Finite Group Databasebeta

← #7682782

Subgroups — #7682782

Order 512.

5199 conjugacy classes of subgroups.

The subgroup lattice has 1713 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59503C212yesmaximal, complemented
2#59500C212yesmaximal, complemented
3#59498C212yesmaximal, complemented
4#59497C212yesmaximal, complemented
5#59285C214yesmaximal, complemented
6#59264C212yesmaximal, complemented
7#59260C212yesmaximal, complemented
8#59258C212yesmaximal, complemented
9#59219C212yesmaximal, complemented
10#59012C214yesmaximal, complemented
11#45206C212yesmaximal, complemented
12#45191C212yesmaximal, complemented
13#45181C212yesmaximal, complemented
14#45050C212yesmaximal, complemented
15#45030C212yesmaximal, complemented
16#45012C212yesmaximal, complemented
17#44910C212yesmaximal, complemented
18#44910C212yesmaximal, complemented
19#43076C214yesmaximal, complemented
20#43051C214yesmaximal, complemented
21#35585C211yesmaximal, characteristic, complemented
22#35555C211yesmaximal, characteristic, complemented
23#35544C211yesmaximal, characteristic, complemented
24#35543C211yesmaximal, characteristic, complemented
25#35540C211yesmaximal, characteristic
26#35515C211yesmaximal, characteristic, complemented
27#34814C211yesmaximal, characteristic, complemented
28#34739C211yesmaximal, characteristic, complemented
29C2×#2422C211yesmaximal, characteristic
30#34255C211yesmaximal, characteristic, complemented
31#34248C211yesmaximal, characteristic, complemented
32#34214C211yesmaximal, characteristic, complemented
33#34204C211yesmaximal, characteristic
34#34186C211yesmaximal, characteristic, complemented
35#34180C211yesmaximal, characteristic, complemented
36C2×#552C2214yescomplemented
37C2×#533C2211yescharacteristic
38C22×#123C2212yes—
39C22×#121C2211yescharacteristic
40C2×#518C2211yescharacteristic
41C2×#518C2211yescharacteristic
42C22×C4×D4C2211yescharacteristic
43C22×#117C2211yescharacteristic
44#2779C2214yescomplemented
45#2779C2214yescomplemented
46#2771C2214yescomplemented
47#2771C2214yescomplemented
48#2770C2214yescomplemented
49#2770C2214yescomplemented
50#2765C2214yescomplemented
51#2765C2214yescomplemented
52#2765C2214yescomplemented
53#2764C2214yescomplemented
54#2761C2214yescomplemented
55#2747C2214yescomplemented
56#2743C2214yescomplemented
57#2741C2214yescomplemented
58#2739C2214yescomplemented
59#2738C2214yescomplemented
60#2707C2214yescomplemented
61#2702C2214yescomplemented
62#2695C2214yescomplemented
63#2695C2214yescomplemented
64#2694C2214yescomplemented
65#2694C2214yescomplemented
66#2690C2214yescomplemented
67#2687C2214yescomplemented
68#2611C2214yescomplemented
69#2601C2214yescomplemented
70#2599C2214yescomplemented
71#2599C2214yescomplemented
72#2580C2212yescomplemented
73#2580C2212yescomplemented
74#2577C2214yescomplemented
75#2571C2212yescomplemented
76#2570C2212yescomplemented
77#2570C2212yescomplemented
78#2570C2212yescomplemented
79#2570C2212yescomplemented
80#2569C2214yes—
81#2558C2214yescomplemented
82#2553C2214yescomplemented
83#2552C2212yescomplemented
84#2552C2212yescomplemented
85#2552C2212yescomplemented
86#2538C2212yescomplemented
87#2538C2212yescomplemented
88#2536C2214yescomplemented
89#2530C2214yescomplemented
90#2527C2214yescomplemented
91#2515C2214yescomplemented
92#2509C2212yescomplemented
93#2509C2212yescomplemented
94#2509C2212yescomplemented
95#2508C2212yescomplemented
96#2508C2212yescomplemented
97#2508C2212yescomplemented
98#2507C2212yescomplemented
99#2507C2212yescomplemented
100#2507C2212yescomplemented
101#2507C2212yescomplemented
102#2507C2212yescomplemented
103#2506C2212yescomplemented
104#2506C2212yescomplemented
105#2506C2212yescomplemented
106#2506C2212yescomplemented
