Finite Group Databasebeta

← #7780450

Subgroups — #7780450

Order 512.

5382 conjugacy classes of subgroups.

The subgroup lattice has 1803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C211yesmaximal, characteristic, complemented
2#59815C211yesmaximal, characteristic, complemented
3#59676C212yesmaximal, complemented
4#59426C211yesmaximal, characteristic, complemented
5#59411C211yesmaximal, characteristic, complemented
6#59023C212yesmaximal, complemented
7#50024C214yesmaximal, complemented
8#48406C214yesmaximal, complemented
9#46736C214yesmaximal, complemented
10#46571C214yesmaximal, complemented
11#45616C212yesmaximal, complemented
12#45598C212yesmaximal, complemented
13#44942C212yesmaximal, complemented
14#44876C212yesmaximal, complemented
15#42580C212yesmaximal, complemented
16#42536C212yesmaximal, complemented
17#40148C212yesmaximal, complemented
18#39887C212yesmaximal, complemented
19#39169C211yesmaximal, characteristic, complemented
20#39144C212yesmaximal, complemented
21#39066C212yesmaximal, complemented
22#38977C211yesmaximal, characteristic, complemented
23#38950C212yesmaximal, complemented
24#38252C212yesmaximal, complemented
25#37368C212yesmaximal, complemented
26#36496C211yesmaximal, characteristic, complemented
27#36493C211yesmaximal, characteristic, complemented
28#36275C211yesmaximal, characteristic, complemented
29#36270C211yesmaximal, characteristic, complemented
30#36154C211yesmaximal, characteristic, complemented
31#36101C211yesmaximal, characteristic, complemented
32#35288C211yesmaximal, characteristic, complemented
33#34916C211yesmaximal, characteristic, complemented
34#34494C212yesmaximal, complemented
35C4×#535C211yesmaximal, characteristic, complemented
36C2×#559C2211yescharacteristic, complemented
37C2×#554C2211yescharacteristic
38C2×#554C2211yescharacteristic, complemented
39C2×#552C2212yescomplemented
40C2×#550C2212yes—
41C2×#550C2211yescharacteristic
42C2×#547C2212yescomplemented
43C2×#535C2211yescharacteristic
44C2×#525C2212yes—
45C2×C4×#41C2211yescharacteristic
46C22×C4×D4C2211yescharacteristic
47#2861C2212yescomplemented
48#2860C2212yes—
49#2859C2211yescharacteristic, complemented
50#2858C2211yescharacteristic, complemented
51#2857C2211yescharacteristic
52#2856C2211yescharacteristic
53#2855C2212yescomplemented
54#2850C2212yescomplemented
55#2848C2212yes—
56#2847C2212yes—
57#2827C2214yescomplemented
58#2826C2214yescomplemented
59#2801C2214yescomplemented
60#2795C2214yescomplemented
61#2790C2214yescomplemented
62#2780C2214yes—
63#2779C2214yescomplemented
64#2778C2214yes—
65#2778C2214yes—
66#2765C2214yescomplemented
67#2759C2214yescomplemented
68#2757C2214yescomplemented
69#2752C2214yes—
70#2750C2214yescomplemented
71#2748C2214yes—
72#2746C2214yescomplemented
73#2746C2214yescomplemented
74#2746C2214yescomplemented
75#2743C2214yescomplemented
76#2741C2214yescomplemented
77#2739C2214yescomplemented
78#2732C2214yescomplemented
79#2718C2214yescomplemented
80#2708C2214yescomplemented
81#2707C2214yescomplemented
82#2706C2214yescomplemented
83#2705C2214yes—
84#2704C2214yescomplemented
85#2702C2214yescomplemented
86#2701C2214yescomplemented
87#2699C2214yes—
88#2693C2214yescomplemented
89#2691C2214yescomplemented
90#2688C2214yes—
91#2687C2214yescomplemented
92#2685C2214yes—
93#2685C2214yes—
94#2682C2214yescomplemented
95#2678C2214yes—
96#2676C2214yescomplemented
97#2676C2214yescomplemented
98#2668C2214yes—
99#2645C2212yescomplemented
100#2644C2212yescomplemented
101#2643C2214yescomplemented
102#2641C2212yes—
103#2636C2214yescomplemented
104#2633C2214yescomplemented
105#2624C2212yes—
106#2618C2214yescomplemented
107#2602C2214yes—
108#2601C2214yescomplemented
109#2598C2214yes—
110#2592C2212yes—
111#2590C2212yescomplemented
112#2589C2212yes—
113#2588C2212yescomplemented
114#2587C2212yes—
115#2587C2214yescomplemented
116#2582C2211yescharacteristic, complemented
117#2567C2211yescharacteristic, complemented
118#2566C2214yes—
119#2566C2212yescomplemented
120#2566C2212yescomplemented
121#2563C2211yescharacteristic
122#2562C2212yescomplemented
123#2558C2214yescomplemented
124#2552C2212yescomplemented
125#2544C2212yes—
126#2544C2212yes—
127#2543C2214yes—
128#2542C2212yescomplemented
129#2541C2212yes—
130#2541C2211yescharacteristic
131#2541C2211yescharacteristic, complemented
132#2540C2212yes—
133#2538C2211yescharacteristic
134#2538C2211yescharacteristic
135#2538C2214yescomplemented
136#2538C2211yescharacteristic, complemented
137#2538C2212yescomplemented
138#2537C2212yescomplemented
139#2536C2212yescomplemented
140#2535C2212yes—
