717#376C2311yescharacteristic
718C2×#95C2312yes—
719C2×#95C2314yes—
720C2×#95C2314yes—
721C2×#95C2314yes—
722C2×#95C2314yes—
723C2×#95C2312yes—
724C43C2312yes—
725C25C2412yes—
726C25C2414yes—
727C25C2411yescharacteristic
728C25C2412yes—
729H(5,𝔽2)—464no—
730C2×#41—28no—
731C2×#41—28no—
732C2×#41—24no—
733C2×#41—28no—
734C2×#41—28no—
735C2×#41—44no—
736C2×#41—42no—
737C2×#41—48no—
738C2×#41—48no—
739C2×#41—48no—
740C2×#41—44no—
741C2×#41—48no—
742C2×#41—44no—
743C2×#41—44no—
744C2×#41—44no—
745C2×#41—44no—
746C2×#41—44no—
747C2×#41—44no—
748C2×#41—464no—
749C22×Q8—48no—
750C22×Q8—44no—
751C22×Q8—42no—
752C22×Q8—48no—
753C22×Q8—48no—
754C22×Q8C2412yes—
755C22×Q8C2411yescharacteristic
756C22×Q8C2412yes—
757C22×Q8C2414yes—
758C22×Q8C2414yes—
759C22×Q8C2411yescharacteristic
760C22×Q8C2412yes—
761C22×Q8C2414yes—
762C22×Q8C2412yes—
763C22×Q8C2411yescharacteristic
764C22×D4—28no—
765C22×D4—28no—
766C22×D4—24no—
767C22×D4—28no—
768C22×D4—28no—
769C22×D4—42no—
770C22×D4—44no—
771C22×D4—48no—
772C22×D4—44no—
773C22×D4—48no—
774C22×D4—48no—
775C22×D4—44no—
776C22×D4—48no—
777C22×D4—48no—
778C22×D4—48no—
779C22×D4—48no—
780C22×D4—48no—
781C22×D4C2412yes—
782C22×D4C2414yes—
783C22×D4C2414yes—
784C22×D4C2412yes—
785C22×D4C2412yes—
786C22×D4C2411yescharacteristic
787C22×D4C2412yes—
788C22×D4C2411yescharacteristic
789C22×D4C2412yes—
790C22×D4C2414yes—
791C22×D4C2414yes—
792C22×D4C2412yes—
793C22×D4C2412yes—
794C22×D4C2414yes—
795C22×D4C2414yes—
796C22×D4C2412yes—
797C22×D4C2414yes—
798C22×D4C2414yes—
799C22×D4C2411yescharacteristic
800C22×D4C2414yes—
801C22×D4C2412yes—
802C22×D4C2412yes—
803C22×D4C2414yes—
804C22×D4C2411yescharacteristic
805C23×C4—44no—
806C23×C4—42no—
807C23×C4—44no—
808C23×C4—48no—
809C23×C4C2414yes—
810C23×C4C2412yes—
811C23×C4C2411yescharacteristic
812C23×C4C2412yes—
813C23×C4C2412yes—
814C23×C4C2411yescharacteristic
815C23×C4C2414yes—
816C23×C4C2414yes—
817C23×C4C2412yes—
818C23×C4C2414yes—
819C23×C4C2414yes—
820C23×C4C2411yescharacteristic
821C23×C4C2412yes—
822C23×C4C2412yes—
823C23×C4C2414yes—
824C23×C4C2414yes—
825C4⋊Q8—44no—
826C4⋊Q8—44no—
827C4⋊Q8—44no—
828C4⋊Q8—42no—
829C4⋊Q8—44no—
830#127—44no—
831#125—44no—
832#124—28no—
833#124—216no—
834#124—48no—
835#124—48no—
836#124—44no—
837#124—48no—
838#124—48no—
839#124—44no—
840#124—44no—
841#124—42no—
842#124—48no—
843#124—48no—
844#124—48no—
845#124—44no—
846#124—48no—
847#124—48no—
848#124—48no—
849#124—44no—
850#124—48no—
851#123—48no—
852#123—48no—
853#123—44no—
854#123—48no—
855#123—48no—
856C22⋊Q8—48no—
857C22⋊Q8—48no—
858C22⋊Q8—48no—
859C22⋊Q8—48no—
860C22⋊Q8—44no—
861C22⋊Q8—42no—
862C22⋊Q8—44no—
863C22⋊Q8—44no—
864C22⋊Q8—44no—
865C22⋊Q8—44no—
866#121—44no—
867#121—44no—
868#121—42no—
869#121—44no—
870#121—44no—
871#121—48no—
872#121—44no—
873#121—48no—
874#121—48no—
875#121—48no—
876#120—24no—
877#120—48no—
878#120—44no—
879#120—48no—
880#120—48no—
881#120—48no—
882#120—44no—
883#120—48no—
884#120—48no—
885#120—48no—
886#120—44no—
887C4×Q8—44no—
