Finite Group Databasebeta

← #7780449

Subgroups — #7780449

Order 512.

5530 conjugacy classes of subgroups.

The subgroup lattice has 1845 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#59441C212yesmaximal, complemented
4#59427C211yesmaximal, characteristic, complemented
5#59410C211yesmaximal, characteristic, complemented
6#59024C212yesmaximal, complemented
7#50044C214yesmaximal, complemented
8#49198C214yesmaximal, complemented
9#46810C214yesmaximal, complemented
10#46509C214yesmaximal, complemented
11#45623C212yesmaximal, complemented
12#45593C212yesmaximal, complemented
13#44972C212yesmaximal, complemented
14#44892C212yesmaximal, complemented
15#42732C212yesmaximal, complemented
16#42552C212yesmaximal, complemented
17#40221C212yesmaximal, complemented
18#39862C212yesmaximal, complemented
19#39193C211yesmaximal, characteristic, complemented
20#39165C212yesmaximal, complemented
21#38951C211yesmaximal, characteristic, complemented
22#38928C212yesmaximal, complemented
23#38908C212yesmaximal, complemented
24#38034C212yesmaximal, complemented
25#37341C212yesmaximal, complemented
26#36504C211yesmaximal, characteristic, complemented
27#36468C211yesmaximal, characteristic, complemented
28#36406C211yesmaximal, characteristic, complemented
29#36259C211yesmaximal, characteristic, complemented
30#36153C211yesmaximal, characteristic, complemented
31#36100C211yesmaximal, characteristic, complemented
32#35291C211yesmaximal, characteristic, complemented
33#34914C211yesmaximal, characteristic, complemented
34#34477C212yesmaximal, complemented
35C4×#535C211yesmaximal, characteristic, complemented
36C2×#556C2211yescharacteristic, complemented
37C2×#554C2212yescomplemented
38C2×#553C2212yescomplemented
39C2×#550C2212yes—
40C2×#547C2211yescharacteristic
41C2×#547C2211yescharacteristic
42C2×#547C2212yes—
43C2×#547C2211yescharacteristic, complemented
44C2×#546C2212yes—
45C2×#535C2211yescharacteristic
46C2×#529C2212yes—
47C2×#525C2212yes—
48C2×C4×#41C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50#2862C2211yescharacteristic, complemented
51#2859C2211yescharacteristic, complemented
52#2857C2211yescharacteristic
53#2857C2211yescharacteristic
54#2857C2212yescomplemented
55#2854C2212yes—
56#2854C2212yescomplemented
57#2850C2212yescomplemented
58#2848C2212yes—
59#2847C2212yes—
60#2827C2214yescomplemented
61#2825C2214yescomplemented
62#2800C2214yescomplemented
63#2783C2214yescomplemented
64#2780C2214yescomplemented
65#2779C2214yescomplemented
66#2778C2214yescomplemented
67#2777C2214yescomplemented
68#2770C2214yes—
69#2768C2214yescomplemented
70#2765C2214yescomplemented
71#2757C2214yes—
72#2757C2214yescomplemented
73#2757C2214yescomplemented
74#2756C2214yescomplemented
75#2750C2214yescomplemented
76#2750C2214yescomplemented
77#2749C2214yescomplemented
78#2732C2214yescomplemented
79#2725C2214yescomplemented
80#2707C2214yescomplemented
81#2707C2214yescomplemented
82#2706C2214yescomplemented
83#2706C2214yescomplemented
84#2706C2214yescomplemented
85#2705C2214yescomplemented
86#2703C2214yes—
87#2703C2214yescomplemented
88#2702C2214yescomplemented
89#2697C2214yes—
90#2696C2214yescomplemented
91#2695C2214yes—
92#2695C2214yescomplemented
93#2693C2214yes—
94#2693C2214yescomplemented
95#2682C2214yes—
96#2682C2214yescomplemented
97#2681C2214yes—
98#2678C2214yes—
99#2678C2214yes—
100#2673C2214yes—
101#2669C2214yes—
102#2648C2214yescomplemented
103#2646C2214yescomplemented
104#2645C2212yescomplemented
105#2639C2214yescomplemented
106#2636C2214yescomplemented
107#2625C2212yes—
108#2625C2212yescomplemented
109#2620C2212yes—
110#2606C2214yescomplemented
111#2603C2214yes—
112#2602C2214yescomplemented
113#2592C2212yes—
114#2587C2214yescomplemented
115#2568C2212yescomplemented
116#2562C2212yescomplemented
117#2560C2212yescomplemented
118#2559C2212yes—
119#2559C2214yescomplemented
120#2558C2214yes—
121#2558C2212yescomplemented
122#2557C2212yes—
123#2554C2214yes—
124#2554C2214yescomplemented
125#2553C2214yescomplemented
126#2553C2214yescomplemented
127#2552C2212yescomplemented
128#2547C2211yescharacteristic
129#2546C2211yescharacteristic, complemented
130#2545C2212yes—
131#2542C2211yescharacteristic
132#2542C2211yescharacteristic, complemented
133#2541C2212yescomplemented
134#2540C2212yes—
135#2540C2212yes—
136#2538C2212yes—
137#2538C2211yescharacteristic, complemented
138#2538C2212yescomplemented
139#2538C2212yescomplemented
140#2538C2212yescomplemented
141#2537C2211yescharacteristic
142#2537C2211yescharacteristic
143#2537C2211yescharacteristic, complemented
144#2536C2212yes—
145#2535C2214yes—
146#2535C2212yescomplemented
147#2532C2214yescomplemented
148#2514C2212yescomplemented
149#2512C2211yescharacteristic, complemented
150#2510C2214yescomplemented
151#2509C2212yescomplemented
152#2508C2212yescomplemented
153#2506C2211yescharacteristic, complemented
154#2504C2212yescomplemented
155#2502C2212yescomplemented
156#2499C2212yescomplemented
157#2497C2212yescomplemented
158#2496C2211yescharacteristic
159#2496C2212yescomplemented
160#2495C2212yes—
161#2495C2212yescomplemented
162#2495C2212yescomplemented
163#2495C2212yescomplemented
164#2494C2212yes—
165#2491C2211yescharacteristic
