Finite Group Databasebeta

← #7806306

Subgroups — #7806306

Order 512.

5106 conjugacy classes of subgroups.

The subgroup lattice has 1751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59856C212yesmaximal, complemented
2#59826C212yesmaximal, complemented
3#59677C212yesmaximal, complemented
4#59440C212yesmaximal, complemented
5#59321C211yesmaximal, characteristic, complemented
6#59312C211yesmaximal, characteristic, complemented
7#59305C211yesmaximal, characteristic, complemented
8#59305C212yesmaximal, complemented
9#59304C212yesmaximal, complemented
10#59304C211yesmaximal, characteristic, complemented
11#59249C211yesmaximal, characteristic, complemented
12#59235C211yesmaximal, characteristic, complemented
13#59218C211yesmaximal, characteristic, complemented
14#59217C211yesmaximal, characteristic, complemented
15#59140C212yesmaximal, complemented
16#59139C212yesmaximal, complemented
17#47755C214yesmaximal, complemented
18#47754C214yesmaximal, complemented
19#42460C212yesmaximal, complemented
20#42459C212yesmaximal, complemented
21#42456C212yesmaximal, complemented
22#42455C212yesmaximal, complemented
23#42022C214yesmaximal, complemented
24#37620C211yesmaximal, characteristic, complemented
25#35807C214yesmaximal, complemented
26#35745C212yesmaximal, complemented
27#35736C212yesmaximal, complemented
28#35708C212yesmaximal, complemented
29#35699C212yesmaximal, complemented
30#34964C211yesmaximal, characteristic, complemented
31#34964C211yesmaximal, characteristic, complemented
32C2×#2552C211yesmaximal, characteristic, complemented
33#34243C211yesmaximal, characteristic, complemented
34#34243C211yesmaximal, characteristic, complemented
35#34183C211yesmaximal, characteristic, complemented
36C2×#553C2212yes—
37C2×#553C2214yes—
38C2×#552C2212yes—
39C2×#529C2211yescharacteristic
40C2×#529C2211yescharacteristic
41C22×#125C2212yes—
42C2×#520C2212yes—
43C2×C4×#41C2211yescharacteristic
44#2839C2214yes—
45#2837C2214yes—
46#2823C2214yes—
47#2802C2214yes—
48#2800C2214yes—
49#2791C2214yes—
50#2790C2214yes—
51#2790C2214yes—
52#2790C2214yes—
53#2783C2214yes—
54#2781C2214yes—
55#2780C2214yes—
56#2779C2214yes—
57#2772C2214yes—
58#2767C2214yes—
59#2744C2214yes—
60#2739C2214yes—
61#2725C2214yes—
62#2725C2214yes—
63#2721C2214yes—
64#2719C2214yes—
65#2718C2214yes—
66#2718C2214yes—
67#2718C2214yes—
68#2711C2214yes—
69#2707C2214yes—
70#2701C2214yes—
71#2667C2214yes—
72#2664C2214yes—
73#2654C2214yes—
74#2652C2214yes—
75#2637C2214yes—
76#2630C2214yes—
77#2629C2212yes—
78#2629C2212yes—
79#2620C2212yes—
80#2620C2212yes—
81#2618C2214yes—
82#2609C2214yes—
83#2608C2214yes—
84#2601C2214yes—
85#2601C2214yes—
86#2601C2212yes—
87#2601C2212yes—
88#2601C2212yes—
89#2601C2212yes—
90#2592C2211yescharacteristic
91#2592C2211yescharacteristic
92#2590C2214yes—
93#2587C2214yes—
94#2585C2214yes—
95#2584C2211yescharacteristic
96#2584C2211yescharacteristic
97#2582C2211yescharacteristic
98#2579C2214yes—
99#2579C2214yes—
100#2579C2214yes—
101#2569C2214yes—
102#2566C2212yes—
103#2566C2214yes—
104#2565C2212yes—
105#2562C2212yes—
106#2562C2212yes—
107#2562C2211yescharacteristic
108#2562C2211yescharacteristic
109#2559C2214yes—
110#2558C2214yes—
111#2553C2214yes—
112#2552C2211yescharacteristic
113#2552C2211yescharacteristic
114#2552C2211yescharacteristic
115#2552C2211yescharacteristic
116#2552C2212yes—
117#2552C2212yes—
118#2552C2214yes—
119#2552C2212yes—
