Finite Group Databasebeta

← #7688164

Subgroups — #7688164

Order 512.

5634 conjugacy classes of subgroups.

The subgroup lattice has 1814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59641C211yesmaximal, characteristic, complemented
2#59634C212yesmaximal, complemented
3#59480C212yesmaximal, complemented
4#59474C212yesmaximal, complemented
5#59414C212yesmaximal, complemented
6#59078C211yesmaximal, characteristic, complemented
7#59059C212yesmaximal, complemented
8#59057C211yesmaximal, characteristic, complemented
9#59022C212yesmaximal, complemented
10#44378C214yesmaximal, complemented
11#44183C214yesmaximal, complemented
12#44134C214yesmaximal, complemented
13#40103C212yesmaximal, complemented
14#40099C212yesmaximal, complemented
15#40003C212yesmaximal, complemented
16#39863C212yesmaximal, complemented
17#39533C212yesmaximal, complemented
18#39220C212yesmaximal, complemented
19#36573C212yesmaximal, complemented
20#36562C211yesmaximal, characteristic, complemented
21#36476C211yesmaximal, characteristic, complemented
22#36445C211yesmaximal, characteristic, complemented
23#36287C211yesmaximal, characteristic, complemented
24#36272C211yesmaximal, characteristic, complemented
25#36154C211yesmaximal, characteristic, complemented
26#36149C211yesmaximal, characteristic, complemented
27#36143C212yesmaximal, complemented
28#35698C214yesmaximal, complemented
29#34977C211yesmaximal, characteristic, complemented
30#34936C211yesmaximal, characteristic, complemented
31#34934C211yesmaximal, characteristic, complemented
32#34331C212yesmaximal, complemented
33#34233C212yesmaximal, complemented
34C4×#556C211yesmaximal, characteristic, complemented
35C4×#546C211yesmaximal, characteristic, complemented
36C2×#559C2212yes—
37C2×#557C2211yescharacteristic, complemented
38C2×#556C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#552C2212yescomplemented
41C2×#546C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#532C2211yescharacteristic, complemented
44C2×#529C2212yescomplemented
45C2×#525C2212yes—
46C2×#525C2212yes—
47C2×C4×#41C2211yescharacteristic
48C22×C4×D4C2211yescharacteristic
49#2862C2211yescharacteristic, complemented
50#2859C2212yescomplemented
51#2859C2212yescomplemented
52#2859C2212yescomplemented
53#2857C2211yescharacteristic
54#2857C2212yescomplemented
55#2857C2211yescharacteristic, complemented
56#2855C2212yescomplemented
57#2848C2212yes—
58#2798C2214yescomplemented
59#2796C2214yescomplemented
60#2777C2214yescomplemented
61#2773C2214yescomplemented
62#2752C2214yescomplemented
63#2749C2214yes—
64#2740C2214yescomplemented
65#2730C2214yescomplemented
66#2721C2214yescomplemented
67#2718C2214yes—
68#2711C2214yes—
69#2711C2214yescomplemented
70#2710C2214yes—
71#2710C2214yescomplemented
72#2707C2214yescomplemented
73#2706C2214yes—
74#2705C2214yes—
75#2705C2214yescomplemented
76#2694C2214yes—
77#2685C2214yes—
78#2670C2214yes—
79#2667C2214yescomplemented
80#2649C2214yescomplemented
81#2636C2214yescomplemented
82#2612C2214yescomplemented
83#2611C2214yescomplemented
84#2610C2214yescomplemented
85#2607C2214yescomplemented
86#2603C2214yescomplemented
87#2600C2214yes—
88#2589C2214yescomplemented
89#2580C2212yes—
90#2580C2212yescomplemented
91#2580C2214yescomplemented
92#2580C2214yescomplemented
93#2575C2214yescomplemented
94#2570C2212yescomplemented
95#2567C2211yescharacteristic, complemented
96#2566C2212yes—
97#2565C2212yescomplemented
98#2563C2211yescharacteristic
99#2557C2214yes—
100#2556C2214yes—
101#2556C2214yescomplemented
102#2556C2214yescomplemented
103#2554C2214yescomplemented
104#2554C2214yescomplemented
105#2553C2214yes—
106#2553C2214yescomplemented
107#2552C2211yescharacteristic, complemented
108#2548C2211yescharacteristic, complemented
109#2548C2211yescharacteristic, complemented
110#2545C2212yescomplemented
111#2542C2211yescharacteristic
112#2542C2211yescharacteristic
113#2542C2212yescomplemented
114#2541C2211yescharacteristic
115#2541C2211yescharacteristic
116#2540C2212yes—
117#2540C2212yes—
118#2540C2212yescomplemented
119#2539C2214yes—
120#2539C2214yes—
121#2538C2211yescharacteristic
122#2538C2212yescomplemented
123#2535C2212yes—
124#2534C2214yes—
125#2516C2214yescomplemented
126#2512C2212yescomplemented
127#2506C2212yescomplemented
128#2501C2212yes—
129#2501C2212yescomplemented
130#2500C2212yescomplemented
131#2497C2212yes—
132#2496C2212yescomplemented
133#2492C2212yescomplemented
134#2491C2212yescomplemented
135#2490C2212yes—
136#2490C2212yescomplemented
137#2490C2212yescomplemented
138#2489C2212yescomplemented
139#2487C2212yes—
140#2479C2214yescomplemented
141#2471C2214yes—
142#2470C2214yes—
143#2467C2214yescomplemented
144#2466C2214yescomplemented
145#2464C2214yes—
146#2460C2214yescomplemented
147#2457C2214yes—
148#2456C2214yes—
149#2455C2214yescomplemented
150#2454C2212yes—
151#2454C2212yes—
152#2454C2214yescomplemented
153#2454C2214yescomplemented
154#2454C2214yescomplemented
155#2454C2214yescomplemented
156#2454C2212yescomplemented