166#2490C2212yescomplemented
167#2489C2212yes—
168#2486C2212yes—
169#2486C2212yes—
170#2480C2214yes—
171#2479C2214yescomplemented
172#2472C2214yes—
173#2467C2214yes—
174#2460C2214yes—
175#2455C2214yes—
176#2454C2214yescomplemented
177#2453C2212yescomplemented
178#2452C2211yescharacteristic, complemented
179#2450C2214yescomplemented
180#2445C2211yescharacteristic, complemented
181#2445C2214yescomplemented
182#2443C2214yes—
183#2442C2212yescomplemented
184#2442C2214yescomplemented
185#2439C2212yescomplemented
186#2432C2212yes—
187#2431C2212yes—
188#2431C2212yescomplemented
189#2429C2212yescomplemented
190#2428C2212yes—
191#2428C2211yescharacteristic
192#2427C2212yes—
193#2427C2214yes—
194#2427C2212yes—
195#2427C2212yescomplemented
196#2427C2212yescomplemented
197#2426C2212yescomplemented
198#2425C2214yes—
199#2425C2214yes—
200#2424C2214yes—
201#2423C2212yescomplemented
202#2423C2212yescomplemented
203#2422C2212yes—
204#2422C2211yescharacteristic
205#2421C2212yes—
206#2418C2214yes—
207#2418C2214yes—
208#2417C2212yes—
209#2417C2212yescomplemented
210#2417C2212yescomplemented
211#2417C2212yescomplemented
212#2417C2212yescomplemented
213#2417C2212yescomplemented
214#2417C2214yescomplemented
215#2416C2212yes—
216#2416C2214yes—
217#2416C2212yes—
218#2416C2212yescomplemented
219#2416C2212yescomplemented
220#2415C2212yes—
221#2415C2212yes—
222#2414C2212yes—
223#2413C2214yescomplemented
224#2412C2214yes—
225#2408C2212yes—
226#2407C2212yes—
227#2407C2212yes—
228#2407C2212yes—
229#2407C2212yescomplemented
230#2407C2212yescomplemented
231#2407C2212yescomplemented
232#2398C2212yescomplemented
233#2392C2212yes—
234#2380C2214yescomplemented
235#2377C2214yescomplemented
236#2366C2212yes—
237#2364C2214yescomplemented
238#2363C2212yescomplemented
239#2361C2212yes—
240#2360C2212yescomplemented
241#2360C2212yescomplemented
242#2356C2212yescomplemented
243#2355C2211yescharacteristic, complemented
244#2354C2211yescharacteristic
245#2354C2212yes—
246#2353C2214yescomplemented
247#2352C2212yescomplemented
248#2352C2212yescomplemented
249D4×C4⋊C4C2212yes—
250D4×C4⋊C4C2211yescharacteristic
251D4×C4⋊C4C2212yescomplemented
252D4×C4⋊C4C2211yescharacteristic, complemented
253#2346C2212yescomplemented
254#2341C2212yescomplemented
255#2339C2212yes—
256#2339C2212yescomplemented
257#2333C2214yescomplemented
258#2328C2211yescharacteristic
259#2328C2211yescharacteristic
260#2328C2214yescomplemented
261#2326C2211yescharacteristic
262#2326C2211yescharacteristic
263#2325C2214yescomplemented
264#2324C2212yes—
265#2324C2212yes—
266#2324C2212yes—
267#2323C2212yes—
268#2321C2212yes—
269#2321C2212yes—
270#2320C2212yescomplemented
271#2318C2214yescomplemented
272#2317C2211yescharacteristic
273#2311C2211yescharacteristic
274#2311C2212yescomplemented
275#2309C2211yescharacteristic
276C4×C4⋊Q8C2211yescharacteristic, complemented
277C4×C4⋊Q8C2211yescharacteristic, complemented
278C4×C4⋊Q8C2211yescharacteristic, complemented
279C4×#127C2211yescharacteristic
280C4×#127C2211yescharacteristic
281C4×#127C2211yescharacteristic, complemented
282C4×#124C2211yescharacteristic
283C4×#124C2211yescharacteristic
284C4×C22⋊Q8C2212yescomplemented
285C4×#121C2211yescharacteristic
286C4×#121C2212yes—
287C4×#121C2212yes—
288C4×#121C2211yescharacteristic
289C4×#121C2212yescomplemented
290C4×#120C2212yes—
291C4×#120C2212yes—
292#2297C2212yes—
293#2293C2211yescharacteristic, complemented
294C2×#389C2212yescomplemented
295#2290C2212yescomplemented
296C2×#380C2212yes—
297C42×D4C2211yescharacteristic, complemented
298C4×#117C2211yescharacteristic
299C22×#41C2311yescharacteristic
300C22×#41C2312yes—
301C22×#41C2312yes—
302C22×#41C2312yes—
303C23×D4C2311yescharacteristic
304C24×C4C2312yes—
305#556—44no—
306#554—48no—
307#553—48no—
308#550—216no—
309#547—44no—
310#547—44no—
311#547—44no—
312#547—48no—
313#546—48no—
314#535—28no—
315C2×C4⋊Q8C2311yescharacteristic
316C2×C4⋊Q8C2311yescharacteristic
317C2×C4⋊Q8C2311yescharacteristic
318C2×C4⋊Q8C2312yes—
319C2×#127C2311yescharacteristic
320C2×#127C2314yes—
321C2×#127C2311yescharacteristic
322C2×#127C2311yescharacteristic
323#529—48no—
324C2×#126C2312yes—
325C2×#126C2314yes—
326C2×#126C2312yes—
327C2×#126C2314yes—
328C2×#125C2312yes—
329C2×#125C2312yes—
330C2×#125C2314yes—
331C2×#124C2311yescharacteristic
332C2×#124C2311yescharacteristic
333C2×#124C2312yes—
334C2×#124C2312yes—
335C2×#124C2312yes—
336#525—48no—
337C2×#123C2314yes—
338C2×#123C2314yes—
339C2×#123C2314yes—
340C2×#123C2314yes—
341C2×#123C2314yes—
342C2×#123C2312yes—
343C2×#123C2312yes—
344C2×#123C2314yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2312yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2312yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2312yes—
357C2×C22⋊Q8C2312yes—
358C2×C22⋊Q8C2314yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2314yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2312yes—
364C2×#121C2314yes—
365C2×#121C2314yes—
366C2×#121C2312yes—
367C2×#121C2311yescharacteristic
368C2×#121C2311yescharacteristic
369C2×#121C2312yes—
370C2×#121C2312yes—
371C2×#121C2312yes—
372C2×#121C2312yes—
373C2×#121C2312yes—
374C2×#121C2312yes—
375C2×#121C2314yes—
376C2×#121C2312yes—