141#2534C2214yes—
142#2514C2212yescomplemented
143#2513C2212yescomplemented
144#2512C2212yes—
145#2511C2211yescharacteristic, complemented
146#2510C2214yescomplemented
147#2508C2212yescomplemented
148#2507C2211yescharacteristic, complemented
149#2506C2212yescomplemented
150#2505C2214yescomplemented
151#2503C2212yescomplemented
152#2498C2214yescomplemented
153#2497C2211yescharacteristic
154#2496C2212yescomplemented
155#2494C2212yescomplemented
156#2494C2212yescomplemented
157#2492C2211yescharacteristic
158#2490C2212yes—
159#2489C2212yescomplemented
160#2487C2212yes—
161#2487C2212yes—
162#2471C2214yescomplemented
163#2469C2214yescomplemented
164#2467C2214yes—
165#2461C2214yescomplemented
166#2461C2214yescomplemented
167#2457C2214yes—
168#2456C2214yes—
169#2456C2214yes—
170#2454C2212yes—
171#2454C2212yes—
172#2454C2212yescomplemented
173#2454C2212yescomplemented
174#2453C2212yescomplemented
175#2451C2211yescharacteristic, complemented
176#2450C2214yes—
177#2450C2214yes—
178#2449C2214yes—
179#2448C2212yescomplemented
180#2448C2212yescomplemented
181#2447C2212yes—
182#2447C2212yescomplemented
183#2447C2212yescomplemented
184#2446C2211yescharacteristic, complemented
185#2445C2212yes—
186#2445C2212yes—
187#2445C2212yes—
188#2445C2212yes—
189#2445C2212yescomplemented
190#2443C2214yescomplemented
191#2442C2212yes—
192#2442C2212yescomplemented
193#2441C2212yes—
194#2439C2212yescomplemented
195#2438C2214yescomplemented
196#2437C2214yes—
197#2433C2212yes—
198#2432C2212yescomplemented
199#2431C2212yes—
200#2430C2214yes—
201#2429C2211yescharacteristic
202#2427C2212yes—
203#2427C2212yescomplemented
204#2426C2212yes—
205#2426C2212yescomplemented
206#2426C2212yescomplemented
207#2425C2214yescomplemented
208#2424C2214yes—
209#2424C2214yes—
210#2423C2211yescharacteristic
211#2422C2212yescomplemented
212#2420C2212yes—
213#2419C2214yescomplemented
214#2418C2214yes—
215#2417C2212yes—
216#2417C2212yes—
217#2417C2212yescomplemented
218#2417C2212yescomplemented
219#2416C2212yescomplemented
220#2416C2212yescomplemented
221#2416C2212yescomplemented
222#2416C2212yescomplemented
223#2414C2212yes—
224#2407C2212yes—
225#2407C2212yescomplemented
226#2407C2212yescomplemented
227#2407C2214yescomplemented
228#2404C2214yes—
229#2402C2212yescomplemented
230#2396C2212yes—
231#2377C2214yescomplemented
232#2377C2214yescomplemented
233#2366C2212yes—
234#2366C2212yes—
235#2366C2212yescomplemented
236#2363C2212yes—
237#2361C2212yes—
238#2361C2214yescomplemented
239#2361C2212yescomplemented
240#2361C2212yescomplemented
241#2355C2211yescharacteristic, complemented
242#2355C2212yescomplemented
243#2354C2211yescharacteristic
244#2352C2212yescomplemented
245#2349C2212yes—
246#2349C2212yescomplemented
247D4×C4⋊C4C2211yescharacteristic
248D4×C4⋊C4C2212yescomplemented
249D4×C4⋊C4C2212yescomplemented
250D4×C4⋊C4C2211yescharacteristic, complemented
251#2347C2212yescomplemented
252#2339C2212yes—
253#2339C2212yescomplemented
254#2339C2214yescomplemented
255D4×C22⋊C4C2212yes—
256#2328C2211yescharacteristic
257#2328C2211yescharacteristic
258#2328C2212yescomplemented
259#2326C2211yescharacteristic
260#2326C2211yescharacteristic
261#2325C2214yescomplemented
262#2325C2214yescomplemented
263#2324C2212yes—
264#2324C2212yes—
265#2324C2212yes—
266#2324C2214yescomplemented
267#2321C2212yes—
268#2321C2212yes—
269#2319C2212yes—
270#2319C2212yescomplemented
271#2317C2211yescharacteristic
272#2311C2211yescharacteristic
273#2311C2214yescomplemented
274#2309C2211yescharacteristic
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×C4⋊Q8C2211yescharacteristic, complemented
277C4×C4⋊Q8C2211yescharacteristic, complemented
278C4×#127C2211yescharacteristic
279C4×#127C2211yescharacteristic
280C4×#127C2212yes—
281C4×#127C2211yescharacteristic, complemented
282C4×#124C2211yescharacteristic
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2212yescomplemented
289C4×#120C2212yes—
290C4×#120C2212yes—
291#2298C2212yes—
292#2295C2211yescharacteristic, complemented
293#2295C2212yescomplemented
294#2293C2212yescomplemented
295C2×#389C2212yescomplemented
296C2×#380C2212yes—
297C42×Q8C2211yescharacteristic, complemented
298C4×#117C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2314yes—
301C22×#41C2312yes—
302C23×D4C2311yescharacteristic
303C24×C4C2312yes—
304#559—44no—
305#554—44no—
306#554—44no—
307#552—48no—
308#550—216no—
309#550—44no—
310#547—48no—
311#535—28no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×#127C2311yescharacteristic
316C2×#127C2312yes—
317C2×#127C2311yescharacteristic
