Finite Group Databasebeta

← #7880571

Subgroups — #7880571

Order 512.

5357 conjugacy classes of subgroups.

The subgroup lattice has 1753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59679C211yesmaximal, characteristic, complemented
2#59646C211yesmaximal, characteristic, complemented
3#59480C212yesmaximal, complemented
4#59427C211yesmaximal, characteristic, complemented
5#59147C212yesmaximal, complemented
6#51471C214yesmaximal, complemented
7#49759C214yesmaximal, complemented
8#46791C214yesmaximal, complemented
9#45146C212yesmaximal, complemented
10#45097C212yesmaximal, complemented
11#45031C212yesmaximal, complemented
12#44959C212yesmaximal, complemented
13#43477C214yesmaximal, complemented
14#42976C212yesmaximal, complemented
15#42607C212yesmaximal, complemented
16#40033C212yesmaximal, complemented
17#39823C212yesmaximal, complemented
18#39789C212yesmaximal, complemented
19#39363C211yesmaximal, characteristic, complemented
20#39361C211yesmaximal, characteristic
21#39202C211yesmaximal, characteristic, complemented
22#38987C211yesmaximal, characteristic, complemented
23#38250C212yesmaximal, complemented
24#36595C211yesmaximal, characteristic, complemented
25#36595C211yesmaximal, characteristic, complemented
26D4×#124C211yesmaximal, characteristic, complemented
27#36041C212yesmaximal, complemented
28#35897C212yesmaximal, complemented
29#35677C212yesmaximal, complemented
30#35560C212yesmaximal, complemented
31#34902C211yesmaximal, characteristic, complemented
32#34893C211yesmaximal, characteristic, complemented
33#34493C211yesmaximal, characteristic, complemented
34#34330C211yesmaximal, characteristic, complemented
35#34311C211yesmaximal, characteristic, complemented
36C2×#559C2212yescomplemented
37C2×#559C2212yescomplemented
38C2×#550C2211yescharacteristic
39C2×D4×Q8C2211yescharacteristic
40C2×D42C2211yescharacteristic
41C2×#536C2212yescomplemented
42C2×#535C2212yes—
43C22×#124C2212yes—
44C2×#519C2212yescomplemented
45#2867C2211yescharacteristic
46#2858C2211yescharacteristic
47#2858C2211yescharacteristic, complemented
48#2858C2212yescomplemented
49#2850C2212yes—
50#2829C2214yescomplemented
51#2803C2214yescomplemented
52#2800C2214yescomplemented
53#2800C2214yescomplemented
54#2797C2214yescomplemented
55#2797C2214yescomplemented
56#2786C2214yescomplemented
57#2783C2214yescomplemented
58#2778C2214yescomplemented
59#2757C2214yescomplemented
60#2753C2214yescomplemented
61#2752C2214yescomplemented
62#2749C2214yescomplemented
63#2749C2214yescomplemented
64#2740C2214yescomplemented
65#2730C2214yescomplemented
66#2712C2214yescomplemented
67#2710C2214yescomplemented
68#2706C2214yescomplemented
69#2701C2214yescomplemented
70#2700C2214yescomplemented
71#2697C2214yescomplemented
72#2697C2214yescomplemented
73#2693C2214yescomplemented
74#2687C2214yescomplemented
75#2686C2214yescomplemented
76#2685C2214yescomplemented
77#2685C2214yescomplemented
78#2684C2214yescomplemented
79#2684C2214yescomplemented
80#2681C2214yescomplemented
81#2681C2214yescomplemented
82#2669C2214yes—
83#2669C2214yes—
84#2662C2214yescomplemented
85#2649C2214yescomplemented
86#2648C2214yescomplemented
87#2644C2212yescomplemented
88#2632C2214yescomplemented
89#2624C2212yescomplemented
90#2620C2212yescomplemented
91#2619C2212yes—
92#2610C2214yescomplemented
93#2603C2214yescomplemented
94#2602C2214yescomplemented
95#2600C2214yescomplemented
96#2598C2214yescomplemented
97#2597C2214yescomplemented
98#2596C2212yescomplemented
99#2594C2212yescomplemented
100#2592C2212yes—
101#2592C2211yescharacteristic
102#2589C2212yescomplemented
103#2587C2212yescomplemented
104#2584C2211yescharacteristic, complemented
105#2581C2211yescharacteristic, complemented
106#2580C2211yescharacteristic
107#2576C2214yescomplemented
108#2570C2211yescharacteristic, complemented
109#2568C2212yescomplemented
110#2566C2211yescharacteristic
111#2566C2212yescomplemented
112#2557C2214yescomplemented
113#2557C2214yescomplemented
114#2554C2214yescomplemented
115#2550C2211yescharacteristic, complemented
116#2548C2211yescharacteristic
117#2548C2212yes—
118#2548C2211yescharacteristic
119#2548C2212yes—
120#2548C2212yescomplemented
121#2548C2212yescomplemented
122#2548C2212yescomplemented
123#2548C2212yescomplemented
124#2548C2212yescomplemented
125#2548C2211yescharacteristic, complemented
126#2547C2211yescharacteristic
127#2547C2212yescomplemented
128#2546C2211yescharacteristic, complemented
129#2545C2212yes—
130#2545C2211yescharacteristic
131#2545C2212yescomplemented
132#2545C2212yescomplemented
133#2544C2212yes—
134#2544C2212yescomplemented
135#2544C2212yescomplemented
136#2544C2214yescomplemented
137#2541C2211yescharacteristic
138#2534C2214yescomplemented
139#2532C2214yescomplemented
140#2526C2214yescomplemented
141#2525C2212yescomplemented
142#2522C2212yescomplemented
143#2514C2211yescharacteristic, complemented
144#2513C2212yescomplemented
145#2513C2212yescomplemented
146#2513C2212yescomplemented
147#2512C2211yescharacteristic
148#2512C2212yescomplemented
149#2512C2212yescomplemented
150#2509C2211yescharacteristic, complemented
151#2507C2211yescharacteristic, complemented
152#2500C2212yescomplemented
153#2497C2212yescomplemented
154#2495C2212yescomplemented
155#2491C2212yes—
156#2491C2212yes—
157#2490C2212yescomplemented
