Finite Group Databasebeta

← #7779555

Subgroups — #7779555

Order 512.

5131 conjugacy classes of subgroups.

The subgroup lattice has 1785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59550C212yesmaximal, complemented
2#59249C211yesmaximal, characteristic, complemented
3#59218C211yesmaximal, characteristic, complemented
4#59078C211yesmaximal, characteristic, complemented
5#59066C211yesmaximal, characteristic, complemented
6#59059C212yesmaximal, complemented
7#50807C214yesmaximal, complemented
8#49962C214yesmaximal, complemented
9#47591C214yesmaximal, complemented
10#46679C214yesmaximal, complemented
11#45632C212yesmaximal, complemented
12#45632C212yesmaximal, complemented
13#45393C212yesmaximal, complemented
14#45358C212yesmaximal, complemented
15#42871C212yesmaximal, complemented
16#42571C212yesmaximal, complemented
17#40118C212yesmaximal, complemented
18#40031C212yesmaximal, complemented
19#39725C211yesmaximal, characteristic, complemented
20#39599C211yesmaximal, characteristic, complemented
21#39029C212yesmaximal, complemented
22#38920C212yesmaximal, complemented
23#37970C212yesmaximal, complemented
24#37785C212yesmaximal, complemented
25#37286C212yesmaximal, complemented
26#36599C211yesmaximal, characteristic, complemented
27#36445C211yesmaximal, characteristic, complemented
28#36410C211yesmaximal, characteristic, complemented
29#36186C211yesmaximal, characteristic, complemented
30#36117C211yesmaximal, characteristic, complemented
31#36117C211yesmaximal, characteristic, complemented
32#35292C211yesmaximal, characteristic, complemented
33#34947C211yesmaximal, characteristic, complemented
34#34383C212yesmaximal, complemented
35C4×#537C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic
37C2×#552C2212yes—
38C2×#550C2211yescharacteristic
39C2×#547C2212yes—
40C2×#537C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#529C2212yes—
44C2×#529C2212yes—
45C2×C4×#41C2211yescharacteristic
46C2×C4×#41C2211yescharacteristic
47#2857C2212yes—
48#2857C2212yes—
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2856C2211yescharacteristic
52#2856C2211yescharacteristic
53#2854C2212yes—
54#2854C2212yes—
55#2854C2212yes—
56#2854C2212yes—
57#2837C2214yes—
58#2837C2214yes—
59#2808C2214yes—
60#2807C2214yes—
61#2807C2214yes—
62#2784C2214yes—
63#2783C2214yes—
64#2781C2214yes—
65#2781C2214yes—
66#2779C2214yes—
67#2767C2214yes—
68#2754C2214yes—
69#2748C2214yes—
70#2748C2214yes—
71#2742C2214yes—
72#2741C2214yes—
73#2726C2214yes—
74#2721C2214yes—
75#2718C2214yes—
76#2718C2214yes—
77#2718C2214yes—
78#2717C2214yes—
79#2714C2214yes—
80#2711C2214yes—
81#2711C2214yes—
82#2706C2214yes—
83#2706C2214yes—
84#2705C2214yes—
85#2705C2214yes—
86#2705C2214yes—
87#2705C2214yes—
88#2705C2214yes—
89#2704C2214yes—
90#2703C2214yes—
91#2703C2214yes—
92#2702C2214yes—
93#2693C2214yes—
94#2693C2214yes—
95#2693C2214yes—
96#2691C2214yes—
97#2676C2214yes—
98#2671C2214yes—
99#2662C2214yes—
100#2652C2214yes—
101#2650C2214yes—
102#2629C2212yes—
103#2624C2214yes—
104#2624C2212yes—
105#2619C2212yes—
106#2615C2212yes—
107#2601C2214yes—
108#2592C2212yes—
109#2589C2214yes—
110#2587C2214yes—
111#2585C2214yes—
112#2584C2212yes—
113#2582C2211yescharacteristic
114#2582C2212yes—
115#2580C2212yes—
116#2580C2212yes—
117#2569C2214yes—
118#2568C2211yescharacteristic
119#2567C2211yescharacteristic
120#2566C2212yes—
121#2565C2212yes—
122#2564C2212yes—
123#2564C2212yes—
124#2563C2211yescharacteristic
125#2558C2214yes—
126#2557C2214yes—
127#2554C2214yes—
128#2554C2214yes—
129#2553C2214yes—
130#2552C2211yescharacteristic
131#2552C2211yescharacteristic
