Finite Group Databasebeta

← #7698358

Subgroups — #7698358

Order 512.

10879 conjugacy classes of subgroups.

The subgroup lattice has 1869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C212yesmaximal, complemented
2C2×#3485C212yesmaximal, complemented
3#59818C211yesmaximal, characteristic, complemented
4#59313C212yesmaximal, complemented
5#59002C212yesmaximal, complemented
6#58995C214yesmaximal, complemented
7#52103C211yesmaximal, characteristic, complemented
8C2×#2680C212yesmaximal, complemented
9#45332C212yesmaximal, complemented
10#45321C211yesmaximal, characteristic, complemented
11#45134C212yesmaximal, complemented
12#45103C211yesmaximal, characteristic, complemented
13#44758C212yesmaximal, complemented
14#44447C214yesmaximal, complemented
15#43492C214yesmaximal, complemented
16#43017C212yesmaximal, complemented
17#39360C212yesmaximal, complemented
18#39354C214yesmaximal, complemented
19#37656C212yesmaximal, complemented
20#37654C214yesmaximal, complemented
21#37651C212yesmaximal, complemented
22#37647C214yesmaximal, complemented
23#36213C212yesmaximal, complemented
24#36179C211yesmaximal, characteristic, complemented
25#36085C211yesmaximal, characteristic, complemented
26#36020C212yesmaximal, complemented
27#36009C212yesmaximal, complemented
28#35750C211yesmaximal, characteristic, complemented
29#34309C212yesmaximal, complemented
30C22×2−1+4C2211yescharacteristic, complemented
31C22×H(5,𝔽2)C2211yescharacteristic
32C23×#41C2212yescomplemented
33#3489—232no—
34#3485—232no—
35C2×D4×Q8C2212yescomplemented
36C2×D4×Q8C2212yescomplemented
37C2×#548C2212yescomplemented
38C2×#548C2212yescomplemented
39C2×#547C2212yes—
40C2×#547C2212yes—
41C2×#547C2212yescomplemented
42C2×#547C2214yescomplemented
43C2×#547C2214yescomplemented
44C2×#547C2212yescomplemented
45C2×#547C2212yescomplemented
46C2×#547C2214yescomplemented
47C2×#547C2212yescomplemented
48C2×#547C2214yescomplemented
49C2×#547C2211yescharacteristic, complemented
50C2×#547C2211yescharacteristic, complemented
51C2×#546C2214yes—
52C2×#546C2214yes—
53C2×#546C2212yes—
54C2×#546C2212yes—
55C2×#546C2214yescomplemented
56C2×#546C2214yescomplemented
57C2×#546C2212yescomplemented
58C2×#546C2212yescomplemented
59C2×#546C2212yescomplemented
60C2×#537C2212yescomplemented
61C2×#537C2214yescomplemented
62C2×#536C2212yes—
63C2×#536C2214yescomplemented
64C2×#536C2212yescomplemented
65C2×#536C2212yescomplemented
66C2×#534C2214yes—
67C2×#534C2214yescomplemented
68C2×#525C2212yes—
69C2×#525C2214yescomplemented
70C2×#525C2212yescomplemented
71C2×#525C2212yescomplemented
72C22×#123C2214yes—
73C22×#123C2214yescomplemented
74C22×C22⋊Q8C2214yescomplemented
75C22×C22⋊Q8C2212yescomplemented
76C2×#520C2212yescomplemented
77C2×#518C2212yescomplemented
78#2868C2211yescharacteristic, complemented
79#2856C2212yescomplemented
80#2849C2214yescomplemented
81#2848C2212yescomplemented
82#2683C2211yescharacteristic, complemented
83#2682C2212yescomplemented
84#2681C2212yescomplemented
85#2681C2214yescomplemented
86#2681C2214yescomplemented
87#2681C2212yescomplemented
88#2680C2212yescomplemented
89#2680C2214yescomplemented
90#2680C2214yescomplemented
91#2680C2214yescomplemented
92#2680C2214yescomplemented
93#2680C2212yescomplemented
94#2680C2214yescomplemented
95#2680C2214yescomplemented
96#2680C2211yescharacteristic, complemented
97#2680C2212yescomplemented
98#2680C2214yescomplemented
99#2680C2211yescharacteristic, complemented
100#2680C2214yescomplemented
101#2680C2214yescomplemented
102#2679C2211yescharacteristic, complemented
103#2678C2212yescomplemented
104#2678C2214yescomplemented
105#2678C2214yescomplemented
106#2678C2212yescomplemented
107#2677C2212yescomplemented
108#2677C2214yescomplemented
109#2674C2214yescomplemented
110#2674C2214yescomplemented
111#2674C2214yescomplemented
112#2672C2214yescomplemented
113#2672C2214yescomplemented
114#2672C2214yescomplemented
115#2671C2214yescomplemented
116#2671C2214yescomplemented
117#2671C2214yescomplemented
118#2669C2212yescomplemented
119#2669C2212yescomplemented
120#2668C2214yescomplemented
121#2668C2212yescomplemented
122#2621C2212yescomplemented
123#2621C2212yescomplemented
124#2618C2214yescomplemented
125#2617C2214yescomplemented
126#2616C2211yescharacteristic
127#2616C2211yescharacteristic, complemented
128#2614C2212yescomplemented
129#2613C2212yes—
130#2555C2212yescomplemented
131#2551C2212yescomplemented
132#2547C2212yescomplemented
133#2546C2212yescomplemented
134#2543C2214yescomplemented
135#2543C2214yescomplemented
136#2542C2211yescharacteristic, complemented
137#2542C2212yescomplemented
138#2542C2212yescomplemented
139#2542C2211yescharacteristic, complemented
140#2537C2212yescomplemented
141#2536C2212yescomplemented
142#2535C2212yescomplemented
143#2501C2212yescomplemented
144#2501C2214yescomplemented
145#2501C2214yescomplemented
146#2501C2212yescomplemented
147#2486C2214yescomplemented
148#2486C2214yescomplemented
149#2472C2214yescomplemented
150#2472C2214yescomplemented
151#2472C2214yescomplemented
152#2464C2214yescomplemented
153#2464C2214yescomplemented
154#2464C2214yescomplemented
155#2461C2214yescomplemented
156#2461C2214yescomplemented
157#2455C2212yescomplemented
158#2455C2214yescomplemented
159#2449C2214yescomplemented
160#2449C2214yescomplemented
161#2449C2214yescomplemented
162#2443C2214yescomplemented
163#2443C2214yescomplemented
164#2443C2214yescomplemented
165#2440C2214yescomplemented
166#2440C2214yescomplemented
167#2440C2214yescomplemented