157#2454C2214yescomplemented
158#2454C2212yescomplemented
159#2450C2214yes—
160#2448C2212yescomplemented
161#2448C2212yescomplemented
162#2447C2212yescomplemented
163#2447C2212yescomplemented
164#2445C2212yes—
165#2445C2212yes—
166#2442C2212yes—
167#2441C2212yes—
168#2441C2212yescomplemented
169#2441C2214yescomplemented
170#2437C2214yes—
171#2433C2212yes—
172#2432C2212yes—
173#2431C2212yes—
174#2429C2212yescomplemented
175#2429C2212yescomplemented
176#2428C2212yes—
177#2427C2212yes—
178#2427C2212yescomplemented
179#2427C2212yescomplemented
180#2426C2212yes—
181#2426C2212yescomplemented
182#2425C2214yescomplemented
183#2423C2212yes—
184#2423C2212yescomplemented
185#2422C2212yes—
186#2422C2212yescomplemented
187#2420C2212yes—
188#2420C2212yescomplemented
189#2419C2214yescomplemented
190#2418C2214yes—
191#2417C2212yes—
192#2416C2212yescomplemented
193#2415C2212yescomplemented
194#2414C2212yescomplemented
195#2414C2212yescomplemented
196#2411C2214yes—
197#2407C2212yes—
198#2407C2212yes—
199#2407C2214yescomplemented
200#2397C2214yes—
201#2392C2214yescomplemented
202#2388C2214yescomplemented
203#2373C2212yes—
204#2373C2212yescomplemented
205#2370C2212yescomplemented
206#2369C2211yescharacteristic, complemented
207#2367C2211yescharacteristic
208#2367C2212yes—
209#2367C2212yescomplemented
210#2367C2214yescomplemented
211#2366C2212yes—
212#2365C2211yescharacteristic, complemented
213#2365C2211yescharacteristic, complemented
214#2364C2212yes—
215#2363C2211yescharacteristic
216#2362C2211yescharacteristic
217#2362C2211yescharacteristic, complemented
218#2361C2212yescomplemented
219#2361C2212yescomplemented
220#2360C2211yescharacteristic
221#2360C2212yescomplemented
222#2360C2212yescomplemented
223#2360C2212yescomplemented
224#2359C2212yes—
225#2359C2214yescomplemented
226#2359C2214yescomplemented
227#2358C2214yes—
228#2358C2214yes—
229#2358C2212yes—
230#2357C2212yes—
231#2356C2212yescomplemented
232#2355C2212yescomplemented
233#2355C2211yescharacteristic, complemented
234#2354C2211yescharacteristic
235#2354C2214yescomplemented
236#2353C2214yescomplemented
237#2352C2211yescharacteristic
238Q8×C4⋊C4C2212yescomplemented
239Q8×C4⋊C4C2211yescharacteristic, complemented
240#2349C2212yes—
241#2349C2211yescharacteristic
242#2349C2212yescomplemented
243#2349C2214yescomplemented
244#2349C2214yescomplemented
245D4×C4⋊C4C2211yescharacteristic
246#2347C2211yescharacteristic
247#2347C2211yescharacteristic, complemented
248#2346C2212yes—
249#2342C2212yes—
250#2341C2212yes—
251#2341C2212yes—
252#2339C2212yes—
253#2339C2211yescharacteristic
254#2339C2212yescomplemented
255D4×C22⋊C4C2212yes—
256D4×C22⋊C4C2211yescharacteristic
257#2335C2214yes—
258#2335C2214yes—
259#2335C2214yescomplemented
260#2335C2214yescomplemented
261#2326C2214yescomplemented
262#2318C2214yescomplemented
263C4×C4⋊Q8C2211yescharacteristic, complemented
264C4×#127C2212yes—
265C4×#127C2212yes—
266C4×#127C2212yes—
267C4×#127C2212yes—
268C4×#127C2211yescharacteristic, complemented
269C4×#126C2212yes—
270C4×#126C2212yescomplemented
271C4×#124C2212yes—
272C4×#124C2212yes—
273C4×#124C2211yescharacteristic
274C4×#124C2212yescomplemented
275C4×C22⋊Q8C2211yescharacteristic
276C4×C22⋊Q8C2211yescharacteristic
277C4×C22⋊Q8C2211yescharacteristic, complemented
278C4×C22⋊Q8C2212yescomplemented
279C4×C22⋊Q8C2212yescomplemented
280C4×#123C2212yes—
281C4×#121C2212yes—
282C4×#121C2211yescharacteristic
283C4×#121C2212yescomplemented
284C4×#121C2212yescomplemented
285C4×#121C2212yescomplemented
286C4×#120C2212yes—
287#2295C2212yescomplemented
288#2293C2212yes—
289#2293C2212yescomplemented
290C2×#380C2212yes—
291#2275C2214yescomplemented
292C42×Q8C2212yescomplemented
293C42×Q8C2211yescharacteristic, complemented
294C42×D4C2211yescharacteristic
295C42×D4C2211yescharacteristic
296C4×#117C2211yescharacteristic
297C4×#117C2211yescharacteristic, complemented
298C2×C4×C22⋊C4C2212yes—
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C23×D4C2311yescharacteristic
303C24×C4C2312yes—
304#559—216no—
305#557—44no—
306#556—28no—
307#554—44no—
308#552—48no—
309#546—28no—
310#532—44no—
311#532—44no—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2311yescharacteristic
315C2×C4⋊Q8C2312yes—
316C2×#127C2312yes—
317C2×#127C2312yes—
318C2×#127C2311yescharacteristic
319#529—48no—
320C2×#126C2312yes—
321C2×#126C2312yes—
322C2×#126C2314yes—
323C2×#126C2314yes—
324C2×#125C2312yes—
325C2×#125C2312yes—
326C2×#125C2312yes—
327C2×#125C2314yes—
328C2×#125C2314yes—
329C2×#125C2314yes—
330C2×#124C2314yes—
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336C2×#124C2311yescharacteristic
337#525—216no—
338#525—48no—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2312yes—
343C2×#123C2314yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2311yescharacteristic
348C2×C22⋊Q8C2311yescharacteristic
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2311yescharacteristic
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2314yes—
358C2×C22⋊Q8C2312yes—
359C2×#121C2312yes—
