Finite Group Databasebeta

← #7693112

Subgroups — #7693112

Order 512.

5224 conjugacy classes of subgroups.

The subgroup lattice has 1746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59854C212yesmaximal, complemented
2#59427C211yesmaximal, characteristic, complemented
3#59234C211yesmaximal, characteristic, complemented
4#59231C212yesmaximal, complemented
5#59228C211yesmaximal, characteristic, complemented
6#59226C214yesmaximal, complemented
7#59225C212yesmaximal, complemented
8#59203C212yesmaximal, complemented
9#45402C212yesmaximal, complemented
10#45170C212yesmaximal, complemented
11#43621C214yesmaximal, complemented
12#43222C214yesmaximal, complemented
13#38943C211yesmaximal, characteristic, complemented
14#38940C211yesmaximal, characteristic, complemented
15#38939C212yesmaximal, complemented
16#38938C212yesmaximal, complemented
17#38937C212yesmaximal, complemented
18#38935C214yesmaximal, complemented
19#36261C211yesmaximal, characteristic, complemented
20#36259C211yesmaximal, characteristic, complemented
21#36218C212yesmaximal, complemented
22#36209C211yesmaximal, characteristic, complemented
23#36203C212yesmaximal, complemented
24#36176C212yesmaximal, complemented
25#36174C211yesmaximal, characteristic, complemented
26#36153C211yesmaximal, characteristic, complemented
27#36042C212yesmaximal, complemented
28#35847C212yesmaximal, complemented
29#34943C211yesmaximal, characteristic, complemented
30C2×#2495C212yesmaximal, complemented
31#34195C212yesmaximal, complemented
32#34194C211yesmaximal, characteristic, complemented
33#34191C211yesmaximal, characteristic, complemented
34C4×#547C211yesmaximal, characteristic, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#554C2212yes—
37C2×#547C2211yescharacteristic
38C2×#547C2212yes—
39C2×#546C2211yescharacteristic
40C2×#546C2212yes—
41C2×C4×#41C2211yescharacteristic
42C2×C4×#41C2212yes—
43C22×C4×D4C2211yescharacteristic
44#2859C2211yescharacteristic, complemented
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic, complemented
47#2857C2212yescomplemented
48#2854C2214yes—
49#2854C2212yescomplemented
50#2850C2212yes—
51#2847C2212yes—
52#2803C2214yescomplemented
53#2785C2214yescomplemented
54#2784C2214yescomplemented
55#2783C2214yescomplemented
56#2783C2214yescomplemented
57#2781C2214yes—
58#2781C2214yescomplemented
59#2775C2214yescomplemented
60#2775C2214yescomplemented
61#2775C2214yescomplemented
62#2775C2214yescomplemented
63#2769C2214yescomplemented
64#2769C2214yescomplemented
65#2756C2214yescomplemented
66#2756C2214yescomplemented
67#2744C2214yes—
68#2744C2214yescomplemented
69#2744C2214yescomplemented
70#2737C2214yescomplemented
71#2737C2214yescomplemented
72#2686C2214yes—
73#2642C2212yescomplemented
74#2640C2212yes—
75#2639C2214yes—
76#2639C2214yescomplemented
77#2612C2214yescomplemented
78#2593C2214yescomplemented
79#2592C2212yes—
80#2591C2214yescomplemented
81#2584C2212yescomplemented
82#2583C2214yescomplemented
83#2574C2214yes—
84#2572C2212yes—
85#2572C2212yescomplemented
86#2572C2214yescomplemented
87#2571C2212yescomplemented
88#2571C2211yescharacteristic, complemented
89#2568C2212yescomplemented
90#2563C2211yescharacteristic
91#2563C2212yescomplemented
92#2563C2211yescharacteristic, complemented
93#2562C2212yescomplemented
94#2561C2214yes—
95#2552C2211yescharacteristic, complemented
96#2551C2211yescharacteristic, complemented
97#2550C2212yescomplemented
98#2549C2214yescomplemented
99#2547C2212yes—
100#2547C2211yescharacteristic
101#2546C2211yescharacteristic, complemented
102#2545C2212yes—
103#2543C2214yes—
