Finite Group Databasebeta

← #7968943

Subgroups — #7968943

Order 512.

5319 conjugacy classes of subgroups.

The subgroup lattice has 1824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59418C211yesmaximal, characteristic, complemented
2#59374C212yesmaximal, complemented
3#59219C211yesmaximal, characteristic, complemented
4#59211C211yesmaximal, characteristic, complemented
5#59206C212yesmaximal, complemented
6#48578C214yesmaximal, complemented
7#48441C214yesmaximal, complemented
8#45622C212yesmaximal, complemented
9#45617C212yesmaximal, complemented
10#45062C212yesmaximal, complemented
11#44926C212yesmaximal, complemented
12#43946C214yesmaximal, complemented
13#42539C212yesmaximal, complemented
14#42531C212yesmaximal, complemented
15#40569C214yesmaximal, complemented
16#39885C212yesmaximal, complemented
17#39885C212yesmaximal, complemented
18#39881C212yesmaximal, complemented
19#39531C212yesmaximal, complemented
20#39194C211yesmaximal, characteristic, complemented
21#39127C211yesmaximal, characteristic, complemented
22#37857C212yesmaximal, complemented
23#36445C211yesmaximal, characteristic, complemented
24#36209C211yesmaximal, characteristic, complemented
25#36153C211yesmaximal, characteristic, complemented
26#36143C212yesmaximal, complemented
27#36114C211yesmaximal, characteristic, complemented
28#36100C211yesmaximal, characteristic, complemented
29#35236C211yesmaximal, characteristic, complemented
30#35196C211yesmaximal, characteristic, complemented
31#35023C212yesmaximal, complemented
32#34935C211yesmaximal, characteristic, complemented
33#34700C211yesmaximal, characteristic, complemented
34#34404C212yesmaximal, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic, complemented
37C2×#547C2211yescharacteristic
38C2×#546C2211yescharacteristic
39C2×#546C2212yescomplemented
40C2×#529C2211yescharacteristic
41C2×#529C2212yescomplemented
42C2×#525C2212yes—
43C2×#525C2212yes—
44C2×C4×#41C2211yescharacteristic
45C22×C4×D4C2211yescharacteristic, complemented
46C22×C4×D4C2211yescharacteristic, complemented
47#2859C2211yescharacteristic, complemented
48#2857C2211yescharacteristic, complemented
49#2857C2212yescomplemented
50#2857C2211yescharacteristic, complemented
51#2855C2212yescomplemented
52#2851C2212yescomplemented
53#2850C2212yescomplemented
54#2848C2212yescomplemented
55#2848C2212yescomplemented
56#2847C2212yes—
57#2847C2212yes—
58#2834C2214yescomplemented
59#2827C2214yescomplemented
60#2802C2214yescomplemented
61#2801C2214yescomplemented
62#2800C2214yescomplemented
63#2800C2214yescomplemented
64#2790C2214yescomplemented
65#2790C2214yescomplemented
66#2786C2214yescomplemented
67#2779C2214yescomplemented
68#2777C2214yescomplemented
69#2772C2214yescomplemented
70#2765C2214yescomplemented
71#2756C2214yescomplemented
72#2749C2214yescomplemented
73#2746C2214yes—
74#2746C2214yescomplemented
75#2746C2214yescomplemented
76#2744C2214yescomplemented
77#2740C2214yescomplemented
78#2739C2214yescomplemented
79#2735C2214yescomplemented
80#2725C2214yescomplemented
81#2718C2214yescomplemented
82#2707C2214yescomplemented
83#2707C2214yescomplemented
84#2706C2214yescomplemented
85#2701C2214yes—
86#2701C2214yescomplemented
87#2697C2214yes—
88#2697C2214yescomplemented
89#2685C2214yescomplemented
90#2679C2214yes—
91#2678C2214yes—
92#2678C2214yes—
93#2649C2214yescomplemented
94#2643C2214yescomplemented
95#2636C2214yescomplemented
96#2635C2214yes—
97#2630C2214yescomplemented
98#2630C2214yescomplemented
99#2629C2212yescomplemented
100#2624C2212yescomplemented
101#2622C2214yescomplemented
102#2602C2214yes—
103#2602C2214yescomplemented
104#2597C2214yescomplemented
105#2595C2214yescomplemented
106#2578C2214yescomplemented
107#2576C2214yescomplemented
108#2573C2214yescomplemented
109#2571C2211yescharacteristic, complemented
110#2570C2212yescomplemented
111#2562C2212yescomplemented
112#2562C2212yescomplemented
113#2558C2214yescomplemented
114#2553C2214yescomplemented
115#2547C2211yescharacteristic, complemented
116#2545C2212yescomplemented
117#2542C2211yescharacteristic, complemented
118#2542C2212yescomplemented
119#2540C2212yes—
120#2538C2211yescharacteristic, complemented
