Finite Group Databasebeta

← #10576129

Subgroups — #10576129

Order 512.

10394 conjugacy classes of subgroups.

The subgroup lattice has 1754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3584C211yesmaximal, characteristic, complemented
2C22×#577C211yesmaximal, characteristic, complemented
3#62859C211yesmaximal, characteristic, complemented
4#62852C211yesmaximal, characteristic, complemented
5#61088C214yesmaximal, complemented
6#61087C214yesmaximal, complemented
7#61083C214yesmaximal, complemented
8#61082C214yesmaximal, complemented
9#61062C218yesmaximal, complemented
10#61061C214yesmaximal, complemented
11#61058C214yesmaximal, complemented
12#61055C218yesmaximal, complemented
13#61052C214yesmaximal, complemented
14#61050C214yesmaximal, complemented
15C2×#3154C211yesmaximal, characteristic, complemented
16#60450C211yesmaximal, characteristic, complemented
17C2×#3057C211yesmaximal, characteristic, complemented
18#60427C211yesmaximal, characteristic, complemented
19#60426C211yesmaximal, characteristic, complemented
20#60370C211yesmaximal, characteristic, complemented
21#60369C211yesmaximal, characteristic, complemented
22#60368C211yesmaximal, characteristic, complemented
23#60367C211yesmaximal, characteristic, complemented
24#60167C211yesmaximal, characteristic, complemented
25#60140C211yesmaximal, characteristic, complemented
26C2×#585C2211yescharacteristic
27C2×#585C2211yescharacteristic, complemented
28C22×2−1+4C2211yescharacteristic, complemented
29C22×H(5,𝔽2)C2211yescharacteristic, complemented
30#3584—216no—
31C2×#578C2212yescomplemented
32C2×#578C2212yescomplemented
33C2×#577—216no—
34C2×#577C2214yescomplemented
35C2×#577C2214yescomplemented
36C2×#577C2214yescomplemented
37C2×#577C2214yescomplemented
38C2×#577C2212yescomplemented
39C2×#577C2212yescomplemented
40C2×#577C2212yescomplemented
41C2×#577C2212yescomplemented
42C2×#576C2212yescomplemented
43C2×#576C2212yescomplemented
44C2×#575C2211yescharacteristic
45C2×#575C2211yescharacteristic, complemented
46C2×#575C2214yescomplemented
47C22×#137C2211yescharacteristic, complemented
48C22×#137C2212yescomplemented
49C22×#137C2211yescharacteristic, complemented
50C22×AGL(1,ℤ/8)C2211yescharacteristic, complemented
51C22×AGL(1,ℤ/8)C2212yescomplemented
52C22×AGL(1,ℤ/8)C2211yescharacteristic, complemented
53C22×#135C2211yescharacteristic
54C22×#135C2212yescomplemented
55C22×#135C2211yescharacteristic, complemented
56C22×#135C2214yescomplemented
57C23×SD16C2211yescharacteristic, complemented
58C23×SD16C2212yescomplemented
59C22×#131C2211yescharacteristic, complemented
60C22×#131C2211yescharacteristic, complemented
61#3500—22no—
62#3500—22no—
63#3500C2214yescomplemented
64#3500C2214yescomplemented
65#3499—22no—
66#3499C2214yescomplemented
67#3498—22no—
68#3498C2214yescomplemented
69#3489—24no—
70#3489C2218yescomplemented
71#3488—24no—
72#3488C2218yescomplemented
73#3487C2214yescomplemented
74#3486C2214yescomplemented
75#3485—24no—
76#3485C2214yescomplemented
77#3484—24no—
78#3484C2214yescomplemented
79#3449—22no—
80#3449—22no—
81#3449C2211yescharacteristic
82#3449C2211yescharacteristic, complemented
83#3449C2211yescharacteristic, complemented
84C2×#536—22no—
85C2×#536C2211yescharacteristic, complemented