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2312yes—
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#120C2314yes—
371C2×#120C2312yes—
372C2×#120C2314yes—
373C4×#41—44no—
374C2×C4×Q8C2312yes—
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2312yes—
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2311yescharacteristic
386C2×C4×D4—44no—
387C2×C4×D4C2311yescharacteristic
388C2×C4×D4C2312yes—
389C2×C4×D4C2314yes—
390C2×C4×D4C2314yes—
391C2×C4×D4C2311yescharacteristic
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2314yes—
398C2×C4×D4C2311yescharacteristic
399C2×C4×D4C2311yescharacteristic
400C2×C4×D4C2311yescharacteristic
401C2×C4×D4C2312yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2314yes—
406C2×C4×D4C2314yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2312yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2312yes—
414C2×C4×D4C2312yes—
415C2×C4×D4C2312yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2312yes—
418C2×C4×D4C2314yes—
419C2×C4×D4C2314yes—
420C2×C4×D4C2312yes—
421C2×#117C2311yescharacteristic
422C2×#117C2311yescharacteristic
423C2×#117C2311yescharacteristic
424C2×#117C2312yes—
425C2×#117C2311yescharacteristic
426C2×#117C2314yes—
427C2×#117C2314yes—
428C2×#117C2311yescharacteristic
429C22×C4⋊C4C2312yes—
430C22×C4⋊C4C2311yescharacteristic
431C22×C4⋊C4C2312yes—
432C22×C22⋊C4C2312yes—
433C22×C22⋊C4C2312yes—
434C22×C22⋊C4C2312yes—
435C22×C22⋊C4C2314yes—
436C22×C42C2311yescharacteristic
437C22×C42C2311yescharacteristic
438C22×C42C2312yes—
439C22×C42C2312yes—
440#400C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2314yes—
444#399C2314yes—
445#399C2314yes—
446#399C2314yes—
447#399C2314yes—
448#399C2314yes—
449#399C2314yes—
450#399C2314yes—
451#399C2314yes—
452#399C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#399C2314yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#397C2314yes—
464#397C2314yes—
465#397C2314yes—
466#397C2314yes—
467#397C2314yes—
468#397C2314yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#396C2314yes—
473#396C2314yes—
474#396C2314yes—
475#396C2314yes—
476#396C2314yes—
477#396C2314yes—
478#396C2314yes—
479#396C2314yes—
480#396C2314yes—
481#396C2314yes—
482#396C2314yes—
483#395C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2314yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#394C2314yes—
499#393C2314yes—
500#393C2314yes—
501#393C2314yes—
502#392C2314yes—
503#392C2314yes—
504#392C2314yes—
505#392C2314yes—
506#392C2314yes—
507#392C2314yes—
508#392C2314yes—
509#392C2314yes—
510#391C2312yes—
511#391C2311yescharacteristic
512#391C2312yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2312yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2312yes—
520#391C2312yes—
521#391C2311yescharacteristic
522#391C2312yes—
523#391C2312yes—
524#391C2311yescharacteristic
525#391C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2314yes—
530#390C2314yes—
531#390C2312yes—
532#390C2312yes—
533#390C2314yes—
534#390C2314yes—
535#390C2314yes—
536#390C2312yes—
537#390C2314yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2312yes—
542#390C2312yes—
543#390C2312yes—
544#390C2312yes—
545#390C2311yescharacteristic
546#390C2314yes—
547#390C2314yes—
548#390C2314yes—
549#390C2311yescharacteristic
550#390C2314yes—
551#390C2312yes—
552#390C2312yes—
553#390C2314yes—
554#390C2314yes—
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#389C2312yes—
560#389C2311yescharacteristic
561#389C2311yescharacteristic
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2312yes—
566#389C2312yes—
567#389C2312yes—
568#389C2314yes—
569#389C2314yes—
570#389C2314yes—
571#389C2314yes—
572#389C2314yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2312yes—
578#389C2312yes—
579#389C2312yes—
580#389C2312yes—
581#389C2314yes—
582#389C2312yes—
583#389C2311yescharacteristic
584#389C2311yescharacteristic
585#389C2311yescharacteristic
586#389C2311yescharacteristic
587#389C2314yes—
588#389C2314yes—
589#389C2312yes—
590#389C2314yes—
591#389C2312yes—
592#389C2312yes—
593#388C2312yes—
594#388C2312yes—
595#388C2312yes—
596#388C2312yes—
597#388C2312yes—
598#388C2312yes—
599#388C2314yes—
600#388C2314yes—
601#388C2314yes—
602#388C2314yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2312yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2312yes—
615#388C2312yes—
616#388C2314yes—
617#388C2314yes—
618#388C2312yes—
619#388C2312yes—
620#388C2312yes—
621#388C2314yes—
622#388C2312yes—
623#388C2312yes—
624#388C2314yes—
625#388C2314yes—
626#388C2314yes—
627#388C2312yes—
628#388C2314yes—
629#388C2312yes—
630#388C2312yes—
631#388C2314yes—
632#387C2312yes—
633#387C2312yes—
634#387C2312yes—
635#387C2312yes—
636#387C2312yes—
637#387C2312yes—
638#387C2314yes—
639#387C2314yes—
640#387C2314yes—
641#387C2314yes—
642#387C2314yes—
643#387C2312yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2314yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2312yes—
652#387C2312yes—
653#387C2312yes—
654#387C2312yes—