121#2538C2211yescharacteristic, complemented
122#2538C2211yescharacteristic, complemented
123#2538C2211yescharacteristic, complemented
124#2538C2212yescomplemented
125#2538C2212yescomplemented
126#2537C2211yescharacteristic
127#2537C2211yescharacteristic
128#2537C2211yescharacteristic
129#2536C2212yes—
130#2536C2212yescomplemented
131#2536C2212yescomplemented
132#2536C2212yescomplemented
133#2535C2212yes—
134#2534C2214yes—
135#2534C2214yescomplemented
136#2534C2214yescomplemented
137#2531C2214yescomplemented
138#2526C2214yescomplemented
139#2525C2214yescomplemented
140#2522C2214yescomplemented
141#2516C2214yescomplemented
142#2516C2214yescomplemented
143#2513C2212yescomplemented
144#2508C2212yescomplemented
145#2508C2212yescomplemented
146#2507C2212yescomplemented
147#2500C2212yes—
148#2500C2214yescomplemented
149#2500C2212yescomplemented
150#2497C2212yescomplemented
151#2496C2212yescomplemented
152#2495C2212yescomplemented
153#2495C2212yescomplemented
154#2495C2212yescomplemented
155#2494C2212yescomplemented
156#2494C2212yescomplemented
157#2494C2212yescomplemented
158#2494C2212yescomplemented
159#2493C2214yescomplemented
160#2490C2212yescomplemented
161#2490C2212yescomplemented
162#2489C2212yescomplemented
163#2489C2212yescomplemented
164#2487C2212yescomplemented
165#2486C2212yescomplemented
166#2486C2212yescomplemented
167#2486C2212yescomplemented
168#2485C2212yes—
169#2485C2212yes—
170#2485C2212yescomplemented
171#2482C2214yescomplemented
172#2480C2212yescomplemented
173#2470C2214yescomplemented
174#2470C2214yescomplemented
175#2470C2214yescomplemented
176#2468C2212yescomplemented
177#2466C2214yescomplemented
178#2466C2214yescomplemented
179#2457C2212yes—
180#2455C2214yescomplemented
181#2454C2212yescomplemented
182#2454C2214yescomplemented
183#2454C2211yescharacteristic, complemented
184#2453C2212yescomplemented
185#2447C2211yescharacteristic, complemented
186#2442C2212yescomplemented
187#2442C2211yescharacteristic, complemented
188#2441C2212yescomplemented
189#2441C2212yescomplemented
190#2441C2214yescomplemented
191#2435C2211yescharacteristic, complemented
192#2432C2212yescomplemented
193#2429C2212yescomplemented
194#2429C2212yescomplemented
195#2427C2211yescharacteristic
196#2427C2212yescomplemented
197#2426C2212yes—
198#2426C2212yescomplemented
199#2426C2212yescomplemented
200#2426C2212yescomplemented
201#2425C2214yescomplemented
202#2422C2212yes—
203#2422C2212yescomplemented
204#2422C2212yescomplemented
205#2421C2212yescomplemented
206#2421C2212yescomplemented
207#2421C2212yescomplemented
208#2420C2211yescharacteristic
209#2420C2212yescomplemented
210#2420C2212yescomplemented
211#2419C2214yescomplemented
212#2418C2212yes—
213#2418C2214yescomplemented
214#2418C2214yescomplemented
215#2417C2211yescharacteristic
216#2417C2212yescomplemented
217#2416C2212yes—
218#2415C2212yescomplemented
219#2412C2214yescomplemented
220#2411C2214yescomplemented
221#2408C2211yescharacteristic
222#2408C2212yescomplemented
223#2408C2212yescomplemented
224#2408C2212yescomplemented
225#2407C2212yes—
226#2395C2212yescomplemented
227#2392C2212yes—
228#2392C2214yescomplemented
229#2376C2214yescomplemented
230#2376C2214yescomplemented
231#2367C2211yescharacteristic, complemented
232#2364C2212yes—
233#2363C2211yescharacteristic
234#2362C2212yescomplemented
235#2361C2212yescomplemented
236#2361C2212yescomplemented
237#2360C2212yescomplemented
238#2360C2212yescomplemented
239#2360C2211yescharacteristic, complemented
240#2359C2214yescomplemented
241#2359C2212yescomplemented
242#2358C2212yes—
243#2357C2212yescomplemented
244#2356C2212yescomplemented
245#2354C2211yescharacteristic, complemented
246#2353C2214yescomplemented
247#2352C2211yescharacteristic
248Q8×C4⋊C4C2212yescomplemented
249Q8×C4⋊C4C2211yescharacteristic, complemented
250Q8×C4⋊C4C2211yescharacteristic, complemented
251#2349C2211yescharacteristic, complemented
252#2349C2214yescomplemented
253D4×C4⋊C4C2212yescomplemented
254D4×C4⋊C4C2211yescharacteristic, complemented
255#2347C2212yescomplemented
256#2346C2212yescomplemented
257#2346C2212yescomplemented
258#2344C2212yescomplemented
259#2342C2212yescomplemented
