Finite Group Databasebeta

← #7692375

Subgroups — #7692375

Order 512.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59642C211yesmaximal, characteristic, complemented
2#59600C214yesmaximal, complemented
3#59562C212yesmaximal
4#59504C212yesmaximal, complemented
5#59488C212yesmaximal, complemented
6#59259C211yesmaximal, characteristic, complemented
7#59214C211yesmaximal, characteristic, complemented
8#59025C212yesmaximal, complemented
9#45161C212yesmaximal, complemented
10#45117C212yesmaximal, complemented
11#44839C214yesmaximal, complemented
12#44358C214yesmaximal, complemented
13#40166C212yesmaximal, complemented
14#40051C212yesmaximal, complemented
15#38965C211yesmaximal, characteristic, complemented
16#38911C211yesmaximal, characteristic, complemented
17#38551C214yesmaximal, complemented
18#37856C212yesmaximal, complemented
19#36507C212yesmaximal, complemented
20#36450C211yesmaximal, characteristic, complemented
21#36427C212yesmaximal, complemented
22#36299C211yesmaximal, characteristic, complemented
23#36299C212yesmaximal, complemented
24#36272C211yesmaximal, characteristic, complemented
25#36210C211yesmaximal, characteristic, complemented
26D4×C22⋊Q8C211yesmaximal, characteristic, complemented
27#35993C212yesmaximal, complemented
28#35832C212yesmaximal, complemented
29#34893C212yesmaximal, complemented
30#34700C211yesmaximal, characteristic
31#34311C211yesmaximal, characteristic, complemented
32#34242C211yesmaximal, characteristic, complemented
33#34203C212yesmaximal, complemented
34C4×#556C211yesmaximal, characteristic, complemented
35D4×#117C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#552C2212yescomplemented
38C2×D4×Q8C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C22×C22⋊Q8C2212yes—
41C2×#519C2212yescomplemented
42C22×C4×D4C2211yescharacteristic
43C22×#117C2212yes—
44#2863C2212yescomplemented
45#2863C2212yescomplemented
46#2859C2211yescharacteristic, complemented
47#2859C2212yescomplemented
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic, complemented
50#2853C2214yescomplemented
51#2848C2212yes—
52#2807C2214yescomplemented
53#2789C2214yescomplemented
54#2780C2214yescomplemented
55#2778C2214yes—
56#2777C2214yescomplemented
57#2776C2214yescomplemented
58#2768C2214yes—
59#2768C2214yescomplemented
60#2755C2214yescomplemented
61#2746C2214yes—
62#2744C2214yes—
63#2741C2214yescomplemented
64#2738C2214yes—
65#2738C2214yescomplemented
66#2735C2214yes—
67#2735C2214yes—
68#2704C2214yescomplemented
69#2700C2214yes—
70#2689C2214yes—
71#2689C2214yescomplemented
72#2687C2214yescomplemented
73#2655C2214yescomplemented
74#2637C2214yescomplemented
75#2629C2212yescomplemented
76#2625C2212yescomplemented
77#2611C2214yescomplemented
78#2609C2214yes—
79#2601C2214yescomplemented
80#2589C2214yescomplemented
81#2589C2214yescomplemented
82#2587C2214yescomplemented
83#2587C2214yescomplemented
84#2585C2214yescomplemented
85#2584C2212yescomplemented
86#2582C2211yescharacteristic, complemented
87#2582C2212yescomplemented
88#2580C2212yes—
89#2578C2214yes—
90#2577C2214yes—
91#2577C2214yescomplemented
92#2577C2214yescomplemented
93#2576C2214yes—
94#2576C2214yes—
95#2573C2214yescomplemented
96#2570C2212yescomplemented
97#2568C2211yescharacteristic, complemented
98#2566C2212yes—
99#2565C2212yescomplemented
100#2562C2212yes—
101#2560C2214yescomplemented
102#2553C2214yescomplemented
103#2552C2211yescharacteristic, complemented
104#2552C2211yescharacteristic, complemented
105#2550C2212yescomplemented
106#2542C2211yescharacteristic
107#2538C2212yes—
108#2538C2211yescharacteristic
109#2538C2212yescomplemented
110#2528C2214yescomplemented
111#2523C2214yescomplemented
112#2522C2214yescomplemented
113#2520C2214yescomplemented
114#2518C2214yescomplemented
115#2515C2214yescomplemented
116#2515C2214yescomplemented
117#2515C2214yescomplemented
118#2515C2214yescomplemented
