Finite Group Databasebeta

← #8425203

Subgroups — #8425203

Order 512.

5319 conjugacy classes of subgroups.

The subgroup lattice has 1826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59647C211yesmaximal, characteristic, complemented
2#59093C212yesmaximal, complemented
3#59080C211yesmaximal, characteristic, complemented
4#59051C211yesmaximal, characteristic, complemented
5#59033C212yesmaximal, complemented
6#55015C214yesmaximal, complemented
7#54780C214yesmaximal, complemented
8#53128C212yesmaximal, complemented
9#53046C212yesmaximal, complemented
10#53004C212yesmaximal, complemented
11#52975C212yesmaximal, complemented
12#52402C214yesmaximal, complemented
13#42985C212yesmaximal, complemented
14#42805C212yesmaximal, complemented
15#42602C212yesmaximal, complemented
16#42596C212yesmaximal, complemented
17#40649C214yesmaximal, complemented
18#39350C211yesmaximal, characteristic, complemented
19#39340C211yesmaximal, characteristic, complemented
20#39159C211yesmaximal, characteristic, complemented
21#39124C211yesmaximal, characteristic, complemented
22#39004C212yesmaximal, complemented
23#38997C212yesmaximal, complemented
24#37780C212yesmaximal, complemented
25#37772C212yesmaximal, complemented
26#37618C211yesmaximal, characteristic, complemented
27#37616C211yesmaximal, characteristic, complemented
28#37516C212yesmaximal, complemented
29#37494C212yesmaximal, complemented
30#36454C211yesmaximal, characteristic, complemented
31#36303C211yesmaximal, characteristic, complemented
32#36149C211yesmaximal, characteristic, complemented
33#34925C211yesmaximal, characteristic, complemented
34#34917C211yesmaximal, characteristic, complemented
35#34889C211yesmaximal, characteristic, complemented
36C2×#550C2212yes—
37C2×D4×Q8C2211yescharacteristic
38C2×#548C2212yes—
39C2×#547C2211yescharacteristic
40C2×#542C2212yes—
41C2×#537C2212yes—
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic
44C2×#532C2211yescharacteristic
45C2×#532C2212yes—
46C2×#532C2212yes—
47C2×#529C2211yescharacteristic
48#2862C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2211yescharacteristic
51#2855C2212yes—
52#2850C2212yes—
53#2832C2214yes—
54#2831C2214yes—
55#2831C2214yes—
56#2828C2214yes—
57#2827C2214yes—
58#2826C2214yes—
59#2825C2214yes—
60#2824C2214yes—
61#2824C2214yes—
62#2824C2214yes—
63#2819C2214yes—
64#2815C2214yes—
65#2815C2214yes—
66#2813C2214yes—
67#2797C2214yes—
68#2765C2214yes—
69#2763C2214yes—
70#2761C2214yes—
71#2760C2214yes—
72#2758C2214yes—
73#2753C2214yes—
74#2750C2214yes—
75#2749C2214yes—
76#2749C2214yes—
77#2749C2214yes—
78#2745C2214yes—
79#2733C2214yes—
80#2730C2214yes—
81#2723C2214yes—
82#2717C2214yes—
83#2714C2214yes—
84#2712C2214yes—
85#2700C2214yes—
86#2700C2214yes—
87#2699C2214yes—
88#2698C2214yes—
89#2696C2214yes—
90#2696C2214yes—
91#2692C2214yes—
92#2688C2214yes—
93#2688C2214yes—
94#2688C2214yes—
95#2688C2214yes—
96#2688C2214yes—
97#2676C2214yes—
98#2676C2214yes—
99#2673C2214yes—
100#2673C2214yes—
101#2673C2214yes—
102#2672C2214yes—
103#2671C2214yes—
104#2665C2214yes—
105#2662C2214yes—
106#2657C2212yes—
107#2653C2214yes—
108#2650C2214yes—
109#2648C2214yes—
110#2645C2212yes—
111#2643C2214yes—
112#2640C2212yes—
113#2639C2214yes—
114#2638C2214yes—
115#2636C2214yes—
116#2636C2214yes—
117#2631C2214yes—
118#2628C2212yes—
119#2625C2212yes—
120#2620C2212yes—
121#2620C2212yes—
122#2620C2212yes—
123#2619C2212yes—
124#2616C2212yes—
125#2615C2212yes—
126#2615C2212yes—
127#2600C2214yes—
128#2578C2212yes—
129#2576C2212yes—
130#2575C2214yes—
131#2570C2211yescharacteristic
132#2568C2212yes—
133#2568C2211yescharacteristic
134#2566C2212yes—
135#2566C2211yescharacteristic
136#2563C2212yes—
137#2562C2211yescharacteristic
138#2559C2212yes—