888C4×Q8—42no—
889C4×D4—28no—
890C4×D4—28no—
891C4×D4—28no—
892C4×D4—24no—
893C4×D4—28no—
894C4×D4—44no—
895C4×D4—44no—
896C4×D4—44no—
897C4×D4—42no—
898C4×D4—44no—
899C2×C4⋊C4—48no—
900C2×C4⋊C4—44no—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2411yescharacteristic
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2414yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2412yes—
920C2×C4⋊C4C2412yes—
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2414yes—
929C2×C22⋊C4—28no—
930C2×C22⋊C4—48no—
931C2×C22⋊C4—48no—
932C2×C22⋊C4—48no—
933C2×C22⋊C4—48no—
934C2×C22⋊C4—48no—
935C2×C22⋊C4—48no—
936C2×C22⋊C4—44no—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2411yescharacteristic
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2412yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2411yescharacteristic
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2412yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2414yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2414yes—
992C2×C22⋊C4C2414yes—
993C2×C22⋊C4C2412yes—
994C2×C22⋊C4C2414yes—
995C2×C22⋊C4C2414yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2412yes—
998C2×C22⋊C4C2412yes—
999C2×C22⋊C4C2412yes—
1000C2×C22⋊C4C2412yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2414yes—
1006C2×C22⋊C4C2414yes—
1007C2×C22⋊C4C2411yescharacteristic
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2412yes—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2411yescharacteristic
1015C2×C42—48no—
1016C2×C42C2412yes—
1017C2×C42C2411yescharacteristic
1018C2×C42C2412yes—
1019C2×C42C2412yes—
1020C2×C42C2412yes—
1021C2×C42C2414yes—
1022C2×C42C2412yes—
1023C2×C42C2412yes—
1024C2×C42C2412yes—
1025C2×C42C2414yes—
1026C2×C42C2414yes—
1027C2×C42C2412yes—
1028C2×C42C2414yes—
1029C2×C42C2412yes—
1030#95C2411yescharacteristic
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2411yescharacteristic
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2412yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2412yes—
1053#95C2411yescharacteristic
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2411yescharacteristic
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2412yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2412yes—
1075#95C2414yes—
1076#95C2414yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2414yes—
1083#95C2414yes—
1084#95C2414yes—
1085C24—24no—
1086C24—24no—
1087C24—28no—
1088C24—28no—
1089C24—28no—
1090C24—28no—
1091C24—22no—
1092C24—41no—
1093C24—42no—
1094C24—44no—
1095C24—42no—
1096C24—44no—
1097C24—42no—
1098C24—44no—
1099C24—44no—
1100C24—42no—
1101C24—44no—
1102C24—44no—
1103C24—41no—
1104C24—42no—
1105C24—44no—
1106C24—42no—
1107C24C2512yes—
1108C24C2514yes—
1109C24C2511yescharacteristic
1110C24C2512yes—
1111C24C2512yes—
1112C24C2511yescharacteristic
1113C24C2512yes—
1114#41—464no—
1115#41—432no—
1116#41—432no—
1117#41—432no—
1118#41—416no—
1119#41—432no—
1120#41—416no—
1121C2×Q8—24no—
