Finite Group Databasebeta

← #7690037

Subgroups — #7690037

Order 512.

5361 conjugacy classes of subgroups.

The subgroup lattice has 1765 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59949C214yesmaximal, complemented
2#59894C212yesmaximal, complemented
3#59863C211yesmaximal, characteristic, complemented
4#59854C212yesmaximal, complemented
5#59234C211yesmaximal, characteristic, complemented
6#59227C211yesmaximal, characteristic, complemented
7#59224C212yesmaximal, complemented
8#59224C212yesmaximal, complemented
9#45402C212yesmaximal, complemented
10#44909C212yesmaximal, complemented
11#44464C214yesmaximal, complemented
12#43222C214yesmaximal, complemented
13#39506C211yesmaximal, characteristic, complemented
14#39503C212yesmaximal, complemented
15#38941C211yesmaximal, characteristic, complemented
16#38939C212yesmaximal, complemented
17#38291C212yesmaximal, complemented
18#38280C214yesmaximal, complemented
19#36302C211yesmaximal, characteristic, complemented
20#36261C211yesmaximal, characteristic, complemented
21#36258C211yesmaximal, characteristic, complemented
22#36258C211yesmaximal, characteristic, complemented
23#36257C212yesmaximal, complemented
24#36238C212yesmaximal, complemented
25#36211C211yesmaximal, characteristic, complemented
26#36176C212yesmaximal, complemented
27#36009C212yesmaximal, complemented
28#35847C212yesmaximal, complemented
29#34800C211yesmaximal, characteristic, complemented
30C2×#2513C212yesmaximal, complemented
31#34310C211yesmaximal, characteristic, complemented
32#34261C212yesmaximal, complemented
33#34191C211yesmaximal, characteristic, complemented
34C4×#547C211yesmaximal, characteristic, complemented
35#34127C211yesmaximal, characteristic, complemented
36C2×#554C2212yes—
37C2×#547C2211yescharacteristic
38C2×#546C2212yes—
39C2×#546C2212yes—
40C2×D42C2211yescharacteristic
41C2×#518C2212yes—
42C2×C4×#41C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2861C2212yescomplemented
45#2859C2211yescharacteristic, complemented
46#2857C2212yescomplemented
47#2856C2211yescharacteristic
48#2856C2211yescharacteristic
49#2854C2212yes—
50#2854C2212yes—
51#2850C2214yescomplemented
52#2808C2214yescomplemented
53#2808C2214yescomplemented
54#2803C2214yescomplemented
55#2803C2214yescomplemented
56#2803C2214yescomplemented
57#2785C2214yescomplemented
58#2783C2214yescomplemented
59#2783C2214yescomplemented
60#2783C2214yescomplemented
61#2781C2214yescomplemented
62#2781C2214yescomplemented
63#2775C2214yescomplemented
64#2775C2214yescomplemented
65#2756C2214yescomplemented
66#2756C2214yescomplemented
67#2744C2214yescomplemented
68#2737C2214yescomplemented
69#2737C2214yescomplemented
70#2737C2214yescomplemented
71#2733C2214yescomplemented
72#2686C2214yescomplemented
73#2640C2212yescomplemented
74#2639C2214yescomplemented
75#2621C2212yescomplemented
76#2617C2214yescomplemented
77#2610C2214yescomplemented
78#2610C2214yescomplemented
79#2593C2214yescomplemented
80#2592C2212yescomplemented
81#2592C2212yescomplemented
82#2591C2214yescomplemented
83#2584C2212yescomplemented
84#2583C2214yescomplemented
85#2574C2214yescomplemented
86#2571C2212yescomplemented
87#2563C2212yescomplemented
88#2563C2212yescomplemented
89#2562C2212yescomplemented
90#2561C2214yescomplemented
91#2561C2214yescomplemented
92#2552C2211yescharacteristic, complemented
93#2551C2211yescharacteristic, complemented
94#2550C2212yescomplemented
95#2549C2214yescomplemented
96#2548C2211yescharacteristic
97#2548C2211yescharacteristic
98#2547C2212yescomplemented
99#2547C2212yescomplemented
100#2543C2214yescomplemented
101#2538C2211yescharacteristic
102#2538C2211yescharacteristic
103#2535C2212yescomplemented
104#2532C2214yescomplemented
105#2532C2214yescomplemented
106#2532C2212yescomplemented
107#2531C2214yescomplemented
108#2531C2214yescomplemented
109#2531C2214yescomplemented
110#2529C2214yescomplemented
