Finite Group Databasebeta

← #7692191

Subgroups — #7692191

Order 512.

5139 conjugacy classes of subgroups.

The subgroup lattice has 1702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59595C214yesmaximal, complemented
2#59563C212yesmaximal, complemented
3#59484C212yesmaximal, complemented
4#59450C211yesmaximal, characteristic, complemented
5#59382C212yesmaximal
6#59245C211yesmaximal, characteristic, complemented
7#59219C211yesmaximal, characteristic, complemented
8#59027C212yesmaximal, complemented
9#45371C212yesmaximal, complemented
10#45116C212yesmaximal, complemented
11#44823C214yesmaximal, complemented
12#44730C214yesmaximal, complemented
13#40178C212yesmaximal, complemented
14#40055C212yesmaximal, complemented
15#38967C211yesmaximal, characteristic, complemented
16#38911C211yesmaximal, characteristic, complemented
17#38559C214yesmaximal, complemented
18#37859C212yesmaximal, complemented
19#36561C211yesmaximal, characteristic, complemented
20#36555C211yesmaximal, characteristic, complemented
21#36516C212yesmaximal, complemented
22#36479C212yesmaximal, complemented
23#36314C211yesmaximal, characteristic, complemented
24#36301C212yesmaximal, complemented
25#36210C211yesmaximal, characteristic, complemented
26D4×C22⋊Q8C211yesmaximal, characteristic, complemented
27#35984C212yesmaximal, complemented
28#35738C212yesmaximal, complemented
29#34969C212yesmaximal, complemented
30#34700C211yesmaximal, characteristic
31#34311C211yesmaximal, characteristic, complemented
32#34243C211yesmaximal, characteristic, complemented
33#34203C212yesmaximal, complemented
34C4×#552C211yesmaximal, characteristic, complemented
35D4×#117C211yesmaximal, characteristic, complemented
36C2×#554C2212yescomplemented
37C2×#552C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C22×C22⋊Q8C2212yes—
41C2×#519C2212yescomplemented
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2864C2212yescomplemented
45#2864C2212yescomplemented
46#2859C2211yescharacteristic, complemented
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic, complemented
49#2857C2212yescomplemented
50#2855C2214yescomplemented
51#2848C2212yes—
52#2802C2214yescomplemented
53#2799C2214yescomplemented
54#2788C2214yes—
55#2788C2214yescomplemented
56#2771C2214yescomplemented
57#2765C2214yescomplemented
58#2758C2214yescomplemented
59#2750C2214yes—
60#2747C2214yescomplemented
61#2745C2214yes—
62#2743C2214yes—
63#2742C2214yescomplemented
64#2739C2214yes—
65#2739C2214yescomplemented
66#2739C2214yescomplemented
67#2736C2214yes—
68#2735C2214yes—
69#2698C2214yes—
70#2689C2214yescomplemented
71#2687C2214yes—
72#2687C2214yescomplemented
73#2655C2214yescomplemented
74#2634C2214yescomplemented
75#2628C2212yescomplemented
76#2625C2212yescomplemented
77#2611C2214yescomplemented
78#2608C2214yescomplemented
79#2607C2214yescomplemented
80#2598C2214yes—
81#2588C2214yescomplemented
82#2587C2214yescomplemented
83#2582C2211yescharacteristic, complemented
84#2578C2214yes—
85#2578C2214yes—
86#2575C2214yescomplemented
87#2575C2214yescomplemented
88#2574C2214yescomplemented
89#2572C2214yes—
90#2571C2211yescharacteristic, complemented
91#2571C2212yescomplemented
92#2568C2211yescharacteristic, complemented
93#2568C2212yescomplemented
94#2564C2214yescomplemented
95#2563C2212yes—
96#2562C2212yes—
97#2561C2214yes—
98#2556C2214yescomplemented
99#2556C2214yescomplemented
100#2551C2211yescharacteristic, complemented
101#2550C2212yescomplemented
102#2550C2212yescomplemented
103#2542C2211yescharacteristic
104#2538C2211yescharacteristic
105#2536C2212yescomplemented
106#2534C2214yes—
107#2533C2214yescomplemented
108#2530C2214yes—
109#2530C2214yescomplemented