104#2538C2211yescharacteristic, complemented
105#2537C2211yescharacteristic
106#2537C2211yescharacteristic
107#2536C2212yes—
108#2534C2214yes—
109#2532C2214yescomplemented
110#2532C2214yescomplemented
111#2532C2214yescomplemented
112#2531C2214yes—
113#2529C2214yescomplemented
114#2526C2214yescomplemented
115#2526C2214yescomplemented
116#2526C2214yescomplemented
117#2518C2214yes—
118#2518C2214yescomplemented
119#2518C2214yescomplemented
120#2513C2212yescomplemented
121#2513C2214yescomplemented
122#2508C2212yescomplemented
123#2508C2212yescomplemented
124#2508C2214yescomplemented
125#2508C2212yescomplemented
126#2504C2214yes—
127#2503C2214yescomplemented
128#2500C2212yescomplemented
129#2497C2212yes—
130#2497C2212yescomplemented
131#2495C2212yes—
132#2495C2212yes—
133#2495C2214yes—
134#2495C2212yes—
135#2495C2214yes—
136#2495C2211yescharacteristic
137#2495C2212yescomplemented
138#2495C2214yescomplemented
139#2495C2212yescomplemented
140#2495C2212yescomplemented
141#2495C2212yescomplemented
142#2495C2211yescharacteristic, complemented
143#2495C2212yescomplemented
144#2495C2214yescomplemented
145#2495C2212yescomplemented
146#2492C2212yescomplemented
147#2492C2212yescomplemented
148#2491C2212yes—
149#2490C2212yes—
150#2490C2212yes—
151#2489C2212yes—
152#2489C2212yes—
153#2489C2212yescomplemented
154#2489C2212yescomplemented
155#2488C2214yes—
156#2488C2214yes—
157#2488C2214yescomplemented
158#2488C2214yescomplemented
159#2488C2214yescomplemented
160#2488C2214yescomplemented
161#2486C2212yes—
162#2486C2212yescomplemented
163#2485C2212yes—
164#2485C2212yes—
165#2485C2212yescomplemented
166#2474C2214yes—
167#2472C2214yes—
168#2472C2214yes—
169#2440C2212yescomplemented
170#2440C2212yescomplemented
171#2439C2212yescomplemented
172#2439C2212yescomplemented
173#2429C2212yes—
174#2429C2212yescomplemented
175#2427C2212yes—
176#2426C2212yes—
177#2425C2214yes—
178#2425C2214yes—
179#2425C2214yescomplemented
180#2424C2214yes—
181#2420C2211yescharacteristic
182#2420C2212yes—
183#2420C2212yescomplemented
184#2420C2211yescharacteristic, complemented
185#2417C2212yes—
186#2416C2212yes—
187#2416C2212yescomplemented
188#2415C2212yes—
189#2415C2212yescomplemented
190#2414C2212yes—
191#2414C2212yescomplemented
192#2413C2214yes—
193#2413C2214yescomplemented
194#2412C2214yes—
195#2411C2214yes—
196#2398C2212yes—
197#2398C2212yescomplemented
198C2×#400C2214yescomplemented
199C2×#397C2214yes—
200#2372C2214yes—
201#2369C2212yescomplemented
202#2367C2211yescharacteristic
203#2365C2211yescharacteristic, complemented
204#2364C2212yes—
205#2363C2211yescharacteristic
206#2363C2212yescomplemented
207#2362C2212yescomplemented
208#2361C2212yescomplemented
209#2360C2211yescharacteristic
210#2359C2212yes—
211#2359C2214yescomplemented
212#2358C2212yes—
213#2356C2212yescomplemented
214#2356C2212yescomplemented
215#2355C2211yescharacteristic, complemented
216#2355C2211yescharacteristic, complemented
217#2354C2211yescharacteristic
218#2354C2211yescharacteristic
219#2354C2212yescomplemented
220#2354C2211yescharacteristic, complemented
221#2353C2214yescomplemented
222#2353C2214yescomplemented
223#2352C2212yes—
224#2352C2212yes—
225#2352C2211yescharacteristic
226#2352C2212yescomplemented
227#2352C2212yescomplemented
228#2349C2211yescharacteristic
229#2349C2212yes—
230D4×C4⋊C4C2211yescharacteristic
231D4×C4⋊C4C2211yescharacteristic
232D4×C4⋊C4C2211yescharacteristic
233#2347C2212yescomplemented
234#2347C2212yescomplemented
235#2346C2212yes—
236#2346C2212yescomplemented
237#2346C2212yescomplemented
238#2346C2212yescomplemented