111#2529C2214yescomplemented
112#2526C2214yescomplemented
113#2526C2212yescomplemented
114#2518C2212yescomplemented
115#2518C2214yescomplemented
116#2513C2212yes—
117#2513C2212yes—
118#2513C2212yes—
119#2513C2212yes—
120#2513C2211yescharacteristic
121#2513C2212yescomplemented
122#2513C2214yescomplemented
123#2513C2212yescomplemented
124#2513C2212yescomplemented
125#2513C2214yescomplemented
126#2513C2214yescomplemented
127#2513C2212yescomplemented
128#2513C2214yescomplemented
129#2513C2212yescomplemented
130#2513C2212yescomplemented
131#2508C2212yescomplemented
132#2508C2211yescharacteristic, complemented
133#2508C2212yescomplemented
134#2504C2214yescomplemented
135#2500C2212yes—
136#2500C2211yescharacteristic
137#2500C2212yescomplemented
138#2497C2211yescharacteristic, complemented
139#2495C2212yescomplemented
140#2495C2214yescomplemented
141#2492C2212yescomplemented
142#2491C2212yes—
143#2491C2211yescharacteristic
144#2491C2212yescomplemented
145#2491C2212yescomplemented
146#2490C2212yescomplemented
147#2490C2212yescomplemented
148#2490C2212yescomplemented
149#2489C2212yescomplemented
150#2489C2212yescomplemented
151#2489C2212yescomplemented
152#2488C2214yescomplemented
153#2488C2214yescomplemented
154#2488C2214yescomplemented
155#2488C2214yescomplemented
156#2486C2214yescomplemented
157#2485C2214yescomplemented
158#2485C2211yescharacteristic, complemented
159#2476C2214yescomplemented
160#2474C2214yescomplemented
161#2474C2214yescomplemented
162#2472C2214yescomplemented
163#2472C2214yescomplemented
164#2472C2214yescomplemented
165#2472C2214yescomplemented
166#2459C2212yescomplemented
167#2440C2212yescomplemented
168#2440C2212yescomplemented
169#2439C2211yescharacteristic, complemented
170#2427C2212yescomplemented
171#2427C2212yescomplemented
172#2426C2212yes—
173#2426C2212yes—
174#2425C2214yescomplemented
175#2425C2214yescomplemented
176#2424C2214yes—
177#2424C2214yes—
178#2420C2212yescomplemented
179#2420C2212yescomplemented
180#2420C2212yescomplemented
181#2416C2212yes—
182#2416C2212yes—
183#2415C2212yescomplemented
184#2415C2212yescomplemented
185#2414C2211yescharacteristic
186#2414C2212yes—
187#2414C2212yes—
188#2414C2212yescomplemented
189#2414C2212yescomplemented
190#2412C2214yescomplemented
191#2412C2214yescomplemented
192#2411C2214yes—
193#2411C2214yes—
194#2408C2212yes—
195#2408C2212yes—
196#2398C2212yescomplemented
197#2392C2212yescomplemented
198C2×#397C2214yescomplemented
199C2×#397C2214yescomplemented
200#2369C2212yescomplemented
201#2366C2211yescharacteristic
202#2365C2211yescharacteristic, complemented
203#2363C2212yes—
204#2363C2212yescomplemented
205#2363C2212yescomplemented
206#2363C2212yescomplemented
207#2362C2211yescharacteristic, complemented
208#2362C2211yescharacteristic, complemented
209#2361C2212yes—
210#2361C2212yescomplemented
211#2359C2212yescomplemented
212#2359C2212yescomplemented
213#2358C2214yes—
214#2357C2212yescomplemented
215#2355C2211yescharacteristic, complemented
216#2355C2211yescharacteristic, complemented
217#2355C2211yescharacteristic, complemented
218#2355C2211yescharacteristic, complemented
219#2354C2211yescharacteristic
220#2354C2212yescomplemented
221#2354C2212yescomplemented
222#2354C2211yescharacteristic, complemented
223#2354C2212yescomplemented
224#2353C2214yescomplemented
225#2352C2212yescomplemented
226#2352C2212yescomplemented
227#2352C2212yescomplemented
228#2352C2214yescomplemented
229#2352C2212yescomplemented
230#2349C2212yes—
231D4×C4⋊C4C2211yescharacteristic
232D4×C4⋊C4C2211yescharacteristic
233D4×C4⋊C4C2211yescharacteristic
234D4×C4⋊C4C2211yescharacteristic
235#2347C2212yescomplemented
236#2347C2212yescomplemented
237#2346C2214yescomplemented
238#2346C2212yescomplemented
239#2346C2212yescomplemented
240#2346C2212yescomplemented
241#2344C2212yescomplemented
242#2343C2214yescomplemented
243#2343C2214yescomplemented