132#2548C2211yescharacteristic
133#2548C2211yescharacteristic
134#2548C2212yes—
135#2546C2212yes—
136#2546C2211yescharacteristic
137#2545C2212yes—
138#2542C2211yescharacteristic
139#2542C2212yes—
140#2542C2211yescharacteristic
141#2540C2212yes—
142#2540C2212yes—
143#2538C2212yes—
144#2538C2211yescharacteristic
145#2538C2212yes—
146#2535C2212yes—
147#2521C2214yes—
148#2519C2214yes—
149#2512C2212yes—
150#2512C2212yes—
151#2512C2212yes—
152#2512C2212yes—
153#2511C2212yes—
154#2511C2212yes—
155#2509C2212yes—
156#2509C2212yes—
157#2506C2212yes—
158#2501C2212yes—
159#2501C2212yes—
160#2498C2214yes—
161#2497C2212yes—
162#2496C2212yes—
163#2496C2212yes—
164#2496C2212yes—
165#2491C2212yes—
166#2490C2212yes—
167#2490C2212yes—
168#2489C2212yes—
169#2489C2212yes—
170#2487C2214yes—
171#2485C2212yes—
172#2479C2214yes—
173#2479C2214yes—
174#2479C2214yes—
175#2478C2214yes—
176#2477C2214yes—
177#2476C2214yes—
178#2473C2214yes—
179#2471C2214yes—
180#2471C2214yes—
181#2464C2214yes—
182#2464C2214yes—
183#2460C2214yes—
184#2456C2214yes—
185#2454C2212yes—
186#2454C2212yes—
187#2454C2212yes—
188#2454C2214yes—
189#2454C2212yes—
190#2454C2214yes—
191#2451C2212yes—
192#2448C2212yes—
193#2448C2212yes—
194#2448C2212yes—
195#2446C2212yes—
196#2445C2212yes—
197#2445C2212yes—
198#2443C2214yes—
199#2442C2212yes—
200#2441C2214yes—
201#2441C2212yes—
202#2432C2212yes—
203#2432C2212yes—
204#2432C2212yes—
205#2431C2212yes—
206#2429C2212yes—
207#2429C2212yes—
208#2428C2212yes—
209#2427C2212yes—
210#2426C2212yes—
211#2425C2214yes—
212#2425C2214yes—
213#2422C2212yes—
214#2421C2212yes—
215#2417C2212yes—
216#2417C2211yescharacteristic
217#2417C2211yescharacteristic
218#2417C2211yescharacteristic
219#2417C2211yescharacteristic
220#2414C2214yes—
221#2414C2212yes—
222#2414C2212yes—
223#2414C2212yes—
224#2407C2212yes—
225#2407C2212yes—
226#2407C2212yes—
227#2407C2212yes—
228#2407C2212yes—
229#2396C2212yes—
230#2396C2212yes—
231#2376C2214yes—
232#2376C2214yes—
233#2370C2212yes—
234#2370C2212yes—
235#2370C2212yes—
236#2367C2212yes—
237#2367C2212yes—
238#2366C2211yescharacteristic
239#2365C2211yescharacteristic
240#2363C2212yes—
241#2362C2212yes—
242#2362C2212yes—
243#2361C2212yes—
244#2361C2212yes—
245#2355C2211yescharacteristic
246#2355C2212yes—
247#2354C2212yes—
248#2354C2212yes—
249#2354C2214yes—
250#2354C2211yescharacteristic
251#2352C2214yes—
252Q8×C4⋊C4C2211yescharacteristic
253Q8×C4⋊C4C2211yescharacteristic
254Q8×C4⋊C4C2212yes—
255D4×C4⋊C4C2212yes—
256#2345C2212yes—
257#2341C2212yes—
258#2341C2212yes—
259#2334C2214yes—
260#2334C2214yes—
261#2325C2212yes—
262#2325C2212yes—
263#2324C2212yes—
264#2324C2211yescharacteristic
265#2324C2211yescharacteristic
266#2324C2212yes—
267#2324C2212yes—
268#2324C2212yes—
269#2323C2211yescharacteristic
270#2323C2212yes—
271#2323C2211yescharacteristic
272#2323C2212yes—
273#2317C2214yes—
274#2316C2211yescharacteristic
275#2314C2214yes—
276#2311C2211yescharacteristic
277#2311C2211yescharacteristic
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2212yes—
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2212yes—
287C4×#121C2212yes—
288C4×#121C2211yescharacteristic
289C4×#121C2212yes—
290C4×#121C2212yes—
291C4×#121C2211yescharacteristic
292#2297C2212yes—
293#2297C2212yes—
294#2285C2212yes—
295#2285C2212yes—
296#2285C2211yescharacteristic
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301C22×#41C2312yes—
302C22×#41C2312yes—
303#557—44no—
304#552—48no—
305#550—44no—
306#547—48no—
307#537—28no—
308#533—44no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×#127C2311yescharacteristic