168#2440C2214yescomplemented
169#2437C2212yescomplemented
170#2437C2214yescomplemented
171#2435C2211yescharacteristic, complemented
172#2434C2212yescomplemented
173#2434C2211yescharacteristic, complemented
174#2434C2212yescomplemented
175#2432C2212yescomplemented
176#2432C2212yescomplemented
177#2432C2212yescomplemented
178#2430C2214yescomplemented
179#2430C2214yescomplemented
180#2430C2214yescomplemented
181#2430C2212yescomplemented
182#2430C2212yescomplemented
183#2429C2212yescomplemented
184#2429C2212yescomplemented
185#2427C2212yescomplemented
186#2427C2212yescomplemented
187#2425C2214yescomplemented
188#2425C2214yescomplemented
189#2425C2214yescomplemented
190#2425C2214yescomplemented
191#2424C2214yescomplemented
192#2424C2214yescomplemented
193#2422C2214yescomplemented
194#2422C2214yescomplemented
195#2422C2214yescomplemented
196#2422C2214yescomplemented
197#2418C2214yescomplemented
198#2418C2214yescomplemented
199#2418C2214yescomplemented
200#2417C2212yescomplemented
201#2417C2212yescomplemented
202#2415C2212yescomplemented
203#2415C2212yescomplemented
204#2413C2214yescomplemented
205#2413C2214yescomplemented
206#2412C2214yescomplemented
207#2412C2214yescomplemented
208#2410C2214yescomplemented
209#2410C2214yescomplemented
210#2409C2211yescharacteristic, complemented
211#2409C2212yescomplemented
212#2409C2212yescomplemented
213#2408C2211yescharacteristic, complemented
214#2407C2212yescomplemented
215#2407C2212yescomplemented
216#2407C2212yescomplemented
217#2406C2212yescomplemented
218#2406C2214yescomplemented
219#2406C2214yescomplemented
220#2406C2214yescomplemented
221#2406C2212yescomplemented
222#2405C2214yescomplemented
223#2405C2214yescomplemented
224#2392C2212yescomplemented
225#2392C2212yescomplemented
226C2×#398C2214yescomplemented
227C2×#397C2214yescomplemented
228#2388C2211yescharacteristic
229#2388C2211yescharacteristic, complemented
230C2×#395C2212yescomplemented
231C2×#394C2212yes—
232#2367C2212yescomplemented
233#2364C2214yescomplemented
234#2362C2212yescomplemented
235#2361C2212yescomplemented
236#2359C2214yescomplemented
237#2358C2214yescomplemented
238#2358C2212yescomplemented
239#2352C2212yescomplemented
240#2349C2212yescomplemented
241D4×C4⋊C4C2214yescomplemented
242#2342C2214yescomplemented
243#2339C2212yescomplemented
244#2339C2212yescomplemented
245#2339C2211yescharacteristic, complemented
246#2339C2211yescharacteristic, complemented
247D4×C22⋊C4C2212yescomplemented
248#2324C2212yescomplemented
249#2323C2212yescomplemented
250#2322C2214yescomplemented
251#2321C2214yescomplemented
252C4×#127C2211yescharacteristic, complemented
253C4×#124C2212yescomplemented
254C4×#121C2214yescomplemented
255C4×#120C2212yescomplemented
256#2293C2212yescomplemented
257C2×#388C2214yescomplemented
258C2×#385C2214yescomplemented
259C2×#384C2212yescomplemented
260C42×D4C2211yescharacteristic, complemented
261C2×2−1+4—216no—
262C2×2−1+4—44no—
263C2×H(5,𝔽2)—216no—
264C2×H(5,𝔽2)—44no—
265C22×#41—216no—
266C22×#41—216no—
267C22×#41—48no—
268C22×#41C2312yes—
269C22×#41C2311yescharacteristic
270C22×#41C2311yescharacteristic
271C22×#41C2314yes—
272C22×#41C2314yes—
273C22×#41C2312yes—
274C22×#41C2312yes—
275C22×#41C2311yescharacteristic
276C22×#41C2312yes—
277C22×#41C2312yes—
278C22×#41C2311yescharacteristic
279C22×#41C2314yes—
280C22×#41C2312yes—
281C22×#41C2312yes—
282C23×Q8C2312yes—
283C23×Q8C2312yes—
284C23×Q8C2312yes—
285C23×Q8C2311yescharacteristic
286C23×D4C2314yes—
287C23×D4C2312yes—
288C23×D4C2314yes—
289C23×D4C2311yescharacteristic
290C23×D4C2312yes—
291C24×C4C2312yes—
292C24×C4C2314yes—
293D4×Q8—216no—
294D4×Q8—216no—
295#548—216no—
296#548—216no—
297#547—216no—
298#547—216no—
299#547—232no—
300#547—232no—
301#547—216no—
302#547—232no—
303#547—232no—
304#547—216no—
305#547—216no—
306#547—216no—
307#547—44no—
308#547—44no—
309#546—216no—
310#546—216no—
311#546—216no—
312#546—216no—
313#546—232no—
314#546—232no—
315#546—232no—
316#546—232no—
317#546D4132yescomplemented
318#537—232no—
319#537—216no—
320#536—216no—
321#536—216no—
322#536—232no—
323#536—216no—
324#534—232no—
325#534—232no—
326C2×C4⋊Q8C2312yes—
327C2×C4⋊Q8C2312yes—
328C2×C4⋊Q8C2314yes—
329C2×C4⋊Q8C2314yes—
330C2×C4⋊Q8C2314yes—
331C2×C4⋊Q8C2312yes—
332C2×C4⋊Q8C2312yes—
333C2×C4⋊Q8C2311yescharacteristic
334C2×C4⋊Q8C2311yescharacteristic
335C2×#127C2311yescharacteristic
336C2×#124C2314yes—
337C2×#124C2314yes—
338C2×#124C2314yes—
339C2×#124C2312yes—
340C2×#124C2312yes—
341C2×#124C2312yes—
342#525—216no—
343#525—232no—
344#525—216no—
345#525—216no—
346C2×#123—232no—
347C2×#123—232no—
348C2×#123C2314yes—
349C2×#123C2314yes—
350C2×#123C2314yes—
351C2×#123C2314yes—
352C2×#123C2314yes—
353C2×#123C2314yes—
354C2×#123C2312yes—
355C2×#123C2314yes—
356C2×#123C2314yes—
357C2×#123C2314yes—
358C2×#123C2314yes—
359C2×#123C2314yes—
360C2×#123C2314yes—
361C2×#123C2314yes—
362C2×#123C2312yes—
363C2×#123C2314yes—
364C2×#123C2314yes—
365C2×#123C2314yes—
366C2×#123C2314yes—
367C2×#123C2312yes—
368C2×#123C2312yes—
369C2×#123C2314yes—
370C2×#123C2314yes—
371C2×#123C2314yes—
372C2×#123C2314yes—
373C2×#123C2314yes—
374C2×#123C2314yes—
375C2×#123C2314yes—
376C2×#123C2312yes—
377C2×#123C2312yes—
378C2×#123C2314yes—
379C2×C22⋊Q8—216no—
380C2×C22⋊Q8—232no—
381C2×C22⋊Q8C2312yes—
382C2×C22⋊Q8C2312yes—
383C2×C22⋊Q8C2312yes—
384C2×C22⋊Q8C2312yes—
385C2×C22⋊Q8C2312yes—
386C2×C22⋊Q8C2312yes—
387C2×C22⋊Q8C2314yes—
388C2×C22⋊Q8C2312yes—
389C2×C22⋊Q8C2312yes—
390C2×C22⋊Q8C2314yes—
391C2×C22⋊Q8C2314yes—
392C2×C22⋊Q8C2314yes—
