Finite Group Databasebeta

← #8425243

Subgroups — #8425243

Order 512.

4952 conjugacy classes of subgroups.

The subgroup lattice has 1801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59659C211yesmaximal, characteristic, complemented
2#59630C212yesmaximal, complemented
3#59244C211yesmaximal, characteristic, complemented
4#59230C211yesmaximal, characteristic, complemented
5#59017C212yesmaximal, complemented
6#58313C214yesmaximal, complemented
7#56494C214yesmaximal, complemented
8#53071C212yesmaximal, complemented
9#53061C212yesmaximal, complemented
10#53015C212yesmaximal, complemented
11#52981C212yesmaximal, complemented
12#52494C214yesmaximal, complemented
13#42991C212yesmaximal, complemented
14#42905C212yesmaximal, complemented
15#42882C212yesmaximal, complemented
16#42473C212yesmaximal, complemented
17#41139C214yesmaximal, complemented
18#40102C212yesmaximal, complemented
19#39934C212yesmaximal, complemented
20#39562C212yesmaximal, complemented
21#39505C211yesmaximal, characteristic, complemented
22#39469C211yesmaximal, characteristic, complemented
23#39377C211yesmaximal, characteristic, complemented
24#39125C211yesmaximal, characteristic, complemented
25#37669C212yesmaximal, complemented
26#37636C211yesmaximal, characteristic, complemented
27#37621C211yesmaximal, characteristic, complemented
28#37516C212yesmaximal, complemented
29#37480C212yesmaximal, complemented
30#36456C211yesmaximal, characteristic, complemented
31#36194C211yesmaximal, characteristic, complemented
32#36160C211yesmaximal, characteristic, complemented
33#34935C211yesmaximal, characteristic, complemented
34#34715C211yesmaximal, characteristic, complemented
35#34700C211yesmaximal, characteristic, complemented
36C2×Q82C2211yescharacteristic, complemented
37C2×#556C2212yescomplemented
38C2×#555C2211yescharacteristic
39C2×#542C2212yescomplemented
40C2×#532C2211yescharacteristic, complemented
41C2×#529C2211yescharacteristic
42C2×#525C2212yes—
43C2×C4×#41C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45#2868C2211yescharacteristic, complemented
46#2857C2211yescharacteristic
47#2857C2211yescharacteristic, complemented
48#2857C2212yescomplemented
49#2847C2212yes—
50#2842C2214yes—
51#2840C2214yes—
52#2837C2214yes—
53#2832C2214yescomplemented
54#2832C2214yescomplemented
55#2830C2214yescomplemented
56#2829C2214yes—
57#2826C2214yescomplemented
58#2824C2214yescomplemented
59#2819C2214yes—
60#2819C2214yes—
61#2819C2214yes—
62#2813C2214yes—
63#2813C2214yescomplemented
64#2798C2214yescomplemented
65#2795C2214yescomplemented
66#2785C2214yes—
67#2784C2214yes—
68#2781C2214yescomplemented
69#2777C2214yescomplemented
70#2767C2214yescomplemented
71#2754C2214yescomplemented
72#2751C2214yes—
73#2751C2214yescomplemented
74#2749C2214yes—
75#2731C2214yescomplemented
76#2731C2214yescomplemented
77#2730C2214yescomplemented
78#2718C2214yescomplemented
79#2716C2214yescomplemented
80#2715C2214yescomplemented
81#2712C2214yescomplemented
82#2710C2214yescomplemented
83#2705C2214yes—
84#2705C2214yes—
85#2705C2214yescomplemented
86#2702C2214yescomplemented
87#2702C2214yescomplemented
88#2700C2214yescomplemented
89#2697C2214yes—
90#2696C2214yes—
91#2696C2214yescomplemented
92#2685C2214yes—
93#2678C2214yes—
94#2676C2214yescomplemented
95#2674C2214yescomplemented
96#2674C2214yescomplemented
97#2672C2214yescomplemented
98#2670C2214yes—
99#2670C2214yes—
100#2670C2214yes—
101#2666C2214yescomplemented
102#2665C2214yes—
103#2665C2214yes—
104#2665C2214yescomplemented
105#2665C2214yescomplemented
106#2662C2214yescomplemented
107#2662C2214yescomplemented
108#2650C2214yescomplemented
109#2648C2214yescomplemented
110#2637C2214yescomplemented
111#2632C2214yescomplemented
112#2628C2212yescomplemented
113#2628C2212yescomplemented
114#2628C2212yescomplemented
115#2628C2212yescomplemented
116#2628C2212yescomplemented
117#2624C2212yes—
118#2624C2212yescomplemented
119#2620C2212yes—
120#2619C2212yescomplemented
121#2616C2212yescomplemented
122#2615C2212yes—
123#2615C2212yes—
124#2607C2214yescomplemented
125#2607C2214yescomplemented
126#2596C2214yescomplemented
127#2595C2214yescomplemented
128#2592C2214yescomplemented
129#2574C2214yescomplemented
130#2571C2212yescomplemented
131#2563C2211yescharacteristic
132#2563C2212yes—
133#2563C2212yes—
134#2563C2212yes—
135#2563C2211yescharacteristic, complemented
136#2563C2212yescomplemented
137#2562C2212yescomplemented
138#2557C2214yescomplemented
139#2554C2214yes—
140#2551C2211yescharacteristic, complemented
