Finite Group Databasebeta

← #7681083

Subgroups — #7681083

Order 512.

4967 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C212yesmaximal, complemented
2#59935C212yesmaximal, complemented
3#59564C212yesmaximal, complemented
4#59564C212yesmaximal, complemented
5#59226C214yesmaximal, complemented
6#59225C214yesmaximal, complemented
7#45410C212yesmaximal, complemented
8#45384C212yesmaximal, complemented
9#45170C212yesmaximal, complemented
10#45170C212yesmaximal, complemented
11#43514C214yesmaximal, complemented
12#43056C214yesmaximal, complemented
13#38943C212yesmaximal, complemented
14#38937C212yesmaximal, complemented
15#38289C212yesmaximal, complemented
16#38287C212yesmaximal, complemented
17#38287C212yesmaximal, complemented
18#38284C212yesmaximal, complemented
19#36385C212yesmaximal, complemented
20#36288C212yesmaximal, complemented
21#35667C211yesmaximal, characteristic, complemented
22#35644C211yesmaximal, characteristic, complemented
23#35633C211yesmaximal, characteristic
24#35566C211yesmaximal, characteristic, complemented
25#35320C211yesmaximal, characteristic, complemented
26#35312C211yesmaximal, characteristic, complemented
27#35306C211yesmaximal, characteristic
28#34813C211yesmaximal, characteristic
29C2×#2429C211yesmaximal, characteristic, complemented
30#34266C211yesmaximal, characteristic, complemented
31#34254C211yesmaximal, characteristic, complemented
32#34253C211yesmaximal, characteristic, complemented
33#34203C211yesmaximal, characteristic, complemented
34#34109C211yesmaximal, characteristic, complemented
35#34059C211yesmaximal, characteristic, complemented
36C2×#544C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#533C2211yescharacteristic
40C22×C4⋊Q8C2211yescharacteristic
41C2×#525C2211yescharacteristic
42C22×C22⋊Q8C2211yescharacteristic
43C22×C22⋊Q8C2211yescharacteristic
44C2×#520C2211yescharacteristic
45C2×#519C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47C22×#117C2211yescharacteristic
48#2862C2212yescomplemented
49#2862C2212yescomplemented
50#2862C2212yescomplemented
51#2861C2212yescomplemented
52#2857C2212yes—
53#2850C2212yes—
54#2809C2214yescomplemented
55#2809C2214yescomplemented
56#2795C2214yes—
57#2785C2214yes—
58#2784C2214yes—
59#2783C2214yes—
60#2783C2214yes—
61#2783C2214yescomplemented
62#2783C2214yescomplemented
63#2781C2214yes—
64#2781C2214yes—
65#2775C2214yes—
66#2775C2214yes—
67#2775C2214yescomplemented
68#2775C2214yescomplemented
69#2769C2214yescomplemented
70#2769C2214yescomplemented
71#2769C2214yescomplemented
72#2769C2214yescomplemented
73#2744C2214yes—
74#2744C2214yes—
75#2744C2214yescomplemented
76#2744C2214yescomplemented
77#2731C2214yes—
78#2642C2212yescomplemented
79#2642C2212yescomplemented
80#2642C2212yescomplemented
81#2640C2212yescomplemented
82#2621C2212yes—
83#2620C2212yes—
84#2612C2214yescomplemented
85#2612C2214yescomplemented
86#2612C2214yescomplemented
87#2612C2214yescomplemented
88#2609C2214yes—
89#2593C2214yes—
90#2584C2212yescomplemented
91#2584C2212yescomplemented
92#2574C2214yes—
93#2574C2214yes—
94#2574C2214yescomplemented
95#2574C2214yescomplemented
96#2572C2214yes—
97#2571C2214yescomplemented
98#2568C2212yescomplemented
99#2568C2212yescomplemented
100#2568C2212yescomplemented
101#2568C2212yescomplemented
102#2567C2212yescomplemented
103#2561C2214yes—
104#2552C2212yescomplemented
105#2551C2212yescomplemented
106#2550C2212yescomplemented
