Finite Group Databasebeta

← #7671717

Subgroups — #7671717

Order 512.

5252 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59987C214yesmaximal, complemented
2#59580C212yesmaximal, complemented
3#59507C212yesmaximal, complemented
4#59490C214yesmaximal, complemented
5#59254C212yesmaximal, complemented
6#59208C212yesmaximal, complemented
7#39203C211yesmaximal, characteristic, complemented
8#39193C211yesmaximal, characteristic, complemented
9#38966C211yesmaximal, characteristic, complemented
10#38955C211yesmaximal, characteristic, complemented
11#38588C214yesmaximal, complemented
12#38568C214yesmaximal, complemented
13#38217C212yesmaximal, complemented
14#38204C212yesmaximal, complemented
15#36635C211yesmaximal, characteristic, complemented
16#36599C211yesmaximal, characteristic, complemented
17#36551C211yesmaximal, characteristic, complemented
18#36372C212yesmaximal, complemented
19#36294C212yesmaximal, complemented
20#36291C212yesmaximal, complemented
21#36290C212yesmaximal, complemented
22#36167C212yesmaximal, complemented
23#36154C211yesmaximal, characteristic, complemented
24#36143C212yesmaximal, complemented
25#36100C211yesmaximal, characteristic
26#35653C212yesmaximal, complemented
27#35625C212yesmaximal, complemented
28#35310C212yesmaximal, complemented
29#35209C211yesmaximal, characteristic, complemented
30#35207C211yesmaximal, characteristic, complemented
31#34317C211yesmaximal, characteristic, complemented
32#34308C211yesmaximal, characteristic, complemented
33#34202C212yesmaximal, complemented
34C4×#529C211yesmaximal, characteristic, complemented
35C2×#2293C211yesmaximal, characteristic, complemented
36C2×#554C2211yescharacteristic
37C2×#547C2211yescharacteristic
38C2×#541C2212yescomplemented
39C2×#529C2211yescharacteristic
40C2×#525C2212yes—
41C2×#520C2212yescomplemented
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2864C2212yescomplemented
45#2863C2212yescomplemented
46#2863C2212yescomplemented
47#2862C2211yescharacteristic, complemented
48#2860C2212yes—
49#2859C2212yescomplemented
50#2859C2211yescharacteristic, complemented
51#2857C2211yescharacteristic
52#2857C2211yescharacteristic
53#2857C2212yes—
54#2855C2212yes—
55#2855C2212yes—
56#2854C2212yes—
57#2851C2212yes—
58#2851C2212yes—
59#2851C2212yescomplemented
60#2848C2212yes—
61#2848C2212yes—
62#2798C2214yescomplemented
63#2793C2214yescomplemented
64#2790C2214yescomplemented
65#2787C2214yescomplemented
66#2779C2214yescomplemented
67#2768C2214yescomplemented
68#2766C2214yescomplemented
69#2757C2214yes—
70#2757C2214yescomplemented
71#2754C2214yescomplemented
72#2750C2214yescomplemented
73#2749C2214yes—
74#2740C2214yescomplemented
75#2738C2214yescomplemented
76#2687C2214yescomplemented
77#2687C2214yescomplemented
78#2664C2214yescomplemented
79#2653C2214yescomplemented
80#2629C2212yescomplemented
81#2625C2212yescomplemented
82#2625C2212yescomplemented
83#2621C2212yescomplemented
84#2611C2214yescomplemented
85#2609C2214yescomplemented
86#2603C2214yes—
87#2601C2214yescomplemented
88#2596C2214yescomplemented
89#2596C2214yescomplemented
90#2595C2214yes—
91#2589C2214yescomplemented
92#2585C2214yescomplemented
93#2577C2214yescomplemented
94#2575C2214yescomplemented
95#2573C2214yescomplemented
96#2571C2212yescomplemented
97#2570C2212yescomplemented
98#2569C2214yes—
99#2566C2212yes—
100#2563C2211yescharacteristic
101#2563C2211yescharacteristic, complemented
102#2562C2214yescomplemented
103#2553C2214yescomplemented