655#387C2314yes—
656#386C2314yes—
657#386C2314yes—
658#386C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2312yes—
663#386C2314yes—
664#386C2312yes—
665#386C2314yes—
666#386C2312yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2312yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2312yes—
676#385C2314yes—
677#385C2314yes—
678#385C2314yes—
679#385C2314yes—
680#385C2314yes—
681#385C2314yes—
682#385C2312yes—
683#385C2312yes—
684#385C2314yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2312yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2312yes—
698#385C2314yes—
699#385C2312yes—
700#385C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2311yescharacteristic
706#384C2311yescharacteristic
707#384C2314yes—
708#384C2312yes—
709#383C2312yes—
710#383C2312yes—
711#382C2312yes—
712#382C2312yes—
713#382C2314yes—
714#382C2314yes—
715#382C2312yes—
716#382C2311yescharacteristic
717#382C2312yes—
718#381C2314yes—
719#381C2314yes—
720#381C2312yes—
721#381C2314yes—
722#380C2312yes—
723#380C2312yes—
724#380C2314yes—
725#380C2314yes—
726#380C2314yes—
727#380C2314yes—
728#380C2312yes—
729#380C2312yes—
730#380C2312yes—
731#380C2311yescharacteristic
732#380C2311yescharacteristic
733#380C2312yes—
734#380C2311yescharacteristic
735#380C2314yes—
736#380C2312yes—
737#380C2312yes—
738#380C2314yes—
739#380C2311yescharacteristic
740#380C2314yes—
741#380C2314yes—
742#380C2312yes—
743#379C2314yes—
744#379C2312yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2312yes—
747C4×C4⋊C4C2312yes—
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2311yescharacteristic
750C4×C4⋊C4C2311yescharacteristic
751C4×C4⋊C4C2311yescharacteristic
752C4×C4⋊C4C2311yescharacteristic
753C4×C4⋊C4C2314yes—
754C4×C4⋊C4C2314yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2311yescharacteristic
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2311yescharacteristic
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2311yescharacteristic
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2311yescharacteristic
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2311yescharacteristic
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2311yescharacteristic
778C4×C4⋊C4C2312yes—
779C4×C4⋊C4C2312yes—
780C4×C22⋊C4C2311yescharacteristic
781C4×C22⋊C4C2312yes—
782C4×C22⋊C4C2312yes—
783C4×C22⋊C4C2311yescharacteristic
784C4×C22⋊C4C2312yes—
785C4×C22⋊C4C2312yes—
786C4×C22⋊C4C2312yes—
787C4×C22⋊C4C2314yes—
788C4×C22⋊C4C2312yes—
789C4×C22⋊C4C2312yes—
790C4×C22⋊C4C2312yes—
791C4×C22⋊C4C2314yes—
792C4×C22⋊C4C2314yes—
793C4×C22⋊C4C2314yes—
794C4×C22⋊C4C2314yes—
795C4×C22⋊C4C2311yescharacteristic
796C4×C22⋊C4C2311yescharacteristic
797C4×C22⋊C4C2312yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2314yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2312yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812#376C2314yes—
813#376C2312yes—
814#376C2312yes—
815C2×#95C2314yes—
816C2×#95C2314yes—
817C2×#95C2312yes—
818C2×#95C2312yes—
819C43C2312yes—
820C43C2312yes—
821C43C2312yes—
822C43C2311yescharacteristic
823C25C2412yes—
824C2×#41—24no—
825C2×#41—24no—
826C2×#41—28no—
827C2×#41—44no—
828C2×#41—42no—
829C2×#41—44no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—82no—
833C22×Q8C2411yescharacteristic
834C22×Q8C2412yes—
835C22×Q8C2412yes—
836C22×Q8C2411yescharacteristic
837C22×Q8C2412yes—
838C22×D4—24no—
839C22×D4—24no—
840C22×D4—42no—
841C22×D4C2412yes—
842C22×D4C2412yes—
843C22×D4C2411yescharacteristic
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2411yescharacteristic
850C22×D4C2411yescharacteristic
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C23×C4—28no—
857C23×C4—44no—
858C23×C4—44no—
859C23×C4C2412yes—
860C23×C4C2411yescharacteristic
861C23×C4C2411yescharacteristic
862C23×C4C2411yescharacteristic
863C23×C4C2412yes—
864C23×C4C2412yes—
865C23×C4C2411yescharacteristic
866C23×C4C2411yescharacteristic
867C23×C4C2411yescharacteristic
868C23×C4C2414yes—
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2414yes—
874C23×C4C2412yes—
875C23×C4C2412yes—
876C23×C4C2414yes—
877C23×C4C2414yes—
878C23×C4C2414yes—
879C4⋊Q8—24no—
880C4⋊Q8—24no—
881C4⋊Q8—24no—
882C4⋊Q8—44no—
883#127—28no—
884#127—28no—
885#127—24no—
886#126—28no—
887#126—28no—
888#126—48no—
889#126—48no—
890#125—28no—
891#125—48no—
892#125—44no—
893#125—44no—
894#125—48no—
895#125—84no—
896#124—28no—
897#124—28no—
898#124—216no—
899#124—44no—
900#124—44no—
901#124—44no—
902#124#4118yescomplemented
903#123—216no—
904#123—28no—
905#123—216no—
906#123—216no—
907#123—48no—
908#123—48no—
909#123—48no—
910#123—84no—
911C22⋊Q8—24no—
912C22⋊Q8—24no—
913C22⋊Q8—28no—
914C22⋊Q8—28no—
915C22⋊Q8—24no—
916C22⋊Q8—28no—
917C22⋊Q8—48no—
918C22⋊Q8—44no—
919C22⋊Q8—44no—
920C22⋊Q8—44no—
921C22⋊Q8—44no—
922C22⋊Q8—82no—
923#121—24no—
924#121—28no—
925#121—28no—
926#121—28no—
927#121—28no—
928#121—44no—
929#121—44no—
930#121—44no—
931#121—44no—
932#121—44no—
933#121—84no—
934#120—216no—
935#120—28no—
936#120—48no—
937C4×Q8—28no—
