Finite Group Databasebeta

← #7801156

Subgroups — #7801156

Order 512.

5940 conjugacy classes of subgroups.

The subgroup lattice has 1680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59696C212yesmaximal, complemented
2#59476C212yesmaximal, complemented
3#50108C214yesmaximal, complemented
4#49589C214yesmaximal, complemented
5#48591C214yesmaximal, complemented
6#47996C214yesmaximal, complemented
7#45056C211yesmaximal, characteristic, complemented
8#45041C211yesmaximal, characteristic, complemented
9#44938C211yesmaximal, characteristic, complemented
10#44936C211yesmaximal, characteristic, complemented
11#44266C214yesmaximal, complemented
12#43932C214yesmaximal, complemented
13#43120C214yesmaximal, complemented
14#43000C214yesmaximal, complemented
15#39915C212yesmaximal, complemented
16#39336C212yesmaximal, complemented
17#39282C212yesmaximal, complemented
18#39185C211yesmaximal, characteristic, complemented
19#38953C211yesmaximal, characteristic, complemented
20#38250C212yesmaximal, complemented
21#37334C212yesmaximal, complemented
22#36465C211yesmaximal, characteristic, complemented
23#36370C211yesmaximal, characteristic, complemented
24#36022C211yesmaximal, characteristic, complemented
25#35741C211yesmaximal, characteristic, complemented
26#35702C211yesmaximal, characteristic, complemented
27#35691C211yesmaximal, characteristic, complemented
28#35296C211yesmaximal, characteristic, complemented
29#34881C211yesmaximal, characteristic, complemented
30#34493C212yesmaximal, complemented
31#34210C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic, complemented
33C2×#551C2214yescomplemented
34C2×#550C2211yescharacteristic, complemented
35C2×D4×Q8C2211yescharacteristic, complemented
36C2×#548C2214yescomplemented
37C2×D42C2212yes—
38C2×D42C2211yescharacteristic, complemented
39C2×#534C2214yescomplemented
40C22×#127C2211yescharacteristic
41C2×#518C2211yescharacteristic
42C2×#518C2211yescharacteristic, complemented
43#2864C2211yescharacteristic, complemented
44#2860C2212yescomplemented
45#2858C2211yescharacteristic, complemented
46#2858C2212yescomplemented
47#2854C2212yescomplemented
48#2803C2214yescomplemented
49#2797C2214yescomplemented
50#2797C2214yescomplemented
51#2796C2214yescomplemented
52#2756C2214yescomplemented
53#2741C2214yescomplemented
54#2740C2214yescomplemented
55#2733C2214yescomplemented
56#2730C2214yescomplemented
57#2730C2214yescomplemented
58#2714C2214yescomplemented
59#2714C2214yescomplemented
60#2714C2214yescomplemented
61#2714C2214yescomplemented
62#2710C2214yescomplemented
63#2705C2214yescomplemented
64#2703C2214yescomplemented
65#2703C2214yescomplemented
66#2697C2214yescomplemented
67#2696C2214yescomplemented
68#2696C2214yescomplemented
69#2691C2214yescomplemented
70#2688C2214yescomplemented
71#2688C2214yescomplemented
72#2687C2214yescomplemented
73#2687C2214yescomplemented
74#2685C2214yescomplemented
75#2685C2214yescomplemented
76#2684C2214yescomplemented
77#2684C2214yescomplemented
78#2678C2214yescomplemented
79#2676C2214yescomplemented
80#2673C2214yescomplemented
81#2673C2214yescomplemented
82#2670C2214yescomplemented
83#2670C2214yescomplemented
84#2670C2214yescomplemented
85#2669C2214yescomplemented
86#2669C2214yescomplemented
87#2668C2214yescomplemented
88#2651C2214yescomplemented
89#2644C2212yescomplemented
90#2635C2212yescomplemented
91#2635C2212yescomplemented
92#2628C2211yescharacteristic, complemented
93#2626C2212yescomplemented
94#2624C2212yescomplemented
95#2619C2211yescharacteristic
96#2619C2212yescomplemented
97#2617C2212yes—
98#2613C2214yescomplemented
99#2602C2214yescomplemented
100#2600C2214yescomplemented
101#2598C2214yescomplemented
102#2596C2214yescomplemented
103#2595C2214yescomplemented
104#2593C2212yescomplemented
105#2585C2212yescomplemented
106#2580C2211yescharacteristic, complemented
107#2580C2211yescharacteristic, complemented
108#2573C2212yescomplemented
109#2570C2212yescomplemented
110#2564C2212yescomplemented
111#2563C2211yescharacteristic, complemented
112#2560C2214yescomplemented
113#2557C2214yescomplemented
114#2557C2214yescomplemented
115#2554C2212yes—
116#2543C2214yescomplemented
117#2543C2212yescomplemented
118#2543C2214yescomplemented
119#2543C2214yescomplemented
120#2542C2211yescharacteristic, complemented
121#2542C2212yescomplemented
122#2541C2211yescharacteristic, complemented
123#2541C2212yescomplemented
124#2541C2211yescharacteristic, complemented