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2311yescharacteristic
321C2×#126C2314yes—
322C2×#126C2314yes—
323C2×#125C2312yes—
324C2×#125C2314yes—
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#124C2311yescharacteristic
328C2×#124C2311yescharacteristic
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333#525—48no—
334C2×#123C2314yes—
335C2×#123C2314yes—
336C2×#123C2314yes—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2311yescharacteristic
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2312yes—
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2314yes—
348C2×C22⋊Q8C2314yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×#121C2312yes—
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2314yes—
355C2×#121C2314yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2312yes—
365C2×#121C2314yes—
366C2×#121C2314yes—
367C2×#120C2312yes—
368C2×#120C2312yes—
369C2×#120C2314yes—
370C2×#120C2314yes—
371C4×#41—44no—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2311yescharacteristic
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2312yes—
380C2×C4×D4—44no—
381C2×C4×D4C2311yescharacteristic
382C2×C4×D4C2311yescharacteristic
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2314yes—
395C2×C4×D4C2312yes—
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2314yes—
410C2×C4×D4C2314yes—
411C2×#117C2311yescharacteristic
412C2×#117C2311yescharacteristic
413C2×#117C2312yes—
414C2×#117C2311yescharacteristic
415C2×#117C2314yes—
416C2×#117C2312yes—
417C22×C4⋊C4C2312yes—
418C22×C4⋊C4C2311yescharacteristic
419C22×C4⋊C4C2312yes—
420C22×C4⋊C4C2312yes—
421C22×C4⋊C4C2312yes—
422C22×C4⋊C4C2314yes—
423C22×C22⋊C4C2312yes—
424C22×C22⋊C4C2314yes—
425C22×C42C2311yescharacteristic
426C22×C42C2312yes—
427#401C2314yes—
428#401C2314yes—
429#400C2314yes—
430#400C2312yes—
431#400C2314yes—
432#400C2314yes—
433#400C2314yes—
434#400C2312yes—
435#400C2314yes—
436#400C2312yes—
437#400C2312yes—
438#400C2312yes—
439#400C2314yes—
440#400C2314yes—
441#400C2314yes—
442#399C2314yes—
443#399C2314yes—
444#399C2312yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#398C2312yes—
450#398C2314yes—
451#398C2314yes—
452#398C2312yes—
453#398C2312yes—
454#398C2312yes—
455#398C2312yes—
456#398C2312yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#397C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#396C2312yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2312yes—
483#396C2314yes—
484#396C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2314yes—
489#396C2314yes—
490#395C2314yes—
491#395C2312yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#393C2314yes—
513#393C2312yes—
514#393C2314yes—
515#392C2314yes—
516#392C2314yes—
517#392C2314yes—
518#392C2314yes—
519#392C2314yes—
520#392C2314yes—
521#392C2314yes—
522#392C2314yes—
523#391C2312yes—
524#391C2311yescharacteristic
525#391C2311yescharacteristic
526#391C2312yes—
527#391C2311yescharacteristic
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2314yes—
531#391C2312yes—
532#391C2312yes—
533#391C2312yes—
534#391C2312yes—
535#391C2312yes—
536#391C2311yescharacteristic
537#391C2311yescharacteristic
538#391C2312yes—
539#391C2311yescharacteristic
540#391C2311yescharacteristic
541#390C2311yescharacteristic
542#390C2311yescharacteristic
543#390C2311yescharacteristic
544#390C2311yescharacteristic
545#390C2311yescharacteristic
546#390C2314yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2312yes—
551#390C2312yes—
552#390C2314yes—
553#390C2312yes—
554#390C2312yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2311yescharacteristic
560#390C2314yes—
561#390C2314yes—
562#390C2312yes—
563#390C2312yes—
564#390C2312yes—
565#390C2314yes—
566#390C2312yes—
567#390C2312yes—
568#390C2314yes—
569#390C2314yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2312yes—
575#390C2312yes—
576#390C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2311yescharacteristic
581#389C2312yes—
582#389C2311yescharacteristic
583#389C2312yes—
584#389C2312yes—
585#389C2312yes—
586#389C2312yes—
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2312yes—
595#389C2314yes—
596#389C2314yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2312yes—
603#389C2312yes—
604#389C2312yes—
605#389C2311yescharacteristic
606#389C2311yescharacteristic
607#389C2311yescharacteristic
608#389C2314yes—
609#389C2311yescharacteristic
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2312yes—
622#388C2312yes—
623#388C2312yes—
624#388C2314yes—
625#388C2312yes—
626#388C2312yes—
627#388C2314yes—
628#388C2312yes—
629#388C2312yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#387C2312yes—