119#2514C2212yescomplemented
120#2514C2212yescomplemented
121#2509C2212yescomplemented
122#2509C2212yescomplemented
123#2509C2212yescomplemented
124#2508C2212yescomplemented
125#2507C2212yescomplemented
126#2507C2212yescomplemented
127#2502C2212yescomplemented
128#2499C2212yes—
129#2497C2212yes—
130#2497C2212yescomplemented
131#2496C2212yescomplemented
132#2495C2212yes—
133#2495C2214yescomplemented
134#2495C2212yescomplemented
135#2494C2212yes—
136#2494C2212yes—
137#2494C2212yescomplemented
138#2492C2212yescomplemented
139#2492C2212yescomplemented
140#2489C2212yes—
141#2489C2212yescomplemented
142#2487C2212yescomplemented
143#2485C2212yes—
144#2482C2214yes—
145#2481C2214yescomplemented
146#2480C2212yes—
147#2480C2214yes—
148#2479C2214yes—
149#2479C2214yescomplemented
150#2477C2214yes—
151#2475C2214yes—
152#2475C2214yescomplemented
153#2475C2214yescomplemented
154#2475C2214yescomplemented
155#2472C2214yes—
156#2471C2214yes—
157#2468C2212yes—
158#2465C2214yescomplemented
159#2462C2214yescomplemented
160#2458C2214yescomplemented
161#2457C2212yes—
162#2454C2212yes—
163#2454C2211yescharacteristic
164#2452C2212yes—
165#2449C2214yes—
166#2447C2212yes—
167#2447C2212yes—
168#2447C2211yescharacteristic
169#2442C2211yescharacteristic
170#2441C2212yes—
171#2441C2212yescomplemented
172#2441C2212yescomplemented
173#2440C2212yes—
174#2440C2212yescomplemented
175#2437C2214yes—
176#2435C2211yescharacteristic
177#2427C2211yescharacteristic
178#2423C2212yes—
179#2423C2212yescomplemented
180#2422C2212yes—
181#2421C2212yescomplemented
182#2421C2214yescomplemented
183#2421C2212yescomplemented
184#2420C2211yescharacteristic
185#2420C2212yes—
186#2418C2212yes—
187#2417C2212yes—
188#2417C2211yescharacteristic
189#2415C2212yes—
190#2415C2212yescomplemented
191#2415C2212yescomplemented
192#2411C2214yes—
193#2409C2212yes—
194#2409C2212yescomplemented
195#2408C2211yescharacteristic
196#2396C2214yescomplemented
197#2396C2214yescomplemented
198#2395C2212yes—
199#2392C2212yes—
200#2373C2212yes—
201#2373C2214yescomplemented
202#2373C2212yescomplemented
203#2370C2212yescomplemented
204#2367C2212yes—
205#2367C2212yes—
206#2365C2211yescharacteristic, complemented
207#2365C2212yescomplemented
208#2365C2211yescharacteristic, complemented
209#2363C2212yes—
210#2363C2212yes—
211#2362C2212yes—
212#2362C2212yes—
213#2362C2211yescharacteristic
214#2362C2212yes—
215#2362C2214yescomplemented
216#2362C2212yescomplemented
217#2362C2211yescharacteristic, complemented
218#2362C2212yescomplemented
219#2360C2212yescomplemented
220#2360C2212yescomplemented
221#2360C2214yescomplemented
222#2360C2212yescomplemented
223#2360C2212yescomplemented
224#2356C2212yescomplemented
225#2355C2211yescharacteristic, complemented
226#2355C2212yescomplemented
227#2355C2211yescharacteristic, complemented
228#2355C2212yescomplemented
229#2354C2211yescharacteristic
230#2354C2212yes—
231#2354C2211yescharacteristic
232#2354C2211yescharacteristic
233#2354C2212yescomplemented
234#2352C2212yes—
235#2352C2212yes—
236#2352C2212yescomplemented
237Q8×C4⋊C4C2211yescharacteristic, complemented
238Q8×C4⋊C4C2211yescharacteristic, complemented
239D4×C4⋊C4C2211yescharacteristic
240D4×C4⋊C4C2211yescharacteristic
241D4×C4⋊C4C2211yescharacteristic
242D4×C4⋊C4C2212yes—
243#2347C2211yescharacteristic
244#2347C2211yescharacteristic, complemented
245#2347C2212yescomplemented
246#2344C2212yes—
247#2344C2212yescomplemented
248#2344C2214yescomplemented
249#2344C2214yescomplemented
250#2342C2214yes—
251#2342C2214yes—
252#2342C2214yes—
253Q8×C22⋊C4C2212yescomplemented
254D4×C22⋊C4C2212yes—
255D4×C22⋊C4C2212yes—
256#2335C2214yescomplemented
257#2323C2214yes—
258#2323C2214yes—
259#2323C2214yescomplemented
260#2323C2212yescomplemented
261#2316C2212yescomplemented
262#2314C2212yescomplemented
263#2310C2212yescomplemented
264C4×C4⋊Q8C2212yescomplemented
265C4×C4⋊Q8C2211yescharacteristic, complemented