244#2342C2214yescomplemented
245#2342C2214yescomplemented
246#2339C2211yescharacteristic
247#2339C2212yes—
248#2339C2211yescharacteristic
249#2339C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252D4×C22⋊C4C2212yes—
253D4×C22⋊C4C2212yes—
254#2324C2212yes—
255#2321C2214yes—
256#2320C2212yescomplemented
257#2319C2212yescomplemented
258#2318C2214yescomplemented
259#2318C2214yescomplemented
260#2314C2212yescomplemented
261#2312C2214yescomplemented
262C4×C4⋊Q8C2211yescharacteristic, complemented
263C4×C4⋊Q8C2211yescharacteristic, complemented
264C4×#127C2211yescharacteristic
265C4×#124C2212yescomplemented
266C4×C22⋊Q8C2211yescharacteristic, complemented
267C4×C22⋊Q8C2211yescharacteristic, complemented
268C4×#123C2212yescomplemented
269C4×#123C2212yescomplemented
270C4×#121C2212yes—
271C4×#121C2211yescharacteristic
272C4×#121C2211yescharacteristic
273C4×#121C2212yescomplemented
274#2298C2212yescomplemented
275#2295C2212yescomplemented
276#2293C2211yescharacteristic
277#2293C2212yescomplemented
278C2×#390C2212yes—
279C2×#390C2212yes—
280C2×#390C2212yes—
281C2×#389C2212yescomplemented
282#2290C2214yescomplemented
283#2290C2214yescomplemented
284C2×#388C2214yescomplemented
285C2×#388C2214yescomplemented
286#2285C2211yescharacteristic, complemented
287#2285C2211yescharacteristic, complemented
288#2283C2211yescharacteristic, complemented
289#2283C2212yescomplemented
290#2283C2212yescomplemented
291C2×#382C2212yescomplemented
292#2275C2212yes—
293C42×D4C2211yescharacteristic
294C42×D4C2212yes—
295C42×D4C2211yescharacteristic, complemented
296C4×#117C2211yescharacteristic, complemented
297C2×C4×C4⋊C4C2212yescomplemented
298C2×C4×C4⋊C4C2212yescomplemented
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C23×D4C2312yes—
302C23×D4C2312yes—
303#554—48no—
304#547—28no—
305#546—48no—
306#546—48no—
307D42—28no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×#127C2311yescharacteristic
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#124C2312yes—
316C2×#124C2312yes—
317C2×#124C2312yes—
318C2×#124C2314yes—
319C2×#124C2314yes—
320C2×#123C2312yes—
321C2×#123C2312yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×C22⋊Q8C2311yescharacteristic
325C2×C22⋊Q8C2311yescharacteristic
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2312yes—
340C2×#121C2314yes—
341C2×#121C2311yescharacteristic
342C2×#121C2311yescharacteristic
343C2×#121C2312yes—
344C2×#120C2314yes—
345C2×#120C2314yes—
346C2×#120C2314yes—
347#518—216no—
348C4×#41—28no—
349C4×#41—28no—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C2×#117C2311yescharacteristic
390C2×#117C2314yes—
391C2×#117C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2314yes—
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C22⋊C4C2314yes—
399C22×C22⋊C4C2314yes—
400C22×C22⋊C4C2314yes—
401C22×C22⋊C4C2314yes—
402C22×C22⋊C4C2314yes—
403C22×C22⋊C4C2314yes—
404C22×C22⋊C4C2314yes—
405C22×C42C2312yes—
406C22×C42C2312yes—
407C22×C42C2311yescharacteristic
408C22×C42C2311yescharacteristic
409C22×C42C2312yes—
410C22×C42C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2312yes—
417#400C2312yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2312yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2312yes—
436#397C2312yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2312yes—
448#396C2314yes—
449#396C2312yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#393C2312yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#393C2314yes—
484#393C2312yes—
485#392C2314yes—
486#392C2314yes—
487#392C2312yes—
488#392C2314yes—
489#391C2311yescharacteristic
490#391C2311yescharacteristic
491#391C2312yes—
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2314yes—
500#391C2314yes—
501#391C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2312yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2312yes—
510#390C2312yes—
511#390C2314yes—
