Finite Group Databasebeta

← #7686622

Subgroups — #7686622

Order 512.

7954 conjugacy classes of subgroups.

The subgroup lattice has 1907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic, complemented
3#59801C214yesmaximal, complemented
4#59651C212yesmaximal, complemented
5#59413C211yesmaximal, characteristic, complemented
6#59318C212yesmaximal, complemented
7#59144C211yesmaximal, characteristic, complemented
8#59110C212yesmaximal, complemented
9#59036C211yesmaximal, characteristic, complemented
10#59031C212yesmaximal, complemented
11#45322C212yesmaximal, complemented
12#45237C212yesmaximal, complemented
13#44761C214yesmaximal, complemented
14#43974C214yesmaximal, complemented
15#39470C211yesmaximal, characteristic, complemented
16#39465C212yesmaximal, complemented
17#39435C212yesmaximal, complemented
18#39431C214yesmaximal, complemented
19#38911C211yesmaximal, characteristic, complemented
20#38907C212yesmaximal, complemented
21#36424C212yesmaximal, complemented
22#36276C211yesmaximal, characteristic, complemented
23#36275C211yesmaximal, characteristic, complemented
24#36259C212yesmaximal, complemented
25#36259C211yesmaximal, characteristic, complemented
26#36164C211yesmaximal, characteristic, complemented
27#36139C212yesmaximal, complemented
28#36129C211yesmaximal, characteristic, complemented
29#36085C212yesmaximal, complemented
30#35998C212yesmaximal, complemented
31#34889C211yesmaximal, characteristic, complemented
32C2×#2550C212yesmaximal, complemented
33#34259C212yesmaximal, complemented
34C4×#547C211yesmaximal, characteristic, complemented
35C4×#547C211yesmaximal, characteristic, complemented
36C22×2−1+4C2212yes—
37#3515—216no—
38#3499—216no—
39C2×#557C2211yescharacteristic
40C2×#554C2211yescharacteristic
41C2×#554C2211yescharacteristic
42C2×#553C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×#552C2214yes—
46C2×D4×Q8C2212yes—
47C2×D4×Q8C2211yescharacteristic
48C2×D4×Q8C2211yescharacteristic
49C2×#547C2212yes—
50C2×#547C2211yescharacteristic
51C2×#547C2212yes—
52C2×#547C2212yes—
53C2×#547C2214yes—
54C2×#547C2212yes—
55C2×#547C2211yescharacteristic
56C2×#547C2212yes—
57C2×#547C2211yescharacteristic
58C2×#541C2212yes—
59C2×#539C2214yes—
60C2×#536C2214yes—
61C2×#536C2212yes—
62C2×#533C2211yescharacteristic
63C2×#532C2212yes—
64C2×#532C2211yescharacteristic
65C22×C4⋊Q8C2211yescharacteristic
66C22×C4⋊Q8C2212yes—
67C2×#529C2212yes—
68C2×#529C2211yescharacteristic
69C22×#125C2212yes—
70C2×#520C2212yes—
71C2×C4×#41C2211yescharacteristic
72C2×C4×#41C2211yescharacteristic
73C2×C4×#41C2212yes—
74#2862C2211yescharacteristic
75#2857C2212yes—
76#2857C2211yescharacteristic
77#2857C2211yescharacteristic
78#2855C2212yes—
79#2854C2214yes—
80#2854C2212yes—
81#2850C2212yes—
82#2716C2214yes—
83#2716C2214yes—
84#2715C2214yes—
85#2713C2214yes—
86#2713C2214yes—
87#2713C2214yes—
88#2710C2214yes—
89#2706C2214yes—
90#2704C2214yes—
91#2700C2214yes—
92#2698C2214yes—
93#2695C2214yes—
94#2694C2214yes—
95#2694C2214yes—
96#2692C2214yes—
97#2690C2214yes—
98#2690C2214yes—
99#2689C2214yes—
100#2689C2214yes—
101#2687C2214yes—
102#2681C2214yes—
103#2625C2212yes—
104#2623C2214yes—
105#2616C2212yes—
106#2614C2214yes—
107#2582C2211yescharacteristic
108#2568C2211yescharacteristic
109#2567C2211yescharacteristic
110#2563C2211yescharacteristic
111#2560C2214yes—
112#2559C2212yes—
113#2558C2214yes—
114#2557C2212yes—
115#2556C2214yes—
116#2556C2214yes—
117#2554C2214yes—
118#2553C2214yes—
119#2550C2214yes—
120#2550C2214yes—
121#2550C2212yes—
122#2550C2214yes—
123#2550C2212yes—
124#2550C2212yes—
125#2550C2212yes—
126#2550C2212yes—
127#2550C2211yescharacteristic
128#2550C2212yes—
129#2550C2212yes—
130#2550C2214yes—
131#2550C2212yes—
132#2549C2214yes—
133#2549C2214yes—
134#2546C2212yes—
135#2546C2211yescharacteristic
136#2544C2211yescharacteristic
137#2540C2211yescharacteristic
138#2538C2211yescharacteristic
139#2538C2212yes—
140#2535C2211yescharacteristic
141#2521C2214yes—
142#2521C2212yes—
143#2504C2212yes—
144#2503C2212yes—
145#2502C2212yes—
146#2498C2214yes—
147#2492C2212yes—
148#2492C2211yescharacteristic
149#2492C2212yes—
150#2490C2212yes—
151#2490C2211yescharacteristic
152#2489C2212yes—
153#2489C2212yes—
154#2488C2214yes—
155#2488C2214yes—
156#2488C2214yes—
157#2487C2212yes—
158#2486C2212yes—
159#2486C2212yes—
160#2486C2214yes—
161#2484C2214yes—
162#2474C2214yes—
163#2473C2214yes—
164#2470C2214yes—
165#2468C2214yes—
166#2466C2214yes—
167#2465C2214yes—
168#2464C2212yes—
169#2454C2212yes—
170#2454C2212yes—
171#2453C2212yes—
172#2451C2212yes—
173#2451C2212yes—
174#2451C2212yes—
175#2449C2214yes—
176#2447C2212yes—
177#2446C2212yes—
178#2446C2212yes—
179#2445C2212yes—
180#2443C2214yes—
181#2443C2214yes—
182#2442C2212yes—
183#2442C2212yes—
184#2441C2212yes—
185#2439C2212yes—
186#2439C2212yes—
187#2438C2214yes—
188#2438C2214yes—
189#2434C2212yes—
190#2434C2212yes—
191#2434C2212yes—
192#2430C2214yes—
