Finite Group Databasebeta

← #7806359

Subgroups — #7806359

Order 512.

5132 conjugacy classes of subgroups.

The subgroup lattice has 1705 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59667C211yesmaximal, characteristic, complemented
3#59546C212yesmaximal, complemented
4#59499C212yesmaximal, complemented
5#59483C212yesmaximal, complemented
6#59441C212yesmaximal, complemented
7#59437C211yesmaximal, characteristic, complemented
8#59418C212yesmaximal, complemented
9#59410C211yesmaximal, characteristic, complemented
10#59399C212yesmaximal, complemented
11#59313C211yesmaximal, characteristic, complemented
12#59305C211yesmaximal, characteristic, complemented
13#59113C212yesmaximal, complemented
14#59055C211yesmaximal, characteristic, complemented
15#59040C212yesmaximal, complemented
16#59040C211yesmaximal, characteristic, complemented
17#47148C214yesmaximal, complemented
18#46993C214yesmaximal, complemented
19#42865C212yesmaximal, complemented
20#42846C212yesmaximal, complemented
21#42633C212yesmaximal, complemented
22#42550C212yesmaximal, complemented
23#42145C214yesmaximal, complemented
24#37627C211yesmaximal, characteristic, complemented
25#35993C212yesmaximal, complemented
26#35943C214yesmaximal, complemented
27#35816C212yesmaximal, complemented
28#35715C212yesmaximal, complemented
29#35697C212yesmaximal, complemented
30#34974C211yesmaximal, characteristic, complemented
31#34970C211yesmaximal, characteristic, complemented
32#34929C211yesmaximal, characteristic, complemented
33#34322C211yesmaximal, characteristic, complemented
34#34308C211yesmaximal, characteristic, complemented
35#34214C211yesmaximal, characteristic, complemented
36C2×#557C2212yes—
37C2×#556C2211yescharacteristic
38C2×#554C2212yes—
39C2×#547C2211yescharacteristic
40C2×#547C2212yes—
41C2×#547C2212yes—
42C2×#533C2211yescharacteristic
43C2×#533C2212yes—
44C2×#520C2212yes—
45#2837C2214yes—
46#2836C2214yes—
47#2836C2214yes—
48#2795C2214yes—
49#2791C2214yes—
50#2790C2214yes—
51#2787C2214yes—
52#2786C2214yes—
53#2783C2214yes—
54#2777C2214yes—
55#2768C2214yes—
56#2765C2214yes—
57#2753C2214yes—
58#2743C2214yes—
59#2740C2214yes—
60#2732C2214yes—
61#2726C2214yes—
62#2721C2214yes—
63#2720C2214yes—
64#2713C2214yes—
65#2707C2214yes—
66#2707C2214yes—
67#2705C2214yes—
68#2694C2214yes—
69#2694C2214yes—
70#2694C2214yes—
71#2680C2214yes—
72#2667C2214yes—
73#2663C2214yes—
74#2655C2214yes—
75#2651C2214yes—
76#2651C2214yes—
77#2630C2214yes—
78#2629C2212yes—
79#2629C2214yes—
80#2625C2212yes—
81#2624C2212yes—
82#2620C2212yes—
83#2606C2214yes—
84#2602C2214yes—
85#2602C2214yes—
86#2581C2212yes—
87#2579C2214yes—
88#2577C2214yes—
89#2577C2214yes—
90#2576C2214yes—
91#2566C2214yes—
92#2566C2212yes—
93#2558C2214yes—
94#2558C2214yes—
95#2558C2214yes—
96#2556C2214yes—
97#2556C2214yes—
98#2554C2214yes—
99#2554C2214yes—
100#2552C2211yescharacteristic
101#2552C2212yes—
102#2551C2211yescharacteristic
103#2551C2212yes—
104#2547C2212yes—
105#2547C2211yescharacteristic
106#2546C2211yescharacteristic
107#2542C2211yescharacteristic
108#2542C2212yes—
109#2542C2211yescharacteristic
110#2540C2212yes—
111#2540C2212yes—
112#2538C2212yes—
113#2538C2211yescharacteristic
114#2538C2212yes—
115#2538C2212yes—
116#2538C2214yes—
117#2538C2212yes—
118#2537C2211yescharacteristic
119#2532C2212yes—
120#2531C2212yes—
121#2529C2212yes—
122#2526C2214yes—
123#2526C2212yes—
124#2520C2214yes—
125#2515C2214yes—
126#2514C2212yes—
127#2513C2211yescharacteristic
128#2512C2211yescharacteristic
129#2510C2214yes—
130#2508C2211yescharacteristic
131#2507C2212yes—
132#2507C2211yescharacteristic
133#2506C2212yes—
134#2506C2212yes—
135#2506C2212yes—
136#2502C2212yes—
137#2497C2212yes—
138#2497C2212yes—
139#2497C2211yescharacteristic
140#2495C2212yes—
141#2495C2211yescharacteristic