1122C2×Q8—24no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—24no—
1127C2×Q8—28no—
1128C2×Q8—24no—
1129C2×Q8—28no—
1130C2×Q8—42no—
1131C2×Q8—44no—
1132C2×Q8—42no—
1133C2×Q8—41no—
1134C2×Q8—42no—
1135C2×Q8—41no—
1136C2×Q8—44no—
1137C2×Q8—44no—
1138C2×Q8—44no—
1139C2×Q8—44no—
1140C2×Q8—44no—
1141C2×Q8—42no—
1142C2×Q8—44no—
1143C2×Q8—44no—
1144C2×Q8—42no—
1145C2×Q8—42no—
1146C2×Q8—42no—
1147C2×Q8—416no—
1148C2×Q8—832no—
1149C2×D4—28no—
1150C2×D4—28no—
1151C2×D4—24no—
1152C2×D4—28no—
1153C2×D4—28no—
1154C2×D4—28no—
1155C2×D4—28no—
1156C2×D4—24no—
1157C2×D4—28no—
1158C2×D4—28no—
1159C2×D4—24no—
1160C2×D4—22no—
1161C2×D4—28no—
1162C2×D4—24no—
1163C2×D4—24no—
1164C2×D4—22no—
1165C2×D4—24no—
1166C2×D4—24no—
1167C2×D4—24no—
1168C2×D4—24no—
1169C2×D4—28no—
1170C2×D4—42no—
1171C2×D4—41no—
1172C2×D4—42no—
1173C2×D4—42no—
1174C2×D4—44no—
1175C2×D4—42no—
1176C2×D4—44no—
1177C2×D4—42no—
1178C2×D4—42no—
1179C2×D4—44no—
1180C2×D4—44no—
1181C2×D4—44no—
1182C2×D4—44no—
1183C2×D4—44no—
1184C2×D4—42no—
1185C2×D4—42no—
1186C2×D4—41no—
1187C2×D4—42no—
1188C2×D4—44no—
1189C2×D4—44no—
1190C2×D4—42no—
1191C2×D4—42no—
1192C2×D4—44no—
1193C2×D4—44no—
1194C2×D4—44no—
1195C2×D4—42no—
1196C2×D4—42no—
1197C2×D4—44no—
1198C2×D4—44no—
1199C2×D4—42no—
1200C2×D4—41no—
1201C2×D4—44no—
1202C2×D4—44no—
1203C2×D4—44no—
1204C2×D4—42no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—44no—
1211C2×D4—44no—
1212C2×D4—432no—
1213C2×D4—464no—
1214C2×D4—432no—
1215C2×D4—416no—
1216C2×D4—416no—
1217C2×D4—432no—
1218C2×D4—832no—
1219C2×D4H(5,𝔽2)18yes—
1220C2×D4H(5,𝔽2)14yes—
1221C22×C4—28no—
1222C22×C4—28no—
1223C22×C4—24no—
1224C22×C4—28no—
1225C22×C4—28no—
1226C22×C4—28no—
1227C22×C4—28no—
1228C22×C4—28no—
1229C22×C4—24no—
1230C22×C4—28no—
1231C22×C4—28no—
1232C22×C4—24no—
1233C22×C4—24no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—24no—
1241C22×C4—24no—
1242C22×C4—28no—
1243C22×C4—44no—
1244C22×C4—41no—
1245C22×C4—42no—
1246C22×C4—42no—
1247C22×C4—44no—
1248C22×C4—42no—
1249C22×C4—44no—
1250C22×C4—42no—
1251C22×C4—44no—
1252C22×C4—42no—
1253C22×C4—44no—
1254C22×C4—44no—
1255C22×C4—44no—
1256C22×C4—44no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4—432no—
1264C22×C4—416no—
1265C22×C4C2512yes—
1266C22×C4C2514yes—
1267C22×C4C2511yescharacteristic
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2511yescharacteristic
1271C22×C4C2514yes—
1272C22×C4C2511yescharacteristic
1273C22×C4C2512yes—
1274C22×C4C2512yes—
1275C22×C4C2512yes—
1276C22×C4C2512yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2512yes—
1279C22×C4C2514yes—
1280C22×C4C2514yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2514yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C4⋊C4—24no—
1288C4⋊C4—22no—
1289C4⋊C4—24no—
1290C4⋊C4—24no—
1291C4⋊C4—24no—
1292C4⋊C4—42no—
1293C4⋊C4—41no—
1294C4⋊C4—44no—
1295C4⋊C4—44no—
1296C4⋊C4—44no—
1297C4⋊C4—44no—
1298C4⋊C4—42no—
1299C4⋊C4—42no—
1300C4⋊C4—42no—
1301C4⋊C4—42no—
1302C4⋊C4—41no—
1303C4⋊C4—42no—
1304C4⋊C4—42no—
1305C4⋊C4—42no—