120#2552C2212yes—
121#2552C2212yes—
122#2552C2212yes—
123#2540C2211yescharacteristic
124#2540C2211yescharacteristic
125#2538C2212yes—
126#2538C2211yescharacteristic
127#2538C2211yescharacteristic
128#2537C2212yes—
129#2537C2211yescharacteristic
130#2522C2214yes—
131#2519C2214yes—
132#2512C2212yes—
133#2512C2212yes—
134#2511C2212yes—
135#2511C2212yes—
136#2509C2212yes—
137#2508C2212yes—
138#2507C2214yes—
139#2507C2212yes—
140#2506C2212yes—
141#2502C2212yes—
142#2502C2212yes—
143#2501C2212yes—
144#2501C2212yes—
145#2498C2212yes—
146#2498C2212yes—
147#2497C2212yes—
148#2497C2212yes—
149#2497C2212yes—
150#2497C2212yes—
151#2496C2212yes—
152#2496C2212yes—
153#2496C2212yes—
154#2496C2212yes—
155#2490C2212yes—
156#2490C2212yes—
157#2489C2212yes—
158#2489C2212yes—
159#2487C2214yes—
160#2487C2212yes—
161#2486C2212yes—
162#2485C2212yes—
163#2485C2212yes—
164#2481C2214yes—
165#2481C2214yes—
166#2478C2214yes—
167#2476C2214yes—
168#2475C2214yes—
169#2473C2214yes—
170#2470C2214yes—
171#2468C2214yes—
172#2466C2214yes—
173#2464C2214yes—
174#2462C2214yes—
175#2460C2214yes—
176#2458C2214yes—
177#2444C2214yes—
178#2444C2214yes—
179#2443C2214yes—
180#2443C2214yes—
181#2443C2214yes—
182#2442C2212yes—
183#2442C2214yes—
184#2442C2212yes—
185#2441C2212yes—
186#2441C2212yes—
187#2441C2214yes—
188#2430C2212yes—
189#2430C2212yes—
190#2423C2212yes—
191#2422C2214yes—
192#2422C2212yes—
193#2421C2212yes—
194#2420C2212yes—
195#2417C2211yescharacteristic
196#2417C2212yes—
197#2417C2211yescharacteristic
198#2417C2212yes—
199#2417C2212yes—
200#2417C2212yes—
201#2417C2211yescharacteristic
202#2417C2211yescharacteristic
203#2416C2211yescharacteristic
204#2416C2214yes—
205#2416C2212yes—
206#2416C2211yescharacteristic
207#2416C2212yes—
208#2416C2212yes—
209#2416C2212yes—
210#2416C2211yescharacteristic
211#2416C2211yescharacteristic
212#2413C2214yes—
213#2396C2212yes—
214#2396C2214yes—
215#2396C2212yes—
216#2392C2212yes—
217#2392C2214yes—
218#2392C2212yes—
219C2×#398C2214yes—
220#2370C2212yes—
221#2370C2212yes—
222#2370C2212yes—
223#2370C2212yes—
224#2367C2212yes—
225#2367C2212yes—
226#2364C2214yes—
227#2363C2212yes—
228#2362C2212yes—
229#2361C2214yes—
230#2361C2212yes—
231#2360C2212yes—
232#2359C2214yes—
233#2359C2214yes—
234#2355C2211yescharacteristic
235#2355C2212yes—
236#2355C2211yescharacteristic
237#2354C2211yescharacteristic
238#2354C2212yes—
239#2354C2211yescharacteristic
240#2352C2212yes—
241#2352C2214yes—
242#2352C2212yes—
243Q8×C4⋊C4C2211yescharacteristic
244Q8×C4⋊C4C2212yes—
245Q8×C4⋊C4C2212yes—
246Q8×C4⋊C4C2211yescharacteristic
247D4×C4⋊C4C2212yes—
248D4×C4⋊C4C2212yes—
249D4×C4⋊C4C2212yes—
250D4×C4⋊C4C2212yes—
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2212yes—
253D4×C4⋊C4C2212yes—
254D4×C4⋊C4C2212yes—
255D4×C4⋊C4C2212yes—
256D4×C4⋊C4C2211yescharacteristic
257D4×C4⋊C4C2212yes—
258D4×C4⋊C4C2212yes—
259#2345C2212yes—
260#2345C2212yes—
261#2344C2212yes—
262#2344C2212yes—
263#2334C2214yes—
264#2334C2214yes—
265#2317C2212yes—
266#2317C2212yes—
267#2317C2212yes—
268#2314C2212yes—
269#2314C2212yes—
270C4×C22⋊Q8C2212yes—
271C4×C22⋊Q8C2212yes—
272C4×C22⋊Q8C2211yescharacteristic
273C4×C22⋊Q8C2211yescharacteristic
274C4×C22⋊Q8C2211yescharacteristic
275C4×C22⋊Q8C2211yescharacteristic
276C4×#121C2212yes—
277C4×#121C2212yes—
278C4×#121C2212yes—
279C4×#121C2212yes—
280C4×#121C2212yes—
281C4×#121C2212yes—
282C4×#121C2211yescharacteristic