107#2506C2212yescomplemented
108#2505C2214yes—
109#2498C2214yescomplemented
110#2497C2212yescomplemented
111#2497C2211yescharacteristic, complemented
112#2497C2212yescomplemented
113#2497C2211yescharacteristic, complemented
114#2496C2212yescomplemented
115#2496C2211yescharacteristic, complemented
116#2496C2212yescomplemented
117#2496C2211yescharacteristic, complemented
118#2495C2211yescharacteristic, complemented
119#2495C2212yescomplemented
120#2495C2212yescomplemented
121#2495C2211yescharacteristic, complemented
122#2494C2214yescomplemented
123#2494C2211yescharacteristic, complemented
124#2494C2212yescomplemented
125#2494C2212yescomplemented
126#2494C2211yescharacteristic, complemented
127#2493C2212yes—
128#2493C2214yes—
129#2493C2212yes—
130#2493C2214yescomplemented
131#2493C2214yescomplemented
132#2488C2214yescomplemented
133#2486C2214yescomplemented
134#2485C2214yescomplemented
135#2483C2214yes—
136#2480C2212yes—
137#2480C2214yes—
138#2480C2212yes—
139#2477C2214yescomplemented
140#2475C2214yescomplemented
141#2475C2214yescomplemented
142#2475C2214yescomplemented
143#2473C2214yes—
144#2473C2214yes—
145#2473C2214yes—
146#2473C2214yescomplemented
147#2473C2214yescomplemented
148#2470C2214yescomplemented
149#2470C2214yescomplemented
150#2468C2214yescomplemented
151#2460C2214yescomplemented
152#2458C2214yescomplemented
153#2458C2214yescomplemented
154#2454C2212yescomplemented
155#2454C2212yescomplemented
156#2452C2212yescomplemented
157#2452C2212yescomplemented
158#2442C2214yes—
159#2442C2214yescomplemented
160#2442C2211yescharacteristic, complemented
161#2442C2211yescharacteristic, complemented
162#2441C2211yescharacteristic, complemented
163#2441C2211yescharacteristic, complemented
164#2440C2211yescharacteristic, complemented
165#2440C2211yescharacteristic, complemented
166#2439C2211yescharacteristic, complemented
167#2439C2211yescharacteristic, complemented
168#2438C2212yes—
169#2438C2212yes—
170#2438C2214yescomplemented
171#2437C2214yes—
172#2437C2212yes—
173#2437C2214yes—
174#2437C2212yes—
175#2422C2212yes—
176#2422C2212yes—
177#2422C2212yes—
178#2422C2212yes—
179#2422C2212yes—
180#2422C2212yes—
181#2422C2212yes—
182#2422C2212yes—
183#2422C2212yes—
184#2422C2212yes—
185#2422C2212yes—
186#2422C2212yes—
187#2421C2214yescomplemented
188#2420C2212yes—
189#2420C2212yes—
190#2420C2212yes—
191#2420C2212yes—
192#2419C2214yescomplemented
193#2413C2214yescomplemented
194#2413C2214yescomplemented
195#2405C2214yes—
196#2401C2212yescomplemented
197#2401C2212yescomplemented
198#2396C2212yescomplemented
199#2396C2212yescomplemented
200C2×#397C2212yes—
201C2×#394C2212yes—
202#2363C2212yes—
203#2363C2212yes—
204#2361C2212yes—
205#2361C2212yes—
206#2360C2214yes—
207#2360C2214yes—
208#2360C2214yescomplemented
209#2359C2214yescomplemented
210#2357C2212yescomplemented
211#2357C2212yescomplemented
212#2357C2212yescomplemented
213#2357C2212yescomplemented
214#2357C2212yescomplemented
215#2357C2212yescomplemented
216#2355C2212yescomplemented
217#2355C2212yescomplemented
218#2354C2212yescomplemented
219#2354C2212yescomplemented
220#2354C2212yescomplemented
221#2354C2212yescomplemented
222#2354C2212yescomplemented
223#2354C2212yescomplemented
224Q8×C4⋊C4C2212yescomplemented
225Q8×C4⋊C4C2212yescomplemented
226#2349C2212yescomplemented
227#2349C2212yescomplemented
228#2349C2212yescomplemented
229#2349C2212yescomplemented
230D4×C4⋊C4C2212yescomplemented
231D4×C4⋊C4C2212yescomplemented
232D4×C4⋊C4C2212yescomplemented
233D4×C4⋊C4C2212yescomplemented
234#2347C2212yescomplemented
235#2346C2212yescomplemented
236#2345C2212yescomplemented
237#2344C2212yescomplemented
238#2343C2214yes—
239#2343C2214yescomplemented
240#2342C2214yes—