141#2550C2212yescomplemented
142#2547C2212yescomplemented
143#2545C2214yescomplemented
144#2540C2212yes—
145#2538C2211yescharacteristic
146#2538C2212yes—
147#2538C2212yes—
148#2538C2211yescharacteristic
149#2538C2211yescharacteristic, complemented
150#2538C2211yescharacteristic, complemented
151#2537C2211yescharacteristic
152#2537C2211yescharacteristic
153#2537C2211yescharacteristic
154#2536C2212yes—
155#2536C2212yescomplemented
156#2535C2212yes—
157#2535C2212yescomplemented
158#2534C2214yes—
159#2512C2212yes—
160#2508C2212yescomplemented
161#2501C2212yes—
162#2500C2212yescomplemented
163#2497C2212yes—
164#2497C2212yescomplemented
165#2497C2212yescomplemented
166#2496C2212yescomplemented
167#2496C2212yescomplemented
168#2495C2212yescomplemented
169#2495C2212yescomplemented
170#2492C2212yes—
171#2492C2212yescomplemented
172#2492C2212yescomplemented
173#2492C2212yescomplemented
174#2491C2212yes—
175#2491C2212yes—
176#2491C2212yes—
177#2491C2212yes—
178#2491C2212yes—
179#2491C2212yes—
180#2491C2212yescomplemented
181#2491C2212yescomplemented
182#2491C2212yescomplemented
183#2486C2212yes—
184#2485C2212yes—
185#2485C2212yescomplemented
186#2485C2212yescomplemented
187#2480C2212yes—
188#2476C2212yescomplemented
189#2474C2212yescomplemented
190#2472C2214yes—
191#2469C2214yescomplemented
192#2468C2212yes—
193#2468C2214yescomplemented
194#2467C2214yescomplemented
195#2467C2214yescomplemented
196#2459C2214yes—
197#2459C2212yes—
198#2459C2214yescomplemented
199#2459C2214yescomplemented
200#2458C2214yes—
201#2457C2212yes—
202#2457C2214yescomplemented
203#2456C2212yes—
204#2454C2211yescharacteristic
205#2452C2214yes—
206#2452C2212yescomplemented
207#2451C2211yescharacteristic, complemented
208#2448C2212yes—
209#2447C2211yescharacteristic
210#2445C2211yescharacteristic, complemented
211#2442C2211yescharacteristic
212#2440C2212yescomplemented
213#2439C2212yes—
214#2439C2212yes—
215#2439C2212yes—
216#2439C2211yescharacteristic
217#2439C2212yescomplemented
218#2439C2212yescomplemented
219#2439C2214yescomplemented
220#2439C2212yescomplemented
221#2439C2212yescomplemented
222#2439C2212yescomplemented
223#2439C2212yescomplemented
224#2435C2211yescharacteristic
225#2431C2211yescharacteristic
226#2428C2212yescomplemented
227#2427C2211yescharacteristic
228#2427C2214yescomplemented
229#2426C2212yes—
230#2426C2212yescomplemented
231#2426C2211yescharacteristic, complemented
232#2423C2212yescomplemented
233#2422C2212yescomplemented
234#2421C2212yescomplemented
235#2421C2212yescomplemented
236#2420C2212yes—
237#2420C2211yescharacteristic
238#2420C2211yescharacteristic, complemented
239#2418C2212yes—
240#2417C2212yes—
241#2417C2211yescharacteristic
242#2416C2212yes—
243#2414C2212yes—
244#2414C2211yescharacteristic
245#2414C2212yescomplemented
246#2414C2212yescomplemented
247#2414C2212yescomplemented
248#2408C2211yescharacteristic
249#2408C2212yes—
250#2408C2212yes—
251#2407C2211yescharacteristic
252#2395C2212yes—
253#2392C2214yes—
254#2392C2212yes—
255#2392C2212yes—
256#2388C2212yes—
257#2369C2212yescomplemented
258#2367C2214yescomplemented
259#2365C2212yescomplemented
260#2363C2212yes—
261#2363C2212yes—
262#2362C2212yescomplemented
263#2362C2212yescomplemented
264#2355C2211yescharacteristic, complemented
265#2355C2212yescomplemented
266#2354C2211yescharacteristic
267#2354C2212yes—
268#2352C2212yes—
269#2351C2212yescomplemented
270Q8×C4⋊C4C2211yescharacteristic, complemented
271D4×C4⋊C4C2211yescharacteristic, complemented
272#2345C2212yescomplemented
273#2341C2212yes—
274#2337C2214yescomplemented
275#2323C2212yescomplemented
276#2314C2212yescomplemented
277#2311C2212yescomplemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#124C2211yescharacteristic
280C4×#124C2211yescharacteristic, complemented
281C4×C22⋊Q8C2211yescharacteristic
282C4×C22⋊Q8C2212yescomplemented
283C4×C22⋊Q8C2211yescharacteristic, complemented
284C4×#123C2212yescomplemented
285C4×#121C2211yescharacteristic
286C4×#121C2211yescharacteristic
287C4×#121C2212yes—
288C4×#121C2212yes—
289C4×#120C2212yes—
290#2297C2212yescomplemented
291#2293C2211yescharacteristic
292#2293C2211yescharacteristic, complemented
293#2285C2211yescharacteristic
294#2285C2211yescharacteristic, complemented
295#2280C2212yes—
296#2280C2212yes—
297#2280C2212yes—
298C42×D4C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303Q82—44no—
304#556—48no—
305#555—44no—
306#542—48no—
307#532—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2312yes—