283C4×#121C2211yescharacteristic
284C4×#121C2211yescharacteristic
285C4×#121C2211yescharacteristic
286C2×#389C2212yes—
287C2×#389C2212yes—
288#2285C2211yescharacteristic
289#2285C2211yescharacteristic
290#2285C2211yescharacteristic
291C2×#384C2211yescharacteristic
292C2×#384C2212yes—
293C2×#384C2211yescharacteristic
294C2×#384C2211yescharacteristic
295#2274C2212yes—
296#2274C2212yes—
297C2×C4×C4⋊C4C2211yescharacteristic
298C2×C4×C4⋊C4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300#553—48no—
301#553—416no—
302#552—48no—
303#529—28no—
304#529—28no—
305C2×#126C2312yes—
306C2×#126C2312yes—
307C2×#126C2314yes—
308C2×#126C2314yes—
309C2×#126C2314yes—
310C2×#126C2314yes—
311C2×#125—48no—
312C2×#125C2311yescharacteristic
313C2×#125C2311yescharacteristic
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2314yes—
319C2×#125C2314yes—
320C2×#125C2314yes—
321C2×#125C2314yes—
322C2×#124C2311yescharacteristic
323C2×#124C2311yescharacteristic
324C2×#123C2312yes—
325C2×#123C2312yes—
326C2×#123C2314yes—
327C2×#123C2314yes—
328C2×#123C2314yes—
329C2×#123C2314yes—
330C2×C22⋊Q8C2311yescharacteristic
331C2×C22⋊Q8C2311yescharacteristic
332C2×C22⋊Q8C2311yescharacteristic
333C2×C22⋊Q8C2311yescharacteristic
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2311yescharacteristic
338C2×#121C2312yes—
339C2×#121C2311yescharacteristic
340C2×#121C2312yes—
341C2×#121C2311yescharacteristic
342C2×#121C2311yescharacteristic
343C2×#121C2312yes—
344C2×#121C2312yes—
345C2×#121C2311yescharacteristic
346C2×#121C2314yes—
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2311yescharacteristic
350C2×#121C2314yes—
351C2×#121C2314yes—
352C2×#121C2311yescharacteristic
353#520—48no—
354C4×#41—28no—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2311yescharacteristic
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2314yes—
361C2×C4×Q8C2312yes—
362C2×C4×D4C2311yescharacteristic
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2314yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2311yescharacteristic
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×#117C2312yes—
386C2×#117C2312yes—
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2311yescharacteristic
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2314yes—
395C2×#117C2314yes—
396C2×#117C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2311yescharacteristic
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2312yes—
407C22×C4⋊C4C2312yes—
408C22×C4⋊C4C2312yes—
409C22×C4⋊C4C2312yes—
410C22×C4⋊C4C2311yescharacteristic
411C22×C4⋊C4C2312yes—
412C22×C4⋊C4C2311yescharacteristic
413C22×C4⋊C4C2314yes—
414C22×C4⋊C4C2314yes—
415C22×C42C2311yescharacteristic
416C22×C42C2311yescharacteristic
417C22×C42C2312yes—
418C22×C42C2312yes—
419C22×C42C2311yescharacteristic
420#400C2312yes—
421#400C2314yes—
422#400C2314yes—
423#400C2312yes—
424#400C2314yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#400C2314yes—
430#400C2314yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#399C2312yes—
435#399C2314yes—
436#399C2312yes—
437#399C2314yes—
438#399C2314yes—
439#399C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2314yes—
447#398C2314yes—
448#398C2314yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#398C2312yes—
454#398C2314yes—
455#398C2314yes—
456#398C2312yes—
457#398C2314yes—
458#398C2312yes—
459#398C2314yes—
460#398C2312yes—
461#398C2312yes—