110#2530C2214yescomplemented
111#2527C2214yescomplemented
112#2527C2214yescomplemented
113#2527C2214yescomplemented
114#2524C2214yescomplemented
115#2522C2214yescomplemented
116#2522C2214yescomplemented
117#2514C2212yescomplemented
118#2511C2212yescomplemented
119#2511C2212yescomplemented
120#2511C2212yescomplemented
121#2509C2212yescomplemented
122#2509C2212yescomplemented
123#2509C2212yescomplemented
124#2507C2212yescomplemented
125#2506C2212yescomplemented
126#2503C2212yescomplemented
127#2499C2212yes—
128#2497C2212yes—
129#2497C2212yescomplemented
130#2495C2212yes—
131#2495C2212yes—
132#2494C2212yes—
133#2494C2212yescomplemented
134#2494C2212yescomplemented
135#2494C2212yescomplemented
136#2494C2214yescomplemented
137#2492C2212yes—
138#2492C2212yescomplemented
139#2492C2212yescomplemented
140#2489C2212yescomplemented
141#2486C2212yescomplemented
142#2485C2212yes—
143#2485C2214yescomplemented
144#2480C2214yes—
145#2480C2212yes—
146#2477C2214yes—
147#2477C2214yes—
148#2477C2214yescomplemented
149#2477C2214yescomplemented
150#2477C2214yescomplemented
151#2475C2214yes—
152#2475C2214yescomplemented
153#2473C2214yescomplemented
154#2470C2214yescomplemented
155#2470C2214yescomplemented
156#2468C2212yes—
157#2465C2214yescomplemented
158#2465C2214yescomplemented
159#2457C2214yes—
160#2457C2212yes—
161#2454C2212yes—
162#2454C2211yescharacteristic
163#2454C2212yes—
164#2453C2212yescomplemented
165#2452C2212yes—
166#2452C2212yes—
167#2449C2214yes—
168#2447C2212yes—
169#2447C2212yes—
170#2447C2211yescharacteristic
171#2442C2211yescharacteristic
172#2442C2212yescomplemented
173#2440C2212yes—
174#2439C2212yes—
175#2439C2212yescomplemented
176#2437C2214yes—
177#2435C2211yescharacteristic
178#2427C2211yescharacteristic
179#2423C2212yescomplemented
180#2422C2212yes—
181#2421C2212yes—
182#2421C2212yescomplemented
183#2421C2212yescomplemented
184#2420C2211yescharacteristic
185#2420C2212yes—
186#2418C2212yes—
187#2418C2214yes—
188#2417C2212yes—
189#2417C2211yescharacteristic
190#2417C2212yescomplemented
191#2415C2212yes—
192#2415C2212yescomplemented
193#2409C2212yes—
194#2409C2212yescomplemented
195#2408C2211yescharacteristic
196#2401C2214yescomplemented
197#2398C2214yescomplemented
198#2395C2212yes—
199#2392C2212yes—
200#2373C2212yes—
201#2371C2212yescomplemented
202#2370C2212yescomplemented
203#2370C2211yescharacteristic, complemented
204#2370C2212yescomplemented
205#2369C2212yescomplemented
206#2367C2212yes—
207#2365C2212yescomplemented
208#2365C2211yescharacteristic, complemented
209#2362C2212yes—
210#2362C2212yes—
211#2362C2211yescharacteristic
212#2362C2212yes—
213#2362C2212yescomplemented
214#2362C2214yescomplemented
215#2360C2212yescomplemented
216#2360C2212yescomplemented
217#2360C2211yescharacteristic, complemented
218#2360C2212yescomplemented
219#2360C2212yescomplemented
220#2359C2212yes—
221#2359C2214yescomplemented
222#2357C2212yes—
223#2357C2212yes—
224#2356C2211yescharacteristic, complemented
225#2356C2212yescomplemented
226#2355C2211yescharacteristic, complemented
227#2354C2211yescharacteristic
228#2354C2212yes—
229#2354C2211yescharacteristic
230#2352C2212yes—
231#2352C2212yes—
232#2352C2211yescharacteristic
233#2352C2214yescomplemented
234#2352C2212yescomplemented
235Q8×C4⋊C4C2211yescharacteristic, complemented
236Q8×C4⋊C4C2211yescharacteristic, complemented
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2211yescharacteristic
239D4×C4⋊C4C2211yescharacteristic
240D4×C4⋊C4C2212yes—
241D4×C4⋊C4C2212yescomplemented
242#2347C2212yescomplemented
243#2346C2211yescharacteristic
244#2345C2212yescomplemented
245#2344C2212yes—
246#2344C2211yescharacteristic, complemented
247#2344C2214yescomplemented