512#390C2312yes—
513#390C2312yes—
514#390C2314yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2312yes—
518#390C2312yes—
519#390C2312yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2314yes—
527#390C2312yes—
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2314yes—
532#390C2312yes—
533#390C2311yescharacteristic
534#390C2314yes—
535#390C2311yescharacteristic
536#390C2311yescharacteristic
537#389C2312yes—
538#389C2312yes—
539#389C2311yescharacteristic
540#389C2312yes—
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2312yes—
544#389C2314yes—
545#389C2311yescharacteristic
546#389C2312yes—
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2311yescharacteristic
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2311yescharacteristic
560#389C2312yes—
561#389C2312yes—
562#389C2311yescharacteristic
563#389C2314yes—
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2314yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2312yes—
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#388C2314yes—
590#388C2312yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2312yes—
603#388C2312yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2314yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2312yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2312yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2312yes—
649#387C2312yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2312yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2312yes—
663#386C2314yes—
664#386C2314yes—
665#386C2312yes—
666#386C2312yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2312yes—
672#386C2312yes—
673#385C2312yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2312yes—
681#385C2312yes—
682#385C2312yes—
683#384C2311yescharacteristic
684#384C2311yescharacteristic
685#384C2311yescharacteristic
686#384C2312yes—
687#384C2311yescharacteristic
688#384C2311yescharacteristic
689#383C2314yes—
690#383C2314yes—
691#383C2312yes—
692#383C2314yes—
693#382C2311yescharacteristic
694#382C2312yes—
695#382C2312yes—
696#382C2312yes—
697#382C2312yes—
698#382C2314yes—
699#382C2312yes—
700#382C2314yes—
701#382C2314yes—
702#382C2314yes—
703#382C2312yes—
704#382C2314yes—
705#382C2312yes—
706#382C2314yes—
707#382C2312yes—
708#382C2311yescharacteristic
709#381C2312yes—
710#381C2312yes—
711#381C2314yes—
712#381C2314yes—
713#381C2312yes—
714#381C2314yes—
715#381C2314yes—
716#380C2311yescharacteristic
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2314yes—
724#380C2312yes—
725#380C2314yes—
726#380C2312yes—
727#380C2312yes—
728#380C2314yes—
729#380C2312yes—
730#380C2312yes—
731#380C2311yescharacteristic
732#380C2312yes—
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2311yescharacteristic
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2314yes—
739#380C2311yescharacteristic
740#379C2314yes—
741#379C2314yes—
742#379C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2314yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2314yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2312yes—
793C4×C22⋊C4C2311yescharacteristic
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805#376C2312yes—
806#376C2312yes—
807#376C2314yes—
808#376C2314yes—
809#376C2314yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C2×#95C2312yes—
814C2×#95C2312yes—
815C2×#95C2314yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C25C2414yes—
819C2×#41—24no—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2411yescharacteristic
827C22×Q8C2412yes—
828C22×Q8C2414yes—
829C22×D4—28no—
830C22×D4—28no—
831C22×D4—28no—
832C22×D4—28no—
833C22×D4—44no—
834C22×D4—44no—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2414yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2411yescharacteristic
852C23×C4C2411yescharacteristic
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2411yescharacteristic
