Finite Group Databasebeta

← #8429443

Subgroups — #8429443

Order 512.

4514 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59821C211yesmaximal, characteristic, complemented
2#59753C212yesmaximal, complemented
3#59393C212yesmaximal, complemented
4#59302C211yesmaximal, characteristic, complemented
5#59219C211yesmaximal, characteristic, complemented
6#58350C214yesmaximal, complemented
7#54298C214yesmaximal, complemented
8#53152C212yesmaximal, complemented
9#53098C212yesmaximal, complemented
10#53066C212yesmaximal, complemented
11#53051C212yesmaximal, complemented
12#52506C214yesmaximal, complemented
13#42935C212yesmaximal, complemented
14#42870C212yesmaximal, complemented
15#42752C212yesmaximal, complemented
16#42690C212yesmaximal, complemented
17#40807C214yesmaximal, complemented
18#39822C212yesmaximal, complemented
19#39664C212yesmaximal, complemented
20#39212C212yesmaximal, complemented
21#39191C211yesmaximal, characteristic, complemented
22#39136C211yesmaximal, characteristic, complemented
23#39054C212yesmaximal, complemented
24#38976C211yesmaximal, characteristic, complemented
25#38923C211yesmaximal, characteristic, complemented
26#37628C211yesmaximal, characteristic, complemented
27#37620C211yesmaximal, characteristic, complemented
28#37524C212yesmaximal, complemented
29#37510C212yesmaximal, complemented
30#36504C211yesmaximal, characteristic, complemented
31#36405C211yesmaximal, characteristic, complemented
32#36189C211yesmaximal, characteristic, complemented
33#34976C211yesmaximal, characteristic, complemented
34#34727C211yesmaximal, characteristic, complemented
35#34724C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic
37C2×#556C2211yescharacteristic
38C2×#529C2211yescharacteristic
39C2×#529C2211yescharacteristic
40C2×C4×#41C2211yescharacteristic
41C2×C4×#41C2211yescharacteristic
42#2859C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2855C2212yes—
46#2850C2212yes—
47#2837C2214yes—
48#2837C2214yes—
49#2836C2214yes—
50#2834C2214yes—
51#2829C2214yes—
52#2829C2214yes—
53#2829C2214yes—
54#2828C2214yes—
55#2827C2214yes—
56#2827C2214yes—
57#2827C2214yes—
58#2825C2214yes—
59#2823C2214yes—
60#2813C2214yes—
61#2797C2214yes—
62#2797C2214yes—
63#2796C2214yes—
64#2795C2214yes—
65#2793C2214yes—
66#2791C2214yes—
67#2790C2214yes—
68#2786C2214yes—
69#2783C2214yes—
70#2780C2214yes—
71#2780C2214yes—
72#2778C2214yes—
73#2777C2214yes—
74#2773C2214yes—
75#2766C2214yes—
76#2765C2214yes—
77#2757C2214yes—
78#2756C2214yes—
79#2753C2214yes—
80#2753C2214yes—
81#2748C2214yes—
82#2748C2214yes—
83#2746C2214yes—
84#2740C2214yes—
85#2739C2214yes—
86#2727C2214yes—
87#2727C2214yes—
88#2722C2214yes—
89#2719C2214yes—
90#2711C2214yes—
91#2707C2214yes—
92#2705C2214yes—
93#2705C2214yes—
94#2703C2214yes—
95#2695C2214yes—
96#2691C2214yes—
97#2688C2214yes—
98#2667C2214yes—
99#2664C2214yes—
100#2655C2214yes—
101#2654C2214yes—
102#2654C2214yes—
103#2654C2214yes—
104#2654C2214yes—
105#2652C2214yes—
106#2649C2214yes—
107#2648C2214yes—
108#2647C2212yes—
109#2645C2212yes—
110#2644C2212yes—
111#2629C2212yes—
112#2629C2212yes—
113#2625C2212yes—
114#2625C2212yes—
115#2624C2212yes—
116#2621C2212yes—
117#2620C2212yes—
118#2620C2212yes—
119#2620C2212yes—
120#2618C2214yes—
121#2609C2214yes—
122#2608C2214yes—
123#2597C2214yes—
124#2594C2214yes—
125#2594C2214yes—
126#2590C2214yes—
127#2585C2214yes—
128#2582C2211yescharacteristic
129#2582C2211yescharacteristic
130#2578C2214yes—
131#2571C2211yescharacteristic