645#387C2312yes—
646#387C2314yes—
647#387C2314yes—
648#387C2312yes—
649#387C2312yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2312yes—
656#387C2312yes—
657#387C2312yes—
658#387C2312yes—
659#387C2312yes—
660#387C2314yes—
661#387C2314yes—
662#387C2314yes—
663#387C2314yes—
664#386C2312yes—
665#386C2312yes—
666#386C2312yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2312yes—
671#386C2314yes—
672#386C2312yes—
673#386C2312yes—
674#386C2312yes—
675#386C2312yes—
676#386C2312yes—
677#386C2312yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2314yes—
684#386C2314yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#385C2312yes—
703#385C2314yes—
704#385C2314yes—
705#385C2314yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2312yes—
711#385C2314yes—
712#385C2312yes—
713#385C2312yes—
714#385C2312yes—
715#385C2312yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2312yes—
721#385C2312yes—
722#385C2314yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2314yes—
727#385C2314yes—
728#385C2314yes—
729#385C2314yes—
730#384C2311yescharacteristic
731#384C2312yes—
732#384C2311yescharacteristic
733#384C2311yescharacteristic
734#384C2311yescharacteristic
735#384C2311yescharacteristic
736#384C2311yescharacteristic
737#384C2314yes—
738#383C2314yes—
739#382C2312yes—
740#382C2314yes—
741#382C2311yescharacteristic
742#382C2311yescharacteristic
743#382C2312yes—
744#382C2312yes—
745#381C2314yes—
746#381C2314yes—
747#381C2314yes—
748#381C2314yes—
749#381C2314yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2312yes—
755#380C2312yes—
756#380C2312yes—
757#380C2312yes—
758#380C2314yes—
759#380C2314yes—
760#380C2314yes—
761#380C2314yes—
762#380C2312yes—
763#380C2314yes—
764#380C2311yescharacteristic
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2314yes—
769#380C2314yes—
770#380C2314yes—
771#380C2314yes—
772#380C2314yes—
773#380C2311yescharacteristic
774#379C2312yes—
775#379C2312yes—
776#379C2314yes—
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2314yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2312yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2311yescharacteristic
811C4×C22⋊C4C2311yescharacteristic
812#376C2312yes—
813#376C2311yescharacteristic
814#376C2311yescharacteristic
815C2×#95C2314yes—
816C2×#95C2314yes—
817C2×#95C2314yes—
818C43C2311yescharacteristic
819C43C2311yescharacteristic
820C43C2312yes—
821C25C2412yes—
822C2×#41—24no—
823C2×#41—216no—
824C2×#41—24no—
825C2×#41—42no—
826C2×#41—44no—
827C2×#41—48no—
828C2×#41—44no—
829C2×#41—44no—
830C2×#41—84no—
831C22×Q8C2411yescharacteristic
832C22×Q8C2411yescharacteristic
833C22×Q8C2411yescharacteristic
834C22×Q8C2412yes—
835C22×Q8C2412yes—
836C22×D4—24no—
837C22×D4—24no—
838C22×D4—42no—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2412yes—
843C22×D4C2414yes—
844C22×D4C2412yes—
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2414yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C22×D4C2412yes—
857C22×D4C2412yes—
858C23×C4—44no—
859C23×C4—44no—
860C23×C4—44no—
861C23×C4C2412yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2411yescharacteristic
865C23×C4C2414yes—
866C23×C4C2412yes—
867C23×C4C2411yescharacteristic
868C23×C4C2411yescharacteristic
869C23×C4C2414yes—
870C23×C4C2414yes—
871C23×C4C2414yes—
872C23×C4C2412yes—
873C23×C4C2412yes—
874C23×C4C2414yes—
875C23×C4C2414yes—
876C23×C4C2412yes—
877C23×C4C2414yes—
878C23×C4C2412yes—
879C4⋊Q8—24no—
880C4⋊Q8—24no—
881C4⋊Q8—42no—
882#127—24no—
883#127—28no—
884#127—28no—
885#127—24no—
886#127—44no—
887#127#4118yescomplemented
888#126—48no—
889#126—84no—
890#125—48no—
891#125—44no—
892#125—44no—
893#125—44no—
894#124—24no—
895#124—24no—
896#124—44no—
897#124—44no—
898#124—82no—
899#124—82no—
900#123—48no—
901#123—48no—
902#123—48no—
903#123—48no—
904#123—48no—
905#123—84no—
906C22⋊Q8—24no—
907C22⋊Q8—48no—
908C22⋊Q8—48no—
909C22⋊Q8—48no—
910C22⋊Q8—42no—
911C22⋊Q8—44no—
912C22⋊Q8—44no—
913C22⋊Q8—44no—
914C22⋊Q8—44no—
915C22⋊Q8—44no—
916C22⋊Q8—82no—
917#121—28no—
918#121—28no—
919#121—216no—
920#121—216no—
921#121—216no—
922#121—28no—
923#121—28no—
924#121—48no—
925#121—44no—
926#121—44no—
927#121—44no—
928#121—44no—
929#121—44no—
930#121—84no—
931#121—82no—
932#121—84no—
933#120—28no—
934#120—28no—
935#120—48no—
936#120—84no—
937C4×Q8—24no—
938C4×Q8—28no—
939C4×Q8—24no—
940C4×Q8—24no—
941C4×Q8—24no—
942C4×Q8—42no—
943C4×Q8—42no—
944C4×Q8—82no—
945C4×D4—28no—
946C4×D4—28no—
947C4×D4—28no—
948C4×D4—24no—
949C4×D4—24no—
950C4×D4—24no—
951C4×D4—44no—
952C4×D4—48no—
953C4×D4—42no—