139#2557C2212yes—
140#2555C2214yes—
141#2551C2211yescharacteristic
142#2550C2211yescharacteristic
143#2548C2211yescharacteristic
144#2547C2212yes—
145#2547C2211yescharacteristic
146#2547C2211yescharacteristic
147#2544C2211yescharacteristic
148#2544C2212yes—
149#2544C2212yes—
150#2544C2214yes—
151#2543C2214yes—
152#2542C2211yescharacteristic
153#2541C2212yes—
154#2541C2211yescharacteristic
155#2541C2211yescharacteristic
156#2541C2211yescharacteristic
157#2540C2211yescharacteristic
158#2540C2212yes—
159#2537C2212yes—
160#2537C2211yescharacteristic
161#2535C2212yes—
162#2535C2211yescharacteristic
163#2535C2212yes—
164#2535C2211yescharacteristic
165#2535C2212yes—
166#2535C2212yes—
167#2521C2212yes—
168#2517C2214yes—
169#2515C2212yes—
170#2514C2212yes—
171#2513C2212yes—
172#2511C2212yes—
173#2504C2212yes—
174#2503C2212yes—
175#2497C2211yescharacteristic
176#2496C2212yes—
177#2495C2212yes—
178#2494C2211yescharacteristic
179#2492C2212yes—
180#2492C2212yes—
181#2492C2212yes—
182#2492C2211yescharacteristic
183#2492C2212yes—
184#2491C2212yes—
185#2491C2212yes—
186#2491C2212yes—
187#2490C2212yes—
188#2490C2211yescharacteristic
189#2489C2212yes—
190#2489C2212yes—
191#2488C2214yes—
192#2488C2214yes—
193#2486C2212yes—
194#2467C2214yes—
195#2464C2212yes—
196#2463C2214yes—
197#2459C2214yes—
198#2457C2212yes—
199#2456C2214yes—
200#2456C2214yes—
201#2456C2214yes—
202#2452C2212yes—
203#2451C2212yes—
204#2450C2214yes—
205#2450C2214yes—
206#2447C2212yes—
207#2447C2212yes—
208#2447C2212yes—
209#2447C2212yes—
210#2447C2214yes—
211#2447C2212yes—
212#2444C2214yes—
213#2444C2214yes—
214#2444C2214yes—
215#2440C2212yes—
216#2440C2212yes—
217#2436C2212yes—
218#2436C2212yes—
219#2436C2212yes—
220#2431C2212yes—
221#2431C2212yes—
222#2431C2212yes—
223#2431C2214yes—
224#2430C2214yes—
225#2428C2212yes—
226#2428C2212yes—
227#2428C2212yes—
228#2428C2211yescharacteristic
229#2428C2212yes—
230#2428C2212yes—
231#2427C2212yes—
232#2427C2212yes—
233#2427C2211yescharacteristic
234#2426C2212yes—
235#2426C2212yes—
236#2422C2211yescharacteristic
237#2421C2212yes—
238#2421C2212yes—
239#2420C2212yes—
240#2420C2212yes—
241#2420C2211yescharacteristic
242#2420C2212yes—
243#2417C2212yes—
244#2416C2212yes—
245#2416C2212yes—
246#2409C2212yes—
247#2407C2212yes—
248#2407C2212yes—
249#2407C2212yes—
250#2407C2212yes—
251#2407C2212yes—
252#2407C2212yes—
253#2407C2212yes—
254#2407C2214yes—
255#2401C2212yes—
256#2395C2212yes—
257#2392C2212yes—
258#2388C2212yes—
259#2388C2214yes—
260#2367C2212yes—
261#2366C2212yes—
262#2366C2212yes—
263#2365C2211yescharacteristic
264#2365C2211yescharacteristic
265#2361C2212yes—
266#2361C2212yes—
267#2355C2212yes—
268#2355C2211yescharacteristic
269#2349C2212yes—
270D4×C4⋊C4C2211yescharacteristic
271#2339C2212yes—
272#2339C2212yes—
273#2339C2212yes—
274#2339C2212yes—
275#2339C2214yes—
276#2331C2212yes—
277#2324C2212yes—
278#2318C2214yes—
279C4×#127C2211yescharacteristic
280C4×#125C2211yescharacteristic
281C4×#124C2211yescharacteristic
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2212yes—
284C4×#123C2212yes—
285C4×#121C2212yes—
286C4×#121C2211yescharacteristic
287C4×#121C2212yes—
288C4×#121C2212yes—
289C4×#121C2211yescharacteristic
290C4×#121C2211yescharacteristic
291#2297C2212yes—
292C2×#391C2212yes—
293#2290C2212yes—
294#2285C2211yescharacteristic
295#2283C2211yescharacteristic
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2314yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303C22×#41C2312yes—
304C23×Q8C2312yes—
305#550—48no—
306D4×Q8—44no—
307#548—48no—
308#547—44no—
309#542—48no—
310#537—48no—
311#532—44no—
312#532—44no—
313#532—44no—
314#532—48no—
315#532—48no—
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2312yes—