132#2570C2212yes—
133#2570C2212yes—
134#2548C2212yes—
135#2547C2212yes—
136#2546C2211yescharacteristic
137#2542C2212yes—
138#2542C2211yescharacteristic
139#2540C2212yes—
140#2540C2212yes—
141#2538C2212yes—
142#2538C2211yescharacteristic
143#2538C2211yescharacteristic
144#2538C2211yescharacteristic
145#2538C2212yes—
146#2537C2211yescharacteristic
147#2537C2211yescharacteristic
148#2536C2212yes—
149#2536C2212yes—
150#2522C2214yes—
151#2522C2214yes—
152#2514C2212yes—
153#2513C2212yes—
154#2512C2212yes—
155#2512C2214yes—
156#2511C2212yes—
157#2511C2212yes—
158#2508C2212yes—
159#2507C2212yes—
160#2507C2212yes—
161#2507C2212yes—
162#2506C2212yes—
163#2506C2212yes—
164#2504C2212yes—
165#2499C2212yes—
166#2497C2212yes—
167#2497C2214yes—
168#2497C2212yes—
169#2496C2212yes—
170#2494C2212yes—
171#2494C2212yes—
172#2490C2214yes—
173#2487C2212yes—
174#2487C2212yes—
175#2486C2212yes—
176#2485C2212yes—
177#2485C2212yes—
178#2485C2212yes—
179#2485C2212yes—
180#2485C2212yes—
181#2481C2214yes—
182#2479C2214yes—
183#2479C2212yes—
184#2478C2214yes—
185#2478C2212yes—
186#2471C2212yes—
187#2470C2214yes—
188#2470C2212yes—
189#2468C2214yes—
190#2467C2212yes—
191#2467C2214yes—
192#2466C2212yes—
193#2466C2214yes—
194#2464C2214yes—
195#2460C2214yes—
196#2456C2212yes—
197#2455C2212yes—
198#2454C2211yescharacteristic
199#2453C2212yes—
200#2453C2211yescharacteristic
201#2448C2212yes—
202#2448C2211yescharacteristic
203#2448C2212yes—
204#2447C2212yes—
205#2447C2211yescharacteristic
206#2446C2212yes—
207#2442C2212yes—
208#2441C2212yes—
209#2441C2211yescharacteristic
210#2441C2212yes—
211#2441C2211yescharacteristic
212#2432C2212yes—
213#2432C2211yescharacteristic
214#2431C2211yescharacteristic
215#2429C2212yes—
216#2429C2212yes—
217#2429C2211yescharacteristic
218#2428C2212yes—
219#2428C2211yescharacteristic
220#2427C2212yes—
221#2426C2212yes—
222#2423C2211yescharacteristic
223#2423C2212yes—
224#2423C2212yes—
225#2422C2212yes—
226#2422C2211yescharacteristic
227#2421C2212yes—
228#2420C2214yes—
229#2417C2212yes—
230#2417C2212yes—
231#2417C2212yes—
232#2417C2212yes—
233#2417C2212yes—
234#2416C2212yes—
235#2416C2212yes—
236#2416C2212yes—
237#2415C2212yes—
238#2415C2212yes—
239#2415C2212yes—
240#2415C2211yescharacteristic
241#2414C2211yescharacteristic
242#2414C2212yes—
243#2414C2212yes—
244#2407C2212yes—
245#2407C2212yes—
246#2407C2212yes—
247#2407C2211yescharacteristic
248#2407C2211yescharacteristic
249#2397C2212yes—
250#2395C2212yes—
251#2392C2212yes—
252#2392C2214yes—
253#2392C2212yes—
254#2374C2214yes—
255#2365C2212yes—
256#2363C2212yes—
257#2362C2212yes—
258#2360C2212yes—
259#2360C2212yes—
260#2357C2212yes—
261#2355C2211yescharacteristic
262#2354C2211yescharacteristic
263#2354C2212yes—
264#2354C2212yes—
265#2352C2212yes—
266#2352C2212yes—
267Q8×C4⋊C4C2212yes—
268Q8×C4⋊C4C2211yescharacteristic
269D4×C4⋊C4C2211yescharacteristic
270#2345C2212yes—
271#2345C2212yes—
272#2333C2214yes—
273#2324C2212yes—
274#2323C2212yes—
275#2320C2212yes—
276#2316C2212yes—
277C4×C4⋊Q8C2211yescharacteristic
278C4×C4⋊Q8C2211yescharacteristic
279C4×#127C2211yescharacteristic
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2212yes—
282C4×C22⋊Q8C2211yescharacteristic
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2212yes—
285C4×#123C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic
288C4×#121C2212yes—
289C4×#121C2212yes—
290C4×#121C2211yescharacteristic
291#2296C2212yes—
292#2296C2212yes—
