Finite Group Databasebeta

← #7699824

Subgroups — #7699824

Order 512.

5124 conjugacy classes of subgroups.

The subgroup lattice has 1702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59806C212yesmaximal, complemented
2#59757C214yesmaximal, complemented
3#59643C212yesmaximal, complemented
4#59535C214yesmaximal, complemented
5#59508C212yesmaximal, complemented
6#59450C211yesmaximal, characteristic, complemented
7#59439C214yesmaximal, complemented
8#59381C212yesmaximal, complemented
9#59309C212yesmaximal, complemented
10#59304C211yesmaximal, characteristic, complemented
11#59246C212yesmaximal, complemented
12#59234C211yesmaximal, characteristic, complemented
13#36586C212yesmaximal, complemented
14#36579C211yesmaximal, characteristic, complemented
15#36561C211yesmaximal, characteristic, complemented
16#36518C212yesmaximal, complemented
17#36507C212yesmaximal, complemented
18#36506C212yesmaximal, complemented
19#36504C211yesmaximal, characteristic, complemented
20#36497C211yesmaximal, characteristic, complemented
21#36487C212yesmaximal, complemented
22#36484C212yesmaximal, complemented
23#36453C211yesmaximal, characteristic, complemented
24#36450C211yesmaximal, characteristic, complemented
25#36277C212yesmaximal, complemented
26#36249C214yesmaximal, complemented
27#36189C211yesmaximal, characteristic, complemented
28#36172C212yesmaximal, complemented
29C4×#554C212yesmaximal, complemented
30C4×#556C211yesmaximal, characteristic, complemented
31C4×#553C211yesmaximal, characteristic, complemented
32C4×#553C212yesmaximal, complemented
33C4×#548C211yesmaximal, characteristic, complemented
34#34127C211yesmaximal, characteristic, complemented
35C2×#2355C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#554C2212yes—
38C2×#553C2212yes—
39C2×#553C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43#2865C2214yes—
44#2864C2212yes—
45#2863C2212yes—
46#2859C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2212yes—
50#2855C2212yes—
51#2853C2214yes—
52#2850C2212yes—
53#2850C2212yes—
54#2850C2214yes—
55#2775C2214yes—
56#2773C2214yes—
57#2771C2214yes—
58#2766C2214yes—
59#2761C2214yes—
60#2745C2214yes—
61#2718C2214yes—
62#2710C2214yes—
63#2689C2214yes—
64#2607C2214yes—
65#2605C2214yes—
66#2596C2214yes—
67#2596C2214yes—
68#2596C2214yes—
69#2595C2214yes—
70#2592C2212yes—
71#2589C2214yes—
72#2588C2214yes—
73#2581C2212yes—
74#2577C2214yes—
75#2577C2214yes—
76#2576C2214yes—
77#2576C2214yes—
78#2575C2214yes—
79#2575C2214yes—
80#2571C2212yes—
81#2570C2212yes—
82#2570C2212yes—
83#2569C2214yes—
84#2568C2211yescharacteristic
85#2564C2214yes—
86#2564C2214yes—
87#2560C2214yes—
88#2558C2214yes—
89#2557C2214yes—
90#2556C2214yes—
91#2552C2211yescharacteristic
92#2551C2211yescharacteristic
93#2550C2212yes—
94#2547C2212yes—
95#2543C2214yes—
96#2542C2211yescharacteristic
97#2540C2212yes—
98#2538C2211yescharacteristic
99#2537C2211yescharacteristic
100#2536C2212yes—
101#2533C2214yes—
102#2529C2214yes—
103#2529C2214yes—
104#2528C2214yes—
105#2528C2214yes—
106#2524C2214yes—
107#2523C2214yes—
108#2521C2214yes—
109#2520C2214yes—
110#2519C2214yes—
111#2518C2214yes—
112#2516C2214yes—
113#2515C2214yes—
114#2515C2214yes—
115#2514C2212yes—
116#2514C2214yes—
117#2513C2212yes—
118#2511C2212yes—
119#2511C2212yes—
120#2510C2214yes—
121#2510C2214yes—
122#2507C2212yes—
123#2506C2212yes—
124#2503C2212yes—
125#2501C2212yes—
126#2499C2212yes—
127#2497C2212yes—
128#2496C2212yes—
129#2495C2212yes—
130#2494C2212yes—