462#398C2312yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#397C2312yes—
469#397C2314yes—
470#397C2312yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#396C2312yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#396C2314yes—
491#396C2312yes—
492#396C2312yes—
493#396C2312yes—
494#396C2312yes—
495#396C2312yes—
496#396C2312yes—
497#396C2312yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#396C2314yes—
502#395C2312yes—
503#395C2312yes—
504#394C2314yes—
505#394C2312yes—
506#394C2314yes—
507#394C2312yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2314yes—
514#394C2312yes—
515#394C2314yes—
516#394C2312yes—
517#394C2312yes—
518#394C2314yes—
519#394C2312yes—
520#393C2312yes—
521#393C2312yes—
522#392C2312yes—
523#392C2312yes—
524#391C2311yescharacteristic
525#391C2312yes—
526#391C2312yes—
527#391C2311yescharacteristic
528#391C2311yescharacteristic
529#391C2311yescharacteristic
530#391C2312yes—
531#391C2312yes—
532#390C2311yescharacteristic
533#390C2312yes—
534#390C2314yes—
535#390C2312yes—
536#390C2311yescharacteristic
537#390C2311yescharacteristic
538#390C2311yescharacteristic
539#390C2312yes—
540#390C2312yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2312yes—
553#389C2312yes—
554#389C2312yes—
555#389C2311yescharacteristic
556#389C2311yescharacteristic
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2311yescharacteristic
564#389C2311yescharacteristic
565#389C2311yescharacteristic
566#389C2314yes—
567#389C2314yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2312yes—
575#389C2312yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2312yes—
587#389C2314yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2314yes—
593#389C2314yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#388C2312yes—
613#388C2312yes—
614#388C2312yes—
615#388C2314yes—
616#388C2314yes—
617#388C2314yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2314yes—
658#386C2312yes—
659#386C2312yes—
660#386C2312yes—
661#386C2312yes—
662#386C2314yes—
663#386C2314yes—
664#386C2312yes—
665#386C2312yes—
666#386C2312yes—
667#386C2312yes—
668#386C2312yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2312yes—
676#386C2312yes—
677#386C2312yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2312yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2312yes—
699#385C2312yes—
700#385C2312yes—
701#385C2314yes—
702#384C2312yes—
703#384C2312yes—
704#384C2314yes—
705#384C2312yes—
706#384C2312yes—
707#384C2312yes—
708#384C2312yes—
709#384C2312yes—
710#384C2311yescharacteristic
711#384C2311yescharacteristic
712#384C2311yescharacteristic
713#384C2312yes—
714#384C2312yes—
715#384C2312yes—
716#384C2312yes—
717#384C2312yes—
718#384C2312yes—
719#384C2314yes—
720#384C2312yes—
721#384C2312yes—
722#384C2311yescharacteristic
723#382C2312yes—
724#382C2314yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2312yes—
729#382C2314yes—
730#381C2314yes—
731#381C2314yes—
732#380C2311yescharacteristic
733#380C2311yescharacteristic
734#380C2312yes—
735#380C2311yescharacteristic
736#380C2312yes—
737#380C2311yescharacteristic
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2312yes—
742#380C2311yescharacteristic
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#380C2312yes—
746#380C2312yes—
747#380C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2314yes—
753#380C2314yes—
754#380C2314yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2314yes—