393C2×C22⋊Q8C2314yes—
394C2×C22⋊Q8C2314yes—
395C2×C22⋊Q8C2314yes—
396C2×C22⋊Q8C2314yes—
397C2×C22⋊Q8C2312yes—
398C2×C22⋊Q8C2312yes—
399C2×C22⋊Q8C2314yes—
400C2×C22⋊Q8C2312yes—
401C2×C22⋊Q8C2312yes—
402C2×C22⋊Q8C2312yes—
403C2×C22⋊Q8C2312yes—
404C2×C22⋊Q8C2314yes—
405C2×C22⋊Q8C2314yes—
406C2×C22⋊Q8C2314yes—
407C2×C22⋊Q8C2314yes—
408C2×C22⋊Q8C2312yes—
409C2×C22⋊Q8C2311yescharacteristic
410C2×C22⋊Q8C2311yescharacteristic
411C2×C22⋊Q8C2312yes—
412C2×#121C2314yes—
413C2×#121C2314yes—
414C2×#121C2312yes—
415C2×#121C2312yes—
416C2×#121C2314yes—
417C2×#121C2314yes—
418C2×#121C2312yes—
419C2×#121C2312yes—
420C2×#121C2312yes—
421C2×#121C2312yes—
422C2×#121C2314yes—
423C2×#121C2314yes—
424C2×#121C2314yes—
425C2×#121C2314yes—
426C2×#121C2314yes—
427C2×#121C2314yes—
428C2×#121C2314yes—
429C2×#121C2314yes—
430C2×#121C2314yes—
431C2×#121C2314yes—
432C2×#121C2314yes—
433C2×#121C2312yes—
434C2×#121C2312yes—
435C2×#121C2312yes—
436C2×#121C2314yes—
437C2×#120C2314yes—
438C2×#120C2314yes—
439C2×#120C2312yes—
440C2×#120C2312yes—
441C2×#120C2312yes—
442C2×#120C2314yes—
443C2×#120C2312yes—
444C2×#120C2314yes—
445C2×#120C2314yes—
446C2×#120C2312yes—
447C2×#120C2312yes—
448C2×#120C2314yes—
449#520—216no—
450#518—216no—
451C2×C4×Q8C2312yes—
452C2×C4×Q8C2312yes—
453C2×C4×D4C2312yes—
454C2×C4×D4C2312yes—
455C2×C4×D4C2314yes—
456C2×C4×D4C2314yes—
457C2×C4×D4C2312yes—
458C2×C4×D4C2311yescharacteristic
459C2×C4×D4C2312yes—
460C2×C4×D4C2312yes—
461C2×C4×D4C2314yes—
462C2×C4×D4C2314yes—
463C2×C4×D4C2314yes—
464C2×C4×D4C2314yes—
465C2×C4×D4C2314yes—
466C2×C4×D4C2312yes—
467C2×C4×D4C2312yes—
468C2×C4×D4C2312yes—
469C2×C4×D4C2312yes—
470C2×C4×D4C2312yes—
471C2×C4×D4C2314yes—
472C2×C4×D4C2314yes—
473C2×C4×D4C2314yes—
474C2×C4×D4C2311yescharacteristic
475C2×C4×D4C2311yescharacteristic
476C2×C4×D4C2314yes—
477C2×C4×D4C2312yes—
478C2×C4×D4C2312yes—
479C2×#117C2312yes—
480C2×#117C2312yes—
481C2×#117C2314yes—
482C2×#117C2312yes—
483C22×C4⋊C4C2314yes—
484C22×C4⋊C4C2314yes—
485C22×C4⋊C4C2314yes—
486C22×C4⋊C4C2312yes—
487C22×C4⋊C4C2314yes—
488C22×C4⋊C4C2314yes—
489C22×C4⋊C4C2314yes—
490C22×C4⋊C4C2314yes—
491C22×C4⋊C4C2314yes—
492C22×C4⋊C4C2312yes—
493C22×C4⋊C4C2312yes—
494C22×C22⋊C4C2314yes—
495C22×C22⋊C4C2314yes—
496C22×C22⋊C4C2314yes—
497C22×C22⋊C4C2314yes—
498C22×C22⋊C4C2314yes—
499C22×C22⋊C4C2314yes—
500C22×C22⋊C4C2314yes—
501C22×C22⋊C4C2314yes—
502C22×C22⋊C4C2314yes—
503C22×C42C2312yes—
504#399C2314yes—
505#399C2312yes—
506#399C2312yes—
507#399C2314yes—
508#399C2314yes—
509#399C2314yes—
510#399C2314yes—
511#398C2314yes—
512#398C2314yes—
513#398C2314yes—
514#398C2314yes—
515#398C2314yes—
516#398C2312yes—
517#398C2314yes—
518#398C2314yes—
519#398C2314yes—
520#398C2314yes—
521#398C2314yes—
522#398C2314yes—
523#398C2312yes—
524#397C2314yes—
525#397C2314yes—
526#397C2314yes—
527#397C2314yes—
528#397C2314yes—
529#397C2312yes—
530#397C2314yes—
531#397C2314yes—
532#397C2314yes—
533#397C2314yes—
534#397C2314yes—
535#397C2314yes—
536#397C2312yes—
537#396C2314yes—
538#396C2314yes—
539#396C2314yes—
540#396C2314yes—
541#396C2312yes—
542#396C2312yes—
543#396C2312yes—
544#396C2312yes—
545#395C2312yes—
546#395C2312yes—
547#395C2314yes—
548#395C2312yes—
549#395C2311yescharacteristic
550#395C2314yes—
551#395C2312yes—
552#395C2312yes—
553#395C2314yes—
554#395C2311yescharacteristic
555#395C2314yes—
556#395C2314yes—
557#395C2314yes—
558#394C2312yes—
559#394C2314yes—
560#394C2312yes—
561#394C2314yes—
562#394C2312yes—
563#394C2314yes—
564#394C2314yes—
565#394C2314yes—
566#394C2314yes—
567#394C2314yes—
568#394C2312yes—
569#394C2314yes—
570#394C2311yescharacteristic
571#394C2314yes—
572#394C2312yes—
573#394C2314yes—
574#394C2312yes—
575#394C2312yes—
576#394C2312yes—
577#394C2311yescharacteristic
578#394C2312yes—
579#394C2312yes—
580#394C2312yes—
581#394C2312yes—
582#394C2312yes—
583#394C2314yes—
584#394C2314yes—
585#394C2314yes—
586#394C2314yes—
587#394C2314yes—
588#394C2314yes—
589#393C2311yescharacteristic
590#393C2312yes—
591#393C2314yes—
592#393C2311yescharacteristic
593#393C2314yes—
594#392C2311yescharacteristic
595#392C2314yes—
596#392C2312yes—
597#392C2312yes—
598#392C2314yes—
599#392C2312yes—
600#392C2311yescharacteristic
601#392C2312yes—
602#392C2312yes—
603#392C2314yes—
604#392C2314yes—
605#391C2312yes—
606#391C2312yes—
607#391C2312yes—
608#391C2312yes—
609#391C2312yes—
610#391C2312yes—
611#390C2311yescharacteristic
612#390C2312yes—
613#390C2312yes—
614#390C2311yescharacteristic
615#390C2312yes—
616#390C2314yes—
617#390C2312yes—
618#390C2312yes—
619#390C2314yes—
620#390C2314yes—
621#390C2312yes—
622#390C2312yes—
623#390C2312yes—
624#389C2312yes—
625#389C2314yes—
626#389C2312yes—
627#389C2312yes—
628#389C2314yes—
629#389C2314yes—
630#389C2312yes—
631#389C2314yes—
632#389C2314yes—
633#389C2314yes—
634#389C2314yes—
635#388C2314yes—
636#388C2314yes—
637#388C2314yes—
638#388C2314yes—
639#388C2314yes—
640#388C2314yes—
641#388C2312yes—
642#388C2314yes—
643#388C2314yes—
644#388C2314yes—
645#388C2314yes—
646#388C2312yes—
647#388C2314yes—
648#388C2314yes—
649#388C2314yes—
650#388C2314yes—
651#388C2312yes—
652#388C2314yes—
653#388C2312yes—
654#388C2314yes—
655#388C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#386C2314yes—
660#386C2314yes—
661#386C2314yes—
662#386C2314yes—
663#386C2314yes—
664#386C2312yes—
665#386C2314yes—
666#386C2314yes—
667#386C2314yes—
668#386C2314yes—
669#386C2314yes—
670#386C2314yes—
671#386C2314yes—
672#386C2314yes—
673#386C2314yes—
674#386C2312yes—
675#386C2314yes—
676#386C2314yes—
