Finite Group Databasebeta

← #7979678

Subgroups — #7979678

Order 512.

4973 conjugacy classes of subgroups.

The subgroup lattice has 1759 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59585C212yesmaximal, complemented
2#59435C211yesmaximal, characteristic, complemented
3#59067C211yesmaximal, characteristic, complemented
4#59039C211yesmaximal, characteristic, complemented
5#59019C212yesmaximal, complemented
6#50271C214yesmaximal, complemented
7#48937C214yesmaximal, complemented
8#46061C212yesmaximal, complemented
9#45647C212yesmaximal, complemented
10#45234C212yesmaximal, complemented
11#45052C212yesmaximal, complemented
12#44146C214yesmaximal, complemented
13#42855C212yesmaximal, complemented
14#42768C212yesmaximal, complemented
15#41459C214yesmaximal, complemented
16#39910C212yesmaximal, complemented
17#39243C212yesmaximal, complemented
18#39202C211yesmaximal, characteristic, complemented
19#39127C211yesmaximal, characteristic, complemented
20#39008C212yesmaximal, complemented
21#38998C212yesmaximal, complemented
22#37857C212yesmaximal, complemented
23#36586C211yesmaximal, characteristic, complemented
24#36583C211yesmaximal, characteristic, complemented
25#36460C212yesmaximal, complemented
26#36460C211yesmaximal, characteristic, complemented
27#36150C211yesmaximal, characteristic, complemented
28#36101C211yesmaximal, characteristic, complemented
29#35238C211yesmaximal, characteristic, complemented
30#35185C211yesmaximal, characteristic, complemented
31#35136C212yesmaximal, complemented
32#34946C211yesmaximal, characteristic, complemented
33#34700C211yesmaximal, characteristic, complemented
34#34391C212yesmaximal, complemented
35C4×#552C211yesmaximal, characteristic, complemented
36C2×#557C2211yescharacteristic, complemented
37C2×#552C2211yescharacteristic
38C2×#550C2211yescharacteristic
39C2×#533C2211yescharacteristic
40C2×#532C2211yescharacteristic, complemented
41C2×#529C2211yescharacteristic
42C2×#525C2212yes—
43C22×C4×D4C2211yescharacteristic
44#2864C2212yescomplemented
45#2860C2212yes—
46#2860C2212yescomplemented
47#2858C2212yes—
48#2858C2211yescharacteristic, complemented
49#2857C2211yescharacteristic, complemented
50#2856C2211yescharacteristic
51#2856C2212yes—
52#2850C2212yes—
53#2850C2212yescomplemented
54#2847C2212yes—
55#2829C2214yes—
56#2829C2214yes—
57#2803C2214yes—
58#2797C2214yescomplemented
59#2796C2214yescomplemented
60#2795C2214yescomplemented
61#2780C2214yescomplemented
62#2779C2214yescomplemented
63#2775C2214yescomplemented
64#2770C2214yescomplemented
65#2757C2214yescomplemented
66#2756C2214yes—
67#2752C2214yes—
68#2752C2214yescomplemented
69#2749C2214yes—
70#2746C2214yes—
71#2744C2214yescomplemented
72#2743C2214yes—
73#2740C2214yes—
74#2738C2214yescomplemented
75#2727C2214yescomplemented
76#2725C2214yescomplemented
77#2720C2214yes—
78#2718C2214yescomplemented
79#2714C2214yes—
80#2707C2214yescomplemented
81#2705C2214yes—
82#2699C2214yes—
83#2697C2214yes—
84#2686C2214yescomplemented
85#2685C2214yes—
86#2685C2214yes—
87#2685C2214yes—
88#2678C2214yes—
89#2668C2214yes—
90#2662C2214yescomplemented
91#2654C2214yescomplemented
92#2652C2214yescomplemented
93#2651C2214yescomplemented
94#2650C2214yescomplemented
95#2649C2214yescomplemented
96#2648C2214yescomplemented
97#2629C2212yescomplemented
98#2624C2212yescomplemented
99#2604C2214yescomplemented
100#2596C2214yescomplemented
101#2578C2214yescomplemented
102#2576C2214yescomplemented
103#2571C2212yescomplemented
104#2571C2211yescharacteristic, complemented
105#2567C2211yescharacteristic, complemented
106#2567C2211yescharacteristic, complemented
107#2566C2212yescomplemented
108#2563C2211yescharacteristic
109#2563C2211yescharacteristic
110#2562C2212yes—
111#2562C2212yes—
112#2562C2212yescomplemented
113#2561C2214yes—
114#2559C2214yes—
115#2559C2214yescomplemented
116#2559C2214yescomplemented
117#2558C2214yescomplemented
118#2553C2214yescomplemented
119#2552C2212yescomplemented
120#2548C2212yes—
121#2548C2212yes—
122#2548C2211yescharacteristic, complemented
123#2547C2211yescharacteristic
124#2547C2211yescharacteristic
125#2547C2212yescomplemented
126#2545C2212yes—
127#2544C2212yes—
128#2544C2212yes—
129#2541C2211yescharacteristic
130#2540C2212yes—
131#2538C2211yescharacteristic
132#2538C2212yescomplemented
133#2537C2212yescomplemented
134#2531C2214yescomplemented
135#2531C2214yescomplemented
136#2526C2214yescomplemented
137#2526C2214yescomplemented
138#2526C2214yescomplemented
139#2526C2214yescomplemented
140#2526C2214yescomplemented
141#2514C2212yescomplemented
142#2513C2212yes—
143#2512C2212yes—
144#2512C2214yescomplemented
145#2512C2212yescomplemented
146#2510C2214yescomplemented
147#2510C2214yescomplemented
148#2509C2212yescomplemented
