Finite Group Databasebeta

← #8425219

Subgroups — #8425219

Order 512.

5188 conjugacy classes of subgroups.

The subgroup lattice has 1782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59647C211yesmaximal, characteristic, complemented
2#59454C212yesmaximal, complemented
3#59080C211yesmaximal, characteristic, complemented
4#59066C212yesmaximal, complemented
5#59051C211yesmaximal, characteristic, complemented
6#53615C214yesmaximal, complemented
7#53481C214yesmaximal, complemented
8#53047C212yesmaximal, complemented
9#53041C212yesmaximal, complemented
10#52985C212yesmaximal, complemented
11#52972C212yesmaximal, complemented
12#52478C214yesmaximal, complemented
13#42913C212yesmaximal, complemented
14#42608C212yesmaximal, complemented
15#42560C212yesmaximal, complemented
16#42537C212yesmaximal, complemented
17#40978C214yesmaximal, complemented
18#40045C212yesmaximal, complemented
19#39956C212yesmaximal, complemented
20#39641C211yesmaximal, characteristic, complemented
21#39596C211yesmaximal, characteristic, complemented
22#39360C211yesmaximal, characteristic, complemented
23#39270C212yesmaximal, complemented
24#39146C211yesmaximal, characteristic, complemented
25#37680C212yesmaximal, complemented
26#37625C211yesmaximal, characteristic, complemented
27#37619C211yesmaximal, characteristic, complemented
28#37505C212yesmaximal, complemented
29#37499C212yesmaximal, complemented
30#36599C211yesmaximal, characteristic, complemented
31#36259C211yesmaximal, characteristic, complemented
32#36127C211yesmaximal, characteristic, complemented
33#34937C211yesmaximal, characteristic, complemented
34#34788C211yesmaximal, characteristic, complemented
35#34720C211yesmaximal, characteristic, complemented
36C2×#550C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2212yes—
39C2×#547C2212yes—
40C2×#547C2212yes—
41C2×#547C2211yescharacteristic
42C2×#536C2212yes—
43C2×#533C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C2×#532C2211yescharacteristic
46C2×#532C2212yes—
47C2×C4×#41C2211yescharacteristic
48#2868C2211yescharacteristic
49#2857C2212yes—
50#2857C2211yescharacteristic
51#2857C2211yescharacteristic
52#2854C2212yes—
53#2841C2214yes—
54#2838C2214yes—
55#2838C2214yes—
56#2837C2214yes—
57#2837C2214yes—
58#2829C2214yes—
59#2829C2214yes—
60#2827C2214yes—
61#2827C2214yes—
62#2827C2214yes—
63#2824C2214yes—
64#2824C2214yes—
65#2816C2214yes—
66#2816C2214yes—
67#2803C2214yes—
68#2797C2214yes—
69#2797C2214yes—
70#2796C2214yes—
71#2796C2214yes—
72#2791C2214yes—
73#2791C2214yes—
74#2790C2214yes—
75#2790C2214yes—
76#2780C2214yes—
77#2770C2214yes—
78#2751C2214yes—
79#2750C2214yes—
80#2746C2214yes—
81#2746C2214yes—
82#2742C2214yes—
83#2720C2214yes—
84#2717C2214yes—
85#2709C2214yes—
86#2709C2214yes—
87#2708C2214yes—
88#2708C2214yes—
89#2708C2214yes—
90#2696C2214yes—
91#2692C2214yes—
92#2686C2214yes—
93#2680C2214yes—
94#2680C2214yes—
95#2676C2214yes—
96#2673C2214yes—
97#2672C2214yes—
98#2672C2214yes—
99#2671C2214yes—
100#2671C2214yes—
101#2671C2214yes—
102#2671C2214yes—
103#2671C2214yes—
104#2663C2214yes—
105#2658C2212yes—
106#2653C2214yes—
107#2653C2214yes—
108#2652C2214yes—
109#2648C2214yes—
110#2647C2212yes—
111#2645C2212yes—
112#2644C2212yes—
113#2643C2214yes—
114#2641C2212yes—
115#2640C2212yes—
116#2639C2214yes—
117#2638C2214yes—
118#2633C2214yes—
119#2630C2214yes—
120#2630C2214yes—
121#2628C2212yes—
122#2624C2212yes—
123#2624C2212yes—
124#2624C2212yes—
125#2621C2212yes—
126#2620C2212yes—
127#2602C2214yes—
128#2600C2214yes—
