Finite Group Databasebeta

← #7681082

Subgroups — #7681082

Order 512.

5497 conjugacy classes of subgroups.

The subgroup lattice has 1779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59944C212yesmaximal, complemented
2#59933C212yesmaximal, complemented
3#59752C212yesmaximal, complemented
4#59546C212yesmaximal, complemented
5#59269C214yesmaximal, complemented
6#59266C214yesmaximal, complemented
7#45419C212yesmaximal, complemented
8#45406C212yesmaximal, complemented
9#45282C212yesmaximal, complemented
10#44992C212yesmaximal, complemented
11#44043C214yesmaximal, complemented
12#43975C214yesmaximal, complemented
13#39047C212yesmaximal, complemented
14#39041C212yesmaximal, complemented
15#38205C212yesmaximal, complemented
16#38203C212yesmaximal, complemented
17#38117C212yesmaximal, complemented
18#38111C212yesmaximal, complemented
19#36381C212yesmaximal, complemented
20#36277C212yesmaximal, complemented
21#35662C211yesmaximal, characteristic, complemented
22#35659C211yesmaximal, characteristic
23#35557C211yesmaximal, characteristic, complemented
24#35516C211yesmaximal, characteristic, complemented
25#35280C211yesmaximal, characteristic, complemented
26#35267C211yesmaximal, characteristic, complemented
27#35263C211yesmaximal, characteristic, complemented
28#34813C211yesmaximal, characteristic, complemented
29C2×#2423C211yesmaximal, characteristic, complemented
30#34259C211yesmaximal, characteristic, complemented
31#34257C211yesmaximal, characteristic, complemented
32#34253C211yesmaximal, characteristic, complemented
33#34203C211yesmaximal, characteristic, complemented
34#34136C211yesmaximal, characteristic, complemented
35#34059C211yesmaximal, characteristic, complemented
36C22×2−1+4C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#525C2211yescharacteristic
39C2×#525C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C2×#520C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44C22×C4×Q8C2211yescharacteristic
45C22×#117C2211yescharacteristic
46#2863C2212yescomplemented
47#2860C2212yescomplemented
48#2857C2212yescomplemented
49#2857C2212yescomplemented
50#2855C2212yes—
51#2854C2212yes—
52#2799C2214yescomplemented
53#2798C2214yes—
54#2786C2214yescomplemented
55#2764C2214yes—
56#2762C2214yescomplemented
57#2761C2214yescomplemented
58#2759C2214yes—
59#2756C2214yes—
60#2755C2214yescomplemented
61#2755C2214yescomplemented
62#2754C2214yes—
63#2749C2214yes—
64#2748C2214yes—
65#2747C2214yescomplemented
66#2744C2214yescomplemented
67#2743C2214yes—
68#2741C2214yes—
69#2740C2214yes—
70#2740C2214yescomplemented
71#2739C2214yescomplemented
72#2730C2214yes—
73#2723C2214yescomplemented
74#2722C2214yescomplemented
75#2705C2214yes—
76#2645C2212yescomplemented
77#2644C2212yescomplemented
78#2629C2212yescomplemented
79#2629C2212yescomplemented
80#2625C2212yes—
81#2624C2212yes—
82#2612C2214yescomplemented
83#2607C2214yes—
84#2605C2214yescomplemented
85#2601C2214yescomplemented
86#2589C2214yes—
87#2589C2214yes—
88#2588C2214yescomplemented
89#2582C2212yescomplemented
90#2582C2212yescomplemented
91#2582C2212yescomplemented
92#2582C2212yescomplemented
93#2581C2212yescomplemented
94#2581C2212yescomplemented
95#2577C2214yescomplemented
96#2576C2214yes—
97#2574C2214yescomplemented
98#2573C2214yescomplemented
99#2569C2214yescomplemented
100#2564C2214yes—
101#2560C2214yescomplemented
102#2554C2214yes—
103#2553C2214yes—
104#2553C2214yes—
105#2538C2212yescomplemented
106#2538C2212yescomplemented
107#2532C2214yes—
108#2531C2214yes—
109#2531C2214yescomplemented
110#2526C2214yes—
111#2526C2214yescomplemented
112#2523C2214yescomplemented
113#2522C2214yescomplemented
114#2522C2214yescomplemented