131#2494C2212yes—
132#2494C2212yes—
133#2492C2212yes—
134#2492C2212yes—
135#2491C2212yes—
136#2489C2212yes—
137#2489C2212yes—
138#2488C2214yes—
139#2487C2212yes—
140#2487C2212yes—
141#2481C2214yes—
142#2479C2214yes—
143#2474C2214yes—
144#2469C2214yes—
145#2467C2214yes—
146#2462C2214yes—
147#2461C2214yes—
148#2460C2214yes—
149#2458C2214yes—
150#2453C2212yes—
151#2452C2212yes—
152#2451C2212yes—
153#2448C2214yes—
154#2447C2212yes—
155#2444C2214yes—
156#2444C2214yes—
157#2443C2214yes—
158#2442C2212yes—
159#2441C2212yes—
160#2441C2212yes—
161#2427C2212yes—
162#2423C2212yes—
163#2423C2212yes—
164#2422C2212yes—
165#2421C2212yes—
166#2421C2212yes—
167#2420C2212yes—
168#2419C2214yes—
169#2417C2212yes—
170#2417C2212yes—
171#2416C2212yes—
172#2415C2212yes—
173#2409C2212yes—
174#2407C2212yes—
175#2374C2212yes—
176#2374C2214yes—
177#2373C2214yes—
178#2373C2214yes—
179#2373C2212yes—
180#2370C2214yes—
181#2370C2211yescharacteristic
182#2370C2212yes—
183#2369C2212yes—
184#2368C2214yes—
185#2368C2214yes—
186#2367C2212yes—
187#2367C2211yescharacteristic
188#2367C2212yes—
189#2365C2211yescharacteristic
190#2365C2212yes—
191#2364C2214yes—
192#2364C2212yes—
193#2363C2212yes—
194#2363C2211yescharacteristic
195#2362C2212yes—
196#2362C2212yes—
197#2362C2211yescharacteristic
198#2362C2212yes—
199#2362C2212yes—
200#2361C2211yescharacteristic
201#2361C2212yes—
202#2361C2211yescharacteristic
203#2361C2212yes—
204#2360C2212yes—
205#2360C2212yes—
206#2360C2212yes—
207#2357C2212yes—
208#2357C2211yescharacteristic
209#2356C2212yes—
210#2355C2211yescharacteristic
211#2355C2211yescharacteristic
212#2355C2211yescharacteristic
213#2355C2214yes—
214#2355C2212yes—
215#2355C2212yes—
216#2355C2212yes—
217#2355C2211yescharacteristic
218#2355C2212yes—
219#2355C2211yescharacteristic
220#2355C2212yes—
221#2354C2211yescharacteristic
222#2354C2212yes—
223#2353C2212yes—
224#2353C2214yes—
225#2353C2214yes—
226#2352C2212yes—
227#2352C2212yes—
228#2352C2212yes—
229#2352C2212yes—
230#2352C2211yescharacteristic
231#2352C2211yescharacteristic
232#2352C2212yes—
233#2351C2211yescharacteristic
234#2349C2214yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2211yescharacteristic
237D4×C4⋊C4C2212yes—
238#2347C2212yes—
239#2347C2212yes—
240#2347C2211yescharacteristic
241#2347C2212yes—
242#2345C2212yes—
243#2345C2212yes—
244#2345C2211yescharacteristic
245#2343C2214yes—
246#2341C2211yescharacteristic
247Q8×C22⋊C4C2211yescharacteristic
248#2339C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2212yes—
251C4×#125C2211yescharacteristic
252C4×#125C2212yes—
253C4×#125C2214yes—
254C4×#126C2212yes—
255C4×#126C2214yes—
256C4×#126C2214yes—
257C4×#124C2211yescharacteristic
258C4×#124C2212yes—
259C4×#124C2212yes—
260C4×C22⋊Q8C2214yes—
261C4×C22⋊Q8C2211yescharacteristic
262C4×C22⋊Q8C2214yes—
263C4×C22⋊Q8C2212yes—
264C4×C22⋊Q8C2212yes—
265C4×C22⋊Q8C2212yes—
266C4×C22⋊Q8C2212yes—
267C4×#123C2214yes—
268C4×#123C2212yes—
269C4×#121C2214yes—
270C4×#121C2211yescharacteristic
271C4×#121C2212yes—
272C4×#121C2212yes—
273C4×#121C2211yescharacteristic
274C4×#121C2212yes—
275C4×#121C2212yes—
276C4×#121C2211yescharacteristic
277#2295C2212yes—
278C2×#391C2212yes—
279#2290C2214yes—
280C2×#387C2214yes—
281#2285C2211yescharacteristic
282C2×#384C2211yescharacteristic
283#2283C2212yes—
284C2×#382C2212yes—
285C42×Q8C2211yescharacteristic
286C42×Q8C2212yes—
287C42×D4C2212yes—
288C42×D4C2212yes—
289C42×D4C2211yescharacteristic
290C42×D4C2211yescharacteristic