125#2541C2212yescomplemented
126#2540C2214yescomplemented
127#2540C2214yescomplemented
128#2540C2214yescomplemented
129#2539C2212yes—
130#2539C2212yescomplemented
131#2535C2211yescharacteristic, complemented
132#2535C2211yescharacteristic, complemented
133#2525C2212yescomplemented
134#2516C2212yescomplemented
135#2513C2212yescomplemented
136#2513C2212yescomplemented
137#2507C2212yescomplemented
138#2500C2212yescomplemented
139#2498C2214yescomplemented
140#2496C2212yescomplemented
141#2491C2212yescomplemented
142#2482C2212yescomplemented
143#2479C2214yescomplemented
144#2477C2214yescomplemented
145#2477C2214yescomplemented
146#2476C2214yescomplemented
147#2474C2214yescomplemented
148#2472C2214yescomplemented
149#2472C2214yescomplemented
150#2472C2214yescomplemented
151#2471C2214yescomplemented
152#2471C2214yescomplemented
153#2471C2214yescomplemented
154#2469C2212yescomplemented
155#2468C2214yescomplemented
156#2467C2214yescomplemented
157#2464C2214yescomplemented
158#2464C2214yescomplemented
159#2464C2214yescomplemented
160#2463C2214yescomplemented
161#2461C2214yescomplemented
162#2458C2214yescomplemented
163#2458C2212yescomplemented
164#2456C2214yescomplemented
165#2452C2212yescomplemented
166#2450C2214yescomplemented
167#2445C2212yes—
168#2445C2212yes—
169#2445C2212yescomplemented
170#2445C2212yescomplemented
171#2444C2214yescomplemented
172#2444C2214yescomplemented
173#2439C2212yescomplemented
174#2439C2212yescomplemented
175#2437C2214yescomplemented
176#2436C2214yescomplemented
177#2433C2212yes—
178#2433C2212yes—
179#2433C2212yescomplemented
180#2428C2212yescomplemented
181#2428C2212yescomplemented
182#2428C2212yescomplemented
183#2428C2212yescomplemented
184#2424C2214yescomplemented
185#2424C2214yescomplemented
186#2422C2212yescomplemented
187#2420C2212yescomplemented
188#2418C2214yescomplemented
189#2414C2212yes—
190#2414C2214yescomplemented
191#2414C2214yescomplemented
192#2411C2214yescomplemented
193#2410C2214yes—
194#2410C2214yescomplemented
195#2410C2214yescomplemented
196#2409C2212yescomplemented
197#2408C2214yescomplemented
198#2408C2212yescomplemented
199#2408C2212yescomplemented
200#2404C2214yescomplemented
201#2404C2212yescomplemented
202#2403C2214yescomplemented
203#2402C2211yescharacteristic, complemented
204#2398C2211yescharacteristic, complemented
205#2396C2211yescharacteristic, complemented
206#2395C2212yescomplemented
207#2392C2211yescharacteristic
208#2388C2212yescomplemented
209C2×#393C2212yescomplemented
210C2×#392C2212yes—
211#2375C2214yescomplemented
212#2375C2214yescomplemented
213#2366C2212yescomplemented
214#2366C2212yescomplemented
215#2366C2214yescomplemented
216#2366C2214yescomplemented
217#2364C2214yescomplemented
218#2363C2212yescomplemented
219#2363C2212yescomplemented
220#2363C2214yescomplemented
221#2363C2212yescomplemented
222#2359C2214yescomplemented
223#2357C2211yescharacteristic, complemented
224#2357C2211yescharacteristic, complemented
225#2354C2212yescomplemented
226#2354C2212yescomplemented
227#2349C2211yescharacteristic, complemented
228#2349C2211yescharacteristic, complemented
229#2349C2212yescomplemented
230D4×C22⋊C4C2212yes—
231D4×C22⋊C4C2212yescomplemented
232D4×C22⋊C4C2212yescomplemented
233D4×C22⋊C4C2214yescomplemented
234D4×C22⋊C4C2214yescomplemented
235D4×C22⋊C4C2214yescomplemented
236#2332C2214yescomplemented
237#2331C2211yescharacteristic, complemented
238#2328C2211yescharacteristic
239#2328C2211yescharacteristic
240#2328C2211yescharacteristic, complemented
241#2328C2211yescharacteristic, complemented
242#2328C2211yescharacteristic, complemented
243#2324C2212yescomplemented
244#2324C2214yescomplemented
245#2324C2212yescomplemented
246#2321C2214yescomplemented
247#2321C2214yescomplemented
248#2309C2211yescharacteristic
249#2309C2212yescomplemented
250#2309C2214yescomplemented
251#2309C2211yescharacteristic, complemented
252C4×#127C2211yescharacteristic
253C4×#127C2211yescharacteristic
254C4×#127C2211yescharacteristic, complemented
255C4×#127C2211yescharacteristic, complemented
256C4×#127C2212yescomplemented
257C4×#126C2212yescomplemented
258C4×#123C2212yescomplemented
259#2298C2212yescomplemented
260#2293C2211yescharacteristic, complemented
261#2293C2212yescomplemented
262#2293C2212yescomplemented
263#2293C2212yescomplemented
264#2285C2211yescharacteristic, complemented
265C42×Q8C2211yescharacteristic, complemented
266C4×#117C2211yescharacteristic, complemented
