Finite Group Databasebeta

← #7670986

Subgroups — #7670986

Order 512.

5246 conjugacy classes of subgroups.

The subgroup lattice has 1742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59762C214yesmaximal, complemented
2#59487C212yesmaximal, complemented
3#59486C212yesmaximal, complemented
4#59281C212yesmaximal, complemented
5#59104C212yesmaximal, complemented
6#59081C211yesmaximal, characteristic, complemented
7#59080C211yesmaximal, characteristic, complemented
8#59034C211yesmaximal, characteristic, complemented
9#59033C211yesmaximal, characteristic, complemented
10#40218C212yesmaximal, complemented
11#40145C212yesmaximal, complemented
12#39248C212yesmaximal, complemented
13#39010C212yesmaximal, complemented
14#38521C214yesmaximal, complemented
15#38298C214yesmaximal, complemented
16#36639C211yesmaximal, characteristic, complemented
17#36591C211yesmaximal, characteristic, complemented
18Q8×#124C211yesmaximal, characteristic, complemented
19#36463C211yesmaximal, characteristic, complemented
20#36457C211yesmaximal, characteristic, complemented
21#36373C212yesmaximal, complemented
22#36313C211yesmaximal, characteristic, complemented
23#36306C212yesmaximal, complemented
24#36303C211yesmaximal, characteristic, complemented
25#36195C212yesmaximal, complemented
26#36175C211yesmaximal, characteristic, complemented
27#36141C212yesmaximal, complemented
28#36125C211yesmaximal, characteristic, complemented
29#35480C214yesmaximal, complemented
30#35137C212yesmaximal, complemented
31#35044C212yesmaximal, complemented
32#34327C212yesmaximal, complemented
33#34232C212yesmaximal, complemented
34C4×#529C211yesmaximal, characteristic, complemented
35C4×#529C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#550C2211yescharacteristic
38C2×D4×Q8C2211yescharacteristic
39C2×#548C2212yes—
40C2×#547C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2212yes—
43C2×#532C2211yescharacteristic
44C2×#529C2211yescharacteristic
45C2×#529C2211yescharacteristic
46#2863C2212yes—
47#2862C2211yescharacteristic
48#2862C2211yescharacteristic
49#2862C2212yes—
50#2861C2212yes—
51#2861C2212yes—
52#2861C2212yes—
53#2858C2212yes—
54#2858C2211yescharacteristic
55#2858C2211yescharacteristic
56#2854C2212yes—
57#2851C2212yes—
58#2850C2212yes—
59#2850C2212yes—
60#2850C2212yes—
61#2850C2212yes—
62#2850C2212yes—
63#2850C2212yes—
64#2808C2214yes—
65#2778C2214yes—
66#2770C2214yes—
67#2760C2214yes—
68#2756C2214yes—
69#2751C2214yes—
70#2751C2214yes—
71#2750C2214yes—
72#2739C2214yes—
73#2737C2214yes—
74#2729C2214yes—
75#2710C2214yes—
76#2703C2214yes—
77#2696C2214yes—
78#2688C2214yes—
79#2676C2214yes—
80#2653C2214yes—
81#2650C2214yes—
82#2648C2214yes—
83#2631C2214yes—
84#2610C2214yes—
85#2597C2214yes—
86#2595C2214yes—
87#2593C2214yes—
88#2589C2214yes—
89#2572C2214yes—
90#2572C2214yes—
91#2572C2214yes—
92#2568C2212yes—
93#2568C2211yescharacteristic
94#2568C2211yescharacteristic
95#2563C2211yescharacteristic
96#2563C2212yes—
97#2563C2212yes—
98#2563C2211yescharacteristic
99#2560C2214yes—
100#2559C2214yes—
101#2557C2214yes—
102#2557C2214yes—
103#2550C2212yes—
104#2548C2212yes—
105#2548C2211yescharacteristic
106#2547C2211yescharacteristic
107#2546C2211yescharacteristic
108#2544C2212yes—
109#2541C2211yescharacteristic
110#2536C2212yes—
111#2535C2212yes—
112#2532C2214yes—
113#2532C2214yes—
114#2532C2214yes—
115#2528C2214yes—
116#2527C2214yes—
117#2527C2214yes—
118#2527C2214yes—
119#2526C2214yes—
120#2524C2214yes—
121#2523C2214yes—
122#2516C2214yes—
123#2514C2212yes—
124#2514C2212yes—
125#2514C2212yes—
126#2513C2212yes—
127#2513C2212yes—
128#2510C2214yes—
129#2503C2212yes—
130#2498C2214yes—