129#2595C2214yes—
130#2589C2214yes—
131#2585C2214yes—
132#2583C2214yes—
133#2580C2212yes—
134#2580C2212yes—
135#2580C2212yes—
136#2569C2214yes—
137#2567C2212yes—
138#2564C2214yes—
139#2562C2212yes—
140#2552C2211yescharacteristic
141#2548C2211yescharacteristic
142#2548C2211yescharacteristic
143#2547C2212yes—
144#2547C2211yescharacteristic
145#2546C2212yes—
146#2546C2212yes—
147#2546C2211yescharacteristic
148#2546C2211yescharacteristic
149#2546C2211yescharacteristic
150#2545C2212yes—
151#2544C2212yes—
152#2544C2212yes—
153#2543C2214yes—
154#2542C2212yes—
155#2541C2212yes—
156#2541C2211yescharacteristic
157#2541C2211yescharacteristic
158#2538C2211yescharacteristic
159#2537C2212yes—
160#2537C2212yes—
161#2525C2212yes—
162#2516C2212yes—
163#2513C2212yes—
164#2513C2211yescharacteristic
165#2511C2212yes—
166#2510C2212yes—
167#2509C2211yescharacteristic
168#2509C2212yes—
169#2507C2212yes—
170#2507C2212yes—
171#2504C2212yes—
172#2504C2211yescharacteristic
173#2494C2212yes—
174#2494C2211yescharacteristic
175#2492C2212yes—
176#2491C2212yes—
177#2490C2212yes—
178#2490C2211yescharacteristic
179#2487C2212yes—
180#2487C2211yescharacteristic
181#2486C2212yes—
182#2477C2212yes—
183#2475C2212yes—
184#2463C2214yes—
185#2463C2212yes—
186#2460C2212yes—
187#2456C2214yes—
188#2455C2214yes—
189#2455C2214yes—
190#2454C2212yes—
191#2452C2212yes—
192#2452C2211yescharacteristic
193#2450C2214yes—
194#2449C2214yes—
195#2449C2214yes—
196#2447C2212yes—
197#2446C2212yes—
198#2446C2211yescharacteristic
199#2446C2212yes—
200#2446C2212yes—
201#2445C2214yes—
202#2445C2212yes—
203#2444C2212yes—
204#2443C2214yes—
205#2443C2214yes—
206#2442C2211yescharacteristic
207#2442C2212yes—
208#2442C2212yes—
209#2440C2212yes—
210#2440C2212yes—
211#2439C2211yescharacteristic
212#2436C2212yes—
213#2434C2212yes—
214#2434C2212yes—
215#2432C2212yes—
216#2432C2212yes—
217#2432C2212yes—
218#2432C2211yescharacteristic
219#2432C2212yes—
220#2432C2212yes—
221#2431C2212yes—
222#2429C2212yes—
223#2428C2212yes—
224#2428C2214yes—
225#2428C2212yes—
226#2427C2212yes—
227#2427C2211yescharacteristic
228#2427C2212yes—
229#2426C2212yes—
230#2426C2212yes—
231#2425C2214yes—
232#2423C2212yes—
233#2422C2212yes—
234#2422C2212yes—
235#2422C2212yes—
236#2422C2212yes—
237#2422C2212yes—
238#2422C2214yes—
239#2422C2212yes—
240#2422C2212yes—
241#2421C2211yescharacteristic
242#2420C2212yes—
243#2416C2212yes—
244#2416C2211yescharacteristic
245#2416C2212yes—
246#2416C2212yes—
247#2416C2212yes—
248#2415C2211yescharacteristic
249#2415C2212yes—
250#2413C2214yes—
251#2409C2212yes—
252#2407C2212yes—
253#2407C2212yes—
254#2407C2211yescharacteristic
255#2401C2212yes—
256#2398C2212yes—
257#2395C2212yes—
258#2392C2214yes—
259#2392C2212yes—
260#2370C2212yes—
261#2366C2212yes—
262#2366C2212yes—
263#2365C2211yescharacteristic
264#2365C2211yescharacteristic
265#2361C2212yes—
266#2361C2212yes—
267#2355C2211yescharacteristic
268D4×C4⋊C4C2212yes—
269D4×C4⋊C4C2214yes—
270D4×C4⋊C4C2212yes—
271D4×C4⋊C4C2211yescharacteristic
272#2345C2212yes—
273#2339C2212yes—
274#2330C2212yes—
275#2326C2212yes—
276#2324C2212yes—
277#2322C2214yes—
278C4×#127C2211yescharacteristic
279C4×#125C2211yescharacteristic
280C4×#124C2211yescharacteristic
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2212yes—
283C4×C22⋊Q8C2211yescharacteristic
284C4×#121C2212yes—
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic
288C4×#121C2211yescharacteristic
289C4×#121C2211yescharacteristic
290#2297C2212yes—
291#2295C2211yescharacteristic
