Finite Group Databasebeta

← #7699920

Subgroups — #7699920

Order 512.

6071 conjugacy classes of subgroups.

The subgroup lattice has 1783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C212yesmaximal, complemented
2#59678C211yesmaximal, characteristic, complemented
3#59646C211yesmaximal, characteristic, complemented
4#59644C212yesmaximal, complemented
5#59642C211yesmaximal, characteristic, complemented
6#59638C212yesmaximal, complemented
7#59635C214yesmaximal, complemented
8#59634C212yesmaximal, complemented
9#59630C212yesmaximal, complemented
10#59625C214yesmaximal, complemented
11#59624C214yesmaximal, complemented
12#59147C212yesmaximal, complemented
13#36609C211yesmaximal, characteristic, complemented
14#36606C212yesmaximal, complemented
15#36591C211yesmaximal, characteristic, complemented
16#36580C212yesmaximal, complemented
17#36521C214yesmaximal, complemented
18#36499C212yesmaximal, complemented
19#36487C212yesmaximal, complemented
20#36469C211yesmaximal, characteristic, complemented
21#36454C211yesmaximal, characteristic, complemented
22#36441C212yesmaximal, complemented
23#36303C211yesmaximal, characteristic, complemented
24#36260C211yesmaximal, characteristic
25#36238C212yesmaximal, complemented
26#36237C212yesmaximal, complemented
27#36216C212yesmaximal, complemented
28D4×#124C211yesmaximal, characteristic, complemented
29C4×#559C211yesmaximal, characteristic, complemented
30C4×#554C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, characteristic, complemented
32C4×#547C211yesmaximal, characteristic, complemented
33C4×#546C212yesmaximal, complemented
34C4×D42C211yesmaximal, characteristic, complemented
35C2×#2367C212yesmaximal, complemented
36C2×#559C2211yescharacteristic
37C2×#559C2212yescomplemented
38C2×#554C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic
40C2×#547C2211yescharacteristic
41C2×#546C2212yes—
42C2×#546C2212yes—
43C2×D42C2211yescharacteristic
44C22×#124C2212yes—
45C2×C4×#41C2212yes—
46C22×C4×Q8C2212yescomplemented
47C22×C4×D4C2212yes—
48C22×C4×D4C2212yes—
49#2862C2211yescharacteristic, complemented
50#2861C2212yescomplemented
51#2858C2211yescharacteristic
52#2858C2211yescharacteristic
53#2856C2212yes—
54#2855C2212yescomplemented
55#2854C2212yescomplemented
56#2853C2214yescomplemented
57#2850C2212yes—
58#2850C2212yescomplemented
59#2850C2214yescomplemented
60#2849C2214yescomplemented
61#2807C2214yescomplemented
62#2803C2214yescomplemented
63#2798C2214yescomplemented
64#2796C2214yescomplemented
65#2796C2214yescomplemented
66#2754C2214yescomplemented
67#2751C2214yescomplemented
68#2712C2214yescomplemented
69#2710C2214yescomplemented
70#2607C2214yescomplemented
71#2602C2214yescomplemented
72#2602C2214yescomplemented
73#2602C2214yescomplemented
74#2600C2214yescomplemented
75#2597C2214yescomplemented
76#2596C2214yescomplemented
77#2596C2214yescomplemented
78#2595C2214yescomplemented
79#2595C2214yescomplemented
80#2595C2214yescomplemented
81#2593C2214yescomplemented
82#2592C2212yescomplemented
83#2592C2212yescomplemented
84#2592C2212yescomplemented
85#2592C2214yescomplemented
86#2591C2214yescomplemented
87#2589C2214yescomplemented
88#2589C2214yescomplemented
89#2589C2214yescomplemented
90#2582C2212yescomplemented
91#2580C2212yes—
92#2580C2212yescomplemented
93#2580C2214yescomplemented
94#2575C2214yescomplemented
95#2575C2214yescomplemented
96#2570C2212yescomplemented
97#2568C2211yescharacteristic, complemented
98#2562C2212yescomplemented
99#2561C2214yescomplemented
100#2557C2214yescomplemented
101#2557C2214yescomplemented
102#2548C2211yescharacteristic
103#2548C2212yescomplemented
104#2547C2211yescharacteristic
105#2547C2211yescharacteristic, complemented
106#2544C2212yes—
107#2544C2212yescomplemented
108#2542C2211yescharacteristic
109#2541C2211yescharacteristic
110#2540C2212yes—
111#2540C2212yes—
112#2539C2214yes—
113#2539C2214yes—
114#2517C2214yescomplemented
115#2516C2214yescomplemented
116#2516C2214yescomplemented
117#2516C2214yescomplemented
118#2513C2212yescomplemented
119#2513C2212yescomplemented
120#2513C2212yescomplemented
121#2513C2212yescomplemented
122#2511C2212yescomplemented