115#2521C2214yes—
116#2520C2214yescomplemented
117#2518C2214yes—
118#2515C2214yescomplemented
119#2512C2212yescomplemented
120#2512C2212yescomplemented
121#2511C2212yescomplemented
122#2511C2212yescomplemented
123#2510C2214yes—
124#2498C2214yes—
125#2498C2214yes—
126#2497C2212yescomplemented
127#2497C2212yescomplemented
128#2497C2212yescomplemented
129#2496C2212yescomplemented
130#2496C2212yescomplemented
131#2496C2212yescomplemented
132#2495C2212yescomplemented
133#2494C2212yescomplemented
134#2493C2214yescomplemented
135#2492C2211yescharacteristic
136#2492C2211yescharacteristic
137#2491C2211yescharacteristic
138#2491C2211yescharacteristic
139#2490C2211yescharacteristic
140#2490C2211yescharacteristic
141#2489C2211yescharacteristic
142#2489C2211yescharacteristic
143#2488C2212yes—
144#2488C2214yes—
145#2488C2212yes—
146#2487C2212yes—
147#2487C2212yes—
148#2486C2212yes—
149#2486C2212yes—
150#2485C2212yes—
151#2485C2212yes—
152#2485C2212yes—
153#2485C2212yes—
154#2481C2214yes—
155#2481C2214yes—
156#2481C2214yes—
157#2472C2212yes—
158#2472C2212yes—
159#2471C2214yes—
160#2467C2214yes—
161#2461C2214yes—
162#2453C2212yescomplemented
163#2453C2212yescomplemented
164#2451C2212yescomplemented
165#2451C2212yescomplemented
166#2438C2214yes—
167#2438C2214yes—
168#2438C2214yescomplemented
169#2423C2212yes—
170#2423C2212yes—
171#2423C2212yes—
172#2423C2212yes—
173#2423C2212yes—
174#2423C2212yes—
175#2423C2212yes—
176#2423C2212yes—
177#2423C2212yes—
178#2422C2212yes—
179#2421C2212yes—
180#2420C2212yes—
181#2419C2214yes—
182#2418C2214yes—
183#2417C2214yes—
184#2417C2214yes—
185#2412C2214yes—
186#2409C2212yes—
187#2409C2212yes—
188#2409C2212yes—
189#2409C2212yes—
190#2407C2212yes—
191#2407C2212yes—
192#2407C2212yes—
193#2407C2212yes—
194#2406C2214yes—
195#2404C2214yes—
196#2398C2212yes—
197#2398C2212yes—
198C2×#399C2212yes—
199C2×#398C2212yes—
200#2373C2214yescomplemented
201#2372C2214yes—
202#2368C2214yescomplemented
203#2363C2211yescharacteristic
204#2363C2211yescharacteristic
205#2362C2212yes—
206#2362C2211yescharacteristic
207#2362C2211yescharacteristic
208#2362C2212yes—
209#2361C2211yescharacteristic
210#2361C2211yescharacteristic
211#2360C2211yescharacteristic
212#2360C2212yes—
213#2360C2211yescharacteristic
214#2360C2212yes—
215#2359C2212yes—
216#2359C2212yes—
217#2358C2212yes—
218#2358C2212yes—
219#2353C2214yes—
220#2353C2214yes—
221#2352C2214yes—
222#2347C2212yescomplemented
223#2346C2212yescomplemented
224#2345C2212yescomplemented
225#2344C2214yes—
226#2344C2212yescomplemented
227#2342C2214yes—
228#2341C2212yescomplemented
229#2341C2212yescomplemented
230#2341C2212yescomplemented
231#2341C2212yescomplemented
232Q8×C22⋊C4C2212yescomplemented
233Q8×C22⋊C4C2212yescomplemented
234Q8×C22⋊C4C2212yescomplemented
235Q8×C22⋊C4C2212yescomplemented
236Q8×C22⋊C4C2212yescomplemented
237Q8×C22⋊C4C2212yescomplemented
238#2339C2214yes—
239#2339C2214yes—
240#2339C2212yescomplemented
241#2339C2212yescomplemented
242#2323C2212yes—
243#2323C2212yes—
244#2320C2212yescomplemented
245#2320C2212yescomplemented
246#2320C2212yescomplemented
247#2320C2212yescomplemented
248#2320C2212yescomplemented
249#2319C2212yescomplemented
250#2317C2211yescharacteristic
251#2316C2211yescharacteristic
252#2316C2211yescharacteristic
253#2316C2211yescharacteristic
254#2316C2211yescharacteristic
255#2313C2214yes—
256#2311C2214yes—
257#2311C2211yescharacteristic
258#2311C2211yescharacteristic
259#2311C2211yescharacteristic
260#2311C2211yescharacteristic
261#2311C2211yescharacteristic
262#2311C2212yescomplemented
263#2310C2211yescharacteristic
264#2310C2211yescharacteristic
265#2310C2212yescomplemented