142#2494C2212yes—
143#2492C2212yes—
144#2491C2211yescharacteristic
145#2490C2211yescharacteristic
146#2490C2212yes—
147#2486C2212yes—
148#2486C2212yes—
149#2479C2214yes—
150#2479C2212yes—
151#2477C2214yes—
152#2476C2212yes—
153#2474C2212yes—
154#2471C2214yes—
155#2471C2214yes—
156#2471C2212yes—
157#2471C2214yes—
158#2471C2214yes—
159#2462C2214yes—
160#2462C2214yes—
161#2461C2214yes—
162#2454C2214yes—
163#2454C2214yes—
164#2454C2211yescharacteristic
165#2453C2212yes—
166#2452C2212yes—
167#2452C2214yes—
168#2451C2212yes—
169#2451C2211yescharacteristic
170#2449C2214yes—
171#2448C2211yescharacteristic
172#2448C2212yes—
173#2446C2212yes—
174#2445C2211yescharacteristic
175#2443C2214yes—
176#2442C2212yes—
177#2442C2212yes—
178#2442C2214yes—
179#2440C2214yes—
180#2440C2212yes—
181#2440C2212yes—
182#2438C2214yes—
183#2432C2214yes—
184#2431C2212yes—
185#2429C2214yes—
186#2429C2212yes—
187#2429C2212yes—
188#2428C2211yescharacteristic
189#2426C2212yes—
190#2426C2212yes—
191#2426C2212yes—
192#2426C2212yes—
193#2426C2211yescharacteristic
194#2423C2212yes—
195#2423C2212yes—
196#2423C2212yes—
197#2423C2214yes—
198#2423C2212yes—
199#2423C2211yescharacteristic
200#2422C2212yes—
201#2422C2212yes—
202#2421C2214yes—
203#2420C2211yescharacteristic
204#2417C2212yes—
205#2417C2212yes—
206#2417C2212yes—
207#2417C2212yes—
208#2417C2212yes—
209#2415C2212yes—
210#2414C2212yes—
211#2407C2214yes—
212#2407C2212yes—
213#2406C2214yes—
214#2396C2212yes—
215#2396C2214yes—
216#2396C2214yes—
217#2395C2212yes—
218#2395C2212yes—
219#2392C2212yes—
220#2388C2214yes—
221#2373C2214yes—
222#2373C2214yes—
223#2367C2212yes—
224#2367C2212yes—
225#2366C2212yes—
226#2365C2211yescharacteristic
227#2365C2211yescharacteristic
228#2365C2212yes—
229#2362C2212yes—
230#2361C2212yes—
231#2361C2212yes—
232#2360C2212yes—
233#2360C2212yes—
234#2360C2212yes—
235#2360C2212yes—
236#2360C2212yes—
237#2360C2212yes—
238#2360C2212yes—
239#2359C2214yes—
240#2359C2214yes—
241#2355C2211yescharacteristic
242#2355C2212yes—
243#2355C2212yes—
244#2353C2214yes—
245#2352C2212yes—
246#2351C2212yes—
247Q8×C4⋊C4C2212yes—
248Q8×C4⋊C4C2212yes—
249Q8×C4⋊C4C2212yes—
250D4×C4⋊C4C2211yescharacteristic
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2211yescharacteristic
253D4×C4⋊C4C2212yes—
254#2346C2212yes—
255#2345C2212yes—
256#2344C2212yes—
257#2341C2212yes—
258#2341C2214yes—
259#2341C2212yes—
260#2339C2212yes—
261#2334C2214yes—
262#2330C2212yes—
263#2330C2212yes—
264#2323C2212yes—
265#2323C2212yes—
266#2322C2214yes—
267#2317C2212yes—
268C4×C4⋊Q8C2211yescharacteristic
269C4×C4⋊Q8C2211yescharacteristic
270C4×C4⋊Q8C2211yescharacteristic
271C4×C4⋊Q8C2212yes—
272C4×C4⋊Q8C2211yescharacteristic
273C4×C4⋊Q8C2211yescharacteristic
274C4×#127C2211yescharacteristic
275C4×#125C2211yescharacteristic
276C4×#126C2212yes—
277C4×#124C2212yes—
278C4×#124C2211yescharacteristic
279C4×#124C2212yes—
280C4×C22⋊Q8C2212yes—
281C4×C22⋊Q8C2211yescharacteristic
282C4×#123C2212yes—
283C4×#121C2212yes—
284C4×#121C2212yes—
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2211yescharacteristic
288#2295C2212yes—
289#2293C2211yescharacteristic
290#2293C2211yescharacteristic
291#2293C2212yes—
292C2×#389C2212yes—
293C2×#384C2211yescharacteristic
294#2274C2212yes—
295#2274C2212yes—
296C42×Q8C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C4×#117C2211yescharacteristic
299C22×#41C2312yes—
300C22×#41C2314yes—
301#557—48no—
302#556—28no—
303#554—48no—
304#547—28no—
305#547—48no—
306#547—48no—
307#533—28no—
308#533—48no—
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2311yescharacteristic
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2314yes—
315C2×C4⋊Q8C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#126C2312yes—
318C2×#126C2314yes—
319C2×#125C2311yescharacteristic
320C2×#125C2312yes—