131#2495C2212yes—
132#2494C2212yes—
133#2493C2214yes—
134#2492C2212yes—
135#2492C2212yes—
136#2492C2212yes—
137#2492C2212yes—
138#2492C2212yes—
139#2492C2214yes—
140#2492C2214yes—
141#2491C2212yes—
142#2491C2212yes—
143#2491C2212yes—
144#2491C2214yes—
145#2491C2214yes—
146#2490C2212yes—
147#2490C2212yes—
148#2488C2214yes—
149#2488C2214yes—
150#2477C2214yes—
151#2476C2214yes—
152#2474C2214yes—
153#2468C2214yes—
154#2467C2214yes—
155#2464C2214yes—
156#2464C2214yes—
157#2464C2214yes—
158#2463C2214yes—
159#2459C2214yes—
160#2459C2214yes—
161#2459C2214yes—
162#2459C2214yes—
163#2458C2214yes—
164#2457C2214yes—
165#2456C2214yes—
166#2453C2212yes—
167#2453C2212yes—
168#2452C2212yes—
169#2451C2212yes—
170#2448C2212yes—
171#2448C2212yes—
172#2447C2212yes—
173#2447C2212yes—
174#2447C2212yes—
175#2446C2212yes—
176#2446C2214yes—
177#2445C2212yes—
178#2444C2214yes—
179#2442C2212yes—
180#2439C2212yes—
181#2436C2212yes—
182#2436C2212yes—
183#2432C2212yes—
184#2431C2212yes—
185#2431C2212yes—
186#2429C2212yes—
187#2428C2212yes—
188#2428C2212yes—
189#2428C2212yes—
190#2426C2212yes—
191#2421C2212yes—
192#2420C2212yes—
193#2420C2212yes—
194#2414C2212yes—
195#2407C2212yes—
196#2407C2212yes—
197#2407C2212yes—
198#2372C2214yes—
199#2372C2214yes—
200#2369C2211yescharacteristic
201#2368C2214yes—
202#2367C2212yes—
203#2367C2212yes—
204#2366C2212yes—
205#2366C2211yescharacteristic
206#2366C2212yes—
207#2365C2212yes—
208#2365C2211yescharacteristic
209#2365C2212yes—
210#2365C2211yescharacteristic
211#2364C2214yes—
212#2363C2214yes—
213#2363C2214yes—
214#2362C2212yes—
215#2361C2212yes—
216#2361C2212yes—
217#2359C2214yes—
218#2357C2212yes—
219#2357C2212yes—
220#2356C2212yes—
221#2356C2212yes—
222#2353C2214yes—
223#2353C2214yes—
224#2353C2214yes—
225#2352C2212yes—
226#2341C2212yes—
227#2341C2212yes—
228#2341C2212yes—
229Q8×C22⋊C4C2212yes—
230Q8×C22⋊C4C2212yes—
231#2339C2212yes—
232#2339C2212yes—
233#2339C2212yes—
234#2339C2212yes—
235#2337C2214yes—
236#2337C2214yes—
237#2333C2214yes—
238#2333C2214yes—
239#2332C2214yes—
240#2325C2214yes—
241#2319C2214yes—
242C4×#125C2211yescharacteristic
243C4×#125C2211yescharacteristic
244C4×#125C2211yescharacteristic
245C4×#125C2211yescharacteristic
246C4×#126C2212yes—
247C4×#126C2212yes—
248C4×#126C2212yes—
249C4×#126C2212yes—
250C4×#124C2212yes—
251C4×#124C2211yescharacteristic
252C4×#124C2212yes—
253C4×#124C2212yes—
254C4×#124C2212yes—
255C4×#124C2212yes—
256C4×#124C2212yes—
257C4×#124C2211yescharacteristic
258C4×#124C2212yes—
259C4×#124C2211yescharacteristic
260C4×#124C2211yescharacteristic
261C4×C22⋊Q8C2211yescharacteristic
262C4×C22⋊Q8C2211yescharacteristic
263C4×C22⋊Q8C2211yescharacteristic
264C4×C22⋊Q8C2211yescharacteristic
265C4×#123C2212yes—
266C4×#123C2212yes—
267C4×#123C2212yes—
268C4×#123C2212yes—
269C4×#121C2212yes—
270C4×#121C2211yescharacteristic
271C4×#121C2211yescharacteristic
272C4×#121C2211yescharacteristic
273C4×#121C2211yescharacteristic
274#2298C2212yes—
275#2298C2212yes—
276#2297C2212yes—
277#2297C2212yes—
278#2295C2212yes—
279#2295C2211yescharacteristic
280#2295C2211yescharacteristic
281C2×#391C2212yes—
282#2293C2211yescharacteristic
283#2293C2211yescharacteristic
284#2290C2212yes—
285#2290C2212yes—
286#2283C2212yes—
287#2283C2211yescharacteristic
288#2283C2211yescharacteristic
289#2275C2214yes—
290C42×Q8C2211yescharacteristic
291C42×Q8C2211yescharacteristic
292C42×D4C2212yes—
293C42×D4C2211yescharacteristic
294C42×D4C2212yes—
295C42×D4C2211yescharacteristic
296C4×#117C2212yes—
297C4×#117C2212yes—
298C2×C43C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×Q8C2312yes—
303Q82—44no—
304#550—44no—
305D4×Q8—44no—
