Finite Group Databasebeta

← #8429256

Subgroups — #8429256

Order 512.

4909 conjugacy classes of subgroups.

The subgroup lattice has 1756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59646C211yesmaximal, characteristic, complemented
2#59462C212yesmaximal, complemented
3#59398C212yesmaximal, complemented
4#59084C211yesmaximal, characteristic, complemented
5#59057C211yesmaximal, characteristic, complemented
6#56687C214yesmaximal, complemented
7#55622C214yesmaximal, complemented
8#53101C212yesmaximal, complemented
9#53084C212yesmaximal, complemented
10#53057C212yesmaximal, complemented
11#53044C212yesmaximal, complemented
12#52334C214yesmaximal, complemented
13#42923C212yesmaximal, complemented
14#42895C212yesmaximal, complemented
15#42892C212yesmaximal, complemented
16#42658C212yesmaximal, complemented
17#40497C214yesmaximal, complemented
18#39617C211yesmaximal, characteristic, complemented
19#39607C211yesmaximal, characteristic, complemented
20#39560C212yesmaximal, complemented
21#39514C211yesmaximal, characteristic, complemented
22#39470C211yesmaximal, characteristic, complemented
23#39400C212yesmaximal, complemented
24#39397C212yesmaximal, complemented
25#39287C212yesmaximal, complemented
26#37639C211yesmaximal, characteristic, complemented
27#37625C211yesmaximal, characteristic, complemented
28#37591C212yesmaximal, complemented
29#37512C212yesmaximal, complemented
30#36459C211yesmaximal, characteristic, complemented
31#36456C211yesmaximal, characteristic, complemented
32#36127C211yesmaximal, characteristic, complemented
33#34977C211yesmaximal, characteristic, complemented
34#34793C211yesmaximal, characteristic, complemented
35#34715C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic
37C2×#554C2211yescharacteristic
38C2×#547C2212yes—
39C2×#539C2214yes—
40C2×#532C2211yescharacteristic
41C2×#532C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×C4×#41C2211yescharacteristic
44#2868C2211yescharacteristic
45#2860C2212yes—
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2212yes—
49#2832C2214yes—
50#2831C2214yes—
51#2830C2214yes—
52#2830C2214yes—
53#2829C2214yes—
54#2829C2214yes—
55#2829C2214yes—
56#2829C2214yes—
57#2829C2214yes—
58#2828C2214yes—
59#2819C2214yes—
60#2816C2214yes—
61#2814C2214yes—
62#2813C2214yes—
63#2803C2214yes—
64#2803C2214yes—
65#2803C2214yes—
66#2800C2214yes—
67#2778C2214yes—
68#2770C2214yes—
69#2768C2214yes—
70#2761C2214yes—
71#2759C2214yes—
72#2756C2214yes—
73#2755C2214yes—
74#2753C2214yes—
75#2742C2214yes—
76#2741C2214yes—
77#2731C2214yes—
78#2730C2214yes—
79#2730C2214yes—
80#2716C2214yes—
81#2716C2214yes—
82#2714C2214yes—
83#2714C2214yes—
84#2711C2214yes—
85#2708C2214yes—
86#2707C2214yes—
87#2705C2214yes—
88#2704C2214yes—
89#2700C2214yes—
90#2696C2214yes—
91#2695C2214yes—
92#2690C2214yes—
93#2687C2214yes—
94#2682C2214yes—
95#2681C2214yes—
96#2681C2214yes—
97#2677C2214yes—
98#2677C2214yes—
99#2676C2214yes—
100#2662C2214yes—
101#2661C2214yes—
102#2661C2214yes—
103#2660C2212yes—
104#2651C2214yes—
105#2648C2214yes—
106#2648C2214yes—
107#2644C2212yes—
108#2641C2212yes—
109#2638C2214yes—
110#2636C2214yes—
111#2630C2214yes—
112#2630C2214yes—
113#2629C2212yes—
114#2629C2212yes—
115#2624C2212yes—
116#2620C2212yes—
117#2619C2212yes—
118#2619C2212yes—
119#2616C2212yes—
120#2615C2214yes—
121#2615C2212yes—
122#2615C2212yes—
123#2610C2214yes—
124#2602C2214yes—
125#2602C2214yes—
126#2597C2214yes—
127#2589C2214yes—
128#2578C2214yes—
129#2574C2214yes—
130#2574C2214yes—
131#2570C2212yes—
132#2570C2212yes—
133#2567C2211yescharacteristic
134#2565C2212yes—
135#2563C2212yes—
136#2563C2211yescharacteristic
137#2563C2211yescharacteristic
138#2563C2211yescharacteristic
139#2563C2212yes—
140#2560C2214yes—
141#2559C2214yes—
142#2554C2214yes—