316C2×#127C2312yes—
317#529—216no—
318#529—48no—
319C2×#126C2314yes—
320C2×#126C2314yes—
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#125C2312yes—
328C2×#125C2314yes—
329C2×#125C2314yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2311yescharacteristic
354C2×C22⋊Q8C2311yescharacteristic
355C2×C22⋊Q8C2311yescharacteristic
356C2×C22⋊Q8C2311yescharacteristic
357C2×#121C2312yes—
358C2×#121C2311yescharacteristic
359C2×#121C2312yes—
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2314yes—
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C4×#41—44no—
374C4×#41—44no—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2311yescharacteristic
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2312yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×#117C2314yes—
407C2×#117C2311yescharacteristic
408C2×#117C2311yescharacteristic
409C2×#117C2314yes—
410C2×#117C2311yescharacteristic
411C2×#117C2312yes—
412C2×#117C2311yescharacteristic
413C2×#117C2312yes—
414C2×#117C2314yes—
415C2×#117C2312yes—
416C2×#117C2312yes—
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2311yescharacteristic
419C22×C4⋊C4C2311yescharacteristic
420C22×C4⋊C4C2314yes—
421C22×C4⋊C4C2311yescharacteristic
422C22×C42C2312yes—
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2311yescharacteristic
426C22×C42C2312yes—
427C22×C42C2312yes—
428#400C2312yes—
429#400C2312yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2314yes—
438#400C2314yes—
439#399C2312yes—
440#399C2312yes—
441#399C2314yes—
442#399C2314yes—
443#399C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#398C2312yes—
452#398C2312yes—
453#398C2312yes—
454#398C2312yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#396C2312yes—
477#396C2312yes—
478#396C2312yes—
479#396C2312yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#395C2312yes—
493#395C2312yes—
494#395C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#393C2312yes—
513#393C2312yes—
514#393C2314yes—
515#393C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#392C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2311yescharacteristic
527#391C2312yes—
528#391C2311yescharacteristic
529#391C2311yescharacteristic
530#391C2311yescharacteristic
531#391C2311yescharacteristic
532#391C2311yescharacteristic
533#391C2312yes—
534#391C2314yes—
535#391C2312yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2311yescharacteristic
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2312yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2314yes—
552#390C2314yes—
553#390C2314yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2312yes—
560#390C2312yes—
561#390C2312yes—
562#390C2312yes—
563#390C2314yes—
564#390C2314yes—
565#390C2314yes—
566#390C2314yes—
567#390C2312yes—
568#390C2312yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2314yes—
573#390C2314yes—
574#390C2314yes—
575#389C2311yescharacteristic
576#389C2311yescharacteristic
577#389C2311yescharacteristic
578#389C2311yescharacteristic
579#389C2311yescharacteristic
580#389C2311yescharacteristic
581#389C2312yes—
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2311yescharacteristic
585#389C2312yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2312yes—
596#389C2314yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2314yes—
601#389C2314yes—
602#389C2314yes—
603#389C2314yes—
604#389C2314yes—
605#389C2314yes—
606#389C2312yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2314yes—
613#389C2314yes—
614#389C2312yes—
615#389C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
626#388C2312yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2312yes—