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2414yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2414yes—
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C4⋊Q8—24no—
869C4⋊Q8—44no—
870C4⋊Q8—42no—
871C4⋊Q8—44no—
872#127—24no—
873#125—44no—
874#125—44no—
875#124—44no—
876#124—44no—
877#124—44no—
878#124—84no—
879#124—84no—
880#123—28no—
881#123—28no—
882#123—48no—
883#123—48no—
884C22⋊Q8—24no—
885C22⋊Q8—24no—
886C22⋊Q8—48no—
887C22⋊Q8—48no—
888C22⋊Q8—48no—
889C22⋊Q8—44no—
890C22⋊Q8—44no—
891#121—28no—
892#121—28no—
893#121—28no—
894#121—44no—
895#121—44no—
896#121—44no—
897#121—42no—
898#121—42no—
899#121—44no—
900#121—44no—
901#121—48no—
902#121—48no—
903#121—82no—
904#120—216no—
905#120—48no—
906#120—48no—
907C4×Q8—24no—
908C4×Q8—24no—
909C4×Q8—24no—
910C4×Q8—24no—
911C4×Q8—44no—
912C4×D4—24no—
913C4×D4—24no—
914C4×D4—28no—
915C4×D4—28no—
916C4×D4—28no—
917C4×D4—24no—
918C4×D4—28no—
919C4×D4—28no—
920C4×D4—216no—
921C4×D4—28no—
922C4×D4—28no—
923C4×D4—28no—
924C4×D4—216no—
925C4×D4—28no—
926C4×D4—24no—
927C4×D4—24no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—42no—
931C4×D4—44no—
932C4×D4—44no—
933C4×D4—42no—
934C4×D4—82no—
935C4×D4#4118yes—
936C4×D4#4118yes—
937#117—24no—
938#117—24no—
939#117—28no—
940#117—28no—
941#117—28no—
942#117—28no—
943#117—48no—
944#117—42no—
945#117—42no—
946#117—44no—
947#117—82no—
948#117—84no—
949C2×C4⋊C4—28no—
950C2×C4⋊C4—44no—
951C2×C4⋊C4—44no—
952C2×C4⋊C4—44no—
953C2×C4⋊C4—44no—
954C2×C4⋊C4—48no—
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2414yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C22⋊C4—216no—
1013C2×C22⋊C4—216no—
1014C2×C22⋊C4—48no—
1015C2×C22⋊C4—48no—
1016C2×C22⋊C4—48no—
1017C2×C22⋊C4—84no—
1018C2×C22⋊C4—84no—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2414yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2414yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2414yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2411yescharacteristic
1036C2×C22⋊C4C2411yescharacteristic
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2411yescharacteristic
1069C2×C22⋊C4C2411yescharacteristic
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C42—28no—
1086C2×C42—28no—
1087C2×C42—24no—
1088C2×C42—24no—
1089C2×C42—44no—
1090C2×C42—84no—
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2414yes—
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2412yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2414yes—
1116C2×C42C2414yes—
1117C2×C42C2414yes—
1118C2×C42C2414yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127#95C2412yes—
1128#95C2412yes—
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2412yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2411yescharacteristic
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2411yescharacteristic
1173#95C2411yescharacteristic
1174#95C2411yescharacteristic
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193C24—28no—
1194C24—28no—
1195C24—28no—
1196C24—44no—
1197C24—44no—
1198C24—44no—
1199C24—44no—
1200C24C2512yes—
1201C24C2514yes—
1202C24C2511yescharacteristic
1203C24C2511yescharacteristic
1204C24C2512yes—
1205#41—416no—
1206#41—416no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×Q8—44no—
1219C2×D4—28no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—28no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—28no—
1228C2×D4—24no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—28no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—24no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—42no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—432no—
1259C2×D4—816no—
1260C2×D4C2×#4114yes—
1261C2×D4C2×#4114yes—
1262C2×D4H(5,𝔽2)14yes—
1263C22×C4—24no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—24no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—24no—
1273C22×C4—28no—
1274C22×C4—28no—