143#2552C2211yescharacteristic
144#2552C2212yes—
145#2550C2212yes—
146#2548C2212yes—
147#2548C2211yescharacteristic
148#2548C2211yescharacteristic
149#2547C2212yes—
150#2542C2212yes—
151#2541C2212yes—
152#2541C2211yescharacteristic
153#2541C2211yescharacteristic
154#2540C2212yes—
155#2538C2211yescharacteristic
156#2538C2212yes—
157#2537C2212yes—
158#2537C2212yes—
159#2537C2212yes—
160#2537C2212yes—
161#2532C2214yes—
162#2530C2212yes—
163#2528C2212yes—
164#2522C2214yes—
165#2517C2212yes—
166#2513C2212yes—
167#2512C2212yes—
168#2512C2212yes—
169#2511C2211yescharacteristic
170#2507C2212yes—
171#2506C2212yes—
172#2506C2211yescharacteristic
173#2500C2212yes—
174#2500C2212yes—
175#2499C2211yescharacteristic
176#2497C2212yes—
177#2497C2212yes—
178#2496C2212yes—
179#2496C2212yes—
180#2496C2212yes—
181#2495C2212yes—
182#2494C2211yescharacteristic
183#2491C2212yes—
184#2491C2212yes—
185#2490C2212yes—
186#2490C2212yes—
187#2490C2212yes—
188#2490C2212yes—
189#2489C2211yescharacteristic
190#2486C2212yes—
191#2485C2212yes—
192#2485C2211yescharacteristic
193#2476C2212yes—
194#2474C2212yes—
195#2473C2214yes—
196#2468C2214yes—
197#2466C2214yes—
198#2463C2214yes—
199#2461C2214yes—
200#2460C2212yes—
201#2459C2212yes—
202#2456C2212yes—
203#2454C2212yes—
204#2454C2212yes—
205#2453C2212yes—
206#2452C2214yes—
207#2452C2212yes—
208#2452C2212yes—
209#2452C2212yes—
210#2451C2211yescharacteristic
211#2445C2212yes—
212#2445C2212yes—
213#2445C2212yes—
214#2445C2211yescharacteristic
215#2443C2214yes—
216#2441C2211yescharacteristic
217#2440C2212yes—
218#2440C2212yes—
219#2439C2212yes—
220#2439C2214yes—
221#2439C2211yescharacteristic
222#2432C2212yes—
223#2432C2212yes—
224#2432C2214yes—
225#2431C2212yes—
226#2431C2211yescharacteristic
227#2428C2212yes—
228#2427C2212yes—
229#2427C2212yes—
230#2426C2212yes—
231#2426C2211yescharacteristic
232#2426C2212yes—
233#2423C2212yes—
234#2423C2212yes—
235#2422C2212yes—
236#2422C2212yes—
237#2422C2212yes—
238#2422C2212yes—
239#2422C2212yes—
240#2422C2212yes—
241#2420C2212yes—
242#2420C2211yescharacteristic
243#2416C2212yes—
244#2415C2212yes—
245#2415C2211yescharacteristic
246#2414C2212yes—
247#2414C2211yescharacteristic
248#2414C2212yes—
249#2407C2214yes—
250#2407C2211yescharacteristic
251#2401C2212yes—
252#2395C2212yes—
253#2392C2212yes—
254#2388C2214yes—
255#2388C2212yes—
256#2369C2211yescharacteristic
257#2369C2211yescharacteristic
258#2367C2212yes—
259#2367C2212yes—
260#2367C2212yes—
261#2366C2212yes—
262#2363C2212yes—
263#2361C2212yes—
264#2354C2211yescharacteristic
265#2354C2212yes—
266#2351C2212yes—
267Q8×C4⋊C4C2211yescharacteristic
268D4×C4⋊C4C2212yes—
269D4×C4⋊C4C2212yes—
270#2347C2212yes—
271#2345C2214yes—
272#2341C2212yes—
273#2326C2212yes—
274#2323C2212yes—
275#2314C2212yes—
276#2311C2212yes—
277C4×#127C2211yescharacteristic
278C4×#127C2212yes—
279C4×#125C2212yes—
280C4×#125C2212yes—
281C4×#125C2211yescharacteristic
282C4×#124C2212yes—
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2212yes—
285C4×C22⋊Q8C2211yescharacteristic
286C4×C22⋊Q8C2211yescharacteristic
287C4×C22⋊Q8C2211yescharacteristic
288C4×#123C2212yes—
289C4×#121C2212yes—
290C4×#121C2211yescharacteristic
291C4×#121C2212yes—
292#2298C2212yes—
293#2297C2212yes—
294#2295C2211yescharacteristic
295#2293C2211yescharacteristic
296#2285C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303Q82—44no—
304#554—44no—
305#547—48no—
306#539—416no—
307#532—44no—
308#532—44no—
309#532—44no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2312yes—
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2314yes—
317C2×C4⋊Q8C2312yes—
318C2×#127C2311yescharacteristic
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2311yescharacteristic
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#126C2314yes—