266C4×#124C2212yes—
267C4×#124C2212yes—
268C4×C22⋊Q8C2212yes—
269C4×C22⋊Q8C2212yes—
270#2297C2211yescharacteristic
271#2297C2214yes—
272#2297C2211yescharacteristic
273#2297C2211yescharacteristic
274#2297C2212yescomplemented
275#2296C2211yescharacteristic
276#2295C2212yescomplemented
277#2295C2212yescomplemented
278#2295C2212yescomplemented
279#2295C2212yescomplemented
280#2295C2212yescomplemented
281C2×#391C2211yescharacteristic
282C2×#391C2212yescomplemented
283#2293C2212yes—
284#2293C2212yescomplemented
285C2×#389C2211yescharacteristic
286#2290C2212yes—
287#2290C2212yes—
288C2×#388C2212yes—
289C2×#387C2212yes—
290C2×#384C2211yescharacteristic
291#2283C2214yes—
292#2280C2211yescharacteristic
293C2×#380C2211yescharacteristic
294#2274C2211yescharacteristic
295C42×D4C2212yes—
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic
298C2×C4×C22⋊C4C2211yescharacteristic
299C2×2−1+4—28no—
300C2×2−1+4—28no—
301C2×2−1+4—44no—
302C22×#41C2311yescharacteristic
303C22×#41C2314yes—
304C22×#41C2312yes—
305C22×#41C2312yes—
306C22×#41C2311yescharacteristic
307C23×Q8C2312yes—
308C23×Q8C2312yes—
309C23×Q8C2311yescharacteristic
310C24×C4C2311yescharacteristic
311#533—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×#126C2314yes—
315C2×#126C2314yes—
316C2×#126C2314yes—
317C2×#125C2311yescharacteristic
318C2×#125C2311yescharacteristic
319C2×#124C2312yes—
320C2×#124C2312yes—
321#525—28no—
322#525—44no—
323C2×#123C2312yes—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×#123C2314yes—
327C2×C22⋊Q8—28no—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×#121C2311yescharacteristic
341C2×#121C2311yescharacteristic
342C2×#121C2311yescharacteristic
343C2×#121C2311yescharacteristic
344C2×#120C2312yes—
345C2×#120C2312yes—
346#520—28no—
347#519—44no—
348C4×#41—44no—
349C2×C4×Q8—28no—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2311yescharacteristic
362C2×C4×Q8C2311yescharacteristic
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×#117—44no—
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2311yescharacteristic
382C2×#117C2311yescharacteristic
383C2×#117C2312yes—
384C2×#117C2314yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2314yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2311yescharacteristic
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2311yescharacteristic
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C22⋊C4C2312yes—
402C22×C22⋊C4C2311yescharacteristic
403C22×C22⋊C4C2312yes—
404C22×C22⋊C4C2311yescharacteristic
405C22×C22⋊C4C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2312yes—
408C22×C42C2311yescharacteristic
409C22×C42C2312yes—
410C22×C42C2312yes—
411#401C2314yes—
412#400C2314yes—
413#400C2312yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2312yes—
424#400C2312yes—
425#400C2314yes—
426#400C2314yes—
427#399C2314yes—
428#399C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#397C2314yes—
448#397C2312yes—
449#397C2312yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2312yes—
457#397C2312yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2314yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2312yes—
478#394C2312yes—
479#394C2312yes—
480#394C2312yes—
481#394C2314yes—
482#394C2314yes—
483#393C2312yes—
484#393C2312yes—
485#393C2314yes—
486#393C2312yes—
487#393C2312yes—
488#393C2314yes—
489#392C2314yes—
490#392C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2312yes—
500#391C2311yescharacteristic
501#391C2312yes—
502#391C2312yes—
503#391C2314yes—
504#391C2314yes—
505#391C2312yes—
506#391C2312yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#391C2312yes—
511#391C2314yes—
512#391C2311yescharacteristic