938C4×Q8—24no—
939C4×Q8—24no—
940C4×Q8—28no—
941C4×Q8—28no—
942C4×Q8—24no—
943C4×Q8—24no—
944C4×Q8—44no—
945C4×Q8—42no—
946C4×Q8—44no—
947C4×Q8—44no—
948C4×Q8—44no—
949C4×D4—28no—
950C4×D4—24no—
951C4×D4—24no—
952C4×D4—216no—
953C4×D4—216no—
954C4×D4—216no—
955C4×D4—24no—
956C4×D4—24no—
957C4×D4—28no—
958C4×D4—24no—
959C4×D4—24no—
960C4×D4—44no—
961C4×D4—48no—
962C4×D4—42no—
963C4×D4—42no—
964C4×D4—42no—
965C4×D4—48no—
966C4×D4—44no—
967C4×D4—48no—
968C4×D4—44no—
969C4×D4—44no—
970C4×D4—44no—
971C4×D4—44no—
972C4×D4—44no—
973C4×D4—44no—
974C4×D4—48no—
975C4×D4—44no—
976C4×D4—44no—
977C4×D4—42no—
978C4×D4—48no—
979C4×D4—44no—
980C4×D4—84no—
981C4×D4—84no—
982C4×D4—82no—
983#117—24no—
984#117—24no—
985#117—24no—
986#117—44no—
987#117—48no—
988#117—48no—
989#117—42no—
990#117#4118yescomplemented
991C2×C4⋊C4—42no—
992C2×C4⋊C4—44no—
993C2×C4⋊C4—44no—
994C2×C4⋊C4C2411yescharacteristic
995C2×C4⋊C4C2411yescharacteristic
996C2×C4⋊C4C2411yescharacteristic
997C2×C4⋊C4C2411yescharacteristic
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2414yes—
1001C2×C4⋊C4C2411yescharacteristic
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2411yescharacteristic
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2414yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2411yescharacteristic
1018C2×C4⋊C4C2414yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2412yes—
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2412yes—
1031C2×C4⋊C4C2414yes—
1032C2×C4⋊C4C2414yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2414yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2412yes—
1038C2×C4⋊C4C2412yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2414yes—
1042C2×C4⋊C4C2414yes—
1043C2×C4⋊C4C2414yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2412yes—
1046C2×C4⋊C4C2414yes—
1047C2×C4⋊C4C2414yes—
1048C2×C4⋊C4C2414yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2414yes—
1051C2×C4⋊C4C2414yes—
1052C2×C4⋊C4C2412yes—
1053C2×C4⋊C4C2411yescharacteristic
1054C2×C4⋊C4C2411yescharacteristic
1055C2×C4⋊C4C2411yescharacteristic
1056C2×C22⋊C4—28no—
1057C2×C22⋊C4—44no—
1058C2×C22⋊C4—44no—
1059C2×C22⋊C4—84no—
1060C2×C22⋊C4C2411yescharacteristic
1061C2×C22⋊C4C2411yescharacteristic
1062C2×C22⋊C4C2412yes—
1063C2×C22⋊C4C2412yes—
1064C2×C22⋊C4C2412yes—
1065C2×C22⋊C4C2412yes—
1066C2×C22⋊C4C2412yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2412yes—
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2414yes—
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
1080C2×C22⋊C4C2414yes—
1081C2×C22⋊C4C2411yescharacteristic
1082C2×C22⋊C4C2411yescharacteristic
1083C2×C22⋊C4C2412yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2414yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2414yes—
1099C2×C22⋊C4C2414yes—
1100C2×C22⋊C4C2414yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2414yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2414yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2414yes—
1110C2×C22⋊C4C2414yes—
1111C2×C22⋊C4C2414yes—
1112C2×C22⋊C4C2412yes—
1113C2×C22⋊C4C2411yescharacteristic
1114C2×C22⋊C4C2414yes—
1115C2×C22⋊C4C2414yes—
1116C2×C22⋊C4C2414yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2414yes—
1119C2×C22⋊C4C2412yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2412yes—
1123C2×C42—24no—
1124C2×C42—24no—
1125C2×C42—44no—
1126C2×C42—44no—
1127C2×C42C2412yes—
1128C2×C42C2412yes—
1129C2×C42C2411yescharacteristic
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135C2×C42C2411yescharacteristic
1136C2×C42C2412yes—
1137C2×C42C2411yescharacteristic
1138C2×C42C2411yescharacteristic
1139C2×C42C2412yes—
1140C2×C42C2412yes—
1141C2×C42C2412yes—
1142C2×C42C2412yes—
1143C2×C42C2414yes—
1144C2×C42C2411yescharacteristic
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2412yes—
1148C2×C42C2412yes—
1149C2×C42C2412yes—
1150C2×C42C2412yes—
1151C2×C42C2414yes—
1152C2×C42C2412yes—
1153C2×C42C2412yes—
1154C2×C42C2411yescharacteristic
1155C2×C42C2412yes—
1156C2×C42C2411yescharacteristic
1157C2×C42C2414yes—
1158C2×C42C2414yes—
1159C2×C42C2412yes—
1160C2×C42C2412yes—
1161C2×C42C2412yes—
1162C2×C42C2412yes—
1163C2×C42C2412yes—
1164C2×C42C2411yescharacteristic
1165C2×C42C2411yescharacteristic
1166#95C2411yescharacteristic
1167#95C2414yes—
1168#95C2411yescharacteristic
1169#95C2412yes—
1170#95C2412yes—
1171#95C2412yes—
1172#95C2412yes—
1173#95C2412yes—
1174#95C2412yes—
1175#95C2412yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2414yes—
1179#95C2414yes—
1180#95C2412yes—
1181#95C2414yes—
1182#95C2414yes—
1183#95C2412yes—
1184#95C2412yes—
1185#95C2412yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2411yescharacteristic
1191#95C2411yescharacteristic
1192#95C2411yescharacteristic
1193#95C2411yescharacteristic
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2412yes—
1198#95C2414yes—
1199#95C2414yes—
1200#95C2412yes—
1201#95C2414yes—
1202#95C2414yes—
1203#95C2412yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2412yes—
1209#95C2412yes—