310C2×C4⋊Q8C2312yes—
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2312yes—
313C2×C4⋊Q8C2312yes—
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×C4⋊Q8C2314yes—
317C2×C4⋊Q8C2312yes—
318C2×#127C2311yescharacteristic
319#529—44no—
320C2×#126C2314yes—
321C2×#126C2312yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#125C2311yescharacteristic
325C2×#124C2311yescharacteristic
326C2×#124C2314yes—
327C2×#124C2314yes—
328C2×#124C2314yes—
329C2×#124C2314yes—
330C2×#124C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#124C2314yes—
334C2×#124C2314yes—
335C2×#124C2314yes—
336#525—48no—
337C2×#123C2314yes—
338C2×#123C2312yes—
339C2×#123C2312yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×#121C2311yescharacteristic
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2311yescharacteristic
357C2×#121C2311yescharacteristic
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2311yescharacteristic
366C2×#121C2312yes—
367C2×#121C2314yes—
368C2×#120C2314yes—
369C2×#120C2312yes—
370C2×#120C2314yes—
371C4×#41—44no—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2312yes—
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2314yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2312yes—
380C2×C4×D4—44no—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2314yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2312yes—
395C2×C4×D4C2314yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×#117C2312yes—
403C2×#117C2312yes—
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2312yes—
410C2×#117C2312yes—
411C2×#117C2311yescharacteristic
412C22×C4⋊C4C2312yes—
413C22×C4⋊C4C2311yescharacteristic
414C22×C22⋊C4C2312yes—
415C22×C42C2311yescharacteristic
416C22×C42C2311yescharacteristic
417C22×C42C2312yes—
418#400C2314yes—
419#400C2314yes—
420#400C2314yes—
421#400C2314yes—
422#400C2314yes—
423#400C2314yes—
424#400C2312yes—
425#400C2314yes—
426#400C2314yes—
427#400C2314yes—
428#400C2314yes—
429#399C2314yes—
430#399C2314yes—
431#399C2314yes—
432#399C2314yes—
433#399C2314yes—
434#399C2314yes—
435#399C2312yes—
436#398C2314yes—
437#398C2312yes—
438#398C2312yes—
439#398C2314yes—
440#398C2314yes—
441#398C2312yes—
442#398C2314yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2312yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#397C2312yes—
455#397C2314yes—
456#397C2312yes—
457#397C2312yes—
458#396C2314yes—
459#396C2314yes—
460#396C2314yes—
461#396C2314yes—
462#396C2312yes—
463#396C2314yes—
464#396C2314yes—
465#396C2312yes—
466#396C2314yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#396C2314yes—
471#396C2312yes—
472#396C2314yes—
473#396C2314yes—
474#396C2312yes—
475#396C2314yes—
476#396C2314yes—
477#395C2314yes—
478#395C2314yes—
479#395C2314yes—
480#395C2314yes—
481#395C2314yes—
482#395C2312yes—
483#394C2314yes—
484#394C2312yes—
485#394C2312yes—
486#394C2312yes—
487#394C2312yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2312yes—
501#394C2314yes—
502#394C2314yes—
503#394C2312yes—
504#394C2314yes—
505#394C2314yes—
506#394C2312yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2312yes—
511#394C2314yes—
512#394C2312yes—
513#394C2312yes—
514#394C2312yes—
515#394C2314yes—
516#394C2314yes—
517#393C2314yes—
518#393C2314yes—
519#393C2314yes—
520#393C2314yes—
521#393C2314yes—
522#393C2314yes—
523#393C2314yes—
524#393C2314yes—
525#393C2314yes—
526#393C2314yes—
527#393C2314yes—
528#393C2314yes—
529#393C2314yes—
530#393C2314yes—
531#393C2314yes—
532#393C2314yes—
533#393C2314yes—
534#393C2314yes—
535#393C2312yes—
536#393C2314yes—
537#393C2314yes—
538#392C2312yes—
539#392C2314yes—
540#392C2314yes—
541#392C2314yes—
542#392C2314yes—
543#392C2314yes—
544#392C2314yes—
545#392C2314yes—
546#392C2314yes—
547#392C2314yes—
548#392C2312yes—
549#392C2312yes—
550#392C2312yes—
551#392C2312yes—
552#391C2312yes—
553#391C2314yes—
554#391C2314yes—
555#391C2314yes—
556#391C2311yescharacteristic
557#391C2314yes—
558#391C2314yes—
559#391C2314yes—
560#391C2314yes—
561#391C2312yes—
562#391C2312yes—
563#391C2312yes—
564#391C2314yes—
565#391C2314yes—
566#391C2312yes—
567#391C2311yescharacteristic
568#391C2311yescharacteristic
569#391C2312yes—
570#391C2311yescharacteristic
571#390C2314yes—
572#390C2314yes—
573#390C2312yes—
574#390C2314yes—
575#390C2311yescharacteristic
576#390C2312yes—
577#390C2312yes—
578#390C2314yes—
579#390C2314yes—
580#390C2314yes—
581#390C2314yes—
582#390C2312yes—
583#390C2314yes—
584#390C2312yes—
585#390C2311yescharacteristic
586#390C2311yescharacteristic