513#391C2312yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2311yescharacteristic
521#391C2311yescharacteristic
522#391C2311yescharacteristic
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2312yes—
527#391C2311yescharacteristic
528#390C2314yes—
529#390C2312yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2311yescharacteristic
536#390C2311yescharacteristic
537#390C2311yescharacteristic
538#390C2311yescharacteristic
539#390C2311yescharacteristic
540#390C2314yes—
541#390C2314yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2312yes—
546#390C2311yescharacteristic
547#389C2312yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2312yes—
567#389C2314yes—
568#389C2314yes—
569#389C2311yescharacteristic
570#389C2311yescharacteristic
571#389C2311yescharacteristic
572#389C2311yescharacteristic
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2314yes—
597#388C2314yes—
598#388C2312yes—
599#388C2312yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2312yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#388C2312yes—
609#388C2312yes—
610#388C2312yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2312yes—
617#388C2312yes—
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#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2312yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2312yes—
661#386C2314yes—
662#386C2314yes—
663#386C2312yes—
664#386C2314yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2312yes—
670#386C2312yes—
671#386C2312yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2312yes—
676#386C2312yes—
677#386C2312yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2312yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2312yes—
689#385C2314yes—
690#385C2312yes—
691#385C2312yes—
692#385C2312yes—
693#385C2312yes—
694#385C2312yes—
695#385C2314yes—
696#385C2314yes—
697#384C2312yes—
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2312yes—
702#383C2314yes—
703#383C2314yes—
704#383C2314yes—
705#383C2314yes—
706#382C2312yes—
707#382C2314yes—
708#382C2314yes—
709#382C2314yes—
710#382C2312yes—
711#382C2312yes—
712#381C2314yes—
713#381C2314yes—
714#381C2314yes—
715#381C2314yes—
716#381C2314yes—
717#381C2314yes—
718#381C2312yes—
719#381C2314yes—
720#380C2314yes—
721#380C2314yes—
722#380C2314yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2314yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2312yes—
735#380C2314yes—
736#380C2314yes—
737#380C2314yes—
738#380C2314yes—
739#380C2314yes—
740#380C2314yes—
741#380C2314yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2312yes—
745#380C2314yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2311yescharacteristic
750#380C2311yescharacteristic
751#379C2312yes—
752C4×C4⋊C4C2314yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2314yes—
764C4×C4⋊C4C2314yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2311yescharacteristic
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2312yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807#376C2312yes—
808#376C2312yes—
809#376C2314yes—
810#376C2314yes—
811#376C2314yes—
812C2×#95C2314yes—
813C2×#95C2314yes—
814C2×#95C2312yes—
815C2×#95C2312yes—
816C2×#95C2312yes—
817C2×#95C2311yescharacteristic
818C2×#95C2311yescharacteristic
819C2×#95C2312yes—
820C43C2312yes—
821C43C2312yes—
822C25C2411yescharacteristic
8232−1+4—464no—
824C2×#41—28no—
825C2×#41—28no—
826C2×#41—216no—
827C2×#41—28no—
828C2×#41—24no—
829C2×#41—216no—
830C2×#41—28no—
831C2×#41—24no—
832C2×#41—24no—
833C2×#41—24no—
834C2×#41—24no—
835C2×#41—48no—
836C2×#41—44no—
837C2×#41—44no—
838C2×#41#4118yes—
839C22×Q8—28no—
840C22×Q8—28no—
841C22×Q8—28no—