260#2341C2212yes—
261#2341C2212yescomplemented
262#2339C2211yescharacteristic
263#2339C2212yescomplemented
264D4×C22⋊C4C2211yescharacteristic, complemented
265#2324C2212yescomplemented
266#2324C2212yescomplemented
267#2324C2212yescomplemented
268#2323C2212yescomplemented
269#2323C2212yescomplemented
270#2321C2214yescomplemented
271#2321C2214yescomplemented
272#2321C2214yescomplemented
273#2319C2214yescomplemented
274#2318C2214yescomplemented
275#2314C2212yescomplemented
276C4×C4⋊Q8C2211yescharacteristic, complemented
277C4×#124C2211yescharacteristic, complemented
278C4×#124C2211yescharacteristic, complemented
279C4×C22⋊Q8C2211yescharacteristic, complemented
280C4×C22⋊Q8C2211yescharacteristic, complemented
281C4×C22⋊Q8C2212yescomplemented
282C4×#123C2212yescomplemented
283C4×#121C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2212yescomplemented
287C4×#121C2212yescomplemented
288C4×#120C2212yes—
289C4×#120C2212yes—
290#2293C2211yescharacteristic, complemented
291#2285C2211yescharacteristic, complemented
292#2285C2211yescharacteristic, complemented
293#2280C2212yescomplemented
294#2280C2212yescomplemented
295C2×#380C2212yescomplemented
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic, complemented
298C2×C4×C22⋊C4C2212yescomplemented
299C22×#41C2312yes—
300C22×#41C2311yescharacteristic
301C23×D4C2311yescharacteristic
302C23×D4C2311yescharacteristic
303C24×C4C2312yes—
304C24×C4C2312yes—
305#557—44no—
306#547—44no—
307#546—28no—
308#546—48no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311#529—44no—
312#529—48no—
313C2×#126C2312yes—
314C2×#126C2314yes—
315C2×#125C2311yescharacteristic
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#124C2311yescharacteristic
320C2×#124C2311yescharacteristic
321C2×#124C2312yes—
322C2×#124C2311yescharacteristic
323#525—216no—
324#525—48no—
325C2×#123C2312yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×#123C2314yes—
329C2×#123C2312yes—
330C2×#123C2314yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×#121C2312yes—
346C2×#121C2311yescharacteristic
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2311yescharacteristic
351C2×#121C2312yes—
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2314yes—
357C2×#120C2314yes—
358C2×#120C2312yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C2×#120C2312yes—
362C2×#120C2314yes—
363C4×#41—44no—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2311yescharacteristic
371C2×C4×Q8C2312yes—
372C2×C4×D4—44no—
373C2×C4×D4—44no—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2314yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2314yes—
408C2×#117C2312yes—
409C2×#117C2311yescharacteristic
410C2×#117C2312yes—
411C22×C4⋊C4C2312yes—
412C22×C4⋊C4C2311yescharacteristic
413C22×C4⋊C4C2312yes—
414C22×C4⋊C4C2311yescharacteristic
415C22×C22⋊C4C2312yes—
416C22×C22⋊C4C2314yes—
417C22×C22⋊C4C2312yes—
418C22×C22⋊C4C2312yes—
419C22×C22⋊C4C2312yes—
420C22×C42C2311yescharacteristic
421C22×C42C2311yescharacteristic
422C22×C42C2312yes—
423C22×C42C2312yes—
424#401C2314yes—
425#401C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2312yes—
435#400C2314yes—
436#399C2314yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#399C2312yes—
441#399C2314yes—
442#398C2314yes—
443#398C2312yes—
444#398C2314yes—
445#398C2312yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2312yes—
468#397C2314yes—
469#397C2312yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2312yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2312yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2312yes—
501#394C2314yes—
502#394C2312yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2312yes—
507#394C2314yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#392C2312yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#391C2312yes—
519#391C2311yescharacteristic
520#391C2311yescharacteristic
521#391C2312yes—
522#391C2312yes—
523#391C2311yescharacteristic
524#391C2312yes—
525#391C2311yescharacteristic
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#390C2314yes—
531#390C2314yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2311yescharacteristic
537#390C2311yescharacteristic