306#548—216no—
307#547—44no—
308#533—44no—
309#532—216no—
310#532—44no—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2312yes—
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2314yes—
319C2×#127C2311yescharacteristic
320C2×#127C2312yes—
321C2×#127C2312yes—
322#529—28no—
323#529—28no—
324C2×#126C2312yes—
325C2×#126C2312yes—
326C2×#125C2311yescharacteristic
327C2×#125C2311yescharacteristic
328C2×#125C2312yes—
329C2×#124C2314yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#124C2314yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2311yescharacteristic
341C2×#123C2312yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2311yescharacteristic
353C2×#121C2314yes—
354C2×#121C2314yes—
355C2×#121C2312yes—
356C2×#121C2314yes—
357C2×#121C2311yescharacteristic
358C2×#121C2311yescharacteristic
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2311yescharacteristic
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2314yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2312yes—
403C2×#117C2312yes—
404C22×C4⋊C4C2312yes—
405C22×C42C2311yescharacteristic
406C22×C42C2312yes—
407C22×C42C2311yescharacteristic
408C22×C42C2311yescharacteristic
409C22×C42C2311yescharacteristic
410C22×C42C2311yescharacteristic
411C22×C42C2311yescharacteristic
412C22×C42C2312yes—
413C22×C42C2311yescharacteristic
414#401C2314yes—
415#401C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#399C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2314yes—
444#396C2314yes—
445#396C2314yes—
446#395C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#392C2314yes—
472#392C2314yes—
473#392C2314yes—
474#392C2314yes—
475#392C2314yes—
476#392C2314yes—
477#392C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2311yescharacteristic
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2312yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#390C2314yes—
512#390C2312yes—
513#390C2311yescharacteristic
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2311yescharacteristic
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2311yescharacteristic
530#390C2314yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2311yescharacteristic
539#389C2311yescharacteristic
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2311yescharacteristic
543#389C2311yescharacteristic
544#389C2311yescharacteristic
545#389C2311yescharacteristic
546#389C2311yescharacteristic
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#388C2312yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2312yes—
606#388C2312yes—
607#388C2312yes—
608#387C2312yes—
609#387C2312yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2312yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
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#387C2314yes—
639#387C2314yes—
640#386C2314yes—
641#386C2314yes—
642#386C2314yes—
643#386C2314yes—
644#386C2314yes—
645#386C2314yes—
646#386C2314yes—
647#386C2314yes—
648#386C2314yes—
649#386C2314yes—
650#386C2314yes—
651#386C2314yes—
652#386C2314yes—
653#386C2314yes—
654#386C2314yes—
655#386C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#386C2312yes—
670#385C2312yes—
671#385C2314yes—
672#385C2314yes—
673#385C2314yes—
674#385C2314yes—
675#385C2314yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2312yes—
680#385C2312yes—
681#385C2312yes—
682#383C2312yes—
683#383C2312yes—
684#383C2314yes—
685#383C2314yes—
686#383C2314yes—
687#383C2314yes—
688#382C2311yescharacteristic
689#382C2311yescharacteristic
690#382C2311yescharacteristic
691#382C2311yescharacteristic
692#382C2312yes—
693#382C2312yes—
694#382C2312yes—
695#382C2312yes—
696#382C2312yes—
697#382C2312yes—