291C42×D4C2212yes—
292C42×D4C2214yes—
293C4×#117C2211yescharacteristic
294C4×#117C2212yes—
295C2×C4×C4⋊C4C2211yescharacteristic
296C2×C4×C4⋊C4C2212yes—
297C2×C4×C4⋊C4C2212yes—
298C2×C4×C4⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C23×Q8C2311yescharacteristic
301#556—28no—
302#554—216no—
303#553—216no—
304#553—28no—
305#548—28no—
306C2×C4⋊Q8C2311yescharacteristic
307C2×C4⋊Q8C2312yes—
308C2×C4⋊Q8C2312yes—
309C2×#126C2312yes—
310C2×#126C2314yes—
311C2×#126C2314yes—
312C2×#125C2312yes—
313C2×#125C2311yescharacteristic
314C2×#125C2314yes—
315C2×#125C2312yes—
316C2×#124C2312yes—
317C2×#124C2311yescharacteristic
318C2×#124C2312yes—
319C2×#124C2314yes—
320C2×#123C2314yes—
321C2×#123C2312yes—
322C2×#123C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2311yescharacteristic
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×#121C2311yescharacteristic
334C2×#121C2312yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#121C2311yescharacteristic
338C2×#121C2314yes—
339C2×#121C2312yes—
340C2×#121C2311yescharacteristic
341C4×#41—28no—
342C2×C4×Q8—28no—
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2314yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×D4C2312yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2314yes—
378C2×#117C2312yes—
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C2×#117C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2312yes—
387C22×C4⋊C4C2311yescharacteristic
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C42C2312yes—
395C22×C42C2312yes—
396C22×C42C2311yescharacteristic
397C22×C42C2311yescharacteristic
398C22×C42C2312yes—
399C22×C42C2312yes—
400C22×C42C2314yes—
401C22×C42C2314yes—
402#401C2314yes—
403#401C2314yes—
404#400C2314yes—
405#400C2314yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#397C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#392C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2314yes—
479#390C2314yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#390C2311yescharacteristic
483#390C2314yes—
484#390C2312yes—
485#390C2311yescharacteristic
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#389C2311yescharacteristic
492#389C2311yescharacteristic
493#389C2312yes—
494#389C2311yescharacteristic
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2311yescharacteristic
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#388C2312yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2312yes—
530#388C2314yes—
531#388C2312yes—
532#388C2314yes—
533#388C2312yes—
534#388C2312yes—
535#388C2314yes—
536#388C2312yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2312yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2312yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2312yes—
614#387C2314yes—
615#387C2312yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#386C2314yes—
622#386C2312yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2312yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2312yes—
635#386C2312yes—
636#386C2312yes—
637#386C2312yes—
638#386C2312yes—
639#386C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#385C2312yes—
649#385C2312yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2312yes—
655#384C2312yes—
656#384C2311yescharacteristic
657#384C2312yes—
658#384C2312yes—
659#384C2311yescharacteristic
660#384C2311yescharacteristic
661#384C2312yes—
662#384C2312yes—
663#383C2312yes—
664#383C2314yes—
665#383C2314yes—
666#383C2314yes—
667#383C2314yes—