241#2342C2214yes—
242#2342C2214yes—
243#2342C2214yes—
244D4×C22⋊C4C2214yes—
245#2330C2212yescomplemented
246#2330C2212yescomplemented
247#2324C2212yes—
248#2324C2212yes—
249#2319C2212yescomplemented
250#2319C2212yescomplemented
251#2317C2211yescharacteristic
252#2317C2211yescharacteristic
253#2317C2211yescharacteristic
254#2317C2211yescharacteristic
255#2317C2211yescharacteristic
256#2317C2211yescharacteristic
257#2316C2211yescharacteristic
258#2316C2211yescharacteristic
259#2315C2214yes—
260#2314C2212yescomplemented
261#2314C2212yescomplemented
262#2312C2214yes—
263#2309C2211yescharacteristic
264#2309C2211yescharacteristic
265C4×C4⋊Q8C2212yescomplemented
266C4×C4⋊Q8C2212yescomplemented
267C4×#126C2212yescomplemented
268C4×#126C2212yescomplemented
269C4×C22⋊Q8C2212yescomplemented
270C4×C22⋊Q8C2212yescomplemented
271C4×#121C2212yes—
272C4×#121C2212yes—
273#2296C2211yescharacteristic
274#2296C2211yescharacteristic
275#2296C2211yescharacteristic
276#2296C2211yescharacteristic
277#2293C2212yescomplemented
278#2293C2212yescomplemented
279C2×#390C2211yescharacteristic
280C2×#389C2211yescharacteristic
281C2×#385C2212yes—
282C2×#385C2214yes—
283#2285C2211yescharacteristic
284#2285C2211yescharacteristic
285#2285C2212yescomplemented
286C2×#384C2211yescharacteristic
287#2283C2212yescomplemented
288#2280C2211yescharacteristic
289#2280C2214yes—
290#2280C2211yescharacteristic
291#2280C2211yescharacteristic
292C2×#380C2211yescharacteristic
293#2274C2211yescharacteristic
294#2274C2211yescharacteristic
295#2274C2211yescharacteristic
296#2274C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C23×D4C2311yescharacteristic
300C23×D4C2312yes—
301C24×C4C2311yescharacteristic
302C24×C4C2312yes—
303#552—416no—
304#533—28no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2311yescharacteristic
307C2×#126C2312yes—
308C2×#126C2312yes—
309C2×#126C2314yes—
310C2×#125C2311yescharacteristic
311C2×#125C2311yescharacteristic
312C2×#125C2314yes—
313C2×#125C2314yes—
314C2×#125C2314yes—
315C2×#125C2314yes—
316C2×#123—48no—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×C22⋊Q8C2312yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×#121—28no—
330C2×#121C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334#518—28no—
335#518—28no—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2314yes—
339C2×C4×Q8C2314yes—
340C2×C4×D4—28no—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×#117—28no—
356C2×#117C2311yescharacteristic
357C2×#117C2311yescharacteristic
358C2×#117C2311yescharacteristic
359C2×#117C2311yescharacteristic
360C2×#117C2312yes—
361C2×#117C2311yescharacteristic
362C2×#117C2311yescharacteristic
363C2×#117C2311yescharacteristic
364C2×#117C2312yes—
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2314yes—
368C2×#117C2314yes—
369C2×#117C2314yes—
370C2×#117C2314yes—
371C2×#117C2314yes—
372C2×#117C2311yescharacteristic
373C22×C4⋊C4C2311yescharacteristic
374C22×C4⋊C4C2311yescharacteristic
375C22×C4⋊C4C2311yescharacteristic
376C22×C4⋊C4C2311yescharacteristic
377C22×C4⋊C4C2311yescharacteristic
378C22×C4⋊C4C2314yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2314yes—
382C22×C4⋊C4C2312yes—
383C22×C22⋊C4C2312yes—
384C22×C22⋊C4C2314yes—
385C22×C22⋊C4C2314yes—
386C22×C22⋊C4C2312yes—
387C22×C22⋊C4C2312yes—
388C22×C22⋊C4C2311yescharacteristic
389C22×C22⋊C4C2312yes—
390C22×C22⋊C4C2312yes—
391C22×C22⋊C4C2312yes—
392C22×C22⋊C4C2311yescharacteristic
393C22×C42C2312yes—
394C22×C42C2311yescharacteristic
395C22×C42C2311yescharacteristic
396#401C2312yes—
397#401C2312yes—
398#401C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2312yes—
408#400C2312yes—
409#400C2312yes—
410#400C2312yes—
411#400C2312yes—
412#400C2312yes—