538#390C2311yescharacteristic
539#390C2311yescharacteristic
540#390C2314yes—
541#390C2312yes—
542#390C2314yes—
543#390C2312yes—
544#390C2311yescharacteristic
545#390C2312yes—
546#390C2311yescharacteristic
547#390C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2311yescharacteristic
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2312yes—
558#389C2312yes—
559#389C2314yes—
560#389C2314yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2311yescharacteristic
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2312yes—
571#389C2312yes—
572#389C2314yes—
573#389C2312yes—
574#389C2314yes—
575#389C2311yescharacteristic
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2311yescharacteristic
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2312yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2312yes—
620#388C2312yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2312yes—
626#388C2312yes—
627#388C2314yes—
628#388C2312yes—
629#388C2312yes—
630#388C2312yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2312yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2312yes—
647#387C2314yes—
648#387C2312yes—
649#387C2314yes—
650#387C2312yes—
651#387C2314yes—
652#386C2312yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2312yes—
658#386C2312yes—
659#386C2312yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2314yes—
668#386C2312yes—
669#386C2312yes—
670#386C2312yes—
671#386C2312yes—
672#386C2314yes—
673#386C2312yes—
674#386C2312yes—
675#386C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2312yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#385C2312yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#385C2314yes—
696#385C2314yes—
697#385C2312yes—
698#385C2312yes—
699#385C2312yes—
700#384C2311yescharacteristic
701#384C2312yes—
702#384C2312yes—
703#384C2311yescharacteristic
704#384C2311yescharacteristic
705#384C2312yes—
706#384C2314yes—
707#383C2314yes—
708#383C2314yes—
709#382C2312yes—
710#382C2312yes—
711#382C2312yes—
712#382C2314yes—
713#382C2311yescharacteristic
714#382C2314yes—
715#382C2312yes—
716#382C2311yescharacteristic
717#382C2312yes—
718#381C2314yes—
719#381C2312yes—
720#381C2312yes—
721#381C2312yes—
722#381C2314yes—
723#381C2314yes—
724#381C2314yes—
725#381C2314yes—
726#380C2311yescharacteristic
727#380C2312yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2314yes—
737#380C2314yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2311yescharacteristic
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#380C2312yes—
753#380C2312yes—
754#380C2314yes—
755#380C2312yes—
756#380C2312yes—
757#380C2311yescharacteristic
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#379C2312yes—
763#379C2312yes—
764#379C2314yes—
765#379C2314yes—
766#379C2312yes—
767#379C2314yes—
768#379C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2311yescharacteristic
816#376C2314yes—
817C2×#95C2312yes—
818C2×#95C2314yes—
819C2×#95C2312yes—
820C43C2311yescharacteristic
821C25C2412yes—
822C25C2412yes—
823C2×#41—28no—
824C2×#41—42no—
825C2×#41—42no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41#4118yescomplemented
829C22×Q8C2411yescharacteristic
830C22×Q8C2412yes—
831C22×Q8C2411yescharacteristic
832C22×D4—24no—
833C22×D4—24no—
834C22×D4—42no—
835C22×D4—42no—
836C22×D4—42no—
837C22×D4—42no—
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2414yes—
843C22×D4C2411yescharacteristic
844C22×D4C2411yescharacteristic
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C23×C4—28no—
854C23×C4—44no—
855C23×C4—44no—
856C23×C4—44no—
857C23×C4—44no—
858C23×C4—44no—
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2412yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2412yes—
877C23×C4C2412yes—
878C23×C4C2412yes—
879C23×C4C2412yes—
880C23×C4C2412yes—
881C4⋊Q8—24no—
882C4⋊Q8—44no—
883#126—44no—
884#126—48no—
885#125—42no—
886#125—44no—
887#125—44no—
888#125—48no—
889#124—24no—
890#124—24no—
891#124—42no—
892#124—44no—
893#123—216no—
894#123—28no—
895#123—48no—
896#123—48no—
897#123—48no—
898#123—48no—
899#123—44no—
900#123—48no—
901C22⋊Q8—28no—
902C22⋊Q8—28no—
903C22⋊Q8—24no—
904C22⋊Q8—44no—