86C2×#536C2211yescharacteristic, complemented
87C2×#535—22no—
88C2×#535C2211yescharacteristic
89C2×#535C2211yescharacteristic, complemented
90#3428C2211yescharacteristic, complemented
91#3428C2211yescharacteristic, complemented
92#3284C22116yescomplemented
93#3282C22116yescomplemented
94#3282C22116yescomplemented
95D4×SD16C22116yescomplemented
96#3278C22116yescomplemented
97#3277C22116yescomplemented
98#3273C22116yescomplemented
99#3272C22116yescomplemented
100#3271C22116yescomplemented
101#3270C22116yescomplemented
102#3269C22116yescomplemented
103#3268C22116yescomplemented
104#3267C22116yescomplemented
105#3266C22116yescomplemented
106#3265C22116yescomplemented
107#3264C22116yescomplemented
108#3154C2214yescomplemented
109#3154C2214yescomplemented
110#3154C2214yescomplemented
111#3154C2214yescomplemented
112C2×#497C2212yescomplemented
113C2×#496C2212yescomplemented
114C2×#495C2212yescomplemented
115C2×#492C2212yescomplemented
116#3061C2214yescomplemented
117#3060C2214yescomplemented
118#3059C2212yescomplemented
119#3058C2212yescomplemented
120#3057C2214yescomplemented
121#3057C2214yescomplemented
122#3057C2212yescomplemented
123#3057C2212yescomplemented
124#3057C2214yescomplemented
125#3057C2214yescomplemented
126#3054C2214yescomplemented
127C2×#468C2214yescomplemented
128#3050C2214yescomplemented
129C2×#465C2214yescomplemented
130#3046C2218yescomplemented
131#3045C2218yescomplemented
132#3044C2214yescomplemented
133#3043C2214yescomplemented
134#3042C2214yescomplemented
135#3041C2214yescomplemented
136#3040C2214yescomplemented
137#3040C2214yescomplemented
138#3039C2214yescomplemented
139#3038C2214yescomplemented
140#3013C2218yescomplemented
141#3012C2218yescomplemented
142#3011C2214yescomplemented
143#3011C2214yescomplemented
144#3011C2214yescomplemented
145#3010C2214yescomplemented
146#3010C2214yescomplemented
147#3010C2214yescomplemented
148#3009C2214yescomplemented
149#3009C2214yescomplemented
150#3009C2214yescomplemented
151#3008C2214yescomplemented
152#3008C2214yescomplemented
153#3008C2214yescomplemented
154#3007C2218yescomplemented
155#3006C2218yescomplemented
156#3005C2214yescomplemented
157#3005C2214yescomplemented
158#3004C2214yescomplemented
159#3003C2214yescomplemented
160#2952C2214yescomplemented
161#2951C2214yescomplemented
162#2950C2212yescomplemented
163#2949C2212yescomplemented
164#2949C2212yescomplemented
165#2948C2212yescomplemented
166#2943C2214yescomplemented
167C4×#135C2214yescomplemented
168#2932C2214yescomplemented
169#2931C2214yescomplemented
170#2930C2214yescomplemented
171#2930C2214yescomplemented
172#2929C2214yescomplemented
173#2929C2214yescomplemented
174C2×#427C2211yescharacteristic, complemented
175#2905C2211yescharacteristic, complemented
176#2896C2211yescharacteristic, complemented
177#2896C2211yescharacteristic, complemented
178#2896C2211yescharacteristic, complemented
179#2896C2211yescharacteristic, complemented
180C2×#419C2211yescharacteristic, complemented
181C2×#418C2211yescharacteristic, complemented
182#2879C2211yescharacteristic, complemented
183#2879C2211yescharacteristic, complemented
184C2×#405C2211yescharacteristic, complemented
185#585—28no—
186#585—28no—
187#585—44no—
188#585—44no—
189C2×2−1+4—22no—
190C2×2−1+4—22no—