292#2293C2211yescharacteristic
293C2×#389C2212yes—
294#2290C2212yes—
295#2290C2212yes—
296#2283C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303C23×Q8C2312yes—
304#550—48no—
305D4×Q8—44no—
306#548—48no—
307#547—44no—
308#547—48no—
309#547—48no—
310#536—48no—
311#533—44no—
312#532—44no—
313#532—44no—
314#532—48no—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2312yes—
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2311yescharacteristic
322C2×C4⋊Q8C2311yescharacteristic
323C2×C4⋊Q8C2312yes—
324C2×C4⋊Q8C2312yes—
325C2×#127C2311yescharacteristic
326C2×#127C2312yes—
327C2×#127C2312yes—
328C2×#127C2314yes—
329C2×#125C2311yescharacteristic
330C2×#125C2312yes—
331C2×#125C2312yes—
332C2×#124C2312yes—
333C2×#124C2311yescharacteristic
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2314yes—
338C2×#124C2312yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2311yescharacteristic
358C2×C22⋊Q8C2311yescharacteristic
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2312yes—
361C2×#121C2311yescharacteristic
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2314yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2314yes—
376C2×#121C2314yes—
377C2×#121C2311yescharacteristic
378C2×#121C2312yes—
379C2×#121C2312yes—
380C2×#121C2312yes—
381C4×#41—44no—
382C2×C4×Q8C2311yescharacteristic
383C2×C4×Q8C2311yescharacteristic
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2311yescharacteristic
388C2×C4×D4C2311yescharacteristic
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2314yes—
397C2×C4×D4C2314yes—
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2314yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2311yescharacteristic
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2311yescharacteristic
413C2×#117C2312yes—
414C2×#117C2312yes—
415C2×#117C2312yes—
416C2×#117C2311yescharacteristic
417C22×C4⋊C4C2311yescharacteristic
418C22×C4⋊C4C2314yes—
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2314yes—
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2311yescharacteristic
423C22×C42C2311yescharacteristic
424C22×C42C2311yescharacteristic
425C22×C42C2312yes—
426C22×C42C2312yes—
427#401C2312yes—
428#401C2314yes—
429#400C2314yes—
430#400C2312yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2314yes—
437#400C2312yes—
438#400C2312yes—
439#400C2314yes—
440#400C2312yes—
441#400C2314yes—
442#400C2312yes—
443#400C2312yes—
444#399C2312yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2314yes—
453#398C2314yes—
454#398C2314yes—
455#398C2314yes—
456#398C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2312yes—
467#398C2314yes—
468#398C2312yes—
469#398C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2312yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2312yes—
480#397C2314yes—
481#397C2314yes—
482#397C2314yes—
483#397C2312yes—
484#397C2314yes—
485#397C2314yes—
486#397C2314yes—
487#397C2314yes—
488#397C2312yes—
489#397C2314yes—
490#397C2314yes—
491#397C2312yes—
492#397C2312yes—
493#397C2312yes—
494#397C2312yes—
495#396C2314yes—
496#396C2314yes—
497#396C2312yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#396C2314yes—
503#396C2314yes—
504#396C2312yes—
505#396C2312yes—
506#395C2314yes—
507#395C2314yes—
508#395C2314yes—
509#395C2314yes—
510#395C2314yes—
511#394C2314yes—
512#394C2312yes—
513#394C2314yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2314yes—
525#394C2314yes—
526#394C2314yes—
527#394C2314yes—
528#394C2314yes—
529#394C2314yes—
530#394C2314yes—