149#2503C2212yes—
150#2500C2212yes—
151#2500C2214yescomplemented
152#2496C2212yescomplemented
153#2496C2212yescomplemented
154#2495C2212yescomplemented
155#2494C2212yescomplemented
156#2493C2214yescomplemented
157#2490C2212yescomplemented
158#2490C2212yescomplemented
159#2490C2214yescomplemented
160#2490C2212yescomplemented
161#2490C2214yescomplemented
162#2490C2212yescomplemented
163#2487C2212yescomplemented
164#2480C2212yes—
165#2476C2214yescomplemented
166#2471C2214yescomplemented
167#2469C2214yescomplemented
168#2468C2212yes—
169#2466C2214yes—
170#2462C2214yescomplemented
171#2460C2214yescomplemented
172#2457C2214yes—
173#2457C2212yes—
174#2456C2214yes—
175#2454C2211yescharacteristic
176#2454C2212yescomplemented
177#2453C2212yescomplemented
178#2453C2212yescomplemented
179#2448C2212yes—
180#2448C2212yes—
181#2448C2212yescomplemented
182#2448C2212yescomplemented
183#2447C2211yescharacteristic
184#2447C2212yescomplemented
185#2446C2212yescomplemented
186#2445C2212yes—
187#2445C2212yes—
188#2442C2211yescharacteristic
189#2441C2212yes—
190#2441C2212yescomplemented
191#2435C2212yes—
192#2435C2211yescharacteristic
193#2433C2212yes—
194#2430C2214yescomplemented
195#2430C2214yescomplemented
196#2429C2212yes—
197#2429C2212yescomplemented
198#2428C2212yes—
199#2427C2212yes—
200#2427C2211yescharacteristic
201#2426C2212yes—
202#2426C2212yes—
203#2426C2212yes—
204#2426C2212yescomplemented
205#2424C2214yes—
206#2423C2212yes—
207#2422C2212yescomplemented
208#2421C2212yescomplemented
209#2420C2212yes—
210#2420C2211yescharacteristic
211#2420C2212yescomplemented
212#2420C2212yescomplemented
213#2418C2212yes—
214#2417C2211yescharacteristic
215#2416C2212yescomplemented
216#2416C2212yescomplemented
217#2414C2212yes—
218#2414C2212yes—
219#2408C2211yescharacteristic
220#2407C2212yes—
221#2407C2212yes—
222#2407C2212yescomplemented
223#2398C2214yes—
224#2395C2212yes—
225#2392C2212yes—
226#2375C2214yes—
227#2375C2214yes—
228#2373C2212yes—
229#2371C2212yescomplemented
230#2370C2211yescharacteristic, complemented
231#2367C2212yescomplemented
232#2366C2212yes—
233#2366C2211yescharacteristic, complemented
234#2365C2211yescharacteristic, complemented
235#2363C2212yes—
236#2363C2212yes—
237#2363C2214yescomplemented
238#2362C2211yescharacteristic
239#2362C2212yes—
240#2361C2212yes—
241#2360C2211yescharacteristic, complemented
242#2359C2212yes—
243#2357C2214yescomplemented
244#2357C2212yescomplemented
245#2356C2212yescomplemented
246#2356C2211yescharacteristic, complemented
247#2354C2211yescharacteristic
248#2353C2214yescomplemented
249#2352C2211yescharacteristic
250#2352C2212yescomplemented
251Q8×C4⋊C4C2211yescharacteristic, complemented
252Q8×C4⋊C4C2212yescomplemented
253#2349C2212yescomplemented
254#2347C2212yescomplemented
255#2346C2211yescharacteristic
256#2346C2212yescomplemented
257#2344C2211yescharacteristic, complemented
258#2343C2212yescomplemented
259#2341C2212yescomplemented
260#2341C2212yescomplemented
261#2341C2212yescomplemented
262#2339C2212yescomplemented
263#2335C2214yescomplemented
264#2335C2214yescomplemented
265#2333C2214yescomplemented
266#2324C2212yescomplemented
267#2324C2212yescomplemented
268#2324C2212yescomplemented
269#2323C2212yescomplemented
270#2323C2212yescomplemented
271#2319C2214yes—
272#2318C2214yes—
273#2314C2212yescomplemented
274C4×C4⋊Q8C2211yescharacteristic, complemented
275C4×#125C2211yescharacteristic, complemented
276C4×#125C2212yescomplemented
277C4×#126C2212yes—
278C4×#124C2211yescharacteristic
279C4×#124C2212yes—
280C4×#124C2212yes—
281C4×#124C2212yescomplemented
282C4×#124C2212yescomplemented
283C4×C22⋊Q8C2211yescharacteristic
284C4×C22⋊Q8C2211yescharacteristic
285C4×C22⋊Q8C2212yescomplemented
286C4×C22⋊Q8C2211yescharacteristic, complemented
287C4×#123C2212yes—
288C4×#121C2211yescharacteristic
289C4×#120C2212yes—
290#2293C2211yescharacteristic
291#2280C2212yes—
292#2280C2212yes—
293#2280C2212yes—
294C42×Q8C2211yescharacteristic, complemented
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2212yescomplemented
298C2×C4×C4⋊C4C2211yescharacteristic, complemented
299C22×#41C2312yes—
300C22×#41C2312yes—
301C23×D4C2311yescharacteristic
302C24×C4C2312yes—
303#557—44no—
304#552—28no—
305#550—44no—
306#533—44no—
307#532—44no—
308C2×C4⋊Q8C2311yescharacteristic
309C2×C4⋊Q8C2311yescharacteristic
310C2×C4⋊Q8C2312yes—
311C2×#127C2311yescharacteristic
312C2×#127C2312yes—
313C2×#127C2312yes—
314#529—44no—
315C2×#126C2312yes—
316C2×#126C2312yes—
317C2×#126C2314yes—
318C2×#126C2314yes—
319C2×#126C2314yes—
320C2×#125C2311yescharacteristic
321C2×#125C2312yes—
322C2×#125C2312yes—
323C2×#125C2312yes—
324C2×#125C2311yescharacteristic
325C2×#125C2314yes—
326C2×#124C2312yes—
327C2×#124C2312yes—
328C2×#124C2311yescharacteristic
