Finite Group Databasebeta

← #7690123

Subgroups — #7690123

Order 512.

5370 conjugacy classes of subgroups.

The subgroup lattice has 1753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C212yesmaximal, complemented
2#59805C214yesmaximal, complemented
3#59510C212yesmaximal, complemented
4#59457C211yesmaximal, characteristic, complemented
5#59272C212yesmaximal, complemented
6#59222C212yesmaximal, complemented
7#59041C211yesmaximal, characteristic, complemented
8#59041C211yesmaximal, characteristic, complemented
9#45066C212yesmaximal, complemented
10#45006C212yesmaximal, complemented
11#43701C214yesmaximal, complemented
12#43064C214yesmaximal, complemented
13#39529C212yesmaximal, complemented
14#39514C211yesmaximal, characteristic, complemented
15#39030C212yesmaximal, complemented
16#38932C211yesmaximal, characteristic, complemented
17#38724C214yesmaximal, complemented
18#38278C212yesmaximal, complemented
19#36526C212yesmaximal, complemented
20#36459C211yesmaximal, characteristic, complemented
21#36301C211yesmaximal, characteristic, complemented
22#36262C212yesmaximal, complemented
23#36240C212yesmaximal, complemented
24#36194C211yesmaximal, characteristic, complemented
25#36176C211yesmaximal, characteristic, complemented
26#36127C211yesmaximal, characteristic, complemented
27#36044C212yesmaximal, complemented
28#35823C212yesmaximal, complemented
29#34917C212yesmaximal, complemented
30#34800C211yesmaximal, characteristic, complemented
31#34310C211yesmaximal, characteristic, complemented
32#34261C212yesmaximal, complemented
33#34236C211yesmaximal, characteristic, complemented
34C4×#553C211yesmaximal, characteristic, complemented
35#34155C211yesmaximal, characteristic, complemented
36C2×#553C2211yescharacteristic
37C2×#551C2214yescomplemented
38C2×#547C2212yescomplemented
39C2×D42C2211yescharacteristic
40C2×#532C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#518C2212yes—
43#2868C2211yescharacteristic, complemented
44#2864C2212yescomplemented
45#2860C2212yes—
46#2857C2211yescharacteristic, complemented
47#2857C2211yescharacteristic, complemented
48#2857C2212yescomplemented
49#2854C2212yes—
50#2852C2214yescomplemented
51#2780C2214yescomplemented
52#2779C2214yescomplemented
53#2770C2214yescomplemented
54#2764C2214yescomplemented
55#2761C2214yescomplemented
56#2757C2214yescomplemented
57#2753C2214yescomplemented
58#2749C2214yescomplemented
59#2747C2214yescomplemented
60#2743C2214yescomplemented
61#2739C2214yescomplemented
62#2728C2214yescomplemented
63#2716C2214yescomplemented
64#2716C2214yescomplemented
65#2703C2214yescomplemented
66#2697C2214yescomplemented
67#2696C2214yescomplemented
68#2687C2214yescomplemented
69#2685C2214yescomplemented
70#2684C2214yes—
71#2684C2214yes—
72#2648C2214yescomplemented
73#2647C2212yescomplemented
74#2630C2214yescomplemented
75#2629C2212yescomplemented
76#2609C2214yescomplemented
77#2602C2214yescomplemented
78#2601C2214yescomplemented
79#2597C2214yescomplemented
80#2580C2212yescomplemented
81#2578C2214yescomplemented
82#2578C2214yescomplemented
83#2576C2214yescomplemented
84#2575C2214yescomplemented
85#2571C2212yescomplemented
86#2571C2211yescharacteristic, complemented
87#2570C2212yescomplemented
88#2570C2212yescomplemented
89#2566C2212yescomplemented
90#2566C2212yescomplemented
91#2563C2211yescharacteristic
92#2563C2211yescharacteristic
93#2563C2211yescharacteristic
94#2563C2211yescharacteristic
95#2562C2212yescomplemented
96#2561C2214yescomplemented
97#2560C2214yescomplemented
98#2560C2214yescomplemented
99#2557C2214yescomplemented
100#2554C2214yescomplemented
101#2552C2211yescharacteristic, complemented
102#2547C2212yescomplemented
103#2538C2212yes—
104#2538C2212yescomplemented
105#2537C2212yescomplemented