954C4×D4—42no—
955C4×D4—42no—
956C4×D4—48no—
957C4×D4—44no—
958C4×D4—44no—
959C4×D4—44no—
960C4×D4—44no—
961C4×D4—44no—
962C4×D4—44no—
963C4×D4—44no—
964C4×D4—44no—
965C4×D4—44no—
966C4×D4—44no—
967C4×D4—44no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—84no—
971C4×D4—84no—
972C4×D4—82no—
973C4×D4—84no—
974C4×D4—84no—
975#117—24no—
976#117—28no—
977#117—24no—
978#117—48no—
979#117—44no—
980#117—42no—
981C2×C4⋊C4—28no—
982C2×C4⋊C4—42no—
983C2×C4⋊C4—44no—
984C2×C4⋊C4—44no—
985C2×C4⋊C4—44no—
986C2×C4⋊C4—84no—
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2411yescharacteristic
993C2×C4⋊C4C2411yescharacteristic
994C2×C4⋊C4C2414yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2412yes—
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2411yescharacteristic
999C2×C4⋊C4C2411yescharacteristic
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2411yescharacteristic
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2412yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2411yescharacteristic
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2414yes—
1020C2×C4⋊C4C2414yes—
1021C2×C4⋊C4C2414yes—
1022C2×C4⋊C4C2414yes—
1023C2×C4⋊C4C2414yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2414yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2412yes—
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2414yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2412yes—
1036C2×C4⋊C4C2412yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2412yes—
1040C2×C4⋊C4C2412yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2412yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2411yescharacteristic
1051C2×C22⋊C4—44no—
1052C2×C22⋊C4—84no—
1053C2×C22⋊C4C2412yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2411yescharacteristic
1057C2×C22⋊C4C2411yescharacteristic
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2411yescharacteristic
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2412yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2412yes—
1073C2×C22⋊C4C2412yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2412yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2414yes—
1088C2×C22⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2414yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2414yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2412yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2412yes—
1104C2×C22⋊C4C2412yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2412yes—
1117C2×C42—24no—
1118C2×C42—44no—
1119C2×C42C2414yes—
1120C2×C42C2411yescharacteristic
1121C2×C42C2412yes—
1122C2×C42C2411yescharacteristic
1123C2×C42C2411yescharacteristic
1124C2×C42C2411yescharacteristic
1125C2×C42C2411yescharacteristic
1126C2×C42C2411yescharacteristic
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2412yes—
1131C2×C42C2411yescharacteristic
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2412yes—
1135C2×C42C2412yes—
1136C2×C42C2412yes—
1137C2×C42C2412yes—
1138C2×C42C2411yescharacteristic
1139C2×C42C2412yes—
1140C2×C42C2414yes—
1141C2×C42C2412yes—
1142C2×C42C2414yes—
1143C2×C42C2411yescharacteristic
1144C2×C42C2412yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2411yescharacteristic
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149#95C2414yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2414yes—
1155#95C2414yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2414yes—
1159#95C2414yes—
1160#95C2411yescharacteristic
1161#95C2411yescharacteristic
1162#95C2411yescharacteristic
1163#95C2411yescharacteristic
1164#95C2411yescharacteristic
1165#95C2411yescharacteristic
1166#95C2411yescharacteristic
1167#95C2411yescharacteristic
1168#95C2412yes—
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2414yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2412yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2414yes—
1192#95C2414yes—
1193#95C2414yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2412yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2412yes—
1203#95C2412yes—
1204#95C2414yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211C24—24no—
1212C24—24no—
1213C24—42no—
1214C24—42no—
1215C24—42no—
1216C24—42no—
1217C24—42no—
1218C24C2512yes—
1219C24C2514yes—
1220C24C2512yes—
1221C24C2512yes—
1222C24C2511yescharacteristic
1223#41—416no—
1224#41—832no—
1225#41—816no—
1226C2×Q8—24no—
1227C2×Q8—22no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—22no—
1236C2×Q8—22no—
1237C2×Q8—22no—
1238C2×Q8—42no—
1239C2×Q8—42no—
1240C2×Q8—42no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—28no—