377C2×#121C2314yes—
378C2×#121C2312yes—
379C2×#121C2314yes—
380C2×#120C2312yes—
381C2×#120C2312yes—
382C2×#120C2314yes—
383C2×#120C2314yes—
384C4×#41—44no—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2311yescharacteristic
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2312yes—
389C2×C4×Q8C2311yescharacteristic
390C2×C4×Q8C2312yes—
391C2×C4×D4—44no—
392C2×C4×D4C2311yescharacteristic
393C2×C4×D4C2311yescharacteristic
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2311yescharacteristic
398C2×C4×D4C2314yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2311yescharacteristic
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2312yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2312yes—
408C2×C4×D4C2312yes—
409C2×C4×D4C2312yes—
410C2×C4×D4C2314yes—
411C2×C4×D4C2314yes—
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2311yescharacteristic
414C2×C4×D4C2311yescharacteristic
415C2×C4×D4C2314yes—
416C2×C4×D4C2312yes—
417C2×C4×D4C2314yes—
418C2×C4×D4C2312yes—
419C2×C4×D4C2312yes—
420C2×C4×D4C2311yescharacteristic
421C2×#117C2311yescharacteristic
422C2×#117C2311yescharacteristic
423C2×#117C2312yes—
424C2×#117C2311yescharacteristic
425C2×#117C2312yes—
426C2×#117C2312yes—
427C2×#117C2312yes—
428C22×C4⋊C4C2312yes—
429C22×C4⋊C4C2311yescharacteristic
430C22×C4⋊C4C2312yes—
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2312yes—
433C22×C4⋊C4C2312yes—
434C22×C4⋊C4C2314yes—
435C22×C22⋊C4C2312yes—
436C22×C22⋊C4C2314yes—
437C22×C42C2311yescharacteristic
438C22×C42C2312yes—
439C22×C42C2312yes—
440#401C2314yes—
441#400C2314yes—
442#400C2314yes—
443#400C2314yes—
444#400C2314yes—
445#400C2314yes—
446#400C2314yes—
447#400C2314yes—
448#400C2314yes—
449#400C2314yes—
450#400C2312yes—
451#400C2312yes—
452#399C2314yes—
453#399C2314yes—
454#399C2314yes—
455#399C2314yes—
456#398C2312yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2314yes—
465#398C2314yes—
466#398C2314yes—
467#398C2314yes—
468#397C2312yes—
469#397C2314yes—
470#397C2314yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2314yes—
475#397C2314yes—
476#397C2314yes—
477#397C2314yes—
478#397C2314yes—
479#397C2314yes—
480#397C2312yes—
481#397C2312yes—
482#397C2314yes—
483#397C2314yes—
484#397C2314yes—
485#396C2314yes—
486#396C2314yes—
487#396C2314yes—
488#396C2312yes—
489#396C2314yes—
490#396C2314yes—
491#396C2314yes—
492#396C2314yes—
493#396C2314yes—
494#396C2312yes—
495#396C2314yes—
496#396C2314yes—
497#396C2314yes—
498#396C2314yes—
499#396C2314yes—
500#396C2314yes—
501#394C2312yes—
502#394C2314yes—
503#394C2312yes—
504#394C2314yes—
505#394C2314yes—
506#394C2314yes—
507#394C2314yes—
508#394C2314yes—
509#394C2314yes—
510#394C2314yes—
511#394C2314yes—
512#394C2314yes—
513#394C2312yes—
514#394C2314yes—
515#394C2314yes—
516#394C2314yes—
517#394C2312yes—
518#394C2312yes—
519#394C2314yes—
520#394C2314yes—
521#394C2314yes—
522#394C2314yes—
523#393C2312yes—
524#393C2314yes—
525#393C2312yes—
526#392C2314yes—
527#392C2314yes—
528#392C2314yes—
529#392C2314yes—
530#392C2312yes—
531#392C2314yes—
532#392C2314yes—
533#392C2314yes—
534#392C2314yes—
535#392C2314yes—
536#391C2312yes—
537#391C2312yes—
538#391C2312yes—
539#391C2311yescharacteristic
540#391C2311yescharacteristic
541#391C2312yes—
542#391C2312yes—
543#391C2312yes—
544#391C2314yes—
545#391C2312yes—
546#391C2312yes—
547#391C2312yes—
548#391C2312yes—
549#391C2312yes—
550#391C2312yes—
551#390C2312yes—
552#390C2311yescharacteristic
553#390C2311yescharacteristic
554#390C2311yescharacteristic
555#390C2311yescharacteristic
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2312yes—
560#390C2311yescharacteristic
561#390C2311yescharacteristic
562#390C2312yes—
563#390C2311yescharacteristic
564#390C2312yes—
565#390C2312yes—
566#390C2311yescharacteristic
567#390C2312yes—
568#390C2314yes—
569#390C2314yes—
570#390C2314yes—
571#390C2312yes—
572#390C2311yescharacteristic
573#390C2312yes—
574#390C2314yes—
575#390C2314yes—
576#390C2311yescharacteristic
577#390C2314yes—
578#390C2314yes—
579#390C2312yes—
580#390C2311yescharacteristic
581#390C2311yescharacteristic
582#390C2314yes—
583#389C2311yescharacteristic
584#389C2312yes—
585#389C2312yes—
586#389C2311yescharacteristic
587#389C2312yes—
588#389C2312yes—
589#389C2312yes—
590#389C2312yes—
591#389C2312yes—
592#389C2312yes—
593#389C2312yes—
594#389C2314yes—
595#389C2312yes—
596#389C2314yes—
597#389C2312yes—
598#389C2312yes—
599#389C2312yes—
600#389C2312yes—
601#389C2312yes—
602#389C2314yes—
603#389C2314yes—
604#389C2312yes—
605#389C2312yes—
606#389C2312yes—
607#389C2314yes—
608#389C2312yes—
609#389C2314yes—
610#389C2314yes—
611#389C2311yescharacteristic
612#389C2311yescharacteristic
613#389C2311yescharacteristic
614#389C2312yes—
615#389C2314yes—
616#389C2311yescharacteristic
617#388C2312yes—
618#388C2312yes—
619#388C2312yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2312yes—
624#388C2312yes—
625#388C2312yes—
626#388C2312yes—
627#388C2312yes—
628#388C2312yes—
629#388C2312yes—
630#388C2312yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2312yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2314yes—
647#388C2314yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#387C2312yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2314yes—