191C2×2−1+4—21no—
192C2×2−1+4—21no—
193C2×2−1+4—28no—
194C2×2−1+4—44no—
195C2×2−1+4C2314yes—
196C2×2−1+4C2314yes—
197C2×2−1+4C2312yes—
198C2×2−1+4C2312yes—
199C2×2−1+4C2312yes—
200C2×2−1+4C2312yescomplemented
201C2×H(5,𝔽2)—22no—
202C2×H(5,𝔽2)—22no—
203C2×H(5,𝔽2)—22no—
204C2×H(5,𝔽2)—21no—
205C2×H(5,𝔽2)—22no—
206C2×H(5,𝔽2)—21no—
207C2×H(5,𝔽2)—28no—
208C2×H(5,𝔽2)—44no—
209C2×H(5,𝔽2)C2314yes—
210C2×H(5,𝔽2)C2314yes—
211C2×H(5,𝔽2)C2312yes—
212C2×H(5,𝔽2)C2312yes—
213C2×H(5,𝔽2)C2312yes—
214C2×H(5,𝔽2)C2312yescomplemented
215C22×#41—22no—
216C22×#41—22no—
217C22×#41—22no—
218C22×#41—22no—
219C22×#41—21no—
220C22×#41—21no—
221C22×#41—22no—
222C22×#41C2311yescharacteristic
223C22×#41C2311yescharacteristic
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2314yes—
227C22×#41C2311yescharacteristic
228C22×#41C2311yescharacteristic
229C22×#41C2311yescharacteristic
230C22×#41C2311yescharacteristic
231C22×#41C2314yescomplemented
232C23×Q8—21no—
233C23×Q8C2311yescharacteristic
234C23×Q8C2312yes—
235C23×D4—21no—
236C23×D4—22no—
237C23×D4C2311yescharacteristic
238C23×D4C2312yes—
239#578—216no—
240#578—216no—
241#577—216no—
242#577—216no—
243#577—232no—
244#577—232no—
245#577—232no—
246#577—232no—
247#577—216no—
248#577—216no—
249#576—216no—
250#576—216no—
251#575—28no—
252#575—28no—
253#575—232no—
254C2×#137—28no—
255C2×#137—216no—
256C2×#137—44no—
257C2×#137C2312yes—
258C2×#137C2312yes—
259C2×#137C2314yes—
260C2×#137C2312yes—
261C2×#137C2314yes—
262C2×#137C2318yes—
263C2×#137C2318yes—
264C2×#137C2314yes—
265C2×#137C2314yescomplemented
266C2×#137C2312yescomplemented
267C2×#137C2314yescomplemented
268C2×#137C2314yescomplemented
269C2×#137C2314yescomplemented
270C2×#137C2314yescomplemented
271C2×AGL(1,ℤ/8)—28no—
272C2×AGL(1,ℤ/8)—216no—
273C2×AGL(1,ℤ/8)—44no—
274C2×AGL(1,ℤ/8)C2312yes—
275C2×AGL(1,ℤ/8)C2312yes—
276C2×AGL(1,ℤ/8)C2314yes—
277C2×AGL(1,ℤ/8)C2312yes—
278C2×AGL(1,ℤ/8)C2314yes—
279C2×AGL(1,ℤ/8)C2318yes—
280C2×AGL(1,ℤ/8)C2318yes—
281C2×AGL(1,ℤ/8)C2314yes—
282C2×AGL(1,ℤ/8)C2314yes—
283C2×AGL(1,ℤ/8)C2314yescomplemented
284C2×AGL(1,ℤ/8)C2312yescomplemented
285C2×AGL(1,ℤ/8)C2314yescomplemented
286C2×AGL(1,ℤ/8)C2314yescomplemented
287C2×AGL(1,ℤ/8)C2314yescomplemented
288C2×#135—232no—
289C2×#135—216no—
290C2×#135—28no—
291C2×#135D4116yescomplemented
292C2×#135C2312yes—
293C2×#135C2312yes—
294C2×#135C2314yes—
295C2×#135C2318yes—
296C2×#135C2318yes—
297C2×#135C2312yes—
298C2×#135C2312yes—
299C2×#135C2312yes—
300C2×#135C2312yes—
301C2×#135C2312yescomplemented
302C2×#135C2312yescomplemented
303C2×#135C2314yescomplemented
304C2×#135C2314yescomplemented
305C2×#135C2314yescomplemented
306C2×#135C2314yescomplemented
307C2×#135C2314yescomplemented
308C22×Q16C2312yes—
309C22×Q16C2311yescharacteristic
310C22×Q16C2311yescharacteristic, complemented
311C22×Q16C2314yescomplemented
312C22×Q16C2312yescomplemented
313C22×SD16—216no—
314C22×SD16—28no—
315C22×SD16C2312yes—
316C22×SD16C2312yes—
317C22×SD16C2312yes—
318C22×SD16C2312yes—
319C22×SD16C2312yes—
320C22×SD16C2312yes—
321C22×SD16C2312yes—
322C22×SD16C2318yes—
323C22×SD16C2312yes—
324C22×SD16C2318yes—
325C22×SD16C2312yes—
326C22×SD16C2311yescharacteristic
327C22×SD16C2311yescharacteristic
328C22×SD16C2311yescharacteristic, complemented