106#2537C2212yescomplemented
107#2535C2212yes—
108#2535C2212yes—
109#2535C2212yes—
110#2535C2212yes—
111#2534C2214yescomplemented
112#2532C2214yescomplemented
113#2532C2214yescomplemented
114#2532C2212yescomplemented
115#2531C2214yescomplemented
116#2527C2214yescomplemented
117#2526C2212yescomplemented
118#2523C2214yescomplemented
119#2518C2212yescomplemented
120#2515C2214yescomplemented
121#2515C2214yescomplemented
122#2513C2212yes—
123#2513C2211yescharacteristic
124#2512C2212yes—
125#2512C2212yes—
126#2510C2214yescomplemented
127#2510C2214yescomplemented
128#2508C2212yescomplemented
129#2508C2211yescharacteristic, complemented
130#2500C2211yescharacteristic
131#2497C2212yescomplemented
132#2497C2212yescomplemented
133#2497C2211yescharacteristic, complemented
134#2496C2212yescomplemented
135#2496C2212yescomplemented
136#2496C2212yescomplemented
137#2495C2212yescomplemented
138#2495C2212yescomplemented
139#2495C2212yescomplemented
140#2495C2212yescomplemented
141#2494C2212yescomplemented
142#2494C2212yescomplemented
143#2492C2214yescomplemented
144#2491C2211yescharacteristic
145#2490C2212yes—
146#2488C2214yescomplemented
147#2488C2214yescomplemented
148#2486C2212yescomplemented
149#2486C2212yescomplemented
150#2485C2212yescomplemented
151#2485C2211yescharacteristic, complemented
152#2485C2212yescomplemented
153#2484C2214yescomplemented
154#2481C2214yescomplemented
155#2480C2214yescomplemented
156#2480C2214yescomplemented
157#2480C2214yescomplemented
158#2480C2214yescomplemented
159#2477C2214yescomplemented
160#2468C2214yescomplemented
161#2467C2214yescomplemented
162#2464C2214yescomplemented
163#2459C2212yescomplemented
164#2457C2214yescomplemented
165#2457C2214yescomplemented
166#2454C2212yescomplemented
167#2452C2212yescomplemented
168#2450C2214yescomplemented
169#2444C2214yescomplemented
170#2442C2212yescomplemented
171#2439C2214yescomplemented
172#2439C2211yescharacteristic, complemented
173#2432C2212yescomplemented
174#2432C2212yescomplemented
175#2424C2214yescomplemented
176#2422C2212yes—
177#2422C2212yescomplemented
178#2422C2212yescomplemented
179#2422C2212yescomplemented
180#2422C2212yescomplemented
181#2420C2212yes—
182#2420C2212yes—
183#2420C2212yes—
184#2420C2212yes—
185#2420C2212yes—
186#2414C2211yescharacteristic
187#2412C2214yescomplemented
188#2411C2214yescomplemented
189#2408C2212yes—
190#2408C2212yes—
191#2408C2212yes—
192#2408C2212yes—
193#2404C2214yes—
194#2404C2214yes—
195#2401C2214yescomplemented
196#2398C2212yescomplemented
197#2392C2212yescomplemented
198#2392C2214yescomplemented
199#2374C2212yescomplemented
200#2373C2212yescomplemented
201#2372C2214yescomplemented
202#2370C2211yescharacteristic, complemented
203#2369C2211yescharacteristic, complemented
204#2369C2211yescharacteristic, complemented
205#2369C2211yescharacteristic, complemented
206#2369C2211yescharacteristic, complemented
207#2366C2211yescharacteristic
208#2366C2211yescharacteristic
209#2366C2211yescharacteristic
210#2364C2212yescomplemented
211#2363C2212yes—
212#2363C2211yescharacteristic
213#2363C2212yescomplemented
214#2363C2212yescomplemented
215#2363C2212yescomplemented
216#2363C2212yescomplemented
217#2361C2212yes—
218#2361C2211yescharacteristic
219#2361C2212yescomplemented
220#2361C2212yescomplemented
221#2358C2214yes—
222#2357C2211yescharacteristic
223#2357C2212yescomplemented
224#2355C2212yescomplemented
225#2354C2211yescharacteristic
226#2354C2212yes—
227#2354C2212yescomplemented
228#2353C2212yescomplemented
229#2353C2214yescomplemented
230#2352C2211yescharacteristic, complemented
231#2352C2212yescomplemented
232#2352C2212yescomplemented
233#2352C2214yescomplemented
234#2349C2212yescomplemented
235#2349C2212yescomplemented
236#2349C2212yescomplemented