661#387C2314yes—
662#387C2312yes—
663#387C2314yes—
664#387C2314yes—
665#386C2312yes—
666#386C2312yes—
667#386C2312yes—
668#386C2314yes—
669#386C2314yes—
670#386C2312yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2314yes—
676#386C2312yes—
677#386C2312yes—
678#386C2312yes—
679#386C2312yes—
680#386C2312yes—
681#386C2312yes—
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#386C2312yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2312yes—
702#386C2314yes—
703#386C2314yes—
704#386C2312yes—
705#385C2312yes—
706#385C2314yes—
707#385C2312yes—
708#385C2312yes—
709#385C2314yes—
710#385C2312yes—
711#385C2312yes—
712#385C2312yes—
713#385C2312yes—
714#385C2314yes—
715#385C2314yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2314yes—
722#385C2314yes—
723#385C2314yes—
724#385C2312yes—
725#385C2314yes—
726#385C2314yes—
727#384C2311yescharacteristic
728#384C2311yescharacteristic
729#384C2311yescharacteristic
730#384C2311yescharacteristic
731#384C2311yescharacteristic
732#384C2311yescharacteristic
733#384C2312yes—
734#384C2312yes—
735#383C2314yes—
736#383C2314yes—
737#383C2314yes—
738#382C2314yes—
739#382C2311yescharacteristic
740#382C2311yescharacteristic
741#382C2314yes—
742#382C2312yes—
743#382C2312yes—
744#382C2312yes—
745#382C2312yes—
746#381C2314yes—
747#381C2314yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2312yes—
752#380C2312yes—
753#380C2312yes—
754#380C2314yes—
755#380C2314yes—
756#380C2312yes—
757#380C2312yes—
758#380C2312yes—
759#380C2312yes—
760#380C2312yes—
761#380C2311yescharacteristic
762#380C2312yes—
763#380C2312yes—
764#380C2314yes—
765#380C2312yes—
766#380C2312yes—
767#380C2312yes—
768#380C2314yes—
769#380C2314yes—
770#380C2312yes—
771#380C2314yes—
772#380C2314yes—
773#380C2312yes—
774#380C2314yes—
775#380C2314yes—
776#380C2314yes—
777#380C2311yescharacteristic
778#379C2312yes—
779#379C2312yes—
780#379C2314yes—
781C4×C4⋊C4C2311yescharacteristic
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2311yescharacteristic
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2312yes—
790C4×C4⋊C4C2312yes—
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2312yes—
793C4×C4⋊C4C2314yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2311yescharacteristic
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2314yes—
800C4×C22⋊C4C2311yescharacteristic
801C4×C22⋊C4C2311yescharacteristic
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2314yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2312yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2314yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2312yes—
811C4×C22⋊C4C2312yes—
812C4×C22⋊C4C2312yes—
813C4×C22⋊C4C2312yes—
814C4×C22⋊C4C2311yescharacteristic
815C4×C22⋊C4C2311yescharacteristic
816C4×C22⋊C4C2312yes—
817#376C2311yescharacteristic
818#376C2311yescharacteristic
819#376C2314yes—
820C2×#95C2314yes—
821C2×#95C2314yes—
822C43C2311yescharacteristic
823C43C2311yescharacteristic
824C25C2412yes—
825C2×#41—24no—
826C2×#41—28no—
827C2×#41—28no—
828C2×#41—24no—
829C2×#41—42no—
830C2×#41—44no—
831C2×#41—44no—
832C2×#41—44no—
833C2×#41—44no—
834C2×#41—44no—
835C2×#41—44no—
836C2×#41—44no—
837C22×Q8C2412yes—
838C22×Q8C2411yescharacteristic
839C22×Q8C2412yes—
840C22×Q8C2412yes—
841C22×D4—24no—
842C22×D4—24no—
843C22×D4—42no—
844C22×D4C2411yescharacteristic
845C22×D4C2411yescharacteristic
846C22×D4C2411yescharacteristic
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2412yes—
850C22×D4C2411yescharacteristic
851C22×D4C2411yescharacteristic
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2414yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2414yes—
860C22×D4C2412yes—
861C22×D4C2414yes—
862C22×D4C2414yes—
863C22×D4C2412yes—
864C22×D4C2412yes—
865C23×C4—44no—
866C23×C4—44no—
867C23×C4—44no—
868C23×C4C2412yes—
869C23×C4C2412yes—
870C23×C4C2412yes—
871C23×C4C2412yes—
872C23×C4C2412yes—
873C23×C4C2411yescharacteristic
874C23×C4C2412yes—
875C23×C4C2411yescharacteristic
876C23×C4C2411yescharacteristic
877C23×C4C2414yes—
878C23×C4C2414yes—
879C23×C4C2414yes—
880C23×C4C2412yes—
881C23×C4C2414yes—
882C23×C4C2412yes—
883C23×C4C2414yes—
884C23×C4C2412yes—
885C23×C4C2412yes—
886C23×C4C2412yes—
887C23×C4C2412yes—
888C4⋊Q8—24no—
889C4⋊Q8—24no—
890C4⋊Q8—24no—
891C4⋊Q8—44no—
892#127—24no—
893#127—216no—
894#127—42no—
895#127#4118yescomplemented
896#126—48no—
897#126—44no—
898#126—44no—
899#126—48no—
900#125—44no—
901#125—44no—
902#125—48no—
903#124—24no—
904#124—24no—
905#124—44no—
906#124—44no—
907#124—44no—
908#123—48no—
909#123—44no—
910#123—48no—
911#123—48no—
912#123—48no—
913#123—44no—
914#123—48no—
915#123—48no—
916#123—48no—
917#123—48no—
918C22⋊Q8—28no—
919C22⋊Q8—28no—
920C22⋊Q8—44no—
921C22⋊Q8—48no—
922C22⋊Q8—44no—
923C22⋊Q8—44no—
924C22⋊Q8—44no—
925C22⋊Q8—44no—
926C22⋊Q8—44no—
927C22⋊Q8—44no—
928C22⋊Q8—44no—
929C22⋊Q8—44no—
930C22⋊Q8—48no—
931C22⋊Q8—44no—
932#121—28no—
933#121—28no—
934#121—28no—
935#121—28no—
936#121—216no—
937#121—216no—
938#121—24no—
939#121—48no—
940#121—48no—
941#121—44no—
942#121—48no—
943#121—42no—
944#121—44no—
945#121—44no—
946#121—44no—
947#121—44no—
948#121—44no—