1244C2×D4—24no—
1245C2×D4—24no—
1246C2×D4—24no—
1247C2×D4—28no—
1248C2×D4—28no—
1249C2×D4—28no—
1250C2×D4—28no—
1251C2×D4—24no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—22no—
1256C2×D4—24no—
1257C2×D4—28no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—22no—
1262C2×D4—22no—
1263C2×D4—24no—
1264C2×D4—24no—
1265C2×D4—22no—
1266C2×D4—24no—
1267C2×D4—416no—
1268C2×D4—42no—
1269C2×D4—42no—
1270C2×D4—42no—
1271C2×D4—42no—
1272C2×D4—42no—
1273C2×D4—44no—
1274C2×D4—42no—
1275C2×D4—44no—
1276C2×D4—42no—
1277C2×D4—42no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—42no—
1281C2×D4—44no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—44no—
1285C2×D4—44no—
1286C2×D4—44no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—44no—
1294C2×D4—44no—
1295C2×D4C2×#4114yes—
1296C2×D4C2×#4114yes—
1297C2×D4C2×#4118yes—
1298C2×D4C2×#4118yes—
1299C22×C4—22no—
1300C22×C4—22no—
1301C22×C4—28no—
1302C22×C4—24no—
1303C22×C4—28no—
1304C22×C4—22no—
1305C22×C4—24no—
1306C22×C4—28no—
1307C22×C4—24no—
1308C22×C4—24no—
1309C22×C4—24no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—24no—
1314C22×C4—24no—
1315C22×C4—24no—
1316C22×C4—24no—
1317C22×C4—22no—
1318C22×C4—28no—
1319C22×C4—22no—
1320C22×C4—42no—
1321C22×C4—44no—
1322C22×C4—42no—
1323C22×C4—42no—
1324C22×C4—44no—
1325C22×C4—44no—
1326C22×C4—42no—
1327C22×C4—42no—
1328C22×C4—42no—
1329C22×C4—42no—
1330C22×C4—42no—
1331C22×C4—44no—
1332C22×C4—44no—
1333C22×C4—44no—
1334C22×C4—42no—
1335C22×C4—44no—
1336C22×C4—41no—
1337C22×C4—41no—
1338C22×C4—42no—
1339C22×C4—42no—
1340C22×C4—42no—
1341C22×C4—42no—
1342C22×C4—44no—
1343C22×C4—44no—
1344C22×C4—44no—
1345C22×C4—44no—
1346C22×C4—44no—
1347C22×C4—44no—
1348C22×C4—44no—
1349C22×C4—44no—
1350C22×C4—44no—
1351C22×C4—44no—
1352C22×C4—816no—
1353C22×C42−1+414yes—
1354C22×C4C2512yes—
1355C22×C4C2512yes—
1356C22×C4C2511yescharacteristic
1357C22×C4C2511yescharacteristic
1358C22×C4C2511yescharacteristic
1359C22×C4C2512yes—
1360C22×C4C2512yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2512yes—
1363C22×C4C2512yes—
1364C22×C4C2514yes—
1365C22×C4C2512yes—
1366C22×C4C2512yes—
1367C22×C4C2514yes—
1368C22×C4C2511yescharacteristic
1369C22×C4C2511yescharacteristic
1370C22×C4C2512yes—
1371C22×C4C2511yescharacteristic
1372C22×C4C2511yescharacteristic
1373C22×C4C2514yes—
1374C22×C4C2512yes—
1375C22×C4C2512yes—
1376C22×C4C2512yes—
1377C22×C4C2511yescharacteristic
1378C22×C4C2511yescharacteristic
1379C22×C4C2512yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C22×C4C2511yescharacteristic
1383C22×C4C2511yescharacteristic
1384C4⋊C4—22no—
1385C4⋊C4—22no—
1386C4⋊C4—24no—
1387C4⋊C4—24no—
1388C4⋊C4—24no—
1389C4⋊C4—24no—
1390C4⋊C4—24no—
1391C4⋊C4—28no—
1392C4⋊C4—22no—
1393C4⋊C4—22no—
1394C4⋊C4—22no—
1395C4⋊C4—24no—
1396C4⋊C4—22no—
1397C4⋊C4—22no—
1398C4⋊C4—24no—
1399C4⋊C4—22no—
1400C4⋊C4—22no—
1401C4⋊C4—24no—
1402C4⋊C4—24no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—24no—
1408C4⋊C4—22no—
1409C4⋊C4—22no—
1410C4⋊C4—24no—
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—42no—
1414C4⋊C4—44no—
1415C4⋊C4—44no—
1416C4⋊C4—44no—
1417C4⋊C4—42no—
1418C4⋊C4—44no—
1419C4⋊C4—44no—
1420C4⋊C4—44no—
1421C4⋊C4—42no—
1422C4⋊C4—44no—
1423C4⋊C4—44no—
1424C4⋊C4—42no—
1425C4⋊C4—42no—
1426C4⋊C4—42no—
1427C4⋊C4—44no—
1428C4⋊C4—42no—
1429C4⋊C4—42no—
1430C4⋊C4—42no—
1431C4⋊C4—42no—
1432C4⋊C4—44no—
1433C4⋊C4—42no—
1434C4⋊C4—42no—
1435C4⋊C4—44no—
1436C4⋊C4—42no—
1437C4⋊C4—42no—
1438C4⋊C4—42no—
1439C4⋊C4—44no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C4—42no—
1444C4⋊C4—42no—
1445C4⋊C4—42no—
1446C4⋊C4—42no—
1447C4⋊C4H(5,𝔽2)14yes—
1448C22⋊C4—28no—
1449C22⋊C4—28no—
1450C22⋊C4—24no—
1451C22⋊C4—24no—
1452C22⋊C4—22no—
1453C22⋊C4—22no—
1454C22⋊C4—22no—
1455C22⋊C4—22no—
1456C22⋊C4—28no—
1457C22⋊C4—24no—
1458C22⋊C4—24no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—28no—
1462C22⋊C4—24no—
1463C22⋊C4—24no—
1464C22⋊C4—28no—
1465C22⋊C4—28no—
1466C22⋊C4—42no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—44no—
1472C22⋊C4—42no—
1473C22⋊C4—42no—
1474C22⋊C4—42no—
1475C22⋊C4—44no—
1476C22⋊C4—42no—
1477C22⋊C4—42no—
1478C22⋊C4—42no—
1479C22⋊C4—42no—
1480C22⋊C4—44no—
1481C22⋊C4—44no—
1482C22⋊C4—44no—
1483C22⋊C4—44no—
1484C22⋊C4—44no—
1485C22⋊C4—42no—
1486C22⋊C4—42no—
1487C22⋊C4—44no—
1488C22⋊C4—44no—
1489C22⋊C4—44no—
1490C22⋊C4—42no—
1491C22⋊C4—42no—
1492C22⋊C4—42no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—44no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—42no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—44no—