123#2511C2212yescomplemented
124#2503C2212yescomplemented
125#2502C2212yescomplemented
126#2501C2212yes—
127#2500C2212yescomplemented
128#2498C2214yescomplemented
129#2492C2212yescomplemented
130#2492C2212yescomplemented
131#2492C2212yescomplemented
132#2491C2212yes—
133#2491C2212yes—
134#2491C2212yescomplemented
135#2490C2212yescomplemented
136#2489C2212yescomplemented
137#2488C2214yescomplemented
138#2488C2214yescomplemented
139#2488C2214yescomplemented
140#2488C2214yescomplemented
141#2487C2212yescomplemented
142#2485C2212yescomplemented
143#2483C2214yescomplemented
144#2482C2214yescomplemented
145#2472C2214yes—
146#2472C2214yes—
147#2472C2214yescomplemented
148#2472C2214yescomplemented
149#2459C2214yescomplemented
150#2459C2214yescomplemented
151#2458C2214yescomplemented
152#2458C2214yescomplemented
153#2455C2214yescomplemented
154#2448C2212yescomplemented
155#2448C2212yescomplemented
156#2448C2212yescomplemented
157#2448C2212yescomplemented
158#2448C2212yescomplemented
159#2447C2212yes—
160#2447C2212yescomplemented
161#2447C2212yescomplemented
162#2447C2212yescomplemented
163#2445C2212yescomplemented
164#2444C2214yescomplemented
165#2443C2214yescomplemented
166#2443C2214yescomplemented
167#2443C2214yescomplemented
168#2436C2212yes—
169#2436C2212yescomplemented
170#2435C2212yes—
171#2433C2212yes—
172#2423C2212yescomplemented
173#2422C2212yescomplemented
174#2422C2212yescomplemented
175#2421C2212yescomplemented
176#2419C2214yescomplemented
177#2419C2214yescomplemented
178#2418C2214yescomplemented
179#2418C2214yescomplemented
180#2412C2214yescomplemented
181#2374C2212yescomplemented
182#2374C2212yescomplemented
183#2374C2214yescomplemented
184#2370C2211yescharacteristic, complemented
185#2370C2211yescharacteristic, complemented
186#2369C2211yescharacteristic, complemented
187#2368C2212yescomplemented
188#2368C2212yescomplemented
189#2367C2212yes—
190#2367C2212yes—
191#2367C2212yes—
192#2367C2211yescharacteristic
193#2367C2212yescomplemented
194#2367C2212yescomplemented
195#2367C2212yescomplemented
196#2367C2214yescomplemented
197#2367C2212yescomplemented
198#2367C2214yescomplemented
199#2367C2214yescomplemented
200#2367C2214yescomplemented
201#2367C2212yescomplemented
202#2367C2211yescharacteristic, complemented
203#2367C2212yescomplemented
204#2366C2211yescharacteristic
205#2366C2211yescharacteristic
206#2365C2211yescharacteristic, complemented
207#2365C2211yescharacteristic, complemented
208#2365C2212yescomplemented
209#2364C2214yescomplemented
210#2363C2212yescomplemented
211#2362C2212yescomplemented
212#2361C2212yes—
213#2361C2212yes—
214#2361C2212yescomplemented
215#2360C2212yescomplemented
216#2360C2212yescomplemented
217#2360C2214yescomplemented
218#2360C2212yescomplemented
219#2359C2214yescomplemented
220#2359C2214yescomplemented
221#2358C2214yes—
222#2358C2214yescomplemented
223#2357C2211yescharacteristic
224#2357C2212yescomplemented
225#2357C2212yescomplemented
226#2357C2212yescomplemented
227#2357C2211yescharacteristic, complemented
228#2355C2212yescomplemented
229#2355C2211yescharacteristic, complemented
230#2355C2211yescharacteristic, complemented
231#2355C2211yescharacteristic, complemented
232#2354C2211yescharacteristic, complemented
233#2352C2212yescomplemented
234Q8×C4⋊C4C2211yescharacteristic, complemented
235#2349C2211yescharacteristic
236#2349C2211yescharacteristic
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2211yescharacteristic
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2211yescharacteristic
241#2345C2212yescomplemented
242#2344C2212yescomplemented
243#2342C2214yescomplemented
244Q8×C22⋊C4C2212yescomplemented
245#2339C2212yes—
246#2339C2212yes—
247#2339C2212yes—
248D4×C22⋊C4C2212yes—
249D4×C22⋊C4C2212yes—
250D4×C22⋊C4C2212yes—
251D4×C22⋊C4C2212yes—
252C4×C4⋊Q8C2211yescharacteristic, complemented
253C4×C4⋊Q8C2211yescharacteristic, complemented
254C4×C4⋊Q8C2212yescomplemented
255C4×C4⋊Q8C2211yescharacteristic, complemented
256C4×#127C2211yescharacteristic
257C4×#127C2211yescharacteristic
258C4×#125C2211yescharacteristic, complemented
259C4×#125C2211yescharacteristic, complemented
260C4×#124C2211yescharacteristic