413#400C2312yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2312yes—
423#399C2312yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2312yes—
433#398C2312yes—
434#398C2312yes—
435#398C2312yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2312yes—
449#397C2312yes—
450#397C2312yes—
451#397C2312yes—
452#397C2312yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#396C2312yes—
460#396C2314yes—
461#396C2312yes—
462#396C2312yes—
463#396C2312yes—
464#396C2312yes—
465#396C2312yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#395C2312yes—
471#395C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2312yes—
483#393C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2314yes—
498#390C2314yes—
499#390C2312yes—
500#390C2312yes—
501#390C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2311yescharacteristic
530#389C2311yescharacteristic
531#389C2311yescharacteristic
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2311yescharacteristic
538#389C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
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#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#387C2312yes—
590#387C2312yes—
591#387C2312yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
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#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2312yes—
618#387C2314yes—
619#387C2314yes—
620#387C2312yes—
621#387C2312yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2312yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2312yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2312yes—
661#385C2312yes—
662#385C2312yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#384C2312yes—
667#384C2312yes—
668#384C2312yes—
669#384C2311yescharacteristic
670#384C2312yes—
671#384C2312yes—
672#384C2312yes—
673#384C2312yes—
674#384C2312yes—
675#384C2312yes—
676#384C2312yes—
677#384C2311yescharacteristic
678#384C2311yescharacteristic
679#384C2311yescharacteristic
680#383C2312yes—
681#383C2312yes—
682#383C2314yes—
683#383C2314yes—
684#382C2312yes—
685#382C2312yes—
686#382C2312yes—
687#382C2312yes—
688#382C2311yescharacteristic
689#382C2312yes—
690#382C2311yescharacteristic
691#382C2314yes—
692#382C2312yes—
693#382C2314yes—
694#382C2314yes—
695#382C2311yescharacteristic
696#382C2311yescharacteristic
697#381C2314yes—
698#381C2314yes—
699#381C2312yes—
700#381C2314yes—
701#381C2312yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#381C2314yes—
706#381C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2314yes—
710#380C2314yes—
711#380C2311yescharacteristic
712#380C2312yes—
713#380C2311yescharacteristic
714#380C2314yes—
715#380C2314yes—
716#380C2314yes—
717#380C2314yes—
718#380C2314yes—
719#380C2314yes—
720#380C2311yescharacteristic
721#380C2311yescharacteristic
722#380C2314yes—
723#380C2312yes—
724#380C2312yes—
725#380C2314yes—
726#380C2314yes—
727#380C2311yescharacteristic
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#380C2311yescharacteristic
732#380C2312yes—
733#380C2311yescharacteristic
734#380C2312yes—
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2311yescharacteristic
742#379C2314yes—
743#379C2314yes—
744#379C2312yes—
745#379C2312yes—
746#379C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2314yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809#376C2312yes—
810#376C2314yes—
811C2×#95C2312yes—
812C2×#95C2312yes—
813C2×#95C2314yes—
814C2×#95C2314yes—
815C2×#95C2311yescharacteristic
816C2×#95C2311yescharacteristic
817C43C2312yes—
818C25C2411yescharacteristic
819C25C2412yes—
820C22×Q8C2412yes—
821C22×Q8C2412yes—
822C22×D4—28no—
823C22×D4—24no—
824C22×D4—24no—
825C22×D4—44no—
826C22×D4—82no—
827C22×D4#4118yes—
828C22×D4C2414yes—