193#2430C2214yes—
194#2430C2214yes—
195#2429C2212yes—
196#2429C2212yes—
197#2429C2212yes—
198#2428C2211yescharacteristic
199#2427C2211yescharacteristic
200#2425C2214yes—
201#2425C2214yes—
202#2425C2214yes—
203#2425C2214yes—
204#2423C2212yes—
205#2423C2212yes—
206#2420C2212yes—
207#2420C2212yes—
208#2419C2214yes—
209#2419C2214yes—
210#2417C2212yes—
211#2417C2212yes—
212#2416C2212yes—
213#2416C2214yes—
214#2415C2212yes—
215#2415C2212yes—
216#2415C2212yes—
217#2413C2214yes—
218#2413C2214yes—
219#2413C2214yes—
220#2409C2212yes—
221#2409C2212yes—
222#2409C2212yes—
223#2406C2214yes—
224#2406C2214yes—
225#2406C2214yes—
226#2395C2212yes—
227C2×#398C2214yes—
228#2388C2212yes—
229C2×#395C2214yes—
230#2367C2212yes—
231#2365C2211yescharacteristic
232#2365C2211yescharacteristic
233#2363C2212yes—
234#2362C2211yescharacteristic
235#2362C2212yes—
236#2362C2211yescharacteristic
237#2361C2212yes—
238#2361C2212yes—
239#2360C2212yes—
240#2360C2212yes—
241#2359C2214yes—
242#2359C2212yes—
243#2359C2212yes—
244#2359C2214yes—
245#2354C2211yescharacteristic
246#2354C2211yescharacteristic
247#2352C2212yes—
248#2349C2212yes—
249#2349C2212yes—
250D4×C4⋊C4C2211yescharacteristic
251D4×C4⋊C4C2211yescharacteristic
252D4×C4⋊C4C2212yes—
253#2344C2212yes—
254#2344C2212yes—
255Q8×C22⋊C4C2212yes—
256Q8×C22⋊C4C2212yes—
257Q8×C22⋊C4C2212yes—
258Q8×C22⋊C4C2212yes—
259#2339C2214yes—
260#2339C2212yes—
261#2339C2212yes—
262#2339C2212yes—
263#2339C2211yescharacteristic
264#2339C2211yescharacteristic
265#2339C2214yes—
266#2339C2214yes—
267#2339C2212yes—
268#2339C2212yes—
269#2339C2214yes—
270#2311C2212yes—
271#2311C2214yes—
272#2310C2212yes—
273#2310C2214yes—
274C4×C4⋊Q8C2211yescharacteristic
275C4×C4⋊Q8C2211yescharacteristic
276C4×#124C2211yescharacteristic
277C4×C22⋊Q8C2212yes—
278C4×C22⋊Q8C2211yescharacteristic
279C4×C22⋊Q8C2211yescharacteristic
280C4×C22⋊Q8C2211yescharacteristic
281C4×#123C2214yes—
282C4×#123C2212yes—
283C4×#123C2212yes—
284C4×#121C2212yes—
285C4×#121C2212yes—
286C4×#121C2212yes—
287C4×#121C2211yescharacteristic
288#2297C2212yes—
289#2297C2214yes—
290C2×#391C2212yes—
291C2×#391C2214yes—
292C2×#389C2212yes—
293C2×#389C2214yes—
294C2×#389C2212yes—
295C2×#382C2212yes—
296C42×D4C2211yescharacteristic
297C42×D4C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4×C4⋊C4C2212yes—
300C2×C4×C4⋊C4C2212yes—
301C2×2−1+4—216no—
302C2×2−1+4—216no—
303C2×2−1+4—48no—
304C22×#41C2312yes—
305C22×#41C2311yescharacteristic
306C22×#41C2312yes—
307C22×#41C2314yes—
308C22×#41C2314yes—
309C22×#41C2314yes—
310C22×#41C2312yes—
311C22×#41C2311yescharacteristic
312C23×Q8C2314yes—
313C23×Q8C2312yes—
314C23×Q8C2312yes—
315C23×Q8C2312yes—
316#557—28no—
317#554—28no—
318#554—28no—
319#553—216no—
320#552—232no—
321#552—216no—
322#552—216no—
323D4×Q8—28no—
324D4×Q8—216no—
325D4×Q8—28no—
326#547—216no—
327#547—216no—
328#547—28no—
329#547—232no—
330#547—216no—
331#547—28no—
332#547—216no—
333#547—48no—
334#547D4116yescomplemented
335#541—216no—
336#539—232no—
337#536—232no—
338#536—216no—
339#533—28no—
340#532—216no—
341#532—28no—
342C2×C4⋊Q8—28no—
343C2×C4⋊Q8—216no—
344C2×C4⋊Q8C2311yescharacteristic
345C2×C4⋊Q8C2311yescharacteristic
346C2×C4⋊Q8C2311yescharacteristic
347C2×C4⋊Q8C2312yes—
348C2×C4⋊Q8C2311yescharacteristic
349C2×C4⋊Q8C2312yes—
350C2×C4⋊Q8C2314yes—
351C2×C4⋊Q8C2312yes—
352C2×C4⋊Q8C2312yes—
353C2×C4⋊Q8C2314yes—
354C2×C4⋊Q8C2312yes—
355C2×C4⋊Q8C2312yes—
356C2×C4⋊Q8C2312yes—
357C2×C4⋊Q8C2311yescharacteristic
358C2×#127C2311yescharacteristic
359#529—216no—
360#529—28no—
361C2×#126C2314yes—
362C2×#126C2314yes—
363C2×#126C2312yes—
364C2×#126C2314yes—
365C2×#125—216no—
366C2×#125C2311yescharacteristic
367C2×#125C2312yes—
368C2×#125C2314yes—
369C2×#125C2314yes—
370C2×#125C2312yes—
371C2×#125C2312yes—
372C2×#125C2314yes—
373C2×#125C2312yes—
374C2×#125C2314yes—
375C2×#124C2311yescharacteristic
376C2×#124C2311yescharacteristic
377C2×#124C2312yes—
378C2×#124C2314yes—
379C2×#123C2314yes—
380C2×#123C2314yes—
381C2×#123C2312yes—
382C2×#123C2312yes—
383C2×#123C2314yes—
384C2×#123C2314yes—
385C2×#123C2312yes—
386C2×#123C2314yes—
387C2×#123C2314yes—
388C2×#123C2314yes—
389C2×#123C2314yes—
390C2×#123C2314yes—
391C2×#123C2314yes—
392C2×#123C2314yes—
393C2×#123C2314yes—
394C2×C22⋊Q8C2314yes—
395C2×C22⋊Q8C2312yes—
396C2×C22⋊Q8C2312yes—
397C2×C22⋊Q8C2312yes—
398C2×C22⋊Q8C2311yescharacteristic
399C2×C22⋊Q8C2311yescharacteristic
400C2×C22⋊Q8C2311yescharacteristic
401C2×C22⋊Q8C2312yes—
402C2×C22⋊Q8C2312yes—
403C2×C22⋊Q8C2311yescharacteristic
404C2×C22⋊Q8C2312yes—
405C2×C22⋊Q8C2312yes—
406C2×C22⋊Q8C2314yes—
407C2×C22⋊Q8C2314yes—
408C2×C22⋊Q8C2314yes—
409C2×C22⋊Q8C2314yes—
410C2×C22⋊Q8C2314yes—
411C2×C22⋊Q8C2312yes—
412C2×C22⋊Q8C2312yes—
413C2×C22⋊Q8C2312yes—
414C2×C22⋊Q8C2312yes—
415C2×#121C2312yes—
416C2×#121C2312yes—
417C2×#121C2311yescharacteristic
418C2×#121C2311yescharacteristic
419C2×#121C2314yes—
420C2×#121C2314yes—
421C2×#121C2311yescharacteristic