318C2×C4⋊Q8C2311yescharacteristic
319C2×C4⋊Q8C2312yes—
320C2×C4⋊Q8C2312yes—
321C2×C4⋊Q8C2311yescharacteristic
322C2×#127C2311yescharacteristic
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#127C2312yes—
326C2×#127C2311yescharacteristic
327C2×#127C2314yes—
328#529—44no—
329C2×#126C2312yes—
330C2×#126C2314yes—
331C2×#125C2311yescharacteristic
332C2×#125C2311yescharacteristic
333C2×#124C2314yes—
334C2×#124C2314yes—
335C2×#124C2312yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2311yescharacteristic
342C2×#124C2314yes—
343C2×#124C2314yes—
344C2×#124C2311yescharacteristic
345C2×#123C2314yes—
346C2×#123C2312yes—
347C2×#123C2314yes—
348C2×#123C2312yes—
349C2×C22⋊Q8C2311yescharacteristic
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2311yescharacteristic
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2314yes—
360C2×C22⋊Q8C2314yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×#121C2311yescharacteristic
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2311yescharacteristic
373C2×#121C2312yes—
374C2×#121C2314yes—
375C2×#121C2312yes—
376C2×#121C2314yes—
377C2×#121C2312yes—
378C2×#121C2314yes—
379C2×#121C2314yes—
380C2×#121C2311yescharacteristic
381C2×#121C2312yes—
382C2×#121C2312yes—
383C2×#121C2314yes—
384C2×#121C2314yes—
385C2×#121C2312yes—
386C2×#121C2314yes—
387C2×#121C2311yescharacteristic
388C2×#121C2312yes—
389C2×#121C2314yes—
390C2×C4×Q8C2311yescharacteristic
391C2×C4×Q8C2312yes—
392C2×C4×Q8C2312yes—
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2312yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2311yescharacteristic
404C2×C4×D4C2312yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2314yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2312yes—
412C2×C4×D4C2312yes—
413C2×C4×D4C2312yes—
414C2×C4×D4C2314yes—
415C2×C4×D4C2314yes—
416C2×C4×D4C2311yescharacteristic
417C2×C4×D4C2312yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2311yescharacteristic
421C2×C4×D4C2311yescharacteristic
422C2×#117C2312yes—
423C2×#117C2312yes—
424C22×C4⋊C4C2312yes—
425C22×C4⋊C4C2312yes—
426C22×C42C2311yescharacteristic
427C22×C42C2311yescharacteristic
428C22×C42C2312yes—
429C22×C42C2312yes—
430#401C2314yes—
431#401C2312yes—
432#400C2312yes—
433#400C2314yes—
434#400C2314yes—
435#400C2314yes—
436#400C2312yes—
437#400C2312yes—
438#400C2314yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2312yes—
446#400C2314yes—
447#400C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2312yes—
451#398C2312yes—
452#398C2314yes—
453#398C2312yes—
454#398C2314yes—
455#398C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2312yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2312yes—
472#397C2314yes—
473#397C2312yes—
474#397C2312yes—
475#397C2314yes—
476#397C2314yes—
477#397C2312yes—
478#397C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2312yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2312yes—
486#396C2312yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#395C2314yes—
493#395C2314yes—
494#395C2314yes—
495#395C2312yes—
496#395C2314yes—
497#394C2312yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2314yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2314yes—
515#394C2312yes—
516#394C2314yes—
517#394C2312yes—
518#394C2314yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#394C2314yes—
524#394C2312yes—
525#394C2312yes—
526#394C2312yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2314yes—
536#393C2312yes—
537#393C2314yes—
538#393C2314yes—
539#392C2312yes—
540#392C2314yes—
541#392C2314yes—
542#392C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2314yes—
549#392C2314yes—
550#392C2314yes—
551#392C2312yes—
552#392C2314yes—
553#392C2314yes—
554#392C2314yes—