325C2×#125C2312yes—
326C2×#125C2311yescharacteristic
327C2×#125C2312yes—
328C2×#125C2312yes—
329C2×#125C2314yes—
330C2×#124C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2314yes—
337C2×#123C2312yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2314yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2314yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2314yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2314yes—
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2314yes—
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2314yes—
362C2×#121C2311yescharacteristic
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2311yescharacteristic
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2314yes—
371C4×#41—44no—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2314yes—
399C2×#117C2312yes—
400C2×#117C2312yes—
401C2×#117C2312yes—
402C2×#117C2311yescharacteristic
403C2×#117C2312yes—
404C2×#117C2311yescharacteristic
405C2×#117C2311yescharacteristic
406C22×C4⋊C4C2314yes—
407C22×C4⋊C4C2312yes—
408C22×C42C2311yescharacteristic
409C22×C42C2311yescharacteristic
410C22×C42C2312yes—
411#401C2312yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2312yes—
419#400C2312yes—
420#400C2312yes—
421#399C2312yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#399C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2314yes—
435#398C2312yes—
436#398C2312yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#397C2314yes—
441#397C2312yes—
442#397C2314yes—
443#397C2312yes—
444#397C2312yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2312yes—
452#397C2314yes—
453#397C2314yes—
454#397C2314yes—
455#397C2314yes—
456#397C2312yes—
457#397C2314yes—
458#397C2314yes—
459#397C2312yes—
460#397C2312yes—
461#396C2314yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2312yes—
474#396C2312yes—
475#396C2312yes—
476#395C2314yes—
477#395C2312yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#394C2314yes—
482#394C2312yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2312yes—
497#394C2312yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2312yes—
516#394C2312yes—
517#394C2312yes—
518#394C2312yes—
519#394C2314yes—
520#393C2314yes—
521#393C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2314yes—
525#393C2314yes—
526#393C2314yes—
527#393C2314yes—
528#393C2312yes—
529#393C2314yes—
530#392C2314yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2312yes—
535#392C2314yes—
536#392C2314yes—
537#392C2314yes—
538#392C2314yes—
539#392C2314yes—
540#392C2314yes—
541#392C2312yes—
542#392C2314yes—
543#392C2312yes—
544#392C2312yes—
545#391C2314yes—
546#391C2311yescharacteristic
547#391C2312yes—
548#391C2314yes—
549#391C2312yes—
550#391C2312yes—
551#391C2314yes—
552#391C2312yes—
553#391C2312yes—
554#391C2311yescharacteristic
555#391C2311yescharacteristic
556#391C2311yescharacteristic
557#391C2314yes—
558#391C2311yescharacteristic
559#391C2311yescharacteristic
560#390C2314yes—
561#390C2312yes—
562#390C2312yes—
563#390C2314yes—
564#390C2314yes—
565#390C2312yes—
566#390C2312yes—
567#390C2312yes—
568#390C2314yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2314yes—
574#390C2314yes—
575#390C2312yes—
576#390C2314yes—
577#390C2312yes—
578#390C2314yes—
579#390C2312yes—
580#390C2314yes—
581#390C2311yescharacteristic
582#390C2312yes—
583#390C2312yes—
584#390C2312yes—
585#390C2312yes—
586#390C2314yes—
587#390C2312yes—
588#390C2311yescharacteristic
589#390C2314yes—
590#390C2311yescharacteristic
591#390C2312yes—
592#390C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2311yescharacteristic
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2311yescharacteristic
602#389C2311yescharacteristic
603#389C2312yes—
604#389C2312yes—
605#389C2312yes—
606#389C2314yes—