239#2346C2212yescomplemented
240#2345C2212yes—
241#2344C2212yescomplemented
242#2343C2214yescomplemented
243#2343C2214yescomplemented
244#2343C2214yescomplemented
245#2342C2212yes—
246#2342C2214yes—
247#2339C2212yes—
248#2339C2212yes—
249#2339C2212yes—
250#2339C2211yescharacteristic
251#2339C2212yes—
252D4×C22⋊C4C2211yescharacteristic
253D4×C22⋊C4C2212yes—
254#2320C2212yescomplemented
255#2320C2212yescomplemented
256#2320C2212yescomplemented
257#2319C2212yes—
258#2318C2214yes—
259#2318C2214yescomplemented
260#2318C2214yescomplemented
261#2318C2214yescomplemented
262C4×C4⋊Q8C2211yescharacteristic, complemented
263C4×C4⋊Q8C2211yescharacteristic, complemented
264C4×#124C2211yescharacteristic
265C4×C22⋊Q8C2211yescharacteristic
266C4×C22⋊Q8C2212yescomplemented
267C4×#123C2212yes—
268C4×#123C2214yescomplemented
269C4×#121C2211yescharacteristic
270C4×#121C2211yescharacteristic
271C4×#121C2212yes—
272C4×#121C2212yes—
273C4×#121C2211yescharacteristic, complemented
274C4×#121C2212yescomplemented
275C4×#120C2212yes—
276C2×#389C2212yescomplemented
277C2×#389C2212yescomplemented
278C2×#388C2214yes—
279#2285C2211yescharacteristic
280#2285C2211yescharacteristic, complemented
281#2283C2211yescharacteristic
282#2283C2212yescomplemented
283#2283C2211yescharacteristic, complemented
284#2283C2212yescomplemented
285#2283C2214yescomplemented
286#2283C2212yescomplemented
287C2×#383C2214yescomplemented
288C2×#382C2212yescomplemented
289#2280C2212yes—
290C2×#380C2212yes—
291C2×#380C2212yes—
292#2275C2212yes—
293#2275C2212yes—
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C42×D4C2211yescharacteristic, complemented
297C2×C4×C4⋊C4C2212yescomplemented
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303#554—48no—
304#547—28no—
305#547—48no—
306#546—28no—
307#546—48no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#124C2311yescharacteristic
316C2×#124C2312yes—
317C2×#124C2314yes—
318C2×#123C2312yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×C22⋊Q8C2311yescharacteristic
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2314yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2311yescharacteristic
334C2×#121C2314yes—
335C2×#121C2311yescharacteristic
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2314yes—
339C2×#121C2311yescharacteristic
340C2×#121C2312yes—
341C2×#120C2312yes—
342C2×#120C2314yes—
343C4×#41—28no—
344C4×#41—216no—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×D4—28no—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×#117C2312yes—
377C2×#117C2314yes—
378C2×#117C2311yescharacteristic
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2314yes—
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2312yes—
393C22×C22⋊C4C2314yes—
394C22×C22⋊C4C2314yes—
395C22×C22⋊C4C2312yes—
396C22×C42C2312yes—
397C22×C42C2314yes—
398C22×C42C2312yes—
399C22×C42C2311yescharacteristic
400C22×C42C2311yescharacteristic
401C22×C42C2312yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2312yes—
406#400C2312yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2312yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2312yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#394C2314yes—
457#394C2312yes—
458#394C2314yes—
459#394C2312yes—
460#394C2312yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#393C2312yes—
471#393C2314yes—
472#393C2312yes—
473#393C2312yes—
474#393C2312yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#392C2314yes—
480#391C2312yes—
481#391C2312yes—
482#391C2311yescharacteristic
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2311yescharacteristic