531#394C2314yes—
532#394C2314yes—
533#394C2314yes—
534#394C2312yes—
535#394C2314yes—
536#394C2314yes—
537#394C2314yes—
538#394C2314yes—
539#394C2314yes—
540#394C2314yes—
541#394C2312yes—
542#394C2312yes—
543#394C2312yes—
544#394C2312yes—
545#394C2312yes—
546#393C2314yes—
547#393C2314yes—
548#393C2314yes—
549#393C2314yes—
550#393C2314yes—
551#393C2314yes—
552#393C2312yes—
553#393C2312yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2314yes—
559#392C2314yes—
560#392C2312yes—
561#391C2314yes—
562#391C2312yes—
563#391C2312yes—
564#391C2312yes—
565#391C2312yes—
566#391C2312yes—
567#391C2312yes—
568#391C2311yescharacteristic
569#391C2312yes—
570#391C2312yes—
571#391C2312yes—
572#391C2311yescharacteristic
573#391C2312yes—
574#391C2311yescharacteristic
575#391C2311yescharacteristic
576#390C2312yes—
577#390C2312yes—
578#390C2312yes—
579#390C2314yes—
580#390C2312yes—
581#390C2311yescharacteristic
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2311yescharacteristic
587#390C2314yes—
588#390C2311yescharacteristic
589#390C2312yes—
590#390C2312yes—
591#390C2311yescharacteristic
592#390C2312yes—
593#390C2314yes—
594#390C2314yes—
595#390C2312yes—
596#390C2311yescharacteristic
597#390C2312yes—
598#390C2311yescharacteristic
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2314yes—
607#389C2312yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2312yes—
612#389C2314yes—
613#389C2314yes—
614#389C2314yes—
615#389C2312yes—
616#389C2314yes—
617#389C2314yes—
618#389C2312yes—
619#389C2314yes—
620#389C2312yes—
621#389C2312yes—
622#389C2312yes—
623#389C2312yes—
624#389C2314yes—
625#389C2312yes—
626#389C2312yes—
627#389C2311yescharacteristic
628#389C2312yes—
629#389C2311yescharacteristic
630#389C2311yescharacteristic
631#389C2311yescharacteristic
632#389C2311yescharacteristic
633#389C2311yescharacteristic
634#389C2311yescharacteristic
635#388C2314yes—
636#388C2314yes—
637#388C2312yes—
638#388C2314yes—
639#388C2312yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2312yes—
648#388C2314yes—
649#388C2314yes—
650#388C2312yes—
651#388C2312yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#388C2312yes—
656#388C2312yes—
657#388C2312yes—
658#388C2312yes—
659#388C2314yes—
660#387C2312yes—
661#387C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2314yes—
673#387C2312yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2312yes—
678#387C2312yes—
679#387C2314yes—
680#387C2312yes—
681#387C2312yes—
682#387C2312yes—
683#387C2312yes—
684#386C2314yes—
685#386C2314yes—
686#386C2312yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2312yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#386C2314yes—
706#386C2312yes—
707#386C2312yes—
708#386C2312yes—
709#386C2312yes—
710#386C2312yes—
711#386C2312yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2312yes—
717#385C2312yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#385C2314yes—
731#385C2314yes—
732#385C2314yes—
733#385C2314yes—
734#385C2314yes—
735#385C2312yes—
736#385C2314yes—
737#385C2312yes—
738#385C2314yes—
739#385C2312yes—
740#385C2312yes—
741#385C2312yes—
742#384C2311yescharacteristic
743#384C2314yes—
744#384C2312yes—
745#384C2312yes—
746#384C2312yes—
747#384C2312yes—
748#384C2312yes—
749#383C2312yes—
750#382C2311yescharacteristic
751#382C2311yescharacteristic
752#382C2311yescharacteristic
753#382C2312yes—
754#382C2311yescharacteristic
755#381C2312yes—
756#381C2314yes—
757#381C2314yes—
758#380C2311yescharacteristic
759#380C2312yes—
760#380C2312yes—
761#380C2312yes—