607#389C2314yes—
608#389C2314yes—
609#389C2314yes—
610#389C2312yes—
611#389C2311yescharacteristic
612#389C2312yes—
613#389C2312yes—
614#389C2314yes—
615#389C2312yes—
616#389C2312yes—
617#389C2312yes—
618#389C2314yes—
619#389C2311yescharacteristic
620#389C2312yes—
621#389C2312yes—
622#389C2311yescharacteristic
623#389C2311yescharacteristic
624#389C2311yescharacteristic
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2312yes—
633#388C2312yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2312yes—
657#388C2312yes—
658#388C2312yes—
659#388C2312yes—
660#388C2312yes—
661#388C2312yes—
662#387C2314yes—
663#387C2314yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2312yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2312yes—
681#387C2314yes—
682#387C2312yes—
683#387C2312yes—
684#387C2312yes—
685#387C2312yes—
686#387C2312yes—
687#387C2312yes—
688#387C2312yes—
689#387C2312yes—
690#387C2312yes—
691#386C2312yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2312yes—
703#386C2312yes—
704#386C2312yes—
705#386C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2312yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2314yes—
713#385C2314yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2312yes—
720#385C2312yes—
721#385C2312yes—
722#384C2312yes—
723#384C2311yescharacteristic
724#384C2312yes—
725#384C2312yes—
726#384C2312yes—
727#384C2312yes—
728#384C2312yes—
729#384C2312yes—
730#384C2311yescharacteristic
731#384C2311yescharacteristic
732#383C2314yes—
733#382C2312yes—
734#382C2311yescharacteristic
735#382C2312yes—
736#382C2312yes—
737#382C2312yes—
738#382C2314yes—
739#382C2312yes—
740#382C2311yescharacteristic
741#381C2314yes—
742#381C2312yes—
743#380C2312yes—
744#380C2311yescharacteristic
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2314yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2314yes—
753#380C2312yes—
754#380C2311yescharacteristic
755#380C2312yes—
756#380C2314yes—
757#380C2314yes—
758#380C2314yes—
759#380C2312yes—
760#380C2312yes—
761#380C2314yes—
762#380C2314yes—
763#380C2312yes—
764#380C2311yescharacteristic
765#380C2312yes—
766#380C2311yescharacteristic
767#380C2311yescharacteristic
768#380C2311yescharacteristic
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2314yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2314yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812C4×C22⋊C4C2311yescharacteristic
813C4×C22⋊C4C2311yescharacteristic
814#376C2312yes—
815#376C2312yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C2×#41—24no—
819C2×#41—44no—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—42no—
825C2×#41—42no—
826C2×#41—44no—
827C2×#41—44no—
828C2×#41—82no—
829C2×#41—82no—
830C22×Q8C2411yescharacteristic
831C22×Q8C2411yescharacteristic
832C22×Q8C2412yes—
833C22×Q8C2412yes—
834C22×Q8C2414yes—
835C22×Q8C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C23×C4C2412yes—
855C23×C4C2411yescharacteristic
856C23×C4C2411yescharacteristic
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2412yes—
866C23×C4C2412yes—
867C23×C4C2414yes—
868C4⋊Q8—24no—
869C4⋊Q8—24no—
870C4⋊Q8—42no—
871C4⋊Q8—44no—
872C4⋊Q8—44no—
873C4⋊Q8—44no—
874C4⋊Q8—48no—
875C4⋊Q8—82no—
876#127—24no—
877#127—44no—
878#127—44no—
879#127—42no—
880#126—48no—
881#126—48no—
882#126—84no—
883#125—28no—
884#125—42no—
885#125—44no—
886#125—44no—
887#125—48no—
888#124—24no—
889#124—28no—
890#124—44no—
891#124—44no—
892#124—44no—
893#124—44no—
894#124—84no—
895#123—28no—
896#123—48no—
897#123—48no—
898#123—48no—
899#123—48no—
900#123—48no—
901C22⋊Q8—24no—
902C22⋊Q8—48no—
903C22⋊Q8—48no—
904C22⋊Q8—48no—
905C22⋊Q8—48no—
906C22⋊Q8—44no—
907C22⋊Q8—44no—
908C22⋊Q8—44no—
909C22⋊Q8—42no—
910C22⋊Q8—42no—
911C22⋊Q8—44no—
912C22⋊Q8—84no—
913#121—44no—