677#386C2314yes—
678#386C2314yes—
679#386C2314yes—
680#386C2314yes—
681#386C2314yes—
682#386C2314yes—
683#386C2312yes—
684#386C2312yes—
685#385C2314yes—
686#385C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2314yes—
690#385C2314yes—
691#385C2314yes—
692#385C2314yes—
693#385C2314yes—
694#385C2314yes—
695#385C2314yes—
696#385C2312yes—
697#385C2314yes—
698#385C2314yes—
699#385C2314yes—
700#385C2314yes—
701#385C2314yes—
702#385C2314yes—
703#385C2314yes—
704#385C2312yes—
705#385C2312yes—
706#385C2314yes—
707#385C2314yes—
708#385C2314yes—
709#385C2314yes—
710#385C2314yes—
711#385C2314yes—
712#385C2312yes—
713#384C2311yescharacteristic
714#384C2312yes—
715#384C2312yes—
716#384C2312yes—
717#384C2314yes—
718#384C2314yes—
719#384C2314yes—
720#384C2312yes—
721#382C2312yes—
722#381C2314yes—
723#381C2314yes—
724#381C2312yes—
725#381C2312yes—
726#380C2312yes—
727#380C2312yes—
728#380C2312yes—
729#380C2311yescharacteristic
730#380C2311yescharacteristic
731#380C2314yes—
732#380C2314yes—
733#380C2314yes—
734#380C2314yes—
735#380C2314yes—
736#380C2314yes—
737#380C2314yes—
738#379C2314yes—
739#379C2314yes—
740#379C2312yes—
741#379C2312yes—
742#379C2314yes—
743C4×C4⋊C4C2312yes—
744C4×C4⋊C4C2314yes—
745C4×C4⋊C4C2312yes—
746C4×C4⋊C4C2311yescharacteristic
747C4×C22⋊C4C2314yes—
748C4×C22⋊C4C2312yes—
749C4×C22⋊C4C2312yes—
750C4×C22⋊C4C2311yescharacteristic
751C4×C22⋊C4C2311yescharacteristic
752C4×C22⋊C4C2312yes—
753C4×C22⋊C4C2314yes—
754C4×C22⋊C4C2314yes—
755C4×C22⋊C4C2314yes—
756C4×C22⋊C4C2312yes—
757C4×C22⋊C4C2314yes—
758C2×#95C2314yes—
759C2×#95C2312yes—
760C2×#95C2312yes—
761C2×#95C2314yes—
762C2×#95C2314yes—
763C43C2311yescharacteristic
764C25C2412yes—
765C25C2412yes—
766C25C2414yes—
7672−1+4—464no—
768H(5,𝔽2)—464no—
769C2×#41—28no—
770C2×#41—28no—
771C2×#41—28no—
772C2×#41—216no—
773C2×#41—216no—
774C2×#41—28no—
775C2×#41—28no—
776C2×#41—216no—
777C2×#41—28no—
778C2×#41—216no—
779C2×#41—28no—
780C2×#41—216no—
781C2×#41—28no—
782C2×#41—216no—
783C2×#41—28no—
784C2×#41—28no—
785C2×#41—28no—
786C2×#41—24no—
787C2×#41—24no—
788C2×#41—28no—
789C2×#41—28no—
790C2×#41—28no—
791C2×#41—216no—
792C2×#41—216no—
793C2×#41—28no—
794C2×#41—42no—
795C2×#41—42no—
796C2×#41—48no—
797C2×#41—48no—
798C2×#41—44no—
799C2×#41—48no—
800C2×#41—44no—
801C2×#41—44no—
802C2×#41—44no—
803C2×#41—44no—
804C2×#41—4128no—
805C2×#41C2×D4116yes—
806C22×Q8—28no—
807C22×Q8—28no—
808C22×Q8—28no—
809C22×Q8—216no—
810C22×Q8—28no—
811C22×Q8—28no—
812C22×Q8—44no—
813C22×Q8—44no—
814C22×Q8—44no—
815C22×Q8—42no—
816C22×Q8C2411yescharacteristic
817C22×Q8C2412yes—
818C22×Q8C2411yescharacteristic
819C22×Q8C2411yescharacteristic
820C22×Q8C2414yes—
821C22×Q8C2412yes—
822C22×Q8C2414yes—
823C22×Q8C2411yescharacteristic
824C22×Q8C2412yes—
825C22×D4—28no—
826C22×D4—28no—
827C22×D4—216no—
828C22×D4—216no—
829C22×D4—216no—
830C22×D4—216no—
831C22×D4—216no—
832C22×D4—28no—
833C22×D4—42no—
834C22×D4—44no—
835C22×D4—48no—
836C22×D4—48no—
837C22×D4C2×D4116yes—
838C22×D4C2412yes—
839C22×D4C2414yes—
840C22×D4C2412yes—
841C22×D4C2411yescharacteristic
842C22×D4C2411yescharacteristic
843C22×D4C2412yes—
844C22×D4C2414yes—
845C22×D4C2414yes—
846C22×D4C2414yes—
847C22×D4C2412yes—
848C22×D4C2412yes—
849C22×D4C2414yes—
850C22×D4C2414yes—
851C22×D4C2412yes—
852C22×D4C2412yes—
853C22×D4C2412yes—
854C22×D4C2412yes—
855C22×D4C2412yes—
856C22×D4C2414yes—
857C22×D4C2412yes—
858C22×D4C2414yes—
859C22×D4C2411yescharacteristic
860C22×D4C2411yescharacteristic
861C22×D4C2412yes—
862C22×D4C2412yes—
863C22×D4C2414yes—
864C22×D4C2411yescharacteristic
865C23×C4—216no—
866C23×C4—28no—
867C23×C4—216no—
868C23×C4—28no—
869C23×C4—44no—
870C23×C4—48no—
871C23×C4C2412yes—
872C23×C4C2414yes—
873C23×C4C2412yes—
874C23×C4C2411yescharacteristic
875C23×C4C2412yes—
876C23×C4C2411yescharacteristic
877C23×C4C2412yes—
878C23×C4C2414yes—
879C23×C4C2414yes—
880C23×C4C2414yes—
881C23×C4C2412yes—
882C23×C4C2414yes—
883C23×C4C2412yes—
884C23×C4C2412yes—
885C23×C4C2414yes—
886C23×C4C2412yes—
887C23×C4C2414yes—
888C23×C4C2412yes—
889C23×C4C2412yes—
890C23×C4C2414yes—
891C23×C4C2414yes—
892C23×C4C2414yes—
893C23×C4C2414yes—
894C23×C4C2414yes—
895C23×C4C2414yes—
896C4⋊Q8—28no—
897C4⋊Q8—28no—
898C4⋊Q8—216no—
899C4⋊Q8—216no—
900C4⋊Q8—216no—
901C4⋊Q8—28no—
902C4⋊Q8—28no—
903C4⋊Q8—42no—
904C4⋊Q8—42no—
905#127—42no—
906#124—28no—
907#124—28no—
908#124—216no—
909#124—216no—
910#124—216no—
911#124C2×D4116yes—
912#123—216no—
913#123—216no—
914#123—216no—
915#123—216no—
916#123—216no—
917#123—216no—
918#123—28no—
919#123—216no—
920#123—28no—
921#123—216no—
922#123—216no—
923#123—28no—
924#123—216no—
925#123—216no—
926#123—216no—
927#123—216no—
928#123—216no—
929#123—216no—
930#123—216no—
931#123—216no—
932#123—28no—
933#123—216no—
934#123—216no—
935#123—216no—
936#123—216no—
937#123—216no—
938#123—216no—
939#123—48no—
940#123—44no—
941#123—44no—
942#123C2×D4132yes—
943C22⋊Q8—28no—
944C22⋊Q8—28no—
945C22⋊Q8—28no—
946C22⋊Q8—28no—
947C22⋊Q8—28no—
948C22⋊Q8—28no—
949C22⋊Q8—216no—
950C22⋊Q8—28no—
951C22⋊Q8—28no—
952C22⋊Q8—28no—
953C22⋊Q8—28no—
954C22⋊Q8—28no—
955C22⋊Q8—216no—
956C22⋊Q8—28no—
957C22⋊Q8—216no—
958C22⋊Q8—28no—
959C22⋊Q8—216no—
960C22⋊Q8—216no—
961C22⋊Q8—216no—
962C22⋊Q8—216no—
963C22⋊Q8—216no—
964C22⋊Q8—216no—
965C22⋊Q8—216no—
966C22⋊Q8—28no—
967C22⋊Q8—216no—
968C22⋊Q8—216no—
969C22⋊Q8—216no—
970C22⋊Q8—44no—
971C22⋊Q8—42no—
972C22⋊Q8—42no—
973C22⋊Q8C2×D4116yes—
974#121—28no—
975#121—216no—
976#121—28no—
977#121—28no—
978#121—216no—
979#121—216no—