698#382C2312yes—
699#382C2312yes—
700#381C2314yes—
701#381C2312yes—
702#381C2314yes—
703#381C2314yes—
704#381C2314yes—
705#381C2314yes—
706#381C2314yes—
707#381C2314yes—
708#381C2312yes—
709#380C2314yes—
710#380C2314yes—
711#380C2312yes—
712#380C2312yes—
713#380C2312yes—
714#380C2314yes—
715#380C2312yes—
716#380C2314yes—
717#380C2314yes—
718#380C2311yescharacteristic
719#380C2312yes—
720#380C2312yes—
721#380C2311yescharacteristic
722#380C2311yescharacteristic
723#380C2311yescharacteristic
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2312yes—
726C4×C4⋊C4C2312yes—
727C4×C4⋊C4C2312yes—
728C4×C4⋊C4C2312yes—
729C4×C4⋊C4C2312yes—
730C4×C4⋊C4C2312yes—
731C4×C4⋊C4C2312yes—
732C4×C4⋊C4C2312yes—
733C4×C4⋊C4C2312yes—
734C4×C4⋊C4C2312yes—
735C4×C4⋊C4C2312yes—
736C4×C4⋊C4C2314yes—
737C4×C4⋊C4C2311yescharacteristic
738C4×C4⋊C4C2311yescharacteristic
739C4×C4⋊C4C2311yescharacteristic
740C4×C4⋊C4C2312yes—
741C4×C4⋊C4C2311yescharacteristic
742C4×C4⋊C4C2312yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2311yescharacteristic
749C4×C4⋊C4C2314yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C22⋊C4C2312yes—
763C4×C22⋊C4C2312yes—
764C4×C22⋊C4C2312yes—
765C4×C22⋊C4C2312yes—
766C4×C22⋊C4C2312yes—
767C4×C22⋊C4C2312yes—
768C4×C22⋊C4C2312yes—
769C4×C22⋊C4C2312yes—
770C4×C22⋊C4C2312yes—
771C4×C22⋊C4C2312yes—
772C4×C22⋊C4C2312yes—
773C4×C22⋊C4C2312yes—
774C4×C22⋊C4C2314yes—
775C4×C22⋊C4C2312yes—
776C4×C22⋊C4C2314yes—
777C4×C22⋊C4C2314yes—
778C4×C22⋊C4C2314yes—
779C4×C22⋊C4C2314yes—
780C4×C22⋊C4C2312yes—
781C4×C22⋊C4C2314yes—
782C4×C22⋊C4C2314yes—
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801#376C2314yes—
802#376C2312yes—
803#376C2312yes—
804#376C2314yes—
805#376C2312yes—
806#376C2312yes—
807C2×#95C2314yes—
808C2×#95C2314yes—
809C2×#95C2314yes—
810C43C2311yescharacteristic
811C43C2311yescharacteristic
812C43C2311yescharacteristic
813C43C2311yescharacteristic
814C43C2311yescharacteristic
815C43C2311yescharacteristic
816C43C2312yes—
817C43C2311yescharacteristic
818C43C2312yes—
819C43C2311yescharacteristic
820C2×#41—28no—
821C2×#41—28no—
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—44no—
829C22×Q8—28no—
830C22×Q8—44no—
831C22×Q8—44no—
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2411yescharacteristic
835C22×Q8C2411yescharacteristic
836C22×Q8C2412yes—
837C22×Q8C2414yes—
838C22×Q8C2414yes—
839C22×D4C2411yescharacteristic
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2411yescharacteristic
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C23×C4C2412yes—
853C23×C4C2411yescharacteristic
854C23×C4C2412yes—
855C23×C4C2412yes—
856C23×C4C2412yes—
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2414yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2412yes—
865C23×C4C2414yes—
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2414yes—
870C4⋊Q8—28no—
871C4⋊Q8—24no—
872C4⋊Q8—24no—
873C4⋊Q8—24no—
874C4⋊Q8—44no—
875C4⋊Q8—44no—
876C4⋊Q8—44no—
877C4⋊Q8—48no—
878#127—28no—
879#127—24no—
880#127—44no—
881#126—28no—
882#126—28no—
883#125—24no—
884#125—24no—
885#125—44no—
886#124—24no—
887#124—28no—
888#124—216no—
889#124—28no—
890#124—44no—
891#124—44no—
892#124—48no—
893#124—48no—
894#124—44no—
895#124—44no—
896#124—44no—
897#124#4118yescomplemented
898#123—28no—
899#123—28no—
900#123—48no—
901#123—48no—
902C22⋊Q8—24no—
903C22⋊Q8—216no—
904C22⋊Q8—48no—
905C22⋊Q8—44no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8#4118yescomplemented
910#121—24no—
911#121—24no—
912#121—28no—
913#121—216no—
914#121—216no—
915#121—216no—
916#121—48no—
917#121—44no—
918#121—44no—
919#121—44no—
920#121—44no—
921#121—44no—
922C4×Q8—24no—