422C2×#121C2312yes—
423C2×#121C2311yescharacteristic
424C2×#121C2314yes—
425C2×#121C2312yes—
426C2×#121C2312yes—
427#520—216no—
428C4×#41—28no—
429C4×#41—28no—
430C4×#41—48no—
431C2×C4×Q8C2311yescharacteristic
432C2×C4×Q8C2311yescharacteristic
433C2×C4×Q8C2311yescharacteristic
434C2×C4×Q8C2312yes—
435C2×C4×Q8C2312yes—
436C2×C4×Q8C2312yes—
437C2×C4×Q8C2312yes—
438C2×C4×Q8C2311yescharacteristic
439C2×C4×Q8C2311yescharacteristic
440C2×C4×Q8C2312yes—
441C2×C4×Q8C2312yes—
442C2×C4×D4C2311yescharacteristic
443C2×C4×D4C2311yescharacteristic
444C2×C4×D4C2311yescharacteristic
445C2×C4×D4C2312yes—
446C2×C4×D4C2311yescharacteristic
447C2×C4×D4C2312yes—
448C2×C4×D4C2314yes—
449C2×C4×D4C2314yes—
450C2×C4×D4C2311yescharacteristic
451C2×C4×D4C2311yescharacteristic
452C2×C4×D4C2312yes—
453C2×C4×D4C2312yes—
454C2×C4×D4C2311yescharacteristic
455C2×C4×D4C2311yescharacteristic
456C2×C4×D4C2311yescharacteristic
457C2×C4×D4C2312yes—
458C2×C4×D4C2312yes—
459C2×C4×D4C2314yes—
460C2×C4×D4C2312yes—
461C2×C4×D4C2312yes—
462C2×C4×D4C2312yes—
463C2×C4×D4C2312yes—
464C2×C4×D4C2312yes—
465C2×C4×D4C2314yes—
466C2×C4×D4C2314yes—
467C2×C4×D4C2311yescharacteristic
468C2×C4×D4C2312yes—
469C2×C4×D4C2311yescharacteristic
470C2×C4×D4C2311yescharacteristic
471C2×#117C2312yes—
472C2×#117C2314yes—
473C2×#117C2312yes—
474C2×#117C2312yes—
475C2×#117C2312yes—
476C2×#117C2311yescharacteristic
477C2×#117C2311yescharacteristic
478C2×#117C2314yes—
479C2×#117C2314yes—
480C2×#117C2312yes—
481C22×C4⋊C4C2314yes—
482C22×C4⋊C4C2312yes—
483C22×C4⋊C4C2312yes—
484C22×C4⋊C4C2312yes—
485C22×C4⋊C4C2312yes—
486C22×C4⋊C4C2312yes—
487C22×C4⋊C4C2314yes—
488C22×C4⋊C4C2314yes—
489C22×C4⋊C4C2312yes—
490C22×C4⋊C4C2312yes—
491C22×C4⋊C4C2312yes—
492C22×C4⋊C4C2314yes—
493C22×C4⋊C4C2314yes—
494C22×C4⋊C4C2312yes—
495C22×C42C2312yes—
496C22×C42C2312yes—
497C22×C42C2312yes—
498C22×C42C2311yescharacteristic
499C22×C42C2311yescharacteristic
500C22×C42C2314yes—
501C22×C42C2312yes—
502#400C2314yes—
503#400C2314yes—
504#400C2314yes—
505#400C2314yes—
506#400C2312yes—
507#400C2314yes—
508#400C2314yes—
509#400C2314yes—
510#399C2314yes—
511#399C2314yes—
512#399C2312yes—
513#399C2314yes—
514#398C2314yes—
515#398C2314yes—
516#398C2314yes—
517#398C2314yes—
518#398C2312yes—
519#398C2314yes—
520#398C2314yes—
521#398C2314yes—
522#398C2314yes—
523#398C2314yes—
524#398C2314yes—
525#398C2314yes—
526#398C2314yes—
527#398C2314yes—
528#398C2314yes—
529#398C2314yes—
530#398C2314yes—
531#397C2314yes—
532#397C2312yes—
533#397C2314yes—
534#397C2314yes—
535#397C2312yes—
536#397C2312yes—
537#397C2314yes—
538#397C2314yes—
539#397C2314yes—
540#397C2314yes—
541#397C2314yes—
542#396C2314yes—
543#396C2314yes—
544#396C2314yes—
545#396C2314yes—
546#396C2314yes—
547#396C2314yes—
548#396C2314yes—
549#395C2314yes—
550#395C2314yes—
551#395C2314yes—
552#395C2314yes—
553#395C2314yes—
554#395C2312yes—
555#395C2314yes—
556#395C2314yes—
557#395C2314yes—
558#395C2314yes—
559#395C2314yes—
560#395C2314yes—
561#394C2314yes—
562#394C2314yes—
563#394C2314yes—
564#394C2314yes—
565#394C2312yes—
566#394C2312yes—
567#394C2312yes—
568#394C2312yes—
569#394C2312yes—
570#394C2314yes—
571#394C2314yes—
572#393C2314yes—
573#393C2314yes—
574#393C2312yes—
575#393C2314yes—
576#393C2314yes—
577#392C2312yes—
578#392C2312yes—
579#392C2312yes—
580#391C2314yes—
581#391C2311yescharacteristic
582#391C2311yescharacteristic
583#391C2312yes—
584#391C2311yescharacteristic
585#391C2314yes—
586#391C2312yes—
587#391C2314yes—
588#391C2314yes—
589#391C2314yes—
590#391C2312yes—
591#391C2312yes—
592#391C2312yes—
593#391C2314yes—
594#391C2314yes—
595#391C2314yes—
596#391C2314yes—
597#391C2312yes—
598#391C2312yes—
599#391C2312yes—
600#391C2312yes—
601#391C2312yes—
602#391C2312yes—
603#391C2314yes—
604#391C2314yes—
605#391C2314yes—
606#391C2314yes—
607#391C2312yes—
608#391C2312yes—
609#391C2311yescharacteristic
610#391C2311yescharacteristic
611#391C2312yes—
612#391C2312yes—
613#391C2312yes—
614#391C2311yescharacteristic
615#391C2312yes—
616#390C2312yes—
617#390C2312yes—
618#390C2314yes—
619#390C2312yes—
620#390C2311yescharacteristic
621#390C2314yes—
622#390C2312yes—
623#390C2312yes—
624#390C2312yes—
625#390C2311yescharacteristic
626#390C2312yes—
627#389C2312yes—
628#389C2312yes—
629#389C2312yes—
630#389C2312yes—
631#389C2312yes—
632#389C2312yes—
633#389C2312yes—
634#389C2312yes—
635#389C2312yes—
636#389C2314yes—
637#389C2312yes—
638#389C2314yes—
639#389C2312yes—
640#389C2312yes—
641#389C2312yes—
642#389C2312yes—
643#389C2312yes—
644#389C2314yes—
645#389C2311yescharacteristic
646#389C2312yes—
647#389C2311yescharacteristic
648#389C2312yes—
649#389C2314yes—
650#389C2314yes—
651#389C2314yes—
652#389C2314yes—
653#389C2314yes—
654#389C2312yes—
655#389C2314yes—
656#389C2314yes—
657#389C2314yes—
658#389C2311yescharacteristic
659#389C2311yescharacteristic
660#389C2314yes—
661#389C2314yes—
662#389C2312yes—
663#388C2312yes—
664#388C2314yes—