261C4×#124C2212yescomplemented
262C4×#124C2212yescomplemented
263C4×#124C2211yescharacteristic, complemented
264C4×C22⋊Q8C2212yescomplemented
265C4×C22⋊Q8C2212yescomplemented
266C4×C22⋊Q8C2212yescomplemented
267C4×C22⋊Q8C2212yescomplemented
268C4×C22⋊Q8C2214yescomplemented
269C4×C22⋊Q8C2212yescomplemented
270C4×C22⋊Q8C2212yescomplemented
271C4×#123C2214yescomplemented
272C4×#123C2214yescomplemented
273C4×#123C2212yescomplemented
274C4×#123C2212yescomplemented
275C4×#121C2212yes—
276C4×#121C2212yes—
277C4×#121C2212yescomplemented
278C4×#121C2212yescomplemented
279C4×#121C2214yescomplemented
280C4×#120C2214yes—
281C4×#120C2214yescomplemented
282C2×#391C2212yescomplemented
283C2×#390C2212yes—
284C2×#388C2214yescomplemented
285C2×#388C2214yescomplemented
286C2×#385C2214yescomplemented
287C42×Q8C2211yescharacteristic, complemented
288C42×Q8C2211yescharacteristic, complemented
289C42×D4C2211yescharacteristic
290C42×D4C2211yescharacteristic
291C42×D4C2211yescharacteristic
292C42×D4C2212yes—
293C42×D4C2211yescharacteristic
294C42×D4C2212yescomplemented
295C42×D4C2211yescharacteristic, complemented
296C2×C4×C4⋊C4C2212yescomplemented
297C2×C4×C4⋊C4C2212yescomplemented
298C2×C4×C22⋊C4C2214yescomplemented
299C22×#41C2312yes—
300C23×Q8C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303C24×C4C2314yes—
304#559—28no—
305#559—48no—
306#554—28no—
307D4×Q8—28no—
308#547—28no—
309#546—216no—
310#546—48no—
311D42—28no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#127C2311yescharacteristic
318C2×#127C2312yes—
319C2×#125C2311yescharacteristic
320C2×#125C2311yescharacteristic
321C2×#124—216no—
322C2×#124C2312yes—
323C2×#124C2312yes—
324C2×#124C2312yes—
325C2×#124C2312yes—
326C2×#124C2314yes—
327C2×#124C2314yes—
328C2×#124C2311yescharacteristic
329C2×#124C2312yes—
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2311yescharacteristic
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2312yes—
338C2×#123C2312yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×#121C2314yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2314yes—
358C2×#120C2314yes—
359C2×#120C2314yes—
360C2×#120C2314yes—
361C4×#41—48no—
362C2×C4×Q8—48no—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2314yes—
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2314yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×D4—48no—
378C2×C4×D4—48no—
379C2×C4×D4C2312yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2311yescharacteristic
387C2×C4×D4C2312yes—
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2314yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2314yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2314yes—
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2311yescharacteristic
411C2×#117C2314yes—
412C2×#117C2312yes—
413C22×C4⋊C4C2312yes—
414C22×C4⋊C4C2312yes—
415C22×C4⋊C4C2312yes—
416C22×C4⋊C4C2312yes—
417C22×C4⋊C4C2314yes—
418C22×C4⋊C4C2312yes—
419C22×C22⋊C4C2314yes—
420C22×C22⋊C4C2314yes—
421C22×C22⋊C4C2314yes—
422C22×C22⋊C4C2314yes—
423C22×C22⋊C4C2314yes—
424C22×C22⋊C4C2314yes—
425C22×C42C2312yes—
426C22×C42C2312yes—
427C22×C42C2314yes—
428C22×C42C2314yes—
429C22×C42C2312yes—
430C22×C42C2312yes—
431C22×C42C2312yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2314yes—
439#400C2314yes—
440#399C2314yes—
441#399C2314yes—
442#399C2314yes—
443#399C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2314yes—
481#393C2314yes—
482#393C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#391C2312yes—
487#391C2314yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2314yes—
508#391C2312yes—
509#391C2311yescharacteristic
510#391C2314yes—
511#390C2312yes—
512#390C2312yes—
513#390C2312yes—
514#390C2311yescharacteristic
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2312yes—
518#390C2311yescharacteristic
519#390C2312yes—
520#390C2314yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2314yes—
528#390C2312yes—
529#390C2314yes—
530#390C2312yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2311yescharacteristic
536#390C2314yes—
537#390C2312yes—
538#390C2312yes—
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2314yes—