762#380C2312yes—
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2314yes—
775C4×C4⋊C4C2314yes—
776C4×C4⋊C4C2314yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2314yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2314yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2312yes—
815C2×#95C2314yes—
816C2×#95C2312yes—
817C2×#95C2312yes—
818C2×#41—24no—
819C2×#41—24no—
820C2×#41—24no—
821C22×Q8C2411yescharacteristic
822C22×Q8C2411yescharacteristic
823C22×Q8C2411yescharacteristic
824C22×D4C2411yescharacteristic
825C22×D4C2412yes—
826C22×D4C2412yes—
827C22×D4C2411yescharacteristic
828C22×D4C2411yescharacteristic
829C22×D4C2412yes—
830C22×D4C2412yes—
831C22×D4C2411yescharacteristic
832C22×D4C2411yescharacteristic
833C22×D4C2412yes—
834C22×D4C2412yes—
835C22×D4C2414yes—
836C23×C4C2411yescharacteristic
837C23×C4C2411yescharacteristic
838C23×C4C2411yescharacteristic
839C23×C4C2411yescharacteristic
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2412yes—
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2411yescharacteristic
847C23×C4C2411yescharacteristic
848C23×C4C2411yescharacteristic
849C23×C4C2414yes—
850C23×C4C2412yes—
851C23×C4C2414yes—
852C23×C4C2412yes—
853C23×C4C2414yes—
854C23×C4C2414yes—
855C23×C4C2414yes—
856#126—28no—
857#126—28no—
858#126—48no—
859#126—48no—
860#126—48no—
861#126—48no—
862#125—28no—
863#125—28no—
864#125—24no—
865#125—24no—
866#125—44no—
867#125—44no—
868#125—48no—
869#125—48no—
870#125—48no—
871#125—48no—
872#124—24no—
873#124—24no—
874#123—28no—
875#123—28no—
876#123—48no—
877#123—48no—
878#123—48no—
879#123—48no—
880C22⋊Q8—24no—
881C22⋊Q8—24no—
882C22⋊Q8—24no—
883C22⋊Q8—24no—
884C22⋊Q8—44no—
885C22⋊Q8—42no—
886C22⋊Q8—42no—
887C22⋊Q8—44no—
888#121—28no—
889#121—28no—
890#121—28no—
891#121—28no—
892#121—24no—
893#121—24no—
894#121—24no—
895#121—24no—
896#121—48no—
897#121—48no—
898#121—44no—
899#121—42no—
900#121—42no—
901#121—44no—
902#121—48no—
903C4×Q8—24no—
904C4×Q8—24no—
905C4×Q8—24no—
906C4×Q8—24no—
907C4×Q8—44no—
908C4×Q8—48no—
909C4×Q8—44no—
910C4×D4—216no—
911C4×D4—24no—
912C4×D4—24no—
913C4×D4—24no—
914C4×D4—24no—
915C4×D4—28no—
916C4×D4—28no—
917C4×D4—24no—
918C4×D4—24no—
919C4×D4—24no—
920C4×D4—24no—
921C4×D4—44no—
922C4×D4—44no—
923C4×D4—48no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—44no—
928C4×D4—48no—
929C4×D4—48no—
930C4×D4—48no—
931C4×D4—48no—
932C4×D4—48no—
933#117—24no—
934#117—28no—
935#117—24no—
936#117—24no—
937#117—28no—
938#117—28no—
939#117—44no—
940#117—48no—
941#117—48no—
942#117—44no—
943#117—44no—
944#117—44no—
945C2×C4⋊C4—24no—
946C2×C4⋊C4—24no—
947C2×C4⋊C4—28no—
948C2×C4⋊C4—44no—
949C2×C4⋊C4—44no—
950C2×C4⋊C4—44no—
951C2×C4⋊C4—42no—
952C2×C4⋊C4—44no—
953C2×C4⋊C4—42no—
954C2×C4⋊C4—44no—
955C2×C4⋊C4—44no—
956C2×C4⋊C4—48no—
957C2×C4⋊C4—48no—
958C2×C4⋊C4—44no—
959C2×C4⋊C4—44no—
960C2×C4⋊C4—44no—
961C2×C4⋊C4—44no—
962C2×C4⋊C4—48no—
963C2×C4⋊C4C2412yes—
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2414yes—
977C2×C4⋊C4C2414yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2411yescharacteristic
982C2×C4⋊C4C2414yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2412yes—
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2414yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2411yescharacteristic
1046C2×C4⋊C4C2411yescharacteristic
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2411yescharacteristic