329C2×#124C2312yes—
330C2×#124C2312yes—
331C2×#124C2312yes—
332C2×#124C2311yescharacteristic
333C2×#124C2312yes—
334#525—216no—
335C2×#123C2314yes—
336C2×#123C2312yes—
337C2×#123C2312yes—
338C2×#123C2314yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2311yescharacteristic
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2312yes—
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2311yescharacteristic
345C2×C22⋊Q8C2312yes—
346C2×C22⋊Q8C2311yescharacteristic
347C2×#121C2312yes—
348C2×#121C2312yes—
349C2×#121C2312yes—
350C2×#121C2314yes—
351C2×#121C2312yes—
352C2×#121C2311yescharacteristic
353C2×#121C2312yes—
354C2×#121C2311yescharacteristic
355C2×#121C2312yes—
356C2×#121C2314yes—
357C2×#121C2312yes—
358C2×#121C2314yes—
359C2×#121C2312yes—
360C2×#121C2314yes—
361C2×#120C2314yes—
362C2×#120C2312yes—
363C2×#120C2314yes—
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2311yescharacteristic
367C2×C4×Q8C2311yescharacteristic
368C2×C4×Q8C2312yes—
369C2×C4×Q8C2312yes—
370C2×C4×Q8C2312yes—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2312yes—
373C2×C4×Q8C2312yes—
374C2×C4×Q8C2312yes—
375C2×C4×D4—44no—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2311yescharacteristic
378C2×C4×D4C2314yes—
379C2×C4×D4C2311yescharacteristic
380C2×C4×D4C2314yes—
381C2×C4×D4C2312yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2312yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×#117C2312yes—
395C2×#117C2311yescharacteristic
396C2×#117C2312yes—
397C2×#117C2312yes—
398C2×#117C2312yes—
399C2×#117C2312yes—
400C2×#117C2311yescharacteristic
401C2×#117C2312yes—
402C22×C4⋊C4C2311yescharacteristic
403C22×C4⋊C4C2311yescharacteristic
404C22×C4⋊C4C2311yescharacteristic
405C22×C22⋊C4C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2312yes—
409#401C2314yes—
410#400C2314yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2314yes—
415#400C2314yes—
416#400C2314yes—
417#400C2314yes—
418#400C2314yes—
419#400C2314yes—
420#400C2312yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2314yes—
425#399C2312yes—
426#399C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#398C2314yes—
431#398C2312yes—
432#398C2312yes—
433#398C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2312yes—
448#397C2312yes—
449#397C2312yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2314yes—
456#396C2314yes—
457#396C2314yes—
458#396C2314yes—
459#396C2314yes—
460#396C2312yes—
461#396C2312yes—
462#396C2314yes—
463#396C2314yes—
464#396C2314yes—
465#396C2314yes—
466#395C2314yes—
467#395C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2312yes—
472#394C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2312yes—
481#394C2312yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2312yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#393C2314yes—
496#393C2314yes—
497#392C2314yes—
498#392C2314yes—
499#392C2312yes—
500#392C2314yes—
501#392C2314yes—
502#392C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2311yescharacteristic
507#391C2312yes—
508#391C2312yes—
509#391C2311yescharacteristic
510#391C2311yescharacteristic
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2312yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2312yes—
523#390C2312yes—
524#390C2312yes—
525#390C2314yes—
526#390C2314yes—
527#390C2314yes—
528#390C2314yes—
529#390C2314yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2312yes—
534#390C2312yes—
535#390C2314yes—
536#390C2314yes—
537#390C2312yes—
538#390C2312yes—
539#390C2314yes—
540#390C2312yes—
541#390C2311yescharacteristic
542#390C2312yes—
543#390C2312yes—
544#390C2314yes—
545#390C2314yes—
546#390C2314yes—
547#390C2312yes—
548#390C2311yescharacteristic
549#390C2311yescharacteristic
550#390C2311yescharacteristic
551#389C2311yescharacteristic
552#389C2311yescharacteristic
553#389C2312yes—
554#389C2312yes—
555#389C2312yes—
556#389C2312yes—
557#389C2312yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2312yes—
562#389C2314yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2312yes—
568#389C2312yes—
569#389C2311yescharacteristic
570#389C2311yescharacteristic
571#389C2314yes—
572#389C2311yescharacteristic
573#389C2311yescharacteristic
574#389C2314yes—
575#389C2314yes—
576#389C2311yescharacteristic
577#389C2312yes—
578#389C2312yes—
579#389C2314yes—
580#389C2314yes—
581#389C2311yescharacteristic
582#388C2312yes—
583#388C2312yes—
584#388C2312yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#388C2312yes—
597#388C2314yes—
598#388C2314yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2312yes—
614#388C2314yes—
615#388C2314yes—
616#388C2312yes—
617#388C2312yes—
618#388C2314yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2314yes—
625#388C2312yes—
626#388C2314yes—
627#388C2312yes—