923C4×Q8—24no—
924C4×Q8—28no—
925C4×Q8—24no—
926C4×Q8—24no—
927C4×Q8—42no—
928C4×Q8—42no—
929C4×Q8—44no—
930C4×Q8—44no—
931C4×Q8—44no—
932C4×Q8—44no—
933C4×Q8—44no—
934C4×D4—24no—
935C4×D4—28no—
936C4×D4—24no—
937C4×D4—216no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—216no—
941C4×D4—216no—
942C4×D4—24no—
943C4×D4—24no—
944C4×D4—42no—
945C4×D4—42no—
946C4×D4—44no—
947C4×D4—44no—
948C4×D4—44no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—48no—
955C4×D4—44no—
956#117—28no—
957#117—28no—
958#117—44no—
959#117—44no—
960#117—44no—
961C2×C4⋊C4—44no—
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2411yescharacteristic
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C22⋊C4C2412yes—
1012C2×C22⋊C4C2412yes—
1013C2×C22⋊C4C2412yes—
1014C2×C22⋊C4C2412yes—
1015C2×C22⋊C4C2412yes—
1016C2×C22⋊C4C2412yes—
1017C2×C22⋊C4C2414yes—
1018C2×C22⋊C4C2414yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2412yes—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2414yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2414yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2412yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2414yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2414yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C42—24no—
1067C2×C42—24no—
1068C2×C42—28no—
1069C2×C42—24no—
1070C2×C42—42no—
1071C2×C42—44no—
1072C2×C42—42no—
1073C2×C42—42no—
1074C2×C42—42no—
1075C2×C42C2411yescharacteristic
1076C2×C42C2411yescharacteristic
1077C2×C42C2411yescharacteristic
1078C2×C42C2411yescharacteristic
1079C2×C42C2412yes—
1080C2×C42C2412yes—
1081C2×C42C2412yes—
1082C2×C42C2411yescharacteristic
1083C2×C42C2411yescharacteristic
1084C2×C42C2412yes—
1085C2×C42C2412yes—
1086C2×C42C2412yes—
1087C2×C42C2412yes—
1088C2×C42C2412yes—
1089C2×C42C2412yes—
1090C2×C42C2414yes—
1091C2×C42C2411yescharacteristic
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2412yes—
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2411yescharacteristic
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2414yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2414yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126#95C2412yes—
1127#95C2412yes—
1128#95C2414yes—
1129#95C2412yes—
1130#95C2412yes—
1131#95C2414yes—
1132#95C2414yes—
1133#95C2414yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2414yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2414yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196C24C2512yes—
1197C24C2514yes—
1198C24C2511yescharacteristic
1199C24C2512yes—
1200#41—816no—
1201#41—816no—
1202#41—816no—
1203C2×Q8—24no—
1204C2×Q8—24no—
1205C2×Q8—28no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—24no—
1211C2×Q8—22no—
1212C2×Q8—22no—
1213C2×Q8—24no—
1214C2×Q8—24no—
1215C2×Q8—44no—
1216C2×Q8—42no—
1217C2×Q8—42no—
1218C2×Q8—44no—
1219C2×Q8—44no—
1220C2×Q8—44no—
1221C2×Q8—44no—
1222C2×Q8—816no—
1223C2×Q8C2×#4114yes—
1224C2×Q8C2×#4114yes—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—24no—
1228C2×D4—28no—
1229C2×D4—28no—
1230C2×D4—28no—
1231C2×D4—28no—
1232C2×D4—28no—
1233C2×D4—22no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—28no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—22no—
1243C2×D4—24no—
1244C2×D4—22no—
1245C2×D4—24no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—42no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—42no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4C2×#4114yes—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—24no—
1269C22×C4—28no—
1270C22×C4—22no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—24no—
1280C22×C4—24no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—28no—