329C22×SD16C2311yescharacteristic, complemented
330C22×SD16C2314yescomplemented
331C22×SD16C2314yescomplemented
332C22×SD16C2312yescomplemented
333C22×D8C2312yes—
334C22×D8C2312yes—
335C22×D8C2311yescharacteristic
336C22×D8C2311yescharacteristic, complemented
337C22×D8C2314yescomplemented
338C2×#131—28no—
339C2×#131—28no—
340C2×#131C2312yes—
341C2×#131C2312yes—
342C2×#131C2312yes—
343C2×#131C2312yes—
344C2×#131C2312yes—
345C2×#131C2312yes—
346C2×#131C2312yescomplemented
347C2×#131C2312yescomplemented
348C22×M16C2311yescharacteristic
349C22×M16C2311yescharacteristic
350C22×M16C2311yescharacteristic
351C22×M16C2312yes—
352C22×M16C2312yescomplemented
353C23×C8C2312yes—
354C23×C8C2311yescharacteristic
355C23×C8C2312yescomplemented
356#550—28no—
357#550C23116yes—
358D4×Q8—28no—
359D4×Q8C23116yescomplemented
360#548—28no—
361#548—28no—
362#548C23116yes—
363#548C23116yescomplemented
364#547—216no—
365#547—28no—
366#547—216no—
367#547C23116yescomplemented
368#546—216no—
369#546—28no—
370#546—216no—
371#546—216no—
372#546—28no—
373#546—216no—
374#546C23116yes—
375#546C23116yescomplemented
376D42—216no—
377D42—28no—
378D42—216no—
379D42C23116yes—
380#537—28no—
381#537—28no—
382#537D414yes—
383#537C2314yes—
384#537C2314yes—
385#536—22no—
386#536—22no—
387#536—21no—
388#536—21no—
389#536—24no—
390#536—24no—
391#536—24no—
392#536—24no—
393#536—28no—
394#536—28no—
395#536—22no—
396#536—22no—
397#536D412yes—
398#536D412yes—
399#536C2314yes—
400#536C2314yes—
401#536C2312yes—
402#536C2312yes—
403#536C2314yescomplemented
404#536C2314yescomplemented
405#535—22no—
406#535—22no—
407#535—21no—
408#535—21no—
409#535—24no—
410#535—24no—
411#535—24no—
412#535—24no—
413#535—28no—
414#535—28no—
415#535—22no—
416#535—22no—
417#535D412yes—
418#535D412yes—
419#535C2314yes—
420#535C2314yes—
421#535C2314yes—
422#535C2314yes—
423#535C2312yes—
424#535C2312yes—
425#534—22no—
426#534—22no—
427#534—28no—
428#534—28no—
429#534D414yes—
430#532—22no—
431#532—22no—
432#532—24no—
433#532—24no—
434#532—24no—
435#532—24no—
436#532C2314yes—
437C2×C4⋊Q8—21no—
438C2×C4⋊Q8—24no—
439C2×C4⋊Q8C2312yescomplemented
440C2×#127—21no—
441C2×#127—24no—
442C2×#127C2312yes—
443C2×#124—21no—
444C2×#124—21no—
445C2×#124—24no—
446C2×#124—24no—
447C2×#124C2312yes—
448C2×#124C2312yescomplemented
449#525—22no—
450#525—22no—
451#525—28no—
452#525—28no—
453#525—28no—
454#525—28no—
455#525C2314yes—
456#525C2314yes—
457#525C2314yes—
458#525C2314yes—
459C2×#123—22no—
460C2×#123—28no—
461C2×#123—22no—
462C2×C22⋊Q8—28no—
463C2×C22⋊Q8—22no—
464C2×C22⋊Q8C2314yescomplemented
465C2×#121—28no—
466C2×#121—22no—
467C2×#121C2314yes—
468C2×#120—22no—
469C2×#120—28no—
470C2×#120—22no—
471#520—22no—
472#520—22no—
473#520C2314yes—
474#520C2314yescomplemented
475#519C2312yes—
476#519C2312yes—
477#518—22no—
478#518—22no—
479#518C2312yes—
480#518C2312yes—
481C4×#41—22no—
482C4×#41—22no—
483C4×#41C2314yes—
484C4×#41C2314yescomplemented
485C2×#117—22no—
486C2×#117—22no—
487C2×#117C2311yescharacteristic
488C2×#117C2311yescharacteristic
489C2×#117C2311yescharacteristic
490#497C2318yescomplemented
491#497C2318yescomplemented
492#496C2318yescomplemented
493#496C2318yescomplemented
494#495C2318yescomplemented
495#495C2318yescomplemented
496#492C2318yescomplemented