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2212yescomplemented
239D4×C4⋊C4C2212yescomplemented
240#2347C2212yescomplemented
241#2347C2211yescharacteristic, complemented
242#2346C2212yescomplemented
243#2345C2211yescharacteristic, complemented
244#2344C2212yescomplemented
245#2342C2214yescomplemented
246#2342C2214yescomplemented
247#2339C2214yescomplemented
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2212yes—
253D4×C22⋊C4C2212yes—
254#2337C2214yescomplemented
255#2324C2212yes—
256#2321C2214yes—
257#2319C2212yes—
258#2319C2212yescomplemented
259#2318C2214yescomplemented
260#2314C2212yescomplemented
261#2312C2214yescomplemented
262C4×C4⋊Q8C2211yescharacteristic, complemented
263C4×#127C2211yescharacteristic
264C4×#125C2211yescharacteristic, complemented
265C4×#125C2212yescomplemented
266C4×#126C2212yescomplemented
267C4×#124C2212yescomplemented
268C4×#123C2214yescomplemented
269C4×#123C2212yescomplemented
270C4×#121C2212yes—
271C4×#121C2211yescharacteristic
272C4×#121C2211yescharacteristic
273C4×#121C2211yescharacteristic
274C4×#121C2211yescharacteristic
275C4×#121C2212yescomplemented
276C4×#121C2212yescomplemented
277C4×#121C2212yescomplemented
278#2298C2212yescomplemented
279#2297C2214yescomplemented
280#2293C2211yescharacteristic
281#2293C2212yes—
282#2293C2212yescomplemented
283#2293C2212yescomplemented
284C2×#390C2212yes—
285#2290C2214yescomplemented
286C2×#388C2214yescomplemented
287#2285C2212yescomplemented
288#2283C2211yescharacteristic, complemented
289#2283C2212yescomplemented
290#2275C2212yescomplemented
291C42×D4C2211yescharacteristic
292C42×D4C2211yescharacteristic, complemented
293C42×D4C2212yescomplemented
294C42×D4C2212yescomplemented
295C42×D4C2212yescomplemented
296C4×#117C2211yescharacteristic, complemented
297C4×#117C2211yescharacteristic, complemented
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#553—28no—
304#551—416no—
305#547—48no—
306D42—28no—
307#532—28no—
308#532—28no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×#127C2311yescharacteristic
315C2×#126C2312yes—
316C2×#126C2314yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#125C2311yescharacteristic
320C2×#125C2312yes—
321C2×#124C2312yes—
322C2×#124C2312yes—
323C2×#124C2312yes—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×#123C2314yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×#121C2312yes—
334C2×#121C2311yescharacteristic
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2311yescharacteristic
338C2×#121C2312yes—
339C2×#121C2312yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2311yescharacteristic
343C2×#121C2311yescharacteristic
344C2×#121C2314yes—
345C2×#120C2314yes—
346C2×#120C2314yes—
347C2×#120C2314yes—
348#518—216no—
349C2×C4×Q8C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2311yescharacteristic
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2314yes—
380C2×C4×D4C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C2×#117C2314yes—
385C2×#117C2314yes—
386C2×#117C2311yescharacteristic
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2314yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2314yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C22⋊C4C2314yes—
395C22×C22⋊C4C2314yes—
396C22×C22⋊C4C2314yes—
397C22×C22⋊C4C2314yes—
398C22×C22⋊C4C2314yes—
399C22×C42C2311yescharacteristic
400C22×C42C2311yescharacteristic
401C22×C42C2312yes—
402C22×C42C2312yes—
403C22×C42C2314yes—
404#401C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2312yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#399C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2312yes—
436#397C2314yes—
437#397C2314yes—
438#397C2312yes—