914#121—44no—
915#121—44no—
916#121—44no—
917#121—44no—
918#121—42no—
919#121—44no—
920#121—42no—
921#121—42no—
922#121—44no—
923#121—44no—
924#121—44no—
925#121—48no—
926#121—48no—
927#121—84no—
928#121—84no—
929C4×Q8—24no—
930C4×Q8—24no—
931C4×Q8—44no—
932C4×Q8—42no—
933C4×Q8—44no—
934C4×Q8—44no—
935C4×D4—24no—
936C4×D4—24no—
937C4×D4—24no—
938C4×D4—44no—
939C4×D4—44no—
940C4×D4—42no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—44no—
947C4×D4—42no—
948C4×D4—42no—
949C4×D4—44no—
950C4×D4—44no—
951C4×D4—48no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—48no—
955C4×D4—84no—
956#117—44no—
957#117—44no—
958#117—44no—
959#117—44no—
960#117—42no—
961#117—42no—
962#117—42no—
963C2×C4⋊C4—216no—
964C2×C4⋊C4—44no—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2414yes—
968C2×C4⋊C4C2414yes—
969C2×C4⋊C4C2414yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2411yescharacteristic
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2412yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2411yescharacteristic
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2414yes—
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2412yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2412yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2414yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2414yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2411yescharacteristic
1065C2×C22⋊C4C2411yescharacteristic
1066C2×C22⋊C4C2411yescharacteristic
1067C2×C22⋊C4C2411yescharacteristic
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2412yes—
1096C2×C42—24no—
1097C2×C42—24no—
1098C2×C42—44no—
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2412yes—
1103C2×C42C2412yes—
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2411yescharacteristic
1109C2×C42C2412yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2414yes—
1121C2×C42C2412yes—
1122C2×C42C2412yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2411yescharacteristic
1128C2×C42C2411yescharacteristic
1129#95C2412yes—
1130#95C2412yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2412yes—
1135#95C2412yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2411yescharacteristic
1140#95C2411yescharacteristic
1141#95C2411yescharacteristic
1142#95C2411yescharacteristic
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2411yescharacteristic
1147#95C2411yescharacteristic
1148#95C2412yes—
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2414yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2414yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193C24C2512yes—
1194C24C2512yes—
1195C24C2511yescharacteristic
1196C24C2511yescharacteristic
1197C24C2514yes—
1198#41—416no—
1199#41—816no—
1200#41—816no—
1201#41—816no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—24no—
1205C2×Q8—24no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—42no—
1210C2×Q8—42no—
1211C2×Q8—42no—
1212C2×Q8—42no—
1213C2×Q8—42no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8—44no—
1217C2×Q8—44no—
1218C2×Q8—44no—
1219C2×Q82−1+414yes—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—22no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—22no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—24no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—42no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—42no—
1245C2×D4—42no—
1246C2×D4—44no—
1247C2×D4—42no—
1248C2×D4—44no—
1249C2×D4—42no—
1250C2×D4—44no—
1251C2×D4—44no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—42no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—44no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—24no—
1281C22×C4—24no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—24no—
1286C22×C4—22no—
1287C22×C4—22no—