1289C22×C4—28no—
1290C22×C4—28no—
1291C22×C4—24no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—42no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—42no—
1308C22×C4—42no—
1309C22×C4—42no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4—44no—
1317C22×C4C2×#4114yes—
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2514yes—
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2511yescharacteristic
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2512yes—
1332C22×C4C2514yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2514yes—
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2511yescharacteristic
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C22×C4C2511yescharacteristic
1347C22×C4C2511yescharacteristic
1348C22×C4C2511yescharacteristic
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—28no—
1353C4⋊C4—28no—
1354C4⋊C4—24no—
1355C4⋊C4—22no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—28no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—22no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—24no—
1370C4⋊C4—22no—
1371C4⋊C4—24no—
1372C4⋊C4—22no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—24no—
1376C4⋊C4—22no—
1377C4⋊C4—22no—
1378C4⋊C4—22no—
1379C4⋊C4—24no—
1380C4⋊C4—22no—
1381C4⋊C4—44no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—42no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4C2×#4118yes—
1397C4⋊C4C2×#4114yes—
1398C22⋊C4—24no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—24no—
1402C22⋊C4—24no—
1403C22⋊C4—24no—
1404C22⋊C4—28no—
1405C22⋊C4—28no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—28no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—28no—
1412C22⋊C4—24no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—28no—
1416C22⋊C4—24no—
1417C22⋊C4—28no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—44no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4C2×#4118yes—
1451C22⋊C4C2×#4118yes—
1452C22⋊C4C2×#4118yes—
1453C42—22no—
1454C42—22no—
1455C42—24no—
1456C42—24no—
1457C42—22no—
1458C42—22no—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—24no—
1463C42—24no—
1464C42—24no—
1465C42—24no—
1466C42—28no—
1467C42—22no—
1468C42—22no—
1469C42—22no—
1470C42—24no—
1471C42—24no—
1472C42—22no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—24no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—24no—
1482C42—24no—
1483C42—24no—
1484C42—41no—
1485C42—41no—
1486C42—41no—
1487C42—41no—
1488C42—42no—
1489C42—42no—
1490C42—41no—
1491C42—41no—
1492C42—41no—
1493C42—41no—
1494C42—42no—
1495C42—44no—
1496C42—42no—
1497C42—44no—
1498C42—42no—
1499C42—42no—
1500C42—44no—
1501C42—44no—
1502C42C2×#4114yes—
1503C42H(5,𝔽2)14yes—
1504C23—21no—
1505C23—22no—
1506C23—22no—
1507C23—21no—
1508C23—22no—
1509C23—22no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—22no—
1514C23—22no—
1515C23—21no—
1516C23—22no—
1517C23—24no—
1518C23—24no—
1519C23—22no—
1520C23—22no—
1521C23—24no—
1522C23—22no—
1523C23—24no—
1524C23—22no—
1525C23—24no—
1526C23—22no—
1527C23—24no—
1528C23—24no—
1529C23—22no—
1530C23C22×#4114yes—
1531C23C22×#4112yes—
1532C23C2611yescharacteristic
1533Q8—28no—
1534Q8—28no—
1535Q8—48no—
1536Q8—48no—
1537Q8—84no—
1538Q8—88no—
1539Q8—164no—
1540D4—28no—
1541D4—416no—
1542D4—48no—
1543D4—48no—
1544D4—44no—
1545D4—48no—
1546D4—48no—
1547D4—84no—
1548D4—88no—
1549D4—88no—
1550D4—88no—
1551D4—88no—
1552D4—164no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—22no—
1556C2×C4—21no—
1557C2×C4—22no—
1558C2×C4—22no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—22no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—22no—