439#397C2312yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2312yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2312yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2312yes—
467#394C2312yes—
468#394C2314yes—
469#394C2312yes—
470#393C2312yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2312yes—
477#392C2314yes—
478#392C2314yes—
479#392C2314yes—
480#392C2312yes—
481#392C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2312yes—
491#390C2314yes—
492#390C2314yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2311yescharacteristic
504#390C2312yes—
505#390C2314yes—
506#390C2311yescharacteristic
507#390C2311yescharacteristic
508#390C2311yescharacteristic
509#390C2311yescharacteristic
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2312yes—
516#390C2312yes—
517#390C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2311yescharacteristic
522#389C2311yescharacteristic
523#389C2311yescharacteristic
524#389C2312yes—
525#389C2311yescharacteristic
526#389C2311yescharacteristic
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2311yescharacteristic
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2311yescharacteristic
548#388C2312yes—
549#388C2312yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2312yes—
576#388C2312yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2312yes—
581#388C2312yes—
582#388C2312yes—
583#388C2314yes—
584#388C2312yes—
585#388C2312yes—
586#388C2312yes—
587#388C2314yes—
588#388C2314yes—
589#388C2312yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2314yes—
598#388C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2312yes—
619#387C2312yes—
620#387C2314yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#386C2312yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
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#386C2312yes—
644#386C2314yes—
645#386C2312yes—
646#386C2312yes—
647#386C2312yes—
648#386C2314yes—
649#386C2314yes—
650#386C2312yes—
651#386C2314yes—
652#386C2312yes—
653#386C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2312yes—
670#384C2311yescharacteristic
671#384C2311yescharacteristic
672#384C2312yes—
673#384C2312yes—
674#384C2312yes—
675#384C2312yes—
676#384C2312yes—
677#383C2312yes—
678#383C2314yes—
679#383C2314yes—
680#383C2312yes—
681#383C2314yes—
682#382C2312yes—
683#382C2311yescharacteristic
684#382C2312yes—
685#382C2312yes—
686#382C2312yes—
687#382C2312yes—
688#382C2312yes—
689#382C2314yes—
690#382C2314yes—
691#382C2312yes—
692#382C2311yescharacteristic
693#382C2311yescharacteristic
694#381C2314yes—
695#381C2314yes—
696#381C2312yes—
697#381C2314yes—
698#381C2314yes—
699#381C2314yes—
700#381C2312yes—
701#381C2314yes—
702#380C2311yescharacteristic
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2312yes—
712#380C2312yes—
713#380C2314yes—
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2312yes—
719#380C2314yes—
720#380C2312yes—
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2311yescharacteristic
726#380C2314yes—
727#380C2314yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#379C2314yes—
732#379C2314yes—
733#379C2314yes—
734#379C2314yes—
735#379C2314yes—
736C4×C4⋊C4C2311yescharacteristic
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807#376C2312yes—
808#376C2314yes—
809#376C2312yes—
810#376C2312yes—
811C2×#95C2314yes—
812C2×#95C2312yes—
813C2×#95C2314yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C43C2312yes—
817C25C2414yes—
818C2×#41—28no—
819C2×#41—28no—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—82no—
823C2×#41—82no—
824C22×Q8C2412yes—
825C22×Q8C2412yes—
826C22×Q8C2412yes—
827C22×D4—28no—
828C22×D4—28no—
829C22×D4—28no—
830C22×D4—44no—
831C22×D4—44no—
832C22×D4—44no—
833C22×D4C2411yescharacteristic
834C22×D4C2412yes—
835C22×D4C2411yescharacteristic
836C22×D4C2414yes—