158#2490C2212yescomplemented
159#2488C2214yescomplemented
160#2472C2214yes—
161#2472C2214yes—
162#2472C2214yescomplemented
163#2471C2214yescomplemented
164#2471C2214yescomplemented
165#2469C2212yescomplemented
166#2466C2214yescomplemented
167#2466C2214yescomplemented
168#2465C2212yescomplemented
169#2459C2214yescomplemented
170#2458C2214yescomplemented
171#2458C2214yescomplemented
172#2457C2214yescomplemented
173#2454C2211yescharacteristic
174#2454C2212yescomplemented
175#2452C2211yescharacteristic
176#2452C2212yescomplemented
177#2452C2212yescomplemented
178#2450C2214yescomplemented
179#2448C2211yescharacteristic
180#2448C2212yescomplemented
181#2448C2212yescomplemented
182#2447C2212yescomplemented
183#2447C2212yescomplemented
184#2447C2212yescomplemented
185#2446C2211yescharacteristic, complemented
186#2445C2212yes—
187#2445C2212yes—
188#2445C2212yes—
189#2445C2212yescomplemented
190#2445C2214yescomplemented
191#2445C2212yescomplemented
192#2445C2212yescomplemented
193#2445C2212yescomplemented
194#2445C2212yescomplemented
195#2445C2212yescomplemented
196#2444C2214yescomplemented
197#2439C2212yescomplemented
198#2436C2212yes—
199#2436C2212yescomplemented
200#2435C2212yes—
201#2433C2212yes—
202#2433C2212yes—
203#2433C2212yes—
204#2432C2212yescomplemented
205#2431C2212yes—
206#2428C2212yes—
207#2428C2212yes—
208#2426C2214yescomplemented
209#2426C2214yescomplemented
210#2426C2214yescomplemented
211#2426C2214yescomplemented
212#2425C2214yescomplemented
213#2422C2212yescomplemented
214#2420C2212yescomplemented
215#2418C2214yescomplemented
216#2418C2214yescomplemented
217#2412C2214yescomplemented
218#2411C2214yescomplemented
219#2411C2214yescomplemented
220#2411C2214yescomplemented
221#2411C2214yescomplemented
222#2401C2212yescomplemented
223#2398C2214yescomplemented
224#2396C2212yescomplemented
225#2396C2212yescomplemented
226#2396C2212yescomplemented
227#2375C2214yes—
228#2367C2212yescomplemented
229#2367C2212yescomplemented
230#2366C2212yes—
231#2366C2211yescharacteristic
232#2366C2211yescharacteristic, complemented
233#2366C2212yescomplemented
234#2366C2212yescomplemented
235#2366C2212yescomplemented
236#2365C2211yescharacteristic, complemented
237#2365C2212yescomplemented
238#2364C2214yescomplemented
239#2363C2212yes—
240#2363C2212yes—
241#2363C2212yescomplemented
242#2363C2212yescomplemented
243#2362C2214yescomplemented
244#2362C2212yescomplemented
245#2358C2214yescomplemented
246#2357C2212yescomplemented
247#2357C2212yescomplemented
248#2356C2212yescomplemented
249#2355C2211yescharacteristic, complemented
250#2354C2211yescharacteristic
251#2354C2212yes—
252#2354C2211yescharacteristic
253Q8×C4⋊C4C2211yescharacteristic, complemented
254#2346C2212yescomplemented
255Q8×C22⋊C4C2212yescomplemented
256#2339C2212yescomplemented
257D4×C22⋊C4C2212yes—
258D4×C22⋊C4C2212yes—
259D4×C22⋊C4C2212yes—
260D4×C22⋊C4C2212yes—
261#2337C2214yescomplemented
262#2333C2214yescomplemented
263#2328C2212yes—
264#2324C2212yes—
265#2324C2212yes—
266#2324C2212yescomplemented
267#2323C2214yescomplemented
268#2323C2212yescomplemented
269#2321C2214yes—
270#2319C2212yescomplemented
271#2309C2212yes—
272#2309C2212yes—
273C4×C4⋊Q8C2211yescharacteristic, complemented
274C4×C4⋊Q8C2212yescomplemented
275C4×C4⋊Q8C2211yescharacteristic, complemented
276C4×C4⋊Q8C2211yescharacteristic, complemented
277C4×#127C2211yescharacteristic
278C4×#127C2211yescharacteristic, complemented
279C4×#127C2212yescomplemented
280C4×#125C2211yescharacteristic, complemented
281C4×#125C2211yescharacteristic, complemented
282C4×#126C2212yescomplemented
283C4×#124C2211yescharacteristic
284C4×#124C2211yescharacteristic
285C4×C22⋊Q8C2212yescomplemented
286C4×#121C2212yescomplemented
287#2298C2212yescomplemented
288#2297C2212yescomplemented
289#2296C2212yescomplemented
290#2295C2211yescharacteristic, complemented
291#2293C2211yescharacteristic
292#2293C2212yes—
293#2293C2211yescharacteristic
294#2293C2211yescharacteristic
295#2275C2212yescomplemented
296C42×Q8C2211yescharacteristic, complemented
297C42×Q8C2211yescharacteristic, complemented
298C42×D4C2211yescharacteristic
299C22×#41C2312yes—
300C23×Q8C2312yes—
301C23×D4C2312yes—
302C23×D4C2312yes—
303#559—48no—
304#559—48no—
305#550—28no—
306D4×Q8—28no—
307D42—28no—
308#536—48no—
309#535—48no—
310C2×C4⋊Q8C2311yescharacteristic
311C2×C4⋊Q8C2312yes—
312C2×C4⋊Q8C2311yescharacteristic
313C2×C4⋊Q8C2311yescharacteristic
314C2×C4⋊Q8C2312yes—
315C2×#127C2311yescharacteristic
316C2×#127C2311yescharacteristic
317C2×#127C2312yes—
318C2×#127C2312yes—
319C2×#127C2312yes—
320C2×#127C2312yes—
321C2×#127C2312yes—
322C2×#127C2312yes—
323C2×#127C2312yes—
324C2×#127C2312yes—
325C2×#126C2312yes—
326C2×#126C2314yes—
327C2×#125C2311yescharacteristic
328C2×#125C2311yescharacteristic
329C2×#124—48no—
330C2×#124C2311yescharacteristic
331C2×#124C2312yes—
332C2×#124C2312yes—
333C2×#124C2311yescharacteristic
334C2×#124C2312yes—
335C2×#124C2314yes—
336C2×#124C2312yes—
337C2×#124C2312yes—
338C2×#124C2312yes—
339C2×#124C2312yes—
340C2×#124C2314yes—
341C2×#124C2314yes—
342C2×#124C2314yes—
343C2×#124C2314yes—
344C2×#124C2312yes—
345C2×#123C2314yes—
346C2×#123C2314yes—
347C2×#123C2314yes—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×#123C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2314yes—