266C4×C4⋊Q8C2211yescharacteristic, complemented
267C4×#125C2212yescomplemented
268C4×#125C2212yescomplemented
269C4×#126C2212yes—
270C4×#126C2212yescomplemented
271C4×#124C2212yes—
272C4×#124C2212yes—
273C4×#124C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2214yescomplemented
277C4×C22⋊Q8C2211yescharacteristic, complemented
278C4×C22⋊Q8C2214yescomplemented
279C4×#121C2211yescharacteristic
280C4×#120C2212yes—
281#2296C2214yescomplemented
282#2293C2211yescharacteristic
283#2293C2212yes—
284#2293C2212yes—
285#2293C2212yes—
286#2293C2212yes—
287#2290C2214yes—
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic, complemented
290#2280C2212yes—
291#2280C2212yes—
292#2274C2212yescomplemented
293C42×Q8C2211yescharacteristic, complemented
294C42×Q8C2212yescomplemented
295C42×D4C2212yes—
296C42×D4C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C4×#117C2211yescharacteristic, complemented
299C23×Q8C2312yes—
300C23×D4C2311yescharacteristic
301C24×C4C2312yes—
302#556—28no—
303#552—48no—
304D4×Q8—28no—
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×C4⋊Q8C2311yescharacteristic
308#529—28no—
309C2×#126C2312yes—
310C2×#126C2312yes—
311C2×#126C2312yes—
312C2×#126C2314yes—
313C2×#125C2311yescharacteristic
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#124C2311yescharacteristic
319C2×#124C2312yes—
320C2×#124C2311yescharacteristic
321C2×#123C2312yes—
322C2×#123C2314yes—
323C2×C22⋊Q8—216no—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×#121C2311yescharacteristic
339C2×#121C2311yescharacteristic
340C2×#120C2312yes—
341#519—48no—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2314yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2314yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×D4—28no—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×#117—48no—
372C2×#117C2312yes—
373C2×#117C2311yescharacteristic
374C2×#117C2311yescharacteristic
375C2×#117C2312yes—
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2314yes—
381C2×#117C2314yes—
382C2×#117C2314yes—
383C2×#117C2314yes—
384C2×#117C2314yes—
385C2×#117C2312yes—
386C2×#117C2314yes—
387C2×#117C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2311yescharacteristic
390C22×C4⋊C4C2314yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C22⋊C4C2314yes—
394C22×C22⋊C4C2312yes—
395C22×C22⋊C4C2314yes—
396C22×C42C2311yescharacteristic
397C22×C42C2311yescharacteristic
398C22×C42C2314yes—
399#401C2314yes—
400#401C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2312yes—
412#400C2314yes—
413#400C2314yes—
414#399C2314yes—
415#399C2312yes—
416#399C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2312yes—
434#398C2312yes—
435#398C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2312yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2312yes—
447#397C2312yes—
448#397C2312yes—
449#397C2314yes—
450#397C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#394C2314yes—
466#394C2314yes—
467#394C2312yes—
468#394C2312yes—
469#394C2312yes—
470#394C2312yes—
471#394C2312yes—
472#394C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#392C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2312yes—
481#391C2311yescharacteristic
482#391C2312yes—
483#391C2311yescharacteristic
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2312yes—
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2311yescharacteristic
492#391C2314yes—
493#391C2312yes—
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2312yes—
497#391C2312yes—
498#390C2314yes—
499#390C2311yescharacteristic
500#390C2312yes—
501#390C2311yescharacteristic
502#390C2312yes—
503#390C2314yes—
504#390C2312yes—
505#390C2312yes—
506#390C2311yescharacteristic
507#390C2312yes—
508#390C2311yescharacteristic
509#389C2311yescharacteristic
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2311yescharacteristic
515#389C2311yescharacteristic