321C2×#125C2312yes—
322C2×#125C2314yes—
323C2×#125C2314yes—
324C2×#125C2314yes—
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2312yes—
330C2×#123C2314yes—
331C2×#123C2312yes—
332C2×#123C2314yes—
333C2×#123C2314yes—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×C22⋊Q8C2312yes—
337C2×C22⋊Q8C2312yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2314yes—
351C2×#121C2311yescharacteristic
352C2×#121C2312yes—
353C2×#121C2311yescharacteristic
354C2×#121C2311yescharacteristic
355C2×#121C2312yes—
356C2×#121C2312yes—
357C2×#121C2312yes—
358#520—48no—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2312yes—
362C2×C4×Q8C2312yes—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2312yes—
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×Q8C2314yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2311yescharacteristic
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2314yes—
374C2×C4×D4C2311yescharacteristic
375C2×C4×D4C2311yescharacteristic
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2311yescharacteristic
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2314yes—
384C2×C4×D4C2314yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2311yescharacteristic
394C2×#117C2311yescharacteristic
395C2×#117C2312yes—
396C2×#117C2312yes—
397C2×#117C2314yes—
398C2×#117C2314yes—
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2312yes—
406C22×C4⋊C4C2312yes—
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409#401C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2312yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2312yes—
418#400C2312yes—
419#400C2314yes—
420#399C2314yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2312yes—
425#399C2312yes—
426#399C2312yes—
427#399C2314yes—
428#399C2314yes—
429#399C2314yes—
430#398C2312yes—
431#398C2314yes—
432#398C2314yes—
433#398C2314yes—
434#398C2312yes—
435#398C2314yes—
436#398C2314yes—
437#398C2314yes—
438#398C2314yes—
439#398C2314yes—
440#398C2314yes—
441#398C2314yes—
442#398C2314yes—
443#398C2314yes—
444#398C2314yes—
445#398C2314yes—
446#398C2312yes—
447#398C2312yes—
448#398C2312yes—
449#398C2314yes—
450#398C2314yes—
451#398C2314yes—
452#398C2314yes—
453#397C2314yes—
454#397C2312yes—
455#397C2314yes—
456#397C2314yes—
457#397C2314yes—
458#397C2312yes—
459#397C2312yes—
460#397C2314yes—
461#397C2314yes—
462#397C2314yes—
463#397C2312yes—
464#397C2314yes—
465#397C2312yes—
466#397C2312yes—
467#397C2312yes—
468#396C2314yes—
469#396C2312yes—
470#396C2314yes—
471#396C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2312yes—
480#396C2314yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2312yes—
486#396C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2312yes—
492#394C2312yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2312yes—
497#394C2314yes—
498#394C2314yes—
499#394C2312yes—
500#394C2312yes—
501#394C2314yes—
502#394C2312yes—
503#394C2312yes—
504#394C2312yes—
505#394C2314yes—
506#394C2314yes—
507#393C2314yes—
508#393C2312yes—
509#392C2314yes—
510#392C2314yes—
511#392C2312yes—
512#392C2314yes—
513#391C2312yes—
514#391C2312yes—
515#391C2312yes—
516#391C2312yes—
517#391C2314yes—
518#391C2312yes—
519#391C2312yes—
520#391C2312yes—
521#391C2312yes—
522#391C2312yes—
523#391C2312yes—
524#391C2314yes—
525#391C2311yescharacteristic
526#391C2312yes—
527#391C2311yescharacteristic
528#390C2311yescharacteristic
529#390C2311yescharacteristic
530#390C2312yes—
531#390C2312yes—
532#390C2311yescharacteristic
533#390C2312yes—
534#390C2314yes—
535#390C2314yes—
536#390C2312yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2314yes—
542#390C2314yes—
543#390C2314yes—
544#390C2314yes—
545#390C2314yes—
546#390C2311yescharacteristic
547#390C2312yes—
548#390C2311yescharacteristic
549#390C2311yescharacteristic