665#388C2314yes—
666#388C2314yes—
667#388C2314yes—
668#388C2314yes—
669#388C2314yes—
670#388C2314yes—
671#388C2314yes—
672#388C2314yes—
673#388C2312yes—
674#388C2312yes—
675#388C2314yes—
676#388C2312yes—
677#388C2312yes—
678#388C2314yes—
679#388C2312yes—
680#388C2314yes—
681#388C2314yes—
682#388C2312yes—
683#388C2312yes—
684#388C2312yes—
685#388C2312yes—
686#388C2312yes—
687#387C2314yes—
688#387C2314yes—
689#387C2314yes—
690#387C2312yes—
691#387C2314yes—
692#387C2312yes—
693#387C2312yes—
694#387C2314yes—
695#387C2312yes—
696#387C2314yes—
697#387C2312yes—
698#387C2314yes—
699#387C2312yes—
700#387C2314yes—
701#387C2314yes—
702#387C2314yes—
703#387C2314yes—
704#387C2312yes—
705#386C2314yes—
706#386C2312yes—
707#386C2314yes—
708#386C2314yes—
709#386C2314yes—
710#386C2314yes—
711#386C2314yes—
712#386C2314yes—
713#386C2314yes—
714#386C2312yes—
715#386C2314yes—
716#386C2314yes—
717#386C2312yes—
718#386C2312yes—
719#386C2312yes—
720#386C2312yes—
721#386C2312yes—
722#386C2314yes—
723#386C2314yes—
724#386C2312yes—
725#386C2314yes—
726#386C2314yes—
727#386C2312yes—
728#386C2314yes—
729#386C2312yes—
730#386C2312yes—
731#385C2314yes—
732#385C2312yes—
733#385C2314yes—
734#385C2312yes—
735#385C2314yes—
736#385C2314yes—
737#385C2314yes—
738#385C2314yes—
739#385C2314yes—
740#385C2314yes—
741#385C2312yes—
742#385C2312yes—
743#385C2314yes—
744#385C2314yes—
745#385C2314yes—
746#385C2314yes—
747#385C2314yes—
748#385C2314yes—
749#385C2314yes—
750#385C2312yes—
751#384C2311yescharacteristic
752#384C2311yescharacteristic
753#384C2312yes—
754#382C2312yes—
755#382C2312yes—
756#382C2312yes—
757#382C2312yes—
758#382C2314yes—
759#382C2314yes—
760#382C2311yescharacteristic
761#381C2312yes—
762#381C2314yes—
763#381C2314yes—
764#381C2314yes—
765#381C2314yes—
766#381C2314yes—
767#381C2314yes—
768#381C2312yes—
769#381C2314yes—
770#381C2314yes—
771#380C2312yes—
772#380C2312yes—
773#380C2311yescharacteristic
774#380C2312yes—
775#380C2312yes—
776#380C2314yes—
777#380C2314yes—
778#380C2314yes—
779#380C2314yes—
780#380C2312yes—
781#380C2311yescharacteristic
782#380C2312yes—
783#380C2314yes—
784#380C2312yes—
785#380C2314yes—
786#380C2314yes—
787#380C2312yes—
788#380C2312yes—
789#380C2312yes—
790#380C2312yes—
791#380C2311yescharacteristic
792#380C2311yescharacteristic
793C4×C4⋊C4C2314yes—
794C4×C4⋊C4C2312yes—
795C4×C4⋊C4C2312yes—
796C4×C4⋊C4C2312yes—
797C4×C4⋊C4C2312yes—
798C4×C4⋊C4C2311yescharacteristic
799C4×C4⋊C4C2311yescharacteristic
800C4×C4⋊C4C2311yescharacteristic
801C4×C4⋊C4C2311yescharacteristic
802C4×C4⋊C4C2312yes—
803C4×C4⋊C4C2312yes—
804C4×C4⋊C4C2311yescharacteristic
805C4×C4⋊C4C2312yes—
806C4×C4⋊C4C2311yescharacteristic
807C4×C4⋊C4C2312yes—
808C4×C4⋊C4C2312yes—
809C4×C4⋊C4C2314yes—
810C4×C4⋊C4C2312yes—
811C4×C4⋊C4C2312yes—
812C4×C4⋊C4C2311yescharacteristic
813C4×C4⋊C4C2312yes—
814C4×C4⋊C4C2312yes—
815C4×C4⋊C4C2311yescharacteristic
816C4×C4⋊C4C2311yescharacteristic
817C4×C22⋊C4C2314yes—
818C4×C22⋊C4C2311yescharacteristic
819C4×C22⋊C4C2314yes—
820C4×C22⋊C4C2314yes—
821C4×C22⋊C4C2314yes—
822C4×C22⋊C4C2312yes—
823C4×C22⋊C4C2312yes—
824C4×C22⋊C4C2312yes—
825C4×C22⋊C4C2312yes—
826C4×C22⋊C4C2311yescharacteristic
827C4×C22⋊C4C2312yes—
828C4×C22⋊C4C2312yes—
829C4×C22⋊C4C2312yes—
830C4×C22⋊C4C2311yescharacteristic
831C4×C22⋊C4C2312yes—
832C4×C22⋊C4C2312yes—
833C4×C22⋊C4C2311yescharacteristic
834C4×C22⋊C4C2314yes—
835C4×C22⋊C4C2312yes—
836C4×C22⋊C4C2312yes—
837C4×C22⋊C4C2311yescharacteristic
838C4×C22⋊C4C2311yescharacteristic
839C4×C22⋊C4C2312yes—
840C2×#95C2312yes—
841C2×#95C2314yes—
842C2×#95C2314yes—
843C2×#95C2314yes—
844C2×#95C2314yes—
845C2×#95C2314yes—
846C2×#95C2314yes—
847C2×#95C2312yes—
848C2×#95C2314yes—
849C43C2311yescharacteristic
8502−1+4—4128no—
851C2×#41—24no—
852C2×#41—24no—
853C2×#41—216no—
854C2×#41—28no—
855C2×#41—216no—
856C2×#41—28no—
857C2×#41—24no—
858C2×#41—216no—
859C2×#41—216no—
860C2×#41—28no—
861C2×#41—28no—
862C2×#41—24no—
863C2×#41—24no—
864C2×#41—28no—
865C2×#41—28no—
866C2×#41—216no—
867C2×#41—28no—
868C2×#41—216no—
869C2×#41—44no—
870C2×#41—48no—
871C2×#41—48no—
872C2×#41—48no—
873C2×#41C2×D4116yes—
874C2×#41#4118yes—
875C22×Q8—28no—
876C22×Q8—28no—
877C22×Q8—28no—
878C22×Q8—28no—
879C22×Q8—216no—
880C22×Q8—28no—
881C22×Q8—216no—
882C22×Q8—28no—
883C22×Q8—48no—
884C22×Q8—44no—
885C22×Q8—44no—
886C22×Q8—44no—
887C22×Q8C2411yescharacteristic
888C22×Q8C2411yescharacteristic
889C22×Q8C2412yes—
890C22×Q8C2414yes—
891C22×Q8C2414yes—
892C22×Q8C2412yes—
893C22×Q8C2414yes—
894C22×Q8C2412yes—
895C22×Q8C2411yescharacteristic
896C22×Q8C2412yes—
897C22×D4C2411yescharacteristic
898C22×D4C2412yes—
899C22×D4C2414yes—
900C22×D4C2412yes—
901C22×D4C2411yescharacteristic
902C22×D4C2412yes—
903C22×D4C2412yes—
904C22×D4C2412yes—
905C22×D4C2411yescharacteristic
906C22×D4C2414yes—
907C22×D4C2412yes—
908C22×D4C2412yes—
909C22×D4C2412yes—
910C22×D4C2411yescharacteristic
911C23×C4C2412yes—
912C23×C4C2414yes—