555#392C2314yes—
556#392C2314yes—
557#392C2314yes—
558#392C2314yes—
559#392C2312yes—
560#392C2314yes—
561#392C2312yes—
562#392C2314yes—
563#392C2314yes—
564#391C2312yes—
565#391C2314yes—
566#391C2312yes—
567#391C2312yes—
568#391C2314yes—
569#391C2312yes—
570#391C2314yes—
571#391C2314yes—
572#391C2312yes—
573#391C2312yes—
574#391C2312yes—
575#391C2312yes—
576#391C2314yes—
577#391C2312yes—
578#391C2312yes—
579#391C2312yes—
580#391C2312yes—
581#391C2312yes—
582#391C2312yes—
583#391C2311yescharacteristic
584#391C2312yes—
585#391C2314yes—
586#391C2312yes—
587#391C2311yescharacteristic
588#390C2312yes—
589#390C2312yes—
590#390C2312yes—
591#390C2314yes—
592#390C2311yescharacteristic
593#390C2312yes—
594#390C2312yes—
595#390C2311yescharacteristic
596#390C2314yes—
597#390C2311yescharacteristic
598#390C2312yes—
599#390C2312yes—
600#390C2312yes—
601#390C2312yes—
602#390C2314yes—
603#390C2314yes—
604#390C2312yes—
605#390C2312yes—
606#390C2314yes—
607#390C2312yes—
608#390C2311yescharacteristic
609#390C2312yes—
610#389C2311yescharacteristic
611#389C2311yescharacteristic
612#389C2311yescharacteristic
613#389C2311yescharacteristic
614#389C2312yes—
615#389C2311yescharacteristic
616#389C2312yes—
617#389C2312yes—
618#389C2312yes—
619#389C2312yes—
620#389C2312yes—
621#389C2311yescharacteristic
622#389C2312yes—
623#389C2312yes—
624#389C2312yes—
625#389C2312yes—
626#388C2312yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2312yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2312yes—
637#388C2312yes—
638#388C2314yes—
639#388C2314yes—
640#388C2312yes—
641#388C2314yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2312yes—
646#388C2312yes—
647#388C2314yes—
648#388C2312yes—
649#388C2312yes—
650#387C2312yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2312yes—
666#387C2312yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2314yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
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#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#386C2312yes—
706#386C2312yes—
707#386C2312yes—
708#386C2312yes—
709#386C2312yes—
710#385C2314yes—
711#385C2312yes—
712#385C2312yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2312yes—
726#385C2312yes—
727#384C2311yescharacteristic
728#384C2312yes—
729#384C2311yescharacteristic
730#384C2311yescharacteristic
731#383C2314yes—
732#383C2312yes—
733#382C2311yescharacteristic
734#382C2314yes—
735#382C2314yes—
736#382C2312yes—
737#382C2311yescharacteristic
738#382C2311yescharacteristic
739#382C2312yes—
740#382C2312yes—
741#382C2312yes—
742#382C2312yes—
743#382C2311yescharacteristic
744#381C2314yes—
745#381C2314yes—
746#381C2312yes—
747#381C2312yes—
748#381C2314yes—
749#381C2314yes—
750#381C2314yes—
751#381C2314yes—
752#381C2314yes—
753#380C2311yescharacteristic
754#380C2311yescharacteristic
755#380C2311yescharacteristic
756#380C2311yescharacteristic
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2314yes—
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2312yes—
769#380C2314yes—
770#380C2311yescharacteristic
771#380C2312yes—
772#380C2311yescharacteristic
773#380C2311yescharacteristic
774#380C2311yescharacteristic
775#380C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2311yescharacteristic
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2311yescharacteristic
817#376C2312yes—
818C2×#95C2314yes—
819C2×#95C2314yes—
820C2×#95C2314yes—
821C43C2311yescharacteristic
822C2×#41—28no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—44no—
826C2×#41—48no—
827C2×#41—48no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—48no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—44no—
834C2×#41—44no—
835C2×#41—44no—
836C2×#41—44no—
837C22×Q8—44no—