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#390C2312yes—
497#390C2314yes—
498#390C2311yescharacteristic
499#390C2311yescharacteristic
500#390C2312yes—
501#390C2312yes—
502#390C2311yescharacteristic
503#390C2314yes—
504#390C2311yescharacteristic
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2311yescharacteristic
521#389C2312yes—
522#389C2312yes—
523#389C2311yescharacteristic
524#389C2311yescharacteristic
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2312yes—
546#389C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2312yes—
582#388C2312yes—
583#388C2312yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2312yes—
588#388C2312yes—
589#388C2312yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2312yes—
615#386C2312yes—
616#386C2312yes—
617#386C2314yes—
618#386C2314yes—
619#386C2312yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#386C2314yes—
631#386C2314yes—
632#386C2312yes—
633#386C2312yes—
634#386C2314yes—
635#386C2314yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#385C2312yes—
649#385C2312yes—
650#385C2314yes—
651#384C2311yescharacteristic
652#384C2311yescharacteristic
653#384C2312yes—
654#384C2311yescharacteristic
655#384C2311yescharacteristic
656#383C2312yes—
657#383C2312yes—
658#383C2312yes—
659#383C2314yes—
660#383C2314yes—
661#383C2312yes—
662#383C2314yes—
663#383C2314yes—
664#383C2314yes—
665#383C2314yes—
666#383C2314yes—
667#383C2314yes—
668#382C2312yes—
669#382C2311yescharacteristic
670#382C2314yes—
671#382C2311yescharacteristic
672#382C2314yes—
673#382C2314yes—
674#382C2312yes—
675#382C2311yescharacteristic
676#382C2312yes—
677#382C2311yescharacteristic
678#382C2312yes—
679#382C2314yes—
680#382C2314yes—
681#382C2312yes—
682#382C2314yes—
683#382C2314yes—
684#382C2314yes—
685#382C2311yescharacteristic
686#382C2312yes—
687#382C2314yes—
688#382C2312yes—
689#381C2314yes—
690#381C2314yes—
691#381C2312yes—
692#381C2312yes—
693#381C2312yes—
694#381C2314yes—
695#381C2312yes—
696#381C2314yes—
697#381C2312yes—
698#381C2314yes—
699#381C2314yes—
700#380C2311yescharacteristic
701#380C2312yes—
702#380C2312yes—
703#380C2312yes—
704#380C2311yescharacteristic
705#380C2311yescharacteristic
706#380C2311yescharacteristic
707#380C2311yescharacteristic
708#380C2311yescharacteristic
709#380C2312yes—
710#380C2312yes—
711#380C2312yes—
712#380C2312yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2312yes—
717#380C2314yes—
718#380C2312yes—
719#380C2312yes—
720#380C2312yes—
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2314yes—
724#380C2312yes—
725#380C2314yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2314yes—
734#380C2312yes—
735#380C2311yescharacteristic
736#379C2312yes—
737#379C2314yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2314yes—
769C4×C22⋊C4C2314yes—
770C4×C22⋊C4C2311yescharacteristic
771C4×C22⋊C4C2312yes—
772C4×C22⋊C4C2311yescharacteristic
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2314yes—
775C4×C22⋊C4C2314yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805#376C2314yes—
806#376C2314yes—
807#376C2314yes—
808C2×#95C2314yes—
809C2×#95C2314yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2312yes—
814C2×#95C2314yes—
815C2×#95C2312yes—
816C2×#95C2314yes—
817C43C2311yescharacteristic
818C25C2412yes—
819C2×#41—24no—
820C2×#41—28no—
821C2×#41—24no—
822C2×#41—28no—
823C2×#41—28no—
824C2×#41—24no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×D4—24no—
830C22×D4—24no—
831C22×D4—24no—
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2414yes—
835C22×D4C2412yes—
836C22×D4C2411yescharacteristic