628#388C2312yes—
629#388C2314yes—
630#388C2314yes—
631#387C2312yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2312yes—
639#387C2312yes—
640#387C2314yes—
641#387C2314yes—
642#387C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2312yes—
653#387C2314yes—
654#387C2312yes—
655#387C2314yes—
656#387C2312yes—
657#387C2314yes—
658#387C2312yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2314yes—
665#386C2314yes—
666#386C2312yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2314yes—
675#386C2312yes—
676#386C2312yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2312yes—
681#386C2312yes—
682#385C2314yes—
683#385C2314yes—
684#385C2314yes—
685#385C2314yes—
686#385C2312yes—
687#385C2312yes—
688#385C2312yes—
689#385C2314yes—
690#385C2312yes—
691#385C2314yes—
692#385C2314yes—
693#385C2312yes—
694#385C2312yes—
695#385C2312yes—
696#385C2314yes—
697#384C2311yescharacteristic
698#384C2312yes—
699#384C2312yes—
700#384C2312yes—
701#384C2314yes—
702#383C2312yes—
703#383C2314yes—
704#383C2314yes—
705#382C2312yes—
706#382C2311yescharacteristic
707#382C2312yes—
708#382C2312yes—
709#382C2312yes—
710#382C2311yescharacteristic
711#382C2314yes—
712#382C2312yes—
713#381C2314yes—
714#381C2314yes—
715#381C2314yes—
716#381C2312yes—
717#381C2314yes—
718#381C2312yes—
719#381C2312yes—
720#381C2314yes—
721#380C2312yes—
722#380C2312yes—
723#380C2312yes—
724#380C2312yes—
725#380C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2311yescharacteristic
730#380C2312yes—
731#380C2312yes—
732#380C2312yes—
733#380C2312yes—
734#380C2314yes—
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2311yescharacteristic
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2314yes—
743#380C2311yescharacteristic
744#380C2311yescharacteristic
745#379C2314yes—
746#379C2314yes—
747#379C2312yes—
748#379C2312yes—
749#379C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2311yescharacteristic
755C4×C4⋊C4C2311yescharacteristic
756C4×C4⋊C4C2311yescharacteristic
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2311yescharacteristic
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2311yescharacteristic
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2314yes—
769C4×C4⋊C4C2311yescharacteristic
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2314yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2312yes—
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C22⋊C4C2311yescharacteristic
783C4×C22⋊C4C2312yes—
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2314yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2314yes—
789C4×C22⋊C4C2314yes—
790C4×C22⋊C4C2314yes—
791C4×C22⋊C4C2312yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2312yes—
794C4×C22⋊C4C2311yescharacteristic
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2314yes—
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2311yescharacteristic
799C4×C22⋊C4C2311yescharacteristic
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2311yescharacteristic
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2311yescharacteristic
808C4×C22⋊C4C2312yes—
809#376C2314yes—
810#376C2312yes—
811#376C2312yes—
812#376C2312yes—
813C2×#95C2314yes—
814C2×#95C2312yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2312yes—
818C25C2412yes—
819C2×#41—28no—
820C2×#41—44no—
821C2×#41—44no—
822C2×#41—44no—
823C2×#41—44no—
824C2×#41—82no—
825C22×Q8C2411yescharacteristic
826C22×Q8C2412yes—
827C22×Q8C2411yescharacteristic
828C22×Q8C2412yes—
829C22×D4—42no—
830C22×D4—42no—
831C22×D4—42no—
832C22×D4C2412yes—
833C22×D4C2412yes—
834C22×D4C2411yescharacteristic
835C22×D4C2411yescharacteristic
836C22×D4C2411yescharacteristic
837C22×D4C2414yes—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2414yes—
841C22×D4C2414yes—
842C22×D4C2414yes—
843C22×D4C2412yes—
844C22×D4C2412yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C23×C4—28no—
848C23×C4—44no—
849C23×C4—44no—
850C23×C4C2411yescharacteristic
851C23×C4C2411yescharacteristic
852C23×C4C2412yes—
853C23×C4C2412yes—
854C23×C4C2411yescharacteristic
855C23×C4C2412yes—
856C23×C4C2411yescharacteristic
857C23×C4C2411yescharacteristic
858C23×C4C2411yescharacteristic
859C23×C4C2412yes—
860C23×C4C2412yes—
861C23×C4C2414yes—
862C23×C4C2412yes—
863C23×C4C2412yes—
864C23×C4C2414yes—
865C23×C4C2414yes—
866C4⋊Q8—24no—
867C4⋊Q8—24no—
868C4⋊Q8—44no—
869#127—24no—
870#127—44no—
871#127—44no—
872#126—28no—
873#126—44no—
874#126—84no—
875#126—84no—
876#126—84no—
877#125—28no—
878#125—24no—
879#125—42no—
880#125—44no—
881#125—44no—
882#125—48no—
883#124—44no—
884#124—44no—
885#124—44no—
886#124—44no—
887#124—44no—
888#124—42no—
889#124—42no—
890#124—44no—
891#123—216no—
892#123—28no—
893#123—44no—
894#123—84no—
895C22⋊Q8—28no—
896C22⋊Q8—24no—