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2414yes—
832C23×C4—28no—
833C23×C4—24no—
834C23×C4—24no—
835C23×C4—24no—
836C23×C4—44no—
837C23×C4—82no—
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2411yescharacteristic
844C23×C4C2411yescharacteristic
845C23×C4C2411yescharacteristic
846C23×C4C2412yes—
847C23×C4C2414yes—
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2412yes—
851C23×C4C2412yes—
852C23×C4C2414yes—
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2412yes—
856C23×C4C2414yes—
857C23×C4C2414yes—
858C23×C4C2411yescharacteristic
859C4⋊Q8—24no—
860C4⋊Q8—24no—
861#126—28no—
862#126—44no—
863#126—48no—
864#125—24no—
865#125—24no—
866#125—48no—
867#125—48no—
868#125—48no—
869#125—84no—
870#123—216no—
871#123—48no—
872#123—48no—
873#123—48no—
874#123—48no—
875#123—84no—
876C22⋊Q8—28no—
877C22⋊Q8—28no—
878C22⋊Q8—28no—
879C22⋊Q8—48no—
880C22⋊Q8—44no—
881C22⋊Q8—48no—
882#121—28no—
883#121—28no—
884#121—28no—
885#121—28no—
886C4×Q8—28no—
887C4×Q8—28no—
888C4×Q8—48no—
889C4×Q8—84no—
890C4×D4—28no—
891C4×D4—28no—
892C4×D4—28no—
893C4×D4—28no—
894C4×D4—28no—
895C4×D4—28no—
896C4×D4—28no—
897C4×D4—28no—
898C4×D4—28no—
899C4×D4—28no—
900C4×D4—28no—
901C4×D4—28no—
902C4×D4—48no—
903C4×D4—84no—
904#117—24no—
905#117—24no—
906#117—24no—
907#117—24no—
908#117—24no—
909#117—24no—
910#117—24no—
911#117—24no—
912#117—24no—
913#117—28no—
914#117—28no—
915#117—48no—
916#117—48no—
917#117—48no—
918#117—48no—
919#117—84no—
920#117#4118yes—
921C2×C4⋊C4—24no—
922C2×C4⋊C4—24no—
923C2×C4⋊C4—24no—
924C2×C4⋊C4—24no—
925C2×C4⋊C4—24no—
926C2×C4⋊C4—44no—
927C2×C4⋊C4—44no—
928C2×C4⋊C4—48no—
929C2×C4⋊C4—84no—
930C2×C4⋊C4—82no—
931C2×C4⋊C4C2412yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2411yescharacteristic
934C2×C4⋊C4C2411yescharacteristic
935C2×C4⋊C4C2412yes—
936C2×C4⋊C4C2412yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2412yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C22⋊C4—28no—
1008C2×C22⋊C4—216no—
1009C2×C22⋊C4—28no—
1010C2×C22⋊C4—28no—
1011C2×C22⋊C4—216no—
1012C2×C22⋊C4—24no—
1013C2×C22⋊C4—44no—
1014C2×C22⋊C4—42no—
1015C2×C22⋊C4—44no—
1016C2×C22⋊C4—44no—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2411yescharacteristic
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C42—24no—
1070C2×C42—24no—
1071C2×C42—28no—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2411yescharacteristic
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2411yescharacteristic
1091C2×C42C2414yes—
1092C2×C42C2414yes—
1093C2×C42C2414yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102#95C2412yes—
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2411yescharacteristic
1109#95C2411yescharacteristic
1110#95C2411yescharacteristic
1111#95C2411yescharacteristic
1112#95C2411yescharacteristic
1113#95C2411yescharacteristic
1114#95C2411yescharacteristic
1115#95C2411yescharacteristic
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2412yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2414yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178C24—24no—
1179C24—24no—
1180C24—22no—
1181C24—22no—
1182C24—22no—
1183C24—22no—
1184C24—42no—
1185C24—42no—
1186C24—41no—
1187C24—42no—
1188C24—41no—
1189C24—42no—
1190C24—41no—
1191C24C2×#4118yes—
1192C24C2511yescharacteristic
1193C24C2514yes—
1194C24C2511yescharacteristic
1195C24C2511yescharacteristic
1196C2×Q8—24no—
1197C2×Q8—24no—
1198C2×Q8—24no—
1199C2×Q8—24no—
1200C2×Q8—42no—
1201C2×Q8—42no—
1202C2×D4—28no—
1203C2×D4—28no—
1204C2×D4—28no—
1205C2×D4—232no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—44no—
1211C2×D4—44no—
1212C2×D4—44no—
1213C2×D4—816no—
1214C2×D4C2×#4118yes—
1215C2×D4C2×#4118yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—28no—