497#492C2318yescomplemented
498#470C2318yescomplemented
499#469C2318yescomplemented
500#468C23116yescomplemented
501#468C2318yescomplemented
502#468C23116yescomplemented
503#468C2318yescomplemented
504#467C2318yescomplemented
505#466C2318yescomplemented
506#465C23116yescomplemented
507#465C2318yescomplemented
508#465C23116yescomplemented
509#465C2318yescomplemented
510#464C23116yescomplemented
511#464C23116yescomplemented
512#463C23116yescomplemented
513#463C23116yescomplemented
514#462C23116yescomplemented
515#461C23116yescomplemented
516#460C23116yescomplemented
517#459C23116yescomplemented
518#452C23116yes—
519#452C23116yescomplemented
520#452C23116yescomplemented
521#452C23116yescomplemented
522#451C23116yescomplemented
523#451C23116yescomplemented
524#450C23116yes—
525#450C23116yescomplemented
526#449C23116yes—
527#449C23116yescomplemented
528#449C23116yescomplemented
529#449C23116yescomplemented
530#448C23116yescomplemented
531#448C23116yescomplemented
532#447C23116yes—
533#447C23116yescomplemented
534#442C2318yescomplemented
535#441C2318yescomplemented
536#440C2318yescomplemented
537#440C2318yescomplemented
538C4×Q16C2318yescomplemented
539C4×SD16C2318yescomplemented
540C4×SD16C2318yescomplemented
541C4×D8C2318yescomplemented
542#436C23116yescomplemented
543#435C23116yescomplemented
544#435C23116yescomplemented
545C8×D4C23116yescomplemented
546#427C2312yes—
547#427C2312yes—
548#427C2312yescomplemented
549#427C2312yescomplemented
550C2×#107C2312yescomplemented
551C2×#106C2312yescomplemented
552#424C2314yes—
553#424C2314yescomplemented
554#423C2314yescomplemented
555#419C2314yes—
556#419C2312yes—
557#419C2312yes—
558#419C2314yescomplemented
559#419C2312yescomplemented
560#419C2312yescomplemented
561#418C2314yes—
562#418C2314yes—
563#418C2312yes—
564#418C2312yes—
565#418C2312yescomplemented
566#418C2312yescomplemented
567#417C2314yes—
568#417C2314yescomplemented
569#417C2314yescomplemented
570#417C2314yescomplemented
571#416C2314yes—
572#416C2314yes—
573#416C2314yes—
574#416C2314yescomplemented
575C2×#103C2314yescomplemented
576C2×#102C2314yes—
577#408C2314yes—
578#408C2314yes—
579#408C2314yes—
580#408C2314yescomplemented
581#407C2314yes—
582#407C2314yescomplemented
583#405C2312yes—
584#405C2312yes—
585#405C2312yescomplemented
586#405C2312yescomplemented
587C2×#97C2312yescomplemented
588C2×C4×C8C2312yescomplemented
589C25—22no—
590C25—21no—
5912−1+4—216no—
5922−1+4—216no—
5932−1+4—28no—
5942−1+4—28no—
5952−1+4—28no—
5962−1+4—28no—
5972−1+4—48no—
5982−1+4—48no—
5992−1+4—44no—
6002−1+4—44no—
6012−1+4—44no—
6022−1+4—44no—
6032−1+4—48no—
6042−1+4—48no—
6052−1+4—416no—
6062−1+4—416no—
607H(5,𝔽2)—28no—
608H(5,𝔽2)—28no—
609H(5,𝔽2)—216no—
610H(5,𝔽2)—216no—
611H(5,𝔽2)—28no—
612H(5,𝔽2)—28no—
613H(5,𝔽2)—416no—
614H(5,𝔽2)—416no—
615H(5,𝔽2)—48no—
616H(5,𝔽2)—48no—
617H(5,𝔽2)—44no—
618H(5,𝔽2)—44no—
619H(5,𝔽2)—44no—
620H(5,𝔽2)—44no—
621H(5,𝔽2)—48no—
622H(5,𝔽2)—48no—
623H(5,𝔽2)—416no—
624H(5,𝔽2)—416no—
625C2×#41—24no—
626C2×#41—22no—
627C2×#41—24no—
628C2×#41—22no—
629C2×#41—22no—
630C2×#41—22no—
631C2×#41—24no—
632C2×#41—24no—
633C2×#41—24no—
634C2×#41—22no—
635C2×#41—24no—
636C2×#41—22no—
637C2×#41—24no—
638C2×#41—28no—
639C2×#41—28no—
640C2×#41—24no—
641C2×#41—22no—
642C2×#41—22no—