905C22⋊Q8—42no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—42no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913#121—28no—
914#121—28no—
915#121—28no—
916#121—24no—
917#121—28no—
918#121—24no—
919#121—44no—
920#121—44no—
921#121—42no—
922#121—44no—
923#121—44no—
924#121—48no—
925#120—216no—
926#120—28no—
927#120—48no—
928#120—48no—
929#120—44no—
930#120—48no—
931C4×Q8—24no—
932C4×Q8—24no—
933C4×Q8—44no—
934C4×Q8—44no—
935C4×Q8—42no—
936C4×Q8—44no—
937C4×Q8—44no—
938C4×Q8—44no—
939C4×D4—24no—
940C4×D4—28no—
941C4×D4—216no—
942C4×D4—216no—
943C4×D4—24no—
944C4×D4—24no—
945C4×D4—24no—
946C4×D4—24no—
947C4×D4—24no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—42no—
951C4×D4—42no—
952C4×D4—42no—
953C4×D4—42no—
954C4×D4—42no—
955C4×D4—42no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—42no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—42no—
965C4×D4—48no—
966C4×D4—48no—
967C4×D4—48no—
968#117—28no—
969#117—44no—
970#117—44no—
971#117—44no—
972#117—44no—
973#117—48no—
974#117—42no—
975#117—44no—
976C2×C4⋊C4—44no—
977C2×C4⋊C4—42no—
978C2×C4⋊C4—42no—
979C2×C4⋊C4—44no—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2411yescharacteristic
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2414yes—
1041C2×C22⋊C4—28no—
1042C2×C22⋊C4—44no—
1043C2×C22⋊C4—44no—
1044C2×C22⋊C4—44no—
1045C2×C22⋊C4—48no—
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2411yescharacteristic
1094C2×C22⋊C4C2411yescharacteristic
1095C2×C22⋊C4C2411yescharacteristic
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2414yes—
1118C2×C42—24no—
1119C2×C42—24no—
1120C2×C42—44no—
1121C2×C42—44no—
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2414yes—
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2414yes—
1140C2×C42C2414yes—
1141C2×C42C2414yes—
1142C2×C42C2412yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2414yes—
1145C2×C42C2414yes—
1146C2×C42C2414yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150#95C2412yes—
1151#95C2411yescharacteristic
1152#95C2411yescharacteristic
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2411yescharacteristic
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2411yescharacteristic
1167#95C2412yes—
1168#95C2412yes—
1169#95C2411yescharacteristic
1170#95C2412yes—
1171#95C2412yes—
1172#95C2411yescharacteristic
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24—24no—
1211C24—24no—
1212C24—24no—
1213C24—24no—
1214C24—42no—
1215C24—42no—
1216C24—42no—
1217C24—42no—
1218C24—42no—
1219C24—42no—
1220C24—42no—
1221C24—42no—
1222C24—42no—
1223C24—42no—
1224C24C2512yes—
1225C24C2512yes—
1226C24C2511yescharacteristic
1227C24C2512yes—
1228C24C2512yes—
1229C24C2511yescharacteristic
1230#41—416no—
1231#41—816no—
1232C2×Q8—22no—
1233C2×Q8—22no—
1234C2×Q8—22no—
1235C2×Q8—24no—
1236C2×Q8—24no—
1237C2×Q8—22no—
1238C2×Q8—24no—
1239C2×Q8—22no—
1240C2×Q8C2×#4114yes—
1241C2×D4—22no—
1242C2×D4—28no—
1243C2×D4—24no—
1244C2×D4—24no—
1245C2×D4—28no—
1246C2×D4—24no—
1247C2×D4—22no—
1248C2×D4—24no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—24no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—41no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—416no—
1284C2×D4—416no—
1285C2×D4C2×#4114yes—
1286C2×D4C2×#4118yes—
1287C2×D4H(5,𝔽2)14yes—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—24no—
1292C22×C4—24no—
1293C22×C4—28no—
1294C22×C4—28no—
1295C22×C4—22no—
1296C22×C4—24no—
1297C22×C4—24no—
1298C22×C4—22no—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—24no—
1319C22×C4—22no—
1320C22×C4—42no—
1321C22×C4—41no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—41no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—44no—
1342C22×C4—42no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—42no—
1347C22×C4—42no—
1348C22×C4—41no—
1349C22×C4—42no—
1350C22×C4—42no—
1351C22×C4—44no—
1352C22×C4—816no—
1353C22×C4—816no—
1354C22×C4C2×#4114yes—
1355C22×C4C2×#4118yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2514yes—
1363C22×C4C2512yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2512yes—
1367C22×C4C2512yes—
1368C22×C4C2512yes—
1369C22×C4C2511yescharacteristic
1370C22×C4C2511yescharacteristic
1371C22×C4C2514yes—
1372C22×C4C2512yes—