1222C22×C4—24no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—24no—
1226C22×C4—24no—
1227C22×C4—28no—
1228C22×C4—28no—
1229C22×C4—28no—
1230C22×C4—24no—
1231C22×C4—22no—
1232C22×C4—24no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—28no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—24no—
1249C22×C4—28no—
1250C22×C4—28no—
1251C22×C4—41no—
1252C22×C4—44no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—42no—
1256C22×C4—42no—
1257C22×C4—42no—
1258C22×C4—42no—
1259C22×C4—41no—
1260C22×C4—42no—
1261C22×C4—44no—
1262C22×C4—44no—
1263C22×C4—44no—
1264C22×C4—44no—
1265C22×C4—42no—
1266C22×C4—44no—
1267C22×C4—42no—
1268C22×C4—44no—
1269C22×C4—42no—
1270C22×C4—42no—
1271C22×C4—44no—
1272C22×C4—44no—
1273C22×C4—44no—
1274C22×C4—44no—
1275C22×C4—41no—
1276C22×C4—416no—
1277C22×C4—816no—
1278C22×C4C2×#4114yes—
1279C22×C4C2×#4114yes—
1280C22×C42−1+414yes—
1281C22×C4C2511yescharacteristic
1282C22×C4C2511yescharacteristic
1283C22×C4C2512yes—
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2511yescharacteristic
1289C22×C4C2511yescharacteristic
1290C22×C4C2514yes—
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2514yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2514yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—24no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—22no—
1321C4⋊C4—22no—
1322C4⋊C4—22no—
1323C4⋊C4—22no—
1324C4⋊C4—22no—
1325C4⋊C4—22no—
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—28no—
1337C4⋊C4—28no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—24no—
1342C4⋊C4—24no—
1343C4⋊C4—24no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—44no—
1353C4⋊C4—44no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4C2×#4114yes—
1387C4⋊C4C2×#4114yes—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—28no—
1393C22⋊C4—28no—
1394C22⋊C4—28no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—28no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—28no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—28no—
1409C22⋊C4—28no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—28no—
1413C22⋊C4—28no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—44no—
1417C22⋊C4—41no—
1418C22⋊C4—41no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—44no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4C2×#4118yes—
1439C22⋊C4H(5,𝔽2)14yes—
1440C42—24no—
1441C42—24no—
1442C42—24no—
1443C42—22no—
1444C42—22no—
1445C42—22no—
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—22no—
1450C42—22no—
1451C42—24no—
1452C42—24no—
1453C42—24no—
1454C42—24no—
1455C42—24no—
1456C42—24no—
1457C42—24no—
1458C42—24no—
1459C42—42no—
1460C42—44no—
1461C42—44no—
1462C42—44no—
1463C42—44no—
1464C42—44no—
1465C42—44no—
1466C42—44no—
1467C42—44no—
1468C42—42no—
1469C42C2×#4118yes—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—24no—
1475C23—21no—
1476C23—21no—
1477C23—24no—
1478C23—21no—
1479C23—24no—
1480C23—24no—
1481C23—21no—
1482C23—24no—
1483C23—21no—
1484C23—21no—
1485C23—24no—
1486C23—216no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—48no—
1495C23—48no—
1496C23—44no—
1497C23—44no—
1498C23—44no—
1499C23—44no—
1500C23—84no—
1501C23—82no—
1502C23—82no—
1503C23—84no—
1504C23—84no—
1505C23—84no—
1506C23—82no—
1507C23C22×#4118yes—
1508C23C22×#4112yes—
1509C23C22×#4112yes—
1510C23C2×H(5,𝔽2)12yes—
1511C23C2×2−1+412yes—
1512C23C2611yescharacteristic
1513Q8—48no—
1514Q8—48no—
1515D4—216no—
1516D4—216no—
1517D4—416no—
1518D4—88no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—22no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—22no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—24no—
1548C2×C4—24no—
1549C2×C4—21no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—24no—