248#2344C2214yescomplemented
249#2343C2212yescomplemented
250#2342C2214yes—
251#2342C2214yes—
252#2342C2214yes—
253Q8×C22⋊C4C2212yescomplemented
254D4×C22⋊C4C2212yes—
255D4×C22⋊C4C2212yes—
256#2334C2214yescomplemented
257#2323C2214yes—
258#2323C2214yes—
259#2323C2214yescomplemented
260#2323C2212yescomplemented
261#2316C2212yescomplemented
262#2314C2212yescomplemented
263#2310C2212yescomplemented
264C4×C4⋊Q8C2211yescharacteristic, complemented
265C4×C4⋊Q8C2212yescomplemented
266C4×#125C2211yescharacteristic, complemented
267C4×#125C2212yescomplemented
268C4×#126C2212yes—
269C4×#124C2211yescharacteristic
270C4×#124C2212yes—
271C4×C22⋊Q8C2211yescharacteristic
272C4×C22⋊Q8C2211yescharacteristic
273C4×C22⋊Q8C2211yescharacteristic, complemented
274C4×C22⋊Q8C2212yescomplemented
275C4×C22⋊Q8C2214yescomplemented
276C4×C22⋊Q8C2214yescomplemented
277C4×#123C2212yes—
278C4×#123C2214yescomplemented
279C4×#121C2211yescharacteristic
280C4×#121C2212yes—
281C4×#121C2212yes—
282C4×#120C2212yes—
283#2295C2212yescomplemented
284#2293C2211yescharacteristic
285#2293C2212yes—
286#2293C2212yes—
287#2290C2214yes—
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic, complemented
290#2280C2212yes—
291#2280C2212yes—
292#2274C2212yescomplemented
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2212yes—
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2212yescomplemented
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#554—48no—
303#552—28no—
304D4×Q8—28no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309#529—28no—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#125C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2311yescharacteristic
315C2×#125C2312yes—
316C2×#125C2314yes—
317C2×#124C2311yescharacteristic
318C2×#124C2311yescharacteristic
319C2×#123C2312yes—
320C2×#123C2312yes—
321C2×#123C2314yes—
322C2×C22⋊Q8—216no—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#120C2312yes—
341#519—48no—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2314yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2314yes—
351C2×C4×Q8C2312yes—
352C2×C4×D4—28no—
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×#117—48no—
371C2×#117C2312yes—
372C2×#117C2312yes—
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2311yescharacteristic
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2314yes—
380C2×#117C2314yes—
381C2×#117C2314yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2314yes—
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C22⋊C4C2314yes—
393C22×C22⋊C4C2312yes—
394C22×C22⋊C4C2314yes—
395C22×C42C2311yescharacteristic
396C22×C42C2311yescharacteristic
397C22×C42C2314yes—
398C22×C42C2312yes—
399#401C2314yes—
400#401C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2312yes—
424#399C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2312yes—
429#398C2312yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2312yes—
442#397C2312yes—
443#397C2312yes—
444#397C2312yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2312yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#396C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#394C2314yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2312yes—
467#394C2312yes—
468#394C2312yes—
469#394C2314yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#392C2312yes—
477#391C2312yes—
478#391C2314yes—
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2311yescharacteristic
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2314yes—
495#391C2312yes—
496#391C2314yes—
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2311yescharacteristic
500#390C2311yescharacteristic
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2311yescharacteristic