1275C22×C4—28no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—24no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—28no—
1297C22×C4—28no—
1298C22×C4—42no—
1299C22×C4—42no—
1300C22×C4—42no—
1301C22×C4—41no—
1302C22×C4—42no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—42no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4—41no—
1317C22×C4—41no—
1318C22×C4C2×#4118yes—
1319C22×C4C2×#4118yes—
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2511yescharacteristic
1323C22×C4C2511yescharacteristic
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2512yes—
1336C22×C4C2512yes—
1337C22×C4C2512yes—
1338C22×C4C2514yes—
1339C22×C4C2514yes—
1340C22×C4C2512yes—
1341C22×C4C2511yescharacteristic
1342C22×C4C2512yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2511yescharacteristic
1345C22×C4C2512yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C22×C4C2511yescharacteristic
1350C4⋊C4—22no—
1351C4⋊C4—24no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—22no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—22no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—42no—
1380C4⋊C4—44no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—41no—
1394C4⋊C4—42no—
1395C4⋊C4—42no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—42no—
1405C4⋊C4C2×#4114yes—
1406C4⋊C4C2×#4114yes—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—28no—
1412C22⋊C4—24no—
1413C22⋊C4—28no—
1414C22⋊C4—24no—
1415C22⋊C4—24no—
1416C22⋊C4—28no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—24no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—28no—
1424C22⋊C4—24no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—28no—
1428C22⋊C4—22no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—41no—
1454C22⋊C4—41no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—41no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—42no—
1465C22⋊C4—44no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4C2×#4118yes—
1472C22⋊C4C2×#4118yes—
1473C42—22no—
1474C42—22no—
1475C42—24no—
1476C42—24no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—24no—
1481C42—22no—
1482C42—24no—
1483C42—24no—
1484C42—24no—
1485C42—28no—
1486C42—24no—
1487C42—24no—
1488C42—24no—
1489C42—22no—
1490C42—22no—
1491C42—24no—
1492C42—24no—
1493C42—22no—
1494C42—42no—
1495C42—42no—
1496C42—42no—
1497C42—44no—
1498C42—44no—
1499C42—44no—
1500C42—44no—
1501C42—44no—
1502C42—42no—
1503C42—42no—
1504C42—44no—
1505C42—41no—
1506C42—41no—
1507C42C2×#4114yes—
1508C42C2×#4114yes—
1509C23—22no—
1510C23—22no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—24no—
1519C23—22no—
1520C23—24no—
1521C23—22no—
1522C23—24no—
1523C23—21no—
1524C23—21no—
1525C23—22no—
1526C23—21no—
1527C23—24no—
1528C23—21no—
1529C23—21no—
1530C23—21no—
1531C23—24no—
1532C23—24no—
1533C23—21no—
1534C23—21no—
1535C23—22no—
1536C23—22no—
1537C23—21no—
1538C23—22no—
1539C23—24no—
1540C23—21no—
1541C23—416no—
1542C23—88no—
1543C23—88no—
1544C23—88no—
1545C23—88no—
1546C23—88no—
1547C23—88no—
1548C23C22×#4114yes—
1549C23C22×#4114yes—
1550C23C2×H(5,𝔽2)14yes—
1551C23C2611yescharacteristic
1552Q8—44no—
1553Q8—44no—
1554Q8—84no—
1555Q8—164no—
1556D4—44no—
1557D4—416no—
1558D4—48no—
1559D4—48no—
1560D4—48no—
1561D4—48no—
1562D4—44no—
1563D4—84no—
1564D4—88no—
1565D4—84no—
1566D4—84no—
1567D4—164no—
1568D4—164no—
1569D4#555116yes—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—22no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—216no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—24no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—22no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—24no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—24no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—22no—
1649C2×C4—48no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—48no—
1653C2×C4—48no—
1654C2×C4—48no—