587#390C2312yes—
588#390C2312yes—
589#390C2314yes—
590#390C2311yescharacteristic
591#390C2312yes—
592#390C2311yescharacteristic
593#390C2312yes—
594#390C2311yescharacteristic
595#390C2311yescharacteristic
596#390C2311yescharacteristic
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2314yes—
601#389C2312yes—
602#389C2314yes—
603#389C2314yes—
604#389C2311yescharacteristic
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2312yes—
609#389C2312yes—
610#389C2312yes—
611#389C2314yes—
612#389C2312yes—
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#389C2311yescharacteristic
617#389C2311yescharacteristic
618#389C2311yescharacteristic
619#389C2311yescharacteristic
620#389C2311yescharacteristic
621#389C2311yescharacteristic
622#389C2311yescharacteristic
623#389C2312yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2314yes—
628#388C2314yes—
629#388C2312yes—
630#388C2314yes—
631#388C2312yes—
632#388C2312yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2312yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2312yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2312yes—
654#388C2312yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2312yes—
660#388C2312yes—
661#388C2312yes—
662#388C2312yes—
663#388C2312yes—
664#387C2314yes—
665#387C2314yes—
666#387C2314yes—
667#387C2312yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2312yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2312yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2312yes—
685#386C2314yes—
686#386C2314yes—
687#386C2312yes—
688#386C2314yes—
689#386C2312yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2312yes—
696#386C2312yes—
697#386C2312yes—
698#386C2312yes—
699#386C2312yes—
700#386C2312yes—
701#386C2312yes—
702#386C2314yes—
703#386C2312yes—
704#385C2314yes—
705#385C2314yes—
706#385C2312yes—
707#385C2314yes—
708#385C2312yes—
709#385C2312yes—
710#385C2312yes—
711#385C2312yes—
712#385C2312yes—
713#384C2311yescharacteristic
714#384C2312yes—
715#384C2312yes—
716#384C2311yescharacteristic
717#384C2311yescharacteristic
718#384C2312yes—
719#384C2312yes—
720#383C2314yes—
721#382C2314yes—
722#382C2314yes—
723#382C2314yes—
724#382C2312yes—
725#382C2312yes—
726#382C2312yes—
727#382C2312yes—
728#382C2311yescharacteristic
729#382C2312yes—
730#382C2311yescharacteristic
731#381C2312yes—
732#381C2312yes—
733#381C2314yes—
734#381C2314yes—
735#381C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2311yescharacteristic
741#380C2312yes—
742#380C2312yes—
743#380C2312yes—
744#380C2312yes—
745#380C2312yes—
746#380C2312yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2314yes—
751#380C2314yes—
752#380C2311yescharacteristic
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#380C2314yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2311yescharacteristic
762#380C2312yes—
763#380C2312yes—
764#380C2312yes—
765#380C2312yes—
766#380C2311yescharacteristic
767#380C2312yes—
768#380C2312yes—
769#380C2312yes—
770#380C2312yes—
771#379C2312yes—
772#379C2314yes—
773#379C2314yes—
774#379C2312yes—
775#379C2312yes—
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2314yes—
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2311yescharacteristic
809C4×C22⋊C4C2311yescharacteristic
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2311yescharacteristic
817C4×C22⋊C4C2311yescharacteristic
818C43C2311yescharacteristic
819C25C2412yes—
820C2×#41—24no—
821C2×#41—24no—
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—44no—
825C2×#41—42no—
826C22×Q8C2411yescharacteristic
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×Q8C2414yes—
830C22×Q8C2414yes—
831C22×Q8C2414yes—
832C22×Q8C2412yes—
833C22×D4—42no—
834C22×D4—42no—
835C22×D4—42no—
836C22×D4C2411yescharacteristic
837C22×D4C2411yescharacteristic
838C22×D4C2411yescharacteristic
839C22×D4C2411yescharacteristic
840C22×D4C2411yescharacteristic
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2412yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C23×C4—28no—
855C23×C4—44no—
856C23×C4—44no—
857C23×C4C2412yes—
858C23×C4C2411yescharacteristic
859C23×C4C2411yescharacteristic
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2411yescharacteristic
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2412yes—
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2411yescharacteristic
871C23×C4C2414yes—
872C23×C4C2412yes—
873C4⋊Q8—24no—
874C4⋊Q8—44no—
875C4⋊Q8—44no—
876C4⋊Q8—42no—
877C4⋊Q8—44no—
878C4⋊Q8—44no—
879C4⋊Q8—44no—
880C4⋊Q8—44no—