293#2295C2211yescharacteristic
294#2293C2211yescharacteristic
295#2290C2212yes—
296#2285C2211yescharacteristic
297C2×#384C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2311yescharacteristic
301#556—44no—
302#556—44no—
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2312yes—
306C2×#127C2311yescharacteristic
307#529—44no—
308#529—44no—
309C2×#126C2312yes—
310C2×#126C2312yes—
311C2×#126C2314yes—
312C2×#126C2314yes—
313C2×#126C2314yes—
314C2×#125C2311yescharacteristic
315C2×#125C2311yescharacteristic
316C2×#125C2312yes—
317C2×#125C2314yes—
318C2×#124C2312yes—
319C2×#124C2311yescharacteristic
320C2×#124C2311yescharacteristic
321C2×#124C2312yes—
322C2×#123C2312yes—
323C2×#123C2312yes—
324C2×#123C2312yes—
325C2×#123C2314yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2311yescharacteristic
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2311yescharacteristic
339C2×#121C2312yes—
340C2×#121C2312yes—
341C2×#121C2312yes—
342C2×#121C2312yes—
343C2×#121C2311yescharacteristic
344C2×#121C2312yes—
345C2×#121C2311yescharacteristic
346C2×#121C2311yescharacteristic
347C2×#121C2311yescharacteristic
348C2×#121C2314yes—
349C2×#121C2314yes—
350C4×#41—44no—
351C4×#41—44no—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2311yescharacteristic
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2312yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2314yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C2×#117C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C42C2311yescharacteristic
397C22×C42C2311yescharacteristic
398C22×C42C2312yes—
399C22×C42C2312yes—
400#401C2314yes—
401#401C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2312yes—
406#400C2314yes—
407#400C2314yes—
408#400C2314yes—
409#400C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#399C2312yes—
417#399C2314yes—
418#399C2314yes—
419#399C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2312yes—
424#399C2314yes—
425#399C2312yes—
426#399C2312yes—
427#399C2312yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2312yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2312yes—
448#398C2314yes—
449#398C2314yes—
450#398C2312yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2314yes—
459#397C2314yes—
460#397C2314yes—
461#397C2312yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2312yes—
473#397C2312yes—
474#397C2312yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2314yes—
493#396C2314yes—
494#396C2312yes—
495#396C2312yes—
496#396C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2312yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2312yes—
513#394C2312yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#394C2314yes—
518#394C2312yes—
519#394C2314yes—
520#394C2312yes—
521#394C2312yes—
522#394C2312yes—
523#394C2314yes—
524#392C2312yes—
525#392C2312yes—
526#392C2314yes—
527#392C2314yes—
528#392C2312yes—
529#392C2314yes—
530#392C2314yes—
531#392C2312yes—
532#392C2312yes—
533#392C2312yes—
534#391C2311yescharacteristic
535#391C2312yes—
536#391C2311yescharacteristic
537#391C2312yes—
538#391C2312yes—
539#391C2312yes—
540#391C2312yes—
541#391C2312yes—
542#391C2312yes—
543#391C2311yescharacteristic
544#391C2312yes—
545#391C2312yes—
546#391C2311yescharacteristic
547#391C2311yescharacteristic
548#391C2311yescharacteristic
549#390C2311yescharacteristic
550#390C2311yescharacteristic
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2314yes—
556#390C2314yes—
557#390C2314yes—
558#390C2311yescharacteristic