949#121—44no—
950#121—44no—
951#120—28no—
952#120—28no—
953#120—48no—
954#120—48no—
955C4×Q8—28no—
956C4×Q8—24no—
957C4×Q8—44no—
958C4×Q8—42no—
959C4×Q8—44no—
960C4×Q8—44no—
961C4×D4—216no—
962C4×D4—28no—
963C4×D4—28no—
964C4×D4—24no—
965C4×D4—28no—
966C4×D4—24no—
967C4×D4—24no—
968C4×D4—24no—
969C4×D4—24no—
970C4×D4—24no—
971C4×D4—44no—
972C4×D4—48no—
973C4×D4—42no—
974C4×D4—42no—
975C4×D4—42no—
976C4×D4—42no—
977C4×D4—48no—
978C4×D4—44no—
979C4×D4—44no—
980C4×D4—44no—
981C4×D4—44no—
982C4×D4—44no—
983C4×D4—44no—
984C4×D4—44no—
985C4×D4—48no—
986C4×D4—44no—
987C4×D4—44no—
988C4×D4—44no—
989C4×D4—48no—
990#117—24no—
991#117—28no—
992#117—24no—
993#117—44no—
994#117—44no—
995#117—42no—
996#117—44no—
997C2×C4⋊C4—28no—
998C2×C4⋊C4—42no—
999C2×C4⋊C4—44no—
1000C2×C4⋊C4—44no—
1001C2×C4⋊C4—44no—
1002C2×C4⋊C4—48no—
1003C2×C4⋊C4—44no—
1004C2×C4⋊C4C2411yescharacteristic
1005C2×C4⋊C4C2411yescharacteristic
1006C2×C4⋊C4C2411yescharacteristic
1007C2×C4⋊C4C2412yes—
1008C2×C4⋊C4C2412yes—
1009C2×C4⋊C4C2412yes—
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2412yes—
1012C2×C4⋊C4C2411yescharacteristic
1013C2×C4⋊C4C2414yes—
1014C2×C4⋊C4C2414yes—
1015C2×C4⋊C4C2411yescharacteristic
1016C2×C4⋊C4C2411yescharacteristic
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2411yescharacteristic
1020C2×C4⋊C4C2411yescharacteristic
1021C2×C4⋊C4C2411yescharacteristic
1022C2×C4⋊C4C2411yescharacteristic
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2414yes—
1027C2×C4⋊C4C2411yescharacteristic
1028C2×C4⋊C4C2412yes—
1029C2×C4⋊C4C2412yes—
1030C2×C4⋊C4C2414yes—
1031C2×C4⋊C4C2411yescharacteristic
1032C2×C4⋊C4C2412yes—
1033C2×C4⋊C4C2412yes—
1034C2×C4⋊C4C2412yes—
1035C2×C4⋊C4C2414yes—
1036C2×C4⋊C4C2414yes—
1037C2×C4⋊C4C2414yes—
1038C2×C4⋊C4C2414yes—
1039C2×C4⋊C4C2414yes—
1040C2×C4⋊C4C2414yes—
1041C2×C4⋊C4C2412yes—
1042C2×C4⋊C4C2412yes—
1043C2×C4⋊C4C2412yes—
1044C2×C4⋊C4C2414yes—
1045C2×C4⋊C4C2414yes—
1046C2×C4⋊C4C2412yes—
1047C2×C4⋊C4C2412yes—
1048C2×C4⋊C4C2412yes—
1049C2×C4⋊C4C2412yes—
1050C2×C4⋊C4C2412yes—
1051C2×C4⋊C4C2412yes—
1052C2×C4⋊C4C2414yes—
1053C2×C4⋊C4C2414yes—
1054C2×C4⋊C4C2412yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2414yes—
1058C2×C4⋊C4C2414yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2411yescharacteristic
1065C2×C22⋊C4—44no—
1066C2×C22⋊C4—48no—
1067C2×C22⋊C4C2412yes—
1068C2×C22⋊C4C2412yes—
1069C2×C22⋊C4C2412yes—
1070C2×C22⋊C4C2414yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2411yescharacteristic
1073C2×C22⋊C4C2411yescharacteristic
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2411yescharacteristic
1076C2×C22⋊C4C2411yescharacteristic
1077C2×C22⋊C4C2414yes—
1078C2×C22⋊C4C2412yes—
1079C2×C22⋊C4C2412yes—
1080C2×C22⋊C4C2412yes—
1081C2×C22⋊C4C2414yes—
1082C2×C22⋊C4C2412yes—
1083C2×C22⋊C4C2414yes—
1084C2×C22⋊C4C2412yes—
1085C2×C22⋊C4C2412yes—
1086C2×C22⋊C4C2412yes—
1087C2×C22⋊C4C2412yes—
1088C2×C22⋊C4C2412yes—
1089C2×C22⋊C4C2412yes—
1090C2×C22⋊C4C2412yes—
1091C2×C22⋊C4C2412yes—
1092C2×C22⋊C4C2412yes—
1093C2×C22⋊C4C2412yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2414yes—
1096C2×C22⋊C4C2414yes—
1097C2×C22⋊C4C2412yes—
1098C2×C22⋊C4C2412yes—
1099C2×C22⋊C4C2412yes—
1100C2×C22⋊C4C2412yes—
1101C2×C22⋊C4C2414yes—
1102C2×C22⋊C4C2412yes—
1103C2×C22⋊C4C2414yes—
1104C2×C22⋊C4C2414yes—
1105C2×C22⋊C4C2414yes—
1106C2×C22⋊C4C2414yes—
1107C2×C22⋊C4C2412yes—
1108C2×C22⋊C4C2414yes—
1109C2×C22⋊C4C2412yes—
1110C2×C22⋊C4C2412yes—
1111C2×C22⋊C4C2412yes—
1112C2×C22⋊C4C2414yes—
1113C2×C22⋊C4C2412yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2412yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2414yes—
1121C2×C22⋊C4C2414yes—
1122C2×C22⋊C4C2414yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2412yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2412yes—
1130C2×C22⋊C4C2412yes—
1131C2×C22⋊C4C2412yes—
1132C2×C22⋊C4C2412yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2412yes—
1135C2×C22⋊C4C2412yes—
1136C2×C22⋊C4C2412yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2414yes—
1139C2×C42—24no—
1140C2×C42—44no—
1141C2×C42—44no—
1142C2×C42C2411yescharacteristic
1143C2×C42C2411yescharacteristic
1144C2×C42C2414yes—
1145C2×C42C2411yescharacteristic
1146C2×C42C2412yes—
1147C2×C42C2411yescharacteristic
1148C2×C42C2411yescharacteristic
1149C2×C42C2411yescharacteristic
1150C2×C42C2411yescharacteristic
1151C2×C42C2411yescharacteristic
1152C2×C42C2412yes—
1153C2×C42C2411yescharacteristic
1154C2×C42C2411yescharacteristic
1155C2×C42C2412yes—
1156C2×C42C2414yes—
1157C2×C42C2412yes—
1158C2×C42C2414yes—
1159C2×C42C2414yes—
1160C2×C42C2412yes—
1161C2×C42C2412yes—
1162C2×C42C2412yes—
1163C2×C42C2411yescharacteristic
1164C2×C42C2411yescharacteristic
1165C2×C42C2411yescharacteristic
1166C2×C42C2411yescharacteristic
1167C2×C42C2414yes—
1168C2×C42C2411yescharacteristic
1169C2×C42C2411yescharacteristic
1170#95C2412yes—
1171#95C2412yes—
1172#95C2414yes—
1173#95C2414yes—
1174#95C2414yes—
1175#95C2414yes—
1176#95C2414yes—
1177#95C2414yes—
1178#95C2412yes—
1179#95C2412yes—
1180#95C2411yescharacteristic
1181#95C2411yescharacteristic
1182#95C2411yescharacteristic
1183#95C2411yescharacteristic
1184#95C2411yescharacteristic
1185#95C2411yescharacteristic