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2311yescharacteristic
546#389C2311yescharacteristic
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2314yes—
551#389C2311yescharacteristic
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2311yescharacteristic
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2314yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2312yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2314yes—
595#388C2314yes—
596#388C2312yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2314yes—
621#387C2314yes—
622#387C2312yes—
623#387C2312yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2312yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2312yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2312yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2312yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2312yes—
664#386C2314yes—
665#386C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2312yes—
679#385C2314yes—
680#385C2314yes—
681#385C2312yes—
682#385C2314yes—
683#385C2314yes—
684#385C2312yes—
685#385C2312yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2314yes—
691#384C2311yescharacteristic
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2311yescharacteristic
695#384C2312yes—
696#382C2311yescharacteristic
697#382C2311yescharacteristic
698#382C2312yes—
699#382C2311yescharacteristic
700#382C2312yes—
701#382C2314yes—
702#382C2312yes—
703#382C2311yescharacteristic
704#382C2312yes—
705#381C2314yes—
706#381C2314yes—
707#381C2314yes—
708#381C2314yes—
709#381C2314yes—
710#381C2314yes—
711#381C2312yes—
712#381C2312yes—
713#380C2312yes—
714#380C2312yes—
715#380C2312yes—
716#380C2312yes—
717#380C2312yes—
718#380C2312yes—
719#380C2312yes—
720#380C2314yes—
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#379C2314yes—
725#379C2314yes—
726#379C2314yes—
727C4×C4⋊C4C2311yescharacteristic
728C4×C4⋊C4C2311yescharacteristic
729C4×C4⋊C4C2311yescharacteristic
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2311yescharacteristic
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2314yes—
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2314yes—
742C4×C4⋊C4C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2312yes—
780C4×C22⋊C4C2314yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2314yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2314yes—
814C2×#95C2314yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C43C2311yescharacteristic
820C43C2311yescharacteristic
821C43C2311yescharacteristic
822C43C2312yes—
823C25C2414yes—
824C2×#41—28no—
825C2×#41—28no—
826C2×#41—28no—
827C22×Q8—28no—
828C22×Q8—28no—
829C22×Q8—44no—
830C22×Q8C2412yes—
831C22×Q8C2412yes—
832C22×Q8C2411yescharacteristic
833C22×Q8C2414yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2412yes—
836C22×D4—28no—
837C22×D4—28no—
838C22×D4—28no—
839C22×D4—28no—
840C22×D4—28no—
841C22×D4—44no—
842C22×D4C2411yescharacteristic
843C22×D4C2414yes—
844C22×D4C2414yes—
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2414yes—
849C22×D4C2411yescharacteristic
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2411yescharacteristic
855C23×C4—48no—
856C23×C4—48no—
857C23×C4—48no—
858C23×C4C2414yes—
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2412yes—
864C23×C4C2414yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2412yes—
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2414yes—
874C23×C4C2412yes—
875C23×C4C2414yes—
876C23×C4C2412yes—
877C4⋊Q8—28no—
878C4⋊Q8—24no—
879C4⋊Q8—24no—
880C4⋊Q8—24no—
881#127—24no—
882#127—24no—
883#127—44no—
884#125—24no—
885#125—24no—
886#124—28no—
887#124—24no—
888#124—28no—
889#124—216no—
890#124—216no—
891#124—28no—
892#124—28no—
893#124—28no—
894#124—48no—
895#124—44no—
896#124—44no—
897#124—44no—
898#124#4118yescomplemented
899#123—216no—
900#123—216no—
901#123—28no—
902#123—28no—
903#123—48no—
904#123—48no—
905#123—48no—
906#123—48no—
907C22⋊Q8—28no—
908C22⋊Q8—28no—
909C22⋊Q8—28no—
910C22⋊Q8—28no—
911C22⋊Q8—216no—
912C22⋊Q8—28no—
913C22⋊Q8—28no—
914C22⋊Q8—44no—
915#121—28no—
916#121—216no—
917#121—28no—
918#121—28no—
919#121—28no—
920#121—44no—
921#121—48no—