550#390C2311yescharacteristic
551#390C2311yescharacteristic
552#390C2311yescharacteristic
553#390C2311yescharacteristic
554#389C2311yescharacteristic
555#389C2311yescharacteristic
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2311yescharacteristic
566#389C2311yescharacteristic
567#389C2312yes—
568#389C2314yes—
569#389C2312yes—
570#389C2314yes—
571#389C2314yes—
572#389C2312yes—
573#389C2312yes—
574#389C2314yes—
575#389C2312yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2314yes—
580#389C2314yes—
581#389C2311yescharacteristic
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2314yes—
588#389C2314yes—
589#389C2312yes—
590#389C2314yes—
591#389C2311yescharacteristic
592#389C2311yescharacteristic
593#389C2314yes—
594#389C2312yes—
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2314yes—
598#389C2311yescharacteristic
599#389C2312yes—
600#389C2311yescharacteristic
601#389C2311yescharacteristic
602#389C2312yes—
603#388C2312yes—
604#388C2312yes—
605#388C2312yes—
606#388C2314yes—
607#388C2314yes—
608#388C2312yes—
609#388C2314yes—
610#388C2314yes—
611#388C2312yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2314yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2312yes—
622#388C2314yes—
623#388C2312yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#388C2314yes—
630#388C2314yes—
631#388C2312yes—
632#388C2312yes—
633#388C2312yes—
634#388C2312yes—
635#388C2314yes—
636#388C2312yes—
637#388C2312yes—
638#388C2312yes—
639#388C2312yes—
640#388C2312yes—
641#388C2312yes—
642#388C2312yes—
643#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2312yes—
672#387C2312yes—
673#387C2312yes—
674#387C2314yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2312yes—
679#386C2314yes—
680#386C2314yes—
681#386C2312yes—
682#386C2312yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2312yes—
687#386C2312yes—
688#386C2312yes—
689#385C2312yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2314yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2312yes—
702#385C2314yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#384C2311yescharacteristic
708#384C2311yescharacteristic
709#384C2311yescharacteristic
710#384C2311yescharacteristic
711#384C2312yes—
712#384C2314yes—
713#384C2312yes—
714#384C2312yes—
715#384C2312yes—
716#384C2312yes—
717#384C2314yes—
718#384C2312yes—
719#383C2312yes—
720#383C2314yes—
721#382C2311yescharacteristic
722#382C2314yes—
723#382C2312yes—
724#382C2314yes—
725#382C2311yescharacteristic
726#382C2312yes—
727#381C2314yes—
728#381C2314yes—
729#381C2312yes—
730#380C2314yes—
731#380C2314yes—
732#380C2312yes—
733#380C2312yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2311yescharacteristic
743#380C2312yes—
744#380C2312yes—
745#380C2314yes—
746#380C2311yescharacteristic
747#380C2311yescharacteristic
748#380C2312yes—
749#380C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2311yescharacteristic
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2311yescharacteristic
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2314yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2314yes—
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2314yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2314yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2311yescharacteristic
787C4×C22⋊C4C2312yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2314yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2314yes—
805C4×C22⋊C4C2311yescharacteristic
806C4×C22⋊C4C2311yescharacteristic
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812#376C2311yescharacteristic
813#376C2311yescharacteristic
814#376C2314yes—
815C2×#95C2314yes—
816C43C2312yes—
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C2×#41—28no—
820C2×#41—28no—
821C2×#41—48no—
822C2×#41—44no—
823C2×#41—48no—