516#389C2314yes—
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2312yes—
533#389C2312yes—
534#389C2312yes—
535#389C2314yes—
536#389C2312yes—
537#389C2312yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2311yescharacteristic
547#389C2312yes—
548#389C2311yescharacteristic
549#389C2311yescharacteristic
550#389C2312yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2314yes—
555#389C2311yescharacteristic
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2312yes—
583#388C2314yes—
584#388C2314yes—
585#388C2312yes—
586#388C2314yes—
587#388C2312yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2312yes—
594#388C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2312yes—
598#388C2312yes—
599#388C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2312yes—
631#387C2312yes—
632#387C2314yes—
633#387C2312yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#386C2312yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2312yes—
651#386C2312yes—
652#386C2312yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2312yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#385C2314yes—
664#385C2314yes—
665#385C2314yes—
666#385C2314yes—
667#385C2314yes—
668#385C2314yes—
669#385C2314yes—
670#385C2312yes—
671#385C2312yes—
672#385C2312yes—
673#385C2312yes—
674#385C2312yes—
675#384C2312yes—
676#384C2311yescharacteristic
677#384C2311yescharacteristic
678#384C2312yes—
679#384C2312yes—
680#384C2311yescharacteristic
681#384C2311yescharacteristic
682#384C2312yes—
683#384C2312yes—
684#383C2312yes—
685#383C2312yes—
686#383C2314yes—
687#383C2314yes—
688#383C2314yes—
689#382C2312yes—
690#382C2312yes—
691#382C2312yes—
692#382C2312yes—
693#382C2311yescharacteristic
694#382C2312yes—
695#382C2314yes—
696#382C2314yes—
697#382C2312yes—
698#382C2314yes—
699#381C2314yes—
700#381C2314yes—
701#381C2312yes—
702#381C2314yes—
703#381C2314yes—
704#381C2312yes—
705#380C2312yes—
706#380C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710#380C2312yes—
711#380C2314yes—
712#380C2314yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2312yes—
717#380C2314yes—
718#380C2311yescharacteristic
719#380C2312yes—
720#380C2312yes—
721#380C2312yes—
722#380C2312yes—
723#380C2311yescharacteristic
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2311yescharacteristic
729#380C2311yescharacteristic
730#380C2312yes—
731#379C2314yes—
732#379C2314yes—
733#379C2312yes—
734#379C2312yes—
735#379C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2312yes—
738C4×C4⋊C4C2312yes—
739C4×C4⋊C4C2312yes—
740C4×C4⋊C4C2314yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2314yes—
746C4×C4⋊C4C2314yes—
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2314yes—
757C4×C4⋊C4C2314yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2311yescharacteristic
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812#376C2312yes—
813#376C2312yes—
814C43C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C25C2412yes—
819C22×Q8—28no—
820C22×Q8—28no—
821C22×Q8—44no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2412yes—
825C22×Q8C2414yes—
826C22×Q8C2411yescharacteristic
827C22×D4—24no—
828C22×D4—24no—
829C22×D4—42no—
830C22×D4C2411yescharacteristic
831C22×D4C2412yes—
832C22×D4C2411yescharacteristic
833C22×D4C2411yescharacteristic
834C22×D4C2412yes—
835C22×D4C2412yes—
836C23×C4—28no—
837C23×C4—28no—
838C23×C4—44no—
839C23×C4C2412yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2411yescharacteristic
843C23×C4C2414yes—
844C23×C4C2414yes—
845C23×C4C2412yes—
846C23×C4C2412yes—
847C23×C4C2412yes—
848C23×C4C2412yes—
849C23×C4C2411yescharacteristic
850C23×C4C2411yescharacteristic
851C23×C4C2414yes—
852C23×C4C2411yescharacteristic
853C23×C4C2414yes—
854C4⋊Q8—28no—
855C4⋊Q8—24no—
856C4⋊Q8—24no—
857#126—28no—
858#126—28no—
859#126—28no—
860#126—48no—
861#125—24no—
862#125—44no—
863#125—44no—
864#125—48no—
865#125—44no—
866#124—24no—