1507C22⋊C4—42no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C42—22no—
1513C42—24no—
1514C42—24no—
1515C42—22no—
1516C42—22no—
1517C42—22no—
1518C42—24no—
1519C42—28no—
1520C42—24no—
1521C42—22no—
1522C42—24no—
1523C42—22no—
1524C42—24no—
1525C42—22no—
1526C42—22no—
1527C42—22no—
1528C42—22no—
1529C42—42no—
1530C42—42no—
1531C42—41no—
1532C42—42no—
1533C42—42no—
1534C42—44no—
1535C42—44no—
1536C42—42no—
1537C42—41no—
1538C42—41no—
1539C42—41no—
1540C42C2×#4114yes—
1541C42H(5,𝔽2)14yes—
1542C23—21no—
1543C23—21no—
1544C23—22no—
1545C23—22no—
1546C23—22no—
1547C23—22no—
1548C23—21no—
1549C23—22no—
1550C23—22no—
1551C23—21no—
1552C23—22no—
1553C23—22no—
1554C23—21no—
1555C23—22no—
1556C23—22no—
1557C23—21no—
1558C23—22no—
1559C23—22no—
1560C23—22no—
1561C23—24no—
1562C23—22no—
1563C23—24no—
1564C23—22no—
1565C23—24no—
1566C23—24no—
1567C23—22no—
1568C23—24no—
1569C23—22no—
1570C23—22no—
1571C23—22no—
1572C23—24no—
1573C23—24no—
1574C23—48no—
1575C23—48no—
1576C23—84no—
1577C23—84no—
1578C23—84no—
1579C23—84no—
1580C23—84no—
1581C23C22×#4114yes—
1582C23C22×#4114yes—
1583C23C2×2−1+412yes—
1584C23C2611yescharacteristic
1585Q8—48no—
1586Q8—44no—
1587Q8—44no—
1588Q8—44no—
1589Q8—84no—
1590D4—28no—
1591D4—28no—
1592D4—48no—
1593D4—48no—
1594D4—48no—
1595D4—416no—
1596D4—48no—
1597D4—48no—
1598D4—44no—
1599D4—48no—
1600D4—84no—
1601D4—84no—
1602D4—88no—
1603D4—84no—
1604D4—88no—
1605D4—88no—
1606D4—88no—
1607D4—88no—
1608D4—164no—
1609C2×C4—22no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—21no—
1613C2×C4—21no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—28no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—22no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—24no—
1634C2×C4—21no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—21no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—24no—
1649C2×C4—24no—
1650C2×C4—22no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—24no—
1656C2×C4—22no—
1657C2×C4—21no—
1658C2×C4—21no—
1659C2×C4—21no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—21no—
1667C2×C4—22no—
1668C2×C4—21no—
1669C2×C4—21no—
1670C2×C4—24no—
1671C2×C4—22no—
1672C2×C4—22no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—21no—
1676C2×C4—22no—
1677C2×C4—24no—
1678C2×C4—22no—
1679C2×C4—21no—
1680C2×C4—22no—
1681C2×C4—21no—
1682C2×C4—24no—
1683C2×C4—24no—
1684C2×C4—22no—
1685C2×C4—22no—
1686C2×C4—22no—
1687C2×C4—21no—
1688C2×C4—22no—
1689C2×C4—48no—
1690C2×C4—416no—
1691C2×C4—48no—
1692C2×C4—48no—
1693C2×C4—44no—
1694C2×C4—48no—
1695C2×C4—82no—
1696C2×C4—88no—
1697C2×C4—88no—
1698C2×C4—84no—
1699C2×C4—84no—
1700C2×C4—84no—
1701C2×C4—84no—
1702C2×C4—88no—
1703C2×C4—164no—
1704C2×C4—164no—
1705C2×C4—164no—
1706C2×C4C22×#4112yes—
1707C2×C4C22×#4112yes—
1708C2×C4C22×#4112yes—
1709C2×C4C2×H(5,𝔽2)14yes—
1710C2×C4C2×H(5,𝔽2)12yes—
1711C2×C4C2×H(5,𝔽2)12yes—
1712C2×C4C2×H(5,𝔽2)12yes—
1713C2×C4C2×H(5,𝔽2)12yes—
1714C2×C4C2×2−1+412yes—
1715C2×C4C2×2−1+412yes—
1716C2×C4#58512yes—
1717C22—24no—
1718C22—24no—
1719C22—24no—
1720C22—24no—
1721C22—22no—
1722C22—24no—
1723C22—24no—
1724C22—22no—
1725C22—22no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—42no—
1730C22—42no—
1731C22—42no—
1732C22—41no—
1733C22—42no—
1734C22—42no—
1735C22—42no—
1736C22—42no—
1737C22—42no—
1738C22—44no—
1739C22—42no—
1740C22—44no—
1741C22—42no—
1742C22—42no—
1743C22—44no—
1744C22—42no—
1745C22—44no—
1746C22—44no—
1747C22—42no—
1748C22—44no—
1749C22—42no—
1750C22—44no—
1751C22—42no—
1752C22—816no—
1753C22C23×#4111yescharacteristic
1754C22C22×H(5,𝔽2)11yescharacteristic
1755C22C22×H(5,𝔽2)11yescharacteristic
1756C22C22×2−1+411yescharacteristic
1757C22C2×#58511yescharacteristic
1758C22H(7,𝔽2)11yescharacteristic
1759C22H(7,𝔽2)11yescharacteristic
1760C4—24no—
1761C4—22no—
1762C4—22no—
1763C4—22no—
1764C4—22no—
1765C4—44no—
1766C4—42no—
1767C4—41no—
1768C4—41no—
1769C4—42no—
1770C4—42no—
1771C4—42no—
1772C4—42no—
1773C4—41no—
1774C4—42no—
1775C4—42no—
1776C4—42no—
1777C4—42no—
1778C4—41no—
1779C4—42no—
1780C4—42no—
1781C4—42no—
1782C4—44no—
1783C4—41no—
1784C4—41no—
1785C4—44no—
1786C4—41no—
1787C4—41no—
1788C4#352014yes—
1789C4#354614yes—
1790C2—44no—
1791C2—44no—
1792C2—42no—
1793C2—84no—
1794C2—82no—
1795C2C2×#354611yescharacteristic
1796C2C2×#352011yescharacteristic
1797C2#6288011yescharacteristic
1798C2#6291711yescharacteristic
1799C2#6292611yescharacteristic
1800C2#6298311yescharacteristic
1801C2#6299211yescharacteristic
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. #59815C2semidirect
3. #59676C2semidirect
4. #59426C2semidirect
5. #59411C2semidirect