762#380C2312yes—
763#380C2314yes—
764#380C2312yes—
765#380C2314yes—
766#380C2314yes—
767#380C2314yes—
768#380C2314yes—
769#380C2312yes—
770#380C2312yes—
771#380C2312yes—
772#380C2314yes—
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2311yescharacteristic
776#380C2311yescharacteristic
777#380C2312yes—
778#380C2312yes—
779#380C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2311yescharacteristic
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2311yescharacteristic
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2311yescharacteristic
817#376C2312yes—
818#376C2312yes—
819C2×#95C2314yes—
820C2×#95C2312yes—
821C43C2311yescharacteristic
822C2×#41—24no—
823C2×#41—28no—
824C2×#41—24no—
825C2×#41—28no—
826C2×#41—42no—
827C2×#41—44no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—44no—
834C22×Q8—44no—
835C22×Q8—44no—
836C22×Q8—44no—
837C22×Q8C2411yescharacteristic
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2412yes—
841C22×Q8C2412yes—
842C22×Q8C2414yes—
843C22×D4C2411yescharacteristic
844C22×D4C2412yes—
845C22×D4C2412yes—
846C22×D4C2411yescharacteristic
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2411yescharacteristic
850C22×D4C2412yes—
851C22×D4C2412yes—
852C22×D4C2414yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2414yes—
856C22×D4C2414yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C23×C4C2411yescharacteristic
861C23×C4C2412yes—
862C23×C4C2411yescharacteristic
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2412yes—
866C23×C4C2411yescharacteristic
867C23×C4C2414yes—
868C23×C4C2414yes—
869C23×C4C2414yes—
870C23×C4C2412yes—
871C23×C4C2411yescharacteristic
872C23×C4C2411yescharacteristic
873C23×C4C2414yes—
874C23×C4C2414yes—
875C23×C4C2412yes—
876C23×C4C2414yes—
877C23×C4C2412yes—
878C4⋊Q8—24no—
879C4⋊Q8—24no—
880C4⋊Q8—42no—
881C4⋊Q8—44no—
882C4⋊Q8—44no—
883C4⋊Q8—42no—
884C4⋊Q8—44no—
885C4⋊Q8—44no—
886C4⋊Q8—44no—
887C4⋊Q8—44no—
888#127—28no—
889#127—24no—
890#127—44no—
891#127—48no—
892#125—24no—
893#125—44no—
894#125—44no—
895#124—28no—
896#124—24no—
897#124—44no—
898#124—44no—
899#124—44no—
900#124—44no—
901#124—48no—
902#123—48no—
903#123—48no—
904#123—48no—
905#123—48no—
906#123—48no—
907#123—48no—
908#123—48no—
909#123—48no—
910C22⋊Q8—28no—
911C22⋊Q8—24no—
912C22⋊Q8—48no—
913C22⋊Q8—48no—
914C22⋊Q8—44no—
915C22⋊Q8—48no—
916C22⋊Q8—44no—
917C22⋊Q8—48no—
918C22⋊Q8—42no—
919C22⋊Q8—42no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924#121—24no—
925#121—28no—
926#121—24no—
927#121—44no—
928#121—48no—
929#121—48no—
930#121—48no—
931#121—48no—
932#121—48no—
933#121—48no—
934#121—42no—
935#121—44no—
936#121—44no—
937#121—44no—
938#121—44no—
939#121—44no—
940#121—44no—
941#121—44no—
942#121—44no—
943#121—48no—
944C4×Q8—24no—
945C4×Q8—24no—
946C4×Q8—44no—
947C4×Q8—42no—
948C4×Q8—44no—
949C4×Q8—44no—
950C4×D4—24no—
951C4×D4—28no—
952C4×D4—24no—
953C4×D4—24no—
954C4×D4—44no—
955C4×D4—42no—
956C4×D4—42no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—42no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—48no—
970C4×D4—44no—
971C4×D4—48no—
972C4×D4—48no—
973C4×D4—48no—
974C4×D4—48no—
975#117—44no—
976#117—44no—
977#117—44no—
978#117—42no—
979C2×C4⋊C4—24no—
980C2×C4⋊C4—44no—
981C2×C4⋊C4—42no—
982C2×C4⋊C4—48no—
983C2×C4⋊C4—48no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2411yescharacteristic
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2411yescharacteristic
1088C2×C22⋊C4C2411yescharacteristic
1089C2×C22⋊C4C2411yescharacteristic