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2414yes—
842C22×D4C2411yescharacteristic
843C23×C4—28no—
844C23×C4—44no—
845C23×C4—44no—
846C23×C4C2412yes—
847C23×C4C2414yes—
848C23×C4C2411yescharacteristic
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2414yes—
857C23×C4C2414yes—
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870C4⋊Q8—42no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873#125—44no—
874#125—44no—
875#124—24no—
876#124—44no—
877#124—48no—
878#123—28no—
879#123—216no—
880#123—48no—
881#123—48no—
882#123—48no—
883C22⋊Q8—24no—
884C22⋊Q8—28no—
885C22⋊Q8—48no—
886C22⋊Q8—48no—
887C22⋊Q8—48no—
888C22⋊Q8—44no—
889C22⋊Q8—44no—
890C22⋊Q8—44no—
891#121—28no—
892#121—28no—
893#121—24no—
894#121—44no—
895#121—42no—
896#121—44no—
897#121—42no—
898#121—44no—
899#121—48no—
900#121—48no—
901#120—28no—
902#120—48no—
903C4×Q8—24no—
904C4×Q8—28no—
905C4×Q8—24no—
906C4×Q8—28no—
907C4×Q8—44no—
908C4×D4—24no—
909C4×D4—28no—
910C4×D4—24no—
911C4×D4—28no—
912C4×D4—28no—
913C4×D4—24no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—216no—
917C4×D4—24no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—216no—
921C4×D4—24no—
922C4×D4—24no—
923C4×D4—24no—
924C4×D4—42no—
925C4×D4—42no—
926C4×D4—44no—
927C4×D4—42no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—42no—
931C4×D4#4118yes—
932C4×D4#4118yes—
933#117—24no—
934#117—28no—
935#117—28no—
936#117—216no—
937#117—44no—
938#117—44no—
939#117—44no—
940#117—44no—
941C2×C4⋊C4—28no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—44no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4—44no—
946C2×C4⋊C4—48no—
947C2×C4⋊C4—48no—
948C2×C4⋊C4C2411yescharacteristic
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C22⋊C4—28no—
1006C2×C22⋊C4—28no—
1007C2×C22⋊C4—44no—
1008C2×C22⋊C4—48no—
1009C2×C22⋊C4—48no—
1010C2×C22⋊C4C2411yescharacteristic
1011C2×C22⋊C4C2411yescharacteristic
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C42—28no—
1070C2×C42—216no—
1071C2×C42—24no—
1072C2×C42—24no—
1073C2×C42—28no—
1074C2×C42—44no—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2411yescharacteristic
1078C2×C42C2414yes—
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2414yes—
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2414yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2414yes—
1102C2×C42C2411yescharacteristic
1103C2×C42C2414yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108#95C2412yes—
1109#95C2412yes—
1110#95C2411yescharacteristic
1111#95C2411yescharacteristic
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2411yescharacteristic
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2411yescharacteristic
1162#95C2412yes—
1163#95C2412yes—
1164#95C2411yescharacteristic
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2411yescharacteristic
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184C24—24no—
1185C24—24no—
1186C24—24no—
1187C24—24no—
1188C24—42no—
1189C24—42no—
1190C24—42no—
1191C24C2512yes—
1192C24C2512yes—
1193C24C2511yescharacteristic
1194C24C2511yescharacteristic
1195C24C2512yes—
1196#41—416no—
1197#41—432no—
1198C2×Q8—24no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—22no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8—44no—
1208C2×Q8—44no—
1209C2×Q8—44no—
1210C2×D4—24no—
1211C2×D4—28no—
1212C2×D4—24no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—28no—
1216C2×D4—28no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—22no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—24no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—41no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—44no—