643C2×#41—21no—
644C2×#41—21no—
645C2×#41—21no—
646C2×#41—21no—
647C2×#41—24no—
648C2×#41—24no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—21no—
652C2×#41—24no—
653C2×#41—21no—
654C2×#41—24no—
655C2×#41—24no—
656C2×#41—24no—
657C2×#41—24no—
658C2×#41—24no—
659C2×#41—24no—
660C2×#41—24no—
661C2×#41—24no—
662C2×#41—24no—
663C2×#41—216no—
664C2×#41—216no—
665C2×#41—28no—
666C2×#41—28no—
667C2×#41—24no—
668C2×#41—24no—
669C2×#41—24no—
670C2×#41—24no—
671C2×#41—44no—
672C2×#41—44no—
673C2×#41—48no—
674C2×#41—48no—
675C2×#41—48no—
676C2×#41—48no—
677C2×#41—416no—
678C2×#41—416no—
679C2×#41—416no—
680C2×#41—416no—
681C2×#41—416no—
682C2×#41C2×D418yes—
683C2×#41C2×D412yes—
684C2×#41C2×D412yes—
685C2×#41C2×D412yes—
686C2×#41C2×D412yes—
687C2×#41C2×D418yescomplemented
688C2×#41C2412yes—
689C2×#41C2412yes—
690C2×#41C2412yes—
691C2×#41C2412yes—
692C2×#41C2414yes—
693C2×#41C2418yes—
694C2×#41C2414yes—
695C2×#41C2418yes—
696C2×#41C2414yes—
697C2×#41C2414yes—
698C2×#41C2412yes—
699C2×#41C2412yes—
700C2×#41C2412yes—
701C2×#41C2412yes—
702C2×#41C2412yes—
703C2×#41C2412yes—
704C2×#41C2412yes—
705C2×#41C2412yes—
706C22×Q8—24no—
707C22×Q8—22no—
708C22×Q8—24no—
709C22×Q8—22no—
710C22×Q8—22no—
711C22×Q8—22no—
712C22×Q8—21no—
713C22×Q8—21no—
714C22×Q8—22no—
715C22×Q8—21no—
716C22×Q8—24no—
717C22×Q8—28no—
718C22×Q8—24no—
719C22×Q8—24no—
720C22×Q8—44no—
721C22×Q8—48no—
722C22×Q8C2×D411yescharacteristic
723C22×Q8C2×D411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2414yes—
730C22×Q8C2418yes—
731C22×Q8C2414yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2411yescharacteristic
734C22×D4—21no—
735C22×D4—21no—
736C22×D4—28no—
737C22×D4—21no—
738C22×D4—21no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—24no—
742C22×D4—24no—
743C22×D4—24no—
744C22×D4—24no—
745C22×D4—24no—
746C22×D4—24no—
747C22×D4—22no—
748C22×D4—24no—
749C22×D4—22no—
750C22×D4—24no—
751C22×D4—22no—
752C22×D4—28no—
753C22×D4—28no—
754C22×D4—22no—
755C22×D4—24no—
756C22×D4—216no—
757C22×D4—24no—
758C22×D4—21no—
759C22×D4—21no—
760C22×D4—22no—
761C22×D4—21no—
762C22×D4—24no—
763C22×D4—24no—
764C22×D4—24no—
765C22×D4—44no—
766C22×D4—48no—
767C22×D4—416no—
768C22×D4C2×D412yes—
769C22×D4C2×D411yescharacteristic
770C22×D4C2×D412yes—
771C22×D4C2×D411yescharacteristic
772C22×D4C2412yes—
773C22×D4C2412yes—
774C22×D4C2411yescharacteristic
775C22×D4C2411yescharacteristic
776C22×D4C2412yes—
777C22×D4C2414yes—
778C22×D4C2418yes—
779C22×D4C2414yes—
780C22×D4C2411yescharacteristic
781C22×D4C2411yescharacteristic
782C23×C4—21no—
783C23×C4—21no—
784C23×C4—21no—
785C23×C4—22no—
786C23×C4—24no—
787C23×C4—21no—
788C23×C4—21no—
789C23×C4—24no—
790C23×C4—22no—
791C23×C4—22no—
792C23×C4C2412yes—
793C23×C4C2412yes—
794C23×C4C2411yescharacteristic
795#137—216no—
796#137—216no—
797#137—28no—
798#137—28no—
799#137—28no—
800#137—28no—
801#137—232no—
802#137—232no—
803#137—216no—
804#137—216no—
805#137—216no—
806#137—216no—
807#137—48no—
808#137—48no—
809AGL(1,ℤ/8)—216no—
810AGL(1,ℤ/8)—216no—
811AGL(1,ℤ/8)—28no—
812AGL(1,ℤ/8)—28no—
813AGL(1,ℤ/8)—28no—
814AGL(1,ℤ/8)—28no—
815AGL(1,ℤ/8)—216no—
816AGL(1,ℤ/8)—216no—
817AGL(1,ℤ/8)—232no—
818AGL(1,ℤ/8)—232no—
819AGL(1,ℤ/8)—216no—
820AGL(1,ℤ/8)—216no—
821AGL(1,ℤ/8)—48no—
822AGL(1,ℤ/8)—48no—