881C4⋊Q8—48no—
882C4⋊Q8—82no—
883#127—42no—
884#126—44no—
885#126—48no—
886#126—48no—
887#126—48no—
888#125—42no—
889#124—24no—
890#124—48no—
891#124—48no—
892#124—44no—
893#124—48no—
894#124—48no—
895#124—42no—
896#124—42no—
897#124—48no—
898#124—84no—
899#124—84no—
900#123—44no—
901#123—48no—
902#123—44no—
903#123—48no—
904#123—84no—
905C22⋊Q8—28no—
906C22⋊Q8—28no—
907C22⋊Q8—24no—
908C22⋊Q8—48no—
909C22⋊Q8—42no—
910C22⋊Q8—44no—
911C22⋊Q8—44no—
912C22⋊Q8—42no—
913C22⋊Q8—82no—
914C22⋊Q8—84no—
915C22⋊Q8—82no—
916#121—24no—
917#121—44no—
918#121—44no—
919#121—44no—
920#121—44no—
921#121—42no—
922#121—44no—
923#121—44no—
924#121—42no—
925#121—42no—
926#121—42no—
927#121—44no—
928#121—44no—
929#121—44no—
930#121—84no—
931#120—44no—
932#120—48no—
933#120—84no—
934C4×Q8—28no—
935C4×Q8—24no—
936C4×Q8—24no—
937C4×Q8—44no—
938C4×Q8—48no—
939C4×Q8—42no—
940C4×Q8—44no—
941C4×Q8—44no—
942C4×D4—24no—
943C4×D4—24no—
944C4×D4—24no—
945C4×D4—24no—
946C4×D4—24no—
947C4×D4—44no—
948C4×D4—42no—
949C4×D4—42no—
950C4×D4—42no—
951C4×D4—42no—
952C4×D4—44no—
953C4×D4—44no—
954C4×D4—44no—
955C4×D4—42no—
956C4×D4—44no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—48no—
962C4×D4—48no—
963#117—44no—
964#117—44no—
965#117—44no—
966#117—44no—
967#117—42no—
968#117—44no—
969#117—44no—
970#117—44no—
971#117—44no—
972#117—44no—
973C2×C4⋊C4—44no—
974C2×C4⋊C4—42no—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2412yes—
979C2×C4⋊C4C2411yescharacteristic
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2411yescharacteristic
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2414yes—
990C2×C4⋊C4C2414yes—
991C2×C4⋊C4C2411yescharacteristic
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2411yescharacteristic
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2414yes—
1028C2×C4⋊C4C2414yes—
1029C2×C4⋊C4C2414yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2414yes—
1034C2×C22⋊C4—44no—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2412yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2411yescharacteristic
1042C2×C22⋊C4C2411yescharacteristic
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2412yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2412yes—
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2412yes—
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2412yes—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2414yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2412yes—
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2411yescharacteristic
1079C2×C22⋊C4C2411yescharacteristic
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2412yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C42—24no—
1111C2×C42—24no—
1112C2×C42—44no—
1113C2×C42C2411yescharacteristic
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2412yes—
1118C2×C42C2412yes—
1119C2×C42C2412yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2411yescharacteristic
1122C2×C42C2411yescharacteristic
1123C2×C42C2412yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2414yes—
1128C2×C42C2414yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2414yes—
1131C2×C42C2412yes—
1132C2×C42C2414yes—
1133C2×C42C2414yes—
1134C2×C42C2414yes—
1135C2×C42C2412yes—
1136C2×C42C2414yes—
1137C2×C42C2414yes—
1138C2×C42C2411yescharacteristic
1139C2×C42C2411yescharacteristic
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2411yescharacteristic
1144#95C2411yescharacteristic
1145#95C2414yes—
1146#95C2411yescharacteristic
1147#95C2411yescharacteristic
1148#95C2411yescharacteristic
1149#95C2411yescharacteristic
1150#95C2412yes—
1151#95C2412yes—
1152#95C2414yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2412yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2412yes—
1160#95C2414yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2414yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2414yes—
1195#95C2414yes—
1196#95C2414yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2414yes—
1200C24—24no—
1201C24—42no—
1202C24—42no—
1203C24—42no—
1204C24—42no—
1205C24—42no—
1206C24—42no—
1207C24C2512yes—
1208C24C2512yes—
1209C24C2511yescharacteristic
1210C24C2512yes—
1211C24C2512yes—
1212C24C2511yescharacteristic
1213#41—416no—
1214#41—816no—
1215C2×Q8—22no—
1216C2×Q8—22no—
1217C2×Q8—24no—
1218C2×Q8—22no—
1219C2×Q8—22no—
1220C2×Q8—22no—
1221C2×Q8—44no—
1222C2×Q8—42no—
1223C2×Q8—42no—
1224C2×Q8—42no—
1225C2×Q8—44no—
1226C2×Q8—44no—
1227C2×Q8—42no—
1228C2×Q8—42no—
1229C2×Q8—44no—
1230C2×Q8—44no—