1210#95C2412yes—
1211#95C2412yes—
1212#95C2412yes—
1213#95C2412yes—
1214#95C2412yes—
1215#95C2412yes—
1216#95C2414yes—
1217#95C2414yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224C24—24no—
1225C24—24no—
1226C24—24no—
1227C24—42no—
1228C24—42no—
1229C24—42no—
1230C24—42no—
1231C24C2511yescharacteristic
1232C24C2514yes—
1233C24C2511yescharacteristic
1234C24C2512yes—
1235C24C2512yes—
1236#41—416no—
1237#41—816no—
1238#41—816no—
1239C2×Q8—22no—
1240C2×Q8—24no—
1241C2×Q8—24no—
1242C2×Q8—24no—
1243C2×Q8—22no—
1244C2×Q8—22no—
1245C2×Q8—22no—
1246C2×Q8—24no—
1247C2×Q8—24no—
1248C2×Q8—24no—
1249C2×Q8—22no—
1250C2×Q8—42no—
1251C2×Q8—42no—
1252C2×Q8—42no—
1253C2×Q8C2×#4114yes—
1254C2×D4—22no—
1255C2×D4—28no—
1256C2×D4—24no—
1257C2×D4—28no—
1258C2×D4—28no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—24no—
1262C2×D4—28no—
1263C2×D4—28no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—28no—
1267C2×D4—28no—
1268C2×D4—24no—
1269C2×D4—24no—
1270C2×D4—24no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—28no—
1274C2×D4—24no—
1275C2×D4—24no—
1276C2×D4—24no—
1277C2×D4—24no—
1278C2×D4—22no—
1279C2×D4—24no—
1280C2×D4—42no—
1281C2×D4—42no—
1282C2×D4—44no—
1283C2×D4—44no—
1284C2×D4—41no—
1285C2×D4—44no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—44no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—44no—
1292C2×D4—44no—
1293C2×D4—42no—
1294C2×D4—44no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—416no—
1298C2×D4C2×#4114yes—
1299C2×D42−1+414yes—
1300C22×C4—22no—
1301C22×C4—22no—
1302C22×C4—24no—
1303C22×C4—28no—
1304C22×C4—24no—
1305C22×C4—24no—
1306C22×C4—24no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—24no—
1311C22×C4—24no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—24no—
1317C22×C4—24no—
1318C22×C4—24no—
1319C22×C4—24no—
1320C22×C4—22no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—22no—
1324C22×C4—24no—
1325C22×C4—28no—
1326C22×C4—24no—
1327C22×C4—24no—
1328C22×C4—28no—
1329C22×C4—22no—
1330C22×C4—24no—
1331C22×C4—28no—
1332C22×C4—42no—
1333C22×C4—41no—
1334C22×C4—42no—
1335C22×C4—42no—
1336C22×C4—42no—
1337C22×C4—42no—
1338C22×C4—42no—
1339C22×C4—44no—
1340C22×C4—44no—
1341C22×C4—44no—
1342C22×C4—42no—
1343C22×C4—42no—
1344C22×C4—42no—
1345C22×C4—42no—
1346C22×C4—44no—
1347C22×C4—44no—
1348C22×C4—44no—
1349C22×C4—41no—
1350C22×C4—44no—
1351C22×C4—42no—
1352C22×C4—42no—
1353C22×C4—44no—
1354C22×C4—41no—
1355C22×C4—42no—
1356C22×C4—44no—
1357C22×C4—44no—
1358C22×C4—44no—
1359C22×C4—816no—
1360C22×C4C2×#4114yes—
1361C22×C4C2511yescharacteristic
1362C22×C4C2511yescharacteristic
1363C22×C4C2511yescharacteristic
1364C22×C4C2512yes—
1365C22×C4C2511yescharacteristic
1366C22×C4C2512yes—
1367C22×C4C2514yes—
1368C22×C4C2512yes—
1369C22×C4C2512yes—
1370C22×C4C2512yes—
1371C22×C4C2512yes—
1372C22×C4C2512yes—
1373C22×C4C2514yes—
1374C22×C4C2514yes—
1375C22×C4C2512yes—
1376C22×C4C2511yescharacteristic
1377C22×C4C2512yes—
1378C22×C4C2511yescharacteristic
1379C22×C4C2512yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C22×C4C2511yescharacteristic
1383C22×C4C2512yes—
1384C22×C4C2512yes—
1385C22×C4C2512yes—
1386C22×C4C2511yescharacteristic
1387C22×C4C2512yes—
1388C22×C4C2511yescharacteristic
1389C22×C4C2511yescharacteristic
1390C22×C4C2511yescharacteristic
1391C4⋊C4—22no—
1392C4⋊C4—24no—
1393C4⋊C4—24no—
1394C4⋊C4—22no—
1395C4⋊C4—22no—
1396C4⋊C4—28no—
1397C4⋊C4—28no—
1398C4⋊C4—22no—
1399C4⋊C4—24no—
1400C4⋊C4—24no—
1401C4⋊C4—24no—
1402C4⋊C4—28no—
1403C4⋊C4—24no—
1404C4⋊C4—24no—
1405C4⋊C4—24no—
1406C4⋊C4—24no—
1407C4⋊C4—22no—
1408C4⋊C4—22no—
1409C4⋊C4—22no—
1410C4⋊C4—22no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—22no—
1414C4⋊C4—28no—
1415C4⋊C4—24no—
1416C4⋊C4—22no—
1417C4⋊C4—24no—
1418C4⋊C4—24no—
1419C4⋊C4—24no—
1420C4⋊C4—28no—
1421C4⋊C4—28no—
1422C4⋊C4—24no—
1423C4⋊C4—24no—
1424C4⋊C4—22no—
1425C4⋊C4—24no—
1426C4⋊C4—22no—
1427C4⋊C4—42no—
1428C4⋊C4—44no—
1429C4⋊C4—44no—
1430C4⋊C4—42no—
1431C4⋊C4—44no—
1432C4⋊C4—44no—
1433C4⋊C4—44no—
1434C4⋊C4—44no—
1435C4⋊C4—42no—
1436C4⋊C4—42no—
1437C4⋊C4—44no—
1438C4⋊C4—44no—
1439C4⋊C4—42no—
1440C4⋊C4—44no—
1441C4⋊C4—44no—
1442C4⋊C4—44no—
1443C4⋊C4—44no—
1444C4⋊C4—44no—
1445C4⋊C4—44no—
1446C4⋊C4—42no—
1447C4⋊C4—44no—
1448C4⋊C4—44no—
1449C4⋊C4—42no—
1450C4⋊C4C2×#4114yes—
1451C4⋊C4C2×#4114yes—
1452C4⋊C4H(5,𝔽2)14yes—
1453C22⋊C4—24no—
1454C22⋊C4—28no—
1455C22⋊C4—22no—
1456C22⋊C4—24no—
1457C22⋊C4—24no—
1458C22⋊C4—22no—
1459C22⋊C4—24no—
1460C22⋊C4—24no—
1461C22⋊C4—28no—
1462C22⋊C4—28no—
1463C22⋊C4—24no—
1464C22⋊C4—22no—
1465C22⋊C4—28no—
1466C22⋊C4—28no—
1467C22⋊C4—28no—
1468C22⋊C4—28no—
1469C22⋊C4—22no—
1470C22⋊C4—24no—
1471C22⋊C4—28no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—24no—
1475C22⋊C4—24no—
1476C22⋊C4—28no—
1477C22⋊C4—28no—
1478C22⋊C4—22no—
1479C22⋊C4—24no—
1480C22⋊C4—42no—
1481C22⋊C4—42no—
1482C22⋊C4—42no—
1483C22⋊C4—42no—
1484C22⋊C4—42no—
1485C22⋊C4—44no—
1486C22⋊C4—44no—
1487C22⋊C4—44no—
1488C22⋊C4—42no—
1489C22⋊C4—42no—
1490C22⋊C4—42no—
1491C22⋊C4—44no—