823#135—216no—
824#135—216no—
825#135—216no—
826#135—232no—
827#135—232no—
828#135—216no—
829#135—216no—
830#135—216no—
831#135—28no—
832#135—28no—
833#135—28no—
834#135—28no—
835#135C2×D4116yescomplemented
836#135C2×D4116yescomplemented
837#135C2×D4116yescomplemented
838#135C2×D4116yescomplemented
839C2×Q16—28no—
840C2×Q16—216no—
841C2×Q16—24no—
842C2×Q16—44no—
843C2×Q16C2×D418yescomplemented
844C2×Q16C2418yes—
845C2×Q16C2412yes—
846C2×Q16C2414yes—
847C2×Q16C2412yes—
848C2×Q16C2414yes—
849C2×Q16C2418yes—
850C2×Q16C2412yes—
851C2×Q16C2412yes—
852C2×SD16—28no—
853C2×SD16—28no—
854C2×SD16—232no—
855C2×SD16—232no—
856C2×SD16—216no—
857C2×SD16—216no—
858C2×SD16—28no—
859C2×SD16—28no—
860C2×SD16—28no—
861C2×SD16—28no—
862C2×SD16—28no—
863C2×SD16—28no—
864C2×SD16—24no—
865C2×SD16—24no—
866C2×SD16—44no—
867C2×SD16—44no—
868C2×SD16C2×D418yescomplemented
869C2×SD16C2×D418yescomplemented
870C2×SD16C2414yes—
871C2×SD16C2414yes—
872C2×SD16C2418yes—
873C2×SD16C2418yes—
874C2×SD16C2414yes—
875C2×SD16C2414yes—
876C2×SD16C2412yes—
877C2×SD16C2412yes—
878C2×SD16C2414yes—
879C2×SD16C2414yes—
880C2×SD16C2412yes—
881C2×SD16C2412yes—
882C2×SD16C2414yes—
883C2×SD16C2414yes—
884C2×SD16C2418yes—
885C2×SD16C2418yes—
886C2×SD16C2412yes—
887C2×SD16C2412yes—
888C2×SD16C2412yes—
889C2×SD16C2412yes—
890C2×D8—28no—
891C2×D8—216no—
892C2×D8—24no—
893C2×D8—44no—
894C2×D8C2×D418yescomplemented
895C2×D8C2418yes—
896C2×D8C2412yes—
897C2×D8C2414yes—
898C2×D8C2412yes—
899C2×D8C2414yes—
900C2×D8C2418yes—
901C2×D8C2412yes—
902C2×D8C2412yes—
903#131—28no—
904#131—28no—
905#131—28no—
906#131—28no—
907#131—28no—
908#131—28no—
909#131—28no—
910#131—28no—
911C2×M16—24no—
912C2×M16—24no—
913C2×M16—24no—
914C2×M16—28no—
915C2×M16—28no—
916C2×M16C2412yes—
917C2×M16C2412yes—
918C2×M16C2412yes—
919C2×M16C2414yes—
920C2×M16C2414yes—
921C2×M16C2412yes—
922C2×M16C2412yes—
923C2×M16C2412yes—
924C2×M16C2414yes—
925C2×M16C2414yes—
926C22×C8—28no—
927C22×C8—28no—
928C22×C8C2×D418yescomplemented
929C22×C8C2412yes—
930C22×C8C2414yes—
931C22×C8C2414yes—
932C22×C8C2412yes—
933C22×C8C2414yes—
934C22×C8C2414yes—
935C22×C8C2412yes—
936C22×C8C2411yescharacteristic
937C22×C8C2411yescharacteristic
938C22×C8C2411yescharacteristic
939C22×C8C2411yescharacteristic
940C22×C8C2411yescharacteristic
941C22×C8C2411yescharacteristic
942C4⋊Q8—22no—
943C4⋊Q8—24no—
944C4⋊Q8—24no—
945C4⋊Q8—22no—
946C4⋊Q8—216no—
947C4⋊Q8—24no—
948C4⋊Q8C2×D414yes—
949C4⋊Q8C2418yes—
950#127—24no—
951#127—22no—
952#127—216no—
953#127—24no—
954#127—22no—
955#127—24no—
956#127C2×D414yes—
957#127C2418yes—
958#124—24no—
959#124—22no—
960#124—24no—
961#124—22no—
962#124—22no—
963#124—24no—
964#124—24no—
965#124—22no—
966#124—216no—
967#124—216no—
968#124—24no—
969#124—24no—
970#124C2×D414yes—
971#124C2×D414yes—
972#124C2418yes—
973#124C2418yes—
974#123—28no—
975#123—28no—
976#123—24no—
977#123—24no—
978#123—24no—
979#123—24no—
980#123—216no—
981#123—216no—
982#123—28no—
983#123—216no—
984#123—28no—
985#123—216no—
986#123C2×D418yes—
987#123C2×D418yes—
988C22⋊Q8—24no—
989C22⋊Q8—24no—
990C22⋊Q8—28no—
991C22⋊Q8—28no—
992C22⋊Q8—216no—
993C22⋊Q8—28no—
994C22⋊Q8—216no—
995C22⋊Q8—216no—
996C22⋊Q8—216no—
997C22⋊Q8C2×D418yes—
998C22⋊Q8C2×D418yes—
999C22⋊Q8C24116yes—