1052C2×C22⋊C4C2411yescharacteristic
1053C2×C22⋊C4C2411yescharacteristic
1054C2×C22⋊C4C2411yescharacteristic
1055C2×C22⋊C4C2411yescharacteristic
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C42—24no—
1103C2×C42—24no—
1104C2×C42—44no—
1105C2×C42—44no—
1106C2×C42#4118yes—
1107C2×C42C2414yes—
1108C2×C42C2414yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2411yescharacteristic
1111C2×C42C2412yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2412yes—
1116C2×C42C2412yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2411yescharacteristic
1119C2×C42C2411yescharacteristic
1120C2×C42C2411yescharacteristic
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2414yes—
1125C2×C42C2414yes—
1126C2×C42C2414yes—
1127C2×C42C2414yes—
1128C2×C42C2412yes—
1129C2×C42C2412yes—
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136#95C2412yes—
1137#95C2412yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2414yes—
1146#95C2414yes—
1147#95C2414yes—
1148#95C2412yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2414yes—
1153#95C2414yes—
1154#95C2412yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196C24C2512yes—
1197C24C2512yes—
1198C24C2511yescharacteristic
1199C24C2511yescharacteristic
1200C24C2511yescharacteristic
1201#41—232no—
1202C2×Q8—22no—
1203C2×Q8—22no—
1204C2×Q8—22no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—22no—
1208C2×Q8—22no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—22no—
1214C2×D4—22no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—24no—
1218C2×D4—24no—
1219C2×D4—24no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—24no—
1226C2×D4—24no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—24no—
1231C2×D4—22no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—42no—
1237C2×D4—42no—
1238C2×D4—42no—
1239C2×D4—42no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—44no—
1243C2×D4—44no—
1244C2×D4—44no—
1245C2×D4H(5,𝔽2)14yes—
1246C2×D42−1+414yes—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—22no—
1257C22×C4—22no—
1258C22×C4—22no—
1259C22×C4—24no—
1260C22×C4—24no—
1261C22×C4—28no—
1262C22×C4—24no—
1263C22×C4—28no—
1264C22×C4—24no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—24no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—24no—
1275C22×C4—24no—
1276C22×C4—24no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—24no—
1282C22×C4—24no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—28no—
1286C22×C4—42no—
1287C22×C4—42no—
1288C22×C4—42no—
1289C22×C4—42no—
1290C22×C4—44no—
1291C22×C4—44no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—44no—
1295C22×C4—44no—
1296C22×C4—44no—
1297C22×C4—44no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—44no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4C2×#4114yes—
1305C22×C4C2×#4114yes—
1306C22×C4C2×#4114yes—
1307C22×C4C2512yes—
1308C22×C4C2514yes—
1309C22×C4C2512yes—
1310C22×C4C2512yes—
1311C22×C4C2512yes—
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2511yescharacteristic
1315C22×C4C2511yescharacteristic
1316C22×C4C2511yescharacteristic
1317C22×C4C2511yescharacteristic
1318C22×C4C2512yes—
1319C22×C4C2512yes—
1320C22×C4C2512yes—
1321C22×C4C2512yes—
1322C22×C4C2514yes—
1323C22×C4C2512yes—
1324C22×C4C2514yes—
1325C22×C4C2512yes—
1326C22×C4C2514yes—
1327C22×C4C2511yescharacteristic
1328C22×C4C2511yescharacteristic