1655C2×C4—44no—
1656C2×C4—44no—
1657C2×C4—44no—
1658C2×C4—44no—
1659C2×C4—82no—
1660C2×C4—88no—
1661C2×C4—88no—
1662C2×C4—84no—
1663C2×C4—88no—
1664C2×C4—88no—
1665C2×C4—88no—
1666C2×C4—84no—
1667C2×C4C22×#4114yes—
1668C2×C4C22×#4112yes—
1669C2×C4C22×#4114yes—
1670C2×C4C22×#4112yes—
1671C2×C4C22×#4112yes—
1672C2×C4C22×#4112yes—
1673C2×C4C22×#4112yes—
1674C2×C4C22×#4112yes—
1675C2×C4C2×H(5,𝔽2)12yes—
1676C2×C4#58512yes—
1677C2×C4#58512yes—
1678C2×C4#58512yes—
1679C22—24no—
1680C22—24no—
1681C22—24no—
1682C22—24no—
1683C22—24no—
1684C22—24no—
1685C22—41no—
1686C22—41no—
1687C22—44no—
1688C22—42no—
1689C22—44no—
1690C22—41no—
1691C22—41no—
1692C22—42no—
1693C22—41no—
1694C22—42no—
1695C22—41no—
1696C22—44no—
1697C22—41no—
1698C22—41no—
1699C22—42no—
1700C22—44no—
1701C22—44no—
1702C22—41no—
1703C22—41no—
1704C22—42no—
1705C22—41no—
1706C22—42no—
1707C22—41no—
1708C22—44no—
1709C22—41no—
1710C22—41no—
1711C22—42no—
1712C22—44no—
1713C22—1616no—
1714C22C2×#55518yes—
1715C22C23×#4111yescharacteristic
1716C22C23×#4111yescharacteristic
1717C22C22×H(5,𝔽2)11yescharacteristic
1718C22C2×#58511yescharacteristic
1719C22C2×#58511yescharacteristic
1720C22C2×#58511yescharacteristic
1721C22H(7,𝔽2)11yescharacteristic
1722C4—22no—
1723C4—22no—
1724C4—22no—
1725C4—24no—
1726C4—22no—
1727C4—24no—
1728C4—42no—
1729C4—42no—
1730C4—41no—
1731C4—44no—
1732C4—42no—
1733C4—42no—
1734C4—44no—
1735C4—42no—
1736C4—41no—
1737C4—41no—
1738C4—41no—
1739C4—42no—
1740C4—42no—
1741C4—41no—
1742C4—44no—
1743C4—42no—
1744C4—42no—
1745C4—41no—
1746C4—41no—
1747C4—42no—
1748C4—42no—
1749C4—42no—
1750C4C2×#55514yes—
1751C4#352114yes—
1752C2—28no—
1753C2—81no—
1754C2—81no—
1755C2—84no—
1756C2—82no—
1757C2C22×#55511yescharacteristic
1758C2C2×#352111yescharacteristic
1759C2#6278111yescharacteristic
1760C2#6292011yescharacteristic
1761C2#6300811yescharacteristic
1762C2#6301011yescharacteristic
1763C2#6302111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59949C2semidirect
2. #59894C2semidirect
3. #59863C2semidirect
4. #59854C2semidirect
5. #59234C2semidirect
6. #59227C2semidirect
7. #59224C2semidirect
8. #59224C2semidirect
9. #45402C2semidirect
10. #44909C2semidirect
11. #44464C2semidirect
12. #43222C2semidirect
13. #39506C2semidirect
14. #39503C2semidirect
15. #38941C2semidirect
16. #38939C2semidirect
17. #38291C2semidirect
18. #38280C2semidirect
19. #36302C2semidirect
20. #36261C2semidirect
21. #36258C2semidirect
22. #36258C2semidirect
23. #36257C2semidirect
24. #36238C2semidirect
25. #36211C2semidirect
26. #36176C2semidirect
27. #36009C2semidirect
28. #35847C2semidirect
29. #34800C2semidirect
30. C2×#2513C2semidirect
31. #34310C2semidirect
32. #34261C2semidirect
33. #34191C2semidirect
34. C4×#547C2semidirect
35. #34127C2semidirect
44. #2861C22semidirect
45. #2859C22semidirect
46. #2857C22semidirect
51. #2850C22semidirect
52. #2808C22semidirect
53. #2808C22semidirect
54. #2803C22semidirect
55. #2803C22semidirect
56. #2803C22semidirect
57. #2785C22semidirect
58. #2783C22semidirect
59. #2783C22semidirect
60. #2783C22semidirect
61. #2781C22semidirect
62. #2781C22semidirect
63. #2775C22semidirect
64. #2775C22semidirect
65. #2756C22semidirect
66. #2756C22semidirect
67. #2744C22semidirect
68. #2737C22semidirect
69. #2737C22semidirect
70. #2737C22semidirect
71. #2733C22semidirect
72. #2686C22semidirect
73. #2640C22semidirect
74. #2639C22semidirect
75. #2621C22semidirect
76. #2617C22semidirect
77. #2610C22semidirect
78. #2610C22semidirect
79. #2593C22semidirect
80. #2592C22semidirect
81. #2592C22semidirect
82. #2591C22semidirect
83. #2584C22semidirect
84. #2583C22semidirect
85. #2574C22semidirect
86. #2571C22semidirect
87. #2563C22semidirect
88. #2563C22semidirect
89. #2562C22semidirect
90. #2561C22semidirect
91. #2561C22semidirect
92. #2552C22semidirect
93. #2551C22semidirect
94. #2550C22semidirect
95. #2549C22semidirect