980#121—216no—
981#121—216no—
982#121—216no—
983#121—216no—
984#121—216no—
985#121—28no—
986#121—216no—
987#121—216no—
988#121—216no—
989#121—28no—
990#121—28no—
991#121—216no—
992#121—216no—
993#121—216no—
994#121—216no—
995#121—44no—
996#121—44no—
997#121C2×D4116yes—
998#121C2×D4132yes—
999#120—216no—
1000#120—216no—
1001#120—28no—
1002#120—216no—
1003#120—28no—
1004#120—216no—
1005#120—28no—
1006#120—28no—
1007#120—216no—
1008#120—44no—
1009#120—44no—
1010#120C2×D4132yes—
1011C4×Q8—28no—
1012C4×Q8—28no—
1013C4×D4—28no—
1014C4×D4—28no—
1015C4×D4—216no—
1016C4×D4—216no—
1017C4×D4—216no—
1018C4×D4—24no—
1019C4×D4—216no—
1020C4×D4—216no—
1021C4×D4—28no—
1022C4×D4—28no—
1023C4×D4—28no—
1024C4×D4—28no—
1025C4×D4—28no—
1026C4×D4—216no—
1027C4×D4—216no—
1028C4×D4—216no—
1029C4×D4—216no—
1030C4×D4—216no—
1031C4×D4—28no—
1032C4×D4—28no—
1033C4×D4—28no—
1034C4×D4—48no—
1035C4×D4—42no—
1036C4×D4—42no—
1037C4×D4C2×D4116yes—
1038C4×D4C2×D4116yes—
1039#117—28no—
1040#117—216no—
1041#117—28no—
1042#117—28no—
1043C2×C4⋊C4—216no—
1044C2×C4⋊C4—216no—
1045C2×C4⋊C4—216no—
1046C2×C4⋊C4—216no—
1047C2×C4⋊C4—216no—
1048C2×C4⋊C4—28no—
1049C2×C4⋊C4—216no—
1050C2×C4⋊C4—216no—
1051C2×C4⋊C4—216no—
1052C2×C4⋊C4—44no—
1053C2×C4⋊C4—44no—
1054C2×C4⋊C4C2414yes—
1055C2×C4⋊C4C2412yes—
1056C2×C4⋊C4C2414yes—
1057C2×C4⋊C4C2412yes—
1058C2×C4⋊C4C2412yes—
1059C2×C4⋊C4C2414yes—
1060C2×C4⋊C4C2414yes—
1061C2×C4⋊C4C2412yes—
1062C2×C4⋊C4C2412yes—
1063C2×C4⋊C4C2412yes—
1064C2×C4⋊C4C2414yes—
1065C2×C4⋊C4C2412yes—
1066C2×C4⋊C4C2414yes—
1067C2×C4⋊C4C2414yes—
1068C2×C4⋊C4C2414yes—
1069C2×C4⋊C4C2414yes—
1070C2×C4⋊C4C2414yes—
1071C2×C4⋊C4C2414yes—
1072C2×C4⋊C4C2414yes—
1073C2×C4⋊C4C2414yes—
1074C2×C4⋊C4C2414yes—
1075C2×C4⋊C4C2414yes—
1076C2×C4⋊C4C2414yes—
1077C2×C4⋊C4C2414yes—
1078C2×C4⋊C4C2414yes—
1079C2×C4⋊C4C2414yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2412yes—
1082C2×C4⋊C4C2412yes—
1083C2×C4⋊C4C2412yes—
1084C2×C4⋊C4C2411yescharacteristic
1085C2×C4⋊C4C2414yes—
1086C2×C4⋊C4C2412yes—
1087C2×C4⋊C4C2414yes—
1088C2×C4⋊C4C2411yescharacteristic
1089C2×C4⋊C4C2411yescharacteristic
1090C2×C4⋊C4C2412yes—
1091C2×C4⋊C4C2412yes—
1092C2×C4⋊C4C2414yes—
1093C2×C4⋊C4C2412yes—
1094C2×C4⋊C4C2412yes—
1095C2×C4⋊C4C2414yes—
1096C2×C4⋊C4C2412yes—
1097C2×C4⋊C4C2412yes—
1098C2×C4⋊C4C2414yes—
1099C2×C4⋊C4C2412yes—
1100C2×C4⋊C4C2412yes—
1101C2×C4⋊C4C2412yes—
1102C2×C4⋊C4C2414yes—
1103C2×C4⋊C4C2412yes—
1104C2×C22⋊C4—216no—
1105C2×C22⋊C4—216no—
1106C2×C22⋊C4—216no—
1107C2×C22⋊C4—216no—
1108C2×C22⋊C4—216no—
1109C2×C22⋊C4—216no—
1110C2×C22⋊C4—216no—
1111C2×C22⋊C4—48no—
1112C2×C22⋊C4C2×D4132yes—
1113C2×C22⋊C4C2414yes—
1114C2×C22⋊C4C2412yes—
1115C2×C22⋊C4C2412yes—
1116C2×C22⋊C4C2412yes—
1117C2×C22⋊C4C2414yes—
1118C2×C22⋊C4C2412yes—
1119C2×C22⋊C4C2414yes—
1120C2×C22⋊C4C2412yes—
1121C2×C22⋊C4C2412yes—
1122C2×C22⋊C4C2412yes—
1123C2×C22⋊C4C2414yes—
1124C2×C22⋊C4C2414yes—
1125C2×C22⋊C4C2414yes—
1126C2×C22⋊C4C2414yes—
1127C2×C22⋊C4C2414yes—
1128C2×C22⋊C4C2414yes—
1129C2×C22⋊C4C2414yes—
1130C2×C22⋊C4C2414yes—
1131C2×C22⋊C4C2414yes—
1132C2×C22⋊C4C2414yes—
1133C2×C22⋊C4C2414yes—
1134C2×C22⋊C4C2414yes—
1135C2×C22⋊C4C2414yes—
1136C2×C22⋊C4C2414yes—
1137C2×C22⋊C4C2412yes—
1138C2×C22⋊C4C2412yes—
1139C2×C22⋊C4C2412yes—
1140C2×C22⋊C4C2412yes—
1141C2×C22⋊C4C2412yes—
1142C2×C22⋊C4C2412yes—
1143C2×C22⋊C4C2414yes—
1144C2×C22⋊C4C2412yes—
1145C2×C22⋊C4C2414yes—
1146C2×C22⋊C4C2412yes—
1147C2×C22⋊C4C2414yes—
1148C2×C22⋊C4C2412yes—
1149C2×C22⋊C4C2412yes—
1150C2×C22⋊C4C2414yes—
1151C2×C22⋊C4C2412yes—
1152C2×C22⋊C4C2414yes—
1153C2×C22⋊C4C2412yes—
1154C2×C22⋊C4C2414yes—
1155C2×C22⋊C4C2414yes—
1156C2×C22⋊C4C2411yescharacteristic
1157C2×C22⋊C4C2412yes—
1158C2×C22⋊C4C2411yescharacteristic
1159C2×C22⋊C4C2412yes—
1160C2×C22⋊C4C2412yes—
1161C2×C22⋊C4C2412yes—
1162C2×C22⋊C4C2414yes—
1163C2×C22⋊C4C2412yes—
1164C2×C22⋊C4C2412yes—
1165C2×C22⋊C4C2414yes—
1166C2×C22⋊C4C2414yes—
1167C2×C22⋊C4C2412yes—
1168C2×C22⋊C4C2414yes—
1169C2×C22⋊C4C2412yes—
1170C2×C22⋊C4C2412yes—
1171C2×C22⋊C4C2412yes—
1172C2×C22⋊C4C2414yes—
1173C2×C22⋊C4C2412yes—
1174C2×C22⋊C4C2412yes—
1175C2×C22⋊C4C2414yes—
1176C2×C22⋊C4C2414yes—
1177C2×C22⋊C4C2414yes—
1178C2×C22⋊C4C2414yes—
1179C2×C22⋊C4C2414yes—
1180C2×C22⋊C4C2412yes—
1181C2×C42—44no—
1182C2×C42C2412yes—
1183C2×C42C2414yes—
1184C2×C42C2412yes—
1185C2×C42C2414yes—
1186C2×C42C2414yes—
1187C2×C42C2411yescharacteristic
1188C2×C42C2412yes—
1189C2×C42C2411yescharacteristic
1190C2×C42C2411yescharacteristic
1191C2×C42C2412yes—
1192C2×C42C2414yes—
1193C2×C42C2412yes—
1194#95C2412yes—
1195#95C2412yes—
1196#95C2411yescharacteristic
1197#95C2411yescharacteristic
1198#95C2412yes—
1199#95C2414yes—
1200#95C2414yes—
1201#95C2412yes—
1202#95C2414yes—
1203#95C2414yes—
1204#95C2412yes—
1205#95C2414yes—
1206#95C2414yes—
1207#95C2414yes—
1208#95C2414yes—
1209#95C2414yes—
1210#95C2414yes—
1211#95C2414yes—
1212#95C2412yes—
1213#95C2412yes—
1214#95C2414yes—
1215#95C2412yes—
1216#95C2411yescharacteristic
1217#95C2412yes—
1218#95C2414yes—
1219#95C2412yes—
1220#95C2411yescharacteristic
1221#95C2414yes—
1222#95C2414yes—
1223#95C2414yes—
1224#95C2412yes—
1225#95C2414yes—
1226#95C2414yes—
1227#95C2414yes—
1228#95C2414yes—
1229C24—28no—
1230C24—28no—
1231C24—24no—
1232C24—28no—
1233C24—24no—
1234C24—44no—
1235C24—42no—
1236C24—44no—
1237C24—44no—
1238C24—44no—
1239C24—42no—
1240C24—42no—
1241C24—42no—
1242C24—42no—
1243C24—42no—
1244C24—42no—
1245C24—42no—
1246C24—44no—
1247C24C22×D4116yes—
1248C24C2511yescharacteristic
1249C24C2512yes—
1250C24C2511yescharacteristic