897C22⋊Q8—42no—
898C22⋊Q8—44no—
899C22⋊Q8—42no—
900C22⋊Q8—44no—
901C22⋊Q8—44no—
902C22⋊Q8#4118yescomplemented
903#121—28no—
904#121—28no—
905#121—48no—
906#121—48no—
907#121—44no—
908#121—42no—
909#121—44no—
910#121—42no—
911#121—44no—
912#121—44no—
913#121—44no—
914#121—48no—
915#121—82no—
916#121—84no—
917#120—216no—
918#120—44no—
919#120—84no—
920C4×Q8—24no—
921C4×Q8—24no—
922C4×Q8—24no—
923C4×Q8—44no—
924C4×Q8—42no—
925C4×Q8—44no—
926C4×Q8—44no—
927C4×Q8—44no—
928C4×Q8—44no—
929C4×Q8—44no—
930C4×Q8—82no—
931C4×D4—24no—
932C4×D4—216no—
933C4×D4—216no—
934C4×D4—24no—
935C4×D4—24no—
936C4×D4—44no—
937C4×D4—42no—
938C4×D4—42no—
939C4×D4—44no—
940C4×D4—44no—
941C4×D4—44no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—44no—
946C4×D4—42no—
947C4×D4—44no—
948C4×D4—42no—
949#117—24no—
950#117—28no—
951#117—28no—
952#117—44no—
953#117—44no—
954#117—44no—
955#117—42no—
956#117—44no—
957C2×C4⋊C4—24no—
958C2×C4⋊C4—42no—
959C2×C4⋊C4—42no—
960C2×C4⋊C4C2411yescharacteristic
961C2×C4⋊C4C2411yescharacteristic
962C2×C4⋊C4C2411yescharacteristic
963C2×C4⋊C4C2411yescharacteristic
964C2×C4⋊C4C2411yescharacteristic
965C2×C4⋊C4C2412yes—
966C2×C4⋊C4C2411yescharacteristic
967C2×C4⋊C4C2412yes—
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2411yescharacteristic
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2411yescharacteristic
973C2×C4⋊C4C2412yes—
974C2×C4⋊C4C2414yes—
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2412yes—
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2412yes—
983C2×C4⋊C4C2412yes—
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2412yes—
987C2×C4⋊C4C2412yes—
988C2×C4⋊C4C2412yes—
989C2×C4⋊C4C2412yes—
990C2×C4⋊C4C2412yes—
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2412yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2414yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2414yes—
1002C2×C4⋊C4C2414yes—
1003C2×C4⋊C4C2414yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2414yes—
1006C2×C4⋊C4C2414yes—
1007C2×C4⋊C4C2414yes—
1008C2×C4⋊C4C2414yes—
1009C2×C4⋊C4C2414yes—
1010C2×C4⋊C4C2414yes—
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2412yes—
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2412yes—
1017C2×C4⋊C4C2414yes—
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2412yes—
1021C2×C22⋊C4—44no—
1022C2×C22⋊C4C2412yes—
1023C2×C22⋊C4C2412yes—
1024C2×C22⋊C4C2411yescharacteristic
1025C2×C22⋊C4C2411yescharacteristic
1026C2×C22⋊C4C2414yes—
1027C2×C22⋊C4C2412yes—
1028C2×C22⋊C4C2412yes—
1029C2×C22⋊C4C2412yes—
1030C2×C22⋊C4C2414yes—
1031C2×C22⋊C4C2414yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2411yescharacteristic
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2412yes—
1039C2×C22⋊C4C2412yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2414yes—
1043C2×C22⋊C4C2414yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2412yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2411yescharacteristic
1048C2×C22⋊C4C2411yescharacteristic
1049C2×C22⋊C4C2412yes—
1050C2×C22⋊C4C2411yescharacteristic
1051C2×C22⋊C4C2412yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2412yes—
1055C2×C22⋊C4C2414yes—
1056C2×C22⋊C4C2414yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2412yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2414yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2414yes—
1085C2×C22⋊C4C2414yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C42—24no—
1090C2×C42—24no—
1091C2×C42—44no—
1092C2×C42C2411yescharacteristic
1093C2×C42C2411yescharacteristic
1094C2×C42C2412yes—
1095C2×C42C2414yes—
1096C2×C42C2412yes—
1097C2×C42C2412yes—
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2411yescharacteristic
1102C2×C42C2411yescharacteristic
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2412yes—
1108C2×C42C2411yescharacteristic
1109C2×C42C2411yescharacteristic
1110C2×C42C2412yes—
1111C2×C42C2414yes—
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2412yes—
1115C2×C42C2411yescharacteristic
1116C2×C42C2414yes—
1117C2×C42C2411yescharacteristic
1118C2×C42C2414yes—
1119C2×C42C2412yes—
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2412yes—
1123C2×C42C2412yes—
1124C2×C42C2412yes—
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127#95C2412yes—
1128#95C2412yes—
1129#95C2412yes—
1130#95C2414yes—
1131#95C2412yes—
1132#95C2412yes—
1133#95C2412yes—
1134#95C2414yes—
1135#95C2411yescharacteristic
1136#95C2411yescharacteristic
1137#95C2412yes—
1138#95C2412yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2412yes—
1145#95C2412yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2414yes—
1149#95C2411yescharacteristic
1150#95C2414yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2411yescharacteristic
1155#95C2414yes—