1492C22⋊C4—44no—
1493C22⋊C4—44no—
1494C22⋊C4—44no—
1495C22⋊C4—41no—
1496C22⋊C4—44no—
1497C22⋊C4—44no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—44no—
1501C22⋊C4—44no—
1502C22⋊C4—44no—
1503C22⋊C4—44no—
1504C22⋊C4—44no—
1505C22⋊C4—44no—
1506C22⋊C4—42no—
1507C22⋊C4—44no—
1508C22⋊C4—44no—
1509C22⋊C4—44no—
1510C22⋊C4—42no—
1511C22⋊C4—44no—
1512C22⋊C4—42no—
1513C22⋊C4C2×#4118yes—
1514C22⋊C4C2×#4118yes—
1515C22⋊C4C2×#4118yes—
1516C42—24no—
1517C42—28no—
1518C42—24no—
1519C42—22no—
1520C42—24no—
1521C42—24no—
1522C42—22no—
1523C42—22no—
1524C42—22no—
1525C42—22no—
1526C42—22no—
1527C42—22no—
1528C42—22no—
1529C42—24no—
1530C42—24no—
1531C42—24no—
1532C42—24no—
1533C42—24no—
1534C42—24no—
1535C42—22no—
1536C42—24no—
1537C42—24no—
1538C42—42no—
1539C42—42no—
1540C42—42no—
1541C42—42no—
1542C42—44no—
1543C42—44no—
1544C42—41no—
1545C42—42no—
1546C42—42no—
1547C42—41no—
1548C42—42no—
1549C42—42no—
1550C42—44no—
1551C42—42no—
1552C42C2×#4118yes—
1553C42C2×#4114yes—
1554C42H(5,𝔽2)14yes—
1555C23—21no—
1556C23—22no—
1557C23—22no—
1558C23—22no—
1559C23—22no—
1560C23—21no—
1561C23—22no—
1562C23—22no—
1563C23—22no—
1564C23—21no—
1565C23—21no—
1566C23—22no—
1567C23—21no—
1568C23—22no—
1569C23—22no—
1570C23—21no—
1571C23—22no—
1572C23—22no—
1573C23—21no—
1574C23—24no—
1575C23—24no—
1576C23—21no—
1577C23—21no—
1578C23—24no—
1579C23—24no—
1580C23—21no—
1581C23—21no—
1582C23—24no—
1583C23—24no—
1584C23—21no—
1585C23—24no—
1586C23—21no—
1587C23—48no—
1588C23—48no—
1589C23—48no—
1590C23—84no—
1591C23—84no—
1592C23—84no—
1593C23—84no—
1594C23C22×#4112yes—
1595C23C22×#4114yes—
1596C23C2×2−1+414yes—
1597C23C2611yescharacteristic
1598Q8—28no—
1599Q8—48no—
1600Q8—44no—
1601Q8—48no—
1602Q8—84no—
1603D4—28no—
1604D4—28no—
1605D4—416no—
1606D4—416no—
1607D4—416no—
1608D4—44no—
1609D4—48no—
1610D4—48no—
1611D4—48no—
1612D4—48no—
1613D4—48no—
1614D4—84no—
1615D4—88no—
1616D4—88no—
1617D4—88no—
1618C2×C4—22no—
1619C2×C4—21no—
1620C2×C4—21no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—22no—
1628C2×C4—22no—
1629C2×C4—22no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—22no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—28no—
1637C2×C4—21no—
1638C2×C4—22no—
1639C2×C4—21no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—24no—
1643C2×C4—22no—
1644C2×C4—22no—
1645C2×C4—22no—
1646C2×C4—21no—
1647C2×C4—22no—
1648C2×C4—22no—
1649C2×C4—24no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—21no—
1655C2×C4—21no—
1656C2×C4—22no—
1657C2×C4—22no—
1658C2×C4—21no—
1659C2×C4—22no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—22no—
1664C2×C4—22no—
1665C2×C4—22no—
1666C2×C4—22no—
1667C2×C4—24no—
1668C2×C4—24no—
1669C2×C4—22no—
1670C2×C4—24no—
1671C2×C4—22no—
1672C2×C4—24no—
1673C2×C4—21no—
1674C2×C4—21no—
1675C2×C4—22no—
1676C2×C4—21no—
1677C2×C4—21no—
1678C2×C4—22no—
1679C2×C4—22no—
1680C2×C4—21no—
1681C2×C4—21no—
1682C2×C4—22no—
1683C2×C4—24no—
1684C2×C4—22no—
1685C2×C4—21no—
1686C2×C4—21no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—22no—
1690C2×C4—22no—
1691C2×C4—24no—
1692C2×C4—22no—
1693C2×C4—24no—
1694C2×C4—44no—
1695C2×C4—48no—
1696C2×C4—44no—
1697C2×C4—48no—
1698C2×C4—48no—
1699C2×C4—44no—
1700C2×C4—44no—
1701C2×C4—88no—
1702C2×C4—84no—
1703C2×C4—84no—
1704C2×C4—82no—
1705C2×C4—84no—
1706C2×C4—84no—
1707C2×C4—88no—
1708C2×C4—88no—
1709C2×C4—88no—
1710C2×C4—84no—
1711C2×C4—84no—
1712C2×C4—164no—
1713C2×C4C22×#4114yes—
1714C2×C4C22×#4114yes—
1715C2×C4C22×#4112yes—
1716C2×C4C22×#4112yes—
1717C2×C4C22×#4114yes—
1718C2×C4C22×#4112yes—
1719C2×C4C22×#4112yes—
1720C2×C4C22×#4112yes—
1721C2×C4C2×H(5,𝔽2)14yes—
1722C2×C4C2×H(5,𝔽2)12yes—
1723C2×C4C2×H(5,𝔽2)12yes—
1724C2×C4C2×H(5,𝔽2)12yes—
1725C2×C4C2×H(5,𝔽2)12yes—
1726C2×C4C2×2−1+412yes—
1727C2×C4#58512yes—
1728C22—24no—
1729C22—24no—
1730C22—22no—
1731C22—24no—
1732C22—24no—
1733C22—24no—
1734C22—22no—
1735C22—24no—
1736C22—22no—
1737C22—42no—
1738C22—41no—
1739C22—42no—
1740C22—42no—
1741C22—41no—
1742C22—41no—
1743C22—42no—
1744C22—42no—
1745C22—42no—
1746C22—41no—
1747C22—42no—
1748C22—42no—
1749C22—44no—
1750C22—41no—
1751C22—44no—
1752C22—41no—
1753C22—44no—
1754C22—41no—
1755C22—41no—
1756C22—44no—
1757C22—41no—
1758C22—44no—
1759C22—41no—
1760C22—44no—
1761C22—41no—
1762C22—44no—
1763C22—816no—
1764C22C23×#4111yescharacteristic
1765C22C23×#4111yescharacteristic
1766C22C22×H(5,𝔽2)11yescharacteristic
1767C22C22×H(5,𝔽2)11yescharacteristic
1768C22C22×2−1+411yescharacteristic
1769C22C2×#58511yescharacteristic
1770C22H(7,𝔽2)11yescharacteristic
1771C4—22no—
1772C4—24no—
1773C4—24no—
1774C4—24no—
1775C4—22no—
1776C4—22no—
1777C4—22no—
1778C4—24no—
1779C4—22no—
1780C4—42no—
1781C4—44no—
1782C4—42no—
1783C4—42no—
1784C4—41no—
1785C4—42no—
1786C4—41no—
1787C4—41no—
1788C4—41no—
1789C4—41no—
1790C4—42no—
1791C4—42no—
1792C4—44no—
1793C4—42no—
1794C4—41no—
1795C4—42no—
1796C4—44no—
1797C4—42no—
1798C4—42no—
1799C4#350814yes—
1800C4#352014yes—
1801C2—44no—
1802C2—44no—
1803C2—42no—
1804C2—84no—
1805C2—81no—