104#2552C2211yescharacteristic, complemented
105#2552C2211yescharacteristic, complemented
106#2552C2212yescomplemented
107#2546C2211yescharacteristic, complemented
108#2542C2211yescharacteristic
109#2538C2211yescharacteristic
110#2537C2211yescharacteristic
111#2534C2214yes—
112#2533C2214yescomplemented
113#2530C2214yescomplemented
114#2530C2214yescomplemented
115#2529C2214yescomplemented
116#2526C2214yes—
117#2519C2214yescomplemented
118#2516C2214yes—
119#2513C2212yes—
120#2513C2212yes—
121#2512C2212yes—
122#2511C2212yescomplemented
123#2509C2212yescomplemented
124#2509C2214yescomplemented
125#2509C2212yescomplemented
126#2508C2212yescomplemented
127#2507C2214yescomplemented
128#2506C2212yescomplemented
129#2505C2214yes—
130#2505C2214yescomplemented
131#2504C2212yes—
132#2503C2212yescomplemented
133#2498C2214yescomplemented
134#2497C2212yescomplemented
135#2495C2212yescomplemented
136#2495C2212yescomplemented
137#2494C2212yescomplemented
138#2494C2212yescomplemented
139#2493C2214yes—
140#2493C2214yescomplemented
141#2490C2212yes—
142#2490C2212yes—
143#2489C2212yescomplemented
144#2489C2212yescomplemented
145#2487C2212yes—
146#2487C2212yes—
147#2483C2214yes—
148#2481C2214yescomplemented
149#2480C2214yes—
150#2480C2214yes—
151#2478C2214yescomplemented
152#2478C2214yescomplemented
153#2475C2214yescomplemented
154#2475C2214yescomplemented
155#2473C2214yes—
156#2473C2214yes—
157#2473C2214yescomplemented
158#2471C2214yes—
159#2470C2214yescomplemented
160#2467C2214yes—
161#2466C2214yescomplemented
162#2460C2214yescomplemented
163#2458C2214yescomplemented
164#2455C2214yes—
165#2454C2212yes—
166#2454C2212yes—
167#2454C2212yescomplemented
168#2450C2214yes—
169#2450C2214yes—
170#2446C2212yescomplemented
171#2442C2212yes—
172#2442C2212yes—
173#2442C2212yescomplemented
174#2442C2212yescomplemented
175#2442C2212yescomplemented
176#2442C2212yescomplemented
177#2441C2212yescomplemented
178#2437C2214yes—
179#2432C2212yescomplemented
180#2429C2212yescomplemented
181#2427C2212yescomplemented
182#2422C2212yes—
183#2422C2212yescomplemented
184#2421C2212yescomplemented
185#2420C2212yes—
186#2420C2212yes—
187#2419C2214yes—
188#2418C2214yes—
189#2418C2214yes—
190#2417C2212yes—
191#2415C2212yes—
192#2408C2212yes—
193#2407C2212yes—
194#2370C2212yescomplemented
195#2370C2212yescomplemented
196#2369C2211yescharacteristic, complemented
197#2365C2211yescharacteristic, complemented
198#2362C2212yescomplemented
199#2362C2214yescomplemented
200#2361C2212yes—
201#2361C2212yes—
202#2360C2212yescomplemented
203#2359C2214yescomplemented
204#2359C2214yescomplemented
205#2359C2214yescomplemented
206#2359C2214yescomplemented
207#2358C2214yes—
208#2358C2214yes—
209#2357C2212yes—
210#2355C2211yescharacteristic, complemented
211#2354C2211yescharacteristic
212#2354C2214yescomplemented
213#2352C2214yes—
214#2352C2214yescomplemented
215#2349C2212yes—
216#2349C2214yes—
217D4×C4⋊C4C2211yescharacteristic
218D4×C4⋊C4C2212yes—
219D4×C4⋊C4C2212yes—
220D4×C4⋊C4C2214yes—
221D4×C4⋊C4C2211yescharacteristic, complemented
222#2345C2212yes—
223#2345C2212yescomplemented
224#2344C2212yescomplemented
225#2344C2212yescomplemented
226#2343C2214yescomplemented
227#2342C2214yes—
228#2339C2212yescomplemented
229D4×C22⋊C4C2212yes—
230#2332C2214yescomplemented
231#2324C2212yescomplemented
232#2324C2212yescomplemented
233#2323C2212yescomplemented
234#2323C2212yescomplemented
235#2323C2212yescomplemented
236#2323C2212yescomplemented
237#2322C2214yescomplemented