842C22×Q8—24no—
843C22×Q8—28no—
844C22×Q8—24no—
845C22×Q8—44no—
846C22×Q8—44no—
847C22×Q8#4118yes—
848C22×Q8C2411yescharacteristic
849C22×Q8C2414yes—
850C22×Q8C2412yes—
851C22×Q8C2412yes—
852C22×Q8C2411yescharacteristic
853C22×Q8C2412yes—
854C22×Q8C2412yes—
855C22×D4C2412yes—
856C22×D4C2411yescharacteristic
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2412yes—
860C22×D4C2411yescharacteristic
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2412yes—
864C23×C4—24no—
865C23×C4—24no—
866C23×C4—24no—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2411yescharacteristic
870C23×C4C2411yescharacteristic
871C23×C4C2411yescharacteristic
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2411yescharacteristic
875C23×C4C2411yescharacteristic
876C23×C4C2414yes—
877C23×C4C2414yes—
878C23×C4C2412yes—
879C23×C4C2412yes—
880C23×C4C2412yes—
881C23×C4C2411yescharacteristic
882C23×C4C2412yes—
883C23×C4C2412yes—
884C23×C4C2412yes—
885C23×C4C2414yes—
886C23×C4C2412yes—
887C23×C4C2412yes—
888C23×C4C2412yes—
889C23×C4C2411yescharacteristic
890C4⋊Q8—42no—
891C4⋊Q8—42no—
892#126—48no—
893#126—84no—
894#126—84no—
895#125—42no—
896#125—42no—
897#124—28no—
898#124—44no—
899#123—28no—
900#123—44no—
901#123—84no—
902#123—84no—
903C22⋊Q8—28no—
904C22⋊Q8—28no—
905C22⋊Q8—28no—
906C22⋊Q8—28no—
907C22⋊Q8—24no—
908C22⋊Q8—24no—
909C22⋊Q8—44no—
910C22⋊Q8—44no—
911C22⋊Q8—48no—
912C22⋊Q8—42no—
913C22⋊Q8—42no—
914C22⋊Q8—84no—
915#121—24no—
916#121—24no—
917#121—42no—
918#121—42no—
919#120—28no—
920#120—44no—
921C4×Q8—28no—
922C4×Q8—28no—
923C4×Q8—28no—
924C4×Q8—28no—
925C4×Q8—28no—
926C4×Q8—44no—
927C4×Q8—44no—
928C4×Q8—42no—
929C4×Q8—42no—
930C4×Q8—44no—
931C4×Q8—44no—
932C4×Q8—44no—
933C4×Q8—44no—
934C4×D4—216no—
935C4×D4—28no—
936C4×D4—28no—
937C4×D4—28no—
938C4×D4—28no—
939C4×D4—42no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946#117—28no—
947#117—24no—
948#117—24no—
949#117—24no—
950#117—24no—
951#117—24no—
952#117—24no—
953#117—44no—
954#117—44no—
955#117—44no—
956#117—48no—
957#117—42no—
958#117—42no—
959#117—84no—
960C2×C4⋊C4—28no—
961C2×C4⋊C4—24no—
962C2×C4⋊C4—28no—
963C2×C4⋊C4—24no—
964C2×C4⋊C4—28no—
965C2×C4⋊C4—24no—
966C2×C4⋊C4—44no—
967C2×C4⋊C4—42no—
968C2×C4⋊C4—42no—
969C2×C4⋊C4—82no—
970C2×C4⋊C4—82no—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2414yes—
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2414yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C22⋊C4—28no—
1031C2×C22⋊C4—24no—
1032C2×C22⋊C4—42no—
1033C2×C22⋊C4—44no—
1034C2×C22⋊C4—82no—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2411yescharacteristic
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2411yescharacteristic
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2411yescharacteristic
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2411yescharacteristic
1063C2×C22⋊C4C2411yescharacteristic
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2411yescharacteristic
1092C2×C42—28no—
1093C2×C42—24no—
1094C2×C42—24no—
1095C2×C42—44no—
1096C2×C42—44no—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2412yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2414yes—
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2414yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2412yes—
1127C2×C42C2414yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2411yescharacteristic
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2411yescharacteristic
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2412yes—
1199#95C2412yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2414yes—
1204C24—22no—
1205C24—22no—
1206C24—22no—
1207C24—22no—
1208C24—41no—
1209C24—41no—