668#382C2312yes—
669#382C2311yescharacteristic
670#382C2314yes—
671#382C2312yes—
672#382C2312yes—
673#382C2312yes—
674#382C2311yescharacteristic
675#382C2314yes—
676#382C2314yes—
677#382C2312yes—
678#382C2312yes—
679#382C2312yes—
680#382C2312yes—
681#382C2312yes—
682#382C2314yes—
683#381C2312yes—
684#381C2314yes—
685#381C2314yes—
686#381C2314yes—
687#381C2314yes—
688#380C2312yes—
689#380C2312yes—
690#380C2314yes—
691#380C2314yes—
692#380C2312yes—
693#380C2314yes—
694#380C2312yes—
695#380C2311yescharacteristic
696#380C2312yes—
697#380C2311yescharacteristic
698#380C2312yes—
699#380C2312yes—
700#380C2311yescharacteristic
701#380C2312yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705#380C2311yescharacteristic
706#380C2312yes—
707#380C2312yes—
708#380C2312yes—
709#380C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2311yescharacteristic
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2314yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2314yes—
722C4×C4⋊C4C2311yescharacteristic
723C4×C4⋊C4C2314yes—
724C4×C4⋊C4C2314yes—
725C4×C4⋊C4C2314yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2311yescharacteristic
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2314yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2311yescharacteristic
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2312yes—
737C4×C4⋊C4C2314yes—
738C4×C4⋊C4C2314yes—
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2312yes—
742C4×C4⋊C4C2311yescharacteristic
743C4×C4⋊C4C2311yescharacteristic
744C4×C4⋊C4C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2314yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2314yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2314yes—
761C4×C4⋊C4C2314yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2311yescharacteristic
768C4×C22⋊C4C2312yes—
769C4×C22⋊C4C2314yes—
770C4×C22⋊C4C2314yes—
771C4×C22⋊C4C2314yes—
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2314yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2312yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2311yescharacteristic
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2311yescharacteristic
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2311yescharacteristic
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2311yescharacteristic
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2311yescharacteristic
804C4×C22⋊C4C2312yes—
805#376C2312yes—
806#376C2314yes—
807#376C2314yes—
808C2×#95C2312yes—
809C2×#95C2314yes—
810C2×#95C2314yes—
811C2×#95C2314yes—
812C2×#95C2314yes—
813C43C2314yes—
814C43C2312yes—
815C43C2311yescharacteristic
816C43C2312yes—
817C2×#41—24no—
818C2×#41—24no—
819C2×#41—42no—
820C22×Q8—24no—
821C22×Q8—24no—
822C22×Q8—42no—
823C22×Q8C2412yes—
824C22×Q8C2411yescharacteristic
825C22×Q8C2412yes—
826C22×Q8C2411yescharacteristic
827C22×Q8C2414yes—
828C22×D4C2411yescharacteristic
829C22×D4C2412yes—
830C22×D4C2411yescharacteristic
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2411yescharacteristic
834C22×D4C2414yes—
835C22×D4C2412yes—
836C23×C4C2412yes—
837C23×C4C2411yescharacteristic
838C23×C4C2412yes—
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2412yes—
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2414yes—
849C23×C4C2414yes—
850C23×C4C2414yes—
851C23×C4C2412yes—
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C4⋊Q8—28no—
856C4⋊Q8—24no—
857C4⋊Q8—44no—
858#126—28no—
859#126—216no—
860#126—216no—
861#125—28no—