1306C4⋊C4—42no—
1307C4⋊C4—42no—
1308C4⋊C4—44no—
1309C4⋊C4—44no—
1310C4⋊C4—44no—
1311C4⋊C4—44no—
1312C4⋊C4—44no—
1313C4⋊C4—44no—
1314C4⋊C4—44no—
1315C22⋊C4—24no—
1316C22⋊C4—24no—
1317C22⋊C4—28no—
1318C22⋊C4—28no—
1319C22⋊C4—28no—
1320C22⋊C4—28no—
1321C22⋊C4—24no—
1322C22⋊C4—28no—
1323C22⋊C4—28no—
1324C22⋊C4—24no—
1325C22⋊C4—24no—
1326C22⋊C4—28no—
1327C22⋊C4—28no—
1328C22⋊C4—24no—
1329C22⋊C4—24no—
1330C22⋊C4—28no—
1331C22⋊C4—24no—
1332C22⋊C4—24no—
1333C22⋊C4—24no—
1334C22⋊C4—42no—
1335C22⋊C4—41no—
1336C22⋊C4—42no—
1337C22⋊C4—44no—
1338C22⋊C4—44no—
1339C22⋊C4—42no—
1340C22⋊C4—44no—
1341C22⋊C4—44no—
1342C22⋊C4—42no—
1343C22⋊C4—44no—
1344C22⋊C4—44no—
1345C22⋊C4—44no—
1346C22⋊C4—42no—
1347C22⋊C4—44no—
1348C22⋊C4—44no—
1349C22⋊C4—44no—
1350C22⋊C4—44no—
1351C22⋊C4—44no—
1352C22⋊C4—44no—
1353C22⋊C4—44no—
1354C22⋊C4—41no—
1355C22⋊C4—42no—
1356C22⋊C4—44no—
1357C22⋊C4—42no—
1358C22⋊C4—42no—
1359C22⋊C4—42no—
1360C22⋊C4—44no—
1361C22⋊C4—42no—
1362C22⋊C4—42no—
1363C22⋊C4—42no—
1364C22⋊C4—41no—
1365C22⋊C4—42no—
1366C22⋊C4—42no—
1367C22⋊C4—42no—
1368C22⋊C4—42no—
1369C22⋊C4—44no—
1370C22⋊C4—44no—
1371C22⋊C4—44no—
1372C22⋊C4—44no—
1373C22⋊C4—44no—
1374C22⋊C4—42no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4—42no—
1378C22⋊C4—44no—
1379C22⋊C4—44no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—42no—
1383C22⋊C4—44no—
1384C22⋊C4—42no—
1385C22⋊C4—44no—
1386C22⋊C4—44no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4—42no—
1391C22⋊C4—42no—
1392C22⋊C4H(5,𝔽2)14yescomplemented
1393C42—24no—
1394C42—28no—
1395C42—24no—
1396C42—24no—
1397C42—22no—
1398C42—24no—
1399C42—24no—
1400C42—24no—
1401C42—44no—
1402C42—44no—
1403C42—42no—
1404C42—42no—
1405C42—44no—
1406C42—42no—
1407C23—22no—
1408C23—24no—
1409C23—22no—
1410C23—21no—
1411C23—22no—
1412C23—22no—
1413C23—21no—
1414C23—22no—
1415C23—22no—
1416C23—24no—
1417C23—22no—
1418C23—21no—
1419C23—22no—
1420C23—22no—
1421C23—22no—
1422C23—22no—
1423C23—22no—
1424C23—24no—
1425C23—24no—
1426C23—22no—
1427C23—22no—
1428C23—21no—
1429C23—22no—
1430C23—24no—
1431C23—24no—
1432C23—22no—
1433C23—22no—
1434C23—22no—
1435C23—24no—
1436C23—22no—
1437C23—24no—
1438C23—24no—
1439C23—22no—
1440C23—22no—
1441C23—21no—
1442C23—22no—
1443C23—22no—
1444C23—24no—
1445C23—416no—
1446C23—48no—
1447C23—44no—
1448C23—48no—
1449C23—48no—
1450C23—416no—
1451C23—84no—
1452C23—88no—
1453C23—84no—
1454C23—82no—
1455C23—88no—
1456C23—88no—
1457C23—88no—
1458C23—88no—
1459C23—88no—
1460C23—88no—
1461C23—82no—
1462C23—84no—
1463C23—164no—
1464C23—162no—
1465C23—162no—
1466C23—164no—
1467C23C2×H(5,𝔽2)12yes—
1468C23C2×H(5,𝔽2)18yes—
1469C23C2×H(5,𝔽2)14yes—
1470C23C2611yescharacteristic
1471Q8—48no—
1472Q8—48no—
1473Q8—44no—
1474Q8—48no—
1475Q8—44no—
1476Q8—88no—
1477Q8—88no—
1478Q8—82no—
1479Q8—88no—
1480Q8—162no—
1481D4—48no—
1482D4—48no—
1483D4—44no—
1484D4—48no—
1485D4—416no—
1486D4—416no—
1487D4—416no—
1488D4—48no—
1489D4—48no—
1490D4—416no—
1491D4—48no—
1492D4—44no—
1493D4—84no—
1494D4—88no—
1495D4—82no—