506#390C2311yescharacteristic
507#390C2311yescharacteristic
508#389C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2312yes—
537#389C2311yescharacteristic
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2311yescharacteristic
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2314yes—
550#389C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2312yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2312yes—
587#388C2314yes—
588#388C2312yes—
589#388C2312yes—
590#388C2314yes—
591#388C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2312yes—
622#387C2312yes—
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#387C2312yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#386C2312yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2312yes—
648#386C2312yes—
649#386C2312yes—
650#386C2312yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2312yes—
664#385C2312yes—
665#385C2312yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2312yes—
670#385C2312yes—
671#385C2312yes—
672#385C2312yes—
673#384C2311yescharacteristic
674#384C2312yes—
675#384C2312yes—
676#384C2311yescharacteristic
677#384C2312yes—
678#384C2311yescharacteristic
679#383C2312yes—
680#383C2314yes—
681#383C2314yes—
682#382C2312yes—
683#382C2311yescharacteristic
684#382C2312yes—
685#382C2312yes—
686#382C2312yes—
687#382C2312yes—
688#382C2312yes—
689#382C2311yescharacteristic
690#382C2314yes—
691#382C2312yes—
692#382C2312yes—
693#381C2314yes—
694#381C2314yes—
695#381C2314yes—
696#381C2314yes—
697#381C2312yes—
698#381C2314yes—
699#381C2312yes—
700#381C2314yes—
701#381C2312yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706#380C2314yes—
707#380C2314yes—
708#380C2312yes—
709#380C2314yes—
710#380C2312yes—
711#380C2312yes—
712#380C2314yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2312yes—
717#380C2314yes—
718#380C2311yescharacteristic
719#380C2312yes—
720#380C2312yes—
721#380C2311yescharacteristic
722#380C2312yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2312yes—
726#380C2314yes—
727#380C2312yes—
728#380C2312yes—
729#380C2311yescharacteristic
730#380C2312yes—
731#379C2312yes—
732#379C2314yes—
733#379C2314yes—
734#379C2312yes—
735#379C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2314yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2314yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2311yescharacteristic
780C4×C22⋊C4C2311yescharacteristic
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810#376C2312yes—
811#376C2312yes—
812#376C2314yes—
813#376C2312yes—
814C2×#95C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C25C2412yes—
819C22×Q8—28no—
820C22×Q8—28no—
821C22×Q8—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2414yes—
825C22×Q8C2411yescharacteristic
826C22×Q8C2414yes—
827C22×D4—24no—
828C22×D4—24no—
829C22×D4—42no—
830C22×D4C2411yescharacteristic
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C23×C4—28no—
837C23×C4—28no—
838C23×C4—44no—
839C23×C4C2411yescharacteristic
840C23×C4C2412yes—
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2414yes—
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2411yescharacteristic
848C23×C4C2412yes—
849C23×C4C2412yes—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2414yes—
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2412yes—
856C4⋊Q8—28no—
857C4⋊Q8—24no—
858C4⋊Q8—44no—
859C4⋊Q8—44no—
860#126—28no—
861#126—28no—
862#125—24no—
863#125—28no—
864#125—24no—
865#125—44no—
866#125—48no—
867#124—24no—
868#124—24no—
869#123—28no—
870#123—28no—
871#123—48no—
872C22⋊Q8—28no—
873C22⋊Q8—24no—
874C22⋊Q8—28no—
875C22⋊Q8—28no—
876C22⋊Q8—28no—
877C22⋊Q8—216no—
878C22⋊Q8—24no—
879C22⋊Q8—216no—