1210C24—41no—
1211C24C2511yescharacteristic
1212C24C2512yes—
1213C24C2512yes—
1214C24C2511yescharacteristic
1215C24C2511yescharacteristic
1216#41—232no—
1217#41—464no—
1218#41—432no—
1219#41—432no—
1220#41—416no—
1221C2×Q8—232no—
1222C2×Q8—22no—
1223C2×Q8—24no—
1224C2×Q8—24no—
1225C2×Q8—28no—
1226C2×Q8—28no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—24no—
1230C2×Q8—24no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—44no—
1236C2×Q8—42no—
1237C2×Q8—42no—
1238C2×Q8—42no—
1239C2×Q8—42no—
1240C2×Q8—432no—
1241C2×Q8—432no—
1242C2×Q8C2×#4114yes—
1243C2×Q8C2×#4118yes—
1244C2×Q8C2×#4118yes—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—24no—
1248C2×D4—28no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—22no—
1256C2×D4—28no—
1257C2×D4—22no—
1258C2×D4—22no—
1259C2×D4—22no—
1260C2×D4—22no—
1261C2×D4—42no—
1262C2×D4—44no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4C2×#4118yes—
1271C2×D4C2×#4114yes—
1272C22×C4—24no—
1273C22×C4—24no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—28no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—28no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—22no—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—28no—
1298C22×C4—28no—
1299C22×C4—28no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—24no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—41no—
1313C22×C4—41no—
1314C22×C4—41no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—42no—
1320C22×C4—42no—
1321C22×C4—41no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—41no—
1327C22×C4—42no—
1328C22×C4—44no—
1329C22×C4—42no—
1330C22×C4—42no—
1331C22×C4—42no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—44no—
1335C22×C4—42no—
1336C22×C4—416no—
1337C22×C4C2×#4118yes—
1338C22×C4C2×#4118yes—
1339C22×C4C2×#4114yes—
1340C22×C4C2×#4114yes—
1341C22×C4H(5,𝔽2)14yes—
1342C22×C4C2512yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2512yes—
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2514yes—
1348C22×C4C2512yes—
1349C22×C4C2512yes—
1350C22×C4C2511yescharacteristic
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2511yescharacteristic
1355C22×C4C2511yescharacteristic
1356C22×C4C2511yescharacteristic
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2514yes—
1362C22×C4C2514yes—
1363C22×C4C2511yescharacteristic
1364C22×C4C2511yescharacteristic
1365C22×C4C2512yes—
1366C22×C4C2514yes—
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2511yescharacteristic
1371C22×C4C2511yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—28no—
1375C4⋊C4—24no—
1376C4⋊C4—28no—
1377C4⋊C4—28no—
1378C4⋊C4—24no—
1379C4⋊C4—24no—
1380C4⋊C4—24no—
1381C4⋊C4—24no—
1382C4⋊C4—28no—
1383C4⋊C4—28no—
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—22no—
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—44no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C22⋊C4—28no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—24no—
1440C22⋊C4—22no—
1441C22⋊C4—24no—
1442C22⋊C4—28no—
1443C22⋊C4—28no—
1444C22⋊C4—24no—
1445C22⋊C4—24no—
1446C22⋊C4—22no—
1447C22⋊C4—22no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—22no—
1452C22⋊C4—22no—
1453C22⋊C4—24no—
1454C22⋊C4—41no—
1455C22⋊C4—41no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—44no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—42no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—42no—
1485C22⋊C4—42no—
1486C22⋊C4—44no—
1487C22⋊C42−1+414yescomplemented
1488C42—28no—
1489C42—22no—
1490C42—22no—
1491C42—28no—
1492C42—22no—
1493C42—22no—
1494C42—24no—
1495C42—28no—
1496C42—24no—
1497C42—22no—
1498C42—22no—
1499C42—22no—
1500C42—22no—
1501C42—24no—
1502C42—24no—