559#390C2312yes—
560#390C2314yes—
561#390C2312yes—
562#390C2312yes—
563#390C2314yes—
564#390C2311yescharacteristic
565#390C2312yes—
566#390C2314yes—
567#390C2311yescharacteristic
568#390C2312yes—
569#390C2311yescharacteristic
570#390C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2312yes—
574#389C2312yes—
575#389C2311yescharacteristic
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2311yescharacteristic
582#389C2312yes—
583#389C2314yes—
584#389C2312yes—
585#389C2312yes—
586#389C2314yes—
587#389C2312yes—
588#389C2314yes—
589#389C2312yes—
590#389C2314yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2314yes—
595#389C2314yes—
596#389C2314yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2314yes—
604#389C2312yes—
605#389C2312yes—
606#389C2314yes—
607#389C2314yes—
608#389C2314yes—
609#389C2311yescharacteristic
610#389C2312yes—
611#389C2312yes—
612#389C2311yescharacteristic
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2311yescharacteristic
617#389C2311yescharacteristic
618#389C2311yescharacteristic
619#389C2311yescharacteristic
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2312yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2312yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2312yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2312yes—
648#388C2314yes—
649#388C2312yes—
650#388C2312yes—
651#388C2314yes—
652#388C2312yes—
653#388C2312yes—
654#388C2312yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2312yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2312yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2312yes—
686#387C2312yes—
687#387C2312yes—
688#387C2312yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2312yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2312yes—
703#386C2312yes—
704#386C2312yes—
705#386C2312yes—
706#386C2312yes—
707#386C2312yes—
708#385C2312yes—
709#385C2314yes—
710#385C2312yes—
711#385C2314yes—
712#385C2314yes—
713#385C2312yes—
714#385C2312yes—
715#385C2314yes—
716#385C2312yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2312yes—
724#385C2312yes—
725#385C2312yes—
726#385C2312yes—
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#384C2311yescharacteristic
730#384C2312yes—
731#384C2312yes—
732#384C2311yescharacteristic
733#384C2311yescharacteristic
734#384C2312yes—
735#384C2314yes—
736#384C2312yes—
737#384C2312yes—
738#383C2314yes—
739#382C2312yes—
740#382C2312yes—
741#382C2312yes—
742#382C2312yes—
743#382C2312yes—
744#382C2314yes—
745#381C2314yes—
746#381C2312yes—
747#381C2314yes—
748#380C2314yes—
749#380C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2314yes—
755#380C2314yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2311yescharacteristic
761#380C2312yes—
762#380C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2311yescharacteristic
769#380C2311yescharacteristic
770#380C2312yes—
771#380C2312yes—
772#380C2314yes—
773#380C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2314yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2314yes—
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814#376C2312yes—
815C43C2311yescharacteristic
816C2×#41—42no—
817C2×#41—42no—
818C2×#41—42no—
819C2×#41—42no—
820C2×#41—42no—
821C2×#41—42no—
822C22×Q8C2411yescharacteristic
823C22×Q8C2412yes—
824C22×Q8C2411yescharacteristic
825C22×Q8C2411yescharacteristic
826C22×D4C2411yescharacteristic
827C22×D4C2411yescharacteristic
828C22×D4C2411yescharacteristic