107#2550C2212yescomplemented
108#2549C2214yes—
109#2546C2212yescomplemented
110#2546C2212yescomplemented
111#2546C2212yescomplemented
112#2545C2212yescomplemented
113#2545C2212yescomplemented
114#2534C2214yes—
115#2532C2214yes—
116#2532C2214yes—
117#2532C2214yescomplemented
118#2532C2214yescomplemented
119#2529C2214yes—
120#2529C2214yes—
121#2529C2214yescomplemented
122#2529C2214yescomplemented
123#2526C2214yes—
124#2526C2214yes—
125#2518C2214yes—
126#2518C2214yes—
127#2508C2214yescomplemented
128#2508C2214yescomplemented
129#2508C2214yescomplemented
130#2508C2214yescomplemented
131#2503C2214yes—
132#2503C2214yes—
133#2503C2214yes—
134#2497C2214yes—
135#2497C2214yescomplemented
136#2495C2214yes—
137#2495C2214yescomplemented
138#2492C2212yes—
139#2492C2212yes—
140#2492C2212yes—
141#2492C2212yes—
142#2492C2211yescharacteristic
143#2492C2211yescharacteristic
144#2492C2212yescomplemented
145#2492C2212yescomplemented
146#2491C2211yescharacteristic
147#2491C2211yescharacteristic
148#2490C2211yescharacteristic
149#2490C2211yescharacteristic
150#2489C2211yescharacteristic
151#2489C2212yes—
152#2489C2212yes—
153#2489C2212yes—
154#2489C2212yes—
155#2489C2211yescharacteristic
156#2489C2212yescomplemented
157#2489C2212yescomplemented
158#2488C2214yes—
159#2488C2212yes—
160#2488C2214yes—
161#2488C2212yes—
162#2486C2214yes—
163#2474C2214yes—
164#2474C2214yes—
165#2472C2212yes—
166#2472C2212yes—
167#2440C2214yes—
168#2439C2214yes—
169#2439C2214yescomplemented
170#2429C2212yes—
171#2429C2212yes—
172#2429C2212yes—
173#2429C2212yes—
174#2429C2212yes—
175#2429C2212yes—
176#2429C2212yes—
177#2429C2212yes—
178#2429C2212yes—
179#2429C2212yes—
180#2429C2212yescomplemented
181#2429C2212yescomplemented
182#2429C2212yescomplemented
183#2429C2212yescomplemented
184#2427C2212yes—
185#2427C2212yes—
186#2417C2212yes—
187#2417C2212yes—
188#2417C2212yes—
189#2417C2212yes—
190#2415C2212yes—
191#2415C2212yes—
192#2415C2212yes—
193#2415C2212yes—
194#2413C2214yes—
195#2413C2214yes—
196#2413C2214yes—
197#2412C2214yes—
198#2398C2212yes—
199#2398C2212yes—
200C2×#398C2212yes—
201C2×#396C2212yes—
202#2372C2214yes—
203#2369C2214yescomplemented
204#2367C2212yescomplemented
205#2367C2212yescomplemented
206#2365C2212yescomplemented
207#2365C2212yescomplemented
208#2362C2212yes—
209#2362C2212yes—
210#2362C2212yescomplemented
211#2362C2212yescomplemented
212#2360C2212yes—
213#2360C2212yes—
214#2360C2212yescomplemented
215#2360C2212yescomplemented
216#2356C2212yescomplemented
217#2356C2212yescomplemented
218#2355C2212yescomplemented
219#2355C2212yescomplemented
220#2353C2214yes—
221#2352C2214yes—
222#2347C2211yescharacteristic
223#2347C2211yescharacteristic
224#2347C2212yescomplemented
225#2346C2211yescharacteristic
226#2346C2211yescharacteristic
227#2346C2214yes—
228#2346C2214yescomplemented
229#2346C2212yescomplemented
230#2345C2211yescharacteristic
231#2345C2211yescharacteristic
232#2345C2212yescomplemented
233#2344C2211yescharacteristic
234#2344C2211yescharacteristic
235#2344C2214yes—
236#2344C2212yescomplemented
237#2343C2214yes—
238#2343C2212yes—
239#2343C2212yes—
240#2343C2214yes—
241#2342C2212yes—
242#2342C2214yes—
243#2342C2212yes—
244#2323C2212yes—
245#2323C2212yes—
246#2322C2214yes—
247#2320C2212yescomplemented
248#2320C2212yescomplemented
249#2320C2212yescomplemented
250#2320C2212yescomplemented
251#2320C2212yescomplemented
252#2320C2212yescomplemented