661#387C2314yes—
662#387C2314yes—
663#387C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#386C2312yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2312yes—
684#386C2312yes—
685#386C2312yes—
686#386C2312yes—
687#386C2312yes—
688#386C2312yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#385C2312yes—
704#385C2312yes—
705#385C2312yes—
706#385C2312yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2312yes—
714#385C2312yes—
715#385C2312yes—
716#385C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#384C2312yes—
727#384C2312yes—
728#384C2314yes—
729#384C2311yescharacteristic
730#384C2312yes—
731#384C2311yescharacteristic
732#384C2312yes—
733#384C2312yes—
734#384C2312yes—
735#384C2312yes—
736#382C2312yes—
737#382C2312yes—
738#382C2314yes—
739#382C2314yes—
740#382C2312yes—
741#382C2312yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2311yescharacteristic
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2311yescharacteristic
751#380C2311yescharacteristic
752#380C2312yes—
753#380C2311yescharacteristic
754#380C2312yes—
755#380C2311yescharacteristic
756#380C2312yes—
757#380C2314yes—
758#380C2314yes—
759#380C2314yes—
760#380C2314yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2314yes—
766#380C2314yes—
767#380C2312yes—
768#380C2312yes—
769#380C2314yes—
770#380C2314yes—
771#380C2312yes—
772#380C2314yes—
773#380C2312yes—
774#380C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2314yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2312yes—
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2312yes—
801C4×C4⋊C4C2312yes—
802C4×C4⋊C4C2312yes—
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2312yes—
805C4×C4⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2314yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2314yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2312yes—
816C4×C22⋊C4C2312yes—
817C4×C22⋊C4C2312yes—
818C4×C22⋊C4C2312yes—
819C2×#95C2312yes—
820C2×#95C2312yes—
821C2×#41—24no—
822C2×#41—24no—
823C2×#41—24no—
824C2×#41—24no—
825C2×#41—42no—
826C2×#41—42no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—44no—
833C22×Q8C2411yescharacteristic
834C22×Q8C2412yes—
835C22×Q8C2411yescharacteristic
836C22×Q8C2411yescharacteristic
837C22×Q8C2411yescharacteristic
838C22×Q8C2412yes—
839C22×D4C2412yes—
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2411yescharacteristic
843C22×D4C2411yescharacteristic
844C22×D4C2411yescharacteristic
845C22×D4C2412yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2411yescharacteristic
870C23×C4C2414yes—
871C23×C4C2414yes—
872C23×C4C2412yes—
873C4⋊Q8—24no—
874C4⋊Q8—42no—
875C4⋊Q8—42no—
876C4⋊Q8—44no—
877C4⋊Q8—44no—
878#127—24no—
879#127—44no—
880#126—216no—
881#126—48no—
882#126—48no—
883#126—84no—
884#126—84no—
885#125—28no—
886#125—28no—
887#125—44no—
888#125—44no—
889#125—48no—
890#125—48no—
891#124—28no—
892#124—44no—
893#124—44no—
894#124—84no—
895#123—216no—
896#123—48no—
897#123—48no—
898#123—48no—
899#123—48no—
900#123—84no—
901#123—84no—
902#123—84no—
903C22⋊Q8—24no—
904C22⋊Q8—28no—
905C22⋊Q8—24no—
906C22⋊Q8—24no—
907C22⋊Q8—28no—
908C22⋊Q8—44no—
909C22⋊Q8—42no—
910C22⋊Q8—44no—
911C22⋊Q8—42no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—42no—
915C22⋊Q8—42no—
916C22⋊Q8—44no—
917C22⋊Q8#4118yescomplemented
918#121—28no—
919#121—24no—
920#121—28no—
921#121—24no—
922#121—28no—
923#121—28no—
924#121—28no—
925#121—48no—
926#121—48no—
927#121—44no—
928#121—44no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—82no—
933#121—82no—
934C4×Q8—28no—
935C4×Q8—24no—
936C4×Q8—24no—