267C22×#41C2312yes—
268C23×Q8C2312yes—
269C23×D4C2312yes—
270C23×D4C2311yescharacteristic
271C23×D4C2314yes—
272C23×D4C2314yes—
273C23×D4C2311yescharacteristic
274C23×D4C2312yes—
275#555—44no—
276#551—416no—
277#550—44no—
278D4×Q8—44no—
279#548—416no—
280D42—216no—
281D42—44no—
282#534—416no—
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2312yes—
285C2×#127—28no—
286C2×#127C2311yescharacteristic
287C2×#127C2311yescharacteristic
288C2×#127C2312yes—
289C2×#127C2311yescharacteristic
290C2×#127C2311yescharacteristic
291C2×#127C2311yescharacteristic
292C2×#127C2314yes—
293C2×#127C2312yes—
294C2×#127C2312yes—
295C2×#126C2312yes—
296C2×#126C2314yes—
297C2×#126C2314yes—
298C2×#124C2314yes—
299C2×#124C2314yes—
300C2×#124C2314yes—
301C2×#124C2314yes—
302C2×#124C2314yes—
303C2×#123C2314yes—
304C2×#123C2312yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×#121C2312yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#120C2314yes—
337C2×#120C2314yes—
338C2×#120C2314yes—
339C2×#120C2314yes—
340C2×#120C2314yes—
341C2×#120C2314yes—
342C2×#120C2314yes—
343C2×#120C2314yes—
344C2×#120C2314yes—
345C2×#120C2314yes—
346#518—44no—
347#518—44no—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2314yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2314yes—
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2314yes—
383C2×#117C2311yescharacteristic
384C2×#117C2314yes—
385C2×#117C2312yes—
386C2×#117C2314yes—
387C22×C22⋊C4C2314yes—
388C22×C22⋊C4C2314yes—
389C22×C22⋊C4C2312yes—
390C22×C22⋊C4C2312yes—
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2312yes—
393C22×C22⋊C4C2314yes—
394C22×C42C2311yescharacteristic
395#400C2311yescharacteristic
396#400C2314yes—
397#400C2312yes—
398#400C2312yes—
399#400C2312yes—
400#400C2314yes—
401#400C2312yes—
402#399C2312yes—
403#399C2312yes—
404#399C2314yes—
405#399C2314yes—
406#399C2314yes—
407#399C2311yescharacteristic
408#399C2312yes—
409#399C2312yes—
410#399C2312yes—
411#398C2314yes—
412#398C2314yes—
413#398C2311yescharacteristic
414#398C2312yes—
415#398C2312yes—
416#398C2314yes—
417#398C2312yes—
418#397C2314yes—
419#397C2311yescharacteristic
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2312yes—
426#397C2314yes—
427#397C2314yes—
428#397C2312yes—
429#397C2314yes—
430#397C2314yes—
431#397C2312yes—
432#397C2314yes—
433#396C2312yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2312yes—
438#396C2314yes—
439#395C2312yes—
440#395C2311yescharacteristic
441#394C2314yes—
442#394C2311yescharacteristic
443#394C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2312yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#393C2314yes—
470#393C2312yes—
471#393C2312yes—
472#393C2312yes—
473#393C2312yes—
474#393C2312yes—
475#393C2311yescharacteristic
476#393C2314yes—
477#393C2314yes—
478#393C2312yes—
479#393C2314yes—
480#392C2314yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2312yes—
487#392C2312yes—
488#392C2312yes—
489#392C2314yes—
490#392C2314yes—
491#392C2312yes—
492#392C2314yes—
493#392C2312yes—
494#392C2314yes—
495#392C2311yescharacteristic
496#392C2312yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2314yes—
501#392C2312yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2314yes—
510#390C2314yes—
511#390C2311yescharacteristic
512#390C2311yescharacteristic
513#390C2311yescharacteristic
514#390C2311yescharacteristic
515#390C2314yes—
516#390C2314yes—
517#390C2311yescharacteristic
518#390C2311yescharacteristic
519#390C2312yes—
520#390C2314yes—
521#390C2311yescharacteristic
522#390C2311yescharacteristic
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2312yes—
527#390C2314yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2314yes—
532#390C2314yes—
533#390C2314yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2314yes—
538#390C2314yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2314yes—
547#390C2312yes—
548#390C2312yes—
549#390C2314yes—
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2314yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#388C2312yes—
568#388C2312yes—
569#388C2312yes—
570#388C2312yes—
571#388C2314yes—
572#388C2314yes—
573#388C2312yes—
574#388C2312yes—
575#388C2312yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2312yes—
589#388C2312yes—
590#388C2312yes—
591#388C2312yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2314yes—
608#388C2314yes—
609#388C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#385C2314yes—