1238C2×D4—44no—
1239C2×D4—44no—
1240C2×D4—416no—
1241C2×D4C2×#4114yes—
1242C2×D4C2×#4114yes—
1243C2×D4H(5,𝔽2)14yes—
1244C22×C4—24no—
1245C22×C4—24no—
1246C22×C4—28no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—28no—
1250C22×C4—28no—
1251C22×C4—24no—
1252C22×C4—22no—
1253C22×C4—28no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—28no—
1257C22×C4—28no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—42no—
1284C22×C4—41no—
1285C22×C4—42no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—44no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—41no—
1297C22×C4—42no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—41no—
1305C22×C4—42no—
1306C22×C4—42no—
1307C22×C4—44no—
1308C22×C4—816no—
1309C22×C4C2×#4118yes—
1310C22×C4C2×#4118yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2514yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2511yescharacteristic
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2514yes—
1327C22×C4C2512yes—
1328C22×C4C2514yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2514yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2512yes—
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C4⋊C4—22no—
1342C4⋊C4—24no—
1343C4⋊C4—22no—
1344C4⋊C4—24no—
1345C4⋊C4—28no—
1346C4⋊C4—22no—
1347C4⋊C4—24no—
1348C4⋊C4—28no—
1349C4⋊C4—24no—
1350C4⋊C4—28no—
1351C4⋊C4—24no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—24no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—41no—
1385C4⋊C4—41no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—42no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—42no—
1396C4⋊C4C2×#4114yes—
1397C4⋊C4C2×#4114yes—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—22no—
1405C22⋊C4—24no—
1406C22⋊C4—28no—
1407C22⋊C4—24no—
1408C22⋊C4—22no—
1409C22⋊C4—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—28no—
1415C22⋊C4—24no—
1416C22⋊C4—22no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—41no—
1440C22⋊C4—42no—
1441C22⋊C4—41no—
1442C22⋊C4—41no—
1443C22⋊C4—42no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C4—42no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4C2×#4118yes—
1456C22⋊C4C2×#4118yes—
1457C42—24no—
1458C42—22no—
1459C42—28no—
1460C42—22no—
1461C42—24no—
1462C42—24no—
1463C42—22no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—24no—
1468C42—28no—
1469C42—24no—
1470C42—28no—
1471C42—24no—
1472C42—24no—
1473C42—24no—
1474C42—22no—
1475C42—22no—
1476C42—24no—
1477C42—22no—
1478C42—42no—
1479C42—42no—
1480C42—41no—
1481C42—44no—
1482C42—44no—
1483C42—44no—
1484C42—44no—
1485C42—44no—
1486C42—41no—
1487C42—44no—
1488C42C2×#4114yes—
1489C42C2×#4114yes—
1490C23—22no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
1499C23—21no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—21no—
1504C23—22no—
1505C23—21no—
1506C23—21no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—21no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—21no—
1515C23—22no—
1516C23—22no—
1517C23—21no—
1518C23—22no—
1519C23—21no—
1520C23—22no—
1521C23—48no—
1522C23—48no—
1523C23—48no—
1524C23—48no—
1525C23—84no—
1526C23—84no—
1527C23—84no—
1528C23C22×#4114yes—
1529C23C22×#4114yes—
1530C23C2×H(5,𝔽2)14yes—
1531C23#58512yes—
1532C23C2611yescharacteristic
1533Q8—44no—
1534Q8—48no—
1535Q8—84no—
1536Q8—164no—
1537D4—44no—
1538D4—48no—
1539D4—48no—
1540D4—416no—
1541D4—44no—
1542D4—44no—
1543D4—84no—
1544D4—84no—
1545D4—84no—
1546D4—164no—
1547D4#555116yes—
1548C2×C4—21no—
1549C2×C4—22no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—216no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—24no—