1373C22×C4C2512yes—
1374C22×C4C2514yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2514yes—
1378C22×C4C2511yescharacteristic
1379C22×C4C2512yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2512yes—
1382C22×C4C2511yescharacteristic
1383C22×C4C2511yescharacteristic
1384C22×C4C2511yescharacteristic
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—22no—
1388C4⋊C4—28no—
1389C4⋊C4—28no—
1390C4⋊C4—22no—
1391C4⋊C4—24no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—22no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—22no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—22no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—44no—
1426C4⋊C4—42no—
1427C4⋊C4—41no—
1428C4⋊C4—41no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—42no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4—44no—
1446C22⋊C4—28no—
1447C22⋊C4—24no—
1448C22⋊C4—22no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—22no—
1457C22⋊C4—24no—
1458C22⋊C4—28no—
1459C22⋊C4—22no—
1460C22⋊C4—24no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—28no—
1464C22⋊C4—28no—
1465C22⋊C4—24no—
1466C22⋊C4—24no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—42no—
1487C22⋊C4—42no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—41no—
1494C22⋊C4—41no—
1495C22⋊C4—42no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—41no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4—44no—
1504C22⋊C4—42no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—42no—
1508C22⋊C4—42no—
1509C22⋊C4—42no—
1510C22⋊C4—44no—
1511C22⋊C4—44no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—42no—
1517C22⋊C4—44no—
1518C42—28no—
1519C42—22no—
1520C42—22no—
1521C42—22no—
1522C42—22no—
1523C42—22no—
1524C42—22no—
1525C42—22no—
1526C42—22no—
1527C42—24no—
1528C42—24no—
1529C42—24no—
1530C42—22no—
1531C42—24no—
1532C42—22no—
1533C42—42no—
1534C42—42no—
1535C42—42no—
1536C42—42no—
1537C42—41no—
1538C42—44no—
1539C42—44no—
1540C42—44no—
1541C42—41no—
1542C42—44no—
1543C42—44no—
1544C42—44no—
1545C42H(5,𝔽2)14yes—
1546C23—21no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—21no—
1551C23—22no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—22no—
1557C23—21no—
1558C23—22no—
1559C23—21no—
1560C23—22no—
1561C23—22no—
1562C23—21no—
1563C23—22no—
1564C23—21no—
1565C23—22no—
1566C23—22no—
1567C23—22no—
1568C23—21no—
1569C23—21no—
1570C23—22no—
1571C23—22no—
1572C23—22no—
1573C23—22no—
1574C23—22no—
1575C23—22no—
1576C23—22no—
1577C23—22no—
1578C23—22no—
1579C23—22no—
1580C23—22no—
1581C23—22no—
1582C23—22no—
1583C23—22no—
1584C23—48no—
1585C23—48no—
1586C23—48no—
1587C23—48no—
1588C23—84no—
1589C23—84no—
1590C23—84no—
1591C23—84no—
1592C23—84no—
1593C23—84no—
1594C23—84no—
1595C23—84no—
1596C23—84no—
1597C23—84no—
1598C23C22×#4112yes—
1599C23C22×#4114yes—
1600C23C2×H(5,𝔽2)14yes—
1601C23#58512yes—
1602C23C2611yescharacteristic
1603Q8—28no—
1604Q8—44no—
1605Q8—48no—
1606D4—28no—
1607D4—28no—
1608D4—48no—
1609D4—416no—
1610D4—48no—
1611D4—44no—
1612D4—48no—
1613D4—48no—
1614D4—44no—
1615D4—44no—
1616D4—84no—
1617D4—88no—
1618D4—84no—
1619D4—88no—
1620D4—164no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—21no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—28no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—24no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—24no—
1655C2×C4—21no—
1656C2×C4—24no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—24no—
1661C2×C4—21no—
1662C2×C4—21no—
1663C2×C4—22no—
1664C2×C4—21no—
1665C2×C4—21no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—24no—
1671C2×C4—24no—
1672C2×C4—21no—
1673C2×C4—24no—
1674C2×C4—24no—
1675C2×C4—24no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—22no—
1683C2×C4—22no—
1684C2×C4—22no—
1685C2×C4—21no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—22no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—22no—
1694C2×C4—22no—
1695C2×C4—21no—
1696C2×C4—24no—
1697C2×C4—22no—
1698C2×C4—22no—
1699C2×C4—21no—
1700C2×C4—48no—
1701C2×C4—44no—
1702C2×C4—48no—
1703C2×C4—48no—
1704C2×C4—44no—
1705C2×C4—48no—
1706C2×C4—44no—
1707C2×C4—48no—
1708C2×C4—44no—
1709C2×C4—82no—
1710C2×C4—84no—