1556C2×C4—24no—
1557C2×C4—24no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—22no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—24no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—24no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—48no—
1602C2×C4—44no—
1603C2×C4—44no—
1604C2×C4—416no—
1605C2×C4—44no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—44no—
1609C2×C4—44no—
1610C2×C4—44no—
1611C2×C4—88no—
1612C2×C4—84no—
1613C2×C4—88no—
1614C2×C4—88no—
1615C2×C4—82no—
1616C2×C4—88no—
1617C2×C4—84no—
1618C2×C4—84no—
1619C2×C4—88no—
1620C2×C4—84no—
1621C2×C4#552116yescomplemented
1622C2×C4C22×#4114yes—
1623C2×C4C22×#4114yes—
1624C2×C4C22×#4112yes—
1625C2×C4C22×#4112yes—
1626C2×C4C22×#4112yes—
1627C2×C4C22×#4112yes—
1628C2×C4C2×H(5,𝔽2)12yes—
1629C2×C4C2×H(5,𝔽2)12yes—
1630C2×C4C2×2−1+412yes—
1631C2×C4C2×2−1+412yes—
1632C2×C4#58512yes—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—28no—
1640C22—22no—
1641C22—22no—
1642C22—28no—
1643C22—22no—
1644C22—28no—
1645C22—44no—
1646C22—41no—
1647C22—41no—
1648C22—44no—
1649C22—44no—
1650C22—41no—
1651C22—44no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—41no—
1657C22—41no—
1658C22—41no—
1659C22—41no—
1660C22—816no—
1661C22—88no—
1662C22C2×#55214yes—
1663C22C23×#4111yescharacteristic
1664C22C23×#4111yescharacteristic
1665C22C22×H(5,𝔽2)11yescharacteristic
1666C22C22×2−1+411yescharacteristic
1667C22C2×#58511yescharacteristic
1668C22H(7,𝔽2)11yescharacteristic
1669C222−1+611yescharacteristic
1670C4—22no—
1671C4—24no—
1672C4—22no—
1673C4—22no—
1674C4—24no—
1675C4—44no—
1676C4—41no—
1677C4—42no—
1678C4—42no—
1679C4—44no—
1680C4—42no—
1681C4—41no—
1682C4—42no—
1683C4—42no—
1684C4—41no—
1685C4—41no—
1686C4—42no—
1687C4—42no—
1688C4—41no—
1689C4—42no—
1690C4—42no—
1691C4—42no—
1692C4—42no—
1693C4—42no—
1694C4—44no—
1695C4—42no—
1696C4—42no—
1697C4—41no—
1698C4—41no—
1699C4C2×#55214yes—
1700C4C2×#55214yes—
1701C2—24no—
1702C2—48no—
1703C2—42no—
1704C2—81no—
1705C2C22×#55211yescharacteristic
1706C2#6283511yescharacteristic
1707C2#6287911yescharacteristic
1708C2#6298311yescharacteristic
1709C2#6298511yescharacteristic
1710C2#6299111yescharacteristic
1711C2#6300811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59503C2semidirect
2. #59500C2semidirect
3. #59498C2semidirect
4. #59497C2semidirect
5. #59285C2semidirect
6. #59264C2semidirect
7. #59260C2semidirect
8. #59258C2semidirect
9. #59219C2semidirect
10. #59012C2semidirect
11. #45206C2semidirect
12. #45191C2semidirect
13. #45181C2semidirect
14. #45050C2semidirect
15. #45030C2semidirect
16. #45012C2semidirect
17. #44910C2semidirect
18. #44910C2semidirect
19. #43076C2semidirect
20. #43051C2semidirect
21. #35585C2semidirect
22. #35555C2semidirect
23. #35544C2semidirect
24. #35543C2semidirect
26. #35515C2semidirect
27. #34814C2semidirect
28. #34739C2semidirect
30. #34255C2semidirect
31. #34248C2semidirect
32. #34214C2semidirect
34. #34186C2semidirect
35. #34180C2semidirect
36. C2×#552C22semidirect
44. #2779C22semidirect
45. #2779C22semidirect
46. #2771C22semidirect
47. #2771C22semidirect
48. #2770C22semidirect
49. #2770C22semidirect
50. #2765C22semidirect
51. #2765C22semidirect
52. #2765C22semidirect
53. #2764C22semidirect
54. #2761C22semidirect
55. #2747C22semidirect
56. #2743C22semidirect
57. #2741C22semidirect
58. #2739C22semidirect
59. #2738C22semidirect
60. #2707C22semidirect
61. #2702C22semidirect
62. #2695C22semidirect
63. #2695C22semidirect
64. #2694C22semidirect
65. #2694C22semidirect
66. #2690C22semidirect
67. #2687C22semidirect
68. #2611C22semidirect
69. #2601C22semidirect
70. #2599C22semidirect
71. #2599C22semidirect
72. #2580C22semidirect