913C23×C4C2411yescharacteristic
914C23×C4C2411yescharacteristic
915C23×C4C2411yescharacteristic
916C23×C4C2412yes—
917C23×C4C2412yes—
918C23×C4C2414yes—
919C23×C4C2411yescharacteristic
920C23×C4C2412yes—
921C23×C4C2414yes—
922C23×C4C2412yes—
923C23×C4C2414yes—
924C23×C4C2414yes—
925C23×C4C2414yes—
926C23×C4C2412yes—
927C23×C4C2412yes—
928C23×C4C2412yes—
929C23×C4C2411yescharacteristic
930C23×C4C2414yes—
931C23×C4C2412yes—
932C23×C4C2414yes—
933C23×C4C2412yes—
934C23×C4C2411yescharacteristic
935C23×C4C2412yes—
936C4⋊Q8—28no—
937C4⋊Q8—28no—
938C4⋊Q8—24no—
939C4⋊Q8—28no—
940C4⋊Q8—24no—
941C4⋊Q8—28no—
942C4⋊Q8—216no—
943C4⋊Q8—216no—
944C4⋊Q8—28no—
945C4⋊Q8—28no—
946C4⋊Q8—24no—
947C4⋊Q8—24no—
948C4⋊Q8—44no—
949C4⋊Q8C2×D418yes—
950#127—24no—
951#126—216no—
952#126—216no—
953#126—28no—
954#126—216no—
955#125—24no—
956#125—28no—
957#125—216no—
958#125—216no—
959#125—28no—
960#125—28no—
961#125—216no—
962#125—216no—
963#125—28no—
964#124—24no—
965#124—216no—
966#124—28no—
967#124—24no—
968#123—216no—
969#123—216no—
970#123—28no—
971#123—216no—
972#123—216no—
973#123—28no—
974#123—216no—
975#123—28no—
976#123—216no—
977#123—216no—
978#123—216no—
979#123—48no—
980#123—48no—
981#123—48no—
982#123C2×D4132yes—
983C22⋊Q8—28no—
984C22⋊Q8—28no—
985C22⋊Q8—24no—
986C22⋊Q8—28no—
987C22⋊Q8—28no—
988C22⋊Q8—28no—
989C22⋊Q8—24no—
990C22⋊Q8—24no—
991C22⋊Q8—28no—
992C22⋊Q8—28no—
993C22⋊Q8—216no—
994C22⋊Q8—216no—
995C22⋊Q8—24no—
996C22⋊Q8—216no—
997C22⋊Q8—216no—
998C22⋊Q8—216no—
999C22⋊Q8—216no—
1000C22⋊Q8—44no—
1001C22⋊Q8—44no—
1002C22⋊Q8—44no—
1003C22⋊Q8C2×D4116yes—
1004#121—24no—
1005#121—24no—
1006#121—216no—
1007#121—216no—
1008#121—28no—
1009#121—28no—
1010#121—24no—
1011#121—24no—
1012#121—28no—
1013#121—44no—
1014#121—48no—
1015#121C2×D4116yes—
1016C4×Q8—28no—
1017C4×Q8—28no—
1018C4×Q8—24no—
1019C4×Q8—24no—
1020C4×Q8—28no—
1021C4×Q8—28no—
1022C4×Q8—24no—
1023C4×Q8—24no—
1024C4×Q8—24no—
1025C4×Q8—44no—
1026C4×Q8—44no—
1027C4×D4—24no—
1028C4×D4—24no—
1029C4×D4—216no—
1030C4×D4—28no—
1031C4×D4—216no—
1032C4×D4—28no—
1033C4×D4—28no—
1034C4×D4—24no—
1035C4×D4—24no—
1036C4×D4—28no—
1037C4×D4—28no—
1038C4×D4—28no—
1039C4×D4—28no—
1040C4×D4—28no—
1041C4×D4—24no—
1042C4×D4—28no—
1043C4×D4—24no—
1044C4×D4—28no—
1045C4×D4—28no—
1046C4×D4—216no—
1047C4×D4—24no—
1048C4×D4—24no—
1049C4×D4—24no—
1050C4×D4—44no—
1051C4×D4—42no—
1052C4×D4—48no—
1053C4×D4—48no—
1054C4×D4C2×D418yes—
1055C4×D4C2×D418yes—
1056#117—28no—
1057#117—216no—
1058#117—24no—
1059#117—24no—
1060#117—28no—
1061#117—28no—
1062#117—28no—
1063#117—216no—
1064#117—48no—
1065#117—44no—
1066C2×C4⋊C4—216no—
1067C2×C4⋊C4—28no—
1068C2×C4⋊C4—216no—
1069C2×C4⋊C4—28no—
1070C2×C4⋊C4—216no—
1071C2×C4⋊C4—28no—
1072C2×C4⋊C4—28no—
1073C2×C4⋊C4—28no—
1074C2×C4⋊C4—28no—
1075C2×C4⋊C4—28no—
1076C2×C4⋊C4—44no—
1077C2×C4⋊C4—48no—
1078C2×C4⋊C4—48no—
1079C2×C4⋊C4C2×D4116yes—
1080C2×C4⋊C4C2411yescharacteristic
1081C2×C4⋊C4C2414yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2411yescharacteristic
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2412yes—
1087C2×C4⋊C4C2412yes—
1088C2×C4⋊C4C2411yescharacteristic
1089C2×C4⋊C4C2411yescharacteristic
1090C2×C4⋊C4C2411yescharacteristic
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2412yes—
1093C2×C4⋊C4C2414yes—
1094C2×C4⋊C4C2412yes—
1095C2×C4⋊C4C2414yes—
1096C2×C4⋊C4C2414yes—
1097C2×C4⋊C4C2414yes—
1098C2×C4⋊C4C2412yes—
1099C2×C4⋊C4C2412yes—
1100C2×C4⋊C4C2414yes—
1101C2×C4⋊C4C2414yes—
1102C2×C4⋊C4C2414yes—
1103C2×C4⋊C4C2414yes—
1104C2×C4⋊C4C2414yes—
1105C2×C4⋊C4C2414yes—
1106C2×C4⋊C4C2412yes—
1107C2×C4⋊C4C2412yes—
1108C2×C4⋊C4C2414yes—
1109C2×C4⋊C4C2412yes—
1110C2×C4⋊C4C2412yes—
1111C2×C4⋊C4C2414yes—
1112C2×C4⋊C4C2412yes—
1113C2×C4⋊C4C2411yescharacteristic
1114C2×C4⋊C4C2411yescharacteristic
1115C2×C4⋊C4C2412yes—
1116C2×C4⋊C4C2412yes—
1117C2×C4⋊C4C2412yes—
1118C2×C4⋊C4C2412yes—
1119C2×C4⋊C4C2412yes—
1120C2×C4⋊C4C2414yes—
1121C2×C4⋊C4C2411yescharacteristic
1122C2×C4⋊C4C2411yescharacteristic
1123C2×C4⋊C4C2411yescharacteristic
1124C2×C4⋊C4C2412yes—
1125C2×C4⋊C4C2414yes—
1126C2×C4⋊C4C2412yes—
1127C2×C4⋊C4C2412yes—
1128C2×C4⋊C4C2412yes—
1129C2×C4⋊C4C2414yes—
1130C2×C4⋊C4C2414yes—
1131C2×C4⋊C4C2414yes—
1132C2×C4⋊C4C2412yes—
1133C2×C4⋊C4C2412yes—
1134C2×C4⋊C4C2414yes—
1135C2×C4⋊C4C2414yes—
1136C2×C4⋊C4C2414yes—
1137C2×C4⋊C4C2414yes—
1138C2×C4⋊C4C2412yes—
1139C2×C4⋊C4C2414yes—
1140C2×C4⋊C4C2412yes—
1141C2×C4⋊C4C2414yes—
1142C2×C4⋊C4C2412yes—
1143C2×C4⋊C4C2411yescharacteristic
1144C2×C4⋊C4C2412yes—
1145C2×C4⋊C4C2414yes—
1146C2×C4⋊C4C2411yescharacteristic
1147C2×C4⋊C4C2411yescharacteristic
1148C2×C22⋊C4C2412yes—
1149C2×C22⋊C4C2412yes—
1150C2×C22⋊C4C2412yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2412yes—
1154C2×C22⋊C4C2412yes—
1155C2×C22⋊C4C2412yes—
1156C2×C22⋊C4C2414yes—
1157C2×C22⋊C4C2412yes—
1158C2×C22⋊C4C2414yes—
1159C2×C22⋊C4C2411yescharacteristic
1160C2×C22⋊C4C2414yes—
1161C2×C22⋊C4C2412yes—