238#2317C2212yescomplemented
239#2314C2212yescomplemented
240#2311C2212yescomplemented
241C4×C4⋊Q8C2211yescharacteristic, complemented
242C4×C4⋊Q8C2211yescharacteristic, complemented
243C4×#125C2212yescomplemented
244C4×#125C2212yescomplemented
245C4×#125C2211yescharacteristic, complemented
246C4×#125C2211yescharacteristic, complemented
247C4×#126C2212yescomplemented
248C4×#126C2212yescomplemented
249C4×#124C2211yescharacteristic, complemented
250C4×#124C2211yescharacteristic, complemented
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2211yescharacteristic
254C4×C22⋊Q8C2212yes—
255C4×C22⋊Q8C2211yescharacteristic
256C4×#123C2212yes—
257C4×#123C2212yes—
258C4×#121C2212yes—
259C4×#121C2211yescharacteristic
260C4×#121C2212yes—
261C4×#121C2211yescharacteristic
262#2298C2212yescomplemented
263#2295C2212yescomplemented
264#2295C2212yescomplemented
265#2295C2211yescharacteristic, complemented
266#2293C2211yescharacteristic
267#2293C2212yes—
268#2293C2211yescharacteristic
269#2293C2211yescharacteristic
270#2293C2212yes—
271#2293C2211yescharacteristic
272#2293C2212yes—
273#2293C2212yes—
274#2293C2211yescharacteristic
275#2293C2211yescharacteristic
276#2293C2212yes—
277#2293C2211yescharacteristic
278#2293C2211yescharacteristic
279#2293C2211yescharacteristic, complemented
280C2×#390C2211yescharacteristic
281C2×#390C2211yescharacteristic
282C2×#389C2211yescharacteristic
283C2×#389C2211yescharacteristic
284C2×#389C2212yescomplemented
285#2290C2212yes—
286C2×#388C2212yes—
287C2×#388C2212yes—
288#2283C2212yes—
289#2283C2211yescharacteristic
290C2×#380C2212yes—
291#2274C2212yescomplemented
292C42×Q8C2211yescharacteristic, complemented
293C42×D4C2212yes—
294C42×D4C2211yescharacteristic, complemented
295C4×#117C2212yescomplemented
296C2×C4×C4⋊C4C2211yescharacteristic
297C2×C4×C22⋊C4C2212yes—
298C2×C43C2211yescharacteristic
299C22×#41C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#554—28no—
303#547—28no—
304#541—48no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308#529—28no—
309C2×#126C2312yes—
310C2×#126C2314yes—
311C2×#126C2314yes—
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2314yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#124C2311yescharacteristic
320#525—216no—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2312yes—
324C2×#123C2314yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2311yescharacteristic
338C2×#120C2314yes—
339#520—48no—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×D4—28no—
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2311yescharacteristic
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2311yescharacteristic
352C2×C4×D4C2314yes—
353C2×C4×D4C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2311yescharacteristic
367C2×#117—48no—
368C2×#117C2312yes—
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2312yes—
374C2×#117C2314yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2311yescharacteristic
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2312yes—
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2314yes—
393C22×C22⋊C4C2312yes—
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2312yes—
396C22×C22⋊C4C2312yes—
397C22×C42C2311yescharacteristic
398C22×C42C2311yescharacteristic
399C22×C42C2311yescharacteristic
400C22×C42C2311yescharacteristic
401C22×C42C2311yescharacteristic
402C22×C42C2312yes—
403C22×C42C2312yes—
404C22×C42C2311yescharacteristic
405C22×C42C2311yescharacteristic