6. #59023C2semidirect
7. #50024C2semidirect
8. #48406C2semidirect
9. #46736C2semidirect
10. #46571C2semidirect
11. #45616C2semidirect
12. #45598C2semidirect
13. #44942C2semidirect
14. #44876C2semidirect
15. #42580C2semidirect
16. #42536C2semidirect
17. #40148C2semidirect
18. #39887C2semidirect
19. #39169C2semidirect
20. #39144C2semidirect
21. #39066C2semidirect
22. #38977C2semidirect
23. #38950C2semidirect
24. #38252C2semidirect
25. #37368C2semidirect
26. #36496C2semidirect
27. #36493C2semidirect
28. #36275C2semidirect
29. #36270C2semidirect
30. #36154C2semidirect
31. #36101C2semidirect
32. #35288C2semidirect
33. #34916C2semidirect
34. #34494C2semidirect
35. C4×#535C2semidirect
36. C2×#559C22semidirect
38. C2×#554C22semidirect
39. C2×#552C22semidirect
42. C2×#547C22semidirect
47. #2861C22semidirect
49. #2859C22semidirect
50. #2858C22semidirect
53. #2855C22semidirect
54. #2850C22semidirect
57. #2827C22semidirect
58. #2826C22semidirect
59. #2801C22semidirect
60. #2795C22semidirect
61. #2790C22semidirect
63. #2779C22semidirect
66. #2765C22semidirect
67. #2759C22semidirect
68. #2757C22semidirect
70. #2750C22semidirect
72. #2746C22semidirect
73. #2746C22semidirect
74. #2746C22semidirect
75. #2743C22semidirect
76. #2741C22semidirect
77. #2739C22semidirect
78. #2732C22semidirect
79. #2718C22semidirect
80. #2708C22semidirect
81. #2707C22semidirect
82. #2706C22semidirect
84. #2704C22semidirect
85. #2702C22semidirect
86. #2701C22semidirect
88. #2693C22semidirect
89. #2691C22semidirect
91. #2687C22semidirect
94. #2682C22semidirect
96. #2676C22semidirect
97. #2676C22semidirect
99. #2645C22semidirect
100. #2644C22semidirect
101. #2643C22semidirect
103. #2636C22semidirect
104. #2633C22semidirect
106. #2618C22semidirect
108. #2601C22semidirect
111. #2590C22semidirect
113. #2588C22semidirect
115. #2587C22semidirect
116. #2582C22semidirect
117. #2567C22semidirect
119. #2566C22semidirect
120. #2566C22semidirect
122. #2562C22semidirect
123. #2558C22semidirect
124. #2552C22semidirect
128. #2542C22semidirect
131. #2541C22semidirect
135. #2538C22semidirect
136. #2538C22semidirect
137. #2538C22semidirect
138. #2537C22semidirect
139. #2536C22semidirect
142. #2514C22semidirect
143. #2513C22semidirect
145. #2511C22semidirect
146. #2510C22semidirect
147. #2508C22semidirect
148. #2507C22semidirect
149. #2506C22semidirect
150. #2505C22semidirect
151. #2503C22semidirect
152. #2498C22semidirect
154. #2496C22semidirect
155. #2494C22semidirect
156. #2494C22semidirect
159. #2489C22semidirect
162. #2471C22semidirect
163. #2469C22semidirect
165. #2461C22semidirect
166. #2461C22semidirect
172. #2454C22semidirect
173. #2454C22semidirect
174. #2453C22semidirect
175. #2451C22semidirect
179. #2448C22semidirect
180. #2448C22semidirect
182. #2447C22semidirect
183. #2447C22semidirect
184. #2446C22semidirect
189. #2445C22semidirect
190. #2443C22semidirect
192. #2442C22semidirect
194. #2439C22semidirect
195. #2438C22semidirect
198. #2432C22semidirect
203. #2427C22semidirect
205. #2426C22semidirect
206. #2426C22semidirect
207. #2425C22semidirect
211. #2422C22semidirect
213. #2419C22semidirect
217. #2417C22semidirect
218. #2417C22semidirect
219. #2416C22semidirect
220. #2416C22semidirect
221. #2416C22semidirect
222. #2416C22semidirect
225. #2407C22semidirect
226. #2407C22semidirect
227. #2407C22semidirect
229. #2402C22semidirect
231. #2377C22semidirect
232. #2377C22semidirect
235. #2366C22semidirect
238. #2361C22semidirect
239. #2361C22semidirect
240. #2361C22semidirect
241. #2355C22semidirect
242. #2355C22semidirect
244. #2352C22semidirect
246. #2349C22semidirect
248. D4×C4⋊C4C22semidirect
249. D4×C4⋊C4C22semidirect
250. D4×C4⋊C4C22semidirect
251. #2347C22semidirect
253. #2339C22semidirect
254. #2339C22semidirect
258. #2328C22semidirect
261. #2325C22semidirect
262. #2325C22semidirect
266. #2324C22semidirect
270. #2319C22semidirect
273. #2311C22semidirect
275. C4×C4⋊Q8C22semidirect
276. C4×C4⋊Q8C22semidirect
277. C4×C4⋊Q8C22semidirect
281. C4×#127C22semidirect
288. C4×#121C22semidirect
292. #2295C22semidirect
293. #2295C22semidirect
294. #2293C22semidirect
295. C2×#389C22semidirect
297. C42×Q8C22semidirect
887. #127#41semidirect

Maximal subgroups

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

subgroupindex
#598232
#598152
#596762
#594262
#594112
#590232
#500242
#484062
#467362
#465712
#456162
#455982
#449422
#448762
#425802
#425362
#401482
#398872
#391692
#391442
#390662
#389772
#389502
#382522
#373682
#364962
#364932
#362752
#362702
#361542
#361012
#352882
#349162
#344942
C4×#5352