1162C2×C22⋊C4C2412yes—
1163C2×C22⋊C4C2414yes—
1164C2×C22⋊C4C2414yes—
1165C2×C22⋊C4C2412yes—
1166C2×C22⋊C4C2414yes—
1167C2×C22⋊C4C2412yes—
1168C2×C22⋊C4C2412yes—
1169C2×C22⋊C4C2411yescharacteristic
1170C2×C22⋊C4C2411yescharacteristic
1171C2×C22⋊C4C2411yescharacteristic
1172C2×C22⋊C4C2412yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2411yescharacteristic
1175C2×C22⋊C4C2412yes—
1176C2×C22⋊C4C2412yes—
1177C2×C22⋊C4C2412yes—
1178C2×C22⋊C4C2412yes—
1179C2×C22⋊C4C2412yes—
1180C2×C22⋊C4C2412yes—
1181C2×C22⋊C4C2414yes—
1182C2×C22⋊C4C2412yes—
1183C2×C22⋊C4C2412yes—
1184C2×C22⋊C4C2411yescharacteristic
1185C2×C22⋊C4C2414yes—
1186C2×C22⋊C4C2414yes—
1187C2×C22⋊C4C2412yes—
1188C2×C22⋊C4C2414yes—
1189C2×C22⋊C4C2414yes—
1190C2×C22⋊C4C2414yes—
1191C2×C22⋊C4C2414yes—
1192C2×C22⋊C4C2412yes—
1193C2×C22⋊C4C2412yes—
1194C2×C22⋊C4C2412yes—
1195C2×C22⋊C4C2414yes—
1196C2×C22⋊C4C2412yes—
1197C2×C22⋊C4C2412yes—
1198C2×C22⋊C4C2412yes—
1199C2×C22⋊C4C2414yes—
1200C2×C22⋊C4C2412yes—
1201C2×C42—28no—
1202C2×C42—28no—
1203C2×C42—24no—
1204C2×C42—24no—
1205C2×C42—28no—
1206C2×C42—44no—
1207C2×C42—48no—
1208C2×C42C2412yes—
1209C2×C42C2411yescharacteristic
1210C2×C42C2414yes—
1211C2×C42C2414yes—
1212C2×C42C2411yescharacteristic
1213C2×C42C2411yescharacteristic
1214C2×C42C2412yes—
1215C2×C42C2412yes—
1216C2×C42C2411yescharacteristic
1217C2×C42C2412yes—
1218C2×C42C2412yes—
1219C2×C42C2412yes—
1220C2×C42C2412yes—
1221C2×C42C2411yescharacteristic
1222C2×C42C2411yescharacteristic
1223C2×C42C2412yes—
1224C2×C42C2411yescharacteristic
1225C2×C42C2411yescharacteristic
1226C2×C42C2411yescharacteristic
1227C2×C42C2412yes—
1228C2×C42C2412yes—
1229C2×C42C2412yes—
1230C2×C42C2412yes—
1231C2×C42C2414yes—
1232C2×C42C2414yes—
1233C2×C42C2414yes—
1234C2×C42C2411yescharacteristic
1235C2×C42C2411yescharacteristic
1236C2×C42C2412yes—
1237C2×C42C2411yescharacteristic
1238C2×C42C2411yescharacteristic
1239#95C2412yes—
1240#95C2411yescharacteristic
1241#95C2411yescharacteristic
1242#95C2412yes—
1243#95C2414yes—
1244#95C2412yes—
1245#95C2412yes—
1246#95C2414yes—
1247#95C2414yes—
1248#95C2412yes—
1249#95C2412yes—
1250#95C2412yes—
1251#95C2412yes—
1252#95C2412yes—
1253#95C2412yes—
1254#95C2412yes—
1255#95C2414yes—
1256#95C2414yes—
1257#95C2414yes—
1258#95C2412yes—
1259#95C2414yes—
1260#95C2414yes—
1261#95C2414yes—
1262#95C2414yes—
1263#95C2414yes—
1264#95C2414yes—
1265#95C2414yes—
1266#95C2414yes—
1267#95C2414yes—
1268#95C2414yes—
1269#95C2414yes—
1270#95C2414yes—
1271#95C2412yes—
1272#95C2411yescharacteristic
1273#95C2411yescharacteristic
1274#95C2412yes—
1275#95C2412yes—
1276#95C2411yescharacteristic
1277#95C2412yes—
1278#95C2412yes—
1279#95C2411yescharacteristic
1280#95C2412yes—
1281#95C2412yes—
1282#95C2412yes—
1283#95C2414yes—
1284#95C2412yes—
1285#95C2412yes—
1286#95C2414yes—
1287#95C2414yes—
1288#95C2412yes—
1289#95C2414yes—
1290#95C2412yes—
1291#95C2414yes—
1292#95C2412yes—
1293#95C2412yes—
1294#95C2412yes—
1295#95C2414yes—
1296#95C2412yes—
1297#95C2414yes—
1298#95C2414yes—
1299#95C2414yes—
1300#95C2414yes—
1301C24C2511yescharacteristic
1302C24C2512yes—
1303C24C2512yes—
1304C24C2511yescharacteristic
1305C24C2512yes—
1306#41—264no—
1307#41—232no—
1308#41—432no—
1309#41—464no—
1310#41—464no—
1311#41—464no—
1312#41—416no—
1313#41—432no—
1314C2×Q8—22no—
1315C2×Q8—22no—
1316C2×Q8—22no—
1317C2×Q8—28no—
1318C2×Q8—28no—
1319C2×Q8—24no—
1320C2×Q8—28no—
1321C2×Q8—24no—
1322C2×Q8—24no—
1323C2×Q8—24no—
1324C2×Q8—22no—
1325C2×Q8—28no—
1326C2×Q8—28no—
1327C2×Q8—24no—
1328C2×Q8—28no—
1329C2×Q8—24no—
1330C2×Q8—24no—
1331C2×Q8—22no—
1332C2×Q8—22no—
1333C2×Q8—24no—
1334C2×Q8—22no—
1335C2×Q8—22no—
1336C2×Q8—42no—
1337C2×Q8—44no—
1338C2×Q8—44no—
1339C2×Q8—44no—
1340C2×Q8—42no—
1341C2×Q8—42no—
1342C2×Q8—464no—
1343C2×Q8—432no—
1344C2×Q8—432no—
1345C2×Q8—432no—
1346C2×Q8C22×D418yes—
1347C2×Q8C2×#4114yes—
1348C2×D4—24no—
1349C2×D4—28no—
1350C2×D4—28no—
1351C2×D4—24no—
1352C2×D4—24no—
1353C2×D4—24no—
1354C2×D4—24no—
1355C2×D4—28no—
1356C2×D4—24no—
1357C2×D4—22no—
1358C2×D4—24no—
1359C2×D4—24no—
1360C2×D4—24no—
1361C2×D4—28no—
1362C2×D4—24no—
1363C2×D4—28no—
1364C2×D4—24no—
1365C2×D4—22no—
1366C2×D4—24no—
1367C2×D4—24no—
1368C2×D4—22no—
1369C2×D4—22no—
1370C2×D4—22no—
1371C2×D4—22no—
1372C2×D4—22no—
1373C2×D4—24no—
1374C2×D4—24no—
1375C2×D4—41no—
1376C2×D4—42no—
1377C2×D4—42no—
1378C2×D4—42no—
1379C2×D4—42no—
1380C2×D4—42no—
1381C2×D4—42no—
1382C2×D4—42no—
1383C2×D4—42no—
1384C2×D4C22×D414yes—
1385C2×D4C22×D4116yes—
1386C2×D4C22×D414yes—
1387C2×D4C2×#4118yes—
1388C2×D4C2×#4114yes—
1389C2×D4H(5,𝔽2)14yes—
1390C22×C4—24no—
1391C22×C4—28no—
1392C22×C4—28no—
1393C22×C4—24no—
1394C22×C4—22no—
1395C22×C4—24no—
1396C22×C4—24no—
1397C22×C4—22no—
1398C22×C4—24no—
1399C22×C4—24no—
1400C22×C4—24no—
1401C22×C4—24no—
1402C22×C4—28no—
1403C22×C4—28no—
1404C22×C4—24no—
1405C22×C4—24no—
1406C22×C4—28no—
1407C22×C4—28no—
1408C22×C4—24no—
1409C22×C4—28no—
1410C22×C4—24no—