824C2×#41—48no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2414yes—
828C22×Q8C2412yes—
829C22×Q8C2412yes—
830C22×D4C2411yescharacteristic
831C22×D4C2411yescharacteristic
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2414yes—
835C22×D4C2412yes—
836C22×D4C2412yes—
837C22×D4C2411yescharacteristic
838C22×D4C2412yes—
839C22×D4C2414yes—
840C23×C4C2411yescharacteristic
841C23×C4C2411yescharacteristic
842C23×C4C2412yes—
843C23×C4C2411yescharacteristic
844C23×C4C2412yes—
845C23×C4C2412yes—
846C23×C4C2414yes—
847C23×C4C2412yes—
848C23×C4C2414yes—
849C23×C4C2412yes—
850C23×C4C2414yes—
851C23×C4C2414yes—
852C23×C4C2414yes—
853C4⋊Q8—28no—
854C4⋊Q8—28no—
855C4⋊Q8—24no—
856C4⋊Q8—24no—
857C4⋊Q8—44no—
858C4⋊Q8—48no—
859C4⋊Q8#4118yescomplemented
860#127—24no—
861#126—216no—
862#126—28no—
863#125—28no—
864#125—24no—
865#125—44no—
866#125—48no—
867#125—48no—
868#125—48no—
869#125—48no—
870#124—28no—
871#124—44no—
872#124—42no—
873#124—44no—
874#123—216no—
875#123—28no—
876#123—48no—
877#123—48no—
878#123—48no—
879#123—48no—
880C22⋊Q8—28no—
881C22⋊Q8—28no—
882C22⋊Q8—28no—
883C22⋊Q8—28no—
884C22⋊Q8—28no—
885C22⋊Q8—48no—
886C22⋊Q8—48no—
887C22⋊Q8—48no—
888C22⋊Q8—48no—
889C22⋊Q8—44no—
890C22⋊Q8—44no—
891C22⋊Q8—42no—
892C22⋊Q8—44no—
893C22⋊Q8—44no—
894C22⋊Q8—48no—
895#121—24no—
896#121—28no—
897#121—24no—
898#121—24no—
899#121—44no—
900#121—44no—
901#121—44no—
902C4×Q8—28no—
903C4×Q8—28no—
904C4×Q8—28no—
905C4×Q8—28no—
906C4×Q8—24no—
907C4×Q8—24no—
908C4×Q8—44no—
909C4×Q8—42no—
910C4×Q8—44no—
911C4×Q8—44no—
912C4×Q8—48no—
913C4×Q8—44no—
914C4×Q8—48no—
915C4×Q8—44no—
916C4×Q8—44no—
917C4×D4—24no—
918C4×D4—24no—
919C4×D4—24no—
920C4×D4—24no—
921C4×D4—24no—
922C4×D4—44no—
923C4×D4—44no—
924C4×D4—44no—
925C4×D4—44no—
926C4×D4—44no—
927C4×D4—48no—
928C4×D4—44no—
929C4×D4—44no—
930C4×D4—44no—
931C4×D4—48no—
932C4×D4—48no—
933C4×D4—48no—
934#117—28no—
935#117—28no—
936#117—24no—
937#117—44no—
938#117—44no—
939#117—48no—
940#117—48no—
941#117—42no—
942C2×C4⋊C4—28no—
943C2×C4⋊C4—28no—
944C2×C4⋊C4—28no—
945C2×C4⋊C4—48no—
946C2×C4⋊C4—44no—
947C2×C4⋊C4—44no—
948C2×C4⋊C4—44no—
949C2×C4⋊C4—44no—
950C2×C4⋊C4C2412yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2411yescharacteristic
954C2×C4⋊C4C2411yescharacteristic
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2414yes—
959C2×C4⋊C4C2414yes—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2414yes—
962C2×C4⋊C4C2412yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2412yes—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2411yescharacteristic
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2414yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2414yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2414yes—
976C2×C4⋊C4C2412yes—
977C2×C4⋊C4C2412yes—
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2414yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2414yes—
987C2×C4⋊C4C2414yes—
988C2×C4⋊C4C2414yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2411yescharacteristic
1025C2×C4⋊C4C2411yescharacteristic
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2414yes—
1029C2×C22⋊C4C2411yescharacteristic
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2411yescharacteristic
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2411yescharacteristic
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2414yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2412yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2414yes—
1083C2×C42—24no—
1084C2×C42—44no—
1085C2×C42C2411yescharacteristic
1086C2×C42C2412yes—
1087C2×C42C2411yescharacteristic
1088C2×C42C2412yes—
1089C2×C42C2414yes—
1090C2×C42C2412yes—
1091C2×C42C2414yes—
1092C2×C42C2414yes—
1093C2×C42C2411yescharacteristic
1094C2×C42C2411yescharacteristic
1095C2×C42C2412yes—