867#124—24no—
868#124—28no—
869#123—28no—
870#123—48no—
871C22⋊Q8—28no—
872C22⋊Q8—24no—
873C22⋊Q8—28no—
874C22⋊Q8—28no—
875C22⋊Q8—28no—
876C22⋊Q8—216no—
877C22⋊Q8—24no—
878C22⋊Q8—216no—
879C22⋊Q8—216no—
880C22⋊Q8—48no—
881C22⋊Q8—42no—
882C22⋊Q8—44no—
883C22⋊Q8—44no—
884C22⋊Q8#4118yes—
885#121—24no—
886#121—24no—
887#120—44no—
888C4×Q8—24no—
889C4×Q8—28no—
890C4×Q8—24no—
891C4×Q8—28no—
892C4×Q8—24no—
893C4×Q8—24no—
894C4×Q8—44no—
895C4×Q8—48no—
896C4×Q8—48no—
897C4×Q8—44no—
898C4×Q8—44no—
899C4×Q8—44no—
900C4×Q8—44no—
901C4×D4—24no—
902C4×D4—28no—
903C4×D4—28no—
904C4×D4—28no—
905C4×D4—28no—
906C4×D4—24no—
907C4×D4—24no—
908C4×D4—28no—
909C4×D4—24no—
910C4×D4—44no—
911C4×D4—44no—
912C4×D4—42no—
913C4×D4—42no—
914C4×D4—44no—
915C4×D4#4118yes—
916#117—28no—
917#117—24no—
918#117—24no—
919#117—24no—
920#117—28no—
921#117—24no—
922#117—44no—
923#117—48no—
924#117—48no—
925#117—48no—
926#117—48no—
927#117—48no—
928#117—48no—
929#117—44no—
930#117—44no—
931#117—44no—
932C2×C4⋊C4—24no—
933C2×C4⋊C4—28no—
934C2×C4⋊C4—216no—
935C2×C4⋊C4—28no—
936C2×C4⋊C4—44no—
937C2×C4⋊C4C2411yescharacteristic
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2412yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2414yes—
946C2×C4⋊C4C2414yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2411yescharacteristic
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2414yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2414yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C22⋊C4—28no—
1010C2×C22⋊C4—216no—
1011C2×C22⋊C4—48no—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2414yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C42—24no—
1065C2×C42—24no—
1066C2×C42—48no—
1067C2×C42C2412yes—
1068C2×C42C2412yes—
1069C2×C42C2411yescharacteristic
1070C2×C42C2412yes—
1071C2×C42C2414yes—
1072C2×C42C2414yes—
1073C2×C42C2412yes—
1074C2×C42C2411yescharacteristic
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2412yes—
1079C2×C42C2411yescharacteristic
1080C2×C42C2411yescharacteristic
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2411yescharacteristic
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2414yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2414yes—
1098C2×C42C2414yes—
1099C2×C42C2412yes—
1100C2×C42C2412yes—
1101C2×C42C2414yes—
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2412yes—
1106C2×C42C2411yescharacteristic
1107#95C2412yes—
1108#95C2412yes—
1109#95C2412yes—
1110#95C2412yes—
1111#95C2412yes—
1112#95C2412yes—
1113#95C2412yes—
1114#95C2412yes—
1115#95C2411yescharacteristic
1116#95C2411yescharacteristic
1117#95C2411yescharacteristic
1118#95C2412yes—
1119#95C2414yes—
1120#95C2414yes—
1121#95C2414yes—
1122#95C2411yescharacteristic
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2412yes—
1126#95C2412yes—
1127#95C2414yes—
1128#95C2414yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2412yes—
1139#95C2414yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2414yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179C24—24no—
1180C24—24no—
1181C24—24no—
1182C24—42no—
1183C24—42no—
1184C24—42no—
1185C24—42no—
1186C24C2511yescharacteristic
1187C24C2511yescharacteristic
1188C24C2512yes—
1189C24C2512yes—
1190C2×Q8—22no—
1191C2×Q8—22no—
1192C2×Q8—24no—
1193C2×Q8—28no—
1194C2×Q8—24no—
1195C2×Q8—28no—
1196C2×Q8—24no—
1197C2×Q8—22no—
1198C2×Q8—24no—
1199C2×Q8—22no—
1200C2×Q8—22no—
1201C2×Q8—24no—
1202C2×Q8—44no—
1203C2×Q8—42no—
1204C2×Q8—432no—
1205C2×Q8C2×#4114yes—
1206C2×D4—24no—
1207C2×D4—22no—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—24no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—41no—
1217C2×D4—42no—
1218C2×D4—42no—
1219C2×D4—42no—
1220C2×D4—42no—
1221C2×D4—42no—
1222C2×D4—416no—
1223C2×D4C2×#4114yes—
1224C2×D42−1+414yes—
1225C22×C4—22no—
1226C22×C4—24no—
1227C22×C4—22no—
1228C22×C4—24no—
1229C22×C4—24no—
1230C22×C4—28no—