1411C22×C4—28no—
1412C22×C4—24no—
1413C22×C4—28no—
1414C22×C4—28no—
1415C22×C4—22no—
1416C22×C4—22no—
1417C22×C4—22no—
1418C22×C4—22no—
1419C22×C4—28no—
1420C22×C4—28no—
1421C22×C4—24no—
1422C22×C4—22no—
1423C22×C4—28no—
1424C22×C4—28no—
1425C22×C4—24no—
1426C22×C4—22no—
1427C22×C4—24no—
1428C22×C4—24no—
1429C22×C4—24no—
1430C22×C4—28no—
1431C22×C4—22no—
1432C22×C4—22no—
1433C22×C4—22no—
1434C22×C4—22no—
1435C22×C4—24no—
1436C22×C4—22no—
1437C22×C4—22no—
1438C22×C4—24no—
1439C22×C4—24no—
1440C22×C4—42no—
1441C22×C4—44no—
1442C22×C4—42no—
1443C22×C4—41no—
1444C22×C4—42no—
1445C22×C4—44no—
1446C22×C4—44no—
1447C22×C4—44no—
1448C22×C4—42no—
1449C22×C4—42no—
1450C22×C4—42no—
1451C22×C4—44no—
1452C22×C4—41no—
1453C22×C4—42no—
1454C22×C4—44no—
1455C22×C4—42no—
1456C22×C4—41no—
1457C22×C4—42no—
1458C22×C4—44no—
1459C22×C4—44no—
1460C22×C4C22×D418yes—
1461C22×C4C22×D4116yes—
1462C22×C4C22×D418yes—
1463C22×C4C2×#4118yes—
1464C22×C4C2×#4114yes—
1465C22×C4C2511yescharacteristic
1466C22×C4C2512yes—
1467C22×C4C2512yes—
1468C22×C4C2511yescharacteristic
1469C22×C4C2512yes—
1470C22×C4C2511yescharacteristic
1471C22×C4C2512yes—
1472C22×C4C2511yescharacteristic
1473C22×C4C2514yes—
1474C22×C4C2512yes—
1475C22×C4C2514yes—
1476C22×C4C2512yes—
1477C22×C4C2511yescharacteristic
1478C22×C4C2514yes—
1479C22×C4C2512yes—
1480C22×C4C2512yes—
1481C22×C4C2511yescharacteristic
1482C22×C4C2512yes—
1483C22×C4C2512yes—
1484C22×C4C2511yescharacteristic
1485C22×C4C2512yes—
1486C22×C4C2514yes—
1487C22×C4C2511yescharacteristic
1488C22×C4C2512yes—
1489C22×C4C2511yescharacteristic
1490C22×C4C2511yescharacteristic
1491C22×C4C2512yes—
1492C22×C4C2511yescharacteristic
1493C22×C4C2511yescharacteristic
1494C22×C4C2511yescharacteristic
1495C4⋊C4—22no—
1496C4⋊C4—28no—
1497C4⋊C4—24no—
1498C4⋊C4—28no—
1499C4⋊C4—24no—
1500C4⋊C4—22no—
1501C4⋊C4—24no—
1502C4⋊C4—24no—
1503C4⋊C4—22no—
1504C4⋊C4—24no—
1505C4⋊C4—28no—
1506C4⋊C4—24no—
1507C4⋊C4—28no—
1508C4⋊C4—28no—
1509C4⋊C4—28no—
1510C4⋊C4—28no—
1511C4⋊C4—28no—
1512C4⋊C4—28no—
1513C4⋊C4—28no—
1514C4⋊C4—24no—
1515C4⋊C4—28no—
1516C4⋊C4—28no—
1517C4⋊C4—24no—
1518C4⋊C4—24no—
1519C4⋊C4—24no—
1520C4⋊C4—22no—
1521C4⋊C4—24no—
1522C4⋊C4—24no—
1523C4⋊C4—28no—
1524C4⋊C4—24no—
1525C4⋊C4—28no—
1526C4⋊C4—22no—
1527C4⋊C4—24no—
1528C4⋊C4—24no—
1529C4⋊C4—24no—
1530C4⋊C4—22no—
1531C4⋊C4—24no—
1532C4⋊C4—22no—
1533C4⋊C4—24no—
1534C4⋊C4—28no—
1535C4⋊C4—24no—
1536C4⋊C4—22no—
1537C4⋊C4—22no—
1538C4⋊C4—24no—
1539C4⋊C4—22no—
1540C4⋊C4—24no—
1541C4⋊C4—28no—
1542C4⋊C4—24no—
1543C4⋊C4—42no—
1544C4⋊C4—42no—
1545C4⋊C4—44no—
1546C4⋊C4—42no—
1547C4⋊C4—44no—
1548C4⋊C4—44no—
1549C4⋊C4—44no—
1550C4⋊C4—44no—
1551C4⋊C4—42no—
1552C4⋊C4—44no—
1553C4⋊C4—44no—
1554C4⋊C4—44no—
1555C4⋊C4—42no—
1556C4⋊C4—44no—
1557C4⋊C4C22×D418yes—
1558C4⋊C4C22×D418yes—
1559C4⋊C4C22×D414yes—
1560C4⋊C4C22×D4116yes—
1561C4⋊C4C22×D414yes—
1562C4⋊C42−1+414yescomplemented
1563C22⋊C4—24no—
1564C22⋊C4—24no—
1565C22⋊C4—24no—
1566C22⋊C4—28no—
1567C22⋊C4—24no—
1568C22⋊C4—24no—
1569C22⋊C4—28no—
1570C22⋊C4—24no—
1571C22⋊C4—28no—
1572C22⋊C4—24no—
1573C22⋊C4—22no—
1574C22⋊C4—24no—
1575C22⋊C4—24no—
1576C22⋊C4—28no—
1577C22⋊C4—24no—
1578C22⋊C4—24no—
1579C22⋊C4—28no—
1580C22⋊C4—28no—
1581C22⋊C4—24no—
1582C22⋊C4—28no—
1583C22⋊C4—24no—
1584C22⋊C4—24no—
1585C22⋊C4—22no—
1586C22⋊C4—24no—
1587C22⋊C4—24no—
1588C22⋊C4—24no—
1589C22⋊C4—22no—
1590C22⋊C4—22no—
1591C22⋊C4—24no—
1592C22⋊C4—24no—
1593C22⋊C4—24no—
1594C22⋊C4—24no—
1595C22⋊C4—22no—
1596C22⋊C4—42no—
1597C22⋊C4—42no—
1598C22⋊C4—42no—
1599C22⋊C4—44no—
1600C22⋊C4—42no—
1601C22⋊C4—42no—
1602C22⋊C4—44no—
1603C22⋊C4—41no—
1604C22⋊C4—42no—
1605C22⋊C4—42no—
1606C22⋊C4—42no—
1607C22⋊C4—44no—
1608C22⋊C4—44no—
1609C22⋊C4—44no—
1610C22⋊C4—44no—
1611C22⋊C4—44no—
1612C22⋊C4—44no—
1613C22⋊C4C22×D418yes—
1614C22⋊C4C22×D4116yes—
1615C22⋊C4C22×D418yes—
1616C42—22no—
1617C42—22no—
1618C42—24no—
1619C42—22no—
1620C42—22no—
1621C42—24no—
1622C42—22no—
1623C42—24no—
1624C42—22no—
1625C42—24no—
1626C42—24no—
1627C42—24no—
1628C42—28no—
1629C42—28no—
1630C42—24no—
1631C42—22no—
1632C42—22no—
1633C42—24no—
1634C42—24no—
1635C42—24no—
1636C42—24no—
1637C42—22no—
1638C42—42no—
1639C42—42no—
1640C42—44no—
1641C42—44no—
1642C42—44no—
1643C42—41no—
1644C42—41no—
1645C42C22×D414yes—
1646C422−1+414yescomplemented
1647C23—22no—
1648C23—22no—
1649C23—22no—
1650C23—22no—
1651C23—21no—
1652C23—22no—
1653C23—22no—
1654C23—21no—
1655C23—21no—
1656C23—22no—
1657C23—22no—
1658C23—21no—
1659C23—21no—
1660C23—22no—
1661C23—21no—
1662C23—22no—
1663C23—21no—
1664C23—22no—
1665C23—21no—
1666C23—22no—
1667C23—21no—
1668C23—22no—
1669C23—22no—
1670C23—21no—
1671C23—22no—
1672C23—21no—
1673C23—21no—
1674C23—22no—
1675C23—22no—
1676C23—21no—
1677C23C23×D414yes—
1678C23C23×D414yes—
1679C23C22×#4112yes—
1680C23C22×#4114yes—
1681C23C2×H(5,𝔽2)14yes—
1682C23C2611yescharacteristic
1683Q8—28no—
1684Q8—216no—
1685Q8—48no—
1686Q8—416no—
1687Q8—416no—
1688Q8—416no—