406#401C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#393C2314yes—
468#393C2314yes—
469#392C2314yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2312yes—
482#391C2311yescharacteristic
483#391C2311yescharacteristic
484#390C2312yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2311yescharacteristic
489#390C2314yes—
490#390C2314yes—
491#390C2312yes—
492#390C2312yes—
493#390C2311yescharacteristic
494#390C2312yes—
495#390C2312yes—
496#390C2311yescharacteristic
497#390C2311yescharacteristic
498#390C2311yescharacteristic
499#390C2312yes—
500#390C2311yescharacteristic
501#390C2311yescharacteristic
502#390C2312yes—
503#390C2311yescharacteristic
504#390C2311yescharacteristic
505#389C2311yescharacteristic
506#389C2312yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2311yescharacteristic
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2311yescharacteristic
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#389C2312yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2311yescharacteristic
555#389C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2314yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2312yes—
591#388C2312yes—
592#388C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
608#387C2312yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2312yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2312yes—
653#386C2314yes—
654#386C2312yes—
655#385C2314yes—
656#385C2314yes—
657#385C2312yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2314yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2312yes—
682#384C2311yescharacteristic
683#384C2311yescharacteristic
684#384C2312yes—
685#384C2312yes—
686#384C2312yes—
687#384C2314yes—
688#383C2312yes—
689#383C2314yes—
690#383C2314yes—
691#382C2312yes—
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2311yescharacteristic
695#382C2312yes—
696#382C2312yes—
697#382C2312yes—
698#382C2312yes—
699#382C2314yes—
700#382C2314yes—
701#382C2314yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#381C2314yes—
706#381C2314yes—
707#381C2312yes—
708#380C2314yes—
709#380C2314yes—
710#380C2314yes—
711#380C2314yes—
712#380C2312yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2314yes—
717#380C2314yes—
718#380C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2312yes—
722#380C2314yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2314yes—
733#380C2311yescharacteristic
734#379C2314yes—
735#379C2314yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2314yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2312yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801#376C2312yes—
802#376C2314yes—
803#376C2312yes—
804C2×#95C2312yes—
805C2×#95C2314yes—
806C2×#95C2314yes—
807C2×#95C2312yes—
808C2×#95C2312yes—
809C43C2311yescharacteristic
810C43C2311yescharacteristic
811C43C2312yes—
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C25C2412yes—
819C2×#41—28no—
820C2×#41—28no—
821C2×#41—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2412yes—
825C22×D4—24no—
826C22×D4—24no—
827C22×D4—42no—
828C22×D4C2411yescharacteristic
829C22×D4C2414yes—
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2411yescharacteristic
834C22×D4C2414yes—
835C23×C4—28no—
836C23×C4—28no—
837C23×C4—44no—
838C23×C4C2411yescharacteristic
839C23×C4C2412yes—
840C23×C4C2412yes—
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2412yes—
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2412yes—
855C23×C4C2414yes—
856C23×C4C2412yes—