667#385C2312yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2312yes—
680#383C2312yes—
681#382C2312yes—
682#382C2311yescharacteristic
683#382C2311yescharacteristic
684#382C2311yescharacteristic
685#382C2311yescharacteristic
686#381C2312yes—
687#381C2314yes—
688#381C2312yes—
689#381C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2314yes—
694#380C2312yes—
695#380C2314yes—
696#380C2312yes—
697#380C2312yes—
698#380C2312yes—
699#379C2314yes—
700#379C2314yes—
701#379C2314yes—
702#379C2314yes—
703#379C2314yes—
704#379C2314yes—
705#379C2314yes—
706#379C2314yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2314yes—
711C4×C4⋊C4C2311yescharacteristic
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2311yescharacteristic
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2314yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2314yes—
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2312yes—
731C4×C22⋊C4C2314yes—
732C4×C22⋊C4C2314yes—
733C4×C22⋊C4C2314yes—
734C4×C22⋊C4C2312yes—
735C4×C22⋊C4C2312yes—
736C4×C22⋊C4C2312yes—
737#376C2311yescharacteristic
738#376C2311yescharacteristic
739C2×#95C2312yes—
740C2×#95C2312yes—
741C2×#95C2314yes—
742C43C2311yescharacteristic
743C43C2311yescharacteristic
744C43C2312yes—
745C25C2412yes—
746C25C2414yes—
747C25C2412yes—
748C2×#41—48no—
749C2×#41—44no—
750C22×Q8—48no—
751C22×Q8—44no—
752C22×Q8C2411yescharacteristic
753C22×Q8C2414yes—
754C22×Q8C2412yes—
755C22×D4—216no—
756C22×D4—216no—
757C22×D4—28no—
758C22×D4—24no—
759C22×D4—42no—
760C22×D4—42no—
761C22×D4—42no—
762C22×D4—42no—
763C22×D4—48no—
764C22×D4—48no—
765C22×D4—44no—
766C22×D4—44no—
767C22×D4—44no—
768C22×D4—84no—
769C22×D4—84no—
770C22×D4—84no—
771C22×D4#4118yescomplemented
772C22×D4C2412yes—
773C22×D4C2411yescharacteristic
774C22×D4C2411yescharacteristic
775C22×D4C2414yes—
776C22×D4C2414yes—
777C22×D4C2414yes—
778C22×D4C2412yes—
779C22×D4C2411yescharacteristic
780C22×D4C2411yescharacteristic
781C22×D4C2412yes—
782C22×D4C2414yes—
783C22×D4C2411yescharacteristic
784C22×D4C2414yes—
785C22×D4C2414yes—
786C22×D4C2412yes—
787C22×D4C2414yes—
788C22×D4C2414yes—
789C22×D4C2414yes—
790C22×D4C2412yes—
791C22×D4C2414yes—
792C22×D4C2414yes—
793C22×D4C2414yes—
794C22×D4C2414yes—
795C22×D4C2414yes—
796C22×D4C2414yes—
797C22×D4C2414yes—
798C22×D4C2412yes—
799C23×C4C2412yes—
800C23×C4C2414yes—
801C23×C4C2412yes—
802C23×C4C2411yescharacteristic
803C23×C4C2412yes—
804C23×C4C2412yes—
805C23×C4C2412yes—
806C23×C4C2414yes—
807C23×C4C2412yes—
808C23×C4C2414yes—
809C23×C4C2412yes—
810C23×C4C2414yes—
811C23×C4C2412yes—
812C23×C4C2412yes—
813C23×C4C2412yes—
814C23×C4C2414yes—
815C4⋊Q8—24no—
816C4⋊Q8—44no—
817#127—24no—
818#127—24no—
819#127—216no—
820#127—24no—
821#127—24no—
822#127—28no—
823#127—24no—
824#127—44no—
825#127—44no—
826#126—28no—
827#126—48no—
828#126—84no—
829#124—48no—
830#124—48no—
831#124—48no—
832#124—48no—
833#124—48no—
834#123—28no—
835#123—216no—
836#123—48no—
837#123—48no—
838#123—48no—
839#123—48no—
840#123—84no—
841C22⋊Q8—216no—
842C22⋊Q8—48no—
843C22⋊Q8—48no—
844C22⋊Q8—48no—
845C22⋊Q8—48no—
846C22⋊Q8—44no—
847#121—28no—
848#121—216no—
849#121—28no—
850#121—216no—
851#121—48no—
852#121—48no—
853#121—48no—
854#121—48no—
855#121—48no—
856#121—48no—
857#121—44no—
858#121—44no—
859#121—44no—
860#121—44no—
861#121—44no—
862#121—44no—
863#121—84no—
864#121—84no—
865#121—84no—
866#121—84no—
867#120—216no—
868#120—216no—
869#120—48no—
870#120—48no—
871#120—48no—
872#120—48no—
873#120—48no—
874#120—48no—
875#120—84no—
876#120—84no—
877C4×Q8—28no—
878C4×Q8—24no—
879C4×D4—28no—
880C4×D4—28no—
881C4×D4—24no—
882C4×D4—24no—
883C4×D4—24no—
884C4×D4—24no—
885C4×D4—24no—
886C4×D4—44no—
887C4×D4—44no—
888C4×D4—42no—
889C4×D4—42no—
890C4×D4—42no—
891C4×D4—42no—
892C4×D4—48no—
893C4×D4—48no—
894C4×D4—44no—
895C4×D4—44no—
896C4×D4—48no—
897C4×D4—48no—
898C4×D4—44no—
899C4×D4—44no—
900C4×D4—44no—
901C4×D4—44no—
902C4×D4—48no—
903C4×D4—84no—
904C4×D4—84no—
905C4×D4—84no—
906#117—24no—
907#117—42no—
908#117—44no—
909#117—48no—
910#117—42no—
911#117—42no—
912#117—48no—
913#117—44no—
914#117—44no—
915#117—84no—
916C2×C4⋊C4C2411yescharacteristic
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2412yes—
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2411yescharacteristic
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2412yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2412yes—
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2411yescharacteristic