838C22×Q8—44no—
839C22×Q8—44no—
840C22×Q8C2412yes—
841C22×Q8C2411yescharacteristic
842C22×Q8C2412yes—
843C22×Q8C2414yes—
844C22×Q8C2414yes—
845C22×Q8C2412yes—
846C22×D4C2411yescharacteristic
847C22×D4C2411yescharacteristic
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2412yes—
856C22×D4C2412yes—
857C22×D4C2414yes—
858C22×D4C2414yes—
859C22×D4C2411yescharacteristic
860C22×D4C2412yes—
861C22×D4C2414yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2412yes—
865C22×D4C2412yes—
866C22×D4C2414yes—
867C22×D4C2414yes—
868C22×D4C2414yes—
869C22×D4C2412yes—
870C22×D4C2414yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2412yes—
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2411yescharacteristic
878C23×C4C2412yes—
879C23×C4C2412yes—
880C23×C4C2414yes—
881C23×C4C2414yes—
882C23×C4C2411yescharacteristic
883C23×C4C2411yescharacteristic
884C23×C4C2414yes—
885C23×C4C2414yes—
886C23×C4C2414yes—
887C23×C4C2414yes—
888C23×C4C2412yes—
889C23×C4C2412yes—
890C4⋊Q8—28no—
891C4⋊Q8—24no—
892C4⋊Q8—24no—
893C4⋊Q8—42no—
894C4⋊Q8—44no—
895C4⋊Q8—44no—
896#127—28no—
897#127—24no—
898#127—44no—
899#127—42no—
900#127—44no—
901#127—48no—
902#126—44no—
903#126—48no—
904#125—42no—
905#125—42no—
906#124—44no—
907#124—48no—
908#124—42no—
909#124—44no—
910#124—42no—
911#124—44no—
912#124—44no—
913#124—44no—
914#124—48no—
915#124—44no—
916#124—48no—
917#124—48no—
918#123—48no—
919#123—44no—
920#123—44no—
921#123—48no—
922C22⋊Q8—24no—
923C22⋊Q8—48no—
924C22⋊Q8—48no—
925C22⋊Q8—48no—
926C22⋊Q8—48no—
927C22⋊Q8—44no—
928C22⋊Q8—42no—
929C22⋊Q8—44no—
930C22⋊Q8—44no—
931C22⋊Q8—44no—
932C22⋊Q8—44no—
933C22⋊Q8—44no—
934#121—28no—
935#121—24no—
936#121—24no—
937#121—28no—
938#121—24no—
939#121—44no—
940#121—44no—
941#121—48no—
942#121—48no—
943#121—48no—
944#121—48no—
945#121—48no—
946#121—48no—
947#121—44no—
948#121—44no—
949#121—44no—
950#121—42no—
951#121—42no—
952#121—44no—
953#121—44no—
954#121—42no—
955#121—44no—
956#121—44no—
957#121—44no—
958#121—44no—
959#121—44no—
960#121—44no—
961#121—48no—
962#121—48no—
963C4×Q8—28no—
964C4×Q8—24no—
965C4×Q8—44no—
966C4×D4—24no—
967C4×D4—24no—
968C4×D4—24no—
969C4×D4—24no—
970C4×D4—24no—
971C4×D4—42no—
972C4×D4—42no—
973C4×D4—42no—
974C4×D4—44no—
975C4×D4—44no—
976C4×D4—44no—
977C4×D4—44no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—48no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—42no—
985C4×D4—42no—
986C4×D4—44no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—44no—
990C4×D4—44no—
991C4×D4—48no—
992C4×D4—48no—
993C4×D4—48no—
994C4×D4—48no—
995#117—44no—
996#117—44no—
997C2×C4⋊C4—44no—
998C2×C4⋊C4—44no—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2411yescharacteristic
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2411yescharacteristic
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2411yescharacteristic
1033C2×C4⋊C4C2411yescharacteristic
1034C2×C4⋊C4C2411yescharacteristic
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2411yescharacteristic
1090C2×C22⋊C4C2411yescharacteristic
1091C2×C22⋊C4C2411yescharacteristic
1092C2×C22⋊C4C2411yescharacteristic
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2414yes—
1121C2×C42—24no—
1122C2×C42—24no—
1123C2×C42—44no—
1124C2×C42—44no—
1125C2×C42C2411yescharacteristic
1126C2×C42C2412yes—
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2411yescharacteristic
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2411yescharacteristic
1137C2×C42C2411yescharacteristic
1138C2×C42C2414yes—
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2411yescharacteristic
1142C2×C42C2412yes—
1143C2×C42C2412yes—
1144C2×C42C2414yes—
1145C2×C42C2414yes—
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150#95C2411yescharacteristic