253#2320C2212yescomplemented
254#2319C2212yescomplemented
255#2317C2211yescharacteristic
256#2316C2211yescharacteristic
257#2316C2211yescharacteristic
258#2313C2214yes—
259#2311C2211yescharacteristic
260#2310C2211yescharacteristic
261#2310C2211yescharacteristic
262#2310C2211yescharacteristic
263#2310C2211yescharacteristic
264#2310C2211yescharacteristic
265C4×#124C2212yes—
266C4×#124C2212yes—
267C4×C22⋊Q8C2212yes—
268C4×C22⋊Q8C2212yes—
269C4×#123C2214yes—
270#2298C2212yes—
271#2298C2212yes—
272#2297C2211yescharacteristic
273#2297C2211yescharacteristic
274#2296C2211yescharacteristic
275#2296C2211yescharacteristic
276#2295C2212yescomplemented
277#2295C2212yescomplemented
278#2295C2212yescomplemented
279#2295C2212yescomplemented
280#2295C2212yescomplemented
281#2295C2212yescomplemented
282#2295C2212yescomplemented
283C2×#391C2211yescharacteristic
284#2293C2212yescomplemented
285C2×#389C2212yes—
286C2×#389C2211yescharacteristic
287C2×#388C2212yes—
288#2283C2214yes—
289#2283C2212yes—
290#2280C2211yescharacteristic
291#2280C2211yescharacteristic
292#2274C2211yescharacteristic
293#2274C2211yescharacteristic
294C4×#117C2211yescharacteristic
295C4×#117C2211yescharacteristic
296C4×#117C2212yes—
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C23×Q8C2311yescharacteristic
301C23×Q8C2311yescharacteristic
302C24×C4C2311yescharacteristic
303#544—44no—
304#536—28no—
305#536—44no—
306#533—44no—
307C2×C4⋊Q8—44no—
308C2×C4⋊Q8C2312yes—
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2314yes—
318C2×C4⋊Q8C2312yes—
319C2×#125C2312yes—
320C2×#125C2312yes—
321C2×#125C2311yescharacteristic
322C2×#125C2311yescharacteristic
323C2×#124C2312yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2312yes—
327#525—44no—
328C2×#123C2314yes—
329C2×#123C2312yes—
330C2×#123C2314yes—
331C2×C22⋊Q8—28no—
332C2×C22⋊Q8—44no—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2311yescharacteristic
352C2×#120C2312yes—
353#520—28no—
354#519—28no—
355C2×C4×Q8—28no—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2312yes—
364C2×C4×Q8C2312yes—
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×#117—28no—
372C2×#117C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2311yescharacteristic
375C2×#117C2311yescharacteristic
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2312yes—
379C2×#117C2314yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2311yescharacteristic
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C2×#117C2312yes—
386C2×#117C2314yes—
387C2×#117C2311yescharacteristic
388C22×C4⋊C4C2311yescharacteristic
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2311yescharacteristic
399C22×C22⋊C4C2312yes—
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2311yescharacteristic
402C22×C22⋊C4C2312yes—
403C22×C22⋊C4C2311yescharacteristic
404C22×C42C2312yes—
405C22×C42C2311yescharacteristic
406C22×C42C2312yes—
407C22×C42C2311yescharacteristic
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2312yes—
417#400C2314yes—
418#400C2314yes—
419#400C2312yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2312yes—
426#400C2314yes—
427#400C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2312yes—
451#397C2312yes—
452#397C2312yes—
453#397C2312yes—
454#397C2314yes—
455#397C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2312yes—
476#394C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2312yes—
484#393C2312yes—
485#393C2314yes—