857C23×C4C2414yes—
858C23×C4C2414yes—
859C4⋊Q8—24no—
860C4⋊Q8—24no—
861C4⋊Q8—44no—
862#126—28no—
863#126—48no—
864#126—48no—
865#125—24no—
866#125—28no—
867#125—44no—
868#125—44no—
869#125—44no—
870#125—48no—
871#125—48no—
872#124—24no—
873#123—28no—
874#123—216no—
875#123—216no—
876#123—48no—
877C22⋊Q8—28no—
878C22⋊Q8—24no—
879C22⋊Q8—28no—
880C22⋊Q8—28no—
881C22⋊Q8—28no—
882C22⋊Q8—216no—
883C22⋊Q8—44no—
884C22⋊Q8—44no—
885C22⋊Q8—44no—
886#121—28no—
887#121—28no—
888#121—44no—
889#121#4118yes—
890#120—216no—
891C4×Q8—24no—
892C4×Q8—24no—
893C4×Q8—28no—
894C4×Q8—24no—
895C4×Q8—44no—
896C4×Q8—44no—
897C4×D4—24no—
898C4×D4—216no—
899C4×D4—24no—
900C4×D4—28no—
901C4×D4—28no—
902C4×D4—28no—
903C4×D4—28no—
904C4×D4—24no—
905C4×D4—28no—
906C4×D4—216no—
907C4×D4—24no—
908C4×D4—24no—
909C4×D4—24no—
910C4×D4—48no—
911C4×D4—44no—
912C4×D4—44no—
913C4×D4—48no—
914C4×D4—44no—
915C4×D4—48no—
916C4×D4#4118yes—
917#117—28no—
918#117—28no—
919#117—28no—
920#117—28no—
921#117—44no—
922#117—44no—
923#117—44no—
924#117—44no—
925#117—44no—
926#117—44no—
927#117—44no—
928#117—48no—
929#117—48no—
930C2×C4⋊C4—28no—
931C2×C4⋊C4—24no—
932C2×C4⋊C4—24no—
933C2×C4⋊C4—28no—
934C2×C4⋊C4—44no—
935C2×C4⋊C4—42no—
936C2×C4⋊C4—44no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—48no—
939C2×C4⋊C4—44no—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2411yescharacteristic
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C22⋊C4—28no—
1008C2×C22⋊C4—44no—
1009C2×C22⋊C4—44no—
1010C2×C22⋊C4—44no—
1011C2×C22⋊C4—48no—
1012C2×C22⋊C4—44no—
1013C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C42—24no—
1065C2×C42—24no—
1066C2×C42—24no—
1067C2×C42—24no—
1068C2×C42—44no—
1069C2×C42—44no—
1070C2×C42—42no—
1071C2×C42—42no—
1072C2×C42—42no—
1073C2×C42C2411yescharacteristic
1074C2×C42C2411yescharacteristic
1075C2×C42C2411yescharacteristic
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2414yes—
1082C2×C42C2414yes—
1083C2×C42C2412yes—
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2412yes—
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2411yescharacteristic
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2414yes—
1105C2×C42C2412yes—
1106C2×C42C2414yes—
1107C2×C42C2414yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2411yescharacteristic
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120#95C2412yes—
1121#95C2412yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186C24—24no—
1187C24—24no—
1188C24—24no—
1189C24—24no—
1190C24—42no—
1191C24—42no—
1192C24—42no—
1193C24C2512yes—
1194C24C2512yes—
1195C24C2512yes—
1196C24C2511yescharacteristic
1197#41—432no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—22no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—28no—
1211C2×D4—28no—
1212C2×D4—28no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—24no—
1218C2×D4—22no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—416no—
1222C2×D4—44no—
1223C2×D4—42no—
1224C2×D4—44no—
1225C2×D4—44no—
1226C2×D4C2×#4114yes—
1227C2×D4C2×#4118yes—
1228C2×D4C2×#4114yes—
1229C22×C4—22no—
1230C22×C4—22no—
1231C22×C4—24no—
1232C22×C4—22no—
1233C22×C4—24no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—24no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—28no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—28no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—28no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—22no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—24no—