1571C2×C4—28no—
1572C2×C4—22no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—24no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—24no—
1592C2×C4—24no—
1593C2×C4—22no—
1594C2×C4—22no—
1595C2×C4—24no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—24no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—24no—
1625C2×C4—24no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—24no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—44no—
1633C2×C4—48no—
1634C2×C4—48no—
1635C2×C4—44no—
1636C2×C4—44no—
1637C2×C4—44no—
1638C2×C4—44no—
1639C2×C4—44no—
1640C2×C4—48no—
1641C2×C4—48no—
1642C2×C4—84no—
1643C2×C4—84no—
1644C2×C4—88no—
1645C2×C4—88no—
1646C2×C4—88no—
1647C2×C4—88no—
1648C2×C4—164no—
1649C2×C4C22×#4112yes—
1650C2×C4C22×#4112yes—
1651C2×C4C22×#4112yes—
1652C2×C4C22×#4114yes—
1653C2×C4C22×#4114yes—
1654C2×C4C22×#4114yes—
1655C2×C4C22×#4112yes—
1656C2×C4C22×#4112yes—
1657C2×C4C2×H(5,𝔽2)12yes—
1658C2×C4C2×H(5,𝔽2)12yes—
1659C2×C4C2×H(5,𝔽2)12yes—
1660C2×C4#58512yes—
1661C2×C4#58512yes—
1662C2×C4#58512yes—
1663C2×C4#58512yes—
1664C22—22no—
1665C22—24no—
1666C22—22no—
1667C22—24no—
1668C22—22no—
1669C22—24no—
1670C22—42no—
1671C22—41no—
1672C22—42no—
1673C22—41no—
1674C22—41no—
1675C22—42no—
1676C22—41no—
1677C22—42no—
1678C22—42no—
1679C22—44no—
1680C22—44no—
1681C22—42no—
1682C22—42no—
1683C22—44no—
1684C22—42no—
1685C22—44no—
1686C22—44no—
1687C22—42no—
1688C22—44no—
1689C22—42no—
1690C22—42no—
1691C22—44no—
1692C22C23×#4111yescharacteristic
1693C22C23×#4111yescharacteristic
1694C22C22×H(5,𝔽2)11yescharacteristic
1695C22C2×#58511yescharacteristic
1696C22C2×#58511yescharacteristic
1697C22C2×#58511yescharacteristic
1698C22C2×#58511yescharacteristic
1699C4—22no—
1700C4—24no—
1701C4—24no—
1702C4—22no—
1703C4—22no—
1704C4—22no—
1705C4—22no—
1706C4—22no—
1707C4—24no—
1708C4—41no—
1709C4—42no—
1710C4—42no—
1711C4—44no—
1712C4—44no—
1713C4—42no—
1714C4—41no—
1715C4—41no—
1716C4—42no—
1717C4—42no—
1718C4—42no—
1719C4—41no—
1720C4—42no—
1721C4—42no—
1722C4—41no—
1723C4—42no—
1724C4—44no—
1725C4—42no—
1726C4—41no—
1727C4—42no—
1728C4#351414yes—
1729C4#351414yes—
1730C2—42no—
1731C2—44no—
1732C2—82no—
1733C2—84no—
1734C2#41211yescharacteristic
1735C2C2×#351411yescharacteristic
1736C2C2×#351411yescharacteristic
1737C2#6279311yescharacteristic
1738C2#6281611yescharacteristic
1739C2#6282711yescharacteristic
1740C2#6283611yescharacteristic
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. #59762C2semidirect
2. #59487C2semidirect
3. #59486C2semidirect
4. #59281C2semidirect
5. #59104C2semidirect
6. #59081C2semidirect
7. #59080C2semidirect
8. #59034C2semidirect
9. #59033C2semidirect
10. #40218C2semidirect
11. #40145C2semidirect
12. #39248C2semidirect
13. #39010C2semidirect
14. #38521C2semidirect
15. #38298C2semidirect
16. #36639C2semidirect
17. #36591C2semidirect
18. Q8×#124C2semidirect
19. #36463C2semidirect
20. #36457C2semidirect
21. #36373C2semidirect
22. #36313C2semidirect
23. #36306C2semidirect
24. #36303C2semidirect
25. #36195C2semidirect
26. #36175C2semidirect
27. #36141C2semidirect
28. #36125C2semidirect
29. #35480C2semidirect
30. #35137C2semidirect
31. #35044C2semidirect
32. #34327C2semidirect
33. #34232C2semidirect
34. C4×#529C2semidirect
35. C4×#529C2semidirect
897. #124#41semidirect
909. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#597622
#594872
#594862
#592812
#591042
#590812
#590802
#590342
#590332
#402182
#401452
#392482
#390102
#385212
#382982
#366392
#365912
Q8×#1242
#364632
#364572
#363732
#363132
#363062
#363032
#361952
#361752
#361412
#361252
#354802
#351372
#350442
#343272
#342322
C4×#5292