937C4×Q8—24no—
938C4×Q8—42no—
939C4×Q8—42no—
940C4×Q8—44no—
941C4×Q8—42no—
942C4×Q8—44no—
943C4×Q8—44no—
944C4×Q8—44no—
945C4×Q8—44no—
946C4×D4—28no—
947C4×D4—28no—
948C4×D4—216no—
949C4×D4—24no—
950C4×D4—42no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—42no—
955C4×D4—42no—
956C4×D4—42no—
957C4×D4—42no—
958C4×D4—42no—
959C4×D4—42no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—48no—
965#117—216no—
966#117—42no—
967#117—42no—
968#117—42no—
969#117—44no—
970#117—44no—
971#117—42no—
972#117—48no—
973#117—44no—
974#117—48no—
975#117—82no—
976C2×C4⋊C4—24no—
977C2×C4⋊C4—24no—
978C2×C4⋊C4—24no—
979C2×C4⋊C4—42no—
980C2×C4⋊C4—48no—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2414yes—
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2411yescharacteristic
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2411yescharacteristic
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2411yescharacteristic
1071C2×C22⋊C4C2411yescharacteristic
1072C2×C22⋊C4C2411yescharacteristic
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2411yescharacteristic
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C42—28no—
1117C2×C42—24no—
1118C2×C42—24no—
1119C2×C42—24no—
1120C2×C42—44no—
1121C2×C42—44no—
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2414yes—
1129C2×C42C2412yes—
1130C2×C42C2411yescharacteristic
1131C2×C42C2412yes—
1132C2×C42C2412yes—
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2412yes—
1138C2×C42C2411yescharacteristic
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2414yes—
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2414yes—
1145C2×C42C2414yes—
1146C2×C42C2414yes—
1147C2×C42C2412yes—
1148C2×C42C2414yes—
1149C2×C42C2414yes—
1150C2×C42C2412yes—
1151C2×C42C2411yescharacteristic
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2412yes—
1200#95C2414yes—
1201#95C2414yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210C24C2514yes—
1211C24C2512yes—
1212C24C2511yescharacteristic
1213C24C2511yescharacteristic
1214C24C2511yescharacteristic
1215#41—416no—
1216#41—416no—
1217#41—816no—
1218#41—816no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—24no—
1225C2×Q8—24no—
1226C2×Q8—22no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—24no—
1231C2×Q8—22no—
1232C2×Q8—41no—
1233C2×Q8—42no—
1234C2×Q8—42no—
1235C2×Q8—42no—
1236C2×Q8C2×#4114yes—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—24no—
1241C2×D4—22no—
1242C2×D4—28no—
1243C2×D4—24no—
1244C2×D4—28no—
1245C2×D4—24no—
1246C2×D4—22no—
1247C2×D4—24no—
1248C2×D4—22no—
1249C2×D4—24no—
1250C2×D4—22no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—22no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—42no—
1262C2×D4—41no—
1263C2×D4—42no—
1264C2×D4—44no—
1265C2×D4—42no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—44no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—24no—
1287C22×C4—24no—
1288C22×C4—24no—
1289C22×C4—28no—
1290C22×C4—24no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—22no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—22no—
1298C22×C4—24no—
1299C22×C4—24no—
1300C22×C4—22no—
1301C22×C4—28no—
1302C22×C4—24no—
1303C22×C4—22no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—24no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—42no—
1314C22×C4—41no—
1315C22×C4—44no—
1316C22×C4—42no—
1317C22×C4—41no—
1318C22×C4—42no—
1319C22×C4—42no—
1320C22×C4—42no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—42no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4—41no—
1327C22×C4—41no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—42no—