1711C2×C4—84no—
1712C2×C4—84no—
1713C2×C4—88no—
1714C2×C4—84no—
1715C2×C4—88no—
1716C2×C4—84no—
1717C2×C4—84no—
1718C2×C4—84no—
1719C2×C4—84no—
1720C2×C4—84no—
1721C2×C4C22×#4112yes—
1722C2×C4C22×#4114yes—
1723C2×C4C22×#4112yes—
1724C2×C4C2×H(5,𝔽2)12yes—
1725C2×C4C2×H(5,𝔽2)12yes—
1726C2×C4C2×H(5,𝔽2)12yes—
1727C2×C4C2×H(5,𝔽2)12yes—
1728C2×C4#58512yes—
1729C2×C4#58512yes—
1730C22—24no—
1731C22—24no—
1732C22—22no—
1733C22—24no—
1734C22—22no—
1735C22—22no—
1736C22—24no—
1737C22—22no—
1738C22—22no—
1739C22—24no—
1740C22—22no—
1741C22—24no—
1742C22—41no—
1743C22—42no—
1744C22—41no—
1745C22—42no—
1746C22—41no—
1747C22—42no—
1748C22—42no—
1749C22—41no—
1750C22—42no—
1751C22—42no—
1752C22—42no—
1753C22—41no—
1754C22—41no—
1755C22—41no—
1756C22—42no—
1757C22—41no—
1758C22—42no—
1759C22—42no—
1760C22—42no—
1761C22—42no—
1762C22—42no—
1763C22—42no—
1764C22—42no—
1765C22—42no—
1766C22—42no—
1767C22—42no—
1768C22—42no—
1769C22—42no—
1770C22—42no—
1771C22—42no—
1772C22—816no—
1773C22—816no—
1774C22C23×#4111yescharacteristic
1775C22C22×H(5,𝔽2)11yescharacteristic
1776C22C22×H(5,𝔽2)11yescharacteristic
1777C22C2×#58511yescharacteristic
1778C22C2×#58511yescharacteristic
1779C22C2×#58511yescharacteristic
1780C222−1+611yescharacteristic
1781C4—22no—
1782C4—24no—
1783C4—22no—
1784C4—41no—
1785C4—42no—
1786C4—44no—
1787C4—41no—
1788C4—42no—
1789C4—44no—
1790C4—42no—
1791C4—42no—
1792C4—42no—
1793C4—41no—
1794C4—41no—
1795C4—44no—
1796C4—41no—
1797C4—42no—
1798C4—41no—
1799C4—42no—
1800C4—41no—
1801C4—42no—
1802C4—42no—
1803C4—41no—
1804C4—42no—
1805C4—41no—
1806C4—44no—
1807C4—42no—
1808C4#350514yes—
1809C4#354214yes—
1810C2—44no—
1811C2—44no—
1812C2—42no—
1813C2—42no—
1814C2—82no—
1815C2—82no—
1816C2C2×#354211yescharacteristic
1817C2C2×#350511yescharacteristic
1818C2#6281611yescharacteristic
1819C2#6292711yescharacteristic
1820C2#6293611yescharacteristic
1821C2#6298511yescharacteristic
1822C2#6301811yescharacteristic
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. #59418C2semidirect
2. #59374C2semidirect
3. #59219C2semidirect
4. #59211C2semidirect
5. #59206C2semidirect
6. #48578C2semidirect
7. #48441C2semidirect
8. #45622C2semidirect
9. #45617C2semidirect
10. #45062C2semidirect
11. #44926C2semidirect
12. #43946C2semidirect
13. #42539C2semidirect
14. #42531C2semidirect
15. #40569C2semidirect
16. #39885C2semidirect
17. #39885C2semidirect
18. #39881C2semidirect
19. #39531C2semidirect
20. #39194C2semidirect
21. #39127C2semidirect
22. #37857C2semidirect
23. #36445C2semidirect
24. #36209C2semidirect
25. #36153C2semidirect
26. #36143C2semidirect
27. #36114C2semidirect
28. #36100C2semidirect
29. #35236C2semidirect
30. #35196C2semidirect
31. #35023C2semidirect
32. #34935C2semidirect
33. #34700C2semidirect
34. #34404C2semidirect
35. C4×#546C2semidirect
36. C2×#557C22semidirect
39. C2×#546C22semidirect
41. C2×#529C22semidirect
45. C22×C4×D4C22semidirect
46. C22×C4×D4C22semidirect
47. #2859C22semidirect
48. #2857C22semidirect
49. #2857C22semidirect
50. #2857C22semidirect
51. #2855C22semidirect
52. #2851C22semidirect
53. #2850C22semidirect
54. #2848C22semidirect
55. #2848C22semidirect
58. #2834C22semidirect
59. #2827C22semidirect
60. #2802C22semidirect
61. #2801C22semidirect
62. #2800C22semidirect
63. #2800C22semidirect
64. #2790C22semidirect
65. #2790C22semidirect
66. #2786C22semidirect
67. #2779C22semidirect
68. #2777C22semidirect
69. #2772C22semidirect
70. #2765C22semidirect
71. #2756C22semidirect
72. #2749C22semidirect
74. #2746C22semidirect
75. #2746C22semidirect
76. #2744C22semidirect
77. #2740C22semidirect
78. #2739C22semidirect
79. #2735C22semidirect
80. #2725C22semidirect
81. #2718C22semidirect
82. #2707C22semidirect
83. #2707C22semidirect
84. #2706C22semidirect
86. #2701C22semidirect
88. #2697C22semidirect
89. #2685C22semidirect
93. #2649C22semidirect
94. #2643C22semidirect
95. #2636C22semidirect
97. #2630C22semidirect
98. #2630C22semidirect
99. #2629C22semidirect
100. #2624C22semidirect
101. #2622C22semidirect
103. #2602C22semidirect
104. #2597C22semidirect
105. #2595C22semidirect
106. #2578C22semidirect
107. #2576C22semidirect
108. #2573C22semidirect
109. #2571C22semidirect