1231C2×Q8—44no—
1232C2×Q8—44no—
1233C2×Q8—44no—
1234C2×Q8—44no—
1235C2×Q8H(5,𝔽2)14yes—
1236C2×D4—22no—
1237C2×D4—24no—
1238C2×D4—24no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—24no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—42no—
1254C2×D4—42no—
1255C2×D4—41no—
1256C2×D4—42no—
1257C2×D4—42no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—42no—
1261C2×D4—42no—
1262C2×D4—42no—
1263C2×D4—42no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—42no—
1267C2×D4—42no—
1268C2×D4—42no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—44no—
1274C2×D4—42no—
1275C2×D4—42no—
1276C2×D4—44no—
1277C2×D4—42no—
1278C2×D4—42no—
1279C2×D4—42no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—42no—
1283C2×D4—42no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—44no—
1288C2×D4—44no—
1289C2×D4—44no—
1290C2×D4—416no—
1291C22×C4—22no—
1292C22×C4—22no—
1293C22×C4—24no—
1294C22×C4—22no—
1295C22×C4—22no—
1296C22×C4—22no—
1297C22×C4—24no—
1298C22×C4—22no—
1299C22×C4—24no—
1300C22×C4—24no—
1301C22×C4—24no—
1302C22×C4—24no—
1303C22×C4—24no—
1304C22×C4—24no—
1305C22×C4—22no—
1306C22×C4—24no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—22no—
1315C22×C4—24no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—22no—
1319C22×C4—24no—
1320C22×C4—24no—
1321C22×C4—42no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—42no—
1325C22×C4—42no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—41no—
1329C22×C4—41no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—42no—
1333C22×C4—42no—
1334C22×C4—42no—
1335C22×C4—44no—
1336C22×C4—44no—
1337C22×C4—44no—
1338C22×C4—816no—
1339C22×C42−1+414yes—
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2512yes—
1343C22×C4C2511yescharacteristic
1344C22×C4C2511yescharacteristic
1345C22×C4C2512yes—
1346C22×C4C2512yes—
1347C22×C4C2512yes—
1348C22×C4C2511yescharacteristic
1349C22×C4C2512yes—
1350C22×C4C2511yescharacteristic
1351C22×C4C2512yes—
1352C22×C4C2514yes—
1353C22×C4C2512yes—
1354C22×C4C2514yes—
1355C22×C4C2512yes—
1356C22×C4C2514yes—
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2514yes—
1361C22×C4C2512yes—
1362C22×C4C2511yescharacteristic
1363C22×C4C2512yes—
1364C22×C4C2511yescharacteristic
1365C22×C4C2511yescharacteristic
1366C22×C4C2511yescharacteristic
1367C22×C4C2511yescharacteristic
1368C22×C4C2511yescharacteristic
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—24no—
1373C4⋊C4—24no—
1374C4⋊C4—22no—
1375C4⋊C4—22no—
1376C4⋊C4—24no—
1377C4⋊C4—22no—
1378C4⋊C4—24no—
1379C4⋊C4—24no—
1380C4⋊C4—24no—
1381C4⋊C4—28no—
1382C4⋊C4—28no—
1383C4⋊C4—22no—
1384C4⋊C4—28no—
1385C4⋊C4—24no—
1386C4⋊C4—24no—
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—24no—
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—44no—
1396C4⋊C4—42no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—41no—
1405C4⋊C4—42no—
1406C4⋊C4—42no—
1407C4⋊C4—42no—
1408C4⋊C4—42no—
1409C4⋊C4—42no—
1410C4⋊C4—44no—
1411C4⋊C4—44no—
1412C4⋊C4—44no—
1413C4⋊C4—44no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—42no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—42no—
1421C4⋊C4—42no—
1422C4⋊C4—42no—
1423C4⋊C4—44no—
1424C4⋊C4—44no—
1425C4⋊C4—44no—
1426C4⋊C4—44no—
1427C4⋊C4—44no—
1428C22⋊C4—22no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—28no—
1434C22⋊C4—28no—
1435C22⋊C4—24no—
1436C22⋊C4—24no—
1437C22⋊C4—24no—
1438C22⋊C4—22no—
1439C22⋊C4—24no—
1440C22⋊C4—24no—
1441C22⋊C4—24no—
1442C22⋊C4—24no—
1443C22⋊C4—24no—
1444C22⋊C4—42no—
1445C22⋊C4—42no—
1446C22⋊C4—42no—
1447C22⋊C4—42no—
1448C22⋊C4—42no—
1449C22⋊C4—42no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—42no—
1454C22⋊C4—42no—
1455C22⋊C4—42no—
1456C22⋊C4—42no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—42no—
1460C22⋊C4—42no—
1461C22⋊C4—41no—
1462C22⋊C4—41no—
1463C22⋊C4—41no—
1464C22⋊C4—41no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—42no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—44no—
1476C22⋊C4—44no—
1477C22⋊C4—44no—
1478C22⋊C4—44no—
1479C22⋊C4—44no—
1480C22⋊C4—44no—
1481C22⋊C4—42no—
1482C22⋊C4—44no—
1483C22⋊C4—42no—
1484C22⋊C4—44no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—42no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—44no—
1494C22⋊C4—42no—
1495C22⋊C4—42no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C42—22no—
1504C42—22no—
1505C42—22no—
1506C42—22no—
1507C42—22no—
1508C42—22no—
1509C42—24no—
1510C42—22no—
1511C42—24no—
1512C42—24no—
1513C42—28no—
1514C42—22no—
1515C42—22no—
1516C42—24no—
1517C42—22no—