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C22⋊C4—44no—
957C2×C22⋊C4—44no—
958C2×C22⋊C4—44no—
959C2×C22⋊C4—44no—
960C2×C22⋊C4—48no—
961C2×C22⋊C4—48no—
962C2×C22⋊C4—48no—
963C2×C22⋊C4C2411yescharacteristic
964C2×C22⋊C4C2411yescharacteristic
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2414yes—
980C2×C22⋊C4C2412yes—
981C2×C22⋊C4C2412yes—
982C2×C22⋊C4C2412yes—
983C2×C22⋊C4C2414yes—
984C2×C22⋊C4C2414yes—
985C2×C22⋊C4C2414yes—
986C2×C22⋊C4C2414yes—
987C2×C22⋊C4C2414yes—
988C2×C22⋊C4C2412yes—
989C2×C22⋊C4C2412yes—
990C2×C22⋊C4C2414yes—
991C2×C22⋊C4C2414yes—
992C2×C22⋊C4C2412yes—
993C2×C22⋊C4C2412yes—
994C2×C22⋊C4C2412yes—
995C2×C22⋊C4C2412yes—
996C2×C22⋊C4C2414yes—
997C2×C22⋊C4C2414yes—
998C2×C22⋊C4C2414yes—
999C2×C22⋊C4C2414yes—
1000C2×C22⋊C4C2414yes—
1001C2×C22⋊C4C2414yes—
1002C2×C22⋊C4C2414yes—
1003C2×C22⋊C4C2414yes—
1004C2×C22⋊C4C2414yes—
1005C2×C22⋊C4C2412yes—
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2412yes—
1008C2×C22⋊C4C2414yes—
1009C2×C22⋊C4C2414yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2414yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C42—24no—
1038C2×C42C2411yescharacteristic
1039C2×C42C2412yes—
1040C2×C42C2411yescharacteristic
1041C2×C42C2411yescharacteristic
1042C2×C42C2412yes—
1043C2×C42C2412yes—
1044C2×C42C2412yes—
1045C2×C42C2412yes—
1046C2×C42C2412yes—
1047C2×C42C2412yes—
1048C2×C42C2411yescharacteristic
1049C2×C42C2411yescharacteristic
1050C2×C42C2412yes—
1051C2×C42C2414yes—
1052C2×C42C2414yes—
1053C2×C42C2412yes—
1054C2×C42C2412yes—
1055C2×C42C2412yes—
1056C2×C42C2414yes—
1057C2×C42C2414yes—
1058C2×C42C2412yes—
1059C2×C42C2412yes—
1060C2×C42C2412yes—
1061C2×C42C2411yescharacteristic
1062#95C2411yescharacteristic
1063#95C2411yescharacteristic
1064#95C2412yes—
1065#95C2414yes—
1066#95C2414yes—
1067#95C2412yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2412yes—
1073#95C2412yes—
1074#95C2412yes—
1075#95C2412yes—
1076#95C2414yes—
1077#95C2412yes—
1078#95C2412yes—
1079#95C2412yes—
1080#95C2411yescharacteristic
1081#95C2412yes—
1082#95C2412yes—
1083#95C2412yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2414yes—
1090#95C2412yes—
1091#95C2414yes—
1092#95C2411yescharacteristic
1093#95C2412yes—
1094#95C2412yes—
1095#95C2412yes—
1096#95C2414yes—
1097#95C2414yes—
1098#95C2414yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110C24—24no—
1111C24—28no—
1112C24—42no—
1113C24—42no—
1114C24—44no—
1115C24—42no—
1116C24—42no—
1117C24—44no—
1118C24—44no—
1119C24—44no—
1120C24—44no—
1121C24—44no—
1122C24—44no—
1123C24—44no—
1124C24—44no—
1125C24—44no—
1126C24C2×#4118yes—
1127C24C2512yes—
1128C24C2514yes—
1129C24C2512yes—
1130C24C2512yes—
1131C24C2511yescharacteristic
1132C24C2512yes—
1133C24C2512yes—
1134#41—816no—
1135C2×Q8—24no—
1136C2×Q8—22no—
1137C2×Q8—28no—
1138C2×Q8—24no—
1139C2×Q8—44no—
1140C2×Q8—44no—
1141C2×Q8—44no—
1142C2×Q8—816no—
1143C2×D4—24no—
1144C2×D4—28no—
1145C2×D4—28no—
1146C2×D4—28no—
1147C2×D4—28no—
1148C2×D4—28no—
1149C2×D4—28no—
1150C2×D4—28no—
1151C2×D4—28no—
1152C2×D4—28no—
1153C2×D4—24no—
1154C2×D4—24no—
1155C2×D4—22no—
1156C2×D4—22no—
1157C2×D4—22no—
1158C2×D4—22no—
1159C2×D4—22no—
1160C2×D4—22no—
1161C2×D4—22no—
1162C2×D4—28no—
1163C2×D4—28no—
1164C2×D4—28no—
1165C2×D4—24no—
1166C2×D4—24no—
1167C2×D4—28no—
1168C2×D4—24no—
1169C2×D4—24no—
1170C2×D4—22no—
1171C2×D4—22no—
1172C2×D4—24no—
1173C2×D4—22no—
1174C2×D4—22no—
1175C2×D4—416no—
1176C2×D4—42no—
1177C2×D4—42no—
1178C2×D4—44no—
1179C2×D4—44no—
1180C2×D4—44no—
1181C2×D4—42no—
1182C2×D4—42no—
1183C2×D4—42no—
1184C2×D4—42no—
1185C2×D4—416no—
1186C2×D4—44no—
1187C2×D4—44no—
1188C2×D4—44no—
1189C2×D4—44no—
1190C2×D4—44no—
1191C2×D4—44no—
1192C2×D4—44no—
1193C2×D4—44no—
1194C2×D4—44no—
1195C2×D4—44no—
1196C2×D4—44no—
1197C2×D4—44no—
1198C2×D4—44no—
1199C2×D4—44no—
1200C2×D4—44no—
1201C2×D4—44no—
1202C2×D4—44no—
1203C2×D4—44no—
1204C2×D4—44no—
1205C2×D4—44no—
1206C2×D4—44no—
1207C2×D4—44no—
1208C2×D4—44no—
1209C2×D4—44no—
1210C2×D4—44no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—44no—
1214C2×D4—44no—
1215C2×D4—44no—
1216C2×D4—44no—
1217C2×D4—44no—
1218C2×D4—44no—
1219C2×D4—44no—
1220C2×D4—816no—
1221C2×D4—832no—
1222C2×D4—832no—
1223C2×D4—816no—
1224C2×D4C2×#4114yes—
1225C2×D4C2×#4114yes—
1226C2×D4C2×#4118yes—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—24no—
1230C22×C4—28no—
1231C22×C4—24no—
1232C22×C4—28no—