837C22×D4C2414yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2414yes—
857C23×C4C2412yes—
858C23×C4C2414yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2412yes—
866C4⋊Q8—24no—
867C4⋊Q8—24no—
868C4⋊Q8—42no—
869C4⋊Q8—44no—
870C4⋊Q8—82no—
871#127#4118yes—
872#126—28no—
873#126—48no—
874#126—48no—
875#126—84no—
876#125—24no—
877#125—44no—
878#124—28no—
879#124—28no—
880#124—28no—
881#123—28no—
882#123—216no—
883#123—48no—
884#123—48no—
885#123—48no—
886C22⋊Q8—44no—
887C22⋊Q8—48no—
888C22⋊Q8—44no—
889C22⋊Q8—48no—
890#121—28no—
891#121—28no—
892#121—28no—
893#121—28no—
894#121—28no—
895#121—28no—
896#121—24no—
897#121—24no—
898#121—28no—
899#121—48no—
900#121—42no—
901#121—42no—
902#120—216no—
903#120—48no—
904#120—84no—
905C4×Q8—44no—
906C4×D4—28no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—28no—
910C4×D4—28no—
911C4×D4—216no—
912C4×D4—28no—
913C4×D4—28no—
914C4×D4—216no—
915C4×D4—24no—
916C4×D4—28no—
917C4×D4—28no—
918C4×D4—24no—
919C4×D4—24no—
920C4×D4—24no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—42no—
929C4×D4—44no—
930C4×D4—42no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—44no—
934C4×D4—48no—
935C4×D4—84no—
936C4×D4#4118yescomplemented
937#117—28no—
938#117—24no—
939#117—28no—
940#117—48no—
941#117—48no—
942#117—42no—
943#117—42no—
944#117—42no—
945#117—84no—
946C2×C4⋊C4—24no—
947C2×C4⋊C4—44no—
948C2×C4⋊C4—42no—
949C2×C4⋊C4—48no—
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C22⋊C4—216no—
1007C2×C22⋊C4—216no—
1008C2×C22⋊C4—48no—
1009C2×C22⋊C4—48no—
1010C2×C22⋊C4—84no—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2411yescharacteristic
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2411yescharacteristic
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2414yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C42—24no—
1078C2×C42—24no—
1079C2×C42—44no—
1080C2×C42—44no—
1081C2×C42—84no—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2414yes—
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2412yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2414yes—
1103C2×C42C2414yes—
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2414yes—
1108C2×C42C2414yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2412yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118#95C2412yes—
1119#95C2412yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2411yescharacteristic
1151#95C2412yes—
1152#95C2412yes—
1153#95C2411yescharacteristic
1154#95C2411yescharacteristic
1155#95C2412yes—
1156#95C2412yes—
1157#95C2411yescharacteristic
1158#95C2414yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—28no—
1187C24—28no—
1188C24—44no—
1189C24—44no—
1190C24—44no—
1191C24—44no—
1192C24—44no—
1193C24C2512yes—
1194C24C2511yescharacteristic
1195C24C2512yes—
1196C24C2514yes—
1197C24C2511yescharacteristic
1198#41—816no—
1199#41—816no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—42no—
1204C2×Q8—42no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8—42no—
1208C2×Q8—42no—
1209C2×D4—28no—
1210C2×D4—24no—
1211C2×D4—28no—
1212C2×D4—28no—
1213C2×D4—24no—
1214C2×D4—22no—
1215C2×D4—28no—
1216C2×D4—28no—
1217C2×D4—24no—
1218C2×D4—28no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—41no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—44no—
1242C2×D4—44no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—432no—
1248C2×D4—816no—
1249C2×D4C2×#4114yes—
1250C2×D4C2×#4118yes—
1251C2×D4C2×#4118yes—
1252C2×D4C2×#4118yes—
1253C22×C4—28no—
1254C22×C4—22no—
1255C22×C4—28no—
1256C22×C4—28no—
1257C22×C4—24no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—28no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—24no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—28no—