1251C24C2512yes—
1252C24C2514yes—
1253C24C2512yes—
1254C24C2512yes—
1255#41—264no—
1256#41—416no—
1257#41—416no—
1258#41—464no—
1259#41—432no—
1260#41—432no—
1261#41—464no—
1262#41—464no—
1263#41—432no—
1264#41—432no—
1265#41—432no—
1266#41—432no—
1267#41—416no—
1268#41—416no—
1269C2×Q8—24no—
1270C2×Q8—24no—
1271C2×Q8—28no—
1272C2×Q8—28no—
1273C2×Q8—28no—
1274C2×Q8—24no—
1275C2×Q8—28no—
1276C2×Q8—24no—
1277C2×Q8—28no—
1278C2×Q8—24no—
1279C2×Q8—24no—
1280C2×Q8—24no—
1281C2×Q8—24no—
1282C2×Q8—22no—
1283C2×Q8—24no—
1284C2×Q8—22no—
1285C2×Q8—41no—
1286C2×Q8—44no—
1287C2×Q8—42no—
1288C2×Q8—44no—
1289C2×Q8—41no—
1290C2×Q8—432no—
1291C2×Q8—432no—
1292C2×Q8—432no—
1293C2×Q8—416no—
1294C2×Q8C22×D418yes—
1295C2×D4—28no—
1296C2×D4—28no—
1297C2×D4—28no—
1298C2×D4—28no—
1299C2×D4—264no—
1300C2×D4—24no—
1301C2×D4—28no—
1302C2×D4—28no—
1303C2×D4—24no—
1304C2×D4—28no—
1305C2×D4—24no—
1306C2×D4—28no—
1307C2×D4—24no—
1308C2×D4—28no—
1309C2×D4—28no—
1310C2×D4—28no—
1311C2×D4—28no—
1312C2×D4—28no—
1313C2×D4—24no—
1314C2×D4—28no—
1315C2×D4—24no—
1316C2×D4—28no—
1317C2×D4—24no—
1318C2×D4—24no—
1319C2×D4—24no—
1320C2×D4—28no—
1321C2×D4—24no—
1322C2×D4—28no—
1323C2×D4—24no—
1324C2×D4—28no—
1325C2×D4—24no—
1326C2×D4—24no—
1327C2×D4—24no—
1328C2×D4—24no—
1329C2×D4—24no—
1330C2×D4—22no—
1331C2×D4—22no—
1332C2×D4—44no—
1333C2×D4—42no—
1334C2×D4—41no—
1335C2×D4—42no—
1336C2×D4—44no—
1337C2×D4—44no—
1338C2×D4—44no—
1339C2×D4—42no—
1340C2×D4—42no—
1341C2×D4—44no—
1342C2×D4—42no—
1343C2×D4—42no—
1344C2×D4—42no—
1345C2×D4—41no—
1346C2×D4—41no—
1347C2×D4—41no—
1348C2×D4—42no—
1349C2×D4—44no—
1350C2×D4—42no—
1351C2×D4—42no—
1352C2×D4—42no—
1353C2×D4—41no—
1354C2×D4—42no—
1355C2×D4—42no—
1356C2×D4—41no—
1357C2×D4—44no—
1358C2×D4—42no—
1359C2×D4—44no—
1360C2×D4—42no—
1361C2×D4—44no—
1362C2×D4—42no—
1363C2×D4—42no—
1364C2×D4—416no—
1365C2×D4—464no—
1366C2×D4—464no—
1367C2×D4—432no—
1368C2×D4C22×D4116yes—
1369C2×D4C22×D4116yes—
1370C2×D4C22×D418yes—
1371C2×D4C22×D418yes—
1372C2×D4C22×D4116yes—
1373C2×D4C22×D418yes—
1374C2×D4H(5,𝔽2)14yes—
1375C22×C4—28no—
1376C22×C4—28no—
1377C22×C4—24no—
1378C22×C4—24no—
1379C22×C4—24no—
1380C22×C4—24no—
1381C22×C4—28no—
1382C22×C4—28no—
1383C22×C4—28no—
1384C22×C4—28no—
1385C22×C4—24no—
1386C22×C4—28no—
1387C22×C4—28no—
1388C22×C4—28no—
1389C22×C4—28no—
1390C22×C4—24no—
1391C22×C4—28no—
1392C22×C4—24no—
1393C22×C4—28no—
1394C22×C4—24no—
1395C22×C4—24no—
1396C22×C4—28no—
1397C22×C4—28no—
1398C22×C4—28no—
1399C22×C4—28no—
1400C22×C4—28no—
1401C22×C4—24no—
1402C22×C4—28no—
1403C22×C4—24no—
1404C22×C4—24no—
1405C22×C4—28no—
1406C22×C4—24no—
1407C22×C4—24no—
1408C22×C4—24no—
1409C22×C4—24no—
1410C22×C4—24no—
1411C22×C4—28no—
1412C22×C4—24no—
1413C22×C4—22no—
1414C22×C4—22no—
1415C22×C4—24no—
1416C22×C4—28no—
1417C22×C4—28no—
1418C22×C4—28no—
1419C22×C4—44no—
1420C22×C4—42no—
1421C22×C4—44no—
1422C22×C4—42no—
1423C22×C4—44no—
1424C22×C4—42no—
1425C22×C4—44no—
1426C22×C4—44no—
1427C22×C4—42no—
1428C22×C4—44no—
1429C22×C4—42no—
1430C22×C4—44no—
1431C22×C4—432no—
1432C22×C4—44no—
1433C22×C4—44no—
1434C22×C4—44no—
1435C22×C4—44no—
1436C22×C4—44no—
1437C22×C4—44no—
1438C22×C4—44no—
1439C22×C4—44no—
1440C22×C4—44no—
1441C22×C4—44no—
1442C22×C4—464no—
1443C22×C4C22×D4116yes—
1444C22×C4C22×D418yes—
1445C22×C4C22×D418yes—
1446C22×C4C22×D4116yes—
1447C22×C4C2512yes—
1448C22×C4C2514yes—
1449C22×C4C2511yescharacteristic
1450C22×C4C2512yes—
1451C22×C4C2512yes—
1452C22×C4C2512yes—
1453C22×C4C2514yes—
1454C22×C4C2512yes—
1455C22×C4C2511yescharacteristic
1456C22×C4C2512yes—
1457C22×C4C2512yes—
1458C22×C4C2514yes—
1459C22×C4C2511yescharacteristic
1460C22×C4C2512yes—
1461C22×C4C2512yes—
1462C22×C4C2512yes—
1463C22×C4C2514yes—
1464C22×C4C2514yes—
1465C22×C4C2512yes—
1466C22×C4C2512yes—
1467C22×C4C2511yescharacteristic
1468C22×C4C2511yescharacteristic
1469C4⋊C4—28no—
1470C4⋊C4—24no—
1471C4⋊C4—24no—
1472C4⋊C4—28no—
1473C4⋊C4—28no—
1474C4⋊C4—24no—
1475C4⋊C4—24no—
1476C4⋊C4—24no—
1477C4⋊C4—28no—
1478C4⋊C4—28no—
1479C4⋊C4—24no—
1480C4⋊C4—28no—
1481C4⋊C4—28no—
1482C4⋊C4—24no—
1483C4⋊C4—28no—
1484C4⋊C4—28no—
1485C4⋊C4—28no—
1486C4⋊C4—28no—
1487C4⋊C4—28no—
1488C4⋊C4—28no—
1489C4⋊C4—28no—
1490C4⋊C4—28no—
1491C4⋊C4—28no—
1492C4⋊C4—28no—
1493C4⋊C4—28no—
1494C4⋊C4—28no—
1495C4⋊C4—24no—
1496C4⋊C4—24no—
1497C4⋊C4—24no—
1498C4⋊C4—24no—
1499C4⋊C4—24no—
1500C4⋊C4—28no—
1501C4⋊C4—28no—
1502C4⋊C4—22no—
1503C4⋊C4—41no—
1504C4⋊C4—41no—
1505C4⋊C4—42no—
1506C4⋊C4—42no—
1507C4⋊C4—44no—
1508C4⋊C4—42no—
1509C4⋊C4—42no—
1510C4⋊C4—42no—
1511C4⋊C4—42no—
1512C4⋊C4—44no—
1513C4⋊C4—44no—
1514C4⋊C4—42no—
1515C4⋊C4—42no—
1516C4⋊C4C22×D418yes—
1517C4⋊C4C22×D4116yes—
1518C4⋊C4C22×D418yes—
1519C22⋊C4—24no—
1520C22⋊C4—28no—
1521C22⋊C4—24no—
1522C22⋊C4—28no—
1523C22⋊C4—28no—
1524C22⋊C4—28no—
1525C22⋊C4—28no—
1526C22⋊C4—28no—
1527C22⋊C4—28no—
1528C22⋊C4—28no—
1529C22⋊C4—28no—
1530C22⋊C4—24no—
1531C22⋊C4—24no—
1532C22⋊C4—28no—
1533C22⋊C4—28no—
1534C22⋊C4—28no—
1535C22⋊C4—24no—
1536C22⋊C4—24no—
1537C22⋊C4—28no—
1538C22⋊C4—24no—
1539C22⋊C4—24no—
1540C22⋊C4—24no—
1541C22⋊C4—28no—
1542C22⋊C4—28no—
1543C22⋊C4—28no—
1544C22⋊C4—28no—
1545C22⋊C4—28no—
1546C22⋊C4—28no—
1547C22⋊C4—24no—
1548C22⋊C4—24no—
1549C22⋊C4—24no—
1550C22⋊C4—24no—
1551C22⋊C4—24no—
1552C22⋊C4—28no—
1553C22⋊C4—24no—
1554C22⋊C4—24no—
1555C22⋊C4—24no—
1556C22⋊C4—28no—
1557C22⋊C4—24no—
1558C22⋊C4—28no—
1559C22⋊C4—24no—
1560C22⋊C4—44no—
1561C22⋊C4—44no—
1562C22⋊C4—42no—
1563C22⋊C4—44no—
1564C22⋊C4—42no—
1565C22⋊C4—44no—
1566C22⋊C4—44no—
1567C22⋊C4—42no—