354C2×C22⋊Q8C2314yes—
355C2×C22⋊Q8C2314yes—
356C2×C22⋊Q8C2312yes—
357C2×#121C2312yes—
358C2×#121C2312yes—
359C2×#121C2314yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2312yes—
363C2×#121C2314yes—
364C2×#121C2314yes—
365C2×#120C2314yes—
366C2×#120C2314yes—
367C2×#120C2314yes—
368C2×#120C2314yes—
369C2×#120C2314yes—
370#519—48no—
371C2×C4×Q8C2312yes—
372C2×C4×Q8C2311yescharacteristic
373C2×C4×Q8C2311yescharacteristic
374C2×C4×Q8C2311yescharacteristic
375C2×C4×Q8C2311yescharacteristic
376C2×C4×Q8C2311yescharacteristic
377C2×C4×Q8C2312yes—
378C2×C4×Q8C2314yes—
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2312yes—
381C2×C4×Q8C2314yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×C4×D4C2312yes—
387C2×C4×D4C2312yes—
388C2×C4×D4C2312yes—
389C2×C4×D4C2312yes—
390C2×C4×D4C2312yes—
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2314yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2312yes—
396C2×C4×D4C2311yescharacteristic
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2314yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2314yes—
403C2×C4×D4C2311yescharacteristic
404C2×#117C2312yes—
405C2×#117C2312yes—
406C2×#117C2312yes—
407C2×#117C2312yes—
408C2×#117C2312yes—
409C2×#117C2314yes—
410C2×#117C2314yes—
411C22×C22⋊C4C2314yes—
412C22×C22⋊C4C2314yes—
413C22×C22⋊C4C2314yes—
414C22×C42C2312yes—
415#401C2312yes—
416#400C2314yes—
417#400C2314yes—
418#400C2312yes—
419#400C2312yes—
420#400C2312yes—
421#400C2312yes—
422#400C2312yes—
423#400C2312yes—
424#399C2314yes—
425#399C2312yes—
426#399C2312yes—
427#399C2312yes—
428#399C2314yes—
429#398C2312yes—
430#398C2312yes—
431#398C2312yes—
432#398C2312yes—
433#398C2312yes—
434#398C2312yes—
435#398C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2312yes—
440#397C2312yes—
441#397C2312yes—
442#397C2314yes—
443#397C2314yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#397C2314yes—
448#397C2314yes—
449#397C2314yes—
450#397C2314yes—
451#397C2314yes—
452#397C2314yes—
453#397C2314yes—
454#396C2312yes—
455#396C2312yes—
456#396C2314yes—
457#396C2314yes—
458#396C2312yes—
459#396C2314yes—
460#396C2314yes—
461#396C2312yes—
462#396C2312yes—
463#396C2314yes—
464#396C2314yes—
465#396C2312yes—
466#396C2312yes—
467#396C2314yes—
468#396C2314yes—
469#396C2314yes—
470#395C2312yes—
471#395C2312yes—
472#395C2312yes—
473#394C2314yes—
474#394C2314yes—
475#394C2314yes—
476#394C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
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#394C2314yes—
500#394C2314yes—
501#394C2314yes—
502#393C2312yes—
503#393C2312yes—
504#393C2312yes—
505#393C2314yes—
506#393C2314yes—
507#393C2314yes—
508#393C2314yes—
509#393C2314yes—
510#392C2314yes—
511#392C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2314yes—
515#392C2314yes—
516#392C2314yes—
517#391C2312yes—
518#391C2311yescharacteristic
519#391C2312yes—
520#391C2311yescharacteristic
521#391C2314yes—
522#391C2311yescharacteristic
523#391C2314yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#391C2312yes—
528#391C2311yescharacteristic
529#391C2312yes—
530#391C2311yescharacteristic
531#391C2312yes—
532#391C2311yescharacteristic
533#390C2312yes—
534#390C2312yes—
535#390C2312yes—
536#390C2312yes—
537#390C2312yes—
538#390C2314yes—
539#390C2312yes—
540#390C2314yes—
541#390C2312yes—
542#390C2312yes—
543#390C2311yescharacteristic
544#390C2311yescharacteristic
545#390C2314yes—
546#390C2314yes—
547#390C2312yes—
548#390C2312yes—
549#390C2312yes—
550#390C2314yes—
551#390C2312yes—
552#390C2314yes—
553#390C2311yescharacteristic
554#390C2311yescharacteristic
555#390C2312yes—
556#390C2312yes—
557#390C2312yes—
558#390C2312yes—
559#390C2314yes—
560#390C2311yescharacteristic
561#390C2312yes—
562#390C2314yes—
563#390C2311yescharacteristic
564#390C2311yescharacteristic
565#390C2311yescharacteristic
566#390C2312yes—
567#390C2312yes—
568#390C2314yes—
569#390C2312yes—
570#390C2312yes—
571#390C2312yes—
572#390C2312yes—
573#390C2312yes—
574#390C2314yes—
575#390C2314yes—
576#390C2312yes—
577#390C2314yes—
578#390C2312yes—
579#390C2312yes—
580#390C2314yes—
581#390C2312yes—
582#390C2312yes—
583#390C2312yes—
584#390C2314yes—
585#390C2314yes—
586#389C2311yescharacteristic
587#389C2311yescharacteristic
588#389C2311yescharacteristic
589#389C2311yescharacteristic
590#389C2311yescharacteristic
591#389C2312yes—
592#389C2314yes—
593#389C2312yes—
594#389C2311yescharacteristic
595#389C2311yescharacteristic
596#389C2312yes—
597#389C2312yes—
598#389C2312yes—
599#389C2311yescharacteristic
600#389C2311yescharacteristic
601#389C2312yes—
602#389C2314yes—
603#389C2312yes—
604#389C2311yescharacteristic
605#389C2311yescharacteristic
606#389C2311yescharacteristic
607#389C2312yes—
608#389C2312yes—
609#389C2311yescharacteristic
610#389C2312yes—
611#389C2312yes—
612#389C2311yescharacteristic
613#389C2312yes—
614#389C2312yes—
615#389C2312yes—
616#388C2312yes—
617#388C2312yes—
618#388C2312yes—
619#388C2314yes—
620#388C2314yes—
621#388C2314yes—
622#388C2314yes—
623#388C2314yes—
624#388C2312yes—
625#388C2312yes—
626#388C2314yes—
627#388C2314yes—
628#388C2312yes—
629#388C2314yes—
630#388C2314yes—
631#388C2314yes—
632#388C2314yes—
633#388C2314yes—
634#388C2314yes—
635#388C2312yes—
636#388C2312yes—
637#388C2312yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2314yes—