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2411yescharacteristic
1166#95C2412yes—
1167#95C2411yescharacteristic
1168#95C2411yescharacteristic
1169#95C2412yes—
1170#95C2412yes—
1171#95C2411yescharacteristic
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2411yescharacteristic
1176#95C2412yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216C24C2511yescharacteristic
1217C24C2512yes—
1218C24C2512yes—
1219C24C2514yes—
1220C24C2511yescharacteristic
1221C24C2512yes—
1222#41—816no—
1223#41—832no—
1224#41—816no—
1225#41—816no—
1226#41—816no—
1227C2×Q8—22no—
1228C2×Q8—24no—
1229C2×Q8—24no—
1230C2×Q8—22no—
1231C2×Q8—24no—
1232C2×Q8—24no—
1233C2×Q8—28no—
1234C2×Q8—24no—
1235C2×Q8—22no—
1236C2×Q8—24no—
1237C2×Q8—42no—
1238C2×Q8—44no—
1239C2×Q8—44no—
1240C2×Q8—44no—
1241C2×Q8—42no—
1242C2×Q8—44no—
1243C2×Q8—44no—
1244C2×Q8—42no—
1245C2×Q8—816no—
1246C2×D4—28no—
1247C2×D4—28no—
1248C2×D4—24no—
1249C2×D4—28no—
1250C2×D4—24no—
1251C2×D4—28no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—22no—
1257C2×D4—24no—
1258C2×D4—28no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—24no—
1263C2×D4—24no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—24no—
1267C2×D4—24no—
1268C2×D4—22no—
1269C2×D4—42no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4—42no—
1274C2×D4—44no—
1275C2×D4—42no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—44no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—42no—
1285C2×D4—44no—
1286C2×D4—42no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—42no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—42no—
1295C2×D4—42no—
1296C2×D4—42no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—44no—
1300C2×D4—42no—
1301C2×D4—42no—
1302C2×D4—44no—
1303C2×D4—44no—
1304C2×D4—42no—
1305C2×D4—44no—
1306C2×D4—42no—
1307C2×D4—44no—
1308C2×D4—42no—
1309C2×D4—44no—
1310C2×D4—42no—
1311C2×D4—42no—
1312C2×D4—44no—
1313C2×D4—42no—
1314C2×D4—44no—
1315C2×D4—44no—
1316C2×D4—44no—
1317C2×D4—44no—
1318C2×D4—44no—
1319C2×D4—44no—
1320C2×D4H(5,𝔽2)14yes—
1321C22×C4—24no—
1322C22×C4—28no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—22no—
1326C22×C4—22no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—24no—
1330C22×C4—24no—
1331C22×C4—22no—
1332C22×C4—24no—
1333C22×C4—24no—
1334C22×C4—24no—
1335C22×C4—22no—
1336C22×C4—22no—
1337C22×C4—22no—
1338C22×C4—22no—
1339C22×C4—24no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—24no—
1344C22×C4—24no—
1345C22×C4—24no—
1346C22×C4—24no—
1347C22×C4—22no—
1348C22×C4—22no—
1349C22×C4—28no—
1350C22×C4—42no—
1351C22×C4—42no—
1352C22×C4—42no—
1353C22×C4—42no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C4—44no—
1358C22×C4—44no—
1359C22×C4—44no—
1360C22×C4—44no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—41no—
1364C22×C4—41no—
1365C22×C4—42no—
1366C22×C4—42no—
1367C22×C4—41no—
1368C22×C4—41no—
1369C22×C4—42no—
1370C22×C4—42no—
1371C22×C4—44no—
1372C22×C4—44no—
1373C22×C4—44no—
1374C22×C4—44no—
1375C22×C4—44no—
1376C22×C4—44no—
1377C22×C4—44no—
1378C22×C4C2512yes—
1379C22×C4C2512yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2512yes—
1382C22×C4C2512yes—
1383C22×C4C2511yescharacteristic
1384C22×C4C2511yescharacteristic
1385C22×C4C2511yescharacteristic
1386C22×C4C2511yescharacteristic
1387C22×C4C2511yescharacteristic
1388C22×C4C2511yescharacteristic
1389C22×C4C2512yes—
1390C22×C4C2512yes—
1391C22×C4C2514yes—
1392C22×C4C2514yes—
1393C22×C4C2512yes—
1394C22×C4C2512yes—
1395C22×C4C2511yescharacteristic
1396C22×C4C2514yes—
1397C22×C4C2512yes—
1398C22×C4C2512yes—
1399C22×C4C2512yes—
1400C22×C4C2512yes—
1401C22×C4C2511yescharacteristic
1402C22×C4C2511yescharacteristic
1403C22×C4C2512yes—
1404C22×C4C2511yescharacteristic