1090C2×C22⋊C4C2411yescharacteristic
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2412yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C42—24no—
1116C2×C42—24no—
1117C2×C42—44no—
1118C2×C42—44no—
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2411yescharacteristic
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2412yes—
1133C2×C42C2412yes—
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2412yes—
1139C2×C42C2414yes—
1140C2×C42C2414yes—
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2411yescharacteristic
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2411yescharacteristic
1162#95C2411yescharacteristic
1163#95C2411yescharacteristic
1164#95C2411yescharacteristic
1165#95C2411yescharacteristic
1166#95C2411yescharacteristic
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2414yes—
1191#95C2412yes—
1192#95C2414yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211C24C2512yes—
1212C24C2511yescharacteristic
1213C24C2514yes—
1214C24C2512yes—
1215C24C2511yescharacteristic
1216#41—416no—
1217#41—816no—
1218#41—816no—
1219#41—816no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—24no—
1223C2×Q8—24no—
1224C2×Q8—22no—
1225C2×Q8—24no—
1226C2×Q8—22no—
1227C2×Q8—24no—
1228C2×Q8—24no—
1229C2×Q8—22no—
1230C2×Q8—24no—
1231C2×Q8—22no—
1232C2×Q8—42no—
1233C2×Q8—44no—
1234C2×Q8—44no—
1235C2×Q8—44no—
1236C2×Q8—42no—
1237C2×Q8—42no—
1238C2×Q8—816no—
1239C2×D4—22no—
1240C2×D4—28no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—24no—
1244C2×D4—28no—
1245C2×D4—24no—
1246C2×D4—28no—
1247C2×D4—28no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—24no—
1254C2×D4—24no—
1255C2×D4—24no—
1256C2×D4—28no—
1257C2×D4—22no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—22no—
1261C2×D4—24no—
1262C2×D4—22no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—41no—
1266C2×D4—44no—
1267C2×D4—42no—
1268C2×D4—44no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—44no—
1281C2×D4—42no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—42no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4H(5,𝔽2)14yes—
1290C22×C4—22no—
1291C22×C4—22no—
1292C22×C4—24no—
1293C22×C4—28no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—24no—
1299C22×C4—24no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—24no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—28no—
1313C22×C4—24no—
1314C22×C4—28no—
1315C22×C4—42no—
1316C22×C4—42no—
1317C22×C4—42no—
1318C22×C4—42no—
1319C22×C4—44no—
1320C22×C4—44no—
1321C22×C4—44no—
1322C22×C4—44no—
1323C22×C4—44no—
1324C22×C4—42no—
1325C22×C4—44no—
1326C22×C4—44no—
1327C22×C4—44no—
1328C22×C4—44no—
1329C22×C4—44no—
1330C22×C4—44no—
1331C22×C4—44no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—44no—
1335C22×C4—44no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—44no—
1339C22×C4—41no—
1340C22×C4—41no—
1341C22×C4—42no—
1342C22×C4—42no—
1343C22×C4H(5,𝔽2)14yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2512yes—
1346C22×C4C2511yescharacteristic
1347C22×C4C2512yes—
1348C22×C4C2512yes—
1349C22×C4C2511yescharacteristic
1350C22×C4C2511yescharacteristic
1351C22×C4C2511yescharacteristic
1352C22×C4C2512yes—
1353C22×C4C2512yes—
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2512yes—
1358C22×C4C2512yes—
1359C22×C4C2512yes—
1360C22×C4C2514yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2512yes—
1364C22×C4C2514yes—
1365C22×C4C2514yes—
1366C22×C4C2512yes—
1367C22×C4C2512yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2512yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2511yescharacteristic