862#125—24no—
863#125—216no—
864#125—82no—
865#124—24no—
866#124—28no—
867#124—28no—
868#124—84no—
869#123—28no—
870#123—216no—
871#123—84no—
872C22⋊Q8—28no—
873C22⋊Q8—216no—
874C22⋊Q8—28no—
875C22⋊Q8—24no—
876C22⋊Q8—216no—
877C22⋊Q8—28no—
878C22⋊Q8—28no—
879C22⋊Q8—44no—
880C22⋊Q8—44no—
881C22⋊Q8—44no—
882#121—28no—
883#121—28no—
884#121—216no—
885#121—28no—
886#121—24no—
887#121—24no—
888#121—44no—
889#121#4118yes—
890C4×Q8—24no—
891C4×Q8—24no—
892C4×Q8—24no—
893C4×Q8—28no—
894C4×Q8—24no—
895C4×Q8—28no—
896C4×Q8—24no—
897C4×Q8—28no—
898C4×Q8—28no—
899C4×Q8—42no—
900C4×Q8—44no—
901C4×Q8—84no—
902C4×Q8#4118yes—
903C4×D4—28no—
904C4×D4—216no—
905C4×D4—28no—
906C4×D4—24no—
907C4×D4—28no—
908C4×D4—28no—
909C4×D4—24no—
910C4×D4—216no—
911C4×D4—28no—
912C4×D4—24no—
913C4×D4—28no—
914C4×D4—24no—
915C4×D4—28no—
916C4×D4—24no—
917C4×D4—28no—
918C4×D4—24no—
919C4×D4—28no—
920C4×D4—24no—
921C4×D4—44no—
922C4×D4—42no—
923C4×D4—44no—
924C4×D4—84no—
925#117—24no—
926#117—28no—
927#117—28no—
928#117—24no—
929#117—28no—
930#117—42no—
931#117—82no—
932C2×C4⋊C4—28no—
933C2×C4⋊C4—24no—
934C2×C4⋊C4—28no—
935C2×C4⋊C4—28no—
936C2×C4⋊C4—44no—
937C2×C4⋊C4—44no—
938C2×C4⋊C4—42no—
939C2×C4⋊C4—82no—
940C2×C4⋊C4#4118yescomplemented
941C2×C4⋊C4C2411yescharacteristic
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2411yescharacteristic
944C2×C4⋊C4C2412yes—
945C2×C4⋊C4C2411yescharacteristic
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2412yes—
952C2×C4⋊C4C2411yescharacteristic
953C2×C4⋊C4C2414yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2411yescharacteristic
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2414yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2412yes—
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2414yes—
979C2×C4⋊C4C2414yes—
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C22⋊C4C2412yes—
1007C2×C22⋊C4C2412yes—
1008C2×C22⋊C4C2412yes—
1009C2×C22⋊C4C2412yes—
1010C2×C22⋊C4C2414yes—
1011C2×C22⋊C4C2414yes—
1012C2×C22⋊C4C2411yescharacteristic
1013C2×C22⋊C4C2411yescharacteristic
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2414yes—
1016C2×C22⋊C4C2414yes—
1017C2×C22⋊C4C2412yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2414yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2414yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2411yescharacteristic
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2414yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C42—24no—
1054C2×C42—28no—
1055C2×C42—24no—
1056C2×C42—28no—
1057C2×C42—44no—
1058C2×C42—44no—
1059C2×C42—84no—
1060C2×C42—84no—
1061C2×C42C2411yescharacteristic
1062C2×C42C2412yes—
1063C2×C42C2412yes—
1064C2×C42C2414yes—
1065C2×C42C2414yes—
1066C2×C42C2412yes—
1067C2×C42C2411yescharacteristic
1068C2×C42C2411yescharacteristic
1069C2×C42C2411yescharacteristic
1070C2×C42C2412yes—
1071C2×C42C2414yes—
1072C2×C42C2412yes—
1073C2×C42C2411yescharacteristic
1074C2×C42C2412yes—
1075C2×C42C2412yes—
1076C2×C42C2412yes—
1077C2×C42C2412yes—
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2411yescharacteristic
1082C2×C42C2411yescharacteristic
1083C2×C42C2412yes—
1084C2×C42C2412yes—
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2412yes—
1089C2×C42C2414yes—
1090C2×C42C2414yes—
1091C2×C42C2412yes—
1092C2×C42C2414yes—
1093C2×C42C2412yes—
1094C2×C42C2414yes—
1095C2×C42C2414yes—
1096C2×C42C2414yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2412yes—
1100C2×C42C2414yes—