1405C22×C4C2511yescharacteristic
1406C22×C4C2511yescharacteristic
1407C4⋊C4—22no—
1408C4⋊C4—22no—
1409C4⋊C4—24no—
1410C4⋊C4—24no—
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—22no—
1414C4⋊C4—24no—
1415C4⋊C4—24no—
1416C4⋊C4—24no—
1417C4⋊C4—24no—
1418C4⋊C4—24no—
1419C4⋊C4—28no—
1420C4⋊C4—28no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—22no—
1424C4⋊C4—24no—
1425C4⋊C4—22no—
1426C4⋊C4—22no—
1427C4⋊C4—22no—
1428C4⋊C4—22no—
1429C4⋊C4—44no—
1430C4⋊C4—44no—
1431C4⋊C4—42no—
1432C4⋊C4—42no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—41no—
1439C4⋊C4—41no—
1440C4⋊C4—41no—
1441C4⋊C4—42no—
1442C4⋊C4—42no—
1443C4⋊C4—42no—
1444C4⋊C4—44no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4—44no—
1448C4⋊C4—42no—
1449C4⋊C4—44no—
1450C4⋊C4—44no—
1451C4⋊C4—44no—
1452C4⋊C4—44no—
1453C4⋊C4—44no—
1454C4⋊C4—42no—
1455C4⋊C4—42no—
1456C4⋊C4—42no—
1457C4⋊C4H(5,𝔽2)14yes—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—28no—
1461C22⋊C4—24no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—24no—
1465C22⋊C4—24no—
1466C22⋊C4—28no—
1467C22⋊C4—24no—
1468C22⋊C4—24no—
1469C22⋊C4—24no—
1470C22⋊C4—22no—
1471C22⋊C4—22no—
1472C22⋊C4—42no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—41no—
1485C22⋊C4—41no—
1486C22⋊C4—42no—
1487C22⋊C4—42no—
1488C22⋊C4—42no—
1489C22⋊C4—41no—
1490C22⋊C4—41no—
1491C22⋊C4—44no—
1492C22⋊C4—42no—
1493C22⋊C4—42no—
1494C22⋊C4—42no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—42no—
1500C22⋊C4—42no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—42no—
1508C22⋊C4—42no—
1509C22⋊C4—44no—
1510C22⋊C4—44no—
1511C22⋊C4—42no—
1512C22⋊C4—44no—
1513C22⋊C4—44no—
1514C22⋊C4—44no—
1515C22⋊C4—44no—
1516C22⋊C4—44no—
1517C22⋊C4—44no—
1518C22⋊C4—44no—
1519C22⋊C4—44no—
1520C22⋊C4—44no—
1521C22⋊C4—44no—
1522C22⋊C4—42no—
1523C22⋊C4—42no—
1524C22⋊C4—44no—
1525C22⋊C4—42no—
1526C22⋊C4—42no—
1527C22⋊C4—44no—
1528C22⋊C4—44no—
1529C42—22no—
1530C42—22no—
1531C42—22no—
1532C42—22no—
1533C42—22no—
1534C42—22no—
1535C42—22no—
1536C42—22no—
1537C42—24no—
1538C42—24no—
1539C42—24no—
1540C42—24no—
1541C42—28no—
1542C42—22no—
1543C42—22no—
1544C42—22no—
1545C42—24no—
1546C42—42no—
1547C42—42no—
1548C42—42no—
1549C42—42no—
1550C42—41no—
1551C42—44no—
1552C42—44no—
1553C42H(5,𝔽2)14yes—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—21no—
1561C23—22no—
1562C23—22no—
1563C23—22no—
1564C23—24no—
1565C23—22no—
1566C23—21no—
1567C23—21no—
1568C23—24no—
1569C23—24no—
1570C23—21no—
1571C23—22no—
1572C23—21no—
1573C23—22no—
1574C23—21no—
1575C23—21no—
1576C23—22no—
1577C23—21no—
1578C23—22no—
1579C23—21no—
1580C23—22no—
1581C23—24no—
1582C23—24no—
1583C23—22no—
1584C23—21no—
1585C23—21no—
1586C23—21no—
1587C23—24no—
1588C23—22no—
1589C23—22no—
1590C23—21no—
1591C23—22no—
1592C23—24no—
1593C23—22no—
1594C23—21no—
1595C23C2×H(5,𝔽2)14yes—
1596C23C2611yescharacteristic
1597Q8—44no—
1598Q8—48no—
1599Q8—48no—
1600Q8—88no—
1601Q8—88no—
1602Q8—84no—
1603D4—28no—
1604D4—416no—
1605D4—48no—
1606D4—44no—
1607D4—44no—
1608D4—44no—
1609D4—48no—
1610D4—48no—
1611D4—84no—
1612D4—84no—
1613D4—88no—
1614D4—84no—
1615D4—88no—
1616D4—88no—
1617D4—88no—
1618D4—88no—
1619D4—84no—
1620D4—84no—
1621D4—84no—
1622D4—84no—
1623D4—84no—
1624D4—88no—
1625D4—88no—
1626D4—88no—
1627D4—164no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—22no—
1648C2×C4—24no—
1649C2×C4—22no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—24no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—22no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—24no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—24no—
1665C2×C4—24no—
1666C2×C4—24no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—21no—
1671C2×C4—21no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—22no—