922#120—216no—
923#120—216no—
924#120—48no—
925C4×Q8—24no—
926C4×Q8—24no—
927C4×Q8—28no—
928C4×Q8—24no—
929C4×Q8—24no—
930C4×Q8—24no—
931C4×Q8—44no—
932C4×Q8—48no—
933C4×Q8—48no—
934C4×Q8—42no—
935C4×Q8—44no—
936C4×Q8—44no—
937C4×Q8—44no—
938C4×Q8—44no—
939C4×D4—28no—
940C4×D4—24no—
941C4×D4—24no—
942C4×D4—24no—
943C4×D4—24no—
944C4×D4—28no—
945C4×D4—24no—
946C4×D4—24no—
947C4×D4—24no—
948C4×D4—28no—
949C4×D4—24no—
950C4×D4—28no—
951C4×D4—24no—
952C4×D4—28no—
953C4×D4—24no—
954C4×D4—24no—
955C4×D4—44no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—48no—
962C4×D4—48no—
963C4×D4—48no—
964C4×D4—44no—
965C4×D4—48no—
966C4×D4—48no—
967C4×D4—48no—
968C4×D4—48no—
969C4×D4#4118yes—
970C4×D4#4118yes—
971#117—48no—
972#117—44no—
973C2×C4⋊C4—28no—
974C2×C4⋊C4—28no—
975C2×C4⋊C4—28no—
976C2×C4⋊C4—44no—
977C2×C4⋊C4—44no—
978C2×C4⋊C4—48no—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2411yescharacteristic
1036C2×C4⋊C4C2411yescharacteristic
1037C2×C22⋊C4—216no—
1038C2×C22⋊C4—216no—
1039C2×C22⋊C4—216no—
1040C2×C22⋊C4—48no—
1041C2×C22⋊C4—48no—
1042C2×C22⋊C4—48no—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C42—28no—
1102C2×C42—44no—
1103C2×C42—44no—
1104C2×C42—48no—
1105C2×C42—44no—
1106C2×C42—44no—
1107C2×C42—48no—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2412yes—
1112C2×C42C2411yescharacteristic
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2414yes—
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2412yes—
1121C2×C42C2411yescharacteristic
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2414yes—
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2412yes—
1135C2×C42C2414yes—
1136C2×C42C2414yes—
1137C2×C42C2412yes—
1138C2×C42C2414yes—
1139C2×C42C2414yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2412yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2411yescharacteristic
1148C2×C42C2412yes—
1149C2×C42C2411yescharacteristic
1150C2×C42C2411yescharacteristic
1151C2×C42C2411yescharacteristic
1152#95C2411yescharacteristic
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2411yescharacteristic
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2411yescharacteristic
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2412yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2411yescharacteristic
1201#95C2411yescharacteristic
1202#95C2412yes—
1203#95C2412yes—
1204#95C2411yescharacteristic
1205#95C2412yes—
1206#95C2412yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2412yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216C24—28no—
1217C24—28no—
1218C24—28no—
1219C24—28no—
1220C24—44no—
1221C24—44no—
1222C24—44no—
1223C24C2514yes—
1224C24C2512yes—
1225C24C2512yes—
1226C24C2512yes—
1227#41—432no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—24no—
1232C2×Q8—28no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—28no—
1236C2×Q8—24no—
1237C2×Q8—24no—
1238C2×Q8—22no—
1239C2×Q8—24no—
1240C2×Q8—24no—
1241C2×Q8—44no—
1242C2×Q8—41no—
1243C2×Q8—42no—
1244C2×Q8—42no—
1245C2×Q8—432no—
1246C2×Q8C2×#4114yes—
1247C2×D4—24no—
1248C2×D4—28no—
1249C2×D4—28no—
1250C2×D4—28no—
1251C2×D4—28no—
1252C2×D4—28no—
1253C2×D4—28no—
1254C2×D4—28no—
1255C2×D4—24no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—28no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—24no—
1266C2×D4—28no—
1267C2×D4—22no—
1268C2×D4—24no—
1269C2×D4—22no—
1270C2×D4—24no—
1271C2×D4—432no—
1272C2×D4—44no—
1273C2×D4—42no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—42no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—432no—
1284C2×D4C2×#4114yes—
1285C2×D4C2×#4114yes—
1286C2×D4C2×#4114yes—
1287C2×D4H(5,𝔽2)14yes—
1288C22×C4—24no—
1289C22×C4—24no—
1290C22×C4—28no—
1291C22×C4—24no—
1292C22×C4—28no—
1293C22×C4—28no—
1294C22×C4—24no—
1295C22×C4—28no—
1296C22×C4—28no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—24no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—28no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—28no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—24no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—28no—
1317C22×C4—28no—
1318C22×C4—42no—
1319C22×C4—44no—
1320C22×C4—42no—