1096C2×C42C2411yescharacteristic
1097C2×C42C2411yescharacteristic
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2412yes—
1103C2×C42C2411yescharacteristic
1104C2×C42C2411yescharacteristic
1105C2×C42C2411yescharacteristic
1106C2×C42C2412yes—
1107C2×C42C2411yescharacteristic
1108C2×C42C2414yes—
1109C2×C42C2414yes—
1110C2×C42C2411yescharacteristic
1111C2×C42C2411yescharacteristic
1112C2×C42C2414yes—
1113C2×C42C2414yes—
1114C2×C42C2414yes—
1115C2×C42C2414yes—
1116C2×C42C2412yes—
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121#95C2412yes—
1122#95C2414yes—
1123#95C2414yes—
1124#95C2414yes—
1125#95C2412yes—
1126#95C2411yescharacteristic
1127#95C2411yescharacteristic
1128#95C2411yescharacteristic
1129#95C2411yescharacteristic
1130#95C2411yescharacteristic
1131#95C2411yescharacteristic
1132#95C2411yescharacteristic
1133#95C2411yescharacteristic
1134#95C2414yes—
1135#95C2414yes—
1136#95C2412yes—
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2414yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2414yes—
1148#95C2414yes—
1149#95C2414yes—
1150#95C2414yes—
1151#95C2414yes—
1152#95C2412yes—
1153#95C2414yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2412yes—
1158#95C2412yes—
1159#95C2412yes—
1160#95C2412yes—
1161#95C2414yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2414yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2412yes—
1169#95C2412yes—
1170#95C2414yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2412yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2414yes—
1186#95C2414yes—
1187C24C2512yes—
1188C24C2512yes—
1189C24C2512yes—
1190C24C2511yescharacteristic
1191#41—432no—
1192#41—832no—
1193C2×Q8—22no—
1194C2×Q8—24no—
1195C2×Q8—24no—
1196C2×Q8—22no—
1197C2×Q8—24no—
1198C2×Q8—28no—
1199C2×Q8—28no—
1200C2×Q8—24no—
1201C2×Q8—24no—
1202C2×Q8—22no—
1203C2×Q8—24no—
1204C2×Q8—44no—
1205C2×Q8—42no—
1206C2×Q8—42no—
1207C2×Q8C2×#4118yes—
1208C2×D4—24no—
1209C2×D4—24no—
1210C2×D4—28no—
1211C2×D4—24no—
1212C2×D4—24no—
1213C2×D4—24no—
1214C2×D4—24no—
1215C2×D4—22no—
1216C2×D4—22no—
1217C2×D4—22no—
1218C2×D4—28no—
1219C2×D4—22no—
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—24no—
1223C2×D4—24no—
1224C2×D4—24no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—42no—
1228C2×D4—44no—
1229C2×D4—42no—
1230C2×D4—42no—
1231C2×D4—42no—
1232C2×D4—42no—
1233C2×D4—44no—
1234C2×D4—44no—
1235C2×D4—42no—
1236C2×D4—44no—
1237C2×D42−1+414yes—
1238C22×C4—22no—
1239C22×C4—22no—
1240C22×C4—22no—
1241C22×C4—24no—
1242C22×C4—28no—
1243C22×C4—28no—
1244C22×C4—22no—
1245C22×C4—22no—
1246C22×C4—24no—
1247C22×C4—28no—
1248C22×C4—24no—
1249C22×C4—24no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—24no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—22no—
1256C22×C4—24no—
1257C22×C4—24no—
1258C22×C4—24no—
1259C22×C4—22no—
1260C22×C4—24no—
1261C22×C4—28no—
1262C22×C4—28no—
1263C22×C4—24no—
1264C22×C4—42no—
1265C22×C4—44no—
1266C22×C4—42no—
1267C22×C4—44no—
1268C22×C4—44no—
1269C22×C4—44no—
1270C22×C4—44no—
1271C22×C4—42no—
1272C22×C4—44no—
1273C22×C4—44no—
1274C22×C4—44no—
1275C22×C4—44no—
1276C22×C4—44no—
1277C22×C4C2511yescharacteristic
1278C22×C4C2512yes—
1279C22×C4C2512yes—
1280C22×C4C2512yes—
1281C22×C4C2512yes—
1282C22×C4C2511yescharacteristic
1283C22×C4C2511yescharacteristic
1284C22×C4C2511yescharacteristic
1285C22×C4C2511yescharacteristic
1286C22×C4C2512yes—
1287C22×C4C2512yes—
1288C22×C4C2512yes—
1289C22×C4C2514yes—
1290C22×C4C2512yes—
1291C22×C4C2514yes—
1292C22×C4C2512yes—
1293C22×C4C2511yescharacteristic
1294C22×C4C2512yes—
1295C22×C4C2514yes—
1296C22×C4C2512yes—
1297C22×C4C2511yescharacteristic
1298C22×C4C2511yescharacteristic
1299C22×C4C2511yescharacteristic
1300C22×C4C2514yes—
1301C22×C4C2512yes—
1302C22×C4C2512yes—
1303C22×C4C2511yescharacteristic