1186#95C2411yescharacteristic
1187#95C2411yescharacteristic
1188#95C2414yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2412yes—
1197#95C2414yes—
1198#95C2414yes—
1199#95C2412yes—
1200#95C2412yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2412yes—
1207#95C2412yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2414yes—
1213#95C2414yes—
1214#95C2414yes—
1215#95C2414yes—
1216#95C2412yes—
1217#95C2412yes—
1218#95C2414yes—
1219#95C2414yes—
1220#95C2414yes—
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2414yes—
1225#95C2414yes—
1226C24—24no—
1227C24—24no—
1228C24—42no—
1229C24—42no—
1230C24—42no—
1231C24—42no—
1232C24—42no—
1233C24C2512yes—
1234C24C2512yes—
1235C24C2512yes—
1236C24C2512yes—
1237C24C2512yes—
1238C24C2511yescharacteristic
1239#41—416no—
1240#41—816no—
1241#41—816no—
1242#41—816no—
1243C2×Q8—24no—
1244C2×Q8—22no—
1245C2×Q8—22no—
1246C2×Q8—24no—
1247C2×Q8—24no—
1248C2×Q8—24no—
1249C2×Q8—24no—
1250C2×Q8—22no—
1251C2×Q8—24no—
1252C2×Q8—24no—
1253C2×Q8—42no—
1254C2×Q8—42no—
1255C2×D4—24no—
1256C2×D4—24no—
1257C2×D4—24no—
1258C2×D4—24no—
1259C2×D4—24no—
1260C2×D4—24no—
1261C2×D4—28no—
1262C2×D4—28no—
1263C2×D4—28no—
1264C2×D4—28no—
1265C2×D4—24no—
1266C2×D4—22no—
1267C2×D4—24no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—22no—
1276C2×D4—24no—
1277C2×D4—22no—
1278C2×D4—24no—
1279C2×D4—22no—
1280C2×D4—22no—
1281C2×D4—22no—
1282C2×D4—416no—
1283C2×D4—42no—
1284C2×D4—42no—
1285C2×D4—42no—
1286C2×D4—42no—
1287C2×D4—42no—
1288C2×D4—42no—
1289C2×D4—42no—
1290C2×D4—44no—
1291C2×D4—42no—
1292C2×D4—44no—
1293C2×D4—42no—
1294C2×D4—42no—
1295C2×D4—44no—
1296C2×D4—44no—
1297C2×D4—44no—
1298C2×D4—44no—
1299C2×D4—44no—
1300C2×D4—44no—
1301C2×D4—42no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—42no—
1305C2×D4—42no—
1306C2×D4—42no—
1307C2×D4—42no—
1308C2×D4—42no—
1309C2×D4—44no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—44no—
1313C2×D4—44no—
1314C2×D4—44no—
1315C2×D4C2×#4114yes—
1316C2×D4C2×#4114yes—
1317C2×D4C2×#4118yes—
1318C2×D4C2×#4118yes—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—24no—
1322C22×C4—28no—
1323C22×C4—28no—
1324C22×C4—24no—
1325C22×C4—24no—
1326C22×C4—22no—
1327C22×C4—24no—
1328C22×C4—24no—
1329C22×C4—24no—
1330C22×C4—24no—
1331C22×C4—24no—
1332C22×C4—24no—
1333C22×C4—24no—
1334C22×C4—24no—
1335C22×C4—24no—
1336C22×C4—24no—
1337C22×C4—24no—
1338C22×C4—22no—
1339C22×C4—24no—
1340C22×C4—24no—
1341C22×C4—24no—
1342C22×C4—22no—
1343C22×C4—22no—
1344C22×C4—28no—
1345C22×C4—24no—
1346C22×C4—42no—
1347C22×C4—42no—
1348C22×C4—42no—
1349C22×C4—42no—
1350C22×C4—42no—
1351C22×C4—44no—
1352C22×C4—44no—
1353C22×C4—44no—
1354C22×C4—44no—
1355C22×C4—44no—
1356C22×C4—44no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—42no—
1361C22×C4—44no—
1362C22×C4—42no—
1363C22×C4—42no—
1364C22×C4—42no—
1365C22×C4—42no—
1366C22×C4—42no—
1367C22×C4—41no—
1368C22×C4—41no—
1369C22×C4—42no—
1370C22×C4—44no—
1371C22×C4—42no—
1372C22×C4—42no—
1373C22×C4—42no—
1374C22×C4—44no—
1375C22×C4—44no—
1376C22×C4—44no—
1377C22×C4—44no—
1378C22×C4—816no—
1379C22×C4H(5,𝔽2)14yes—
1380C22×C4C2511yescharacteristic
1381C22×C4C2511yescharacteristic
1382C22×C4C2512yes—
1383C22×C4C2511yescharacteristic
1384C22×C4C2511yescharacteristic
1385C22×C4C2514yes—
1386C22×C4C2511yescharacteristic
1387C22×C4C2512yes—
1388C22×C4C2511yescharacteristic
1389C22×C4C2514yes—
1390C22×C4C2512yes—
1391C22×C4C2512yes—
1392C22×C4C2512yes—
1393C22×C4C2514yes—
1394C22×C4C2511yescharacteristic
1395C22×C4C2512yes—
1396C22×C4C2511yescharacteristic
1397C22×C4C2512yes—
1398C22×C4C2514yes—
1399C22×C4C2512yes—
1400C22×C4C2512yes—
1401C22×C4C2512yes—
1402C22×C4C2511yescharacteristic
1403C22×C4C2511yescharacteristic
1404C22×C4C2512yes—
1405C22×C4C2511yescharacteristic
1406C22×C4C2511yescharacteristic
1407C22×C4C2511yescharacteristic
1408C22×C4C2511yescharacteristic
1409C4⋊C4—22no—
1410C4⋊C4—22no—
1411C4⋊C4—24no—
1412C4⋊C4—24no—
1413C4⋊C4—28no—
1414C4⋊C4—24no—
1415C4⋊C4—28no—
1416C4⋊C4—22no—
1417C4⋊C4—22no—
1418C4⋊C4—22no—
1419C4⋊C4—24no—
1420C4⋊C4—24no—
1421C4⋊C4—22no—
1422C4⋊C4—24no—
1423C4⋊C4—22no—
1424C4⋊C4—28no—
1425C4⋊C4—24no—
1426C4⋊C4—22no—
1427C4⋊C4—22no—
1428C4⋊C4—22no—
1429C4⋊C4—22no—
1430C4⋊C4—24no—
1431C4⋊C4—24no—
1432C4⋊C4—24no—
1433C4⋊C4—24no—
1434C4⋊C4—28no—
1435C4⋊C4—24no—
1436C4⋊C4—24no—
1437C4⋊C4—22no—
1438C4⋊C4—22no—
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—42no—
1448C4⋊C4—42no—
1449C4⋊C4—42no—
1450C4⋊C4—42no—
1451C4⋊C4—42no—
1452C4⋊C4—42no—
1453C4⋊C4—42no—
1454C4⋊C4—44no—
1455C4⋊C4—44no—
1456C4⋊C4—42no—
1457C4⋊C4—42no—
1458C4⋊C4—42no—
1459C4⋊C4—42no—
1460C4⋊C4—44no—
1461C4⋊C4—44no—
1462C4⋊C4—42no—
1463C4⋊C4—42no—
1464C4⋊C4—44no—
1465C4⋊C4—44no—
1466C4⋊C4—44no—
1467C4⋊C4—44no—
1468C4⋊C4—44no—
1469C4⋊C4H(5,𝔽2)14yes—
1470C22⋊C4—28no—
1471C22⋊C4—28no—
1472C22⋊C4—24no—
1473C22⋊C4—24no—
1474C22⋊C4—24no—
1475C22⋊C4—28no—
1476C22⋊C4—22no—
1477C22⋊C4—22no—
1478C22⋊C4—24no—
1479C22⋊C4—22no—
1480C22⋊C4—22no—
1481C22⋊C4—24no—
1482C22⋊C4—24no—
1483C22⋊C4—24no—
1484C22⋊C4—24no—
1485C22⋊C4—24no—
1486C22⋊C4—24no—
1487C22⋊C4—28no—
1488C22⋊C4—24no—
1489C22⋊C4—24no—
1490C22⋊C4—24no—
1491C22⋊C4—24no—
1492C22⋊C4—24no—
1493C22⋊C4—24no—