486#393C2312yes—
487#393C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2312yes—
509#391C2314yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2312yes—
520#391C2311yescharacteristic
521#391C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2314yes—
526#391C2311yescharacteristic
527#391C2312yes—
528#391C2311yescharacteristic
529#390C2312yes—
530#390C2311yescharacteristic
531#390C2312yes—
532#390C2311yescharacteristic
533#390C2311yescharacteristic
534#390C2312yes—
535#390C2311yescharacteristic
536#389C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2311yescharacteristic
554#389C2311yescharacteristic
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2311yescharacteristic
560#389C2311yescharacteristic
561#389C2312yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2311yescharacteristic
567#389C2311yescharacteristic
568#389C2311yescharacteristic
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2314yes—
577#389C2312yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
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#387C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2312yes—
666#386C2314yes—
667#386C2312yes—
668#386C2312yes—
669#386C2314yes—
670#386C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2312yes—
676#385C2312yes—
677#385C2312yes—
678#385C2312yes—
679#385C2314yes—
680#384C2314yes—
681#384C2312yes—
682#383C2314yes—
683#383C2314yes—
684#383C2314yes—
685#383C2314yes—
686#383C2314yes—
687#383C2312yes—
688#383C2312yes—
689#382C2314yes—
690#382C2314yes—
691#382C2314yes—
692#382C2314yes—
693#382C2312yes—
694#382C2314yes—
695#382C2314yes—
696#382C2314yes—
697#382C2312yes—
698#382C2314yes—
699#382C2314yes—
700#382C2314yes—
701#382C2314yes—
702#382C2312yes—
703#382C2314yes—
704#382C2312yes—
705#382C2314yes—
706#382C2312yes—
707#381C2314yes—
708#381C2314yes—
709#381C2314yes—
710#381C2314yes—
711#381C2314yes—
712#381C2312yes—
713#381C2314yes—
714#381C2312yes—
715#381C2312yes—
716#381C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2314yes—
724#380C2314yes—
725#380C2311yescharacteristic
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#380C2314yes—
732#380C2311yescharacteristic
733#380C2311yescharacteristic
734#380C2311yescharacteristic
735#380C2311yescharacteristic
736#379C2312yes—
737#379C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2311yescharacteristic
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2314yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2314yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2314yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C22⋊C4C2314yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2312yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2314yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2311yescharacteristic
788C4×C22⋊C4C2311yescharacteristic
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2311yescharacteristic
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804#376C2312yes—
805#376C2312yes—
806#376C2312yes—
807#376C2312yes—
808#376C2312yes—
809#376C2314yes—
810#376C2314yes—
811#376C2314yes—
812#376C2314yes—
813#376C2314yes—
814C2×#95C2312yes—
815C2×#95C2311yescharacteristic
816C2×#95C2311yescharacteristic
817C2×#95C2312yes—
818C2×#95C2312yes—
819C43C2312yes—
820C43C2312yes—
821C43C2312yes—
822C25C2411yescharacteristic
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—24no—
826C22×Q8—24no—