110. #2570C22semidirect
111. #2562C22semidirect
112. #2562C22semidirect
113. #2558C22semidirect
114. #2553C22semidirect
115. #2547C22semidirect
116. #2545C22semidirect
117. #2542C22semidirect
118. #2542C22semidirect
120. #2538C22semidirect
121. #2538C22semidirect
122. #2538C22semidirect
123. #2538C22semidirect
124. #2538C22semidirect
125. #2538C22semidirect
130. #2536C22semidirect
131. #2536C22semidirect
132. #2536C22semidirect
135. #2534C22semidirect
136. #2534C22semidirect
137. #2531C22semidirect
138. #2526C22semidirect
139. #2525C22semidirect
140. #2522C22semidirect
141. #2516C22semidirect
142. #2516C22semidirect
143. #2513C22semidirect
144. #2508C22semidirect
145. #2508C22semidirect
146. #2507C22semidirect
148. #2500C22semidirect
149. #2500C22semidirect
150. #2497C22semidirect
151. #2496C22semidirect
152. #2495C22semidirect
153. #2495C22semidirect
154. #2495C22semidirect
155. #2494C22semidirect
156. #2494C22semidirect
157. #2494C22semidirect
158. #2494C22semidirect
159. #2493C22semidirect
160. #2490C22semidirect
161. #2490C22semidirect
162. #2489C22semidirect
163. #2489C22semidirect
164. #2487C22semidirect
165. #2486C22semidirect
166. #2486C22semidirect
167. #2486C22semidirect
170. #2485C22semidirect
171. #2482C22semidirect
172. #2480C22semidirect
173. #2470C22semidirect
174. #2470C22semidirect
175. #2470C22semidirect
176. #2468C22semidirect
177. #2466C22semidirect
178. #2466C22semidirect
180. #2455C22semidirect
181. #2454C22semidirect
182. #2454C22semidirect
183. #2454C22semidirect
184. #2453C22semidirect
185. #2447C22semidirect
186. #2442C22semidirect
187. #2442C22semidirect
188. #2441C22semidirect
189. #2441C22semidirect
190. #2441C22semidirect
191. #2435C22semidirect
192. #2432C22semidirect
193. #2429C22semidirect
194. #2429C22semidirect
196. #2427C22semidirect
198. #2426C22semidirect
199. #2426C22semidirect
200. #2426C22semidirect
201. #2425C22semidirect
203. #2422C22semidirect
204. #2422C22semidirect
205. #2421C22semidirect
206. #2421C22semidirect
207. #2421C22semidirect
209. #2420C22semidirect
210. #2420C22semidirect
211. #2419C22semidirect
213. #2418C22semidirect
214. #2418C22semidirect
216. #2417C22semidirect
218. #2415C22semidirect
219. #2412C22semidirect
220. #2411C22semidirect
222. #2408C22semidirect
223. #2408C22semidirect
224. #2408C22semidirect
226. #2395C22semidirect
228. #2392C22semidirect
229. #2376C22semidirect
230. #2376C22semidirect
231. #2367C22semidirect
234. #2362C22semidirect
235. #2361C22semidirect
236. #2361C22semidirect
237. #2360C22semidirect
238. #2360C22semidirect
239. #2360C22semidirect
240. #2359C22semidirect
241. #2359C22semidirect
243. #2357C22semidirect
244. #2356C22semidirect
245. #2354C22semidirect
246. #2353C22semidirect
248. Q8×C4⋊C4C22semidirect
249. Q8×C4⋊C4C22semidirect
250. Q8×C4⋊C4C22semidirect
251. #2349C22semidirect
252. #2349C22semidirect
253. D4×C4⋊C4C22semidirect
254. D4×C4⋊C4C22semidirect
255. #2347C22semidirect
256. #2346C22semidirect
257. #2346C22semidirect
258. #2344C22semidirect
259. #2342C22semidirect
261. #2341C22semidirect
263. #2339C22semidirect
264. D4×C22⋊C4C22semidirect
265. #2324C22semidirect
266. #2324C22semidirect
267. #2324C22semidirect
268. #2323C22semidirect
269. #2323C22semidirect
270. #2321C22semidirect
271. #2321C22semidirect
272. #2321C22semidirect
273. #2319C22semidirect
274. #2318C22semidirect
275. #2314C22semidirect
276. C4×C4⋊Q8C22semidirect
277. C4×#124C22semidirect
278. C4×#124C22semidirect
279. C4×C22⋊Q8C22semidirect
280. C4×C22⋊Q8C22semidirect
281. C4×C22⋊Q8C22semidirect
282. C4×#123C22semidirect
286. C4×#121C22semidirect
287. C4×#121C22semidirect
290. #2293C22semidirect
291. #2285C22semidirect
292. #2285C22semidirect
293. #2280C22semidirect
294. #2280C22semidirect
295. C2×#380C22semidirect
297. C42×D4C22semidirect
298. C2×C4×C22⋊C4C22semidirect
828. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
#594182
#593742
#592192
#592112
#592062
#485782
#484412
#456222
#456172
#450622
#449262
#439462
#425392
#425312
#405692
#398852
#398812
#395312
#391942
#391272
#378572
#364452
#362092
#361532
#361432
#361142
#361002
#352362
#351962
#350232
#349352
#347002
#344042
C4×#5462