1262C22×C4—22no—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—41no—
1267C22×C4—42no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—42no—
1272C22×C4—44no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—432no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—42no—
1279C22×C4—42no—
1280C22×C4—44no—
1281C22×C4—42no—
1282C22×C4—44no—
1283C22×C4—42no—
1284C22×C4—44no—
1285C22×C4—44no—
1286C22×C4—44no—
1287C22×C4—44no—
1288C22×C4—44no—
1289C22×C4—44no—
1290C22×C4C2×#4114yes—
1291C22×C4C2×#4118yes—
1292C22×C42−1+414yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2514yes—
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2514yes—
1308C22×C4C2512yes—
1309C22×C4C2512yes—
1310C22×C4C2514yes—
1311C22×C4C2511yescharacteristic
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2511yescharacteristic
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C4⋊C4—22no—
1325C4⋊C4—24no—
1326C4⋊C4—22no—
1327C4⋊C4—24no—
1328C4⋊C4—28no—
1329C4⋊C4—28no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—22no—
1335C4⋊C4—28no—
1336C4⋊C4—28no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—28no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—24no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—28no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—22no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—28no—
1361C4⋊C4—24no—
1362C4⋊C4—44no—
1363C4⋊C4—42no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—42no—
1368C4⋊C4—42no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—44no—
1373C4⋊C4—42no—
1374C4⋊C4—44no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4C2×#4114yes—
1390C4⋊C4C2×#4114yes—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—28no—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—28no—
1400C22⋊C4—24no—
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—24no—
1410C22⋊C4—24no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4C2×#4118yes—
1441C22⋊C4C2×#4118yes—
1442C42—22no—
1443C42—22no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—28no—
1450C42—24no—
1451C42—24no—
1452C42—22no—
1453C42—22no—
1454C42—22no—
1455C42—24no—
1456C42—24no—
1457C42—28no—
1458C42—24no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—24no—
1464C42—22no—
1465C42—22no—
1466C42—24no—
1467C42—22no—
1468C42—22no—
1469C42—24no—
1470C42—41no—
1471C42—41no—
1472C42—41no—
1473C42—42no—
1474C42—42no—
1475C42—41no—
1476C42—41no—
1477C42—41no—
1478C42—41no—
1479C42—41no—
1480C42—42no—
1481C42—42no—
1482C42—44no—
1483C42—44no—
1484C42—42no—
1485C42—44no—
1486C42—44no—
1487C42C2×#4114yes—
1488C42H(5,𝔽2)14yes—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—22no—
1494C23—22no—
1495C23—22no—
1496C23—22no—
1497C23—22no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23—22no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—48no—
1513C23—48no—
1514C23—48no—
1515C23—48no—
1516C23—84no—
1517C23—84no—
1518C23—84no—
1519C23C22×#4114yes—
1520C23C22×#4114yes—
1521C23C22×#4112yes—
1522C23C2×2−1+412yes—
1523C23#58512yes—
1524C23C2611yescharacteristic
1525Q8—44no—
1526Q8—48no—
1527Q8—84no—
1528D4—216no—
1529D4—28no—
1530D4—28no—
1531D4—48no—
1532D4—416no—
1533D4—44no—
1534D4—88no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—21no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—28no—
1552C2×C4—216no—
1553C2×C4—28no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—24no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—24no—