827C22×Q8—24no—
828C22×Q8—24no—
829C22×Q8—24no—
830C22×Q8—24no—
831C22×Q8—24no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2412yes—
835C22×Q8C2412yes—
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×Q8C2412yes—
839C22×Q8C2414yes—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2412yes—
844C23×C4—24no—
845C23×C4—24no—
846C23×C4—24no—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2412yes—
852C23×C4C2411yescharacteristic
853C23×C4C2411yescharacteristic
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C4⋊Q8—28no—
866C4⋊Q8—42no—
867C4⋊Q8—42no—
868C4⋊Q8—44no—
869C4⋊Q8—44no—
870C4⋊Q8—44no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—44no—
875C4⋊Q8—48no—
876#125—42no—
877#125—42no—
878#125—44no—
879#125—44no—
880#124—28no—
881#124—28no—
882#124—44no—
883#124—44no—
884#123—216no—
885#123—44no—
886#123—48no—
887C22⋊Q8—28no—
888C22⋊Q8—28no—
889C22⋊Q8—28no—
890C22⋊Q8—28no—
891C22⋊Q8—28no—
892C22⋊Q8—28no—
893C22⋊Q8—44no—
894C22⋊Q8—44no—
895C22⋊Q8—48no—
896C22⋊Q8—44no—
897C22⋊Q8—44no—
898C22⋊Q8—44no—
899C22⋊Q8—44no—
900C22⋊Q8—42no—
901C22⋊Q8—42no—
902C22⋊Q8—44no—
903C22⋊Q8—44no—
904#121—42no—
905#121—42no—
906#120—44no—
907C4×Q8—28no—
908C4×Q8—28no—
909C4×Q8—28no—
910C4×Q8—28no—
911C4×Q8—28no—
912C4×Q8—28no—
913C4×Q8—28no—
914C4×Q8—28no—
915C4×Q8—28no—
916C4×Q8—44no—
917C4×Q8—44no—
918C4×D4—216no—
919C4×D4—28no—
920C4×D4—44no—
921C4×D4—44no—
922#117—24no—
923#117—24no—
924#117—24no—
925#117—24no—
926#117—24no—
927#117—24no—
928#117—24no—
929#117—24no—
930#117—28no—
931#117—28no—
932#117—216no—
933#117—28no—
934#117—28no—
935#117—44no—
936#117—48no—
937#117#4118yes—
938C2×C4⋊C4—28no—
939C2×C4⋊C4—28no—
940C2×C4⋊C4—24no—
941C2×C4⋊C4—24no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—28no—
944C2×C4⋊C4—44no—
945C2×C4⋊C4—44no—
946C2×C4⋊C4—44no—
947C2×C4⋊C4—44no—
948C2×C4⋊C4#4118yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2414yes—
957C2×C4⋊C4C2414yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2414yes—
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2414yes—
966C2×C4⋊C4C2414yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2414yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C22⋊C4—28no—
1014C2×C22⋊C4—28no—
1015C2×C22⋊C4—24no—
1016C2×C22⋊C4—42no—
1017C2×C22⋊C4—44no—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2411yescharacteristic
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2414yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2411yescharacteristic
1026C2×C22⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2411yescharacteristic
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2411yescharacteristic
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2411yescharacteristic
1066C2×C42—28no—
1067C2×C42—24no—
1068C2×C42—24no—
1069C2×C42—28no—
1070C2×C42C2412yes—
1071C2×C42C2412yes—
1072C2×C42C2412yes—
1073C2×C42C2412yes—
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2414yes—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2414yes—
1080C2×C42C2414yes—
1081C2×C42C2412yes—
1082C2×C42C2412yes—
1083C2×C42C2412yes—
1084C2×C42C2411yescharacteristic
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2411yescharacteristic
1090C2×C42C2414yes—
1091C2×C42C2414yes—
1092C2×C42C2412yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2414yes—
1097C2×C42C2412yes—
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2414yes—
1106C2×C42C2414yes—