880C22⋊Q8—216no—
881C22⋊Q8—48no—
882C22⋊Q8—48no—
883C22⋊Q8—42no—
884C22⋊Q8—44no—
885C22⋊Q8—44no—
886C22⋊Q8#4118yes—
887#121—24no—
888#121—24no—
889#120—44no—
890C4×Q8—24no—
891C4×Q8—24no—
892C4×Q8—28no—
893C4×Q8—24no—
894C4×Q8—24no—
895C4×Q8—48no—
896C4×Q8—48no—
897C4×Q8—44no—
898C4×Q8—44no—
899C4×Q8—44no—
900C4×D4—24no—
901C4×D4—28no—
902C4×D4—28no—
903C4×D4—28no—
904C4×D4—28no—
905C4×D4—24no—
906C4×D4—24no—
907C4×D4—28no—
908C4×D4—24no—
909C4×D4—44no—
910C4×D4—44no—
911C4×D4—42no—
912C4×D4—48no—
913C4×D4—44no—
914C4×D4—42no—
915C4×D4—48no—
916C4×D4#4118yes—
917#117—28no—
918#117—24no—
919#117—28no—
920#117—24no—
921#117—28no—
922#117—44no—
923#117—48no—
924#117—48no—
925#117—48no—
926#117—48no—
927#117—44no—
928#117—44no—
929#117—44no—
930#117—44no—
931C2×C4⋊C4—24no—
932C2×C4⋊C4—28no—
933C2×C4⋊C4—216no—
934C2×C4⋊C4—24no—
935C2×C4⋊C4—28no—
936C2×C4⋊C4—24no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4C2411yescharacteristic
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2411yescharacteristic
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2411yescharacteristic
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C22⋊C4—28no—
1009C2×C22⋊C4—216no—
1010C2×C22⋊C4—48no—
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2414yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2411yescharacteristic
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2414yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C42—24no—
1062C2×C42—24no—
1063C2×C42—48no—
1064C2×C42—44no—
1065C2×C42C2412yes—
1066C2×C42C2411yescharacteristic
1067C2×C42C2412yes—
1068C2×C42C2414yes—
1069C2×C42C2412yes—
1070C2×C42C2411yescharacteristic
1071C2×C42C2414yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2414yes—
1088C2×C42C2414yes—
1089C2×C42C2414yes—
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2412yes—
1093C2×C42C2414yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2411yescharacteristic
1103#95C2412yes—
1104#95C2412yes—
1105#95C2412yes—
1106#95C2412yes—
1107#95C2411yescharacteristic
1108#95C2411yescharacteristic
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2411yescharacteristic
1123#95C2412yes—
1124#95C2414yes—
1125#95C2414yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2412yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2414yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179C24—24no—
1180C24—24no—
1181C24—24no—
1182C24—42no—
1183C24—42no—
1184C24—42no—
1185C24—42no—
1186C24C2511yescharacteristic
1187C24C2512yes—
1188C24C2512yes—
1189C24C2511yescharacteristic
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—28no—
1193C2×Q8—24no—
1194C2×Q8—28no—
1195C2×Q8—24no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—22no—
1199C2×Q8—22no—
1200C2×Q8—44no—
1201C2×Q8—44no—
1202C2×Q8—44no—
1203C2×Q8—44no—
1204C2×Q8—432no—
1205C2×Q8C2×#4114yes—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—22no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—24no—
1212C2×D4—22no—
1213C2×D4—24no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—42no—
1219C2×D4—41no—
1220C2×D4—42no—
1221C2×D4—42no—
1222C2×D4—416no—
1223C2×D4C2×#4114yes—
1224C2×D42−1+414yes—
1225C22×C4—22no—
1226C22×C4—24no—
1227C22×C4—22no—
1228C22×C4—24no—
1229C22×C4—24no—
1230C22×C4—28no—
1231C22×C4—24no—
1232C22×C4—22no—
1233C22×C4—24no—
1234C22×C4—28no—
1235C22×C4—22no—
1236C22×C4—22no—
1237C22×C4—22no—
1238C22×C4—22no—
1239C22×C4—24no—
1240C22×C4—28no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—22no—
1244C22×C4—24no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—28no—
1256C22×C4—28no—
1257C22×C4—24no—
1258C22×C4—42no—
1259C22×C4—42no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—44no—