1568C22⋊C4—42no—
1569C22⋊C4—42no—
1570C22⋊C4—44no—
1571C22⋊C4—42no—
1572C22⋊C4—42no—
1573C22⋊C4—41no—
1574C22⋊C4—41no—
1575C22⋊C4—42no—
1576C22⋊C4—42no—
1577C22⋊C4—42no—
1578C22⋊C4—44no—
1579C22⋊C4—42no—
1580C22⋊C4C22×D4116yes—
1581C22⋊C4C22×D4116yes—
1582C22⋊C4C22×D4116yes—
1583C22⋊C4C22×D4116yes—
1584C22⋊C4C22×D418yes—
1585C22⋊C4C22×D4116yes—
1586C22⋊C4C22×D418yes—
1587C42—28no—
1588C42—24no—
1589C42—28no—
1590C42—28no—
1591C42—24no—
1592C42—22no—
1593C42—22no—
1594C42—24no—
1595C42—44no—
1596C42—41no—
1597C42—42no—
1598C42C22×D418yes—
1599C23—22no—
1600C23—24no—
1601C23—22no—
1602C23—22no—
1603C23—22no—
1604C23—24no—
1605C23—22no—
1606C23—22no—
1607C23—24no—
1608C23—22no—
1609C23—24no—
1610C23—22no—
1611C23—22no—
1612C23—24no—
1613C23—24no—
1614C23—22no—
1615C23—22no—
1616C23—22no—
1617C23—24no—
1618C23—22no—
1619C23—22no—
1620C23—232no—
1621C23—22no—
1622C23—22no—
1623C23—22no—
1624C23—22no—
1625C23—21no—
1626C23—22no—
1627C23—21no—
1628C23—21no—
1629C23—22no—
1630C23—21no—
1631C23—21no—
1632C23—22no—
1633C23—22no—
1634C23—22no—
1635C23—22no—
1636C23—22no—
1637C23—21no—
1638C23—416no—
1639C23—416no—
1640C23—48no—
1641C23—48no—
1642C23—48no—
1643C23—88no—
1644C23—88no—
1645C23—88no—
1646C23—88no—
1647C23—84no—
1648C23—84no—
1649C23—84no—
1650C23—88no—
1651C23—88no—
1652C23—84no—
1653C23—84no—
1654C23—162no—
1655C23—162no—
1656C23C23×D414yes—
1657C23C23×D418yes—
1658C23C23×D414yes—
1659C23C23×D418yes—
1660C23C2×H(5,𝔽2)14yes—
1661C23C2611yescharacteristic
1662Q8—216no—
1663Q8—44no—
1664Q8—416no—
1665Q8—48no—
1666Q8—416no—
1667Q8—44no—
1668Q8—44no—
1669Q8—48no—
1670Q8—44no—
1671D4—232no—
1672D4—232no—
1673D4—216no—
1674D4—416no—
1675D4—48no—
1676D4—48no—
1677D4—416no—
1678D4—48no—
1679D4—44no—
1680D4—416no—
1681D4—48no—
1682D4—416no—
1683D4—44no—
1684D4—48no—
1685D4—48no—
1686D4—416no—
1687D4—48no—
1688D4—84no—
1689D4—84no—
1690D4—82no—
1691D4—82no—
1692D4—84no—
1693D4—88no—
1694D4—84no—
1695D4—84no—
1696D4—88no—
1697D4D42116yes—
1698C2×C4—22no—
1699C2×C4—24no—
1700C2×C4—22no—
1701C2×C4—21no—
1702C2×C4—22no—
1703C2×C4—22no—
1704C2×C4—24no—
1705C2×C4—22no—
1706C2×C4—24no—
1707C2×C4—22no—
1708C2×C4—22no—
1709C2×C4—22no—
1710C2×C4—21no—
1711C2×C4—24no—
1712C2×C4—232no—
1713C2×C4—216no—
1714C2×C4—216no—
1715C2×C4—22no—
1716C2×C4—22no—
1717C2×C4—24no—
1718C2×C4—22no—
1719C2×C4—22no—
1720C2×C4—24no—
1721C2×C4—22no—
1722C2×C4—24no—
1723C2×C4—22no—
1724C2×C4—24no—
1725C2×C4—22no—
1726C2×C4—22no—
1727C2×C4—24no—
1728C2×C4—24no—
1729C2×C4—21no—
1730C2×C4—22no—
1731C2×C4—22no—
1732C2×C4—21no—
1733C2×C4—21no—
1734C2×C4—22no—
1735C2×C4—24no—
1736C2×C4—22no—
1737C2×C4—22no—
1738C2×C4—22no—
1739C2×C4—24no—
1740C2×C4—22no—
1741C2×C4—22no—
1742C2×C4—22no—
1743C2×C4—22no—
1744C2×C4—22no—
1745C2×C4—24no—
1746C2×C4—22no—
1747C2×C4—24no—
1748C2×C4—22no—
1749C2×C4—22no—
1750C2×C4—24no—
1751C2×C4—22no—
1752C2×C4—416no—
1753C2×C4—48no—
1754C2×C4—48no—
1755C2×C4—48no—
1756C2×C4—48no—
1757C2×C4—416no—
1758C2×C4—416no—
1759C2×C4—48no—
1760C2×C4—416no—
1761C2×C4—416no—
1762C2×C4—416no—
1763C2×C4—416no—
1764C2×C4—48no—
1765C2×C4—48no—
1766C2×C4—48no—
1767C2×C4—44no—
1768C2×C4—44no—
1769C2×C4—88no—
1770C2×C4—88no—
1771C2×C4—88no—
1772C2×C4—88no—
1773C2×C4—88no—
1774C2×C4C23×D414yes—
1775C2×C4C23×D418yes—
1776C2×C4C23×D414yes—
1777C2×C4C23×D414yes—
1778C2×C4C23×D418yes—
1779C2×C4C23×D414yes—
1780C2×C4C23×D414yes—
1781C2×C4C2×H(5,𝔽2)12yes—
1782C2×C4#58512yes—
1783C22—28no—
1784C22—24no—
1785C22—28no—
1786C22—24no—
1787C22—24no—
1788C22—28no—
1789C22—24no—
1790C22—24no—
1791C22—24no—
1792C22—28no—
1793C22—24no—
1794C22—24no—
1795C22—28no—
1796C22—42no—
1797C22—44no—
1798C22—42no—
1799C22—42no—
1800C22—42no—
1801C22—44no—
1802C22—44no—
1803C22—42no—
1804C22—42no—
1805C22—42no—
1806C22—42no—
1807C22—44no—
1808C22—42no—
1809C22—42no—
1810C22—42no—
1811C22—42no—
1812C22—41no—
1813C22—42no—
1814C22—41no—
1815C22—42no—
1816C22—42no—
1817C22—42no—
1818C22—42no—
1819C22—41no—
1820C22—42no—
1821C22—41no—
1822C22—41no—
1823C22—42no—
1824C22—41no—
1825C22—832no—
1826C22—816no—
1827C22—168no—
1828C22C2×D4218yes—
1829C22C24×D412yes—
1830C22C22×H(5,𝔽2)11yescharacteristic
1831C22C2×#58511yescharacteristic
1832C222−1+612yes—
1833C222−1+611yescharacteristic
1834C4—24no—
1835C4—28no—
1836C4—24no—
1837C4—22no—
1838C4—24no—
1839C4—24no—
1840C4—28no—
1841C4—42no—
1842C4—42no—
1843C4—44no—
1844C4—41no—
1845C4—44no—
1846C4—42no—
1847C4—42no—
1848C4—42no—
1849C4—42no—
1850C4—41no—
1851C4—42no—
1852C4—44no—
1853C4—41no—
1854C4—42no—
1855C4C2×D4214yes—
1856C2—28no—
1857C2—44no—
1858C2—44no—
1859C2—48no—
1860C2—81no—
1861C2—82no—
1862C2—81no—
1863C2C22×D4211yescharacteristic
1864C2#6285912yes—
1865C2#6289811yescharacteristic
1866C2#6298812yes—
1867C2#6306311yescharacteristic
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×#3489C2semidirect
2. C2×#3485C2semidirect
3. #59818C2semidirect
4. #59313C2semidirect
5. #59002C2semidirect
6. #58995C2semidirect
7. #52103C2semidirect
8. C2×#2680C2semidirect
9. #45332C2semidirect
10. #45321C2semidirect
11. #45134C2semidirect
12. #45103C2semidirect
13. #44758C2semidirect
14. #44447C2semidirect
15. #43492C2semidirect
16. #43017C2semidirect
17. #39360C2semidirect
18. #39354C2semidirect
19. #37656C2semidirect
20. #37654C2semidirect
21. #37651C2semidirect
22. #37647C2semidirect
23. #36213C2semidirect
24. #36179C2semidirect
25. #36085C2semidirect
26. #36020C2semidirect
27. #36009C2semidirect
28. #35750C2semidirect
29. #34309C2semidirect
30. C22×2−1+4C22semidirect