1503C42—24no—
1504C42—24no—
1505C42—24no—
1506C42—24no—
1507C42—42no—
1508C42—42no—
1509C42—42no—
1510C42—42no—
1511C42—42no—
1512C42—42no—
1513C42—44no—
1514C42—44no—
1515C42—42no—
1516C42—44no—
1517C42—42no—
1518C42—42no—
1519C42—44no—
1520C42—42no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—21no—
1526C23—21no—
1527C23—22no—
1528C23—21no—
1529C23—22no—
1530C23—22no—
1531C23—21no—
1532C23—22no—
1533C23—22no—
1534C23—21no—
1535C23—21no—
1536C23—22no—
1537C23—21no—
1538C23—21no—
1539C23—22no—
1540C23—22no—
1541C23—21no—
1542C23—22no—
1543C23—22no—
1544C23—21no—
1545C23—22no—
1546C23—21no—
1547C23—22no—
1548C23—21no—
1549C23—22no—
1550C23—21no—
1551C23—44no—
1552C23—44no—
1553C23—44no—
1554C23—44no—
1555C23—82no—
1556C23—82no—
1557C23—82no—
1558C23C22×#4114yes—
1559C23C22×#4112yes—
1560C23C22×#4112yes—
1561C23C2×H(5,𝔽2)12yes—
1562C23C2×2−1+412yes—
1563C23C2611yescharacteristic
1564Q8—216no—
1565Q8—216no—
1566Q8—28no—
1567Q8—416no—
1568Q8—44no—
1569Q8—84no—
1570Q8—84no—
1571D4—216no—
1572D4—28no—
1573D4—416no—
1574D4—48no—
1575D4—48no—
1576D4—44no—
1577D4—84no—
1578D4—84no—
1579D4—84no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—216no—
1591C2×C4—216no—
1592C2×C4—21no—
1593C2×C4—22no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—24no—
1601C2×C4—24no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—21no—
1609C2×C4—21no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—24no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—24no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—22no—
1650C2×C4—24no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—24no—
1661C2×C4—416no—
1662C2×C4—44no—
1663C2×C4—44no—
1664C2×C4—44no—
1665C2×C4—416no—
1666C2×C4—44no—
1667C2×C4—44no—
1668C2×C4—44no—
1669C2×C4—44no—
1670C2×C4—44no—
1671C2×C4—48no—
1672C2×C4—84no—
1673C2×C4—84no—
1674C2×C4—82no—
1675C2×C4—84no—
1676C2×C4—84no—
1677C2×C4—84no—
1678C2×C4—88no—
1679C2×C4—84no—
1680C2×C4—84no—
1681C2×C4#551116yes—
1682C2×C4C22×#4118yes—
1683C2×C4C22×#4114yes—
1684C2×C4C22×#4112yes—
1685C2×C4C22×#4112yes—
1686C2×C4C22×#4112yes—
1687C2×C4C22×#4112yes—
1688C2×C4C2×H(5,𝔽2)12yes—
1689C2×C4C2×H(5,𝔽2)12yes—
1690C2×C4C2×2−1+412yes—
1691C2×C4C2×2−1+412yes—
1692C2×C4#58512yes—
1693C22—22no—
1694C22—22no—
1695C22—22no—
1696C22—22no—
1697C22—22no—
1698C22—22no—
1699C22—22no—
1700C22—22no—
1701C22—24no—
1702C22—24no—
1703C22—22no—
1704C22—24no—
1705C22—42no—
1706C22—42no—
1707C22—41no—
1708C22—41no—
1709C22—41no—
1710C22—42no—
1711C22—42no—
1712C22—41no—
1713C22—42no—
1714C22—41no—
1715C22—42no—
1716C22—41no—
1717C22—42no—
1718C22—41no—
1719C22—41no—
1720C22—42no—
1721C22—41no—
1722C22—42no—
1723C22—42no—
1724C22—41no—
1725C22—42no—
1726C22—41no—
1727C22—88no—
1728C22C2×#55114yes—
1729C22C23×#4111yescharacteristic
1730C22C23×#4111yescharacteristic
1731C22C22×H(5,𝔽2)11yescharacteristic
1732C22C22×2−1+411yescharacteristic
1733C22C2×#58511yescharacteristic
1734C22H(7,𝔽2)11yescharacteristic
1735C222−1+611yescharacteristic
1736C4—22no—
1737C4—22no—
1738C4—22no—
1739C4—24no—
1740C4—28no—
1741C4—41no—
1742C4—41no—
1743C4—41no—
1744C4—44no—
1745C4—44no—
1746C4—42no—
1747C4—42no—
1748C4—42no—
1749C4—44no—
1750C4—42no—
1751C4—41no—
1752C4—42no—
1753C4—42no—
1754C4—42no—
1755C4—42no—
1756C4—41no—
1757C4—42no—
1758C4—42no—
1759C4—42no—
1760C4—42no—
1761C4—41no—
1762C4—41no—
1763C4—42no—
1764C4C2×#55114yes—
1765C4C2×#55114yes—
1766C2—24no—
1767C2—44no—
1768C2—42no—
1769C2—82no—
1770C2—81no—
1771C2C22×#55111yescharacteristic
1772C2#6280511yescharacteristic
1773C2#6285711yescharacteristic
1774C2#6292711yescharacteristic
1775C2#6294411yescharacteristic
1776C2#6299811yescharacteristic