1263C22×C4—41no—
1264C22×C4—432no—
1265C22×C4—44no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—41no—
1271C22×C4—44no—
1272C22×C4—44no—
1273C22×C4—42no—
1274C22×C4—41no—
1275C22×C4C2×#4118yes—
1276C22×C4C2×#4114yes—
1277C22×C4C2511yescharacteristic
1278C22×C4C2511yescharacteristic
1279C22×C4C2511yescharacteristic
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2511yescharacteristic
1283C22×C4C2511yescharacteristic
1284C22×C4C2512yes—
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2514yes—
1289C22×C4C2512yes—
1290C22×C4C2512yes—
1291C22×C4C2511yescharacteristic
1292C22×C4C2512yes—
1293C22×C4C2514yes—
1294C22×C4C2514yes—
1295C22×C4C2514yes—
1296C22×C4C2512yes—
1297C22×C4C2511yescharacteristic
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2512yes—
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C4⋊C4—22no—
1309C4⋊C4—24no—
1310C4⋊C4—22no—
1311C4⋊C4—28no—
1312C4⋊C4—24no—
1313C4⋊C4—28no—
1314C4⋊C4—28no—
1315C4⋊C4—28no—
1316C4⋊C4—24no—
1317C4⋊C4—22no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—24no—
1321C4⋊C4—22no—
1322C4⋊C4—24no—
1323C4⋊C4—24no—
1324C4⋊C4—22no—
1325C4⋊C4—24no—
1326C4⋊C4—22no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—28no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—28no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—28no—
1341C4⋊C4—24no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—44no—
1347C4⋊C4—42no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—44no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—41no—
1361C4⋊C4—41no—
1362C4⋊C4—44no—
1363C4⋊C4—42no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4C2×#4114yes—
1375C4⋊C4C2×#4118yes—
1376C4⋊C4C2×#4114yes—
1377C4⋊C4H(5,𝔽2)14yes—
1378C22⋊C4—24no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—24no—
1382C22⋊C4—24no—
1383C22⋊C4—28no—
1384C22⋊C4—24no—
1385C22⋊C4—22no—
1386C22⋊C4—28no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—22no—
1391C22⋊C4—28no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—22no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—44no—
1403C22⋊C4—44no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—44no—
1407C22⋊C4—42no—
1408C22⋊C4—42no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—44no—
1412C22⋊C4—44no—
1413C22⋊C4—41no—
1414C22⋊C4—41no—
1415C22⋊C4—41no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—44no—
1421C22⋊C4—42no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—44no—
1426C22⋊C4C2×#4118yes—
1427C22⋊C4C2×#4118yes—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—22no—
1432C42—22no—
1433C42—22no—
1434C42—24no—
1435C42—24no—
1436C42—24no—
1437C42—22no—
1438C42—24no—
1439C42—24no—
1440C42—28no—
1441C42—24no—
1442C42—22no—
1443C42—28no—
1444C42—24no—
1445C42—24no—
1446C42—22no—
1447C42—24no—
1448C42—24no—
1449C42—22no—
1450C42—42no—
1451C42—42no—
1452C42—44no—
1453C42—44no—
1454C42—42no—
1455C42—42no—
1456C42—41no—
1457C42—44no—
1458C42—42no—
1459C42—42no—
1460C42—44no—
1461C42—44no—
1462C42—44no—
1463C42—41no—
1464C42—44no—
1465C42C2×#4114yes—
1466C23—22no—
1467C23—21no—
1468C23—21no—
1469C23—22no—
1470C23—22no—
1471C23—21no—
1472C23—22no—
1473C23—21no—
1474C23—21no—
1475C23—22no—
1476C23—21no—
1477C23—21no—
1478C23—22no—
1479C23—21no—
1480C23—22no—
1481C23—22no—
1482C23—21no—
1483C23—22no—
1484C23—22no—
1485C23—21no—
1486C23—22no—
1487C23—22no—
1488C23—21no—
1489C23—21no—
1490C23—48no—
1491C23—48no—
1492C23—48no—
1493C23—84no—
1494C23—84no—
1495C23—84no—
1496C23—84no—
1497C23C22×#4112yes—
1498C23C22×#4114yes—
1499C23C2×2−1+414yes—
1500C23#58512yes—
1501C23C2611yescharacteristic
1502Q8—28no—
1503Q8—416no—
1504Q8—48no—
1505Q8—44no—
1506Q8—164no—