642#388C2314yes—
643#388C2314yes—
644#388C2312yes—
645#388C2312yes—
646#388C2312yes—
647#388C2312yes—
648#388C2312yes—
649#388C2314yes—
650#388C2314yes—
651#388C2314yes—
652#388C2314yes—
653#388C2314yes—
654#388C2314yes—
655#388C2314yes—
656#388C2314yes—
657#388C2314yes—
658#388C2314yes—
659#388C2314yes—
660#388C2314yes—
661#388C2312yes—
662#388C2312yes—
663#388C2312yes—
664#387C2312yes—
665#387C2312yes—
666#387C2312yes—
667#387C2312yes—
668#387C2312yes—
669#387C2312yes—
670#387C2312yes—
671#387C2312yes—
672#387C2314yes—
673#387C2312yes—
674#387C2314yes—
675#387C2314yes—
676#387C2312yes—
677#387C2312yes—
678#387C2314yes—
679#387C2312yes—
680#387C2312yes—
681#387C2312yes—
682#387C2314yes—
683#387C2314yes—
684#387C2312yes—
685#386C2314yes—
686#386C2314yes—
687#386C2314yes—
688#386C2314yes—
689#386C2314yes—
690#386C2314yes—
691#386C2314yes—
692#386C2314yes—
693#386C2314yes—
694#386C2314yes—
695#386C2314yes—
696#386C2314yes—
697#386C2314yes—
698#386C2314yes—
699#386C2314yes—
700#386C2314yes—
701#386C2314yes—
702#386C2314yes—
703#386C2314yes—
704#386C2314yes—
705#386C2314yes—
706#386C2314yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#385C2312yes—
715#385C2312yes—
716#385C2314yes—
717#385C2314yes—
718#385C2314yes—
719#385C2314yes—
720#385C2314yes—
721#385C2312yes—
722#385C2312yes—
723#385C2314yes—
724#385C2314yes—
725#385C2314yes—
726#385C2312yes—
727#385C2312yes—
728#384C2311yescharacteristic
729#384C2311yescharacteristic
730#384C2312yes—
731#384C2311yescharacteristic
732#383C2312yes—
733#383C2314yes—
734#382C2311yescharacteristic
735#382C2311yescharacteristic
736#382C2312yes—
737#382C2314yes—
738#382C2311yescharacteristic
739#382C2311yescharacteristic
740#381C2314yes—
741#381C2314yes—
742#381C2314yes—
743#381C2314yes—
744#380C2314yes—
745#380C2312yes—
746#380C2314yes—
747#380C2312yes—
748#380C2312yes—
749#380C2312yes—
750#380C2312yes—
751#380C2314yes—
752#379C2314yes—
753#379C2314yes—
754#379C2314yes—
755#379C2314yes—
756#379C2314yes—
757C4×C4⋊C4C2311yescharacteristic
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2311yescharacteristic
761C4×C4⋊C4C2311yescharacteristic
762C4×C4⋊C4C2311yescharacteristic
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2312yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2314yes—
770C4×C4⋊C4C2312yes—
771C4×C4⋊C4C2312yes—
772C4×C4⋊C4C2312yes—
773C4×C4⋊C4C2312yes—
774C4×C4⋊C4C2312yes—
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2311yescharacteristic
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2311yescharacteristic
780C4×C4⋊C4C2311yescharacteristic
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2311yescharacteristic
783C4×C4⋊C4C2312yes—
784C4×C4⋊C4C2312yes—
785C4×C4⋊C4C2311yescharacteristic
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2312yes—
788C4×C4⋊C4C2311yescharacteristic
789C4×C4⋊C4C2311yescharacteristic
790C4×C4⋊C4C2311yescharacteristic
791C4×C4⋊C4C2311yescharacteristic
792C4×C4⋊C4C2311yescharacteristic
793C4×C4⋊C4C2311yescharacteristic
794C4×C22⋊C4C2312yes—
795C4×C22⋊C4C2312yes—
796C4×C22⋊C4C2312yes—
797C4×C22⋊C4C2314yes—
798C4×C22⋊C4C2314yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2312yes—
801C4×C22⋊C4C2314yes—
802C4×C22⋊C4C2314yes—
803C4×C22⋊C4C2312yes—
804C4×C22⋊C4C2312yes—
805C4×C22⋊C4C2312yes—
806C4×C22⋊C4C2314yes—
807C4×C22⋊C4C2312yes—
808C4×C22⋊C4C2312yes—
809C4×C22⋊C4C2314yes—
810C4×C22⋊C4C2314yes—
811C4×C22⋊C4C2314yes—
812#376C2312yes—
813#376C2314yes—
814C2×#95C2314yes—
815C43C2312yes—
816C43C2311yescharacteristic
817C43C2311yescharacteristic
818C43C2311yescharacteristic
819C25C2414yes—
820C2×#41—28no—
821C2×#41—44no—
822C2×#41—44no—
823C22×Q8—28no—
824C22×Q8—28no—
825C22×Q8—44no—
826C22×Q8C2412yes—
827C22×Q8C2411yescharacteristic
828C22×Q8C2414yes—
829C22×Q8C2411yescharacteristic
830C22×Q8C2411yescharacteristic
831C22×Q8C2412yes—
832C22×D4—28no—
833C22×D4—28no—
834C22×D4—44no—
835C22×D4—44no—
836C22×D4—44no—
837C22×D4—44no—
838C22×D4C2412yes—
839C22×D4C2412yes—
840C22×D4C2412yes—
841C22×D4C2412yes—
842C22×D4C2411yescharacteristic
843C22×D4C2411yescharacteristic
844C22×D4C2414yes—
845C22×D4C2412yes—
846C22×D4C2414yes—
847C22×D4C2414yes—
848C22×D4C2414yes—
849C22×D4C2412yes—
850C22×D4C2414yes—
851C22×D4C2414yes—
852C22×D4C2414yes—
853C22×D4C2414yes—
854C22×D4C2414yes—
855C22×D4C2414yes—
856C23×C4C2412yes—
857C23×C4C2414yes—
858C23×C4C2412yes—
859C23×C4C2414yes—
860C23×C4C2412yes—
861C23×C4C2412yes—
862C23×C4C2414yes—
863C23×C4C2414yes—
864C23×C4C2414yes—
865C23×C4C2414yes—
866C4⋊Q8—24no—
867C4⋊Q8—28no—
868C4⋊Q8—24no—
869C4⋊Q8—42no—
870C4⋊Q8—44no—
871#127—28no—
872#127—24no—
873#127—24no—
874#127—28no—
875#127—44no—
876#127—44no—
877#127—44no—
878#127—44no—
879#127—44no—
880#127—82no—
881#126—44no—
882#126—84no—
883#125—42no—
884#125—42no—
885#124—24no—
886#124—28no—
887#124—28no—
888#124—24no—
889#124—48no—
890#124—44no—
891#124—44no—
892#124—48no—
893#124—44no—
894#124—44no—
895#124—48no—
896#124—44no—
897#124—44no—
898#124—48no—
899#124—48no—
900#123—48no—
901#123—48no—
902#123—48no—
903#123—48no—
904#123—48no—
905#123—48no—
906#123—84no—
907C22⋊Q8—28no—
908C22⋊Q8—216no—
909C22⋊Q8—44no—
910C22⋊Q8—48no—
911C22⋊Q8—48no—
912#121—28no—
913#121—28no—
914#121—28no—
915#121—216no—
916#121—48no—
917#121—48no—