1107C2×C42C2412yes—
1108#95C2411yescharacteristic
1109#95C2411yescharacteristic
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2411yescharacteristic
1114#95C2411yescharacteristic
1115#95C2411yescharacteristic
1116#95C2411yescharacteristic
1117#95C2411yescharacteristic
1118#95C2411yescharacteristic
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2414yes—
1124#95C2412yes—
1125#95C2412yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190C24—22no—
1191C24—22no—
1192C24—22no—
1193C24—22no—
1194C24—41no—
1195C24—41no—
1196C24—41no—
1197C24C2511yescharacteristic
1198C24C2512yes—
1199C24C2511yescharacteristic
1200C24C2511yescharacteristic
1201#41—416no—
1202C2×Q8—24no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—24no—
1206C2×Q8—22no—
1207C2×Q8—24no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—22no—
1212C2×Q8—24no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—24no—
1218C2×Q8—24no—
1219C2×Q8—42no—
1220C2×Q8—42no—
1221C2×Q8—42no—
1222C2×Q8—42no—
1223C2×Q8—44no—
1224C2×Q8—44no—
1225C2×Q8—44no—
1226C2×Q8—416no—
1227C2×Q8—416no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—42no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—24no—
1250C22×C4—22no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—24no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—22no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—22no—
1270C22×C4—22no—
1271C22×C4—22no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—28no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—42no—
1282C22×C4—41no—
1283C22×C4—42no—
1284C22×C4—44no—
1285C22×C4—42no—
1286C22×C4—44no—
1287C22×C4—42no—
1288C22×C4—41no—
1289C22×C4—42no—
1290C22×C4—416no—
1291C22×C4C2×#4118yes—
1292C22×C4C2×#4114yes—
1293C22×C4C2×#4114yes—
1294C22×C4H(5,𝔽2)14yes—
1295C22×C4C2511yescharacteristic
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2512yes—
1300C22×C4C2512yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C22×C4C2512yes—
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2514yes—
1313C22×C4C2514yes—
1314C22×C4C2514yes—
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2511yescharacteristic
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2514yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C4⋊C4—22no—
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—28no—
1333C4⋊C4—28no—
1334C4⋊C4—28no—
1335C4⋊C4—28no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—28no—
1340C4⋊C4—28no—
1341C4⋊C4—28no—
1342C4⋊C4—28no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—28no—
1354C4⋊C4—24no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—44no—
1358C4⋊C4—44no—
1359C4⋊C4—44no—
1360C4⋊C4—44no—
1361C4⋊C4—44no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—44no—
1380C4⋊C4—44no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4C2×#4118yes—
1387C4⋊C4C2×#4114yes—
1388C4⋊C4C2×#4114yes—
1389C4⋊C4C2×#4118yes—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—24no—
1396C22⋊C4—22no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—28no—
1402C22⋊C4—28no—
1403C22⋊C4—28no—
1404C22⋊C4—28no—
1405C22⋊C4—28no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—24no—
1413C22⋊C4—41no—
1414C22⋊C4—41no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4C2×#4118yes—
1437C22⋊C42−1+414yes—
1438C42—24no—
1439C42—24no—
1440C42—24no—
1441C42—22no—
1442C42—22no—
1443C42—28no—
1444C42—22no—
1445C42—22no—
1446C42—28no—
1447C42—28no—