1496D4—88no—
1497D4—84no—
1498D4—84no—
1499D4—88no—
1500D4—164no—
1501D4—162no—
1502D4—164no—
1503D4—164no—
1504D4H(3,𝔽4)116yescomplemented
1505C2×C4—22no—
1506C2×C4—22no—
1507C2×C4—22no—
1508C2×C4—22no—
1509C2×C4—22no—
1510C2×C4—24no—
1511C2×C4—24no—
1512C2×C4—22no—
1513C2×C4—22no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—21no—
1517C2×C4—22no—
1518C2×C4—21no—
1519C2×C4—22no—
1520C2×C4—24no—
1521C2×C4—21no—
1522C2×C4—24no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—24no—
1526C2×C4—24no—
1527C2×C4—24no—
1528C2×C4—24no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—22no—
1535C2×C4—24no—
1536C2×C4—24no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—21no—
1542C2×C4—24no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—24no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—24no—
1553C2×C4—24no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—24no—
1560C2×C4—21no—
1561C2×C4—416no—
1562C2×C4—416no—
1563C2×C4—44no—
1564C2×C4—48no—
1565C2×C4—48no—
1566C2×C4—416no—
1567C2×C4—416no—
1568C2×C4—416no—
1569C2×C4—48no—
1570C2×C4—44no—
1571C2×C4—48no—
1572C2×C4—48no—
1573C2×C4—44no—
1574C2×C4—84no—
1575C2×C4—88no—
1576C2×C4—88no—
1577C2×C4C2×H(5,𝔽2)14yes—
1578C2×C4C2×H(5,𝔽2)14yes—
1579C2×C4C2×H(5,𝔽2)12yes—
1580C2×C4#58514yes—
1581C22—28no—
1582C22—24no—
1583C22—24no—
1584C22—28no—
1585C22—24no—
1586C22—22no—
1587C22—41no—
1588C22—42no—
1589C22—41no—
1590C22—42no—
1591C22—44no—
1592C22—44no—
1593C22—42no—
1594C22—42no—
1595C22—42no—
1596C22—44no—
1597C22—42no—
1598C22—42no—
1599C22—42no—
1600C22—41no—
1601C22—42no—
1602C22—44no—
1603C22—41no—
1604C22—42no—
1605C22—44no—
1606C22—42no—
1607C22—42no—
1608C22—42no—
1609C22—42no—
1610C22—44no—
1611C22—44no—
1612C22—42no—
1613C22—42no—
1614C22—44no—
1615C22—42no—
1616C22—42no—
1617C22—42no—
1618C22—44no—
1619C22—42no—
1620C22—41no—
1621C22—816no—
1622C22—88no—
1623C22—1616no—
1624C22—168no—
1625C22C2×H(3,𝔽4)18yes—
1626C22C22×H(5,𝔽2)11yescharacteristic
1627C22C22×H(5,𝔽2)12yes—
1628C22C22×H(5,𝔽2)11yescharacteristic
1629C22C2×#58512yes—
1630C222−1+611yescharacteristic
1631C4—24no—
1632C4—24no—
1633C4—44no—
1634C4—44no—
1635C4—42no—
1636C4—44no—
1637C4—41no—
1638C4—42no—
1639C4—42no—
1640C4—42no—
1641C4—44no—
1642C4—41no—
1643C4—42no—
1644C4—42no—
1645C4—42no—
1646C4—42no—
1647C4—41no—
1648C4—42no—
1649C4—42no—
1650C4—41no—
1651C4—44no—
1652C4C2×H(3,𝔽4)14yes—
1653C2—28no—
1654C2—42no—
1655C2—82no—
1656C2—82no—
1657C2—82no—
1658C2—84no—
1659C2—81no—
1660C2C22×H(3,𝔽4)11yescharacteristic
1661C2#6291411yescharacteristic
1662C2#6292112yes—
1663C2#6301212yes—
1664C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53080C2semidirect
2. #53046C2semidirect
3. #52990C2semidirect
4. #52958C2semidirect
5. #52530C2semidirect
6. #52395C2semidirect
7. #52367C2semidirect
8. #52310C2semidirect
9. #52294C2semidirect
10. C2×#2712C2semidirect
11. #46099C2semidirect
12. #46054C2semidirect
13. #46043C2semidirect
14. #46031C2semidirect
15. #46016C2semidirect