829C22×D4C2411yescharacteristic
830C22×D4C2412yes—
831C22×D4C2412yes—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2412yes—
836C22×D4C2414yes—
837C22×D4C2412yes—
838C22×D4C2412yes—
839C22×D4C2414yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2412yes—
844C23×C4C2412yes—
845C23×C4C2411yescharacteristic
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2412yes—
850C23×C4C2412yes—
851C23×C4C2414yes—
852C23×C4C2414yes—
853C23×C4C2412yes—
854C23×C4C2412yes—
855C4⋊Q8—24no—
856C4⋊Q8—44no—
857C4⋊Q8—42no—
858#127—42no—
859#126—44no—
860#126—44no—
861#126—48no—
862#126—48no—
863#126—84no—
864#125—42no—
865#125—42no—
866#125—82no—
867#125—84no—
868#124—42no—
869#124—42no—
870#124—44no—
871#124—44no—
872#123—28no—
873#123—44no—
874#123—44no—
875#123—84no—
876C22⋊Q8—42no—
877C22⋊Q8—44no—
878C22⋊Q8—44no—
879C22⋊Q8—44no—
880C22⋊Q8—44no—
881C22⋊Q8—42no—
882C22⋊Q8—44no—
883C22⋊Q8—44no—
884C22⋊Q8—44no—
885C22⋊Q8—42no—
886C22⋊Q8—42no—
887C22⋊Q8—44no—
888C22⋊Q8—44no—
889#121—28no—
890#121—44no—
891#121—44no—
892#121—44no—
893#121—44no—
894#121—42no—
895#121—42no—
896#121—42no—
897#121—42no—
898#121—84no—
899#121—84no—
900C4×Q8—24no—
901C4×Q8—24no—
902C4×Q8—24no—
903C4×Q8—44no—
904C4×Q8—44no—
905C4×Q8—42no—
906C4×Q8—42no—
907C4×Q8—44no—
908C4×Q8—44no—
909C4×D4—24no—
910C4×D4—24no—
911C4×D4—24no—
912C4×D4—24no—
913C4×D4—44no—
914C4×D4—42no—
915C4×D4—42no—
916C4×D4—42no—
917C4×D4—42no—
918C4×D4—44no—
919C4×D4—44no—
920C4×D4—44no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—84no—
929#117—44no—
930#117—44no—
931#117—44no—
932#117—44no—
933#117—44no—
934#117—44no—
935#117—42no—
936#117—42no—
937#117—44no—
938#117—44no—
939#117—82no—
940C2×C4⋊C4—44no—
941C2×C4⋊C4—44no—
942C2×C4⋊C4—44no—
943C2×C4⋊C4—82no—
944C2×C4⋊C4C2411yescharacteristic
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2412yes—
948C2×C4⋊C4C2412yes—
949C2×C4⋊C4C2412yes—
950C2×C4⋊C4C2411yescharacteristic
951C2×C4⋊C4C2411yescharacteristic
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2411yescharacteristic
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2411yescharacteristic
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2412yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2414yes—
998C2×C4⋊C4C2414yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C22⋊C4C2412yes—
1019C2×C22⋊C4C2412yes—
1020C2×C22⋊C4C2412yes—
1021C2×C22⋊C4C2411yescharacteristic
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2412yes—
1025C2×C22⋊C4C2412yes—
1026C2×C22⋊C4C2412yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2414yes—
1035C2×C22⋊C4C2414yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2411yescharacteristic
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2411yescharacteristic
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2411yescharacteristic
1081C2×C42—24no—
1082C2×C42—24no—
1083C2×C42—44no—
1084C2×C42—44no—
1085C2×C42C2411yescharacteristic
1086C2×C42C2411yescharacteristic
1087C2×C42C2411yescharacteristic
1088C2×C42C2411yescharacteristic
1089C2×C42C2412yes—
1090C2×C42C2412yes—
1091C2×C42C2412yes—
1092C2×C42C2411yescharacteristic
1093C2×C42C2412yes—
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2411yescharacteristic
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2414yes—
1104C2×C42C2414yes—
1105C2×C42C2414yes—
1106C2×C42C2414yes—
1107C2×C42C2412yes—
1108C2×C42C2412yes—
1109C2×C42C2414yes—
1110C2×C42C2414yes—
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2411yescharacteristic