1233C22×C4—24no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—24no—
1237C22×C4—24no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—28no—
1241C22×C4—28no—
1242C22×C4—44no—
1243C22×C4—42no—
1244C22×C4—44no—
1245C22×C4—44no—
1246C22×C4—44no—
1247C22×C4—44no—
1248C22×C4—44no—
1249C22×C4—44no—
1250C22×C4—44no—
1251C22×C4—44no—
1252C22×C4—44no—
1253C22×C4—44no—
1254C22×C4—44no—
1255C22×C4—42no—
1256C22×C4—42no—
1257C22×C4—42no—
1258C22×C4—42no—
1259C22×C4—44no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4—44no—
1266C22×C4C2×#4114yes—
1267C22×C4C2512yes—
1268C22×C4C2512yes—
1269C22×C4C2512yes—
1270C22×C4C2511yescharacteristic
1271C22×C4C2514yes—
1272C22×C4C2514yes—
1273C22×C4C2512yes—
1274C22×C4C2512yes—
1275C22×C4C2512yes—
1276C22×C4C2512yes—
1277C22×C4C2512yes—
1278C22×C4C2512yes—
1279C22×C4C2511yescharacteristic
1280C22×C4C2512yes—
1281C22×C4C2514yes—
1282C22×C4C2512yes—
1283C22×C4C2512yes—
1284C22×C4C2511yescharacteristic
1285C22×C4C2512yes—
1286C22×C4C2511yescharacteristic
1287C22×C4C2511yescharacteristic
1288C22×C4C2512yes—
1289C22×C4C2512yes—
1290C22×C4C2511yescharacteristic
1291C4⋊C4—24no—
1292C4⋊C4—24no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—24no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—24no—
1302C4⋊C4—28no—
1303C4⋊C4—24no—
1304C4⋊C4—28no—
1305C4⋊C4—28no—
1306C4⋊C4—24no—
1307C4⋊C4—24no—
1308C4⋊C4—24no—
1309C4⋊C4—24no—
1310C4⋊C4—22no—
1311C4⋊C4—24no—
1312C4⋊C4—24no—
1313C4⋊C4—42no—
1314C4⋊C4—42no—
1315C4⋊C4—42no—
1316C4⋊C4—44no—
1317C4⋊C4—44no—
1318C4⋊C4—44no—
1319C4⋊C4—44no—
1320C4⋊C4—42no—
1321C4⋊C4—44no—
1322C4⋊C4—44no—
1323C4⋊C4—42no—
1324C4⋊C4—42no—
1325C4⋊C4—44no—
1326C4⋊C4—44no—
1327C4⋊C4—44no—
1328C4⋊C4—44no—
1329C4⋊C4—42no—
1330C4⋊C4H(5,𝔽2)18yes—
1331C22⋊C4—24no—
1332C22⋊C4—28no—
1333C22⋊C4—28no—
1334C22⋊C4—24no—
1335C22⋊C4—28no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—24no—
1339C22⋊C4—28no—
1340C22⋊C4—24no—
1341C22⋊C4—24no—
1342C22⋊C4—24no—
1343C22⋊C4—24no—
1344C22⋊C4—24no—
1345C22⋊C4—24no—
1346C22⋊C4—28no—
1347C22⋊C4—28no—
1348C22⋊C4—24no—
1349C22⋊C4—28no—
1350C22⋊C4—24no—
1351C22⋊C4—24no—
1352C22⋊C4—24no—
1353C22⋊C4—28no—
1354C22⋊C4—28no—
1355C22⋊C4—28no—
1356C22⋊C4—42no—
1357C22⋊C4—42no—
1358C22⋊C4—44no—
1359C22⋊C4—44no—
1360C22⋊C4—42no—
1361C22⋊C4—42no—
1362C22⋊C4—42no—
1363C22⋊C4—42no—
1364C22⋊C4—44no—
1365C22⋊C4—44no—
1366C22⋊C4—44no—
1367C22⋊C4—44no—
1368C22⋊C4—42no—
1369C22⋊C4—42no—
1370C22⋊C4—42no—
1371C22⋊C4—44no—
1372C22⋊C4—44no—
1373C22⋊C4—44no—
1374C22⋊C4—44no—
1375C22⋊C4—44no—
1376C22⋊C4—44no—
1377C22⋊C4—44no—
1378C22⋊C4—44no—
1379C22⋊C4—44no—
1380C22⋊C4—44no—
1381C22⋊C4—44no—
1382C22⋊C4—44no—
1383C22⋊C4—44no—
1384C22⋊C4—44no—
1385C22⋊C4—44no—
1386C22⋊C4—44no—
1387C22⋊C4—44no—
1388C22⋊C4—44no—
1389C22⋊C4—44no—
1390C22⋊C4—44no—
1391C22⋊C4—44no—
1392C22⋊C4—42no—
1393C22⋊C4—42no—
1394C22⋊C4—44no—
1395C22⋊C4—44no—
1396C22⋊C4—44no—
1397C22⋊C4—44no—
1398C22⋊C4—44no—
1399C22⋊C4—44no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—44no—
1405C42—22no—
1406C42—24no—
1407C42—22no—
1408C42—24no—
1409C42—22no—
1410C42—24no—
1411C42—24no—
1412C42—24no—
1413C42—24no—
1414C42—24no—
1415C42—22no—
1416C42—22no—
1417C42—24no—
1418C42—44no—
1419C42—44no—
1420C42—42no—
1421C42—42no—
1422C42—44no—
1423C42—42no—
1424C42—44no—
1425C42—42no—
1426C42—42no—
1427C42—42no—
1428C42H(5,𝔽2)14yes—
1429C23—21no—
1430C23—22no—
1431C23—24no—
1432C23—22no—
1433C23—22no—
1434C23—24no—
1435C23—21no—
1436C23—22no—
1437C23—22no—
1438C23—24no—
1439C23—24no—
1440C23—22no—
1441C23—22no—
1442C23—24no—
1443C23—22no—
1444C23—22no—
1445C23—22no—
1446C23—24no—
1447C23—24no—
1448C23—22no—
1449C23—22no—
1450C23—24no—
1451C23—24no—
1452C23—22no—
1453C23—22no—
1454C23—24no—
1455C23—22no—
1456C23—22no—
1457C23—24no—
1458C23—22no—
1459C23—24no—
1460C23—24no—
1461C23—24no—
1462C23—22no—
1463C23—24no—
1464C23—22no—
1465C23—48no—
1466C23—416no—
1467C23—48no—
1468C23—88no—
1469C23—88no—
1470C23—88no—
1471C23—88no—
1472C23—88no—
1473C23—88no—
1474C23—162no—
1475C23—164no—
1476C23—162no—
1477C23—162no—
1478C23—162no—
1479C23—164no—
1480C23—164no—
1481C23—164no—
1482C23C22×#4112yes—
1483C23C22×#4114yes—
1484C23C22×#4114yes—
1485C23C2611yescharacteristic
1486Q8—28no—
1487Q8—88no—
1488Q8—84no—
1489D4—28no—
1490D4—28no—
1491D4—48no—
1492D4—416no—
1493D4—416no—
1494D4—416no—
1495D4—48no—
1496D4—48no—
1497D4—44no—
1498D4—44no—
1499D4—44no—
1500D4—48no—
1501D4—84no—
1502D4—88no—
1503D4—84no—
1504D4—88no—
1505D4—88no—