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2511yescharacteristic
1332C22×C4C2512yes—
1333C22×C4C2512yes—
1334C22×C4C2511yescharacteristic
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—24no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—22no—
1352C4⋊C4—22no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—24no—
1359C4⋊C4—24no—
1360C4⋊C4—28no—
1361C4⋊C4—28no—
1362C4⋊C4—28no—
1363C4⋊C4—28no—
1364C4⋊C4—28no—
1365C4⋊C4—24no—
1366C4⋊C4—24no—
1367C4⋊C4—24no—
1368C4⋊C4—24no—
1369C4⋊C4—28no—
1370C4⋊C4—24no—
1371C4⋊C4—22no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—24no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—24no—
1378C4⋊C4—24no—
1379C4⋊C4—22no—
1380C4⋊C4—22no—
1381C4⋊C4—22no—
1382C4⋊C4—24no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—42no—
1386C4⋊C4—42no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—44no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—44no—
1398C4⋊C4—44no—
1399C4⋊C4—44no—
1400C4⋊C4—44no—
1401C4⋊C4—44no—
1402C4⋊C4—44no—
1403C4⋊C4—44no—
1404C4⋊C4—44no—
1405C4⋊C4—42no—
1406C4⋊C4—44no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—44no—
1410C4⋊C4—42no—
1411C4⋊C4—42no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4H(5,𝔽2)14yes—
1420C4⋊C42−1+414yes—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—24no—
1424C22⋊C4—24no—
1425C22⋊C4—28no—
1426C22⋊C4—28no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—22no—
1432C22⋊C4—22no—
1433C22⋊C4—22no—
1434C22⋊C4—22no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—24no—
1439C22⋊C4—24no—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—28no—
1444C22⋊C4—24no—
1445C22⋊C4—24no—
1446C22⋊C4—24no—
1447C22⋊C4—24no—
1448C22⋊C4—24no—
1449C22⋊C4—24no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—42no—
1458C22⋊C4—42no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—42no—
1471C22⋊C4—44no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—44no—
1475C22⋊C4—44no—
1476C42—22no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—22no—
1481C42—22no—
1482C42—24no—
1483C42—24no—
1484C42—24no—
1485C42—24no—
1486C42—28no—
1487C42—28no—
1488C42—24no—
1489C42—24no—
1490C42—42no—
1491C42—42no—
1492C42—42no—
1493C42—42no—
1494C42—44no—
1495C42—44no—
1496C42—44no—
1497C42—44no—
1498C42—44no—
1499C42—44no—
1500C42—44no—
1501C42C2×#4114yes—
1502C42C2×#4114yes—
1503C42C2×#4114yes—
1504C42C2×#4114yes—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—22no—
1522C23—22no—
1523C23—22no—
1524C23—22no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—22no—
1532C23—22no—
1533C23—22no—
1534C23—22no—
1535C23C22×#4112yes—
1536C23C2×H(5,𝔽2)12yes—
1537C23C2×H(5,𝔽2)12yes—
1538C23C2×2−1+412yes—
1539C23C2×2−1+412yes—
1540C23C2611yescharacteristic
1541Q8—28no—
1542Q8—44no—
1543Q8—44no—
1544D4—28no—
1545D4—28no—
1546D4—28no—
1547D4—48no—
1548D4—48no—
1549D4—48no—
1550D4—48no—
1551D4—44no—
1552D4—44no—
1553D4—84no—
1554D4—84no—
1555D4—164no—
1556C2×C4—28no—
1557C2×C4—28no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—22no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—28no—
1575C2×C4—28no—
1576C2×C4—28no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—22no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—24no—
1591C2×C4—22no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—24no—
1600C2×C4—24no—
1601C2×C4—22no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—24no—
1606C2×C4—24no—
1607C2×C4—22no—