1677C2×C4—22no—
1678C2×C4—24no—
1679C2×C4—21no—
1680C2×C4—21no—
1681C2×C4—22no—
1682C2×C4—22no—
1683C2×C4—21no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—24no—
1691C2×C4—22no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—22no—
1696C2×C4—24no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—22no—
1700C2×C4—22no—
1701C2×C4—21no—
1702C2×C4—22no—
1703C2×C4—21no—
1704C2×C4—22no—
1705C2×C4—22no—
1706C2×C4—48no—
1707C2×C4—48no—
1708C2×C4—44no—
1709C2×C4—48no—
1710C2×C4—44no—
1711C2×C4—48no—
1712C2×C4—44no—
1713C2×C4—48no—
1714C2×C4—44no—
1715C2×C4—82no—
1716C2×C4—82no—
1717C2×C4—88no—
1718C2×C4—88no—
1719C2×C4—84no—
1720C2×C4—84no—
1721C2×C4—88no—
1722C2×C4—88no—
1723C2×C4—88no—
1724C2×C4—164no—
1725C2×C4C2×H(5,𝔽2)12yes—
1726C2×C4C2×H(5,𝔽2)14yes—
1727C2×C4C2×H(5,𝔽2)12yes—
1728C2×C4C2×H(5,𝔽2)12yes—
1729C2×C4C2×H(5,𝔽2)12yes—
1730C2×C4C2×H(5,𝔽2)12yes—
1731C2×C4#58512yes—
1732C2×C4#58512yes—
1733C2×C4#58512yes—
1734C22—24no—
1735C22—24no—
1736C22—24no—
1737C22—42no—
1738C22—42no—
1739C22—42no—
1740C22—42no—
1741C22—42no—
1742C22—41no—
1743C22—41no—
1744C22—42no—
1745C22—44no—
1746C22—41no—
1747C22—41no—
1748C22—44no—
1749C22—42no—
1750C22—42no—
1751C22—42no—
1752C22—44no—
1753C22—42no—
1754C22—41no—
1755C22—41no—
1756C22—41no—
1757C22—41no—
1758C22—42no—
1759C22—44no—
1760C22—42no—
1761C22—42no—
1762C22—41no—
1763C22—44no—
1764C22—42no—
1765C22—41no—
1766C22—42no—
1767C22—44no—
1768C22—41no—
1769C22—42no—
1770C22—41no—
1771C22—41no—
1772C22—41no—
1773C22—44no—
1774C22—42no—
1775C22—42no—
1776C22C22×H(5,𝔽2)11yescharacteristic
1777C22C22×H(5,𝔽2)11yescharacteristic
1778C22C22×H(5,𝔽2)11yescharacteristic
1779C22C2×#58511yescharacteristic
1780C22C2×#58511yescharacteristic
1781C22C2×#58511yescharacteristic
1782C222−1+611yescharacteristic
1783C4—22no—
1784C4—24no—
1785C4—22no—
1786C4—41no—
1787C4—42no—
1788C4—41no—
1789C4—42no—
1790C4—44no—
1791C4—41no—
1792C4—41no—
1793C4—42no—
1794C4—44no—
1795C4—42no—
1796C4—42no—
1797C4—44no—
1798C4—42no—
1799C4—41no—
1800C4—42no—
1801C4—41no—
1802C4—42no—
1803C4—42no—
1804C4—42no—
1805C4—41no—
1806C4—42no—
1807C4—41no—
1808C4—41no—
1809C4—42no—
1810C4#354614yes—
1811C4#355814yes—
1812C2—44no—
1813C2—81no—
1814C2—81no—
1815C2—82no—
1816C2—82no—
1817C2—84no—
1818C2C2×#355811yescharacteristic
1819C2C2×#354611yescharacteristic
1820C2#6276211yescharacteristic
1821C2#6292111yescharacteristic
1822C2#6292211yescharacteristic
1823C2#6292511yescharacteristic
1824C2#6301211yescharacteristic
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. #59093C2semidirect
3. #59080C2semidirect
4. #59051C2semidirect
5. #59033C2semidirect
6. #55015C2semidirect
7. #54780C2semidirect
8. #53128C2semidirect
9. #53046C2semidirect
10. #53004C2semidirect
11. #52975C2semidirect
12. #52402C2semidirect
13. #42985C2semidirect
14. #42805C2semidirect
15. #42602C2semidirect
16. #42596C2semidirect
17. #40649C2semidirect
18. #39350C2semidirect
19. #39340C2semidirect
20. #39159C2semidirect
21. #39124C2semidirect
22. #39004C2semidirect
23. #38997C2semidirect
24. #37780C2semidirect
25. #37772C2semidirect
26. #37618C2semidirect
27. #37616C2semidirect
28. #37516C2semidirect
29. #37494C2semidirect
30. #36454C2semidirect
31. #36303C2semidirect
32. #36149C2semidirect
33. #34925C2semidirect
34. #34917C2semidirect
35. #34889C2semidirect

Maximal subgroups

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

subgroupindex
#596472
#590932
#590802
#590512
#590332
#550152
#547802
#531282
#530462
#530042
#529752
#524022
#429852
#428052
#426022
#425962
#406492
#393502
#393402
#391592
#391242
#390042
#389972
#377802
#377722
#376182
#376162
#375162
#374942
#364542
#363032
#361492
#349252
#349172
#348892