1373C22×C4C2511yescharacteristic
1374C4⋊C4—22no—
1375C4⋊C4—24no—
1376C4⋊C4—22no—
1377C4⋊C4—28no—
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—24no—
1381C4⋊C4—22no—
1382C4⋊C4—24no—
1383C4⋊C4—24no—
1384C4⋊C4—24no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—24no—
1392C4⋊C4—22no—
1393C4⋊C4—24no—
1394C4⋊C4—24no—
1395C4⋊C4—22no—
1396C4⋊C4—22no—
1397C4⋊C4—24no—
1398C4⋊C4—22no—
1399C4⋊C4—22no—
1400C4⋊C4—24no—
1401C4⋊C4—22no—
1402C4⋊C4—24no—
1403C4⋊C4—42no—
1404C4⋊C4—44no—
1405C4⋊C4—44no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—44no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—42no—
1413C4⋊C4—42no—
1414C4⋊C4—42no—
1415C4⋊C4—42no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—41no—
1419C4⋊C4—42no—
1420C4⋊C4—42no—
1421C4⋊C4—44no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—42no—
1428C4⋊C4—42no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—44no—
1436C4⋊C4—44no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C42−1+414yes—
1440C22⋊C4—22no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—28no—
1444C22⋊C4—28no—
1445C22⋊C4—28no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—22no—
1453C22⋊C4—28no—
1454C22⋊C4—24no—
1455C22⋊C4—24no—
1456C22⋊C4—24no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—44no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—42no—
1464C22⋊C4—42no—
1465C22⋊C4—42no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—44no—
1472C22⋊C4—41no—
1473C22⋊C4—41no—
1474C22⋊C4—41no—
1475C22⋊C4—44no—
1476C22⋊C4—41no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—44no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—44no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—42no—
1494C22⋊C4—44no—
1495C22⋊C4—42no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—42no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—22no—
1508C42—22no—
1509C42—22no—
1510C42—24no—
1511C42—24no—
1512C42—24no—
1513C42—22no—
1514C42—24no—
1515C42—22no—
1516C42—24no—
1517C42—22no—
1518C42—22no—
1519C42—22no—
1520C42—24no—
1521C42—42no—
1522C42—42no—
1523C42—42no—
1524C42—42no—
1525C42—41no—
1526C42—44no—
1527C42—44no—
1528C42—44no—
1529C42H(5,𝔽2)14yes—
1530C23—22no—
1531C23—21no—
1532C23—22no—
1533C23—21no—
1534C23—21no—
1535C23—22no—
1536C23—22no—
1537C23—21no—
1538C23—22no—
1539C23—21no—
1540C23—21no—
1541C23—22no—
1542C23—22no—
1543C23—21no—
1544C23—22no—
1545C23—21no—
1546C23—24no—
1547C23—24no—
1548C23—22no—
1549C23—24no—
1550C23—21no—
1551C23—24no—
1552C23—22no—
1553C23—21no—
1554C23—22no—
1555C23—21no—
1556C23—24no—
1557C23—21no—
1558C23—24no—
1559C23—22no—
1560C23—22no—
1561C23—21no—
1562C23—24no—
1563C23C2×H(5,𝔽2)12yes—
1564C23C2×H(5,𝔽2)14yes—
1565C23C2611yescharacteristic
1566Q8—44no—
1567Q8—48no—
1568Q8—44no—
1569Q8—48no—
1570Q8—84no—
1571Q8—88no—
1572D4—28no—
1573D4—44no—
1574D4—416no—
1575D4—48no—
1576D4—48no—
1577D4—48no—
1578D4—44no—
1579D4—48no—
1580D4—84no—
1581D4—84no—
1582D4—88no—
1583D4—84no—
1584D4—88no—
1585D4—88no—
1586D4—88no—
1587D4—88no—
1588D4—164no—
1589C2×C4—21no—
1590C2×C4—22no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—28no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—22no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—24no—
1619C2×C4—24no—
1620C2×C4—21no—
1621C2×C4—24no—
1622C2×C4—22no—
1623C2×C4—24no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—21no—