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2412yes—
1106#95C2412yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2412yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2412yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119#95C2414yes—
1120#95C2412yes—
1121#95C2412yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2412yes—
1126#95C2414yes—
1127#95C2412yes—
1128#95C2412yes—
1129#95C2414yes—
1130#95C2414yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2411yescharacteristic
1134#95C2411yescharacteristic
1135#95C2412yes—
1136#95C2412yes—
1137#95C2411yescharacteristic
1138#95C2411yescharacteristic
1139#95C2412yes—
1140#95C2411yescharacteristic
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2411yescharacteristic
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180C24C2512yes—
1181C24C2511yescharacteristic
1182C24C2512yes—
1183C24C2511yescharacteristic
1184#41—416no—
1185C2×Q8—22no—
1186C2×Q8—24no—
1187C2×Q8—22no—
1188C2×Q8—24no—
1189C2×Q8—24no—
1190C2×Q8—24no—
1191C2×Q8—22no—
1192C2×Q8—28no—
1193C2×Q8—22no—
1194C2×Q8—24no—
1195C2×Q8—22no—
1196C2×Q8—42no—
1197C2×Q8—44no—
1198C2×Q8—44no—
1199C2×Q8—416no—
1200C2×Q8C2×#4114yes—
1201C2×D4—24no—
1202C2×D4—24no—
1203C2×D4—24no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—24no—
1207C2×D4—24no—
1208C2×D4—22no—
1209C2×D4—24no—
1210C2×D4—28no—
1211C2×D4—22no—
1212C2×D4—24no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—24no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—42no—
1219C2×D4—42no—
1220C2×D4—44no—
1221C2×D4—44no—
1222C2×D4—42no—
1223C2×D4C2×#4118yes—
1224C2×D4C2×#4114yes—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—22no—
1229C22×C4—24no—
1230C22×C4—24no—
1231C22×C4—22no—
1232C22×C4—24no—
1233C22×C4—28no—
1234C22×C4—28no—
1235C22×C4—24no—
1236C22×C4—24no—
1237C22×C4—22no—
1238C22×C4—24no—
1239C22×C4—24no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—22no—
1243C22×C4—24no—
1244C22×C4—22no—
1245C22×C4—24no—
1246C22×C4—24no—
1247C22×C4—22no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—24no—
1251C22×C4—22no—
1252C22×C4—24no—
1253C22×C4—24no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—28no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—42no—
1260C22×C4—42no—
1261C22×C4—42no—
1262C22×C4—42no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—42no—
1266C22×C4—42no—
1267C22×C4—42no—
1268C22×C4—42no—
1269C22×C4—42no—
1270C22×C4—44no—
1271C22×C4—44no—
1272C22×C4—44no—
1273C22×C4—42no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—42no—
1277C22×C4—44no—
1278C22×C4—42no—
1279C22×C4C2×#4114yes—
1280C22×C4C2×#4114yes—
1281C22×C4C2×#4118yes—
1282C22×C4C2512yes—
1283C22×C4C2511yescharacteristic
1284C22×C4C2512yes—
1285C22×C4C2511yescharacteristic
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2511yescharacteristic
1290C22×C4C2511yescharacteristic
1291C22×C4C2512yes—
1292C22×C4C2511yescharacteristic
1293C22×C4C2512yes—
1294C22×C4C2514yes—
1295C22×C4C2514yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2514yes—
1299C22×C4C2514yes—
1300C22×C4C2511yescharacteristic
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2512yes—
1304C22×C4C2512yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2512yes—
1307C22×C4C2511yescharacteristic
1308C22×C4C2511yescharacteristic
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C4⋊C4—24no—
1314C4⋊C4—24no—
1315C4⋊C4—24no—
1316C4⋊C4—22no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—28no—