1281C22×C4—28no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—42no—
1285C22×C4—44no—
1286C22×C4—42no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—42no—
1290C22×C4—42no—
1291C22×C4—42no—
1292C22×C4—44no—
1293C22×C4—44no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—44no—
1298C22×C4—42no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—42no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4C2×#4118yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2512yes—
1317C22×C4C2512yes—
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2511yescharacteristic
1321C22×C4C2512yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2512yes—
1326C22×C4C2512yes—
1327C22×C4C2514yes—
1328C22×C4C2514yes—
1329C22×C4C2514yes—
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2511yescharacteristic
1333C22×C4C2512yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C4⋊C4—22no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—22no—
1356C4⋊C4—28no—
1357C4⋊C4—24no—
1358C4⋊C4—28no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—44no—
1378C4⋊C4—41no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4C2×#4114yes—
1396C22⋊C4—28no—
1397C22⋊C4—28no—
1398C22⋊C4—28no—
1399C22⋊C4—28no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—28no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—28no—
1406C22⋊C4—28no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—22no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—22no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—22no—
1421C22⋊C4—44no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—41no—
1440C22⋊C4—41no—
1441C22⋊C4—44no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—42no—
1452C22⋊C4—42no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—42no—
1460C22⋊C4C2×#4118yes—
1461C22⋊C4H(5,𝔽2)14yes—
1462C42—22no—
1463C42—22no—
1464C42—22no—
1465C42—22no—
1466C42—22no—
1467C42—22no—
1468C42—28no—
1469C42—24no—
1470C42—24no—
1471C42—24no—
1472C42—24no—
1473C42—22no—
1474C42—24no—
1475C42—22no—
1476C42—24no—
1477C42—22no—
1478C42—24no—
1479C42—24no—
1480C42—24no—
1481C42—22no—
1482C42—42no—
1483C42—42no—
1484C42—42no—
1485C42—42no—
1486C42—42no—
1487C42—42no—
1488C42—44no—
1489C42—44no—
1490C42—42no—
1491C42—42no—
1492C42—42no—
1493C42—44no—
1494C42—44no—
1495C42—41no—
1496C42C2×#4114yes—
1497C42C2×#4114yes—
1498C23—24no—
1499C23—21no—
1500C23—22no—
1501C23—21no—
1502C23—22no—
1503C23—24no—
1504C23—21no—
1505C23—21no—
1506C23—24no—
1507C23—24no—
1508C23—24no—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—21no—
1513C23—22no—
1514C23—21no—
1515C23—24no—
1516C23—22no—
1517C23—21no—
1518C23—22no—
1519C23—21no—
1520C23—22no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—21no—
1530C23—416no—
1531C23—88no—
1532C23—88no—
1533C23—88no—
1534C23—88no—
1535C23—164no—
1536C23—164no—
1537C23C22×#4118yes—
1538C23C22×#4114yes—
1539C23C2×H(5,𝔽2)12yes—
1540C23C2611yescharacteristic
1541Q8—84no—
1542Q8—84no—
1543Q8—84no—
1544D4—28no—
1545D4—216no—
1546D4—216no—
1547D4—48no—
1548D4—44no—
1549D4—48no—
1550D4—416no—
1551D4—416no—
1552D4—44no—
1553D4—84no—
1554D4—84no—
1555D4—88no—
1556D4—88no—
1557D4—84no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—24no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—24no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—21no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—48no—
1637C2×C4—44no—
1638C2×C4—416no—
1639C2×C4—44no—
1640C2×C4—44no—
1641C2×C4—44no—
1642C2×C4—48no—
1643C2×C4—44no—
1644C2×C4—44no—
1645C2×C4—48no—
1646C2×C4—88no—
1647C2×C4—84no—
1648C2×C4—84no—
1649C2×C4—88no—
1650C2×C4—84no—
1651C2×C4—88no—
1652C2×C4—88no—
1653C2×C4—88no—
1654C2×C4—164no—
1655C2×C4C22×#4114yes—
1656C2×C4C22×#4112yes—
1657C2×C4C22×#4112yes—
1658C2×C4C22×#4112yes—