918#121—44no—
919#121—44no—
920#120—216no—
921#120—48no—
922#120—48no—
923#120—48no—
924#120—84no—
925C4×Q8—24no—
926C4×Q8—24no—
927C4×Q8—24no—
928C4×Q8—24no—
929C4×Q8—28no—
930C4×Q8—24no—
931C4×Q8—42no—
932C4×Q8—44no—
933C4×Q8—42no—
934C4×Q8—48no—
935C4×Q8—48no—
936C4×Q8—44no—
937C4×Q8—44no—
938C4×D4—28no—
939C4×D4—28no—
940C4×D4—24no—
941C4×D4—48no—
942C4×D4—44no—
943C4×D4—44no—
944C4×D4—44no—
945C4×D4—42no—
946C4×D4—44no—
947C4×D4—42no—
948C4×D4—44no—
949C4×D4—48no—
950C4×D4—44no—
951C4×D4—44no—
952C4×D4—44no—
953C4×D4—82no—
954C4×D4—84no—
955C4×D4—82no—
956C4×D4—84no—
957C4×D4#4118yes—
958#117—28no—
959#117—44no—
960#117—44no—
961#117—48no—
962#117—48no—
963#117—44no—
964#117—44no—
965C2×C4⋊C4C2411yescharacteristic
966C2×C4⋊C4C2412yes—
967C2×C4⋊C4C2411yescharacteristic
968C2×C4⋊C4C2412yes—
969C2×C4⋊C4C2412yes—
970C2×C4⋊C4C2412yes—
971C2×C4⋊C4C2412yes—
972C2×C4⋊C4C2414yes—
973C2×C4⋊C4C2411yescharacteristic
974C2×C4⋊C4C2411yescharacteristic
975C2×C4⋊C4C2411yescharacteristic
976C2×C4⋊C4C2411yescharacteristic
977C2×C4⋊C4C2411yescharacteristic
978C2×C4⋊C4C2411yescharacteristic
979C2×C4⋊C4C2412yes—
980C2×C4⋊C4C2411yescharacteristic
981C2×C4⋊C4C2412yes—
982C2×C4⋊C4C2411yescharacteristic
983C2×C4⋊C4C2411yescharacteristic
984C2×C4⋊C4C2412yes—
985C2×C4⋊C4C2412yes—
986C2×C4⋊C4C2411yescharacteristic
987C2×C4⋊C4C2411yescharacteristic
988C2×C4⋊C4C2411yescharacteristic
989C2×C4⋊C4C2411yescharacteristic
990C2×C4⋊C4C2411yescharacteristic
991C2×C4⋊C4C2412yes—
992C2×C4⋊C4C2412yes—
993C2×C4⋊C4C2414yes—
994C2×C4⋊C4C2412yes—
995C2×C4⋊C4C2414yes—
996C2×C4⋊C4C2414yes—
997C2×C4⋊C4C2412yes—
998C2×C4⋊C4C2412yes—
999C2×C4⋊C4C2412yes—
1000C2×C4⋊C4C2412yes—
1001C2×C4⋊C4C2412yes—
1002C2×C4⋊C4C2412yes—
1003C2×C4⋊C4C2412yes—
1004C2×C4⋊C4C2412yes—
1005C2×C4⋊C4C2412yes—
1006C2×C4⋊C4C2412yes—
1007C2×C4⋊C4C2411yescharacteristic
1008C2×C4⋊C4C2411yescharacteristic
1009C2×C4⋊C4C2411yescharacteristic
1010C2×C4⋊C4C2411yescharacteristic
1011C2×C4⋊C4C2414yes—
1012C2×C4⋊C4C2414yes—
1013C2×C4⋊C4C2412yes—
1014C2×C4⋊C4C2412yes—
1015C2×C4⋊C4C2412yes—
1016C2×C4⋊C4C2414yes—
1017C2×C4⋊C4C2412yes—
1018C2×C4⋊C4C2412yes—
1019C2×C4⋊C4C2412yes—
1020C2×C4⋊C4C2412yes—
1021C2×C4⋊C4C2412yes—
1022C2×C4⋊C4C2412yes—
1023C2×C4⋊C4C2412yes—
1024C2×C4⋊C4C2412yes—
1025C2×C4⋊C4C2412yes—
1026C2×C4⋊C4C2411yescharacteristic
1027C2×C22⋊C4—48no—
1028C2×C22⋊C4—48no—
1029C2×C22⋊C4—84no—
1030C2×C22⋊C4C2412yes—
1031C2×C22⋊C4C2412yes—
1032C2×C22⋊C4C2414yes—
1033C2×C22⋊C4C2414yes—
1034C2×C22⋊C4C2412yes—
1035C2×C22⋊C4C2412yes—
1036C2×C22⋊C4C2412yes—
1037C2×C22⋊C4C2414yes—
1038C2×C22⋊C4C2414yes—
1039C2×C22⋊C4C2414yes—
1040C2×C22⋊C4C2412yes—
1041C2×C22⋊C4C2412yes—
1042C2×C22⋊C4C2412yes—
1043C2×C22⋊C4C2412yes—
1044C2×C22⋊C4C2414yes—
1045C2×C22⋊C4C2414yes—
1046C2×C22⋊C4C2412yes—
1047C2×C22⋊C4C2412yes—
1048C2×C22⋊C4C2414yes—
1049C2×C22⋊C4C2414yes—
1050C2×C22⋊C4C2414yes—
1051C2×C22⋊C4C2414yes—
1052C2×C22⋊C4C2414yes—
1053C2×C22⋊C4C2414yes—
1054C2×C22⋊C4C2414yes—
1055C2×C22⋊C4C2412yes—
1056C2×C22⋊C4C2412yes—
1057C2×C22⋊C4C2412yes—
1058C2×C22⋊C4C2414yes—
1059C2×C22⋊C4C2412yes—
1060C2×C22⋊C4C2414yes—
1061C2×C22⋊C4C2414yes—
1062C2×C22⋊C4C2414yes—
1063C2×C22⋊C4C2414yes—
1064C2×C22⋊C4C2414yes—
1065C2×C22⋊C4C2414yes—
1066C2×C22⋊C4C2414yes—
1067C2×C22⋊C4C2414yes—
1068C2×C22⋊C4C2414yes—
1069C2×C22⋊C4C2414yes—
1070C2×C22⋊C4C2412yes—
1071C2×C22⋊C4C2412yes—
1072C2×C22⋊C4C2414yes—
1073C2×C22⋊C4C2414yes—
1074C2×C22⋊C4C2414yes—
1075C2×C22⋊C4C2414yes—
1076C2×C22⋊C4C2412yes—
1077C2×C22⋊C4C2412yes—
1078C2×C22⋊C4C2414yes—
1079C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
1089C2×C22⋊C4C2414yes—
1090C2×C22⋊C4C2414yes—
1091C2×C22⋊C4C2414yes—
1092C2×C22⋊C4C2414yes—
1093C2×C22⋊C4C2414yes—
1094C2×C22⋊C4C2412yes—
1095C2×C22⋊C4C2412yes—
1096C2×C22⋊C4C2412yes—
1097C2×C42—44no—
1098C2×C42C2412yes—
1099C2×C42C2411yescharacteristic
1100C2×C42C2411yescharacteristic
1101C2×C42C2412yes—
1102C2×C42C2414yes—
1103C2×C42C2412yes—
1104C2×C42C2412yes—
1105C2×C42C2411yescharacteristic
1106C2×C42C2411yescharacteristic
1107C2×C42C2411yescharacteristic
1108C2×C42C2412yes—
1109C2×C42C2411yescharacteristic
1110C2×C42C2412yes—
1111C2×C42C2411yescharacteristic
1112C2×C42C2412yes—
1113C2×C42C2412yes—
1114C2×C42C2411yescharacteristic
1115C2×C42C2411yescharacteristic
1116C2×C42C2411yescharacteristic
1117C2×C42C2411yescharacteristic
1118C2×C42C2412yes—
1119C2×C42C2411yescharacteristic
1120C2×C42C2414yes—
1121C2×C42C2414yes—
1122C2×C42C2414yes—
1123C2×C42C2414yes—
1124C2×C42C2411yescharacteristic
1125C2×C42C2412yes—
1126C2×C42C2411yescharacteristic
1127C2×C42C2414yes—
1128C2×C42C2411yescharacteristic
1129C2×C42C2411yescharacteristic
1130C2×C42C2412yes—
1131C2×C42C2412yes—
1132C2×C42C2411yescharacteristic
1133C2×C42C2411yescharacteristic
1134C2×C42C2411yescharacteristic
1135#95C2412yes—
1136#95C2412yes—
1137#95C2414yes—
1138#95C2414yes—
1139#95C2412yes—
1140#95C2412yes—
1141#95C2412yes—
1142#95C2412yes—
1143#95C2412yes—
1144#95C2414yes—
1145#95C2414yes—
1146#95C2412yes—
1147#95C2412yes—
1148#95C2412yes—
1149#95C2412yes—
1150#95C2412yes—
1151#95C2412yes—
1152#95C2412yes—
1153#95C2412yes—
1154#95C2412yes—
1155#95C2412yes—
1156#95C2414yes—
1157#95C2414yes—
1158#95C2412yes—
1159#95C2414yes—
1160#95C2412yes—
1161#95C2412yes—
1162#95C2412yes—
1163#95C2412yes—
1164#95C2412yes—