1507D4—28no—
1508D4—28no—
1509D4—48no—
1510D4—48no—
1511D4—44no—
1512D4—48no—
1513C2×C4—21no—
1514C2×C4—22no—
1515C2×C4—22no—
1516C2×C4—21no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—21no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—28no—
1526C2×C4—216no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—22no—
1533C2×C4—21no—
1534C2×C4—22no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—24no—
1540C2×C4—22no—
1541C2×C4—24no—
1542C2×C4—21no—
1543C2×C4—24no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—24no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—24no—
1552C2×C4—24no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—22no—
1560C2×C4—21no—
1561C2×C4—22no—
1562C2×C4—24no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—24no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—24no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—48no—
1597C2×C4—44no—
1598C2×C4—48no—
1599C2×C4—48no—
1600C2×C4—48no—
1601C2×C4—416no—
1602C2×C4—44no—
1603C2×C4—48no—
1604C2×C4—44no—
1605C2×C4—44no—
1606C2×C4—82no—
1607C2×C4—88no—
1608C2×C4—88no—
1609C2×C4—84no—
1610C2×C4—88no—
1611C2×C4C22×#4112yes—
1612C2×C4C22×#4112yes—
1613C2×C4C22×#4114yes—
1614C2×C4C22×#4114yes—
1615C2×C4C22×#4114yes—
1616C2×C4C22×#4112yes—
1617C2×C4C22×#4112yes—
1618C2×C4C22×#4112yes—
1619C2×C4C2×H(5,𝔽2)14yes—
1620C2×C4C2×H(5,𝔽2)12yes—
1621C2×C4C2×2−1+412yes—
1622C2×C4#58512yes—
1623C22—22no—
1624C22—24no—
1625C22—22no—
1626C22—24no—
1627C22—24no—
1628C22—22no—
1629C22—24no—
1630C22—24no—
1631C22—22no—
1632C22—22no—
1633C22—24no—
1634C22—22no—
1635C22—41no—
1636C22—42no—
1637C22—41no—
1638C22—42no—
1639C22—42no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—42no—
1644C22—42no—
1645C22—41no—
1646C22—42no—
1647C22—42no—
1648C22—41no—
1649C22—42no—
1650C22—41no—
1651C22—816no—
1652C22C23×#4111yescharacteristic
1653C22C23×#4111yescharacteristic
1654C22C22×H(5,𝔽2)11yescharacteristic
1655C22C22×2−1+411yescharacteristic
1656C22C2×#58511yescharacteristic
1657C22C2×#58511yescharacteristic
1658C222−1+611yescharacteristic
1659C4—22no—
1660C4—24no—
1661C4—24no—
1662C4—22no—
1663C4—24no—
1664C4—24no—
1665C4—42no—
1666C4—41no—
1667C4—41no—
1668C4—42no—
1669C4—41no—
1670C4—42no—
1671C4—41no—
1672C4—44no—
1673C4—42no—
1674C4—42no—
1675C4—41no—
1676C4—41no—
1677C4—42no—
1678C4—42no—
1679C4—44no—
1680C4—41no—
1681C4—41no—
1682C4—44no—
1683C4—42no—
1684C4—42no—
1685C4—41no—
1686C4—42no—
1687C4—44no—
1688C4#348114yes—
1689C4#349514yes—
1690C2—42no—
1691C2—44no—
1692C2—44no—
1693C2—42no—
1694C2C2×#348111yescharacteristic
1695C2C2×#349511yescharacteristic
1696C2#6281611yescharacteristic
1697C2#6292111yescharacteristic
1698C2#6299311yescharacteristic
1699C2#6299811yescharacteristic
1700C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2408C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59595C2semidirect
2. #59563C2semidirect
3. #59484C2semidirect
4. #59450C2semidirect
6. #59245C2semidirect
7. #59219C2semidirect
8. #59027C2semidirect
9. #45371C2semidirect
10. #45116C2semidirect
11. #44823C2semidirect
12. #44730C2semidirect
13. #40178C2semidirect
14. #40055C2semidirect
15. #38967C2semidirect
16. #38911C2semidirect
17. #38559C2semidirect
18. #37859C2semidirect
19. #36561C2semidirect
20. #36555C2semidirect
21. #36516C2semidirect
22. #36479C2semidirect
23. #36314C2semidirect
24. #36301C2semidirect
25. #36210C2semidirect
26. D4×C22⋊Q8C2semidirect
27. #35984C2semidirect
28. #35738C2semidirect
29. #34969C2semidirect
31. #34311C2semidirect
32. #34243C2semidirect
33. #34203C2semidirect
34. C4×#552C2semidirect
35. D4×#117C2semidirect
36. C2×#554C22semidirect
41. C2×#519C22semidirect
44. #2864C22semidirect