1806C2#41211yescharacteristic
1807C2C2×#352011yescharacteristic
1808C2C2×#350811yescharacteristic
1809C2#6292411yescharacteristic
1810C2#6298611yescharacteristic
1811C2#6300011yescharacteristic
1812C2#6301311yescharacteristic
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. #59641C2semidirect
2. #59634C2semidirect
3. #59480C2semidirect
4. #59474C2semidirect
5. #59414C2semidirect
6. #59078C2semidirect
7. #59059C2semidirect
8. #59057C2semidirect
9. #59022C2semidirect
10. #44378C2semidirect
11. #44183C2semidirect
12. #44134C2semidirect
13. #40103C2semidirect
14. #40099C2semidirect
15. #40003C2semidirect
16. #39863C2semidirect
17. #39533C2semidirect
18. #39220C2semidirect
19. #36573C2semidirect
20. #36562C2semidirect
21. #36476C2semidirect
22. #36445C2semidirect
23. #36287C2semidirect
24. #36272C2semidirect
25. #36154C2semidirect
26. #36149C2semidirect
27. #36143C2semidirect
28. #35698C2semidirect
29. #34977C2semidirect
30. #34936C2semidirect
31. #34934C2semidirect
32. #34331C2semidirect
33. #34233C2semidirect
34. C4×#556C2semidirect
35. C4×#546C2semidirect
37. C2×#557C22semidirect
40. C2×#552C22semidirect
43. C2×#532C22semidirect
44. C2×#529C22semidirect
49. #2862C22semidirect
50. #2859C22semidirect
51. #2859C22semidirect
52. #2859C22semidirect
54. #2857C22semidirect
55. #2857C22semidirect
56. #2855C22semidirect
58. #2798C22semidirect
59. #2796C22semidirect
60. #2777C22semidirect
61. #2773C22semidirect
62. #2752C22semidirect
64. #2740C22semidirect
65. #2730C22semidirect
66. #2721C22semidirect
69. #2711C22semidirect
71. #2710C22semidirect
72. #2707C22semidirect
75. #2705C22semidirect
79. #2667C22semidirect
80. #2649C22semidirect
81. #2636C22semidirect
82. #2612C22semidirect
83. #2611C22semidirect
84. #2610C22semidirect
85. #2607C22semidirect
86. #2603C22semidirect
88. #2589C22semidirect
90. #2580C22semidirect
91. #2580C22semidirect
92. #2580C22semidirect
93. #2575C22semidirect
94. #2570C22semidirect
95. #2567C22semidirect
97. #2565C22semidirect
101. #2556C22semidirect
102. #2556C22semidirect
103. #2554C22semidirect
104. #2554C22semidirect
106. #2553C22semidirect
107. #2552C22semidirect
108. #2548C22semidirect
109. #2548C22semidirect
110. #2545C22semidirect
113. #2542C22semidirect
118. #2540C22semidirect
122. #2538C22semidirect
125. #2516C22semidirect
126. #2512C22semidirect
127. #2506C22semidirect
129. #2501C22semidirect
130. #2500C22semidirect
132. #2496C22semidirect
133. #2492C22semidirect
134. #2491C22semidirect
136. #2490C22semidirect
137. #2490C22semidirect
138. #2489C22semidirect
140. #2479C22semidirect
143. #2467C22semidirect
144. #2466C22semidirect
146. #2460C22semidirect
149. #2455C22semidirect
152. #2454C22semidirect
153. #2454C22semidirect
154. #2454C22semidirect
155. #2454C22semidirect
156. #2454C22semidirect
157. #2454C22semidirect
158. #2454C22semidirect
160. #2448C22semidirect
161. #2448C22semidirect
162. #2447C22semidirect
163. #2447C22semidirect
168. #2441C22semidirect
169. #2441C22semidirect
174. #2429C22semidirect
175. #2429C22semidirect
178. #2427C22semidirect
179. #2427C22semidirect
181. #2426C22semidirect
182. #2425C22semidirect
184. #2423C22semidirect
186. #2422C22semidirect
188. #2420C22semidirect
189. #2419C22semidirect
192. #2416C22semidirect
193. #2415C22semidirect
194. #2414C22semidirect
195. #2414C22semidirect
199. #2407C22semidirect
201. #2392C22semidirect
202. #2388C22semidirect
204. #2373C22semidirect
205. #2370C22semidirect
206. #2369C22semidirect
209. #2367C22semidirect
210. #2367C22semidirect
212. #2365C22semidirect
213. #2365C22semidirect
217. #2362C22semidirect
218. #2361C22semidirect
219. #2361C22semidirect
221. #2360C22semidirect
222. #2360C22semidirect
223. #2360C22semidirect
225. #2359C22semidirect
226. #2359C22semidirect
231. #2356C22semidirect
232. #2355C22semidirect
233. #2355C22semidirect
235. #2354C22semidirect
236. #2353C22semidirect
238. Q8×C4⋊C4C22semidirect
239. Q8×C4⋊C4C22semidirect
242. #2349C22semidirect
243. #2349C22semidirect
244. #2349C22semidirect
247. #2347C22semidirect
254. #2339C22semidirect
259. #2335C22semidirect
260. #2335C22semidirect
261. #2326C22semidirect
262. #2318C22semidirect
263. C4×C4⋊Q8C22semidirect
268. C4×#127C22semidirect
270. C4×#126C22semidirect
274. C4×#124C22semidirect
277. C4×C22⋊Q8C22semidirect
278. C4×C22⋊Q8C22semidirect
279. C4×C22⋊Q8C22semidirect
283. C4×#121C22semidirect
284. C4×#121C22semidirect
285. C4×#121C22semidirect
287. #2295C22semidirect
289. #2293C22semidirect
291. #2275C22semidirect
292. C42×Q8C22semidirect
293. C42×Q8C22semidirect
297. C4×#117C22semidirect
902. #124#41semidirect
990. #117#41semidirect

Maximal subgroups

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

subgroupindex
#596412
#596342
#594802
#594742
#594142
#590782
#590592
#590572
#590222
#443782
#441832
#441342
#401032
#400992
#400032
#398632
#395332
#392202
#365732
#365622
#364762
#364452
#362872
#362722
#361542
#361492
#361432
#356982
#349772
#349362
#349342
#343312
#342332
C4×#5562
C4×#5462