1494C22⋊C4—28no—
1495C22⋊C4—24no—
1496C22⋊C4—42no—
1497C22⋊C4—42no—
1498C22⋊C4—44no—
1499C22⋊C4—44no—
1500C22⋊C4—42no—
1501C22⋊C4—42no—
1502C22⋊C4—42no—
1503C22⋊C4—42no—
1504C22⋊C4—42no—
1505C22⋊C4—42no—
1506C22⋊C4—44no—
1507C22⋊C4—44no—
1508C22⋊C4—42no—
1509C22⋊C4—42no—
1510C22⋊C4—42no—
1511C22⋊C4—42no—
1512C22⋊C4—42no—
1513C22⋊C4—42no—
1514C22⋊C4—44no—
1515C22⋊C4—42no—
1516C22⋊C4—42no—
1517C22⋊C4—42no—
1518C22⋊C4—42no—
1519C22⋊C4—42no—
1520C22⋊C4—42no—
1521C22⋊C4—44no—
1522C22⋊C4—44no—
1523C22⋊C4—44no—
1524C22⋊C4—44no—
1525C22⋊C4—42no—
1526C22⋊C4—42no—
1527C22⋊C4—44no—
1528C22⋊C4—42no—
1529C22⋊C4—44no—
1530C22⋊C4—42no—
1531C22⋊C4—42no—
1532C22⋊C4—44no—
1533C22⋊C4—42no—
1534C22⋊C4—44no—
1535C22⋊C4—44no—
1536C22⋊C4—44no—
1537C22⋊C4—44no—
1538C22⋊C4—44no—
1539C22⋊C4—44no—
1540C22⋊C4—44no—
1541C22⋊C4—44no—
1542C42—22no—
1543C42—28no—
1544C42—22no—
1545C42—22no—
1546C42—22no—
1547C42—22no—
1548C42—24no—
1549C42—24no—
1550C42—28no—
1551C42—22no—
1552C42—24no—
1553C42—22no—
1554C42—22no—
1555C42—22no—
1556C42—22no—
1557C42—42no—
1558C42—42no—
1559C42—42no—
1560C42—42no—
1561C42—41no—
1562C42—41no—
1563C42—41no—
1564C42—41no—
1565C42—44no—
1566C42—44no—
1567C42—44no—
1568C42C2×#4114yes—
1569C42H(5,𝔽2)14yes—
1570C23—21no—
1571C23—22no—
1572C23—22no—
1573C23—22no—
1574C23—22no—
1575C23—21no—
1576C23—21no—
1577C23—22no—
1578C23—22no—
1579C23—22no—
1580C23—22no—
1581C23—21no—
1582C23—22no—
1583C23—22no—
1584C23—22no—
1585C23—22no—
1586C23—21no—
1587C23—21no—
1588C23—22no—
1589C23—22no—
1590C23—22no—
1591C23—22no—
1592C23—22no—
1593C23—22no—
1594C23—22no—
1595C23—22no—
1596C23—22no—
1597C23—22no—
1598C23—22no—
1599C23—22no—
1600C23—22no—
1601C23—22no—
1602C23—22no—
1603C23—22no—
1604C23—22no—
1605C23—22no—
1606C23—22no—
1607C23—22no—
1608C23—22no—
1609C23—48no—
1610C23—48no—
1611C23—84no—
1612C23—84no—
1613C23—84no—
1614C23—84no—
1615C23—84no—
1616C23C22×#4114yes—
1617C23C22×#4114yes—
1618C23C2×H(5,𝔽2)12yes—
1619C23C2611yescharacteristic
1620Q8—44no—
1621Q8—48no—
1622Q8—48no—
1623Q8—84no—
1624D4—28no—
1625D4—28no—
1626D4—48no—
1627D4—48no—
1628D4—48no—
1629D4—48no—
1630D4—48no—
1631D4—44no—
1632D4—44no—
1633D4—44no—
1634D4—84no—
1635D4—88no—
1636D4—84no—
1637D4—88no—
1638D4—84no—
1639D4—84no—
1640D4—88no—
1641D4—88no—
1642D4—84no—
1643D4—88no—
1644D4—164no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—22no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—21no—
1653C2×C4—21no—
1654C2×C4—22no—
1655C2×C4—28no—
1656C2×C4—21no—
1657C2×C4—21no—
1658C2×C4—24no—
1659C2×C4—24no—
1660C2×C4—22no—
1661C2×C4—22no—
1662C2×C4—22no—
1663C2×C4—21no—
1664C2×C4—22no—
1665C2×C4—21no—
1666C2×C4—22no—
1667C2×C4—21no—
1668C2×C4—21no—
1669C2×C4—22no—
1670C2×C4—22no—
1671C2×C4—22no—
1672C2×C4—21no—
1673C2×C4—21no—
1674C2×C4—24no—
1675C2×C4—21no—
1676C2×C4—22no—
1677C2×C4—21no—
1678C2×C4—21no—
1679C2×C4—22no—
1680C2×C4—22no—
1681C2×C4—22no—
1682C2×C4—24no—
1683C2×C4—24no—
1684C2×C4—24no—
1685C2×C4—21no—
1686C2×C4—24no—
1687C2×C4—22no—
1688C2×C4—22no—
1689C2×C4—24no—
1690C2×C4—22no—
1691C2×C4—22no—
1692C2×C4—22no—
1693C2×C4—22no—
1694C2×C4—22no—
1695C2×C4—24no—
1696C2×C4—22no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—22no—
1701C2×C4—22no—
1702C2×C4—22no—
1703C2×C4—24no—
1704C2×C4—21no—
1705C2×C4—22no—
1706C2×C4—22no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—21no—
1710C2×C4—21no—
1711C2×C4—21no—
1712C2×C4—21no—
1713C2×C4—21no—
1714C2×C4—21no—
1715C2×C4—24no—
1716C2×C4—22no—
1717C2×C4—22no—
1718C2×C4—21no—
1719C2×C4—21no—
1720C2×C4—22no—
1721C2×C4—24no—
1722C2×C4—48no—
1723C2×C4—48no—
1724C2×C4—48no—
1725C2×C4—48no—
1726C2×C4—48no—
1727C2×C4—44no—
1728C2×C4—48no—
1729C2×C4—82no—
1730C2×C4—84no—
1731C2×C4—88no—
1732C2×C4—88no—
1733C2×C4—88no—
1734C2×C4—84no—
1735C2×C4—84no—
1736C2×C4—84no—
1737C2×C4—84no—
1738C2×C4—84no—
1739C2×C4—88no—
1740C2×C4—164no—
1741C2×C4C22×#4112yes—
1742C2×C4C22×#4112yes—
1743C2×C4C22×#4112yes—
1744C2×C4C2×H(5,𝔽2)14yes—
1745C2×C4C2×H(5,𝔽2)12yes—
1746C2×C4C2×H(5,𝔽2)12yes—
1747C2×C4C2×H(5,𝔽2)12yes—
1748C2×C4C2×H(5,𝔽2)12yes—
1749C2×C4C2×H(5,𝔽2)12yes—
1750C2×C4C2×H(5,𝔽2)12yes—
1751C2×C4#58512yes—
1752C22—24no—
1753C22—24no—
1754C22—24no—
1755C22—24no—
1756C22—22no—
1757C22—24no—
1758C22—24no—
1759C22—22no—
1760C22—22no—
1761C22—41no—
1762C22—41no—
1763C22—41no—
1764C22—42no—
1765C22—42no—
1766C22—42no—
1767C22—41no—
1768C22—42no—
1769C22—42no—
1770C22—42no—
1771C22—42no—
1772C22—42no—
1773C22—42no—
1774C22—42no—
1775C22—42no—
1776C22—42no—
1777C22—42no—
1778C22—42no—
1779C22—42no—
1780C22—42no—
1781C22—42no—
1782C22—42no—
1783C22—42no—
1784C22—42no—
1785C22—42no—
1786C22—42no—
1787C22—42no—
1788C22—42no—
1789C22—42no—
1790C22—42no—
1791C22—42no—
1792C22—42no—
1793C22—42no—
1794C22—816no—
1795C22C23×#4111yescharacteristic
1796C22C22×H(5,𝔽2)11yescharacteristic
1797C22C22×H(5,𝔽2)11yescharacteristic
1798C22C22×H(5,𝔽2)11yescharacteristic
1799C22C2×#58511yescharacteristic
1800C222−1+611yescharacteristic
1801C222−1+611yescharacteristic
1802C4—22no—
1803C4—22no—
1804C4—22no—
1805C4—22no—
1806C4—24no—
1807C4—41no—
1808C4—44no—
1809C4—41no—
1810C4—42no—
1811C4—42no—
1812C4—42no—
1813C4—41no—
1814C4—44no—
1815C4—42no—
1816C4—42no—
1817C4—42no—