73. #2580C22semidirect
74. #2577C22semidirect
75. #2571C22semidirect
76. #2570C22semidirect
77. #2570C22semidirect
78. #2570C22semidirect
79. #2570C22semidirect
81. #2558C22semidirect
82. #2553C22semidirect
83. #2552C22semidirect
84. #2552C22semidirect
85. #2552C22semidirect
86. #2538C22semidirect
87. #2538C22semidirect
88. #2536C22semidirect
89. #2530C22semidirect
90. #2527C22semidirect
91. #2515C22semidirect
92. #2509C22semidirect
93. #2509C22semidirect
94. #2509C22semidirect
95. #2508C22semidirect
96. #2508C22semidirect
97. #2508C22semidirect
98. #2507C22semidirect
99. #2507C22semidirect
100. #2507C22semidirect
101. #2507C22semidirect
102. #2507C22semidirect
103. #2506C22semidirect
104. #2506C22semidirect
105. #2506C22semidirect
106. #2506C22semidirect
107. #2506C22semidirect
109. #2498C22semidirect
110. #2497C22semidirect
111. #2497C22semidirect
112. #2497C22semidirect
113. #2497C22semidirect
114. #2496C22semidirect
115. #2496C22semidirect
116. #2496C22semidirect
117. #2496C22semidirect
118. #2495C22semidirect
119. #2495C22semidirect
120. #2495C22semidirect
121. #2495C22semidirect
122. #2494C22semidirect
123. #2494C22semidirect
124. #2494C22semidirect
125. #2494C22semidirect
126. #2494C22semidirect
130. #2493C22semidirect
131. #2493C22semidirect
132. #2488C22semidirect
133. #2486C22semidirect
134. #2485C22semidirect
139. #2477C22semidirect
140. #2475C22semidirect
141. #2475C22semidirect
142. #2475C22semidirect
146. #2473C22semidirect
147. #2473C22semidirect
148. #2470C22semidirect
149. #2470C22semidirect
150. #2468C22semidirect
151. #2460C22semidirect
152. #2458C22semidirect
153. #2458C22semidirect
154. #2454C22semidirect
155. #2454C22semidirect
156. #2452C22semidirect
157. #2452C22semidirect
159. #2442C22semidirect
160. #2442C22semidirect
161. #2442C22semidirect
162. #2441C22semidirect
163. #2441C22semidirect
164. #2440C22semidirect
165. #2440C22semidirect
166. #2439C22semidirect
167. #2439C22semidirect
170. #2438C22semidirect
187. #2421C22semidirect
192. #2419C22semidirect
193. #2413C22semidirect
194. #2413C22semidirect
196. #2401C22semidirect
197. #2401C22semidirect
198. #2396C22semidirect
199. #2396C22semidirect
208. #2360C22semidirect
209. #2359C22semidirect
210. #2357C22semidirect
211. #2357C22semidirect
212. #2357C22semidirect
213. #2357C22semidirect
214. #2357C22semidirect
215. #2357C22semidirect
216. #2355C22semidirect
217. #2355C22semidirect
218. #2354C22semidirect
219. #2354C22semidirect
220. #2354C22semidirect
221. #2354C22semidirect
222. #2354C22semidirect
223. #2354C22semidirect
224. Q8×C4⋊C4C22semidirect
225. Q8×C4⋊C4C22semidirect
226. #2349C22semidirect
227. #2349C22semidirect
228. #2349C22semidirect
229. #2349C22semidirect
230. D4×C4⋊C4C22semidirect
231. D4×C4⋊C4C22semidirect
232. D4×C4⋊C4C22semidirect
233. D4×C4⋊C4C22semidirect
234. #2347C22semidirect
235. #2346C22semidirect
236. #2345C22semidirect
237. #2344C22semidirect
239. #2343C22semidirect
245. #2330C22semidirect
246. #2330C22semidirect
249. #2319C22semidirect
250. #2319C22semidirect
260. #2314C22semidirect
261. #2314C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×#126C22semidirect
268. C4×#126C22semidirect
269. C4×C22⋊Q8C22semidirect
270. C4×C22⋊Q8C22semidirect
277. #2293C22semidirect
278. #2293C22semidirect
285. #2285C22semidirect
287. #2283C22semidirect
1621. C2×C4#552semidirect

Maximal subgroups

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

subgroupindex
#595032
#595002
#594982
#594972
#592852
#592642
#592602
#592582
#592192
#590122
#452062
#451912
#451812
#450502
#450302
#450122
#449102
#430762
#430512
#355852
#355552
#355442
#355432
#355402
#355152
#348142
#347392
C2×#24222
#342552
#342482
#342142
#342042
#341862
#341802