1114#95C2412yes—
1115#95C2412yes—
1116#95C2412yes—
1117#95C2412yes—
1118#95C2412yes—
1119#95C2411yescharacteristic
1120#95C2414yes—
1121#95C2414yes—
1122#95C2412yes—
1123#95C2411yescharacteristic
1124#95C2411yescharacteristic
1125#95C2411yescharacteristic
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2412yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2414yes—
1133#95C2412yes—
1134#95C2414yes—
1135#95C2414yes—
1136#95C2414yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2414yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2414yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2414yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178C24C2512yes—
1179C24C2512yes—
1180C24C2512yes—
1181C24C2511yescharacteristic
1182C24C2511yescharacteristic
1183#41—416no—
1184#41—416no—
1185C2×Q8—22no—
1186C2×Q8—22no—
1187C2×Q8—22no—
1188C2×Q8—24no—
1189C2×Q8—22no—
1190C2×Q8—24no—
1191C2×Q8—22no—
1192C2×Q8—24no—
1193C2×Q8—22no—
1194C2×Q8—22no—
1195C2×Q8—22no—
1196C2×Q8—22no—
1197C2×D4—22no—
1198C2×D4—24no—
1199C2×D4—24no—
1200C2×D4—24no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—24no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—42no—
1212C2×D4—42no—
1213C2×D4—41no—
1214C2×D4—41no—
1215C2×D4—42no—
1216C2×D4—42no—
1217C2×D4—42no—
1218C2×D4—42no—
1219C2×D4—42no—
1220C2×D4—42no—
1221C2×D4—42no—
1222C2×D4—42no—
1223C2×D4—42no—
1224C2×D4—42no—
1225C2×D4—44no—
1226C2×D4—44no—
1227C2×D4—42no—
1228C2×D4—42no—
1229C2×D4—44no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—42no—
1234C2×D4—42no—
1235C2×D4—42no—
1236C2×D4—44no—
1237C2×D4—44no—
1238C2×D4—44no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—22no—
1242C22×C4—22no—
1243C22×C4—22no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—24no—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—24no—
1253C22×C4—24no—
1254C22×C4—24no—
1255C22×C4—24no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—22no—
1261C22×C4—22no—
1262C22×C4—24no—
1263C22×C4—22no—
1264C22×C4—24no—
1265C22×C4—24no—
1266C22×C4—42no—
1267C22×C4—42no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—42no—
1271C22×C4—42no—
1272C22×C4—42no—
1273C22×C4—42no—
1274C22×C4—42no—
1275C22×C4—42no—
1276C22×C4—42no—
1277C22×C4—42no—
1278C22×C4—44no—
1279C22×C4—44no—
1280C22×C4—44no—
1281C22×C4—44no—
1282C22×C4—44no—
1283C22×C4—44no—
1284C22×C4C2511yescharacteristic
1285C22×C4C2512yes—
1286C22×C4C2512yes—
1287C22×C4C2511yescharacteristic
1288C22×C4C2511yescharacteristic
1289C22×C4C2511yescharacteristic
1290C22×C4C2512yes—
1291C22×C4C2514yes—
1292C22×C4C2514yes—
1293C22×C4C2512yes—
1294C22×C4C2512yes—
1295C22×C4C2512yes—
1296C22×C4C2512yes—
1297C22×C4C2512yes—
1298C22×C4C2512yes—
1299C22×C4C2511yescharacteristic
1300C22×C4C2514yes—
1301C22×C4C2512yes—
1302C22×C4C2511yescharacteristic
1303C22×C4C2512yes—
1304C22×C4C2514yes—
1305C22×C4C2511yescharacteristic
1306C22×C4C2511yescharacteristic
1307C22×C4C2512yes—
1308C22×C4C2512yes—
1309C22×C4C2511yescharacteristic
1310C22×C4C2511yescharacteristic
1311C22×C4C2511yescharacteristic
1312C22×C4C2511yescharacteristic
1313C22×C4C2511yescharacteristic
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—24no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—22no—
1320C4⋊C4—24no—
1321C4⋊C4—24no—
1322C4⋊C4—22no—
1323C4⋊C4—24no—
1324C4⋊C4—24no—
1325C4⋊C4—22no—
1326C4⋊C4—24no—
1327C4⋊C4—24no—
1328C4⋊C4—24no—
1329C4⋊C4—22no—
1330C4⋊C4—24no—
1331C4⋊C4—24no—
1332C4⋊C4—24no—