1304C22×C4C2511yescharacteristic
1305C22×C4C2511yescharacteristic
1306C22×C4C2511yescharacteristic
1307C22×C4C2511yescharacteristic
1308C4⋊C4—22no—
1309C4⋊C4—28no—
1310C4⋊C4—22no—
1311C4⋊C4—24no—
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—28no—
1315C4⋊C4—28no—
1316C4⋊C4—28no—
1317C4⋊C4—24no—
1318C4⋊C4—24no—
1319C4⋊C4—24no—
1320C4⋊C4—28no—
1321C4⋊C4—24no—
1322C4⋊C4—28no—
1323C4⋊C4—22no—
1324C4⋊C4—28no—
1325C4⋊C4—24no—
1326C4⋊C4—24no—
1327C4⋊C4—28no—
1328C4⋊C4—24no—
1329C4⋊C4—24no—
1330C4⋊C4—24no—
1331C4⋊C4—22no—
1332C4⋊C4—28no—
1333C4⋊C4—28no—
1334C4⋊C4—24no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—24no—
1339C4⋊C4—24no—
1340C4⋊C4—24no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—42no—
1344C4⋊C4—42no—
1345C4⋊C4—42no—
1346C4⋊C4—44no—
1347C4⋊C4—44no—
1348C4⋊C4—44no—
1349C4⋊C4—44no—
1350C4⋊C4—44no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—42no—
1354C4⋊C4—42no—
1355C4⋊C4—42no—
1356C4⋊C4—44no—
1357C4⋊C4—42no—
1358C4⋊C4—42no—
1359C4⋊C4—44no—
1360C4⋊C4—42no—
1361C4⋊C4—42no—
1362C4⋊C4—42no—
1363C4⋊C4—42no—
1364C4⋊C4—42no—
1365C4⋊C4—44no—
1366C4⋊C4—44no—
1367C4⋊C4—44no—
1368C4⋊C4—44no—
1369C4⋊C4—44no—
1370C4⋊C4—42no—
1371C4⋊C4—44no—
1372C4⋊C4—42no—
1373C4⋊C4—44no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—44no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—44no—
1380C4⋊C4C2×#4118yes—
1381C4⋊C4C2×#4118yes—
1382C4⋊C4H(5,𝔽2)14yes—
1383C4⋊C4H(5,𝔽2)14yes—
1384C4⋊C42−1+414yes—
1385C22⋊C4—24no—
1386C22⋊C4—24no—
1387C22⋊C4—22no—
1388C22⋊C4—22no—
1389C22⋊C4—24no—
1390C22⋊C4—28no—
1391C22⋊C4—28no—
1392C22⋊C4—24no—
1393C22⋊C4—24no—
1394C22⋊C4—24no—
1395C22⋊C4—28no—
1396C22⋊C4—28no—
1397C22⋊C4—24no—
1398C22⋊C4—28no—
1399C22⋊C4—24no—
1400C22⋊C4—24no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—24no—
1404C22⋊C4—24no—
1405C22⋊C4—24no—
1406C22⋊C4—24no—
1407C22⋊C4—24no—
1408C22⋊C4—24no—
1409C22⋊C4—42no—
1410C22⋊C4—42no—
1411C22⋊C4—42no—
1412C22⋊C4—44no—
1413C22⋊C4—42no—
1414C22⋊C4—44no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—44no—
1420C22⋊C4—42no—
1421C22⋊C4—42no—
1422C22⋊C4—44no—
1423C22⋊C4—44no—
1424C22⋊C4—42no—
1425C22⋊C4—42no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—42no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—44no—
1437C22⋊C4—44no—
1438C22⋊C4—42no—
1439C22⋊C4—42no—
1440C22⋊C4—42no—
1441C42—22no—
1442C42—22no—
1443C42—22no—
1444C42—28no—
1445C42—28no—
1446C42—24no—
1447C42—22no—
1448C42—24no—
1449C42—22no—
1450C42—24no—
1451C42—28no—
1452C42—24no—
1453C42—22no—
1454C42—24no—
1455C42—22no—
1456C42—22no—
1457C42—22no—
1458C42—22no—
1459C42—24no—
1460C42—22no—
1461C42—22no—
1462C42—24no—
1463C42—22no—
1464C42—42no—
1465C42—42no—
1466C42—41no—
1467C42—41no—
1468C42—44no—
1469C42—44no—
1470C42—44no—
1471C42—44no—
1472C42—42no—
1473C42—44no—
1474C42—44no—
1475C42—42no—
1476C42C2×#4114yes—
1477C23—21no—
1478C23—22no—
1479C23—22no—
1480C23—22no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—22no—
1485C23—21no—
1486C23—21no—
1487C23—22no—
1488C23—22no—
1489C23—22no—
1490C23—22no—
1491C23—22no—
1492C23—22no—
1493C23—22no—
1494C23—22no—
1495C23—22no—
1496C23—22no—
1497C23—22no—
1498C23—22no—
1499C23—22no—
1500C23—22no—
1501C23—22no—
1502C23—22no—
1503C23C2×2−1+414yes—
1504C23#58512yes—
1505C23C2611yescharacteristic
1506Q8—216no—
1507Q8—416no—
1508Q8—44no—
1509Q8—48no—
1510Q8—84no—
1511D4—28no—
1512D4—48no—
1513D4—416no—
1514D4—48no—
1515D4—48no—
1516D4—48no—
1517D4—44no—
1518D4—44no—
1519D4—84no—
1520D4—88no—
1521C2×C4—28no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—24no—
1526C2×C4—22no—
1527C2×C4—22no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—24no—
1532C2×C4—21no—
1533C2×C4—22no—
1534C2×C4—21no—
1535C2×C4—22no—
1536C2×C4—22no—
1537C2×C4—22no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—22no—
1541C2×C4—24no—