1568C2×C4—21no—
1569C2×C4—24no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—24no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—21no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—24no—
1599C2×C4—22no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—24no—
1607C2×C4—24no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—21no—
1623C2×C4—24no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—48no—
1629C2×C4—44no—
1630C2×C4—48no—
1631C2×C4—416no—
1632C2×C4—44no—
1633C2×C4—44no—
1634C2×C4—48no—
1635C2×C4—44no—
1636C2×C4—48no—
1637C2×C4—44no—
1638C2×C4—84no—
1639C2×C4—82no—
1640C2×C4—84no—
1641C2×C4—84no—
1642C2×C4—84no—
1643C2×C4—84no—
1644C2×C4—84no—
1645C2×C4—88no—
1646C2×C4—88no—
1647C2×C4—88no—
1648C2×C4—84no—
1649C2×C4C22×#4112yes—
1650C2×C4C22×#4114yes—
1651C2×C4C22×#4112yes—
1652C2×C4C22×#4112yes—
1653C2×C4C22×#4114yes—
1654C2×C4C22×#4112yes—
1655C2×C4C22×#4112yes—
1656C2×C4C22×#4112yes—
1657C2×C4C2×H(5,𝔽2)12yes—
1658C2×C4#58512yes—
1659C2×C4#58512yes—
1660C22—24no—
1661C22—24no—
1662C22—24no—
1663C22—24no—
1664C22—24no—
1665C22—24no—
1666C22—22no—
1667C22—22no—
1668C22—22no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—42no—
1674C22—41no—
1675C22—42no—
1676C22—41no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—41no—
1681C22—42no—
1682C22—42no—
1683C22—41no—
1684C22—42no—
1685C22—42no—
1686C22—41no—
1687C22—42no—
1688C22—42no—
1689C22—42no—
1690C22—41no—
1691C22—42no—
1692C22—41no—
1693C22—42no—
1694C22—816no—
1695C22C2×#55518yes—
1696C22C23×#4111yescharacteristic
1697C22C23×#4111yescharacteristic
1698C22C22×H(5,𝔽2)11yescharacteristic
1699C22C2×#58511yescharacteristic
1700C22C2×#58511yescharacteristic
1701C22C2×#58511yescharacteristic
1702C222−1+611yescharacteristic
1703C4—22no—
1704C4—24no—
1705C4—22no—
1706C4—24no—
1707C4—22no—
1708C4—42no—
1709C4—41no—
1710C4—42no—
1711C4—41no—
1712C4—41no—
1713C4—42no—
1714C4—44no—
1715C4—42no—
1716C4—42no—
1717C4—41no—
1718C4—42no—
1719C4—41no—
1720C4—44no—
1721C4—42no—
1722C4—42no—
1723C4—44no—
1724C4—42no—
1725C4—41no—
1726C4—41no—
1727C4—42no—
1728C4—41no—
1729C4—42no—
1730C4—44no—
1731C4C2×#55514yes—
1732C4#352114yes—
1733C2—28no—
1734C2—42no—
1735C2—82no—
1736C2—81no—
1737C2—82no—
1738C2C22×#55511yescharacteristic
1739C2C2×#352111yescharacteristic
1740C2#6281611yescharacteristic
1741C2#6292111yescharacteristic
1742C2#6299111yescharacteristic
1743C2#6299311yescharacteristic
1744C2#6301811yescharacteristic
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. #59854C2semidirect
2. #59427C2semidirect
3. #59234C2semidirect
4. #59231C2semidirect
5. #59228C2semidirect
6. #59226C2semidirect
7. #59225C2semidirect
8. #59203C2semidirect
9. #45402C2semidirect
10. #45170C2semidirect
11. #43621C2semidirect
12. #43222C2semidirect
13. #38943C2semidirect
14. #38940C2semidirect
15. #38939C2semidirect
16. #38938C2semidirect
17. #38937C2semidirect
18. #38935C2semidirect
19. #36261C2semidirect
20. #36259C2semidirect
21. #36218C2semidirect
22. #36209C2semidirect
23. #36203C2semidirect
24. #36176C2semidirect
25. #36174C2semidirect
26. #36153C2semidirect
27. #36042C2semidirect
28. #35847C2semidirect
29. #34943C2semidirect
30. C2×#2495C2semidirect
31. #34195C2semidirect
32. #34194C2semidirect
33. #34191C2semidirect
34. C4×#547C2semidirect
35. C4×#546C2semidirect
44. #2859C22semidirect
46. #2857C22semidirect
47. #2857C22semidirect
49. #2854C22semidirect
52. #2803C22semidirect
53. #2785C22semidirect
54. #2784C22semidirect
55. #2783C22semidirect
56. #2783C22semidirect