1689Q8—48no—
1690Q8—44no—
1691Q8—44no—
1692Q8—84no—
1693D4—232no—
1694D4—216no—
1695D4—28no—
1696D4—48no—
1697D4—44no—
1698D4—48no—
1699D4—48no—
1700D4—48no—
1701D4—48no—
1702D4—416no—
1703D4—44no—
1704D4—84no—
1705D4—84no—
1706D4#546116yes—
1707C2×C4—21no—
1708C2×C4—21no—
1709C2×C4—22no—
1710C2×C4—21no—
1711C2×C4—22no—
1712C2×C4—24no—
1713C2×C4—21no—
1714C2×C4—22no—
1715C2×C4—22no—
1716C2×C4—24no—
1717C2×C4—21no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—22no—
1721C2×C4—21no—
1722C2×C4—21no—
1723C2×C4—22no—
1724C2×C4—21no—
1725C2×C4—21no—
1726C2×C4—21no—
1727C2×C4—232no—
1728C2×C4—216no—
1729C2×C4—216no—
1730C2×C4—28no—
1731C2×C4—216no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—22no—
1735C2×C4—21no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—21no—
1739C2×C4—22no—
1740C2×C4—24no—
1741C2×C4—22no—
1742C2×C4—22no—
1743C2×C4—24no—
1744C2×C4—21no—
1745C2×C4—22no—
1746C2×C4—21no—
1747C2×C4—22no—
1748C2×C4—22no—
1749C2×C4—24no—
1750C2×C4—21no—
1751C2×C4—22no—
1752C2×C4—22no—
1753C2×C4—24no—
1754C2×C4—21no—
1755C2×C4—22no—
1756C2×C4—22no—
1757C2×C4—24no—
1758C2×C4—22no—
1759C2×C4—22no—
1760C2×C4—21no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—22no—
1764C2×C4—21no—
1765C2×C4—21no—
1766C2×C4—22no—
1767C2×C4—22no—
1768C2×C4—24no—
1769C2×C4—21no—
1770C2×C4—21no—
1771C2×C4—22no—
1772C2×C4—24no—
1773C2×C4—22no—
1774C2×C4—24no—
1775C2×C4—21no—
1776C2×C4—22no—
1777C2×C4—22no—
1778C2×C4—21no—
1779C2×C4—22no—
1780C2×C4—22no—
1781C2×C4—21no—
1782C2×C4—22no—
1783C2×C4—22no—
1784C2×C4—22no—
1785C2×C4—24no—
1786C2×C4—44no—
1787C2×C4—416no—
1788C2×C4—48no—
1789C2×C4—416no—
1790C2×C4—48no—
1791C2×C4—48no—
1792C2×C4—416no—
1793C2×C4—416no—
1794C2×C4—416no—
1795C2×C4—48no—
1796C2×C4—48no—
1797C2×C4—44no—
1798C2×C4—44no—
1799C2×C4—44no—
1800C2×C4—82no—
1801C2×C4—84no—
1802C2×C4—84no—
1803C2×C4—84no—
1804C2×C4—88no—
1805C2×C4—88no—
1806C2×C4C23×D414yes—
1807C2×C4C23×D412yes—
1808C2×C4C23×D418yes—
1809C2×C4C23×D414yes—
1810C2×C4C23×D412yes—
1811C2×C4C23×D412yes—
1812C2×C4C22×#4114yes—
1813C2×C4C22×#4112yes—
1814C2×C4C22×#4112yes—
1815C2×C4C2×H(5,𝔽2)12yes—
1816C2×C4C2×2−1+412yes—
1817C2×C4C2×2−1+412yes—
1818C2×C4C2×2−1+414yes—
1819C2×C4C2×2−1+412yes—
1820C2×C4C2×2−1+412yes—
1821C2×C4#58512yes—
1822C22—24no—
1823C22—24no—
1824C22—24no—
1825C22—24no—
1826C22—24no—
1827C22—24no—
1828C22—22no—
1829C22—24no—
1830C22—24no—
1831C22—22no—
1832C22—22no—
1833C22—24no—
1834C22—42no—
1835C22—41no—
1836C22—42no—
1837C22—41no—
1838C22—41no—
1839C22—42no—
1840C22—42no—
1841C22—41no—
1842C22—41no—
1843C22—42no—
1844C22—41no—
1845C22—42no—
1846C22—41no—
1847C22—42no—
1848C22—41no—
1849C22—42no—
1850C22—41no—
1851C22—42no—
1852C22—41no—
1853C22—42no—
1854C22—42no—
1855C22—41no—
1856C22C2×#54618yes—
1857C22C24×D411yescharacteristic
1858C22C23×#4111yescharacteristic
1859C22C22×H(5,𝔽2)11yescharacteristic
1860C22C22×2−1+411yescharacteristic
1861C22C22×2−1+411yescharacteristic
1862C22C2×#58511yescharacteristic
1863C222−1+611yescharacteristic
1864C4—22no—
1865C4—22no—
1866C4—24no—
1867C4—24no—
1868C4—22no—
1869C4—22no—
1870C4—24no—
1871C4—22no—
1872C4—24no—
1873C4—28no—
1874C4—41no—
1875C4—42no—
1876C4—42no—
1877C4—41no—
1878C4—42no—
1879C4—44no—
1880C4—44no—
1881C4—41no—
1882C4—41no—
1883C4—41no—
1884C4—42no—
1885C4—42no—
1886C4—42no—
1887C4—42no—
1888C4—41no—
1889C4—42no—
1890C4—44no—
1891C4—42no—
1892C4C2×#54614yes—
1893C4#349914yes—
1894C2—28no—
1895C2—42no—
1896C2—44no—
1897C2—81no—
1898C2—82no—
1899C2C22×#54611yescharacteristic
1900C2C2×#349911yescharacteristic
1901C2#6280511yescharacteristic
1902C2#6291511yescharacteristic
1903C2#6300111yescharacteristic
1904C2#6300211yescharacteristic
1905C2#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. C2×#3499C2semidirect
2. C2×#3515C2semidirect
3. #59801C2semidirect
4. #59651C2semidirect
5. #59413C2semidirect
6. #59318C2semidirect
7. #59144C2semidirect
8. #59110C2semidirect
9. #59036C2semidirect
10. #59031C2semidirect
11. #45322C2semidirect
12. #45237C2semidirect
13. #44761C2semidirect
14. #43974C2semidirect
15. #39470C2semidirect
16. #39465C2semidirect
17. #39435C2semidirect
18. #39431C2semidirect
19. #38911C2semidirect
20. #38907C2semidirect
21. #36424C2semidirect
22. #36276C2semidirect
23. #36275C2semidirect
24. #36259C2semidirect
25. #36259C2semidirect
26. #36164C2semidirect
27. #36139C2semidirect
28. #36129C2semidirect
29. #36085C2semidirect
30. #35998C2semidirect
31. #34889C2semidirect
32. C2×#2550C2semidirect
33. #34259C2semidirect
34. C4×#547C2semidirect
35. C4×#547C2semidirect
334. #547D4semidirect
1562. C4⋊C42−1+4semidirect
1646. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#35152
#598012
#596512
#594132
#593182
#591442
#591102
#590362
#590312
#453222
#452372
#447612
#439742
#394702
#394652
#394352
#394312
#389112
#389072
#364242
#362762
#362752
#362592
#361642
#361392
#361292
#360852
#359982
#348892
C2×#25502
#342592
C4×#5472