1156#95C2412yes—
1157#95C2411yescharacteristic
1158#95C2411yescharacteristic
1159#95C2412yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2414yes—
1163#95C2414yes—
1164#95C2414yes—
1165#95C2414yes—
1166#95C2414yes—
1167#95C2414yes—
1168#95C2412yes—
1169#95C2414yes—
1170#95C2412yes—
1171#95C2414yes—
1172#95C2414yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2412yes—
1177#95C2412yes—
1178#95C2412yes—
1179#95C2414yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2414yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2414yes—
1188#95C2414yes—
1189#95C2414yes—
1190#95C2414yes—
1191C24—24no—
1192C24—42no—
1193C24—42no—
1194C24—42no—
1195C24—42no—
1196C24—42no—
1197C24—42no—
1198C24C2512yes—
1199C24C2512yes—
1200C24C2514yes—
1201C24C2511yescharacteristic
1202C24C2511yescharacteristic
1203#41—816no—
1204#41—816no—
1205C2×Q8—22no—
1206C2×Q8—22no—
1207C2×Q8—24no—
1208C2×Q8—24no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—24no—
1212C2×Q8—22no—
1213C2×Q8—24no—
1214C2×Q8—42no—
1215C2×Q8—42no—
1216C2×Q8C2×#4114yes—
1217C2×D4—22no—
1218C2×D4—22no—
1219C2×D4—28no—
1220C2×D4—24no—
1221C2×D4—24no—
1222C2×D4—28no—
1223C2×D4—24no—
1224C2×D4—28no—
1225C2×D4—28no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—24no—
1229C2×D4—24no—
1230C2×D4—24no—
1231C2×D4—24no—
1232C2×D4—24no—
1233C2×D4—22no—
1234C2×D4—24no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—42no—
1239C2×D4—41no—
1240C2×D4—42no—
1241C2×D4—42no—
1242C2×D4—42no—
1243C2×D4—42no—
1244C2×D4—44no—
1245C2×D4—44no—
1246C2×D4—44no—
1247C2×D4—44no—
1248C2×D4—44no—
1249C2×D4—42no—
1250C2×D4—42no—
1251C2×D4—42no—
1252C2×D4—44no—
1253C2×D4—44no—
1254C2×D4—44no—
1255C2×D4—42no—
1256C2×D4—44no—
1257C2×D4—44no—
1258C2×D4—44no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—416no—
1263C22×C4—22no—
1264C22×C4—22no—
1265C22×C4—24no—
1266C22×C4—22no—
1267C22×C4—24no—
1268C22×C4—24no—
1269C22×C4—22no—
1270C22×C4—24no—
1271C22×C4—24no—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—24no—
1277C22×C4—24no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—24no—
1281C22×C4—22no—
1282C22×C4—24no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—24no—
1286C22×C4—28no—
1287C22×C4—24no—
1288C22×C4—22no—
1289C22×C4—42no—
1290C22×C4—41no—
1291C22×C4—42no—
1292C22×C4—42no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—44no—
1297C22×C4—44no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—42no—
1301C22×C4—44no—
1302C22×C4—42no—
1303C22×C4—42no—
1304C22×C4—42no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—816no—
1311C22×C4C2×#4114yes—
1312C22×C4C2512yes—
1313C22×C4C2512yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2514yes—
1324C22×C4C2514yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2511yescharacteristic
1327C22×C4C2511yescharacteristic
1328C22×C4C2512yes—
1329C22×C4C2512yes—
1330C22×C4C2512yes—
1331C22×C4C2514yes—
1332C22×C4C2512yes—
1333C22×C4C2511yescharacteristic
1334C22×C4C2511yescharacteristic
1335C22×C4C2512yes—
1336C22×C4C2511yescharacteristic
1337C22×C4C2512yes—
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2511yescharacteristic
1342C4⋊C4—22no—
1343C4⋊C4—24no—
1344C4⋊C4—24no—
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—28no—
1348C4⋊C4—22no—
1349C4⋊C4—24no—
1350C4⋊C4—24no—
1351C4⋊C4—24no—
1352C4⋊C4—22no—
1353C4⋊C4—22no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—24no—
1357C4⋊C4—22no—
1358C4⋊C4—24no—
1359C4⋊C4—22no—
1360C4⋊C4—24no—
1361C4⋊C4—24no—
1362C4⋊C4—22no—
1363C4⋊C4—22no—
1364C4⋊C4—22no—
1365C4⋊C4—22no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—42no—
1369C4⋊C4—42no—
1370C4⋊C4—42no—
1371C4⋊C4—42no—
1372C4⋊C4—42no—
1373C4⋊C4—42no—
1374C4⋊C4—42no—
1375C4⋊C4—42no—
1376C4⋊C4—41no—
1377C4⋊C4—42no—
1378C4⋊C4—41no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—44no—
1382C4⋊C4—44no—
1383C4⋊C4—44no—
1384C4⋊C4—44no—
1385C4⋊C4—44no—
1386C4⋊C4—44no—
1387C4⋊C4—42no—
1388C4⋊C4—44no—
1389C4⋊C4—44no—
1390C4⋊C4—44no—
1391C4⋊C4—44no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—42no—
1395C4⋊C4—44no—
1396C4⋊C4—44no—
1397C4⋊C4—42no—
1398C4⋊C4—44no—
1399C4⋊C4—42no—
1400C4⋊C4—44no—
1401C4⋊C4C2×#4114yes—
1402C4⋊C4C2×#4118yes—
1403C22⋊C4—24no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—24no—
1407C22⋊C4—22no—
1408C22⋊C4—28no—
1409C22⋊C4—24no—
1410C22⋊C4—28no—
1411C22⋊C4—28no—
1412C22⋊C4—28no—
1413C22⋊C4—24no—
1414C22⋊C4—24no—
1415C22⋊C4—42no—
1416C22⋊C4—42no—
1417C22⋊C4—42no—
1418C22⋊C4—42no—
1419C22⋊C4—42no—
1420C22⋊C4—42no—
1421C22⋊C4—44no—
1422C22⋊C4—42no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—44no—
1426C22⋊C4—42no—
1427C22⋊C4—42no—
1428C22⋊C4—44no—
1429C22⋊C4—41no—
1430C22⋊C4—44no—
1431C22⋊C4—44no—
1432C22⋊C4—44no—
1433C22⋊C4—42no—