1542C2×C4—22no—
1543C2×C4—22no—
1544C2×C4—22no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—22no—
1549C2×C4—22no—
1550C2×C4—21no—
1551C2×C4—22no—
1552C2×C4—21no—
1553C2×C4—22no—
1554C2×C4—21no—
1555C2×C4—24no—
1556C2×C4—22no—
1557C2×C4—22no—
1558C2×C4—24no—
1559C2×C4—24no—
1560C2×C4—24no—
1561C2×C4—24no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—22no—
1565C2×C4—22no—
1566C2×C4—22no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—22no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—22no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—22no—
1587C2×C4—21no—
1588C2×C4—22no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—24no—
1597C2×C4—22no—
1598C2×C4—21no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—24no—
1602C2×C4—48no—
1603C2×C4—416no—
1604C2×C4—44no—
1605C2×C4—48no—
1606C2×C4—48no—
1607C2×C4—44no—
1608C2×C4—48no—
1609C2×C4—84no—
1610C2×C4—88no—
1611C2×C4—88no—
1612C2×C4—88no—
1613C2×C4—164no—
1614C2×C4C22×#4118yes—
1615C2×C4C22×#4112yes—
1616C2×C4C22×#4112yes—
1617C2×C4C22×#4112yes—
1618C2×C4C2×H(5,𝔽2)14yes—
1619C2×C4C2×H(5,𝔽2)14yes—
1620C2×C4C2×H(5,𝔽2)12yes—
1621C2×C4C2×H(5,𝔽2)12yes—
1622C2×C4C2×2−1+412yes—
1623C2×C4C2×2−1+412yes—
1624C2×C4C2×2−1+412yes—
1625C2×C4C2×2−1+412yes—
1626C2×C4#58512yes—
1627C22—22no—
1628C22—24no—
1629C22—22no—
1630C22—24no—
1631C22—24no—
1632C22—22no—
1633C22—42no—
1634C22—41no—
1635C22—41no—
1636C22—42no—
1637C22—41no—
1638C22—42no—
1639C22—41no—
1640C22—42no—
1641C22—42no—
1642C22—42no—
1643C22—42no—
1644C22—42no—
1645C22—42no—
1646C22—42no—
1647C22—42no—
1648C22—42no—
1649C22—42no—
1650C22—42no—
1651C22—42no—
1652C22—42no—
1653C22—42no—
1654C22—42no—
1655C22C23×#4111yescharacteristic
1656C22C22×H(5,𝔽2)11yescharacteristic
1657C22C22×H(5,𝔽2)11yescharacteristic
1658C22C22×2−1+411yescharacteristic
1659C22C22×2−1+411yescharacteristic
1660C22C2×#58511yescharacteristic
1661C22C2×#58511yescharacteristic
1662C4—24no—
1663C4—24no—
1664C4—22no—
1665C4—22no—
1666C4—28no—
1667C4—22no—
1668C4—22no—
1669C4—41no—
1670C4—44no—
1671C4—44no—
1672C4—42no—
1673C4—41no—
1674C4—42no—
1675C4—41no—
1676C4—42no—
1677C4—41no—
1678C4—41no—
1679C4—42no—
1680C4—42no—
1681C4—41no—
1682C4—41no—
1683C4—42no—
1684C4—42no—
1685C4—42no—
1686C4—42no—
1687C4—41no—
1688C4—42no—
1689C4—42no—
1690C4—44no—
1691C4#351714yes—
1692C4#352014yes—
1693C2—42no—
1694C2—44no—
1695C2—82no—
1696C2—82no—
1697C2C2×#352011yescharacteristic
1698C2#6278811yescharacteristic
1699C2C2×#351711yescharacteristic
1700C2#6301211yescharacteristic
1701C2#6301611yescharacteristic
1702C2#6302311yescharacteristic
1703C2#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. #59823C2semidirect
2. #59667C2semidirect
3. #59546C2semidirect
4. #59499C2semidirect
5. #59483C2semidirect
6. #59441C2semidirect
7. #59437C2semidirect
8. #59418C2semidirect
9. #59410C2semidirect
10. #59399C2semidirect
11. #59313C2semidirect
12. #59305C2semidirect
13. #59113C2semidirect
14. #59055C2semidirect
15. #59040C2semidirect
16. #59040C2semidirect
17. #47148C2semidirect
18. #46993C2semidirect
19. #42865C2semidirect
20. #42846C2semidirect
21. #42633C2semidirect
22. #42550C2semidirect
23. #42145C2semidirect
24. #37627C2semidirect
25. #35993C2semidirect
26. #35943C2semidirect
27. #35816C2semidirect
28. #35715C2semidirect
29. #35697C2semidirect
30. #34974C2semidirect
31. #34970C2semidirect
32. #34929C2semidirect
33. #34322C2semidirect
34. #34308C2semidirect
35. #34214C2semidirect
859. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598232
#596672
#595462
#594992
#594832
#594412
#594372
#594182
#594102
#593992
#593132
#593052
#591132
#590552
#590402
#471482
#469932
#428652
#428462
#426332
#425502
#421452
#376272
#359932
#359432
#358162
#357152
#356972
#349742
#349702
#349292
#343222
#343082
#342142