1333C4⋊C4—24no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—24no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—44no—
1340C4⋊C4—44no—
1341C4⋊C4—44no—
1342C4⋊C4—42no—
1343C4⋊C4—42no—
1344C4⋊C4—44no—
1345C4⋊C4—42no—
1346C4⋊C4—42no—
1347C4⋊C4—42no—
1348C4⋊C4—42no—
1349C4⋊C4—42no—
1350C4⋊C4—42no—
1351C4⋊C4—42no—
1352C4⋊C4—42no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—41no—
1357C4⋊C4—41no—
1358C4⋊C4—42no—
1359C4⋊C4—42no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—44no—
1363C4⋊C4—44no—
1364C4⋊C4—44no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—42no—
1370C4⋊C4—44no—
1371C4⋊C4—44no—
1372C4⋊C4—44no—
1373C4⋊C4—44no—
1374C4⋊C4—44no—
1375C4⋊C4—44no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—44no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—44no—
1387C4⋊C4—44no—
1388C22⋊C4—24no—
1389C22⋊C4—24no—
1390C22⋊C4—24no—
1391C22⋊C4—24no—
1392C22⋊C4—22no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—42no—
1396C22⋊C4—42no—
1397C22⋊C4—44no—
1398C22⋊C4—42no—
1399C22⋊C4—42no—
1400C22⋊C4—42no—
1401C22⋊C4—42no—
1402C22⋊C4—42no—
1403C22⋊C4—42no—
1404C22⋊C4—42no—
1405C22⋊C4—42no—
1406C22⋊C4—44no—
1407C22⋊C4—44no—
1408C22⋊C4—44no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—41no—
1413C22⋊C4—42no—
1414C22⋊C4—41no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—44no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—41no—
1421C22⋊C4—41no—
1422C22⋊C4—42no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—44no—
1428C22⋊C4—44no—
1429C22⋊C4—44no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—44no—
1433C22⋊C4—44no—
1434C22⋊C4—42no—
1435C22⋊C4—44no—
1436C22⋊C4—44no—
1437C22⋊C4—42no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C42−1+414yes—
1451C42—22no—
1452C42—22no—
1453C42—22no—
1454C42—22no—
1455C42—22no—
1456C42—22no—
1457C42—24no—
1458C42—24no—
1459C42—24no—
1460C42—22no—
1461C42—22no—
1462C42—24no—
1463C42—22no—
1464C42—24no—
1465C42—22no—
1466C42—22no—
1467C42—42no—
1468C42—42no—
1469C42—42no—
1470C42—42no—
1471C42—44no—
1472C42—44no—
1473C42—44no—
1474C42—44no—
1475C42—44no—
1476C42—44no—
1477C42—41no—
1478C42—44no—
1479C42H(5,𝔽2)14yes—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—22no—
1487C23—22no—
1488C23—22no—
1489C23—21no—
1490C23—21no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—22no—
1495C23—21no—
1496C23—22no—
1497C23—22no—
1498C23—21no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—21no—
1503C23—22no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—21no—
1509C23—22no—
1510C23—21no—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23C2×2−1+412yes—
1515C23C2611yescharacteristic
1516Q8—44no—
1517Q8—48no—
1518Q8—44no—
1519Q8—44no—
1520D4—44no—
1521D4—48no—
1522D4—48no—
1523D4—44no—
1524D4—44no—
1525D4—44no—
1526D4—84no—
1527D4—84no—
1528D4—84no—
1529D4—84no—
1530D4—88no—
1531D4—84no—
1532D4—84no—
1533D4—164no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—22no—
1546C2×C4—22no—
1547C2×C4—22no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—22no—
1551C2×C4—22no—
1552C2×C4—22no—
1553C2×C4—22no—
1554C2×C4—24no—
1555C2×C4—21no—
1556C2×C4—22no—
1557C2×C4—21no—
1558C2×C4—22no—
1559C2×C4—22no—
1560C2×C4—22no—
1561C2×C4—22no—
1562C2×C4—22no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—21no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—24no—
1576C2×C4—24no—
1577C2×C4—24no—
1578C2×C4—24no—
1579C2×C4—22no—
1580C2×C4—22no—
1581C2×C4—22no—