1518C42—22no—
1519C42—28no—
1520C42—42no—
1521C42—42no—
1522C42—44no—
1523C42—44no—
1524C42—44no—
1525C42—44no—
1526C42—44no—
1527C42—44no—
1528C42—41no—
1529C42H(5,𝔽2)14yes—
1530C23—21no—
1531C23—21no—
1532C23—21no—
1533C23—21no—
1534C23—21no—
1535C23—21no—
1536C23—21no—
1537C23—22no—
1538C23—22no—
1539C23—22no—
1540C23—22no—
1541C23—22no—
1542C23—22no—
1543C23—22no—
1544C23—22no—
1545C23—21no—
1546C23—21no—
1547C23—22no—
1548C23—22no—
1549C23—22no—
1550C23—22no—
1551C23—22no—
1552C23—22no—
1553C23—22no—
1554C23—22no—
1555C23—22no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—22no—
1562C23—21no—
1563C23—21no—
1564C23—22no—
1565C23—21no—
1566C23—21no—
1567C23—22no—
1568C23—22no—
1569C23—22no—
1570C23—22no—
1571C23—48no—
1572C23—84no—
1573C23—84no—
1574C23—84no—
1575C23—84no—
1576C23—84no—
1577C23—84no—
1578C23C2×2−1+412yes—
1579C23C2611yescharacteristic
1580Q8—28no—
1581Q8—44no—
1582Q8—84no—
1583Q8—88no—
1584Q8—84no—
1585Q8—164no—
1586Q8—164no—
1587D4—44no—
1588D4—48no—
1589D4—48no—
1590D4—44no—
1591D4—44no—
1592D4—44no—
1593D4—44no—
1594D4—84no—
1595D4—88no—
1596D4—84no—
1597D4—88no—
1598D4—84no—
1599D4—84no—
1600D4—84no—
1601D4—84no—
1602D4—84no—
1603D4—164no—
1604D4—164no—
1605C2×C4—21no—
1606C2×C4—22no—
1607C2×C4—21no—
1608C2×C4—21no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—28no—
1614C2×C4—22no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—24no—
1621C2×C4—22no—
1622C2×C4—22no—
1623C2×C4—21no—
1624C2×C4—21no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—21no—
1628C2×C4—24no—
1629C2×C4—22no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—24no—
1635C2×C4—24no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—24no—
1648C2×C4—24no—
1649C2×C4—21no—
1650C2×C4—22no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—22no—
1654C2×C4—22no—
1655C2×C4—22no—
1656C2×C4—21no—
1657C2×C4—22no—
1658C2×C4—24no—
1659C2×C4—24no—
1660C2×C4—21no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—21no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—24no—
1668C2×C4—22no—
1669C2×C4—21no—
1670C2×C4—22no—
1671C2×C4—21no—
1672C2×C4—22no—
1673C2×C4—22no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—24no—
1677C2×C4—22no—
1678C2×C4—22no—
1679C2×C4—24no—
1680C2×C4—24no—
1681C2×C4—21no—
1682C2×C4—21no—
1683C2×C4—48no—
1684C2×C4—44no—
1685C2×C4—48no—
1686C2×C4—48no—
1687C2×C4—44no—
1688C2×C4—48no—
1689C2×C4—48no—
1690C2×C4—44no—
1691C2×C4—82no—
1692C2×C4—82no—
1693C2×C4—84no—
1694C2×C4—84no—
1695C2×C4—84no—
1696C2×C4—84no—
1697C2×C4—164no—
1698C2×C4C2×H(5,𝔽2)12yes—
1699C2×C4C2×H(5,𝔽2)14yes—
1700C2×C4C2×H(5,𝔽2)12yes—
1701C2×C4C2×H(5,𝔽2)12yes—
1702C2×C4C2×H(5,𝔽2)12yes—
1703C2×C4C2×2−1+412yes—
1704C2×C4C2×2−1+412yes—
1705C2×C4#58512yes—
1706C2×C4#58512yes—
1707C2×C4#58512yes—
1708C22—22no—
1709C22—22no—
1710C22—22no—
1711C22—41no—
1712C22—41no—
1713C22—41no—
1714C22—41no—
1715C22—42no—
1716C22—42no—
1717C22—42no—
1718C22—41no—
1719C22—42no—
1720C22—41no—
1721C22—42no—
1722C22—42no—
1723C22—42no—
1724C22—42no—
1725C22—41no—
1726C22—42no—
1727C22—42no—
1728C22—42no—
1729C22—42no—
1730C22—41no—
1731C22—42no—
1732C22—42no—
1733C22—42no—
1734C22—42no—
1735C22—42no—
1736C22—42no—
1737C22—42no—
1738C22—42no—
1739C22—41no—
1740C22—42no—
1741C22—41no—
1742C22—42no—
1743C22—42no—
1744C22—42no—
1745C22—41no—
1746C22—42no—
1747C22—42no—
1748C22—42no—
1749C22—42no—
1750C22—816no—
1751C22C22×H(5,𝔽2)11yescharacteristic
1752C22C22×H(5,𝔽2)11yescharacteristic
1753C22C22×2−1+411yescharacteristic
1754C22C2×#58511yescharacteristic
1755C22C2×#58511yescharacteristic
1756C22C2×#58511yescharacteristic
1757C22H(7,𝔽2)11yescharacteristic
1758C4—22no—
1759C4—24no—
1760C4—22no—
1761C4—22no—
1762C4—41no—
1763C4—42no—
1764C4—42no—
1765C4—41no—
1766C4—41no—
1767C4—42no—
1768C4—42no—
1769C4—42no—
1770C4—41no—
1771C4—44no—
1772C4—42no—
1773C4—42no—
1774C4—42no—
1775C4—44no—
1776C4—44no—
1777C4—41no—
1778C4—41no—
1779C4—42no—
1780C4—41no—
1781C4—41no—
1782C4—42no—
1783C4—42no—
1784C4—44no—
1785C4#353614yes—
1786C4#354014yes—
1787C2—42no—
1788C2—82no—
1789C2—81no—
1790C2—82no—
1791C2—82no—
1792C2—82no—
1793C2C2×#353611yescharacteristic
1794C2C2×#354011yescharacteristic
1795C2#6275211yescharacteristic
1796C2#6292311yescharacteristic
1797C2#6292911yescharacteristic
1798C2#6293011yescharacteristic
1799C2#6302211yescharacteristic
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. #59659C2semidirect
2. #59630C2semidirect
3. #59244C2semidirect
4. #59230C2semidirect
5. #59017C2semidirect