1231C22×C4—24no—
1232C22×C4—28no—
1233C22×C4—22no—
1234C22×C4—22no—
1235C22×C4—22no—
1236C22×C4—24no—
1237C22×C4—28no—
1238C22×C4—24no—
1239C22×C4—22no—
1240C22×C4—24no—
1241C22×C4—24no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—28no—
1245C22×C4—24no—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—28no—
1254C22×C4—42no—
1255C22×C4—42no—
1256C22×C4—42no—
1257C22×C4—44no—
1258C22×C4—44no—
1259C22×C4—432no—
1260C22×C4—44no—
1261C22×C4—44no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—44no—
1265C22×C4—44no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—44no—
1269C22×C4C2×#4118yes—
1270C22×C4C2×#4114yes—
1271C22×C4C2511yescharacteristic
1272C22×C4C2512yes—
1273C22×C4C2511yescharacteristic
1274C22×C4C2511yescharacteristic
1275C22×C4C2512yes—
1276C22×C4C2511yescharacteristic
1277C22×C4C2511yescharacteristic
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2512yes—
1283C22×C4C2514yes—
1284C22×C4C2514yes—
1285C22×C4C2514yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2514yes—
1289C22×C4C2511yescharacteristic
1290C22×C4C2511yescharacteristic
1291C22×C4C2512yes—
1292C22×C4C2512yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2511yescharacteristic
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2511yescharacteristic
1301C22×C4C2511yescharacteristic
1302C4⋊C4—24no—
1303C4⋊C4—22no—
1304C4⋊C4—28no—
1305C4⋊C4—24no—
1306C4⋊C4—28no—
1307C4⋊C4—28no—
1308C4⋊C4—28no—
1309C4⋊C4—22no—
1310C4⋊C4—24no—
1311C4⋊C4—22no—
1312C4⋊C4—24no—
1313C4⋊C4—22no—
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—22no—
1319C4⋊C4—24no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—28no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—24no—
1326C4⋊C4—28no—
1327C4⋊C4—22no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—24no—
1333C4⋊C4—22no—
1334C4⋊C4—24no—
1335C4⋊C4—24no—
1336C4⋊C4—28no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—44no—
1340C4⋊C4—42no—
1341C4⋊C4—42no—
1342C4⋊C4—42no—
1343C4⋊C4—44no—
1344C4⋊C4—44no—
1345C4⋊C4—44no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—44no—
1352C4⋊C4—41no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—42no—
1357C4⋊C4—42no—
1358C4⋊C4—44no—
1359C4⋊C4—42no—
1360C4⋊C4—44no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—42no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4C2×#4114yes—
1371C4⋊C4C2×#4118yes—
1372C4⋊C4C2×#4114yes—
1373C4⋊C4H(5,𝔽2)14yes—
1374C22⋊C4—24no—
1375C22⋊C4—28no—
1376C22⋊C4—24no—
1377C22⋊C4—24no—
1378C22⋊C4—24no—
1379C22⋊C4—28no—
1380C22⋊C4—24no—
1381C22⋊C4—22no—
1382C22⋊C4—28no—
1383C22⋊C4—24no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—28no—
1389C22⋊C4—28no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—22no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—28no—
1396C22⋊C4—24no—
1397C22⋊C4—24no—
1398C22⋊C4—24no—
1399C22⋊C4—44no—
1400C22⋊C4—44no—
1401C22⋊C4—44no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—42no—
1407C22⋊C4—44no—
1408C22⋊C4—44no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—44no—
1413C22⋊C4—41no—
1414C22⋊C4—41no—
1415C22⋊C4—41no—
1416C22⋊C4—44no—
1417C22⋊C4—41no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4C2×#4118yes—
1425C22⋊C4C2×#4118yes—
1426C42—22no—
1427C42—22no—
1428C42—22no—
1429C42—22no—
1430C42—22no—
1431C42—22no—
1432C42—24no—
1433C42—24no—
1434C42—24no—
1435C42—22no—
1436C42—24no—
1437C42—24no—
1438C42—24no—
1439C42—28no—
1440C42—24no—
1441C42—24no—
1442C42—22no—
1443C42—28no—
1444C42—24no—
1445C42—24no—
1446C42—22no—
1447C42—24no—
1448C42—24no—
1449C42—22no—
1450C42—24no—
1451C42—22no—
1452C42—44no—
1453C42—44no—
1454C42—41no—
1455C42—42no—
1456C42—42no—
1457C42—42no—
1458C42—44no—
1459C42—44no—
1460C42—44no—
1461C42—44no—
1462C42—42no—
1463C42—42no—
1464C42—44no—
1465C42C2×#4114yes—
1466C23—22no—
1467C23—22no—
1468C23—22no—
1469C23—21no—
1470C23—22no—
1471C23—21no—
1472C23—22no—