98. #2547C22semidirect
99. #2547C22semidirect
100. #2543C22semidirect
103. #2535C22semidirect
104. #2532C22semidirect
105. #2532C22semidirect
106. #2532C22semidirect
107. #2531C22semidirect
108. #2531C22semidirect
109. #2531C22semidirect
110. #2529C22semidirect
111. #2529C22semidirect
112. #2526C22semidirect
113. #2526C22semidirect
114. #2518C22semidirect
115. #2518C22semidirect
121. #2513C22semidirect
122. #2513C22semidirect
123. #2513C22semidirect
124. #2513C22semidirect
125. #2513C22semidirect
126. #2513C22semidirect
127. #2513C22semidirect
128. #2513C22semidirect
129. #2513C22semidirect
130. #2513C22semidirect
131. #2508C22semidirect
132. #2508C22semidirect
133. #2508C22semidirect
134. #2504C22semidirect
137. #2500C22semidirect
138. #2497C22semidirect
139. #2495C22semidirect
140. #2495C22semidirect
141. #2492C22semidirect
144. #2491C22semidirect
145. #2491C22semidirect
146. #2490C22semidirect
147. #2490C22semidirect
148. #2490C22semidirect
149. #2489C22semidirect
150. #2489C22semidirect
151. #2489C22semidirect
152. #2488C22semidirect
153. #2488C22semidirect
154. #2488C22semidirect
155. #2488C22semidirect
156. #2486C22semidirect
157. #2485C22semidirect
158. #2485C22semidirect
159. #2476C22semidirect
160. #2474C22semidirect
161. #2474C22semidirect
162. #2472C22semidirect
163. #2472C22semidirect
164. #2472C22semidirect
165. #2472C22semidirect
166. #2459C22semidirect
167. #2440C22semidirect
168. #2440C22semidirect
169. #2439C22semidirect
170. #2427C22semidirect
171. #2427C22semidirect
174. #2425C22semidirect
175. #2425C22semidirect
178. #2420C22semidirect
179. #2420C22semidirect
180. #2420C22semidirect
183. #2415C22semidirect
184. #2415C22semidirect
188. #2414C22semidirect
189. #2414C22semidirect
190. #2412C22semidirect
191. #2412C22semidirect
196. #2398C22semidirect
197. #2392C22semidirect
198. C2×#397C22semidirect
199. C2×#397C22semidirect
200. #2369C22semidirect
202. #2365C22semidirect
204. #2363C22semidirect
205. #2363C22semidirect
206. #2363C22semidirect
207. #2362C22semidirect
208. #2362C22semidirect
210. #2361C22semidirect
211. #2359C22semidirect
212. #2359C22semidirect
214. #2357C22semidirect
215. #2355C22semidirect
216. #2355C22semidirect
217. #2355C22semidirect
218. #2355C22semidirect
220. #2354C22semidirect
221. #2354C22semidirect
222. #2354C22semidirect
223. #2354C22semidirect
224. #2353C22semidirect
225. #2352C22semidirect
226. #2352C22semidirect
227. #2352C22semidirect
228. #2352C22semidirect
229. #2352C22semidirect
235. #2347C22semidirect
236. #2347C22semidirect
237. #2346C22semidirect
238. #2346C22semidirect
239. #2346C22semidirect
240. #2346C22semidirect
241. #2344C22semidirect
242. #2343C22semidirect
243. #2343C22semidirect
244. #2342C22semidirect
245. #2342C22semidirect
256. #2320C22semidirect
257. #2319C22semidirect
258. #2318C22semidirect
259. #2318C22semidirect
260. #2314C22semidirect
261. #2312C22semidirect
262. C4×C4⋊Q8C22semidirect
263. C4×C4⋊Q8C22semidirect
265. C4×#124C22semidirect
266. C4×C22⋊Q8C22semidirect
267. C4×C22⋊Q8C22semidirect
268. C4×#123C22semidirect
269. C4×#123C22semidirect
273. C4×#121C22semidirect
274. #2298C22semidirect
275. #2295C22semidirect
277. #2293C22semidirect
281. C2×#389C22semidirect
282. #2290C22semidirect
283. #2290C22semidirect
284. C2×#388C22semidirect
285. C2×#388C22semidirect
286. #2285C22semidirect
287. #2285C22semidirect
288. #2283C22semidirect
289. #2283C22semidirect
290. #2283C22semidirect
291. C2×#382C22semidirect
295. C42×D4C22semidirect
296. C4×#117C22semidirect
297. C2×C4×C4⋊C4C22semidirect
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
#599492
#598942
#598632
#598542
#592342
#592272
#592242
#454022
#449092
#444642
#432222
#395062
#395032
#389412
#389392
#382912
#382802
#363022
#362612
#362582
#362572
#362382
#362112
#361762
#360092
#358472
#348002
C2×#25132
#343102
#342612
#341912
C4×#5472
#341272