1506D4—88no—
1507D4—88no—
1508D4—88no—
1509D4—88no—
1510D4—88no—
1511D4—88no—
1512D4—164no—
1513D4—164no—
1514D4—164no—
1515D4—164no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—22no—
1524C2×C4—22no—
1525C2×C4—22no—
1526C2×C4—28no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—22no—
1531C2×C4—22no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—24no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—24no—
1545C2×C4—22no—
1546C2×C4—24no—
1547C2×C4—24no—
1548C2×C4—22no—
1549C2×C4—24no—
1550C2×C4—24no—
1551C2×C4—24no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—24no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—24no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—24no—
1566C2×C4—22no—
1567C2×C4—22no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—416no—
1573C2×C4—48no—
1574C2×C4—48no—
1575C2×C4—84no—
1576C2×C4—84no—
1577C2×C4—84no—
1578C2×C4—88no—
1579C2×C4—84no—
1580C2×C4—88no—
1581C2×C4—88no—
1582C2×C4—162no—
1583C2×C4—162no—
1584C2×C4—162no—
1585C2×C4—162no—
1586C2×C4—164no—
1587C2×C4C22×#4112yes—
1588C2×C4C22×#4112yes—
1589C2×C4C2×H(5,𝔽2)14yes—
1590C2×C4C2×H(5,𝔽2)14yes—
1591C2×C4C2×H(5,𝔽2)14yes—
1592C2×C4C2×H(5,𝔽2)12yes—
1593C2×C4C2×H(5,𝔽2)12yes—
1594C2×C4C2×H(5,𝔽2)12yes—
1595C2×C4#58512yes—
1596C22—24no—
1597C22—28no—
1598C22—28no—
1599C22—22no—
1600C22—24no—
1601C22—24no—
1602C22—42no—
1603C22—42no—
1604C22—41no—
1605C22—42no—
1606C22—42no—
1607C22—41no—
1608C22—44no—
1609C22—44no—
1610C22—42no—
1611C22—42no—
1612C22—44no—
1613C22—44no—
1614C22—44no—
1615C22—44no—
1616C22—42no—
1617C22—42no—
1618C22—42no—
1619C22—42no—
1620C22—44no—
1621C22—44no—
1622C22—42no—
1623C22—42no—
1624C22—42no—
1625C22—42no—
1626C22—42no—
1627C22—42no—
1628C22—44no—
1629C22—44no—
1630C22—44no—
1631C22—42no—
1632C22—44no—
1633C22—44no—
1634C22—42no—
1635C22—168no—
1636C22—168no—
1637C22—1616no—
1638C22C23×#4111yescharacteristic
1639C22C22×H(5,𝔽2)12yes—
1640C22C22×H(5,𝔽2)11yescharacteristic
1641C22C2×#58511yescharacteristic
1642C22H(7,𝔽2)12yes—
1643C4—24no—
1644C4—24no—
1645C4—22no—
1646C4—24no—
1647C4—22no—
1648C4—22no—
1649C4—44no—
1650C4—42no—
1651C4—42no—
1652C4—42no—
1653C4—42no—
1654C4—42no—
1655C4—44no—
1656C4—41no—
1657C4—42no—
1658C4—42no—
1659C4—41no—
1660C4—42no—
1661C4—42no—
1662C4—42no—
1663C4—44no—
1664C4—42no—
1665C4—42no—
1666C4#350514yes—
1667C2—44no—
1668C2—44no—
1669C2—42no—
1670C2—82no—
1671C2—82no—
1672C2—84no—
1673C2—82no—
1674C2C2×#350511yescharacteristic
1675C2#6283211yescharacteristic
1676C2#6287611yescharacteristic
1677C2#6292312yes—
1678C2#6298312yes—
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. #59696C2semidirect
2. #59476C2semidirect
3. #50108C2semidirect
4. #49589C2semidirect
5. #48591C2semidirect
6. #47996C2semidirect
7. #45056C2semidirect
8. #45041C2semidirect
9. #44938C2semidirect
10. #44936C2semidirect
11. #44266C2semidirect
12. #43932C2semidirect
13. #43120C2semidirect
14. #43000C2semidirect
15. #39915C2semidirect
16. #39336C2semidirect
17. #39282C2semidirect
18. #39185C2semidirect
19. #38953C2semidirect
20. #38250C2semidirect
21. #37334C2semidirect
22. #36465C2semidirect
23. #36370C2semidirect
24. #36022C2semidirect
25. #35741C2semidirect
26. #35702C2semidirect
27. #35691C2semidirect
28. #35296C2semidirect
29. #34881C2semidirect
30. #34493C2semidirect
31. #34210C2semidirect
32. C2×#555C22semidirect
33. C2×#551C22semidirect
34. C2×#550C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×#548C22semidirect
38. C2×D42C22semidirect
39. C2×#534C22semidirect
42. C2×#518C22semidirect
43. #2864C22semidirect
44. #2860C22semidirect
45. #2858C22semidirect
46. #2858C22semidirect
47. #2854C22semidirect
48. #2803C22semidirect
49. #2797C22semidirect
50. #2797C22semidirect
51. #2796C22semidirect
52. #2756C22semidirect
53. #2741C22semidirect
54. #2740C22semidirect
55. #2733C22semidirect
56. #2730C22semidirect
57. #2730C22semidirect
58. #2714C22semidirect
59. #2714C22semidirect
60. #2714C22semidirect
61. #2714C22semidirect
62. #2710C22semidirect
63. #2705C22semidirect
64. #2703C22semidirect
65. #2703C22semidirect
66. #2697C22semidirect
67. #2696C22semidirect
68. #2696C22semidirect
69. #2691C22semidirect
70. #2688C22semidirect
71. #2688C22semidirect
72. #2687C22semidirect
73. #2687C22semidirect
74. #2685C22semidirect
75. #2685C22semidirect
76. #2684C22semidirect
77. #2684C22semidirect
78. #2678C22semidirect
79. #2676C22semidirect
80. #2673C22semidirect
81. #2673C22semidirect