1165#95C2412yes—
1166#95C2412yes—
1167#95C2412yes—
1168#95C2411yescharacteristic
1169#95C2411yescharacteristic
1170#95C2411yescharacteristic
1171#95C2411yescharacteristic
1172#95C2412yes—
1173#95C2411yescharacteristic
1174#95C2412yes—
1175#95C2411yescharacteristic
1176#95C2412yes—
1177#95C2412yes—
1178#95C2414yes—
1179#95C2412yes—
1180#95C2414yes—
1181#95C2414yes—
1182#95C2412yes—
1183#95C2412yes—
1184#95C2414yes—
1185#95C2414yes—
1186#95C2412yes—
1187#95C2412yes—
1188#95C2412yes—
1189#95C2412yes—
1190#95C2412yes—
1191#95C2412yes—
1192#95C2412yes—
1193#95C2412yes—
1194#95C2412yes—
1195#95C2414yes—
1196#95C2414yes—
1197C24—28no—
1198C24—44no—
1199C24—44no—
1200C24—44no—
1201C24—44no—
1202C24—44no—
1203C24—44no—
1204C24C2512yes—
1205C24C2514yes—
1206C24C2514yes—
1207C24C2512yes—
1208#41—816no—
1209C2×Q8—22no—
1210C2×Q8—22no—
1211C2×Q8—28no—
1212C2×Q8—24no—
1213C2×Q8—22no—
1214C2×Q8—24no—
1215C2×Q8—22no—
1216C2×Q8—28no—
1217C2×Q8—22no—
1218C2×Q8—24no—
1219C2×Q8—22no—
1220C2×Q8—24no—
1221C2×Q8—44no—
1222C2×Q8—41no—
1223C2×Q8—41no—
1224C2×Q8—42no—
1225C2×Q8—42no—
1226C2×Q8—432no—
1227C2×Q8H(5,𝔽2)14yes—
1228C2×D4—28no—
1229C2×D4—28no—
1230C2×D4—28no—
1231C2×D4—24no—
1232C2×D4—22no—
1233C2×D4—24no—
1234C2×D4—24no—
1235C2×D4—24no—
1236C2×D4—24no—
1237C2×D4—28no—
1238C2×D4—24no—
1239C2×D4—24no—
1240C2×D4—24no—
1241C2×D4—24no—
1242C2×D4—24no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—28no—
1246C2×D4—28no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—24no—
1250C2×D4—24no—
1251C2×D4—24no—
1252C2×D4—24no—
1253C2×D4—28no—
1254C2×D4—44no—
1255C2×D4—44no—
1256C2×D4—42no—
1257C2×D4—44no—
1258C2×D4—42no—
1259C2×D4—44no—
1260C2×D4—44no—
1261C2×D4—44no—
1262C2×D4—44no—
1263C2×D4—44no—
1264C2×D4—42no—
1265C2×D4—42no—
1266C2×D4—44no—
1267C2×D4—44no—
1268C2×D4—44no—
1269C2×D4—44no—
1270C2×D4—44no—
1271C2×D4—44no—
1272C2×D4—44no—
1273C2×D4—44no—
1274C2×D4—44no—
1275C2×D4—44no—
1276C2×D4—44no—
1277C2×D4—44no—
1278C2×D4—44no—
1279C2×D4—44no—
1280C2×D4—44no—
1281C2×D4—816no—
1282C2×D4—816no—
1283C2×D4C2×#4114yes—
1284C22×C4—24no—
1285C22×C4—24no—
1286C22×C4—28no—
1287C22×C4—24no—
1288C22×C4—28no—
1289C22×C4—24no—
1290C22×C4—24no—
1291C22×C4—28no—
1292C22×C4—44no—
1293C22×C4—42no—
1294C22×C4—42no—
1295C22×C4—42no—
1296C22×C4—42no—
1297C22×C4—42no—
1298C22×C4—44no—
1299C22×C4—44no—
1300C22×C4—42no—
1301C22×C4—44no—
1302C22×C4—44no—
1303C22×C4—44no—
1304C22×C4—44no—
1305C22×C4—44no—
1306C22×C4—44no—
1307C22×C4—44no—
1308C22×C4—44no—
1309C22×C4—44no—
1310C22×C4—44no—
1311C22×C4—44no—
1312C22×C4—44no—
1313C22×C4C2×#4118yes—
1314C22×C4C2512yes—
1315C22×C4C2512yes—
1316C22×C4C2511yescharacteristic
1317C22×C4C2512yes—
1318C22×C4C2511yescharacteristic
1319C22×C4C2511yescharacteristic
1320C22×C4C2512yes—
1321C22×C4C2511yescharacteristic
1322C22×C4C2512yes—
1323C22×C4C2512yes—
1324C22×C4C2512yes—
1325C22×C4C2511yescharacteristic
1326C22×C4C2514yes—
1327C22×C4C2512yes—
1328C22×C4C2512yes—
1329C22×C4C2511yescharacteristic
1330C22×C4C2511yescharacteristic
1331C22×C4C2512yes—
1332C22×C4C2514yes—
1333C22×C4C2512yes—
1334C22×C4C2512yes—
1335C22×C4C2511yescharacteristic
1336C22×C4C2511yescharacteristic
1337C22×C4C2511yescharacteristic
1338C22×C4C2512yes—
1339C22×C4C2511yescharacteristic
1340C22×C4C2511yescharacteristic
1341C22×C4C2512yes—
1342C22×C4C2511yescharacteristic
1343C22×C4C2511yescharacteristic
1344C22×C4C2511yescharacteristic
1345C4⋊C4—22no—
1346C4⋊C4—24no—
1347C4⋊C4—22no—
1348C4⋊C4—24no—
1349C4⋊C4—24no—
1350C4⋊C4—22no—
1351C4⋊C4—28no—
1352C4⋊C4—24no—
1353C4⋊C4—24no—
1354C4⋊C4—24no—
1355C4⋊C4—24no—
1356C4⋊C4—22no—
1357C4⋊C4—24no—
1358C4⋊C4—28no—
1359C4⋊C4—22no—
1360C4⋊C4—22no—
1361C4⋊C4—22no—
1362C4⋊C4—22no—
1363C4⋊C4—24no—
1364C4⋊C4—24no—
1365C4⋊C4—24no—
1366C4⋊C4—22no—
1367C4⋊C4—24no—
1368C4⋊C4—22no—
1369C4⋊C4—22no—
1370C4⋊C4—22no—
1371C4⋊C4—22no—
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—22no—
1375C4⋊C4—42no—
1376C4⋊C4—42no—
1377C4⋊C4—44no—
1378C4⋊C4—44no—
1379C4⋊C4—42no—
1380C4⋊C4—42no—
1381C4⋊C4—42no—
1382C4⋊C4—42no—
1383C4⋊C4—42no—
1384C4⋊C4—42no—
1385C4⋊C4—41no—
1386C4⋊C4—41no—
1387C4⋊C4—41no—
1388C4⋊C4—41no—
1389C4⋊C4—42no—
1390C4⋊C4—42no—
1391C4⋊C4—42no—
1392C4⋊C4—42no—
1393C4⋊C4—44no—
1394C4⋊C4—44no—
1395C4⋊C4—42no—
1396C4⋊C4—44no—
1397C4⋊C4—42no—
1398C4⋊C4—42no—
1399C4⋊C4—42no—
1400C4⋊C4—42no—
1401C4⋊C4—42no—
1402C4⋊C4—42no—
1403C4⋊C4—42no—
1404C4⋊C4—42no—
1405C4⋊C4—42no—
1406C4⋊C4C2×#4114yes—
1407C22⋊C4—28no—
1408C22⋊C4—24no—
1409C22⋊C4—28no—
1410C22⋊C4—28no—
1411C22⋊C4—24no—
1412C22⋊C4—24no—
1413C22⋊C4—28no—
1414C22⋊C4—28no—
1415C22⋊C4—24no—
1416C22⋊C4—24no—
1417C22⋊C4—28no—
1418C22⋊C4—24no—
1419C22⋊C4—24no—
1420C22⋊C4—28no—
1421C22⋊C4—24no—
1422C22⋊C4—24no—
1423C22⋊C4—44no—
1424C22⋊C4—44no—
1425C22⋊C4—44no—
1426C22⋊C4—44no—
1427C22⋊C4—42no—
1428C22⋊C4—42no—
1429C22⋊C4—44no—
1430C22⋊C4—44no—
1431C22⋊C4—42no—
1432C22⋊C4—42no—
1433C22⋊C4—44no—
1434C22⋊C4—44no—
1435C22⋊C4—42no—
1436C22⋊C4—42no—
1437C22⋊C4—44no—
1438C22⋊C4—44no—
1439C22⋊C4—44no—
1440C22⋊C4—44no—
1441C22⋊C4—42no—
1442C22⋊C4—42no—
1443C22⋊C4—44no—
1444C22⋊C4—44no—
1445C22⋊C4—44no—
1446C22⋊C4—44no—
1447C22⋊C4—44no—
1448C22⋊C4—44no—
1449C22⋊C4—44no—
1450C22⋊C4—44no—
1451C22⋊C4—44no—
1452C22⋊C4—44no—
1453C22⋊C4—44no—
1454C22⋊C4—44no—
1455C22⋊C4—44no—
1456C22⋊C4—42no—
1457C22⋊C4—42no—