1288C22×C4—22no—
1289C22×C4—22no—
1290C22×C4—24no—
1291C22×C4—24no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—24no—
1296C22×C4—22no—
1297C22×C4—28no—
1298C22×C4—28no—
1299C22×C4—28no—
1300C22×C4—24no—
1301C22×C4—42no—
1302C22×C4—42no—
1303C22×C4—41no—
1304C22×C4—41no—
1305C22×C4—42no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—42no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4—44no—
1314C22×C4—44no—
1315C22×C4—44no—
1316C22×C4C2511yescharacteristic
1317C22×C4C2511yescharacteristic
1318C22×C4C2512yes—
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2511yescharacteristic
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2512yes—
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2511yescharacteristic
1332C22×C4C2511yescharacteristic
1333C22×C4C2512yes—
1334C22×C4C2514yes—
1335C22×C4C2514yes—
1336C22×C4C2512yes—
1337C22×C4C2514yes—
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C22×C4C2511yescharacteristic
1343C22×C4C2512yes—
1344C22×C4C2511yescharacteristic
1345C22×C4C2511yescharacteristic
1346C4⋊C4—28no—
1347C4⋊C4—28no—
1348C4⋊C4—28no—
1349C4⋊C4—22no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—24no—
1353C4⋊C4—22no—
1354C4⋊C4—22no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—24no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—22no—
1366C4⋊C4—24no—
1367C4⋊C4—22no—
1368C4⋊C4—24no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—24no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—44no—
1377C4⋊C4—42no—
1378C4⋊C4—42no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—41no—
1383C4⋊C4—41no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—44no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—44no—
1396C4⋊C4—42no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—42no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4—44no—
1407C4⋊C4—44no—
1408C4⋊C4—42no—
1409C4⋊C4—44no—
1410C4⋊C4H(5,𝔽2)14yes—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—24no—
1418C22⋊C4—24no—
1419C22⋊C4—28no—
1420C22⋊C4—24no—
1421C22⋊C4—24no—
1422C22⋊C4—28no—
1423C22⋊C4—42no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—42no—
1427C22⋊C4—44no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—42no—
1431C22⋊C4—42no—
1432C22⋊C4—41no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—41no—
1436C22⋊C4—41no—
1437C22⋊C4—41no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—44no—
1441C22⋊C4—42no—
1442C22⋊C4—44no—
1443C22⋊C4—42no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—44no—
1462C22⋊C4—42no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—42no—
1471C22⋊C4—44no—
1472C22⋊C4—44no—
1473C22⋊C4—44no—
1474C22⋊C4—42no—
1475C22⋊C4—42no—
1476C22⋊C4—42no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—22no—
1483C42—24no—
1484C42—22no—
1485C42—24no—
1486C42—24no—
1487C42—22no—
1488C42—24no—
1489C42—22no—
1490C42—24no—
1491C42—24no—
1492C42—24no—
1493C42—22no—
1494C42—22no—
1495C42—42no—
1496C42—42no—
1497C42—44no—
1498C42—42no—
1499C42—42no—
1500C42—44no—
1501C42—42no—
1502C42—44no—
1503C42—44no—
1504C42—44no—
1505C42—41no—
1506C42H(5,𝔽2)14yes—
1507C23—22no—
1508C23—22no—
1509C23—21no—
1510C23—21no—
1511C23—22no—
1512C23—22no—
1513C23—24no—
1514C23—24no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—22no—
1519C23—24no—
1520C23—22no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—21no—
1525C23—24no—
1526C23—24no—
1527C23—21no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—21no—
1532C23—21no—
1533C23—22no—
1534C23—24no—
1535C23—22no—
1536C23—22no—
1537C23—22no—
1538C23—21no—
1539C23—22no—
1540C23—24no—
1541C23—21no—
1542C23C2611yescharacteristic
1543Q8—28no—
1544Q8—44no—
1545Q8—84no—
1546Q8—84no—
1547Q8—84no—
1548Q8—164no—
1549D4—44no—
1550D4—48no—
1551D4—48no—
1552D4—44no—