32. C23×#41C22semidirect
35. C2×D4×Q8C22semidirect
36. C2×D4×Q8C22semidirect
37. C2×#548C22semidirect
38. C2×#548C22semidirect
41. C2×#547C22semidirect
42. C2×#547C22semidirect
43. C2×#547C22semidirect
44. C2×#547C22semidirect
45. C2×#547C22semidirect
46. C2×#547C22semidirect
47. C2×#547C22semidirect
48. C2×#547C22semidirect
49. C2×#547C22semidirect
50. C2×#547C22semidirect
55. C2×#546C22semidirect
56. C2×#546C22semidirect
57. C2×#546C22semidirect
58. C2×#546C22semidirect
59. C2×#546C22semidirect
60. C2×#537C22semidirect
61. C2×#537C22semidirect
63. C2×#536C22semidirect
64. C2×#536C22semidirect
65. C2×#536C22semidirect
67. C2×#534C22semidirect
69. C2×#525C22semidirect
70. C2×#525C22semidirect
71. C2×#525C22semidirect
73. C22×#123C22semidirect
74. C22×C22⋊Q8C22semidirect
75. C22×C22⋊Q8C22semidirect
76. C2×#520C22semidirect
77. C2×#518C22semidirect
78. #2868C22semidirect
79. #2856C22semidirect
80. #2849C22semidirect
81. #2848C22semidirect
82. #2683C22semidirect
83. #2682C22semidirect
84. #2681C22semidirect
85. #2681C22semidirect
86. #2681C22semidirect
87. #2681C22semidirect
88. #2680C22semidirect
89. #2680C22semidirect
90. #2680C22semidirect
91. #2680C22semidirect
92. #2680C22semidirect
93. #2680C22semidirect
94. #2680C22semidirect
95. #2680C22semidirect
96. #2680C22semidirect
97. #2680C22semidirect
98. #2680C22semidirect
99. #2680C22semidirect
100. #2680C22semidirect
101. #2680C22semidirect
102. #2679C22semidirect
103. #2678C22semidirect
104. #2678C22semidirect
105. #2678C22semidirect
106. #2678C22semidirect
107. #2677C22semidirect
108. #2677C22semidirect
109. #2674C22semidirect
110. #2674C22semidirect
111. #2674C22semidirect
112. #2672C22semidirect
113. #2672C22semidirect
114. #2672C22semidirect
115. #2671C22semidirect
116. #2671C22semidirect
117. #2671C22semidirect
118. #2669C22semidirect
119. #2669C22semidirect
120. #2668C22semidirect
121. #2668C22semidirect
122. #2621C22semidirect
123. #2621C22semidirect
124. #2618C22semidirect
125. #2617C22semidirect
127. #2616C22semidirect
128. #2614C22semidirect
130. #2555C22semidirect
131. #2551C22semidirect
132. #2547C22semidirect
133. #2546C22semidirect
134. #2543C22semidirect
135. #2543C22semidirect
136. #2542C22semidirect
137. #2542C22semidirect
138. #2542C22semidirect
139. #2542C22semidirect
140. #2537C22semidirect
141. #2536C22semidirect
142. #2535C22semidirect
143. #2501C22semidirect
144. #2501C22semidirect
145. #2501C22semidirect
146. #2501C22semidirect
147. #2486C22semidirect
148. #2486C22semidirect
149. #2472C22semidirect
150. #2472C22semidirect
151. #2472C22semidirect
152. #2464C22semidirect
153. #2464C22semidirect
154. #2464C22semidirect
155. #2461C22semidirect
156. #2461C22semidirect
157. #2455C22semidirect
158. #2455C22semidirect
159. #2449C22semidirect
160. #2449C22semidirect
161. #2449C22semidirect
162. #2443C22semidirect
163. #2443C22semidirect
164. #2443C22semidirect
165. #2440C22semidirect
166. #2440C22semidirect
167. #2440C22semidirect
168. #2440C22semidirect
169. #2437C22semidirect
170. #2437C22semidirect
171. #2435C22semidirect
172. #2434C22semidirect
173. #2434C22semidirect
174. #2434C22semidirect
175. #2432C22semidirect
176. #2432C22semidirect
177. #2432C22semidirect
178. #2430C22semidirect
179. #2430C22semidirect
180. #2430C22semidirect
181. #2430C22semidirect
182. #2430C22semidirect
183. #2429C22semidirect
184. #2429C22semidirect
185. #2427C22semidirect
186. #2427C22semidirect
187. #2425C22semidirect
188. #2425C22semidirect
189. #2425C22semidirect
190. #2425C22semidirect
191. #2424C22semidirect
192. #2424C22semidirect
193. #2422C22semidirect
194. #2422C22semidirect
195. #2422C22semidirect
196. #2422C22semidirect
197. #2418C22semidirect
198. #2418C22semidirect
199. #2418C22semidirect
200. #2417C22semidirect
201. #2417C22semidirect
202. #2415C22semidirect
203. #2415C22semidirect
204. #2413C22semidirect
205. #2413C22semidirect
206. #2412C22semidirect
207. #2412C22semidirect
208. #2410C22semidirect
209. #2410C22semidirect
210. #2409C22semidirect
211. #2409C22semidirect
212. #2409C22semidirect
213. #2408C22semidirect
214. #2407C22semidirect
215. #2407C22semidirect
216. #2407C22semidirect
217. #2406C22semidirect
218. #2406C22semidirect
219. #2406C22semidirect
220. #2406C22semidirect
221. #2406C22semidirect
222. #2405C22semidirect
223. #2405C22semidirect
224. #2392C22semidirect
225. #2392C22semidirect
226. C2×#398C22semidirect
227. C2×#397C22semidirect
229. #2388C22semidirect
230. C2×#395C22semidirect
232. #2367C22semidirect
233. #2364C22semidirect
234. #2362C22semidirect
235. #2361C22semidirect
236. #2359C22semidirect
237. #2358C22semidirect
238. #2358C22semidirect
239. #2352C22semidirect
240. #2349C22semidirect
241. D4×C4⋊C4C22semidirect
242. #2342C22semidirect
243. #2339C22semidirect
244. #2339C22semidirect
245. #2339C22semidirect
246. #2339C22semidirect
247. D4×C22⋊C4C22semidirect
248. #2324C22semidirect
249. #2323C22semidirect
250. #2322C22semidirect
251. #2321C22semidirect
252. C4×#127C22semidirect
253. C4×#124C22semidirect
254. C4×#121C22semidirect
255. C4×#120C22semidirect
256. #2293C22semidirect
257. C2×#388C22semidirect
258. C2×#385C22semidirect
259. C2×#384C22semidirect
260. C42×D4C22semidirect
317. #546D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#34852
#598182
#593132
#590022
#589952
#521032
C2×#26802
#453322
#453212
#451342
#451032
#447582
#444472
#434922
#430172
#393602
#393542
#376562
#376542
#376512
#376472
#362132
#361792
#360852
#360202
#360092
#357502
#343092