1321C22×C4—42no—
1322C22×C4—42no—
1323C22×C4—44no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—42no—
1331C22×C4—44no—
1332C22×C4—42no—
1333C22×C4—44no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4—42no—
1338C22×C4—44no—
1339C22×C4—44no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4—832no—
1344C22×C4C2×#4118yes—
1345C22×C4C2×#4118yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2512yes—
1350C22×C4C2512yes—
1351C22×C4C2511yescharacteristic
1352C22×C4C2511yescharacteristic
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2514yes—
1357C22×C4C2514yes—
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2514yes—
1362C22×C4C2512yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2511yescharacteristic
1371C22×C4C2512yes—
1372C22×C4C2511yescharacteristic
1373C22×C4C2512yes—
1374C22×C4C2511yescharacteristic
1375C22×C4C2511yescharacteristic
1376C22×C4C2511yescharacteristic
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—28no—
1381C4⋊C4—24no—
1382C4⋊C4—24no—
1383C4⋊C4—24no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—24no—
1391C4⋊C4—24no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—22no—
1397C4⋊C4—24no—
1398C4⋊C4—28no—
1399C4⋊C4—24no—
1400C4⋊C4—24no—
1401C4⋊C4—28no—
1402C4⋊C4—24no—
1403C4⋊C4—24no—
1404C4⋊C4—28no—
1405C4⋊C4—24no—
1406C4⋊C4—22no—
1407C4⋊C4—24no—
1408C4⋊C4—24no—
1409C4⋊C4—28no—
1410C4⋊C4—22no—
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—24no—
1414C4⋊C4—22no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—44no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—41no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4C2×#4114yes—
1433C4⋊C4C2×#4114yes—
1434C4⋊C4H(5,𝔽2)14yes—
1435C22⋊C4—28no—
1436C22⋊C4—28no—
1437C22⋊C4—28no—
1438C22⋊C4—24no—
1439C22⋊C4—24no—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—28no—
1443C22⋊C4—24no—
1444C22⋊C4—24no—
1445C22⋊C4—24no—
1446C22⋊C4—28no—
1447C22⋊C4—28no—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—28no—
1451C22⋊C4—28no—
1452C22⋊C4—28no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—28no—
1459C22⋊C4—28no—
1460C22⋊C4—28no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—28no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4C2×#4118yes—
1490C22⋊C4C2×#4118yes—
1491C22⋊C4C2×#4118yes—
1492C22⋊C4C2×#4118yes—
1493C42—24no—
1494C42—24no—
1495C42—24no—
1496C42—24no—
1497C42—22no—
1498C42—22no—
1499C42—22no—
1500C42—24no—
1501C42—22no—
1502C42—22no—
1503C42—22no—
1504C42—24no—
1505C42—22no—
1506C42—24no—
1507C42—22no—
1508C42—24no—
1509C42—28no—
1510C42—24no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—42no—
1515C42—42no—
1516C42—44no—
1517C42—42no—
1518C42—42no—
1519C42—42no—
1520C42—42no—
1521C42—44no—
1522C42—44no—
1523C42—42no—
1524C42—44no—
1525C42—44no—
1526C42—42no—
1527C42—41no—
1528C42—42no—
1529C42—41no—
1530C42—41no—
1531C42—42no—
1532C42—41no—
1533C42—41no—
1534C42C2×#4114yes—
1535C42C2×#4114yes—
1536C42C2×#4114yes—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—22no—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—24no—
1548C23—22no—
1549C23—22no—
1550C23—24no—
1551C23—22no—
1552C23—24no—
1553C23—22no—
1554C23—24no—
1555C23—24no—
1556C23—22no—
1557C23—22no—
1558C23—24no—
1559C23—24no—
1560C23—22no—
1561C23—416no—
1562C23—416no—
1563C23—416no—
1564C23—416no—
1565C23—88no—
1566C23—88no—
1567C23—88no—
1568C23C22×#4114yes—
1569C23C22×#4114yes—
1570C23C22×#4114yes—
1571C23C2×H(5,𝔽2)14yes—
1572C23C2611yescharacteristic
1573Q8—28no—
1574Q8—44no—
1575Q8—416no—
1576Q8—48no—
1577Q8—48no—
1578Q8—84no—
1579D4—28no—
1580D4—48no—
1581D4—416no—
1582D4—416no—
1583D4—416no—
1584D4—48no—
1585D4—44no—
1586D4—48no—
1587D4—88no—
1588D4—84no—
1589D4—84no—
1590D4—164no—
1591D4#559116yescomplemented
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—216no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—24no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—24no—
1632C2×C4—24no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—22no—
1639C2×C4—24no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—24no—
1650C2×C4—24no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—21no—