1434C22⋊C4—42no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—42no—
1438C22⋊C4—42no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—44no—
1442C22⋊C4—44no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—42no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—42no—
1451C22⋊C4—44no—
1452C22⋊C4—42no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—44no—
1457C22⋊C4—44no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—42no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—44no—
1467C22⋊C4—42no—
1468C22⋊C4—42no—
1469C22⋊C4C2×#4118yes—
1470C42—24no—
1471C42—28no—
1472C42—24no—
1473C42—22no—
1474C42—22no—
1475C42—22no—
1476C42—22no—
1477C42—22no—
1478C42—22no—
1479C42—22no—
1480C42—24no—
1481C42—24no—
1482C42—24no—
1483C42—24no—
1484C42—22no—
1485C42—24no—
1486C42—24no—
1487C42—22no—
1488C42—22no—
1489C42—42no—
1490C42—42no—
1491C42—42no—
1492C42—42no—
1493C42—42no—
1494C42—44no—
1495C42—41no—
1496C42—44no—
1497C42—42no—
1498C42—44no—
1499C42—44no—
1500C42—41no—
1501C42—44no—
1502C42—42no—
1503C42—42no—
1504C42H(5,𝔽2)14yes—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—22no—
1518C23—22no—
1519C23—24no—
1520C23—22no—
1521C23—22no—
1522C23—24no—
1523C23—24no—
1524C23—24no—
1525C23—22no—
1526C23—22no—
1527C23—22no—
1528C23—22no—
1529C23—22no—
1530C23—22no—
1531C23—24no—
1532C23—22no—
1533C23—24no—
1534C23—22no—
1535C23—22no—
1536C23—22no—
1537C23—24no—
1538C23—48no—
1539C23—84no—
1540C23—84no—
1541C23—84no—
1542C23—84no—
1543C23—84no—
1544C23—84no—
1545C23C22×#4112yes—
1546C23#58512yes—
1547C23C2611yescharacteristic
1548Q8—28no—
1549Q8—48no—
1550Q8—44no—
1551Q8—48no—
1552D4—44no—
1553D4—48no—
1554D4—48no—
1555D4—48no—
1556D4—44no—
1557D4—44no—
1558D4—88no—
1559D4—88no—
1560D4—84no—
1561D4—88no—
1562D4—84no—
1563D4—84no—
1564D4—88no—
1565D4—164no—
1566D4—164no—
1567C2×C4—21no—
1568C2×C4—22no—
1569C2×C4—22no—
1570C2×C4—21no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—21no—
1575C2×C4—28no—
1576C2×C4—21no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—24no—
1580C2×C4—22no—
1581C2×C4—21no—
1582C2×C4—22no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—22no—
1590C2×C4—22no—
1591C2×C4—22no—
1592C2×C4—24no—
1593C2×C4—24no—
1594C2×C4—22no—
1595C2×C4—22no—
1596C2×C4—21no—
1597C2×C4—22no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—22no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—22no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—21no—
1610C2×C4—21no—
1611C2×C4—21no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—22no—
1615C2×C4—22no—
1616C2×C4—22no—
1617C2×C4—22no—
1618C2×C4—21no—
1619C2×C4—24no—
1620C2×C4—22no—
1621C2×C4—24no—
1622C2×C4—24no—
1623C2×C4—22no—
1624C2×C4—22no—
1625C2×C4—21no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—22no—
1631C2×C4—22no—
1632C2×C4—24no—
1633C2×C4—21no—
1634C2×C4—22no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—24no—
1642C2×C4—22no—
1643C2×C4—24no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—22no—
1647C2×C4—21no—
1648C2×C4—48no—
1649C2×C4—44no—
1650C2×C4—44no—
1651C2×C4—48no—
1652C2×C4—48no—
1653C2×C4—44no—
1654C2×C4—44no—
1655C2×C4—82no—
1656C2×C4—84no—
1657C2×C4—84no—
1658C2×C4—88no—
1659C2×C4—84no—
1660C2×C4—84no—
1661C2×C4—88no—
1662C2×C4—164no—
1663C2×C4C22×#4112yes—
1664C2×C4C22×#4114yes—
1665C2×C4C22×#4114yes—
1666C2×C4C22×#4112yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×H(5,𝔽2)12yes—
1669C2×C4C2×H(5,𝔽2)12yes—
1670C2×C4#58512yes—
1671C2×C4#58512yes—
1672C2×C4#58512yes—
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—42no—
1688C22—42no—
1689C22—44no—
1690C22—44no—
1691C22—42no—
1692C22—42no—
1693C22—44no—
1694C22—42no—
1695C22—42no—
1696C22—42no—
1697C22—42no—
1698C22—44no—
1699C22—42no—
1700C22—44no—
1701C22—42no—
1702C22—44no—
1703C22—42no—
1704C22—42no—
1705C22—42no—
1706C22—44no—
1707C22—42no—
1708C22—816no—
1709C22C23×#4111yescharacteristic
1710C22C22×H(5,𝔽2)11yescharacteristic
1711C22C2×#58511yescharacteristic
1712C22C2×#58511yescharacteristic
1713C22C2×#58511yescharacteristic
1714C22C2×#58511yescharacteristic
1715C22H(7,𝔽2)11yescharacteristic
1716C4—22no—
1717C4—24no—
1718C4—24no—
1719C4—22no—
1720C4—41no—
1721C4—41no—
1722C4—42no—
1723C4—44no—
1724C4—41no—
1725C4—42no—
1726C4—44no—
1727C4—41no—
1728C4—42no—
1729C4—42no—
1730C4—41no—
1731C4—42no—
1732C4—42no—
1733C4—42no—
1734C4—41no—
1735C4—41no—
1736C4—41no—
1737C4—44no—
1738C4—42no—
1739C4—42no—
1740C4—41no—
1741C4—42no—
1742C4—42no—
1743C4—42no—
1744C4#351414yes—
1745C4#353914yes—
1746C2—42no—
1747C2—42no—
1748C2—84no—
1749C2—82no—
1750C2—82no—
1751C2C2×#353911yescharacteristic
1752C2C2×#351411yescharacteristic
1753C2#6281611yescharacteristic
1754C2#6292411yescharacteristic
1755C2#6293711yescharacteristic
1756C2#6300611yescharacteristic