1473C23—21no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—21no—
1478C23—21no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—22no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—48no—
1492C23—48no—
1493C23—48no—
1494C23—84no—
1495C23—84no—
1496C23—84no—
1497C23—84no—
1498C23C22×#4112yes—
1499C23C22×#4114yes—
1500C23C2×2−1+414yes—
1501C23C2611yescharacteristic
1502Q8—28no—
1503Q8—48no—
1504Q8—416no—
1505Q8—48no—
1506Q8—44no—
1507D4—28no—
1508D4—28no—
1509D4—44no—
1510D4—48no—
1511D4—84no—
1512D4—84no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—22no—
1516C2×C4—22no—
1517C2×C4—21no—
1518C2×C4—22no—
1519C2×C4—22no—
1520C2×C4—22no—
1521C2×C4—22no—
1522C2×C4—22no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—28no—
1528C2×C4—216no—
1529C2×C4—22no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—22no—
1537C2×C4—21no—
1538C2×C4—22no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—24no—
1542C2×C4—22no—
1543C2×C4—24no—
1544C2×C4—24no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—24no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—24no—
1554C2×C4—22no—
1555C2×C4—24no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—22no—
1562C2×C4—24no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—24no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—48no—
1596C2×C4—416no—
1597C2×C4—48no—
1598C2×C4—48no—
1599C2×C4—416no—
1600C2×C4—44no—
1601C2×C4—48no—
1602C2×C4—44no—
1603C2×C4—44no—
1604C2×C4—82no—
1605C2×C4—82no—
1606C2×C4—88no—
1607C2×C4—88no—
1608C2×C4C22×#4112yes—
1609C2×C4C22×#4112yes—
1610C2×C4C22×#4114yes—
1611C2×C4C22×#4114yes—
1612C2×C4C22×#4114yes—
1613C2×C4C22×#4112yes—
1614C2×C4C22×#4112yes—
1615C2×C4C22×#4112yes—
1616C2×C4C2×H(5,𝔽2)14yes—
1617C2×C4C2×H(5,𝔽2)12yes—
1618C2×C4C2×2−1+412yes—
1619C2×C4#58512yes—
1620C2×C4#58512yes—
1621C22—22no—
1622C22—24no—
1623C22—24no—
1624C22—24no—
1625C22—24no—
1626C22—24no—
1627C22—22no—
1628C22—24no—
1629C22—22no—
1630C22—42no—
1631C22—41no—
1632C22—42no—
1633C22—42no—
1634C22—41no—
1635C22—41no—
1636C22—42no—
1637C22—42no—
1638C22—42no—
1639C22—42no—
1640C22—41no—
1641C22—42no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—816no—
1650C22C23×#4111yescharacteristic
1651C22C23×#4111yescharacteristic
1652C22C22×H(5,𝔽2)11yescharacteristic
1653C22C22×2−1+411yescharacteristic
1654C22C2×#58511yescharacteristic
1655C22C2×#58511yescharacteristic
1656C222−1+611yescharacteristic
1657C4—22no—
1658C4—24no—
1659C4—24no—
1660C4—22no—
1661C4—22no—
1662C4—24no—
1663C4—24no—
1664C4—42no—
1665C4—41no—
1666C4—42no—
1667C4—41no—
1668C4—41no—
1669C4—42no—
1670C4—41no—
1671C4—44no—
1672C4—42no—
1673C4—41no—
1674C4—41no—
1675C4—42no—
1676C4—44no—
1677C4—42no—
1678C4—42no—
1679C4—41no—
1680C4—42no—
1681C4—44no—
1682C4—42no—
1683C4—41no—
1684C4—42no—
1685C4—44no—
1686C4#348114yes—
1687C4#349514yes—
1688C2—44no—
1689C2—44no—
1690C2—42no—
1691C2—81no—
1692C2C2×#348111yescharacteristic
1693C2C2×#349511yescharacteristic
1694C2#6281611yescharacteristic
1695C2#6292211yescharacteristic
1696C2#6299811yescharacteristic
1697C2#6300911yescharacteristic
1698C2#6301311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2408C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59642C2semidirect
2. #59600C2semidirect
4. #59504C2semidirect
5. #59488C2semidirect
6. #59259C2semidirect
7. #59214C2semidirect
8. #59025C2semidirect
9. #45161C2semidirect
10. #45117C2semidirect
11. #44839C2semidirect
12. #44358C2semidirect
13. #40166C2semidirect
14. #40051C2semidirect
15. #38965C2semidirect
16. #38911C2semidirect
17. #38551C2semidirect
18. #37856C2semidirect
19. #36507C2semidirect
20. #36450C2semidirect
21. #36427C2semidirect
22. #36299C2semidirect
23. #36299C2semidirect
24. #36272C2semidirect
25. #36210C2semidirect
26. D4×C22⋊Q8C2semidirect
27. #35993C2semidirect
28. #35832C2semidirect
29. #34893C2semidirect
31. #34311C2semidirect