1553D4—48no—
1554D4—44no—
1555D4—48no—
1556D4—84no—
1557D4—88no—
1558D4—88no—
1559D4—84no—
1560D4—88no—
1561D4—84no—
1562D4—84no—
1563D4—84no—
1564D4—88no—
1565D4—88no—
1566D4—164no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—22no—
1589C2×C4—22no—
1590C2×C4—24no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—24no—
1597C2×C4—24no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—22no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—24no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—24no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—24no—
1646C2×C4—44no—
1647C2×C4—44no—
1648C2×C4—48no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—44no—
1652C2×C4—48no—
1653C2×C4—48no—
1654C2×C4—44no—
1655C2×C4—88no—
1656C2×C4—84no—
1657C2×C4—88no—
1658C2×C4—88no—
1659C2×C4—164no—
1660C2×C4C2×H(5,𝔽2)12yes—
1661C2×C4C2×H(5,𝔽2)12yes—
1662C2×C4C2×H(5,𝔽2)12yes—
1663C2×C4C2×H(5,𝔽2)12yes—
1664C2×C4C2×H(5,𝔽2)12yes—
1665C2×C4C2×H(5,𝔽2)12yes—
1666C2×C4C2×2−1+414yes—
1667C2×C4C2×2−1+412yes—
1668C2×C4#58512yes—
1669C2×C4#58512yes—
1670C2×C4#58512yes—
1671C22—42no—
1672C22—41no—
1673C22—41no—
1674C22—42no—
1675C22—44no—
1676C22—41no—
1677C22—42no—
1678C22—42no—
1679C22—41no—
1680C22—44no—
1681C22—44no—
1682C22—41no—
1683C22—41no—
1684C22—42no—
1685C22—42no—
1686C22—42no—
1687C22—42no—
1688C22—41no—
1689C22—41no—
1690C22—44no—
1691C22—41no—
1692C22—41no—
1693C22—44no—
1694C22—42no—
1695C22—42no—
1696C22—41no—
1697C22—42no—
1698C22—42no—
1699C22—44no—
1700C22—41no—
1701C22—41no—
1702C22—44no—
1703C22—42no—
1704C22—41no—
1705C22—42no—
1706C22C22×H(5,𝔽2)11yescharacteristic
1707C22C22×H(5,𝔽2)11yescharacteristic
1708C22C22×2−1+411yescharacteristic
1709C22C2×#58511yescharacteristic
1710C22C2×#58511yescharacteristic
1711C22C2×#58511yescharacteristic
1712C22H(7,𝔽2)11yescharacteristic
1713C4—24no—
1714C4—22no—
1715C4—22no—
1716C4—22no—
1717C4—22no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—42no—
1723C4—42no—
1724C4—42no—
1725C4—44no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—42no—
1730C4—42no—
1731C4—44no—
1732C4—44no—
1733C4—42no—
1734C4—42no—
1735C4—41no—
1736C4—42no—
1737C4—42no—
1738C4—42no—
1739C4—41no—
1740C4—42no—
1741C4#354114yes—
1742C4#356214yes—
1743C2—82no—
1744C2—81no—
1745C2—81no—
1746C2—82no—
1747C2—84no—
1748C2C2×#354111yescharacteristic
1749C2C2×#356211yescharacteristic
1750C2#6275911yescharacteristic
1751C2#6291211yescharacteristic
1752C2#6293811yescharacteristic
1753C2#6295211yescharacteristic
1754C2#6303911yescharacteristic
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. #59646C2semidirect
2. #59462C2semidirect
3. #59398C2semidirect
4. #59084C2semidirect
5. #59057C2semidirect
6. #56687C2semidirect
7. #55622C2semidirect
8. #53101C2semidirect
9. #53084C2semidirect
10. #53057C2semidirect
11. #53044C2semidirect
12. #52334C2semidirect
13. #42923C2semidirect
14. #42895C2semidirect
15. #42892C2semidirect
16. #42658C2semidirect
17. #40497C2semidirect
18. #39617C2semidirect
19. #39607C2semidirect
20. #39560C2semidirect
21. #39514C2semidirect
22. #39470C2semidirect
23. #39400C2semidirect
24. #39397C2semidirect
25. #39287C2semidirect
26. #37639C2semidirect
27. #37625C2semidirect
28. #37591C2semidirect
29. #37512C2semidirect
30. #36459C2semidirect
31. #36456C2semidirect
32. #36127C2semidirect
33. #34977C2semidirect
34. #34793C2semidirect
35. #34715C2semidirect

Maximal subgroups

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

subgroupindex
#596462
#594622
#593982
#590842
#590572
#566872
#556222
#531012
#530842
#530572
#530442
#523342
#429232
#428952
#428922
#426582
#404972
#396172
#396072
#395602
#395142
#394702
#394002
#393972
#392872
#376392
#376252
#375912
#375122
#364592
#364562
#361272
#349772
#347932
#347152