6. #58313C2semidirect
7. #56494C2semidirect
8. #53071C2semidirect
9. #53061C2semidirect
10. #53015C2semidirect
11. #52981C2semidirect
12. #52494C2semidirect
13. #42991C2semidirect
14. #42905C2semidirect
15. #42882C2semidirect
16. #42473C2semidirect
17. #41139C2semidirect
18. #40102C2semidirect
19. #39934C2semidirect
20. #39562C2semidirect
21. #39505C2semidirect
22. #39469C2semidirect
23. #39377C2semidirect
24. #39125C2semidirect
25. #37669C2semidirect
26. #37636C2semidirect
27. #37621C2semidirect
28. #37516C2semidirect
29. #37480C2semidirect
30. #36456C2semidirect
31. #36194C2semidirect
32. #36160C2semidirect
33. #34935C2semidirect
34. #34715C2semidirect
35. #34700C2semidirect
36. C2×Q82C22semidirect
37. C2×#556C22semidirect
39. C2×#542C22semidirect
40. C2×#532C22semidirect
45. #2868C22semidirect
47. #2857C22semidirect
48. #2857C22semidirect
53. #2832C22semidirect
54. #2832C22semidirect
55. #2830C22semidirect
57. #2826C22semidirect
58. #2824C22semidirect
63. #2813C22semidirect
64. #2798C22semidirect
65. #2795C22semidirect
68. #2781C22semidirect
69. #2777C22semidirect
70. #2767C22semidirect
71. #2754C22semidirect
73. #2751C22semidirect
75. #2731C22semidirect
76. #2731C22semidirect
77. #2730C22semidirect
78. #2718C22semidirect
79. #2716C22semidirect
80. #2715C22semidirect
81. #2712C22semidirect
82. #2710C22semidirect
85. #2705C22semidirect
86. #2702C22semidirect
87. #2702C22semidirect
88. #2700C22semidirect
91. #2696C22semidirect
94. #2676C22semidirect
95. #2674C22semidirect
96. #2674C22semidirect
97. #2672C22semidirect
101. #2666C22semidirect
104. #2665C22semidirect
105. #2665C22semidirect
106. #2662C22semidirect
107. #2662C22semidirect
108. #2650C22semidirect
109. #2648C22semidirect
110. #2637C22semidirect
111. #2632C22semidirect
112. #2628C22semidirect
113. #2628C22semidirect
114. #2628C22semidirect
115. #2628C22semidirect
116. #2628C22semidirect
118. #2624C22semidirect
120. #2619C22semidirect
121. #2616C22semidirect
124. #2607C22semidirect
125. #2607C22semidirect
126. #2596C22semidirect
127. #2595C22semidirect
128. #2592C22semidirect
129. #2574C22semidirect
130. #2571C22semidirect
135. #2563C22semidirect
136. #2563C22semidirect
137. #2562C22semidirect
138. #2557C22semidirect
140. #2551C22semidirect
141. #2550C22semidirect
142. #2547C22semidirect
143. #2545C22semidirect
149. #2538C22semidirect
150. #2538C22semidirect
155. #2536C22semidirect
157. #2535C22semidirect
160. #2508C22semidirect
162. #2500C22semidirect
164. #2497C22semidirect
165. #2497C22semidirect
166. #2496C22semidirect
167. #2496C22semidirect
168. #2495C22semidirect
169. #2495C22semidirect
171. #2492C22semidirect
172. #2492C22semidirect
173. #2492C22semidirect
180. #2491C22semidirect
181. #2491C22semidirect
182. #2491C22semidirect
185. #2485C22semidirect
186. #2485C22semidirect
188. #2476C22semidirect
189. #2474C22semidirect
191. #2469C22semidirect
193. #2468C22semidirect
194. #2467C22semidirect
195. #2467C22semidirect
198. #2459C22semidirect
199. #2459C22semidirect
202. #2457C22semidirect
206. #2452C22semidirect
207. #2451C22semidirect
210. #2445C22semidirect
212. #2440C22semidirect
217. #2439C22semidirect
218. #2439C22semidirect
219. #2439C22semidirect
220. #2439C22semidirect
221. #2439C22semidirect
222. #2439C22semidirect
223. #2439C22semidirect
226. #2428C22semidirect
228. #2427C22semidirect
230. #2426C22semidirect
231. #2426C22semidirect
232. #2423C22semidirect
233. #2422C22semidirect
234. #2421C22semidirect
235. #2421C22semidirect
238. #2420C22semidirect
245. #2414C22semidirect
246. #2414C22semidirect
247. #2414C22semidirect
257. #2369C22semidirect
258. #2367C22semidirect
259. #2365C22semidirect
262. #2362C22semidirect
263. #2362C22semidirect
264. #2355C22semidirect
265. #2355C22semidirect
269. #2351C22semidirect
270. Q8×C4⋊C4C22semidirect
271. D4×C4⋊C4C22semidirect
272. #2345C22semidirect
274. #2337C22semidirect
275. #2323C22semidirect
276. #2314C22semidirect
277. #2311C22semidirect
278. C4×C4⋊Q8C22semidirect
280. C4×#124C22semidirect
282. C4×C22⋊Q8C22semidirect
283. C4×C22⋊Q8C22semidirect
284. C4×#123C22semidirect
290. #2297C22semidirect
292. #2293C22semidirect
294. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#596592
#596302
#592442
#592302
#590172
#583132
#564942
#530712
#530612
#530152
#529812
#524942
#429912
#429052
#428822
#424732
#411392
#401022
#399342
#395622
#395052
#394692
#393772
#391252
#376692
#376362
#376212
#375162
#374802
#364562
#361942
#361602
#349352
#347152
#347002