16. #45977C2semidirect
17. #45601C2semidirect
18. #45568C2semidirect
19. #45539C2semidirect
20. #45479C2semidirect
21. #36303C2semidirect
22. #36238C2semidirect
23. #36213C2semidirect
24. #36212C2semidirect
25. D4×#124C2semidirect
26. #35939C2semidirect
27. #35847C2semidirect
28. #35750C2semidirect
29. #35680C2semidirect
30. C22×H(5,𝔽2)C22semidirect
31. C23×#41C22semidirect
32. C2×H(3,𝔽4)C22semidirect
33. C2×#554C22semidirect
34. C2×D4×Q8C22semidirect
40. C22×#124C22semidirect
41. #2862C22semidirect
42. #2861C22semidirect
43. #2858C22semidirect
44. #2850C22semidirect
45. #2850C22semidirect
46. #2850C22semidirect
47. #2849C22semidirect
48. #2849C22semidirect
49. #2848C22semidirect
50. #2847C22semidirect
51. #2840C22semidirect
52. #2835C22semidirect
53. #2832C22semidirect
54. #2832C22semidirect
55. #2832C22semidirect
56. #2832C22semidirect
57. #2832C22semidirect
58. #2828C22semidirect
59. #2828C22semidirect
60. #2828C22semidirect
61. #2824C22semidirect
62. #2824C22semidirect
63. #2824C22semidirect
64. #2824C22semidirect
65. #2824C22semidirect
66. #2819C22semidirect
67. #2819C22semidirect
68. #2819C22semidirect
69. #2812C22semidirect
70. #2811C22semidirect
71. #2804C22semidirect
72. #2804C22semidirect
73. #2804C22semidirect
74. #2785C22semidirect
75. #2782C22semidirect
76. #2782C22semidirect
77. #2782C22semidirect
78. #2763C22semidirect
79. #2763C22semidirect
80. #2763C22semidirect
81. #2763C22semidirect
82. #2763C22semidirect
83. #2753C22semidirect
84. #2753C22semidirect
85. #2753C22semidirect
86. #2753C22semidirect
87. #2753C22semidirect
88. #2753C22semidirect
89. #2753C22semidirect
90. #2753C22semidirect
91. #2753C22semidirect
92. #2736C22semidirect
93. #2736C22semidirect
94. #2733C22semidirect
95. #2733C22semidirect
96. #2733C22semidirect
97. #2712C22semidirect
98. #2712C22semidirect
99. #2712C22semidirect
100. #2712C22semidirect
101. #2712C22semidirect
102. #2712C22semidirect
103. #2712C22semidirect
104. #2712C22semidirect
105. #2712C22semidirect
106. #2712C22semidirect
107. #2712C22semidirect
108. #2712C22semidirect
109. #2712C22semidirect
110. #2712C22semidirect
111. #2712C22semidirect
112. #2684C22semidirect
113. #2684C22semidirect
114. #2684C22semidirect
115. #2684C22semidirect
116. #2684C22semidirect
117. #2670C22semidirect
118. #2670C22semidirect
119. #2670C22semidirect
120. #2670C22semidirect
121. #2670C22semidirect
122. #2640C22semidirect
123. #2640C22semidirect
124. #2639C22semidirect
125. #2639C22semidirect
126. #2616C22semidirect
127. #2615C22semidirect
128. #2613C22semidirect
129. #2613C22semidirect
130. #2592C22semidirect
131. #2592C22semidirect
132. #2592C22semidirect
133. #2591C22semidirect
134. #2568C22semidirect
135. #2563C22semidirect
136. #2562C22semidirect
137. #2561C22semidirect
138. #2561C22semidirect
139. #2561C22semidirect
140. #2548C22semidirect
141. #2547C22semidirect
142. #2547C22semidirect
143. #2547C22semidirect
144. #2504C22semidirect
145. #2503C22semidirect
146. #2492C22semidirect