1659C2×C4C22×#4112yes—
1660C2×C4C22×#4112yes—
1661C2×C4C22×#4112yes—
1662C2×C4C2×H(5,𝔽2)12yes—
1663C2×C4C2×H(5,𝔽2)12yes—
1664C2×C4#58512yes—
1665C2×C4#58512yes—
1666C2×C4#58512yes—
1667C22—28no—
1668C22—22no—
1669C22—24no—
1670C22—22no—
1671C22—28no—
1672C22—24no—
1673C22—22no—
1674C22—24no—
1675C22—28no—
1676C22—42no—
1677C22—41no—
1678C22—44no—
1679C22—42no—
1680C22—44no—
1681C22—41no—
1682C22—42no—
1683C22—44no—
1684C22—44no—
1685C22—41no—
1686C22—42no—
1687C22—41no—
1688C22—41no—
1689C22—42no—
1690C22—41no—
1691C22—42no—
1692C22—42no—
1693C22—41no—
1694C22—41no—
1695C22—42no—
1696C22—41no—
1697C22—42no—
1698C22—41no—
1699C22—42no—
1700C22—41no—
1701C22—42no—
1702C22—1616no—
1703C22C23×#4111yescharacteristic
1704C22C23×#4111yescharacteristic
1705C22C22×H(5,𝔽2)11yescharacteristic
1706C22C2×#58511yescharacteristic
1707C22C2×#58511yescharacteristic
1708C22C2×#58511yescharacteristic
1709C22H(7,𝔽2)11yescharacteristic
1710C4—22no—
1711C4—22no—
1712C4—22no—
1713C4—24no—
1714C4—22no—
1715C4—22no—
1716C4—41no—
1717C4—44no—
1718C4—44no—
1719C4—42no—
1720C4—42no—
1721C4—42no—
1722C4—42no—
1723C4—42no—
1724C4—42no—
1725C4—41no—
1726C4—41no—
1727C4—42no—
1728C4—42no—
1729C4—44no—
1730C4—42no—
1731C4—41no—
1732C4—42no—
1733C4—42no—
1734C4—42no—
1735C4—41no—
1736C4—41no—
1737C4—42no—
1738C4#347514yes—
1739C4#352114yes—
1740C2—42no—
1741C2—48no—
1742C2—44no—
1743C2—81no—
1744C2—82no—
1745C2C2×#347511yescharacteristic
1746C2C2×#352111yescharacteristic
1747C2#6280011yescharacteristic
1748C2#6293811yescharacteristic
1749C2#6298311yescharacteristic
1750C2#6299211yescharacteristic
1751C2#6302411yescharacteristic
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. #59843C2semidirect
2. #59805C2semidirect
3. #59510C2semidirect
4. #59457C2semidirect
5. #59272C2semidirect
6. #59222C2semidirect
7. #59041C2semidirect
8. #59041C2semidirect
9. #45066C2semidirect
10. #45006C2semidirect
11. #43701C2semidirect
12. #43064C2semidirect
13. #39529C2semidirect
14. #39514C2semidirect
15. #39030C2semidirect
16. #38932C2semidirect
17. #38724C2semidirect
18. #38278C2semidirect
19. #36526C2semidirect
20. #36459C2semidirect
21. #36301C2semidirect
22. #36262C2semidirect
23. #36240C2semidirect
24. #36194C2semidirect
25. #36176C2semidirect
26. #36127C2semidirect
27. #36044C2semidirect
28. #35823C2semidirect
29. #34917C2semidirect
30. #34800C2semidirect
31. #34310C2semidirect
32. #34261C2semidirect
33. #34236C2semidirect
34. C4×#553C2semidirect
35. #34155C2semidirect
37. C2×#551C22semidirect
38. C2×#547C22semidirect
43. #2868C22semidirect
44. #2864C22semidirect
46. #2857C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
50. #2852C22semidirect
51. #2780C22semidirect
52. #2779C22semidirect
53. #2770C22semidirect
54. #2764C22semidirect
55. #2761C22semidirect
56. #2757C22semidirect
57. #2753C22semidirect
58. #2749C22semidirect
59. #2747C22semidirect
60. #2743C22semidirect
61. #2739C22semidirect
62. #2728C22semidirect
63. #2716C22semidirect
64. #2716C22semidirect
65. #2703C22semidirect
66. #2697C22semidirect
67. #2696C22semidirect
68. #2687C22semidirect
69. #2685C22semidirect
72. #2648C22semidirect
73. #2647C22semidirect
74. #2630C22semidirect
75. #2629C22semidirect
76. #2609C22semidirect
77. #2602C22semidirect
78. #2601C22semidirect
79. #2597C22semidirect
80. #2580C22semidirect
81. #2578C22semidirect
82. #2578C22semidirect
83. #2576C22semidirect
84. #2575C22semidirect
85. #2571C22semidirect
86. #2571C22semidirect
87. #2570C22semidirect
88. #2570C22semidirect
89. #2566C22semidirect
90. #2566C22semidirect
95. #2562C22semidirect
96. #2561C22semidirect
97. #2560C22semidirect
98. #2560C22semidirect
99. #2557C22semidirect
100. #2554C22semidirect
101. #2552C22semidirect
102. #2547C22semidirect