1448C42—24no—
1449C42—24no—
1450C42—28no—
1451C42—28no—
1452C42—22no—
1453C42—22no—
1454C42—22no—
1455C42—22no—
1456C42—24no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—24no—
1461C42—24no—
1462C42—24no—
1463C42—42no—
1464C42—42no—
1465C42—44no—
1466C42—42no—
1467C42—42no—
1468C42—44no—
1469C42—42no—
1470C42—42no—
1471C42—44no—
1472C42—42no—
1473C42—42no—
1474C42—44no—
1475C42C2×#4118yes—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—22no—
1489C23—22no—
1490C23—21no—
1491C23—22no—
1492C23—22no—
1493C23—21no—
1494C23—22no—
1495C23—21no—
1496C23—22no—
1497C23—21no—
1498C23—22no—
1499C23—21no—
1500C23—44no—
1501C23—44no—
1502C23—44no—
1503C23—44no—
1504C23—82no—
1505C23—82no—
1506C23—82no—
1507C23C22×#4112yes—
1508C23C22×#4112yes—
1509C23C2×H(5,𝔽2)12yes—
1510C23C2×2−1+412yes—
1511C23C2611yescharacteristic
1512Q8—48no—
1513Q8—48no—
1514Q8—48no—
1515Q8—48no—
1516Q8—44no—
1517Q8—84no—
1518Q8—84no—
1519Q8—164no—
1520D4—48no—
1521D4—44no—
1522D4—84no—
1523D4—84no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—22no—
1529C2×C4—24no—
1530C2×C4—21no—
1531C2×C4—22no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—24no—
1535C2×C4—22no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—22no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—22no—
1546C2×C4—24no—
1547C2×C4—24no—
1548C2×C4—22no—
1549C2×C4—24no—
1550C2×C4—24no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—22no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—24no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—24no—
1568C2×C4—24no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—21no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—48no—
1606C2×C4—44no—
1607C2×C4—48no—
1608C2×C4—44no—
1609C2×C4—44no—
1610C2×C4—44no—
1611C2×C4—48no—
1612C2×C4—48no—
1613C2×C4—44no—
1614C2×C4—44no—
1615C2×C4—44no—
1616C2×C4—44no—
1617C2×C4—48no—
1618C2×C4—88no—
1619C2×C4—84no—
1620C2×C4—82no—
1621C2×C4—84no—
1622C2×C4#555116yes—
1623C2×C4C22×#4114yes—
1624C2×C4C22×#4114yes—
1625C2×C4C22×#4118yes—
1626C2×C4C22×#4112yes—
1627C2×C4C22×#4112yes—
1628C2×C4C22×#4112yes—
1629C2×C4C22×#4112yes—
1630C2×C4C2×H(5,𝔽2)12yes—
1631C2×C4C2×H(5,𝔽2)12yes—
1632C2×C4C2×2−1+412yes—
1633C2×C4C2×2−1+412yes—
1634C2×C4#58512yes—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—42no—
1649C22—41no—
1650C22—42no—
1651C22—41no—
1652C22—42no—
1653C22—41no—
1654C22—42no—
1655C22—41no—
1656C22—42no—
1657C22—41no—
1658C22—41no—
1659C22—42no—
1660C22—41no—
1661C22—42no—
1662C22—88no—
1663C22C2×#55514yes—
1664C22C23×#4111yescharacteristic
1665C22C23×#4111yescharacteristic
1666C22C22×H(5,𝔽2)11yescharacteristic
1667C22C22×2−1+411yescharacteristic
1668C22C2×#58511yescharacteristic
1669C222−1+611yescharacteristic
1670C222−1+611yescharacteristic
1671C4—28no—
1672C4—22no—
1673C4—24no—
1674C4—24no—
1675C4—22no—
1676C4—22no—
1677C4—41no—
1678C4—41no—
1679C4—42no—
1680C4—42no—
1681C4—41no—
1682C4—42no—
1683C4—42no—
1684C4—42no—
1685C4—42no—
1686C4—42no—
1687C4—41no—
1688C4—42no—
1689C4—42no—
1690C4—41no—
1691C4—44no—
1692C4—42no—
1693C4—42no—
1694C4—42no—
1695C4—41no—
1696C4—41no—
1697C4—42no—
1698C4—44no—
1699C4—44no—
1700C4C2×#55514yes—
1701C4C2×#55514yes—
1702C2—24no—
1703C2—42no—
1704C2—82no—
1705C2—81no—
1706C2C22×#55511yescharacteristic
1707C2#6280511yescharacteristic
1708C2#6286111yescharacteristic
1709C2#6294211yescharacteristic
1710C2#6295411yescharacteristic