1331C22×C4—42no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4C2×#4114yes—
1338C22×C42−1+414yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2511yescharacteristic
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2514yes—
1349C22×C4C2514yes—
1350C22×C4C2512yes—
1351C22×C4C2512yes—
1352C22×C4C2512yes—
1353C22×C4C2511yescharacteristic
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2512yes—
1357C22×C4C2514yes—
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2511yescharacteristic
1361C22×C4C2511yescharacteristic
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2512yes—
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C4⋊C4—24no—
1370C4⋊C4—22no—
1371C4⋊C4—28no—
1372C4⋊C4—28no—
1373C4⋊C4—24no—
1374C4⋊C4—28no—
1375C4⋊C4—24no—
1376C4⋊C4—22no—
1377C4⋊C4—24no—
1378C4⋊C4—24no—
1379C4⋊C4—28no—
1380C4⋊C4—24no—
1381C4⋊C4—28no—
1382C4⋊C4—22no—
1383C4⋊C4—24no—
1384C4⋊C4—22no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—28no—
1389C4⋊C4—22no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—24no—
1397C4⋊C4—22no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—44no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—41no—
1408C4⋊C4—41no—
1409C4⋊C4—41no—
1410C4⋊C4—41no—
1411C4⋊C4—42no—
1412C4⋊C4—41no—
1413C4⋊C4—41no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—42no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—44no—
1440C4⋊C4—42no—
1441C4⋊C4C2×#4114yes—
1442C4⋊C4C2×#4118yes—
1443C4⋊C4H(5,𝔽2)14yes—
1444C22⋊C4—28no—
1445C22⋊C4—28no—
1446C22⋊C4—28no—
1447C22⋊C4—28no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—28no—
1453C22⋊C4—24no—
1454C22⋊C4—24no—
1455C22⋊C4—28no—
1456C22⋊C4—28no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—42no—
1462C22⋊C4—41no—
1463C22⋊C4—41no—
1464C22⋊C4—41no—
1465C22⋊C4—41no—
1466C22⋊C4—41no—
1467C22⋊C4—42no—
1468C22⋊C4—41no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—42no—
1490C22⋊C4—44no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—42no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4C2×#4118yes—
1504C42—24no—
1505C42—24no—
1506C42—24no—
1507C42—24no—
1508C42—28no—
1509C42—22no—
1510C42—22no—
1511C42—22no—
1512C42—22no—
1513C42—22no—
1514C42—22no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—24no—
1519C42—24no—
1520C42—24no—
1521C42—24no—
1522C42—24no—
1523C42—42no—
1524C42—42no—
1525C42—42no—
1526C42—42no—
1527C42—44no—
1528C42—44no—
1529C42—44no—
1530C42—44no—
1531C42—44no—
1532C42—44no—
1533C42H(5,𝔽2)14yes—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—24no—
1547C23—21no—
1548C23—22no—
1549C23—22no—
1550C23—21no—
1551C23—24no—
1552C23—22no—
1553C23—24no—
1554C23—21no—
1555C23—24no—
1556C23—22no—
1557C23—21no—
1558C23—22no—
1559C23—21no—
1560C23—24no—
1561C23—21no—
1562C23—22no—
1563C23—24no—
1564C23—24no—
1565C23—21no—
1566C23—22no—
1567C23C22×#4112yes—
1568C23C2×2−1+412yes—
1569C23C2611yescharacteristic
1570Q8—28no—
1571Q8—44no—
1572Q8—44no—
1573Q8—48no—
1574Q8—44no—
1575Q8—84no—
1576D4—44no—
1577D4—44no—
1578D4—48no—
1579D4—44no—
1580D4—48no—
1581D4—44no—
1582D4—48no—
1583D4—84no—
1584D4—84no—
1585D4—84no—
1586D4—88no—
1587D4—88no—
1588D4—88no—
1589D4—88no—
1590D4—164no—
1591C2×C4—22no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—21no—
1598C2×C4—22no—
1599C2×C4—21no—
1600C2×C4—22no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—28no—
1604C2×C4—28no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—24no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—24no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—24no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—24no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—24no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—24no—