58. #2781C22semidirect
59. #2775C22semidirect
60. #2775C22semidirect
61. #2775C22semidirect
62. #2775C22semidirect
63. #2769C22semidirect
64. #2769C22semidirect
65. #2756C22semidirect
66. #2756C22semidirect
68. #2744C22semidirect
69. #2744C22semidirect
70. #2737C22semidirect
71. #2737C22semidirect
73. #2642C22semidirect
76. #2639C22semidirect
77. #2612C22semidirect
78. #2593C22semidirect
80. #2591C22semidirect
81. #2584C22semidirect
82. #2583C22semidirect
85. #2572C22semidirect
86. #2572C22semidirect
87. #2571C22semidirect
88. #2571C22semidirect
89. #2568C22semidirect
91. #2563C22semidirect
92. #2563C22semidirect
93. #2562C22semidirect
95. #2552C22semidirect
96. #2551C22semidirect
97. #2550C22semidirect
98. #2549C22semidirect
101. #2546C22semidirect
104. #2538C22semidirect
109. #2532C22semidirect
110. #2532C22semidirect
111. #2532C22semidirect
113. #2529C22semidirect
114. #2526C22semidirect
115. #2526C22semidirect
116. #2526C22semidirect
118. #2518C22semidirect
119. #2518C22semidirect
120. #2513C22semidirect
121. #2513C22semidirect
122. #2508C22semidirect
123. #2508C22semidirect
124. #2508C22semidirect
125. #2508C22semidirect
127. #2503C22semidirect
128. #2500C22semidirect
130. #2497C22semidirect
137. #2495C22semidirect
138. #2495C22semidirect
139. #2495C22semidirect
140. #2495C22semidirect
141. #2495C22semidirect
142. #2495C22semidirect
143. #2495C22semidirect
144. #2495C22semidirect
145. #2495C22semidirect
146. #2492C22semidirect
147. #2492C22semidirect
153. #2489C22semidirect
154. #2489C22semidirect
157. #2488C22semidirect
158. #2488C22semidirect
159. #2488C22semidirect
160. #2488C22semidirect
162. #2486C22semidirect
165. #2485C22semidirect
169. #2440C22semidirect
170. #2440C22semidirect
171. #2439C22semidirect
172. #2439C22semidirect
174. #2429C22semidirect
179. #2425C22semidirect
183. #2420C22semidirect
184. #2420C22semidirect
187. #2416C22semidirect
189. #2415C22semidirect
191. #2414C22semidirect
193. #2413C22semidirect
197. #2398C22semidirect
198. C2×#400C22semidirect
201. #2369C22semidirect
203. #2365C22semidirect
206. #2363C22semidirect
207. #2362C22semidirect
208. #2361C22semidirect
211. #2359C22semidirect
213. #2356C22semidirect
214. #2356C22semidirect
215. #2355C22semidirect
216. #2355C22semidirect
219. #2354C22semidirect
220. #2354C22semidirect
221. #2353C22semidirect
222. #2353C22semidirect
226. #2352C22semidirect
227. #2352C22semidirect
233. #2347C22semidirect
234. #2347C22semidirect
236. #2346C22semidirect
237. #2346C22semidirect
238. #2346C22semidirect
239. #2346C22semidirect
241. #2344C22semidirect
242. #2343C22semidirect
243. #2343C22semidirect
244. #2343C22semidirect
254. #2320C22semidirect
255. #2320C22semidirect
256. #2320C22semidirect
259. #2318C22semidirect
260. #2318C22semidirect
261. #2318C22semidirect
262. C4×C4⋊Q8C22semidirect
263. C4×C4⋊Q8C22semidirect
266. C4×C22⋊Q8C22semidirect
268. C4×#123C22semidirect
273. C4×#121C22semidirect
274. C4×#121C22semidirect
276. C2×#389C22semidirect
277. C2×#389C22semidirect
280. #2285C22semidirect
282. #2283C22semidirect
283. #2283C22semidirect
284. #2283C22semidirect
285. #2283C22semidirect
286. #2283C22semidirect
287. C2×#383C22semidirect
288. C2×#382C22semidirect
296. C42×D4C22semidirect
297. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#598542
#594272
#592342
#592312
#592282
#592262
#592252
#592032
#454022
#451702
#436212
#432222
#389432
#389402
#389392
#389382
#389372
#389352
#362612
#362592
#362182
#362092
#362032
#361762
#361742
#361532
#360422
#358472
#349432
C2×#24952
#341952
#341942
#341912
C4×#5472
C4×#5462