45. #2864C22semidirect
46. #2859C22semidirect
48. #2857C22semidirect
49. #2857C22semidirect
50. #2855C22semidirect
52. #2802C22semidirect
53. #2799C22semidirect
55. #2788C22semidirect
56. #2771C22semidirect
57. #2765C22semidirect
58. #2758C22semidirect
60. #2747C22semidirect
63. #2742C22semidirect
65. #2739C22semidirect
66. #2739C22semidirect
70. #2689C22semidirect
72. #2687C22semidirect
73. #2655C22semidirect
74. #2634C22semidirect
75. #2628C22semidirect
76. #2625C22semidirect
77. #2611C22semidirect
78. #2608C22semidirect
79. #2607C22semidirect
81. #2588C22semidirect
82. #2587C22semidirect
83. #2582C22semidirect
86. #2575C22semidirect
87. #2575C22semidirect
88. #2574C22semidirect
90. #2571C22semidirect
91. #2571C22semidirect
92. #2568C22semidirect
93. #2568C22semidirect
94. #2564C22semidirect
98. #2556C22semidirect
99. #2556C22semidirect
100. #2551C22semidirect
101. #2550C22semidirect
102. #2550C22semidirect
105. #2536C22semidirect
107. #2533C22semidirect
109. #2530C22semidirect
110. #2530C22semidirect
111. #2527C22semidirect
112. #2527C22semidirect
113. #2527C22semidirect
114. #2524C22semidirect
115. #2522C22semidirect
116. #2522C22semidirect
117. #2514C22semidirect
118. #2511C22semidirect
119. #2511C22semidirect
120. #2511C22semidirect
121. #2509C22semidirect
122. #2509C22semidirect
123. #2509C22semidirect
124. #2507C22semidirect
125. #2506C22semidirect
126. #2503C22semidirect
129. #2497C22semidirect
133. #2494C22semidirect
134. #2494C22semidirect
135. #2494C22semidirect
136. #2494C22semidirect
138. #2492C22semidirect
139. #2492C22semidirect
140. #2489C22semidirect
141. #2486C22semidirect
143. #2485C22semidirect
148. #2477C22semidirect
149. #2477C22semidirect
150. #2477C22semidirect
152. #2475C22semidirect
153. #2473C22semidirect
154. #2470C22semidirect
155. #2470C22semidirect
157. #2465C22semidirect
158. #2465C22semidirect
164. #2453C22semidirect
172. #2442C22semidirect
175. #2439C22semidirect
179. #2423C22semidirect
182. #2421C22semidirect
183. #2421C22semidirect
190. #2417C22semidirect
192. #2415C22semidirect
194. #2409C22semidirect
196. #2401C22semidirect
197. #2398C22semidirect
201. #2371C22semidirect
202. #2370C22semidirect
203. #2370C22semidirect
204. #2370C22semidirect
205. #2369C22semidirect
207. #2365C22semidirect
208. #2365C22semidirect
213. #2362C22semidirect
214. #2362C22semidirect
215. #2360C22semidirect
216. #2360C22semidirect
217. #2360C22semidirect
218. #2360C22semidirect
219. #2360C22semidirect
221. #2359C22semidirect
224. #2356C22semidirect
225. #2356C22semidirect
226. #2355C22semidirect
233. #2352C22semidirect
234. #2352C22semidirect
235. Q8×C4⋊C4C22semidirect
236. Q8×C4⋊C4C22semidirect
241. D4×C4⋊C4C22semidirect
242. #2347C22semidirect
244. #2345C22semidirect
246. #2344C22semidirect
247. #2344C22semidirect
248. #2344C22semidirect
249. #2343C22semidirect
253. Q8×C22⋊C4C22semidirect
256. #2334C22semidirect
259. #2323C22semidirect
260. #2323C22semidirect
261. #2316C22semidirect
262. #2314C22semidirect
263. #2310C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×#125C22semidirect
267. C4×#125C22semidirect
273. C4×C22⋊Q8C22semidirect
274. C4×C22⋊Q8C22semidirect
275. C4×C22⋊Q8C22semidirect
276. C4×C22⋊Q8C22semidirect
278. C4×#123C22semidirect
283. #2295C22semidirect
289. #2285C22semidirect
292. #2274C22semidirect
293. C42×Q8C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#595952
#595632
#594842
#594502
#593822
#592452
#592192
#590272
#453712
#451162
#448232
#447302
#401782
#400552
#389672
#389112
#385592
#378592
#365612
#365552
#365162
#364792
#363142
#363012
#362102
D4×C22⋊Q82
#359842
#357382
#349692
#347002
#343112
#342432
#342032
C4×#5522
D4×#1172