1647C2×C4—22no—
1648C2×C4—21no—
1649C2×C4—22no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—22no—
1653C2×C4—24no—
1654C2×C4—22no—
1655C2×C4—24no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—21no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—416no—
1672C2×C4—48no—
1673C2×C4—48no—
1674C2×C4—44no—
1675C2×C4—44no—
1676C2×C4—44no—
1677C2×C4—44no—
1678C2×C4—48no—
1679C2×C4—44no—
1680C2×C4—84no—
1681C2×C4—82no—
1682C2×C4—82no—
1683C2×C4—84no—
1684C2×C4—84no—
1685C2×C4—84no—
1686C2×C4—88no—
1687C2×C4—88no—
1688C2×C4C22×#4112yes—
1689C2×C4C22×#4114yes—
1690C2×C4C22×#4114yes—
1691C2×C4C22×#4112yes—
1692C2×C4C2×H(5,𝔽2)12yes—
1693C2×C4C2×H(5,𝔽2)14yes—
1694C2×C4C2×H(5,𝔽2)12yes—
1695C2×C4C2×H(5,𝔽2)12yes—
1696C2×C4C2×H(5,𝔽2)12yes—
1697C2×C4C2×2−1+412yes—
1698C2×C4C2×2−1+412yes—
1699C2×C4#58512yes—
1700C22—22no—
1701C22—22no—
1702C22—22no—
1703C22—22no—
1704C22—22no—
1705C22—22no—
1706C22—41no—
1707C22—41no—
1708C22—41no—
1709C22—41no—
1710C22—41no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—44no—
1715C22—41no—
1716C22—42no—
1717C22—41no—
1718C22—42no—
1719C22—44no—
1720C22—44no—
1721C22—42no—
1722C22—41no—
1723C22—42no—
1724C22—41no—
1725C22—44no—
1726C22—41no—
1727C22—42no—
1728C22—44no—
1729C22—44no—
1730C22—42no—
1731C22—41no—
1732C22—44no—
1733C22—42no—
1734C22—41no—
1735C22C23×#4111yescharacteristic
1736C22C22×H(5,𝔽2)11yescharacteristic
1737C22C22×H(5,𝔽2)11yescharacteristic
1738C22C22×2−1+411yescharacteristic
1739C22C2×#58511yescharacteristic
1740C22H(7,𝔽2)11yescharacteristic
1741C222−1+611yescharacteristic
1742C4—24no—
1743C4—24no—
1744C4—22no—
1745C4—22no—
1746C4—24no—
1747C4—22no—
1748C4—42no—
1749C4—42no—
1750C4—41no—
1751C4—41no—
1752C4—42no—
1753C4—41no—
1754C4—42no—
1755C4—44no—
1756C4—42no—
1757C4—42no—
1758C4—42no—
1759C4—44no—
1760C4—41no—
1761C4—41no—
1762C4—42no—
1763C4—41no—
1764C4—41no—
1765C4—42no—
1766C4—42no—
1767C4—42no—
1768C4—42no—
1769C4—44no—
1770C4#352014yes—
1771C4#354614yes—
1772C2—42no—
1773C2—42no—
1774C2—84no—
1775C2—81no—
1776C2—82no—
1777C2C2×#354611yescharacteristic
1778C2C2×#352011yescharacteristic
1779C2#6287511yescharacteristic
1780C2#6291711yescharacteristic
1781C2#6295611yescharacteristic
1782C2#6298511yescharacteristic
1783C2#6300611yescharacteristic
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. #59550C2semidirect
2. #59249C2semidirect
3. #59218C2semidirect
4. #59078C2semidirect
5. #59066C2semidirect
6. #59059C2semidirect
7. #50807C2semidirect
8. #49962C2semidirect
9. #47591C2semidirect
10. #46679C2semidirect
11. #45632C2semidirect
12. #45632C2semidirect
13. #45393C2semidirect
14. #45358C2semidirect
15. #42871C2semidirect
16. #42571C2semidirect
17. #40118C2semidirect
18. #40031C2semidirect
19. #39725C2semidirect
20. #39599C2semidirect
21. #39029C2semidirect
22. #38920C2semidirect
23. #37970C2semidirect
24. #37785C2semidirect
25. #37286C2semidirect
26. #36599C2semidirect
27. #36445C2semidirect
28. #36410C2semidirect
29. #36186C2semidirect
30. #36117C2semidirect
31. #36117C2semidirect
32. #35292C2semidirect
33. #34947C2semidirect
34. #34383C2semidirect
35. C4×#537C2semidirect
917. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#595502
#592492
#592182
#590782
#590662
#590592
#508072
#499622
#475912
#466792
#456322
#453932
#453582
#428712
#425712
#401182
#400312
#397252
#395992
#390292
#389202
#379702
#377852
#372862
#365992
#364452
#364102
#361862
#361172
#352922
#349472
#343832
C4×#5372