1777C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35659C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59944C2semidirect
2. #59933C2semidirect
3. #59752C2semidirect
4. #59546C2semidirect
5. #59269C2semidirect
6. #59266C2semidirect
7. #45419C2semidirect
8. #45406C2semidirect
9. #45282C2semidirect
10. #44992C2semidirect
11. #44043C2semidirect
12. #43975C2semidirect
13. #39047C2semidirect
14. #39041C2semidirect
15. #38205C2semidirect
16. #38203C2semidirect
17. #38117C2semidirect
18. #38111C2semidirect
19. #36381C2semidirect
20. #36277C2semidirect
21. #35662C2semidirect
23. #35557C2semidirect
24. #35516C2semidirect
25. #35280C2semidirect
26. #35267C2semidirect
27. #35263C2semidirect
28. #34813C2semidirect
29. C2×#2423C2semidirect
30. #34259C2semidirect
31. #34257C2semidirect
32. #34253C2semidirect
33. #34203C2semidirect
34. #34136C2semidirect
35. #34059C2semidirect
46. #2863C22semidirect
47. #2860C22semidirect
48. #2857C22semidirect
49. #2857C22semidirect
52. #2799C22semidirect
54. #2786C22semidirect
56. #2762C22semidirect
57. #2761C22semidirect
60. #2755C22semidirect
61. #2755C22semidirect
65. #2747C22semidirect
66. #2744C22semidirect
70. #2740C22semidirect
71. #2739C22semidirect
73. #2723C22semidirect
74. #2722C22semidirect
76. #2645C22semidirect
77. #2644C22semidirect
78. #2629C22semidirect
79. #2629C22semidirect
82. #2612C22semidirect
84. #2605C22semidirect
85. #2601C22semidirect
88. #2588C22semidirect
89. #2582C22semidirect
90. #2582C22semidirect
91. #2582C22semidirect
92. #2582C22semidirect
93. #2581C22semidirect
94. #2581C22semidirect
95. #2577C22semidirect
97. #2574C22semidirect
98. #2573C22semidirect
99. #2569C22semidirect
101. #2560C22semidirect
105. #2538C22semidirect
106. #2538C22semidirect
109. #2531C22semidirect
111. #2526C22semidirect
112. #2523C22semidirect
113. #2522C22semidirect
114. #2522C22semidirect
116. #2520C22semidirect
118. #2515C22semidirect
119. #2512C22semidirect
120. #2512C22semidirect
121. #2511C22semidirect
122. #2511C22semidirect
126. #2497C22semidirect
127. #2497C22semidirect
128. #2497C22semidirect
129. #2496C22semidirect
130. #2496C22semidirect
131. #2496C22semidirect
132. #2495C22semidirect
133. #2494C22semidirect
134. #2493C22semidirect
162. #2453C22semidirect
163. #2453C22semidirect
164. #2451C22semidirect
165. #2451C22semidirect
168. #2438C22semidirect
200. #2373C22semidirect
202. #2368C22semidirect
222. #2347C22semidirect
223. #2346C22semidirect
224. #2345C22semidirect
226. #2344C22semidirect
228. #2341C22semidirect
229. #2341C22semidirect
230. #2341C22semidirect
231. #2341C22semidirect
232. Q8×C22⋊C4C22semidirect
233. Q8×C22⋊C4C22semidirect
234. Q8×C22⋊C4C22semidirect
235. Q8×C22⋊C4C22semidirect
236. Q8×C22⋊C4C22semidirect
237. Q8×C22⋊C4C22semidirect
240. #2339C22semidirect
241. #2339C22semidirect
244. #2320C22semidirect
245. #2320C22semidirect
246. #2320C22semidirect
247. #2320C22semidirect
248. #2320C22semidirect
249. #2319C22semidirect
262. #2311C22semidirect
265. #2310C22semidirect
274. #2297C22semidirect
276. #2295C22semidirect
277. #2295C22semidirect
278. #2295C22semidirect
279. #2295C22semidirect
280. #2295C22semidirect
282. C2×#391C22semidirect
284. #2293C22semidirect
1487. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#599442
#599332
#597522
#595462
#592692
#592662
#454192
#454062
#452822
#449922
#440432
#439752
#390472
#390412
#382052
#382032
#381172
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#363812
#362772
#356622
#356592
#355572
#355162
#352802
#352672
#352632
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C2×#24232
#342592
#342572
#342532
#342032
#341362
#340592