104. #2538C22semidirect
105. #2537C22semidirect
106. #2537C22semidirect
111. #2534C22semidirect
112. #2532C22semidirect
113. #2532C22semidirect
114. #2532C22semidirect
115. #2531C22semidirect
116. #2527C22semidirect
117. #2526C22semidirect
118. #2523C22semidirect
119. #2518C22semidirect
120. #2515C22semidirect
121. #2515C22semidirect
126. #2510C22semidirect
127. #2510C22semidirect
128. #2508C22semidirect
129. #2508C22semidirect
131. #2497C22semidirect
132. #2497C22semidirect
133. #2497C22semidirect
134. #2496C22semidirect
135. #2496C22semidirect
136. #2496C22semidirect
137. #2495C22semidirect
138. #2495C22semidirect
139. #2495C22semidirect
140. #2495C22semidirect
141. #2494C22semidirect
142. #2494C22semidirect
143. #2492C22semidirect
146. #2488C22semidirect
147. #2488C22semidirect
148. #2486C22semidirect
149. #2486C22semidirect
150. #2485C22semidirect
151. #2485C22semidirect
152. #2485C22semidirect
153. #2484C22semidirect
154. #2481C22semidirect
155. #2480C22semidirect
156. #2480C22semidirect
157. #2480C22semidirect
158. #2480C22semidirect
159. #2477C22semidirect
160. #2468C22semidirect
161. #2467C22semidirect
162. #2464C22semidirect
163. #2459C22semidirect
164. #2457C22semidirect
165. #2457C22semidirect
166. #2454C22semidirect
167. #2452C22semidirect
168. #2450C22semidirect
169. #2444C22semidirect
170. #2442C22semidirect
171. #2439C22semidirect
172. #2439C22semidirect
173. #2432C22semidirect
174. #2432C22semidirect
175. #2424C22semidirect
177. #2422C22semidirect
178. #2422C22semidirect
179. #2422C22semidirect
180. #2422C22semidirect
187. #2412C22semidirect
188. #2411C22semidirect
195. #2401C22semidirect
196. #2398C22semidirect
197. #2392C22semidirect
198. #2392C22semidirect
199. #2374C22semidirect
200. #2373C22semidirect
201. #2372C22semidirect
202. #2370C22semidirect
203. #2369C22semidirect
204. #2369C22semidirect
205. #2369C22semidirect
206. #2369C22semidirect
210. #2364C22semidirect
213. #2363C22semidirect
214. #2363C22semidirect
215. #2363C22semidirect
216. #2363C22semidirect
219. #2361C22semidirect
220. #2361C22semidirect
223. #2357C22semidirect
224. #2355C22semidirect
227. #2354C22semidirect
228. #2353C22semidirect
229. #2353C22semidirect
230. #2352C22semidirect
231. #2352C22semidirect
232. #2352C22semidirect
233. #2352C22semidirect
234. #2349C22semidirect
235. #2349C22semidirect
236. #2349C22semidirect
238. D4×C4⋊C4C22semidirect
239. D4×C4⋊C4C22semidirect
240. #2347C22semidirect
241. #2347C22semidirect
242. #2346C22semidirect
243. #2345C22semidirect
244. #2344C22semidirect
245. #2342C22semidirect
246. #2342C22semidirect
247. #2339C22semidirect
254. #2337C22semidirect
258. #2319C22semidirect
259. #2318C22semidirect
260. #2314C22semidirect
261. #2312C22semidirect
262. C4×C4⋊Q8C22semidirect
264. C4×#125C22semidirect
265. C4×#125C22semidirect
266. C4×#126C22semidirect
267. C4×#124C22semidirect
268. C4×#123C22semidirect
269. C4×#123C22semidirect
275. C4×#121C22semidirect
276. C4×#121C22semidirect
277. C4×#121C22semidirect
278. #2298C22semidirect
279. #2297C22semidirect
282. #2293C22semidirect
283. #2293C22semidirect
285. #2290C22semidirect
286. C2×#388C22semidirect
287. #2285C22semidirect
288. #2283C22semidirect
289. #2283C22semidirect
290. #2275C22semidirect
292. C42×D4C22semidirect
293. C42×D4C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
296. C4×#117C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect
936. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#598432
#598052
#595102
#594572
#592722
#592222
#590412
#450662
#450062
#437012
#430642
#395292
#395142
#390302
#389322
#387242
#382782
#365262
#364592
#363012
#362622
#362402
#361942
#361762
#361272
#360442
#358232
#349172
#348002
#343102
#342612
#342362
C4×#5532
#341552