1582C2×C4—24no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—21no—
1586C2×C4—24no—
1587C2×C4—24no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—24no—
1594C2×C4—21no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—22no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—24no—
1607C2×C4—21no—
1608C2×C4—24no—
1609C2×C4—24no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—21no—
1614C2×C4—22no—
1615C2×C4—44no—
1616C2×C4—44no—
1617C2×C4—48no—
1618C2×C4—48no—
1619C2×C4—44no—
1620C2×C4—48no—
1621C2×C4—48no—
1622C2×C4—44no—
1623C2×C4—48no—
1624C2×C4—44no—
1625C2×C4—44no—
1626C2×C4—84no—
1627C2×C4—84no—
1628C2×C4—164no—
1629C2×C4—164no—
1630C2×C4C2×H(5,𝔽2)12yes—
1631C2×C4C2×H(5,𝔽2)12yes—
1632C2×C4C2×H(5,𝔽2)12yes—
1633C2×C4C2×2−1+412yes—
1634C2×C4C2×2−1+412yes—
1635C2×C4#58512yes—
1636C2×C4#58512yes—
1637C2×C4#58512yes—
1638C2×C4#58512yes—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—42no—
1647C22—42no—
1648C22—41no—
1649C22—41no—
1650C22—42no—
1651C22—42no—
1652C22—42no—
1653C22—42no—
1654C22—41no—
1655C22—42no—
1656C22—42no—
1657C22—42no—
1658C22—42no—
1659C22—42no—
1660C22—41no—
1661C22—42no—
1662C22—42no—
1663C22—42no—
1664C22—42no—
1665C22—41no—
1666C22—41no—
1667C22—42no—
1668C22—42no—
1669C22—42no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—41no—
1674C22C22×H(5,𝔽2)11yescharacteristic
1675C22C22×2−1+411yescharacteristic
1676C22C2×#58511yescharacteristic
1677C22C2×#58511yescharacteristic
1678C22C2×#58511yescharacteristic
1679C22C2×#58511yescharacteristic
1680C22H(7,𝔽2)11yescharacteristic
1681C4—22no—
1682C4—22no—
1683C4—22no—
1684C4—41no—
1685C4—41no—
1686C4—42no—
1687C4—42no—
1688C4—42no—
1689C4—41no—
1690C4—41no—
1691C4—42no—
1692C4—42no—
1693C4—42no—
1694C4—44no—
1695C4—42no—
1696C4—41no—
1697C4—42no—
1698C4—41no—
1699C4—42no—
1700C4—44no—
1701C4—42no—
1702C4—41no—
1703C4—42no—
1704C4—42no—
1705C4—42no—
1706C4—44no—
1707C4—44no—
1708C4—41no—
1709C4#353914yes—
1710C4#353914yes—
1711C2—42no—
1712C2—81no—
1713C2—82no—
1714C2—82no—
1715C2—82no—
1716C2C2×#353911yescharacteristic
1717C2C2×#353911yescharacteristic
1718C2#6276111yescharacteristic
1719C2#6293811yescharacteristic
1720C2#6294411yescharacteristic
1721C2#6296611yescharacteristic
1722C2#6302511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59821C2semidirect
2. #59753C2semidirect
3. #59393C2semidirect
4. #59302C2semidirect
5. #59219C2semidirect
6. #58350C2semidirect
7. #54298C2semidirect
8. #53152C2semidirect
9. #53098C2semidirect
10. #53066C2semidirect
11. #53051C2semidirect
12. #52506C2semidirect
13. #42935C2semidirect
14. #42870C2semidirect
15. #42752C2semidirect
16. #42690C2semidirect
17. #40807C2semidirect
18. #39822C2semidirect
19. #39664C2semidirect
20. #39212C2semidirect
21. #39191C2semidirect
22. #39136C2semidirect
23. #39054C2semidirect
24. #38976C2semidirect
25. #38923C2semidirect
26. #37628C2semidirect
27. #37620C2semidirect
28. #37524C2semidirect
29. #37510C2semidirect
30. #36504C2semidirect
31. #36405C2semidirect
32. #36189C2semidirect
33. #34976C2semidirect
34. #34727C2semidirect
35. #34724C2semidirect

Maximal subgroups

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

subgroupindex
#598212
#597532
#593932
#593022
#592192
#583502
#542982
#531522
#530982
#530662
#530512
#525062
#429352
#428702
#427522
#426902
#408072
#398222
#396642
#392122
#391912
#391362
#390542
#389762
#389232
#376282
#376202
#375242
#375102
#365042
#364052
#361892
#349762
#347272
#347242