1568C2×C4—24no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—24no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—24no—
1607C2×C4—24no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—24no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—24no—
1614C2×C4—24no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—48no—
1618C2×C4—44no—
1619C2×C4—44no—
1620C2×C4—48no—
1621C2×C4—44no—
1622C2×C4—44no—
1623C2×C4—48no—
1624C2×C4—48no—
1625C2×C4—416no—
1626C2×C4—44no—
1627C2×C4—48no—
1628C2×C4—48no—
1629C2×C4—84no—
1630C2×C4—88no—
1631C2×C4—84no—
1632C2×C4—84no—
1633C2×C4—164no—
1634C2×C4—164no—
1635C2×C4C22×#4114yes—
1636C2×C4C22×#4112yes—
1637C2×C4C22×#4112yes—
1638C2×C4C22×#4114yes—
1639C2×C4C22×#4112yes—
1640C2×C4C22×#4112yes—
1641C2×C4C22×#4112yes—
1642C2×C4C2×H(5,𝔽2)12yes—
1643C2×C4C2×H(5,𝔽2)12yes—
1644C2×C4C2×H(5,𝔽2)12yes—
1645C2×C4C2×2−1+412yes—
1646C2×C4C2×2−1+412yes—
1647C2×C4#58512yes—
1648C2×C4#58512yes—
1649C22—22no—
1650C22—22no—
1651C22—22no—
1652C22—22no—
1653C22—22no—
1654C22—22no—
1655C22—24no—
1656C22—24no—
1657C22—24no—
1658C22—24no—
1659C22—24no—
1660C22—24no—
1661C22—42no—
1662C22—42no—
1663C22—42no—
1664C22—42no—
1665C22—42no—
1666C22—42no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—42no—
1674C22—42no—
1675C22—42no—
1676C22—816no—
1677C22#351514yes—
1678C22C23×#4111yescharacteristic
1679C22C23×#4111yescharacteristic
1680C22C22×H(5,𝔽2)11yescharacteristic
1681C22C22×2−1+411yescharacteristic
1682C22C2×#58511yescharacteristic
1683C22C2×#58511yescharacteristic
1684C22C2×#58511yescharacteristic
1685C4—24no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—22no—
1690C4—22no—
1691C4—22no—
1692C4—24no—
1693C4—41no—
1694C4—41no—
1695C4—42no—
1696C4—41no—
1697C4—42no—
1698C4—44no—
1699C4—41no—
1700C4—42no—
1701C4—44no—
1702C4—41no—
1703C4—42no—
1704C4—42no—
1705C4—42no—
1706C4—44no—
1707C4—42no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—42no—
1712C4—44no—
1713C4—42no—
1714C4#348114yes—
1715C4#349514yes—
1716C2—24no—
1717C2—44no—
1718C2—44no—
1719C2—82no—
1720C2C2×#348111yescharacteristic
1721C2C2×#351511yescharacteristic
1722C2C2×#349511yescharacteristic
1723C2#6281011yescharacteristic
1724C2#6281611yescharacteristic
1725C2#6283011yescharacteristic
1726C2#6283511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36100C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59987C2semidirect
2. #59580C2semidirect
3. #59507C2semidirect
4. #59490C2semidirect
5. #59254C2semidirect
6. #59208C2semidirect
7. #39203C2semidirect
8. #39193C2semidirect
9. #38966C2semidirect
10. #38955C2semidirect
11. #38588C2semidirect
12. #38568C2semidirect
13. #38217C2semidirect
14. #38204C2semidirect
15. #36635C2semidirect
16. #36599C2semidirect
17. #36551C2semidirect
18. #36372C2semidirect
19. #36294C2semidirect
20. #36291C2semidirect
21. #36290C2semidirect
22. #36167C2semidirect
23. #36154C2semidirect
24. #36143C2semidirect
26. #35653C2semidirect
27. #35625C2semidirect
28. #35310C2semidirect
29. #35209C2semidirect
30. #35207C2semidirect
31. #34317C2semidirect
32. #34308C2semidirect
33. #34202C2semidirect
34. C4×#529C2semidirect
35. C2×#2293C2semidirect
38. C2×#541C22semidirect
41. C2×#520C22semidirect
44. #2864C22semidirect
45. #2863C22semidirect
46. #2863C22semidirect
47. #2862C22semidirect
49. #2859C22semidirect
50. #2859C22semidirect
59. #2851C22semidirect
62. #2798C22semidirect
63. #2793C22semidirect
64. #2790C22semidirect
65. #2787C22semidirect
66. #2779C22semidirect