1757C2#6302911yescharacteristic
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. #59585C2semidirect
2. #59435C2semidirect
3. #59067C2semidirect
4. #59039C2semidirect
5. #59019C2semidirect
6. #50271C2semidirect
7. #48937C2semidirect
8. #46061C2semidirect
9. #45647C2semidirect
10. #45234C2semidirect
11. #45052C2semidirect
12. #44146C2semidirect
13. #42855C2semidirect
14. #42768C2semidirect
15. #41459C2semidirect
16. #39910C2semidirect
17. #39243C2semidirect
18. #39202C2semidirect
19. #39127C2semidirect
20. #39008C2semidirect
21. #38998C2semidirect
22. #37857C2semidirect
23. #36586C2semidirect
24. #36583C2semidirect
25. #36460C2semidirect
26. #36460C2semidirect
27. #36150C2semidirect
28. #36101C2semidirect
29. #35238C2semidirect
30. #35185C2semidirect
31. #35136C2semidirect
32. #34946C2semidirect
33. #34700C2semidirect
34. #34391C2semidirect
35. C4×#552C2semidirect
36. C2×#557C22semidirect
40. C2×#532C22semidirect
44. #2864C22semidirect
46. #2860C22semidirect
48. #2858C22semidirect
49. #2857C22semidirect
53. #2850C22semidirect
58. #2797C22semidirect
59. #2796C22semidirect
60. #2795C22semidirect
61. #2780C22semidirect
62. #2779C22semidirect
63. #2775C22semidirect
64. #2770C22semidirect
65. #2757C22semidirect
68. #2752C22semidirect
71. #2744C22semidirect
74. #2738C22semidirect
75. #2727C22semidirect
76. #2725C22semidirect
78. #2718C22semidirect
80. #2707C22semidirect
84. #2686C22semidirect
90. #2662C22semidirect
91. #2654C22semidirect
92. #2652C22semidirect
93. #2651C22semidirect
94. #2650C22semidirect
95. #2649C22semidirect
96. #2648C22semidirect
97. #2629C22semidirect
98. #2624C22semidirect
99. #2604C22semidirect
100. #2596C22semidirect
101. #2578C22semidirect
102. #2576C22semidirect
103. #2571C22semidirect
104. #2571C22semidirect
105. #2567C22semidirect
106. #2567C22semidirect
107. #2566C22semidirect
112. #2562C22semidirect
115. #2559C22semidirect
116. #2559C22semidirect
117. #2558C22semidirect
118. #2553C22semidirect
119. #2552C22semidirect
122. #2548C22semidirect
125. #2547C22semidirect
132. #2538C22semidirect
133. #2537C22semidirect
134. #2531C22semidirect
135. #2531C22semidirect
136. #2526C22semidirect
137. #2526C22semidirect
138. #2526C22semidirect
139. #2526C22semidirect
140. #2526C22semidirect
141. #2514C22semidirect
144. #2512C22semidirect
145. #2512C22semidirect
146. #2510C22semidirect
147. #2510C22semidirect
148. #2509C22semidirect
151. #2500C22semidirect
152. #2496C22semidirect
153. #2496C22semidirect
154. #2495C22semidirect
155. #2494C22semidirect
156. #2493C22semidirect
157. #2490C22semidirect
158. #2490C22semidirect
159. #2490C22semidirect
160. #2490C22semidirect
161. #2490C22semidirect
162. #2490C22semidirect
163. #2487C22semidirect
165. #2476C22semidirect
166. #2471C22semidirect
167. #2469C22semidirect
170. #2462C22semidirect
171. #2460C22semidirect
176. #2454C22semidirect
177. #2453C22semidirect
178. #2453C22semidirect
181. #2448C22semidirect
182. #2448C22semidirect
184. #2447C22semidirect
185. #2446C22semidirect
190. #2441C22semidirect
194. #2430C22semidirect
195. #2430C22semidirect
197. #2429C22semidirect
204. #2426C22semidirect
207. #2422C22semidirect
208. #2421C22semidirect
211. #2420C22semidirect
212. #2420C22semidirect
215. #2416C22semidirect
216. #2416C22semidirect
222. #2407C22semidirect
229. #2371C22semidirect
230. #2370C22semidirect
231. #2367C22semidirect
233. #2366C22semidirect
234. #2365C22semidirect
237. #2363C22semidirect
241. #2360C22semidirect
243. #2357C22semidirect
244. #2357C22semidirect
245. #2356C22semidirect
246. #2356C22semidirect
248. #2353C22semidirect
250. #2352C22semidirect
251. Q8×C4⋊C4C22semidirect
252. Q8×C4⋊C4C22semidirect
253. #2349C22semidirect
254. #2347C22semidirect
256. #2346C22semidirect
257. #2344C22semidirect
258. #2343C22semidirect
259. #2341C22semidirect
260. #2341C22semidirect
261. #2341C22semidirect
262. #2339C22semidirect
263. #2335C22semidirect
264. #2335C22semidirect
265. #2333C22semidirect
266. #2324C22semidirect
267. #2324C22semidirect
268. #2324C22semidirect
269. #2323C22semidirect
270. #2323C22semidirect
273. #2314C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×#125C22semidirect
276. C4×#125C22semidirect
281. C4×#124C22semidirect
282. C4×#124C22semidirect
285. C4×C22⋊Q8C22semidirect
286. C4×C22⋊Q8C22semidirect
294. C42×Q8C22semidirect
297. C4×#117C22semidirect
298. C2×C4×C4⋊C4C22semidirect
902. C22⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#595852
#594352
#590672
#590392
#590192
#502712
#489372
#460612
#456472
#452342
#450522
#441462
#428552
#427682
#414592
#399102
#392432
#392022
#391272
#390082
#389982
#378572
#365862
#365832
#364602
#361502
#361012
#352382
#351852
#351362
#349462
#347002
#343912
C4×#5522