1818C4—44no—
1819C4—42no—
1820C4—41no—
1821C4—41no—
1822C4—44no—
1823C4—42no—
1824C4—41no—
1825C4—42no—
1826C4—41no—
1827C4—42no—
1828C4—41no—
1829C4#351914yes—
1830C4#354614yes—
1831C2—44no—
1832C2—44no—
1833C2—42no—
1834C2—82no—
1835C2—82no—
1836C2—82no—
1837C2C2×#354611yescharacteristic
1838C2C2×#351911yescharacteristic
1839C2#6288811yescharacteristic
1840C2#6291411yescharacteristic
1841C2#6292511yescharacteristic
1842C2#6298411yescharacteristic
1843C2#6299111yescharacteristic
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. #59441C2semidirect
4. #59427C2semidirect
5. #59410C2semidirect
6. #59024C2semidirect
7. #50044C2semidirect
8. #49198C2semidirect
9. #46810C2semidirect
10. #46509C2semidirect
11. #45623C2semidirect
12. #45593C2semidirect
13. #44972C2semidirect
14. #44892C2semidirect
15. #42732C2semidirect
16. #42552C2semidirect
17. #40221C2semidirect
18. #39862C2semidirect
19. #39193C2semidirect
20. #39165C2semidirect
21. #38951C2semidirect
22. #38928C2semidirect
23. #38908C2semidirect
24. #38034C2semidirect
25. #37341C2semidirect
26. #36504C2semidirect
27. #36468C2semidirect
28. #36406C2semidirect
29. #36259C2semidirect
30. #36153C2semidirect
31. #36100C2semidirect
32. #35291C2semidirect
33. #34914C2semidirect
34. #34477C2semidirect
35. C4×#535C2semidirect
36. C2×#556C22semidirect
37. C2×#554C22semidirect
38. C2×#553C22semidirect
43. C2×#547C22semidirect
50. #2862C22semidirect
51. #2859C22semidirect
54. #2857C22semidirect
56. #2854C22semidirect
57. #2850C22semidirect
60. #2827C22semidirect
61. #2825C22semidirect
62. #2800C22semidirect
63. #2783C22semidirect
64. #2780C22semidirect
65. #2779C22semidirect
66. #2778C22semidirect
67. #2777C22semidirect
69. #2768C22semidirect
70. #2765C22semidirect
72. #2757C22semidirect
73. #2757C22semidirect
74. #2756C22semidirect
75. #2750C22semidirect
76. #2750C22semidirect
77. #2749C22semidirect
78. #2732C22semidirect
79. #2725C22semidirect
80. #2707C22semidirect
81. #2707C22semidirect
82. #2706C22semidirect
83. #2706C22semidirect
84. #2706C22semidirect
85. #2705C22semidirect
87. #2703C22semidirect
88. #2702C22semidirect
90. #2696C22semidirect
92. #2695C22semidirect
94. #2693C22semidirect
96. #2682C22semidirect
102. #2648C22semidirect
103. #2646C22semidirect
104. #2645C22semidirect
105. #2639C22semidirect
106. #2636C22semidirect
108. #2625C22semidirect
110. #2606C22semidirect
112. #2602C22semidirect
114. #2587C22semidirect
115. #2568C22semidirect
116. #2562C22semidirect
117. #2560C22semidirect
119. #2559C22semidirect
121. #2558C22semidirect
124. #2554C22semidirect
125. #2553C22semidirect
126. #2553C22semidirect
127. #2552C22semidirect
129. #2546C22semidirect
132. #2542C22semidirect
133. #2541C22semidirect
137. #2538C22semidirect
138. #2538C22semidirect
139. #2538C22semidirect
140. #2538C22semidirect
143. #2537C22semidirect
146. #2535C22semidirect
147. #2532C22semidirect
148. #2514C22semidirect
149. #2512C22semidirect
150. #2510C22semidirect
151. #2509C22semidirect
152. #2508C22semidirect
153. #2506C22semidirect
154. #2504C22semidirect
155. #2502C22semidirect
156. #2499C22semidirect
157. #2497C22semidirect
159. #2496C22semidirect
161. #2495C22semidirect
162. #2495C22semidirect
163. #2495C22semidirect
166. #2490C22semidirect
171. #2479C22semidirect
176. #2454C22semidirect
177. #2453C22semidirect
178. #2452C22semidirect
179. #2450C22semidirect
180. #2445C22semidirect
181. #2445C22semidirect
183. #2442C22semidirect
184. #2442C22semidirect
185. #2439C22semidirect
188. #2431C22semidirect
189. #2429C22semidirect
195. #2427C22semidirect
196. #2427C22semidirect
197. #2426C22semidirect
201. #2423C22semidirect
202. #2423C22semidirect
209. #2417C22semidirect
210. #2417C22semidirect
211. #2417C22semidirect
212. #2417C22semidirect
213. #2417C22semidirect
214. #2417C22semidirect
218. #2416C22semidirect
219. #2416C22semidirect
223. #2413C22semidirect
229. #2407C22semidirect
230. #2407C22semidirect
231. #2407C22semidirect
232. #2398C22semidirect
234. #2380C22semidirect
235. #2377C22semidirect
237. #2364C22semidirect
238. #2363C22semidirect
240. #2360C22semidirect
241. #2360C22semidirect
242. #2356C22semidirect
243. #2355C22semidirect
246. #2353C22semidirect
247. #2352C22semidirect
248. #2352C22semidirect
251. D4×C4⋊C4C22semidirect
252. D4×C4⋊C4C22semidirect
253. #2346C22semidirect
254. #2341C22semidirect
256. #2339C22semidirect
257. #2333C22semidirect
260. #2328C22semidirect
263. #2325C22semidirect
270. #2320C22semidirect
271. #2318C22semidirect
274. #2311C22semidirect
276. C4×C4⋊Q8C22semidirect
277. C4×C4⋊Q8C22semidirect
278. C4×C4⋊Q8C22semidirect
281. C4×#127C22semidirect
284. C4×C22⋊Q8C22semidirect
289. C4×#121C22semidirect
293. #2293C22semidirect
294. C2×#389C22semidirect
295. #2290C22semidirect
297. C42×D4C22semidirect
895. #127#41semidirect

Maximal subgroups

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

subgroupindex
#598232
#598152
#594412
#594272
#594102
#590242
#500442
#491982
#468102
#465092
#456232
#455932
#449722
#448922
#427322
#425522
#402212
#398622
#391932
#391652
#389512
#389282
#389082
#380342
#373412
#365042
#364682
#364062
#362592
#361532
#361002
#352912
#349142
#344772
C4×#5352