1711C2#6299111yescharacteristic
1712C2#6299811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59951C2semidirect
2. #59935C2semidirect
3. #59564C2semidirect
4. #59564C2semidirect
5. #59226C2semidirect
6. #59225C2semidirect
7. #45410C2semidirect
8. #45384C2semidirect
9. #45170C2semidirect
10. #45170C2semidirect
11. #43514C2semidirect
12. #43056C2semidirect
13. #38943C2semidirect
14. #38937C2semidirect
15. #38289C2semidirect
16. #38287C2semidirect
17. #38287C2semidirect
18. #38284C2semidirect
19. #36385C2semidirect
20. #36288C2semidirect
21. #35667C2semidirect
22. #35644C2semidirect
24. #35566C2semidirect
25. #35320C2semidirect
26. #35312C2semidirect
29. C2×#2429C2semidirect
30. #34266C2semidirect
31. #34254C2semidirect
32. #34253C2semidirect
33. #34203C2semidirect
34. #34109C2semidirect
35. #34059C2semidirect
48. #2862C22semidirect
49. #2862C22semidirect
50. #2862C22semidirect
51. #2861C22semidirect
54. #2809C22semidirect
55. #2809C22semidirect
61. #2783C22semidirect
62. #2783C22semidirect
67. #2775C22semidirect
68. #2775C22semidirect
69. #2769C22semidirect
70. #2769C22semidirect
71. #2769C22semidirect
72. #2769C22semidirect
75. #2744C22semidirect
76. #2744C22semidirect
78. #2642C22semidirect
79. #2642C22semidirect
80. #2642C22semidirect
81. #2640C22semidirect
84. #2612C22semidirect
85. #2612C22semidirect
86. #2612C22semidirect
87. #2612C22semidirect
90. #2584C22semidirect
91. #2584C22semidirect
94. #2574C22semidirect
95. #2574C22semidirect
97. #2571C22semidirect
98. #2568C22semidirect
99. #2568C22semidirect
100. #2568C22semidirect
101. #2568C22semidirect
102. #2567C22semidirect
104. #2552C22semidirect
105. #2551C22semidirect
106. #2550C22semidirect
107. #2550C22semidirect
109. #2546C22semidirect
110. #2546C22semidirect
111. #2546C22semidirect
112. #2545C22semidirect
113. #2545C22semidirect
117. #2532C22semidirect
118. #2532C22semidirect
121. #2529C22semidirect
122. #2529C22semidirect
127. #2508C22semidirect
128. #2508C22semidirect
129. #2508C22semidirect
130. #2508C22semidirect
135. #2497C22semidirect
137. #2495C22semidirect
144. #2492C22semidirect
145. #2492C22semidirect
156. #2489C22semidirect
157. #2489C22semidirect
169. #2439C22semidirect
180. #2429C22semidirect
181. #2429C22semidirect
182. #2429C22semidirect
183. #2429C22semidirect
203. #2369C22semidirect
204. #2367C22semidirect
205. #2367C22semidirect
206. #2365C22semidirect
207. #2365C22semidirect
210. #2362C22semidirect
211. #2362C22semidirect
214. #2360C22semidirect
215. #2360C22semidirect
216. #2356C22semidirect
217. #2356C22semidirect
218. #2355C22semidirect
219. #2355C22semidirect
224. #2347C22semidirect
228. #2346C22semidirect
229. #2346C22semidirect
232. #2345C22semidirect
236. #2344C22semidirect
247. #2320C22semidirect
248. #2320C22semidirect
249. #2320C22semidirect
250. #2320C22semidirect
251. #2320C22semidirect
252. #2320C22semidirect
253. #2320C22semidirect
254. #2319C22semidirect
276. #2295C22semidirect
277. #2295C22semidirect
278. #2295C22semidirect
279. #2295C22semidirect
280. #2295C22semidirect
281. #2295C22semidirect
282. #2295C22semidirect
284. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#599512
#599352
#595642
#592262
#592252
#454102
#453842
#451702
#435142
#430562
#389432
#389372
#382892
#382872
#382842
#363852
#362882
#356672
#356442
#356332
#355662
#353202
#353122
#353062
#348132
C2×#24292
#342662
#342542
#342532
#342032
#341092
#340592