1321C4⋊C4—24no—
1322C4⋊C4—28no—
1323C4⋊C4—24no—
1324C4⋊C4—22no—
1325C4⋊C4—22no—
1326C4⋊C4—24no—
1327C4⋊C4—22no—
1328C4⋊C4—22no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—28no—
1332C4⋊C4—24no—
1333C4⋊C4—28no—
1334C4⋊C4—22no—
1335C4⋊C4—24no—
1336C4⋊C4—24no—
1337C4⋊C4—28no—
1338C4⋊C4—28no—
1339C4⋊C4—24no—
1340C4⋊C4—28no—
1341C4⋊C4—28no—
1342C4⋊C4—28no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—42no—
1355C4⋊C4—44no—
1356C4⋊C4—44no—
1357C4⋊C4—42no—
1358C4⋊C4—44no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—42no—
1364C4⋊C4—44no—
1365C4⋊C4—42no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4C2×#4114yes—
1373C4⋊C4C2×#4114yes—
1374C4⋊C4C2×#4118yes—
1375C4⋊C4C2×#4114yes—
1376C4⋊C4C2×#4118yes—
1377C4⋊C4C2×#4114yes—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—24no—
1381C22⋊C4—28no—
1382C22⋊C4—28no—
1383C22⋊C4—28no—
1384C22⋊C4—24no—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—24no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—28no—
1392C22⋊C4—28no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—28no—
1396C22⋊C4—24no—
1397C22⋊C4—22no—
1398C22⋊C4—24no—
1399C22⋊C4—22no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—28no—
1404C22⋊C4—24no—
1405C22⋊C4—22no—
1406C22⋊C4—24no—
1407C22⋊C4—42no—
1408C22⋊C4—44no—
1409C22⋊C4—44no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—42no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—44no—
1416C22⋊C4—44no—
1417C22⋊C4—44no—
1418C22⋊C4—44no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4C2×#4118yes—
1424C22⋊C42−1+414yes—
1425C42—22no—
1426C42—24no—
1427C42—22no—
1428C42—24no—
1429C42—22no—
1430C42—22no—
1431C42—24no—
1432C42—22no—
1433C42—24no—
1434C42—22no—
1435C42—24no—
1436C42—24no—
1437C42—28no—
1438C42—28no—
1439C42—24no—
1440C42—22no—
1441C42—24no—
1442C42—22no—
1443C42—28no—
1444C42—24no—
1445C42—24no—
1446C42—22no—
1447C42—24no—
1448C42—24no—
1449C42—22no—
1450C42—24no—
1451C42—22no—
1452C42—42no—
1453C42—42no—
1454C42—42no—
1455C42—42no—
1456C42—44no—
1457C42—42no—
1458C42—44no—
1459C42—44no—
1460C42—44no—
1461C42—44no—
1462C42—44no—
1463C42—42no—
1464C42—42no—
1465C42—44no—
1466C42—42no—
1467C42—41no—
1468C42C2×#4114yes—
1469C42C2×#4118yes—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—22no—
1475C23—22no—
1476C23—22no—
1477C23—22no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—22no—
1482C23—21no—
1483C23—22no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—22no—
1488C23—21no—
1489C23—22no—
1490C23—22no—
1491C23—21no—
1492C23—21no—
1493C23—22no—
1494C23C22×#4114yes—
1495C23C22×#4112yes—
1496C23C22×#4112yes—
1497C23C2×2−1+412yes—
1498C23C2611yescharacteristic
1499Q8—28no—
1500Q8—48no—
1501Q8—44no—
1502Q8—48no—
1503Q8—88no—
1504D4—216no—
1505D4—28no—
1506D4—48no—
1507D4—44no—
1508D4—48no—
1509D4—44no—
1510D4—84no—
1511D4—88no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—22no—
1515C2×C4—21no—
1516C2×C4—22no—
1517C2×C4—22no—
1518C2×C4—22no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—22no—
1523C2×C4—22no—
1524C2×C4—21no—
1525C2×C4—22no—
1526C2×C4—21no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—22no—
1530C2×C4—22no—
1531C2×C4—21no—
1532C2×C4—28no—
1533C2×C4—28no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—22no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—22no—
1540C2×C4—22no—
1541C2×C4—22no—
1542C2×C4—21no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—22no—
1547C2×C4—21no—
1548C2×C4—24no—