1627C2×C4—22no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—24no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—22no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—24no—
1656C2×C4—22no—
1657C2×C4—21no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—21no—
1661C2×C4—21no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—21no—
1668C2×C4—22no—
1669C2×C4—22no—
1670C2×C4—48no—
1671C2×C4—48no—
1672C2×C4—44no—
1673C2×C4—44no—
1674C2×C4—48no—
1675C2×C4—44no—
1676C2×C4—88no—
1677C2×C4—84no—
1678C2×C4—82no—
1679C2×C4—82no—
1680C2×C4—88no—
1681C2×C4—88no—
1682C2×C4—88no—
1683C2×C4—84no—
1684C2×C4—84no—
1685C2×C4—88no—
1686C2×C4—88no—
1687C2×C4C2×H(5,𝔽2)12yes—
1688C2×C4C2×H(5,𝔽2)12yes—
1689C2×C4C2×H(5,𝔽2)12yes—
1690C2×C4C2×H(5,𝔽2)12yes—
1691C2×C4C2×H(5,𝔽2)12yes—
1692C2×C4C2×H(5,𝔽2)12yes—
1693C2×C4C2×2−1+414yes—
1694C2×C4C2×2−1+412yes—
1695C2×C4#58512yes—
1696C2×C4#58512yes—
1697C22—22no—
1698C22—24no—
1699C22—22no—
1700C22—24no—
1701C22—24no—
1702C22—22no—
1703C22—42no—
1704C22—41no—
1705C22—42no—
1706C22—41no—
1707C22—41no—
1708C22—41no—
1709C22—42no—
1710C22—42no—
1711C22—42no—
1712C22—41no—
1713C22—44no—
1714C22—41no—
1715C22—42no—
1716C22—44no—
1717C22—44no—
1718C22—41no—
1719C22—42no—
1720C22—44no—
1721C22—41no—
1722C22—42no—
1723C22—41no—
1724C22—44no—
1725C22—42no—
1726C22—41no—
1727C22—44no—
1728C22—42no—
1729C22—41no—
1730C22—42no—
1731C22—44no—
1732C22C22×H(5,𝔽2)11yescharacteristic
1733C22C22×H(5,𝔽2)11yescharacteristic
1734C22C22×H(5,𝔽2)11yescharacteristic
1735C22C22×2−1+411yescharacteristic
1736C22C2×#58511yescharacteristic
1737C22C2×#58511yescharacteristic
1738C222−1+611yescharacteristic
1739C4—22no—
1740C4—22no—
1741C4—24no—
1742C4—22no—
1743C4—41no—
1744C4—42no—
1745C4—42no—
1746C4—44no—
1747C4—44no—
1748C4—42no—
1749C4—41no—
1750C4—41no—
1751C4—42no—
1752C4—44no—
1753C4—42no—
1754C4—42no—
1755C4—41no—
1756C4—42no—
1757C4—41no—
1758C4—42no—
1759C4—42no—
1760C4—42no—
1761C4—41no—
1762C4—42no—
1763C4—41no—
1764C4—42no—
1765C4—42no—
1766C4—41no—
1767C4#353714yes—
1768C4#355414yes—
1769C2—42no—
1770C2—44no—
1771C2—82no—
1772C2—81no—
1773C2—84no—
1774C2C2×#353711yescharacteristic
1775C2C2×#355411yescharacteristic
1776C2#6274811yescharacteristic
1777C2#6292111yescharacteristic
1778C2#6292511yescharacteristic
1779C2#6294611yescharacteristic
1780C2#6301311yescharacteristic
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. #59647C2semidirect
2. #59454C2semidirect
3. #59080C2semidirect
4. #59066C2semidirect
5. #59051C2semidirect
6. #53615C2semidirect
7. #53481C2semidirect
8. #53047C2semidirect
9. #53041C2semidirect
10. #52985C2semidirect
11. #52972C2semidirect
12. #52478C2semidirect
13. #42913C2semidirect
14. #42608C2semidirect
15. #42560C2semidirect
16. #42537C2semidirect
17. #40978C2semidirect
18. #40045C2semidirect
19. #39956C2semidirect
20. #39641C2semidirect
21. #39596C2semidirect
22. #39360C2semidirect
23. #39270C2semidirect
24. #39146C2semidirect
25. #37680C2semidirect
26. #37625C2semidirect
27. #37619C2semidirect
28. #37505C2semidirect
29. #37499C2semidirect
30. #36599C2semidirect
31. #36259C2semidirect
32. #36127C2semidirect
33. #34937C2semidirect
34. #34788C2semidirect
35. #34720C2semidirect

Maximal subgroups

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

subgroupindex
#596472
#594542
#590802
#590662
#590512
#536152
#534812
#530472
#530412
#529852
#529722
#524782
#429132
#426082
#425602
#425372
#409782
#400452
#399562
#396412
#395962
#393602
#392702
#391462
#376802
#376252
#376192
#375052
#374992
#365992
#362592
#361272
#349372
#347882
#347202