1458C22⋊C4—44no—
1459C22⋊C4—44no—
1460C22⋊C4—44no—
1461C22⋊C4—42no—
1462C22⋊C4—44no—
1463C22⋊C4—44no—
1464C22⋊C4—44no—
1465C22⋊C4—44no—
1466C22⋊C4—42no—
1467C22⋊C4—44no—
1468C22⋊C4—44no—
1469C22⋊C4—44no—
1470C22⋊C4—44no—
1471C22⋊C4—42no—
1472C22⋊C4—42no—
1473C22⋊C4C2×#4118yes—
1474C42—24no—
1475C42—24no—
1476C42—22no—
1477C42—24no—
1478C42—24no—
1479C42—24no—
1480C42—22no—
1481C42—28no—
1482C42—24no—
1483C42—24no—
1484C42—22no—
1485C42—22no—
1486C42—22no—
1487C42—22no—
1488C42—24no—
1489C42—22no—
1490C42—22no—
1491C42—22no—
1492C42—22no—
1493C42—22no—
1494C42—24no—
1495C42—22no—
1496C42—42no—
1497C42—42no—
1498C42—44no—
1499C42—44no—
1500C42—44no—
1501C42—44no—
1502C42—42no—
1503C42—41no—
1504C42—41no—
1505C42—44no—
1506C42—41no—
1507C42—41no—
1508C42—41no—
1509C42C2×#4114yes—
1510C42H(5,𝔽2)14yes—
1511C23—22no—
1512C23—22no—
1513C23—22no—
1514C23—22no—
1515C23—22no—
1516C23—22no—
1517C23—24no—
1518C23—22no—
1519C23—24no—
1520C23—22no—
1521C23—24no—
1522C23—24no—
1523C23—22no—
1524C23—24no—
1525C23—24no—
1526C23—22no—
1527C23—24no—
1528C23—22no—
1529C23—22no—
1530C23—24no—
1531C23—24no—
1532C23—24no—
1533C23—24no—
1534C23—24no—
1535C23—22no—
1536C23—24no—
1537C23—24no—
1538C23—88no—
1539C23—88no—
1540C23—88no—
1541C23—88no—
1542C23—88no—
1543C23—164no—
1544C23—164no—
1545C23C22×#4114yes—
1546C23C2611yescharacteristic
1547Q8—28no—
1548Q8—416no—
1549Q8—44no—
1550Q8—48no—
1551Q8—44no—
1552Q8—84no—
1553D4—28no—
1554D4—48no—
1555D4—48no—
1556D4—48no—
1557D4—44no—
1558D4—48no—
1559D4—84no—
1560D4—84no—
1561D4—88no—
1562D4—88no—
1563D4—88no—
1564D4—88no—
1565D4—88no—
1566D4—88no—
1567D4—88no—
1568D4—164no—
1569D4—164no—
1570D4—164no—
1571C2×C4—22no—
1572C2×C4—21no—
1573C2×C4—22no—
1574C2×C4—22no—
1575C2×C4—22no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—216no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—22no—
1588C2×C4—24no—
1589C2×C4—22no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—22no—
1593C2×C4—22no—
1594C2×C4—24no—
1595C2×C4—22no—
1596C2×C4—22no—
1597C2×C4—24no—
1598C2×C4—22no—
1599C2×C4—22no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—22no—
1605C2×C4—21no—
1606C2×C4—21no—
1607C2×C4—21no—
1608C2×C4—22no—
1609C2×C4—24no—
1610C2×C4—22no—
1611C2×C4—22no—
1612C2×C4—22no—
1613C2×C4—22no—
1614C2×C4—21no—
1615C2×C4—21no—
1616C2×C4—21no—
1617C2×C4—21no—
1618C2×C4—21no—
1619C2×C4—21no—
1620C2×C4—22no—
1621C2×C4—21no—
1622C2×C4—21no—
1623C2×C4—21no—
1624C2×C4—22no—
1625C2×C4—22no—
1626C2×C4—24no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—22no—
1632C2×C4—22no—
1633C2×C4—22no—
1634C2×C4—22no—
1635C2×C4—22no—
1636C2×C4—22no—
1637C2×C4—22no—
1638C2×C4—22no—
1639C2×C4—22no—
1640C2×C4—22no—
1641C2×C4—22no—
1642C2×C4—22no—
1643C2×C4—22no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—24no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—22no—
1650C2×C4—21no—
1651C2×C4—22no—
1652C2×C4—22no—
1653C2×C4—416no—
1654C2×C4—48no—
1655C2×C4—88no—
1656C2×C4—84no—
1657C2×C4—84no—
1658C2×C4—164no—
1659C2×C4—164no—
1660C2×C4—164no—
1661C2×C4—164no—
1662C2×C4C22×#4112yes—
1663C2×C4C22×#4114yes—
1664C2×C4C22×#4112yes—
1665C2×C4C22×#4112yes—
1666C2×C4C2×H(5,𝔽2)12yes—
1667C2×C4C2×H(5,𝔽2)12yes—
1668C2×C4C2×H(5,𝔽2)14yes—
1669C2×C4C2×H(5,𝔽2)12yes—
1670C2×C4C2×H(5,𝔽2)12yes—
1671C2×C4#58512yes—
1672C2×C4#58512yes—
1673C2×C4#58512yes—
1674C22—24no—
1675C22—24no—
1676C22—24no—
1677C22—42no—
1678C22—42no—
1679C22—42no—
1680C22—42no—
1681C22—44no—
1682C22—44no—
1683C22—42no—
1684C22—44no—
1685C22—44no—
1686C22—42no—
1687C22—44no—
1688C22—42no—
1689C22—44no—
1690C22—42no—
1691C22—44no—
1692C22—44no—
1693C22—44no—
1694C22—44no—
1695C22—42no—
1696C22—44no—
1697C22—44no—
1698C22—42no—
1699C22—44no—
1700C22—44no—
1701C22—42no—
1702C22—1616no—
1703C22C23×#4111yescharacteristic
1704C22C22×H(5,𝔽2)11yescharacteristic
1705C22C22×H(5,𝔽2)11yescharacteristic
1706C22C2×#58511yescharacteristic
1707C22C2×#58511yescharacteristic
1708C22C2×#58511yescharacteristic
1709C22H(7,𝔽2)11yescharacteristic
1710C4—22no—
1711C4—22no—
1712C4—24no—
1713C4—24no—
1714C4—22no—
1715C4—22no—
1716C4—42no—
1717C4—42no—
1718C4—41no—
1719C4—41no—
1720C4—42no—
1721C4—42no—
1722C4—44no—
1723C4—42no—
1724C4—42no—
1725C4—42no—
1726C4—42no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—41no—
1731C4—42no—
1732C4—42no—
1733C4—42no—
1734C4—41no—
1735C4—44no—
1736C4—41no—
1737C4—41no—
1738C4—42no—
1739C4#351014yes—
1740C4#351914yes—
1741C2—44no—
1742C2—84no—
1743C2—84no—
1744C2—82no—
1745C2C2×#351911yescharacteristic
1746C2C2×#351011yescharacteristic
1747C2#6283611yescharacteristic
1748C2#6292311yescharacteristic
1749C2#6296111yescharacteristic
1750C2#6301011yescharacteristic
1751C2#6301911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39361C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59679C2semidirect
2. #59646C2semidirect
3. #59480C2semidirect
4. #59427C2semidirect
5. #59147C2semidirect
6. #51471C2semidirect
7. #49759C2semidirect
8. #46791C2semidirect
9. #45146C2semidirect
10. #45097C2semidirect
11. #45031C2semidirect
12. #44959C2semidirect
13. #43477C2semidirect
14. #42976C2semidirect
15. #42607C2semidirect
16. #40033C2semidirect
17. #39823C2semidirect
18. #39789C2semidirect
19. #39363C2semidirect
21. #39202C2semidirect
22. #38987C2semidirect
23. #38250C2semidirect