1549C2×C4—24no—
1550C2×C4—21no—
1551C2×C4—24no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—22no—
1555C2×C4—22no—
1556C2×C4—24no—
1557C2×C4—24no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—24no—
1573C2×C4—22no—
1574C2×C4—24no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—24no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—48no—
1592C2×C4—48no—
1593C2×C4—44no—
1594C2×C4—48no—
1595C2×C4—44no—
1596C2×C4—48no—
1597C2×C4—48no—
1598C2×C4—48no—
1599C2×C4—44no—
1600C2×C4—48no—
1601C2×C4—44no—
1602C2×C4—84no—
1603C2×C4—88no—
1604C2×C4—84no—
1605C2×C4—88no—
1606C2×C4—88no—
1607C2×C4—84no—
1608C2×C4C22×#4114yes—
1609C2×C4C22×#4114yes—
1610C2×C4C22×#4114yes—
1611C2×C4C22×#4112yes—
1612C2×C4C22×#4114yes—
1613C2×C4C22×#4112yes—
1614C2×C4C22×#4112yes—
1615C2×C4C22×#4114yes—
1616C2×C4C22×#4112yes—
1617C2×C4C22×#4112yes—
1618C2×C4C22×#4112yes—
1619C2×C4C22×#4112yes—
1620C2×C4C2×2−1+412yes—
1621C2×C4C2×2−1+412yes—
1622C2×C4#58512yes—
1623C2×C4#58512yes—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—24no—
1631C22—24no—
1632C22—24no—
1633C22—42no—
1634C22—42no—
1635C22—42no—
1636C22—42no—
1637C22—42no—
1638C22—41no—
1639C22—41no—
1640C22—42no—
1641C22—42no—
1642C22—41no—
1643C22—42no—
1644C22—41no—
1645C22—41no—
1646C22—42no—
1647C22—41no—
1648C22—42no—
1649C22—42no—
1650C22—41no—
1651C22#348214yes—
1652C22C23×#4111yescharacteristic
1653C22C23×#4111yescharacteristic
1654C22C23×#4111yescharacteristic
1655C22C22×2−1+411yescharacteristic
1656C22C2×#58511yescharacteristic
1657C22C2×#58511yescharacteristic
1658C22H(7,𝔽2)11yescharacteristic
1659C4—24no—
1660C4—24no—
1661C4—22no—
1662C4—24no—
1663C4—22no—
1664C4—22no—
1665C4—22no—
1666C4—24no—
1667C4—22no—
1668C4—24no—
1669C4—41no—
1670C4—44no—
1671C4—42no—
1672C4—42no—
1673C4—41no—
1674C4—41no—
1675C4—42no—
1676C4—44no—
1677C4—44no—
1678C4—42no—
1679C4—42no—
1680C4—42no—
1681C4—41no—
1682C4—42no—
1683C4—41no—
1684C4—42no—
1685C4—44no—
1686C4—42no—
1687C4—41no—
1688C4#347514yes—
1689C4#348014yes—
1690C2—24no—
1691C2—44no—
1692C2—82no—
1693C2—81no—
1694C2C2×#347511yescharacteristic
1695C2C2×#348011yescharacteristic
1696C2C2×#348211yescharacteristic
1697C2#6299211yescharacteristic
1698C2#6300011yescharacteristic
1699C2#6301011yescharacteristic
1700C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59806C2semidirect
2. #59757C2semidirect
3. #59643C2semidirect
4. #59535C2semidirect
5. #59508C2semidirect
6. #59450C2semidirect
7. #59439C2semidirect
8. #59381C2semidirect
9. #59309C2semidirect
10. #59304C2semidirect
11. #59246C2semidirect
12. #59234C2semidirect
13. #36586C2semidirect
14. #36579C2semidirect
15. #36561C2semidirect
16. #36518C2semidirect
17. #36507C2semidirect
18. #36506C2semidirect
19. #36504C2semidirect
20. #36497C2semidirect
21. #36487C2semidirect
22. #36484C2semidirect
23. #36453C2semidirect
24. #36450C2semidirect
25. #36277C2semidirect
26. #36249C2semidirect
27. #36189C2semidirect
28. #36172C2semidirect
29. C4×#554C2semidirect
30. C4×#556C2semidirect
31. C4×#553C2semidirect
32. C4×#553C2semidirect
33. C4×#548C2semidirect
34. #34127C2semidirect
35. C2×#2355C2semidirect
940. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
#598062
#597572
#596432
#595352
#595082
#594502
#594392
#593812
#593092
#593042
#592462
#592342
#365862
#365792
#365612
#365182
#365072
#365062
#365042
#364972
#364872
#364842
#364532
#364502
#362772
#362492
#361892
#361722
C4×#5542
C4×#5562
C4×#5532
C4×#5482
#341272
C2×#23552