147. #2492C22semidirect
148. #2492C22semidirect
149. #2492C22semidirect
150. #2492C22semidirect
151. #2492C22semidirect
152. #2492C22semidirect
153. #2491C22semidirect
154. #2491C22semidirect
155. #2491C22semidirect
156. #2491C22semidirect
157. #2491C22semidirect
158. #2491C22semidirect
159. #2491C22semidirect
160. #2490C22semidirect
161. #2490C22semidirect
162. #2489C22semidirect
163. #2489C22semidirect
164. #2488C22semidirect
165. #2488C22semidirect
166. #2488C22semidirect
167. #2488C22semidirect
168. #2488C22semidirect
169. #2488C22semidirect
170. #2488C22semidirect
171. #2488C22semidirect
172. #2488C22semidirect
173. #2472C22semidirect
174. #2472C22semidirect
175. #2472C22semidirect
176. #2472C22semidirect
177. #2472C22semidirect
178. #2472C22semidirect
179. #2472C22semidirect
180. #2472C22semidirect
181. #2472C22semidirect
182. #2436C22semidirect
183. #2436C22semidirect
184. #2436C22semidirect
185. #2436C22semidirect
186. #2435C22semidirect
187. #2435C22semidirect
188. #2434C22semidirect
189. #2433C22semidirect
190. #2432C22semidirect
191. #2432C22semidirect
192. #2432C22semidirect
193. #2431C22semidirect
194. #2431C22semidirect
195. #2431C22semidirect
196. #2430C22semidirect
197. #2430C22semidirect
198. #2430C22semidirect
199. #2430C22semidirect
200. #2430C22semidirect
201. #2410C22semidirect
202. #2410C22semidirect
203. #2410C22semidirect
204. #2410C22semidirect
205. #2410C22semidirect
206. #2409C22semidirect
207. #2409C22semidirect
209. #2408C22semidirect
211. #2407C22semidirect
212. #2407C22semidirect
213. #2407C22semidirect
214. #2407C22semidirect
215. #2407C22semidirect
216. #2406C22semidirect
217. #2406C22semidirect
218. #2405C22semidirect
219. #2405C22semidirect
220. #2405C22semidirect
222. #2404C22semidirect
223. #2404C22semidirect
225. #2403C22semidirect
226. #2398C22semidirect
227. #2398C22semidirect
228. C2×#397C22semidirect
230. #2388C22semidirect
231. C2×#394C22semidirect
232. C2×#393C22semidirect
234. #2379C22semidirect
235. #2379C22semidirect
236. #2379C22semidirect
237. #2375C22semidirect
238. #2339C22semidirect
239. #2339C22semidirect
240. #2339C22semidirect
241. #2339C22semidirect
242. #2339C22semidirect
243. D4×C22⋊C4C22semidirect
244. D4×C22⋊C4C22semidirect
245. D4×C22⋊C4C22semidirect
246. D4×C22⋊C4C22semidirect
247. D4×C22⋊C4C22semidirect
248. C4×#124C22semidirect
249. C4×#124C22semidirect
250. C4×#124C22semidirect
251. C4×#120C22semidirect
252. C4×#120C22semidirect
253. C2×#391C22semidirect
254. C2×#388C22semidirect
255. C2×#386C22semidirect
256. C2×#385C22semidirect
257. #2275C22semidirect
258. C42×D4C22semidirect
1392. C22⋊C4H(5,𝔽2)semidirect
1504. D4H(3,𝔽4)semidirect

Maximal subgroups

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

subgroupindex
#530802
#530462
#529902
#529582
#525302
#523952
#523672
#523102
#522942
C2×#27122
#460992
#460542
#460432
#460312
#460162
#459772
#456012
#455682
#455392
#454792
#363032
#362382
#362132
#362122
D4×#1242
#359392
#358472
#357502
#356802