67. #2768C22semidirect
68. #2766C22semidirect
70. #2757C22semidirect
71. #2754C22semidirect
72. #2750C22semidirect
74. #2740C22semidirect
75. #2738C22semidirect
76. #2687C22semidirect
77. #2687C22semidirect
78. #2664C22semidirect
79. #2653C22semidirect
80. #2629C22semidirect
81. #2625C22semidirect
82. #2625C22semidirect
83. #2621C22semidirect
84. #2611C22semidirect
85. #2609C22semidirect
87. #2601C22semidirect
88. #2596C22semidirect
89. #2596C22semidirect
91. #2589C22semidirect
92. #2585C22semidirect
93. #2577C22semidirect
94. #2575C22semidirect
95. #2573C22semidirect
96. #2571C22semidirect
97. #2570C22semidirect
101. #2563C22semidirect
102. #2562C22semidirect
103. #2553C22semidirect
104. #2552C22semidirect
105. #2552C22semidirect
106. #2552C22semidirect
107. #2546C22semidirect
112. #2533C22semidirect
113. #2530C22semidirect
114. #2530C22semidirect
115. #2529C22semidirect
117. #2519C22semidirect
122. #2511C22semidirect
123. #2509C22semidirect
124. #2509C22semidirect
125. #2509C22semidirect
126. #2508C22semidirect
127. #2507C22semidirect
128. #2506C22semidirect
130. #2505C22semidirect
132. #2503C22semidirect
133. #2498C22semidirect
134. #2497C22semidirect
135. #2495C22semidirect
136. #2495C22semidirect
137. #2494C22semidirect
138. #2494C22semidirect
140. #2493C22semidirect
143. #2489C22semidirect
144. #2489C22semidirect
148. #2481C22semidirect
151. #2478C22semidirect
152. #2478C22semidirect
153. #2475C22semidirect
154. #2475C22semidirect
157. #2473C22semidirect
159. #2470C22semidirect
161. #2466C22semidirect
162. #2460C22semidirect
163. #2458C22semidirect
167. #2454C22semidirect
170. #2446C22semidirect
173. #2442C22semidirect
174. #2442C22semidirect
175. #2442C22semidirect
176. #2442C22semidirect
177. #2441C22semidirect
179. #2432C22semidirect
180. #2429C22semidirect
181. #2427C22semidirect
183. #2422C22semidirect
184. #2421C22semidirect
194. #2370C22semidirect
195. #2370C22semidirect
196. #2369C22semidirect
197. #2365C22semidirect
198. #2362C22semidirect
199. #2362C22semidirect
202. #2360C22semidirect
203. #2359C22semidirect
204. #2359C22semidirect
205. #2359C22semidirect
206. #2359C22semidirect
210. #2355C22semidirect
212. #2354C22semidirect
214. #2352C22semidirect
221. D4×C4⋊C4C22semidirect
223. #2345C22semidirect
224. #2344C22semidirect
225. #2344C22semidirect
226. #2343C22semidirect
228. #2339C22semidirect
230. #2332C22semidirect
231. #2324C22semidirect
232. #2324C22semidirect
233. #2323C22semidirect
234. #2323C22semidirect
235. #2323C22semidirect
236. #2323C22semidirect
237. #2322C22semidirect
238. #2317C22semidirect
239. #2314C22semidirect
240. #2311C22semidirect
241. C4×C4⋊Q8C22semidirect
242. C4×C4⋊Q8C22semidirect
243. C4×#125C22semidirect
244. C4×#125C22semidirect
245. C4×#125C22semidirect
246. C4×#125C22semidirect
247. C4×#126C22semidirect
248. C4×#126C22semidirect
249. C4×#124C22semidirect
250. C4×#124C22semidirect
262. #2298C22semidirect
263. #2295C22semidirect
264. #2295C22semidirect
265. #2295C22semidirect
279. #2293C22semidirect
284. C2×#389C22semidirect
291. #2274C22semidirect
292. C42×Q8C22semidirect
294. C42×D4C22semidirect
295. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#599872
#595802
#595072
#594902
#592542
#592082
#392032
#391932
#389662
#389552
#385882
#385682
#382172
#382042
#366352
#365992
#365512
#363722
#362942
#362912
#362902
#361672
#361542
#361432
#361002
#356532
#356252
#353102
#352092
#352072
#343172
#343082
#342022
C4×#5292
C2×#22932