24. #36595C2semidirect
25. #36595C2semidirect
26. D4×#124C2semidirect
27. #36041C2semidirect
28. #35897C2semidirect
29. #35677C2semidirect
30. #35560C2semidirect
31. #34902C2semidirect
32. #34893C2semidirect
33. #34493C2semidirect
34. #34330C2semidirect
35. #34311C2semidirect
36. C2×#559C22semidirect
37. C2×#559C22semidirect
41. C2×#536C22semidirect
44. C2×#519C22semidirect
47. #2858C22semidirect
48. #2858C22semidirect
50. #2829C22semidirect
51. #2803C22semidirect
52. #2800C22semidirect
53. #2800C22semidirect
54. #2797C22semidirect
55. #2797C22semidirect
56. #2786C22semidirect
57. #2783C22semidirect
58. #2778C22semidirect
59. #2757C22semidirect
60. #2753C22semidirect
61. #2752C22semidirect
62. #2749C22semidirect
63. #2749C22semidirect
64. #2740C22semidirect
65. #2730C22semidirect
66. #2712C22semidirect
67. #2710C22semidirect
68. #2706C22semidirect
69. #2701C22semidirect
70. #2700C22semidirect
71. #2697C22semidirect
72. #2697C22semidirect
73. #2693C22semidirect
74. #2687C22semidirect
75. #2686C22semidirect
76. #2685C22semidirect
77. #2685C22semidirect
78. #2684C22semidirect
79. #2684C22semidirect
80. #2681C22semidirect
81. #2681C22semidirect
84. #2662C22semidirect
85. #2649C22semidirect
86. #2648C22semidirect
87. #2644C22semidirect
88. #2632C22semidirect
89. #2624C22semidirect
90. #2620C22semidirect
92. #2610C22semidirect
93. #2603C22semidirect
94. #2602C22semidirect
95. #2600C22semidirect
96. #2598C22semidirect
97. #2597C22semidirect
98. #2596C22semidirect
99. #2594C22semidirect
102. #2589C22semidirect
103. #2587C22semidirect
104. #2584C22semidirect
105. #2581C22semidirect
107. #2576C22semidirect
108. #2570C22semidirect
109. #2568C22semidirect
111. #2566C22semidirect
112. #2557C22semidirect
113. #2557C22semidirect
114. #2554C22semidirect
115. #2550C22semidirect
120. #2548C22semidirect
121. #2548C22semidirect
122. #2548C22semidirect
123. #2548C22semidirect
124. #2548C22semidirect
125. #2548C22semidirect
127. #2547C22semidirect
128. #2546C22semidirect
131. #2545C22semidirect
132. #2545C22semidirect
134. #2544C22semidirect
135. #2544C22semidirect
136. #2544C22semidirect
138. #2534C22semidirect
139. #2532C22semidirect
140. #2526C22semidirect
141. #2525C22semidirect
142. #2522C22semidirect
143. #2514C22semidirect
144. #2513C22semidirect
145. #2513C22semidirect
146. #2513C22semidirect
148. #2512C22semidirect
149. #2512C22semidirect
150. #2509C22semidirect
151. #2507C22semidirect
152. #2500C22semidirect
153. #2497C22semidirect
154. #2495C22semidirect
157. #2490C22semidirect
158. #2490C22semidirect
159. #2488C22semidirect
162. #2472C22semidirect
163. #2471C22semidirect
164. #2471C22semidirect
165. #2469C22semidirect
166. #2466C22semidirect
167. #2466C22semidirect
168. #2465C22semidirect
169. #2459C22semidirect
170. #2458C22semidirect
171. #2458C22semidirect
172. #2457C22semidirect
174. #2454C22semidirect
176. #2452C22semidirect
177. #2452C22semidirect
178. #2450C22semidirect
180. #2448C22semidirect
181. #2448C22semidirect
182. #2447C22semidirect
183. #2447C22semidirect
184. #2447C22semidirect
185. #2446C22semidirect
189. #2445C22semidirect
190. #2445C22semidirect
191. #2445C22semidirect
192. #2445C22semidirect
193. #2445C22semidirect
194. #2445C22semidirect
195. #2445C22semidirect
196. #2444C22semidirect
197. #2439C22semidirect
199. #2436C22semidirect
204. #2432C22semidirect
208. #2426C22semidirect
209. #2426C22semidirect
210. #2426C22semidirect
211. #2426C22semidirect
212. #2425C22semidirect
213. #2422C22semidirect
214. #2420C22semidirect
215. #2418C22semidirect
216. #2418C22semidirect
217. #2412C22semidirect
218. #2411C22semidirect
219. #2411C22semidirect
220. #2411C22semidirect
221. #2411C22semidirect
222. #2401C22semidirect
223. #2398C22semidirect
224. #2396C22semidirect
225. #2396C22semidirect
226. #2396C22semidirect
228. #2367C22semidirect
229. #2367C22semidirect
232. #2366C22semidirect
233. #2366C22semidirect
234. #2366C22semidirect
235. #2366C22semidirect
236. #2365C22semidirect
237. #2365C22semidirect
238. #2364C22semidirect
241. #2363C22semidirect
242. #2363C22semidirect
243. #2362C22semidirect
244. #2362C22semidirect
245. #2358C22semidirect
246. #2357C22semidirect
247. #2357C22semidirect
248. #2356C22semidirect
249. #2355C22semidirect
253. Q8×C4⋊C4C22semidirect
254. #2346C22semidirect
255. Q8×C22⋊C4C22semidirect
256. #2339C22semidirect
261. #2337C22semidirect
262. #2333C22semidirect
266. #2324C22semidirect
267. #2323C22semidirect
268. #2323C22semidirect
270. #2319C22semidirect
273. C4×C4⋊Q8C22semidirect
274. C4×C4⋊Q8C22semidirect
275. C4×C4⋊Q8C22semidirect
276. C4×C4⋊Q8C22semidirect
278. C4×#127C22semidirect
279. C4×#127C22semidirect
280. C4×#125C22semidirect
281. C4×#125C22semidirect
282. C4×#126C22semidirect
285. C4×C22⋊Q8C22semidirect
286. C4×#121C22semidirect
287. #2298C22semidirect
288. #2297C22semidirect
289. #2296C22semidirect
290. #2295C22semidirect
295. #2275C22semidirect
296. C42×Q8C22semidirect
297. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#596792
#596462
#594802
#594272
#591472
#514712
#497592
#467912
#451462
#450972
#450312
#449592
#434772
#429762
#426072
#400332
#398232
#397892
#393632
#393612
#392022
#389872
#382502
#365952
D4×#1242
#360412
#358972
#356772
#355602
#349022
#348932
#344932
#343302
#343112