32. #34242C2semidirect
33. #34203C2semidirect
34. C4×#556C2semidirect
35. D4×#117C2semidirect
37. C2×#552C22semidirect
41. C2×#519C22semidirect
44. #2863C22semidirect
45. #2863C22semidirect
46. #2859C22semidirect
47. #2859C22semidirect
49. #2857C22semidirect
50. #2853C22semidirect
52. #2807C22semidirect
53. #2789C22semidirect
54. #2780C22semidirect
56. #2777C22semidirect
57. #2776C22semidirect
59. #2768C22semidirect
60. #2755C22semidirect
63. #2741C22semidirect
65. #2738C22semidirect
68. #2704C22semidirect
71. #2689C22semidirect
72. #2687C22semidirect
73. #2655C22semidirect
74. #2637C22semidirect
75. #2629C22semidirect
76. #2625C22semidirect
77. #2611C22semidirect
79. #2601C22semidirect
80. #2589C22semidirect
81. #2589C22semidirect
82. #2587C22semidirect
83. #2587C22semidirect
84. #2585C22semidirect
85. #2584C22semidirect
86. #2582C22semidirect
87. #2582C22semidirect
91. #2577C22semidirect
92. #2577C22semidirect
95. #2573C22semidirect
96. #2570C22semidirect
97. #2568C22semidirect
99. #2565C22semidirect
101. #2560C22semidirect
102. #2553C22semidirect
103. #2552C22semidirect
104. #2552C22semidirect
105. #2550C22semidirect
109. #2538C22semidirect
110. #2528C22semidirect
111. #2523C22semidirect
112. #2522C22semidirect
113. #2520C22semidirect
114. #2518C22semidirect
115. #2515C22semidirect
116. #2515C22semidirect
117. #2515C22semidirect
118. #2515C22semidirect
119. #2514C22semidirect
120. #2514C22semidirect
121. #2509C22semidirect
122. #2509C22semidirect
123. #2509C22semidirect
124. #2508C22semidirect
125. #2507C22semidirect
126. #2507C22semidirect
127. #2502C22semidirect
130. #2497C22semidirect
131. #2496C22semidirect
133. #2495C22semidirect
134. #2495C22semidirect
137. #2494C22semidirect
138. #2492C22semidirect
139. #2492C22semidirect
141. #2489C22semidirect
142. #2487C22semidirect
145. #2481C22semidirect
149. #2479C22semidirect
152. #2475C22semidirect
153. #2475C22semidirect
154. #2475C22semidirect
158. #2465C22semidirect
159. #2462C22semidirect
160. #2458C22semidirect
171. #2441C22semidirect
172. #2441C22semidirect
174. #2440C22semidirect
179. #2423C22semidirect
181. #2421C22semidirect
182. #2421C22semidirect
183. #2421C22semidirect
190. #2415C22semidirect
191. #2415C22semidirect
194. #2409C22semidirect
196. #2396C22semidirect
197. #2396C22semidirect
201. #2373C22semidirect
202. #2373C22semidirect
203. #2370C22semidirect
206. #2365C22semidirect
207. #2365C22semidirect
208. #2365C22semidirect
215. #2362C22semidirect
216. #2362C22semidirect
217. #2362C22semidirect
218. #2362C22semidirect
219. #2360C22semidirect
220. #2360C22semidirect
221. #2360C22semidirect
222. #2360C22semidirect
223. #2360C22semidirect
224. #2356C22semidirect
225. #2355C22semidirect
226. #2355C22semidirect
227. #2355C22semidirect
228. #2355C22semidirect
233. #2354C22semidirect
236. #2352C22semidirect
237. Q8×C4⋊C4C22semidirect
238. Q8×C4⋊C4C22semidirect
244. #2347C22semidirect
245. #2347C22semidirect
247. #2344C22semidirect
248. #2344C22semidirect
249. #2344C22semidirect
253. Q8×C22⋊C4C22semidirect
256. #2335C22semidirect
259. #2323C22semidirect
260. #2323C22semidirect
261. #2316C22semidirect
262. #2314C22semidirect
263. #2310C22semidirect
264. C4×C4⋊Q8C22semidirect
265. C4×C4⋊Q8C22semidirect
266. C4×C4⋊Q8C22semidirect
267. C4×#125C22semidirect
268. C4×#125C22semidirect
270. C4×#126C22semidirect
276. C4×C22⋊Q8C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
281. #2296C22semidirect
289. #2285C22semidirect
292. #2274C22semidirect
293. C42×Q8C22semidirect
294. C42×Q8C22semidirect
298. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#596422
#596002
#595622
#595042
#594882
#592592
#592142
#590252
#451612
#451172
#448392
#443582
#401662
#400512
#389652
#389112
#385512
#378562
#365072
#364502
#364272
#362992
#362722
#362102
D4×C22⋊Q82
#359932
#358322
#348932
#347002
#343112
#342422
#342032
C4×#5562
D4×#1172