1608C2×C4—22no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—24no—
1616C2×C4—22no—
1617C2×C4—21no—
1618C2×C4—22no—
1619C2×C4—22no—
1620C2×C4—22no—
1621C2×C4—22no—
1622C2×C4—24no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—24no—
1634C2×C4—24no—
1635C2×C4—22no—
1636C2×C4—21no—
1637C2×C4—48no—
1638C2×C4—48no—
1639C2×C4—44no—
1640C2×C4—44no—
1641C2×C4—48no—
1642C2×C4—44no—
1643C2×C4—44no—
1644C2×C4—48no—
1645C2×C4—88no—
1646C2×C4—84no—
1647C2×C4—88no—
1648C2×C4—88no—
1649C2×C4—84no—
1650C2×C4—164no—
1651C2×C4—164no—
1652C2×C4C22×#4112yes—
1653C2×C4C22×#4112yes—
1654C2×C4C22×#4112yes—
1655C2×C4C22×#4112yes—
1656C2×C4C22×#4112yes—
1657C2×C4C22×#4112yes—
1658C2×C4C2×H(5,𝔽2)12yes—
1659C2×C4C2×H(5,𝔽2)14yes—
1660C2×C4C2×H(5,𝔽2)12yes—
1661C2×C4C2×2−1+412yes—
1662C2×C4C2×2−1+414yes—
1663C2×C4C2×2−1+412yes—
1664C2×C4#58512yes—
1665C2×C4#58512yes—
1666C22—22no—
1667C22—22no—
1668C22—22no—
1669C22—22no—
1670C22—22no—
1671C22—22no—
1672C22—22no—
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—42no—
1687C22—42no—
1688C22—42no—
1689C22—42no—
1690C22—42no—
1691C22—42no—
1692C22—42no—
1693C22—42no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—42no—
1698C22—42no—
1699C22—42no—
1700C22#349214yes—
1701C22C23×#4111yescharacteristic
1702C22C22×H(5,𝔽2)11yescharacteristic
1703C22C22×H(5,𝔽2)11yescharacteristic
1704C22C22×2−1+411yescharacteristic
1705C22C22×2−1+411yescharacteristic
1706C22C2×#58511yescharacteristic
1707C22C2×#58511yescharacteristic
1708C4—24no—
1709C4—24no—
1710C4—22no—
1711C4—22no—
1712C4—22no—
1713C4—22no—
1714C4—22no—
1715C4—22no—
1716C4—42no—
1717C4—42no—
1718C4—44no—
1719C4—42no—
1720C4—42no—
1721C4—44no—
1722C4—44no—
1723C4—42no—
1724C4—44no—
1725C4—42no—
1726C4—42no—
1727C4—42no—
1728C4—41no—
1729C4—41no—
1730C4—42no—
1731C4—42no—
1732C4—41no—
1733C4—41no—
1734C4—42no—
1735C4—42no—
1736C4#351114yes—
1737C4#351214yes—
1738C2—24no—
1739C2—42no—
1740C2—42no—
1741C2—82no—
1742C2—82no—
1743C2C2×#349211yescharacteristic
1744C2C2×#351111yescharacteristic
1745C2C2×#351211yescharacteristic
1746C2#6301311yescharacteristic
1747C2#6301311yescharacteristic
1748C2#6301411yescharacteristic
1749C2#6303211yescharacteristic
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. #59856C2semidirect
2. #59826C2semidirect
3. #59677C2semidirect
4. #59440C2semidirect
5. #59321C2semidirect
6. #59312C2semidirect
7. #59305C2semidirect
8. #59305C2semidirect
9. #59304C2semidirect
10. #59304C2semidirect
11. #59249C2semidirect
12. #59235C2semidirect
13. #59218C2semidirect
14. #59217C2semidirect
15. #59140C2semidirect
16. #59139C2semidirect
17. #47755C2semidirect
18. #47754C2semidirect
19. #42460C2semidirect
20. #42459C2semidirect
21. #42456C2semidirect
22. #42455C2semidirect
23. #42022C2semidirect
24. #37620C2semidirect
25. #35807C2semidirect
26. #35745C2semidirect
27. #35736C2semidirect
28. #35708C2semidirect
29. #35699C2semidirect
30. #34964C2semidirect
31. #34964C2semidirect
32. C2×#2552C2semidirect
33. #34243C2semidirect
34. #34243C2semidirect
35. #34183C2semidirect

Maximal subgroups

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

subgroupindex
#598562
#598262
#596772
#594402
#593212
#593122
#593052
#593042
#592492
#592352
#592182
#592172
#591402
#591392
#477552
#477542
#424602
#424592
#424562
#424552
#420222
#376202
#358072
#357452
#357362
#357082
#356992
#349642
C2×#25522
#342432
#341832