1655C2×C4—22no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—24no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—22no—
1665C2×C4—21no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—48no—
1671C2×C4—48no—
1672C2×C4—48no—
1673C2×C4—48no—
1674C2×C4—416no—
1675C2×C4—48no—
1676C2×C4—416no—
1677C2×C4—416no—
1678C2×C4—48no—
1679C2×C4—48no—
1680C2×C4—84no—
1681C2×C4—84no—
1682C2×C4—88no—
1683C2×C4—88no—
1684C2×C4—84no—
1685C2×C4—84no—
1686C2×C4—84no—
1687C2×C4—88no—
1688C2×C4C22×#4112yes—
1689C2×C4C22×#4112yes—
1690C2×C4C22×#4114yes—
1691C2×C4C22×#4112yes—
1692C2×C4C22×#4112yes—
1693C2×C4C22×#4112yes—
1694C2×C4C22×#4114yes—
1695C2×C4C22×#4114yes—
1696C2×C4C22×#4112yes—
1697C2×C4C22×#4112yes—
1698C2×C4C22×#4112yes—
1699C2×C4C22×#4112yes—
1700C2×C4C2×H(5,𝔽2)14yes—
1701C2×C4C2×H(5,𝔽2)12yes—
1702C2×C4C2×H(5,𝔽2)12yes—
1703C2×C4#58512yes—
1704C22—24no—
1705C22—24no—
1706C22—24no—
1707C22—24no—
1708C22—24no—
1709C22—24no—
1710C22—24no—
1711C22—24no—
1712C22—24no—
1713C22—42no—
1714C22—42no—
1715C22—42no—
1716C22—42no—
1717C22—42no—
1718C22—44no—
1719C22—42no—
1720C22—44no—
1721C22—44no—
1722C22—42no—
1723C22—44no—
1724C22—42no—
1725C22—42no—
1726C22—44no—
1727C22—44no—
1728C22—42no—
1729C22—42no—
1730C22—44no—
1731C22—832no—
1732C22C2×#55918yes—
1733C22C23×#4111yescharacteristic
1734C22C23×#4111yescharacteristic
1735C22C23×#4111yescharacteristic
1736C22C22×H(5,𝔽2)11yescharacteristic
1737C22C22×H(5,𝔽2)11yescharacteristic
1738C22C2×#58511yescharacteristic
1739C222−1+611yescharacteristic
1740C4—22no—
1741C4—24no—
1742C4—22no—
1743C4—22no—
1744C4—22no—
1745C4—24no—
1746C4—24no—
1747C4—24no—
1748C4—22no—
1749C4—22no—
1750C4—41no—
1751C4—42no—
1752C4—41no—
1753C4—42no—
1754C4—41no—
1755C4—42no—
1756C4—41no—
1757C4—42no—
1758C4—44no—
1759C4—42no—
1760C4—41no—
1761C4—41no—
1762C4—42no—
1763C4—42no—
1764C4—42no—
1765C4—44no—
1766C4—44no—
1767C4—42no—
1768C4—41no—
1769C4C2×#55914yes—
1770C4#348114yes—
1771C2—28no—
1772C2—44no—
1773C2—82no—
1774C2—84no—
1775C2C22×#55911yescharacteristic
1776C2C2×#348111yescharacteristic
1777C2#41211yescharacteristic
1778C2#6298411yescharacteristic
1779C2#6298511yescharacteristic
1780C2#6299511yescharacteristic
1781C2#6301211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36260C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59862C2semidirect
2. #59678C2semidirect
3. #59646C2semidirect
4. #59644C2semidirect
5. #59642C2semidirect
6. #59638C2semidirect
7. #59635C2semidirect
8. #59634C2semidirect
9. #59630C2semidirect
10. #59625C2semidirect
11. #59624C2semidirect
12. #59147C2semidirect
13. #36609C2semidirect
14. #36606C2semidirect
15. #36591C2semidirect
16. #36580C2semidirect
17. #36521C2semidirect
18. #36499C2semidirect
19. #36487C2semidirect
20. #36469C2semidirect
21. #36454C2semidirect
22. #36441C2semidirect
23. #36303C2semidirect
25. #36238C2semidirect
26. #36237C2semidirect
27. #36216C2semidirect
28. D4×#124C2semidirect
29. C4×#559C2semidirect
30. C4×#554C2semidirect
31. C4×D4×Q8C2semidirect
32. C4×#547C2semidirect
33. C4×#546C2semidirect
34. C4×D42C2semidirect
35. C2×#2367C2semidirect
37. C2×#559C22semidirect
46. C22×C4×Q8C22semidirect
49. #2862C22semidirect
50. #2861C22semidirect
54. #2855C22semidirect
55. #2854C22semidirect
56. #2853C22semidirect
58. #2850C22semidirect
59. #2850C22semidirect
60. #2849C22semidirect
61. #2807C22semidirect
62. #2803C22semidirect
63. #2798C22semidirect
64. #2796C22semidirect
65. #2796C22semidirect
66. #2754C22semidirect
67. #2751C22semidirect
68. #2712C22semidirect
69. #2710C22semidirect
70. #2607C22semidirect
71. #2602C22semidirect
72. #2602C22semidirect
73. #2602C22semidirect
74. #2600C22semidirect
75. #2597C22semidirect
76. #2596C22semidirect
77. #2596C22semidirect
78. #2595C22semidirect
79. #2595C22semidirect
80. #2595C22semidirect
81. #2593C22semidirect
82. #2592C22semidirect
83. #2592C22semidirect
84. #2592C22semidirect
85. #2592C22semidirect
86. #2591C22semidirect
87. #2589C22semidirect
88. #2589C22semidirect
89. #2589C22semidirect
90. #2582C22semidirect
92. #2580C22semidirect
93. #2580C22semidirect
94. #2575C22semidirect
95. #2575C22semidirect
96. #2570C22semidirect