82. #2670C22semidirect
83. #2670C22semidirect
84. #2670C22semidirect
85. #2669C22semidirect
86. #2669C22semidirect
87. #2668C22semidirect
88. #2651C22semidirect
89. #2644C22semidirect
90. #2635C22semidirect
91. #2635C22semidirect
92. #2628C22semidirect
93. #2626C22semidirect
94. #2624C22semidirect
96. #2619C22semidirect
98. #2613C22semidirect
99. #2602C22semidirect
100. #2600C22semidirect
101. #2598C22semidirect
102. #2596C22semidirect
103. #2595C22semidirect
104. #2593C22semidirect
105. #2585C22semidirect
106. #2580C22semidirect
107. #2580C22semidirect
108. #2573C22semidirect
109. #2570C22semidirect
110. #2564C22semidirect
111. #2563C22semidirect
112. #2560C22semidirect
113. #2557C22semidirect
114. #2557C22semidirect
116. #2543C22semidirect
117. #2543C22semidirect
118. #2543C22semidirect
119. #2543C22semidirect
120. #2542C22semidirect
121. #2542C22semidirect
122. #2541C22semidirect
123. #2541C22semidirect
124. #2541C22semidirect
125. #2541C22semidirect
126. #2540C22semidirect
127. #2540C22semidirect
128. #2540C22semidirect
130. #2539C22semidirect
131. #2535C22semidirect
132. #2535C22semidirect
133. #2525C22semidirect
134. #2516C22semidirect
135. #2513C22semidirect
136. #2513C22semidirect
137. #2507C22semidirect
138. #2500C22semidirect
139. #2498C22semidirect
140. #2496C22semidirect
141. #2491C22semidirect
142. #2482C22semidirect
143. #2479C22semidirect
144. #2477C22semidirect
145. #2477C22semidirect
146. #2476C22semidirect
147. #2474C22semidirect
148. #2472C22semidirect
149. #2472C22semidirect
150. #2472C22semidirect
151. #2471C22semidirect
152. #2471C22semidirect
153. #2471C22semidirect
154. #2469C22semidirect
155. #2468C22semidirect
156. #2467C22semidirect
157. #2464C22semidirect
158. #2464C22semidirect
159. #2464C22semidirect
160. #2463C22semidirect
161. #2461C22semidirect
162. #2458C22semidirect
163. #2458C22semidirect
164. #2456C22semidirect
165. #2452C22semidirect
166. #2450C22semidirect
169. #2445C22semidirect
170. #2445C22semidirect
171. #2444C22semidirect
172. #2444C22semidirect
173. #2439C22semidirect
174. #2439C22semidirect
175. #2437C22semidirect
176. #2436C22semidirect
179. #2433C22semidirect
180. #2428C22semidirect
181. #2428C22semidirect
182. #2428C22semidirect
183. #2428C22semidirect
184. #2424C22semidirect
185. #2424C22semidirect
186. #2422C22semidirect
187. #2420C22semidirect
188. #2418C22semidirect
190. #2414C22semidirect
191. #2414C22semidirect
192. #2411C22semidirect
194. #2410C22semidirect
195. #2410C22semidirect
196. #2409C22semidirect
197. #2408C22semidirect
198. #2408C22semidirect
199. #2408C22semidirect
200. #2404C22semidirect
201. #2404C22semidirect
202. #2403C22semidirect
203. #2402C22semidirect
204. #2398C22semidirect
205. #2396C22semidirect
206. #2395C22semidirect
208. #2388C22semidirect
209. C2×#393C22semidirect
211. #2375C22semidirect
212. #2375C22semidirect
213. #2366C22semidirect
214. #2366C22semidirect
215. #2366C22semidirect
216. #2366C22semidirect
217. #2364C22semidirect
218. #2363C22semidirect
219. #2363C22semidirect
220. #2363C22semidirect
221. #2363C22semidirect
222. #2359C22semidirect
223. #2357C22semidirect
224. #2357C22semidirect
225. #2354C22semidirect
226. #2354C22semidirect
227. #2349C22semidirect
228. #2349C22semidirect
229. #2349C22semidirect
231. D4×C22⋊C4C22semidirect
232. D4×C22⋊C4C22semidirect
233. D4×C22⋊C4C22semidirect
234. D4×C22⋊C4C22semidirect
235. D4×C22⋊C4C22semidirect
236. #2332C22semidirect
237. #2331C22semidirect
240. #2328C22semidirect
241. #2328C22semidirect
242. #2328C22semidirect
243. #2324C22semidirect
244. #2324C22semidirect
245. #2324C22semidirect
246. #2321C22semidirect
247. #2321C22semidirect
249. #2309C22semidirect
250. #2309C22semidirect
251. #2309C22semidirect
254. C4×#127C22semidirect
255. C4×#127C22semidirect
256. C4×#127C22semidirect
257. C4×#126C22semidirect
258. C4×#123C22semidirect
259. #2298C22semidirect
260. #2293C22semidirect
261. #2293C22semidirect
262. #2293C22semidirect
263. #2293C22semidirect
264. #2285C22semidirect
265. C42×Q8C22semidirect
266. C4×#117C22semidirect
771. C22×D4#41semidirect

Maximal subgroups

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

subgroupindex
#596962
#594762
#501082
#495892
#485912
#479962
#450562
#450412
#449382
#449362
#442662
#439322
#431202
#430002
#399152
#393362
#392822
#391852
#389532
#382502
#373342
#364652
#363702
#360222
#357412
#357022
#356912
#352962
#348812
#344932
#342102