97. #2568C22semidirect
98. #2562C22semidirect
99. #2561C22semidirect
100. #2557C22semidirect
101. #2557C22semidirect
103. #2548C22semidirect
105. #2547C22semidirect
107. #2544C22semidirect
114. #2517C22semidirect
115. #2516C22semidirect
116. #2516C22semidirect
117. #2516C22semidirect
118. #2513C22semidirect
119. #2513C22semidirect
120. #2513C22semidirect
121. #2513C22semidirect
122. #2511C22semidirect
123. #2511C22semidirect
124. #2503C22semidirect
125. #2502C22semidirect
127. #2500C22semidirect
128. #2498C22semidirect
129. #2492C22semidirect
130. #2492C22semidirect
131. #2492C22semidirect
134. #2491C22semidirect
135. #2490C22semidirect
136. #2489C22semidirect
137. #2488C22semidirect
138. #2488C22semidirect
139. #2488C22semidirect
140. #2488C22semidirect
141. #2487C22semidirect
142. #2485C22semidirect
143. #2483C22semidirect
144. #2482C22semidirect
147. #2472C22semidirect
148. #2472C22semidirect
149. #2459C22semidirect
150. #2459C22semidirect
151. #2458C22semidirect
152. #2458C22semidirect
153. #2455C22semidirect
154. #2448C22semidirect
155. #2448C22semidirect
156. #2448C22semidirect
157. #2448C22semidirect
158. #2448C22semidirect
160. #2447C22semidirect
161. #2447C22semidirect
162. #2447C22semidirect
163. #2445C22semidirect
164. #2444C22semidirect
165. #2443C22semidirect
166. #2443C22semidirect
167. #2443C22semidirect
169. #2436C22semidirect
172. #2423C22semidirect
173. #2422C22semidirect
174. #2422C22semidirect
175. #2421C22semidirect
176. #2419C22semidirect
177. #2419C22semidirect
178. #2418C22semidirect
179. #2418C22semidirect
180. #2412C22semidirect
181. #2374C22semidirect
182. #2374C22semidirect
183. #2374C22semidirect
184. #2370C22semidirect
185. #2370C22semidirect
186. #2369C22semidirect
187. #2368C22semidirect
188. #2368C22semidirect
193. #2367C22semidirect
194. #2367C22semidirect
195. #2367C22semidirect
196. #2367C22semidirect
197. #2367C22semidirect
198. #2367C22semidirect
199. #2367C22semidirect
200. #2367C22semidirect
201. #2367C22semidirect
202. #2367C22semidirect
203. #2367C22semidirect
206. #2365C22semidirect
207. #2365C22semidirect
208. #2365C22semidirect
209. #2364C22semidirect
210. #2363C22semidirect
211. #2362C22semidirect
214. #2361C22semidirect
215. #2360C22semidirect
216. #2360C22semidirect
217. #2360C22semidirect
218. #2360C22semidirect
219. #2359C22semidirect
220. #2359C22semidirect
222. #2358C22semidirect
224. #2357C22semidirect
225. #2357C22semidirect
226. #2357C22semidirect
227. #2357C22semidirect
228. #2355C22semidirect
229. #2355C22semidirect
230. #2355C22semidirect
231. #2355C22semidirect
232. #2354C22semidirect
233. #2352C22semidirect
234. Q8×C4⋊C4C22semidirect
241. #2345C22semidirect
242. #2344C22semidirect
243. #2342C22semidirect
244. Q8×C22⋊C4C22semidirect
252. C4×C4⋊Q8C22semidirect
253. C4×C4⋊Q8C22semidirect
254. C4×C4⋊Q8C22semidirect
255. C4×C4⋊Q8C22semidirect
258. C4×#125C22semidirect
259. C4×#125C22semidirect
261. C4×#124C22semidirect
262. C4×#124C22semidirect
263. C4×#124C22semidirect
264. C4×C22⋊Q8C22semidirect
265. C4×C22⋊Q8C22semidirect
266. C4×C22⋊Q8C22semidirect
267. C4×C22⋊Q8C22semidirect
268. C4×C22⋊Q8C22semidirect
269. C4×C22⋊Q8C22semidirect
270. C4×C22⋊Q8C22semidirect
271. C4×#123C22semidirect
272. C4×#123C22semidirect
273. C4×#123C22semidirect
274. C4×#123C22semidirect
277. C4×#121C22semidirect
278. C4×#121C22semidirect
279. C4×#121C22semidirect
281. C4×#120C22semidirect
282. C2×#391C22semidirect
284. C2×#388C22semidirect
285. C2×#388C22semidirect
286. C2×#385C22semidirect
287. C42×Q8C22semidirect
288. C42×Q8C22semidirect
294. C42×D4C22semidirect
295. C42×D4C22semidirect
296. C2×C4×C4⋊C4C22semidirect
297. C2×C4×C4⋊C4C22semidirect
298. C2×C4×C22⋊C4C22semidirect
898. #124#41semidirect
1591. D4#559semidirect

Maximal subgroups

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

subgroupindex
#598622
#596782
#596462
#596442
#596422
#596382
#596352
#596342
#596302
#596252
#596242
#591472
#366092
#366062
#365912
#365802
#365212
#364992
#364872
#364692
#364542
#364412
#363032
#362602
#362382
#362372
#362162
D4×#1242
C4×#5592
C4×#5542
C4×D4×Q82
C4×#5472
C4×#5462
C4×D422
C2×#23672