1000C22⋊Q8C2418yes—
1001C22⋊Q8C2418yes—
1002#121—24no—
1003#121—216no—
1004#121—24no—
1005#121—216no—
1006#121—216no—
1007#121—28no—
1008#121—28no—
1009#121—28no—
1010#121—28no—
1011#121—28no—
1012#121—216no—
1013#121—216no—
1014#121—216no—
1015#121—216no—
1016#121—216no—
1017#121C2×D418yes—
1018#121C2×D418yes—
1019#121C2×D4116yes—
1020#121C24116yes—
1021#121C2418yes—
1022#121C2418yes—
1023#120—24no—
1024#120—24no—
1025#120—28no—
1026#120—216no—
1027#120—28no—
1028#120—216no—
1029#120—24no—
1030#120—24no—
1031#120—28no—
1032#120—216no—
1033#120—28no—
1034#120—216no—
1035#120C2×D418yes—
1036#120C2×D418yes—
1037C4×Q8—24no—
1038C4×Q8—24no—
1039C4×Q8C2418yes—
1040C4×Q8C2418yes—
1041C4×D4—216no—
1042C4×D4—28no—
1043C4×D4—28no—
1044C4×D4—28no—
1045C4×D4—28no—
1046C4×D4—24no—
1047C4×D4—24no—
1048C4×D4—216no—
1049C4×D4—28no—
1050C4×D4—28no—
1051C4×D4—216no—
1052C4×D4—216no—
1053C4×D4C2418yes—
1054C4×D4C2418yes—
1055C4×D4C24116yes—
1056#117—21no—
1057#117—21no—
1058#117—21no—
1059#117—21no—
1060#117—24no—
1061#117—24no—
1062#117—24no—
1063#117—24no—
1064#117—24no—
1065#117—24no—
1066#117C2×D412yes—
1067#117C2×D412yes—
1068#117C2412yes—
1069#117C2412yes—
1070#117C2412yes—
1071#117C2412yes—
1072#117C2412yes—
1073#117C2412yes—
1074C2×C4⋊C4—24no—
1075C2×C4⋊C4—24no—
1076C2×C4⋊C4—24no—
1077C2×C4⋊C4—24no—
1078C2×C4⋊C4—216no—
1079C2×C4⋊C4C2×D412yes—
1080C2×C4⋊C4C2412yes—
1081C2×C4⋊C4C2412yes—
1082C2×C22⋊C4—21no—
1083C2×C22⋊C4—21no—
1084C2×C22⋊C4—24no—
1085C2×C22⋊C4—24no—
1086C2×C22⋊C4—24no—
1087C2×C22⋊C4—24no—
1088C2×C22⋊C4—24no—
1089C2×C22⋊C4—24no—
1090C2×C22⋊C4—216no—
1091C2×C22⋊C4—216no—
1092C2×C22⋊C4C2×D412yes—
1093C2×C42—21no—
1094C2×C42—21no—
1095C2×C42—24no—
1096C2×C42—24no—
1097C2×C42C2412yes—
1098#107C2414yes—
1099#107C2414yes—
1100#106C2414yes—
1101#106C2414yes—
1102C4⋊C8C24116yes—
1103#103C24116yes—
1104#103C2418yes—
1105#103C2418yes—
1106#103C2418yes—
1107#103C2418yes—
1108#102C24116yes—
1109#102C2418yes—
1110#102C2418yes—
1111#102C2418yes—
1112#102C2418yes—
1113C22⋊C8C24116yes—
1114C22⋊C8C24116yes—
1115#97C2414yes—
1116#97C2414yes—
1117C4×C8C2414yes—
1118C4×C8C2414yes—
1119C24—21no—
1120C24—21no—
1121C24—24no—
1122C24—21no—
1123C24—28no—
1124C24—22no—
1125C24—22no—
1126C24—22no—
1127C24—24no—
1128C24—21no—
1129C24—48no—
1130C24—44no—
1131C24—162no—
1132C24—164no—
1133C24C22×D412yes—
1134C24C22×D412yes—
1135C24C22×D411yescharacteristic
1136#41—28no—
1137#41—28no—
1138#41—28no—
1139#41—28no—
1140#41—28no—
1141#41—28no—
1142#41—28no—
1143#41—28no—
1144#41—24no—
1145#41—24no—
1146#41—24no—
1147#41—24no—
1148#41—24no—
1149#41—24no—
1150#41—24no—
1151#41—24no—
1152#41—24no—
1153#41—24no—
1154#41—24no—
1155#41—24no—
1156#41—28no—
1157#41—28no—
1158#41—216no—
1159#41—216no—
1160#41—28no—
1161#41—28no—
1162#41—24no—
1163#41—24no—
1164#41—24no—
1165#41—24no—
1166#41—24no—
1167#41—24no—
1168#41—24no—
1169#41—24no—
1170#41—416no—
1171#41—416no—
1172#41—48no—
1173#41—44no—
1174#41—44no—
1175#41—44no—
1176#41—44no—
1177#41—48no—
1178#41—416no—
1179#41—416no—
1180#41—416no—
1181#41—416no—
1182#41—416no—
1183#41—48no—
1184#41—48no—
1185#41—416no—
1186#41—416no—
1187#41—416no—
1188#41—416no—
1189#41—416no—
1190#41—48no—
1191#41—48no—
1192#41—416no—
1193#41—416no—
1194#41—432no—
1195#41—432no—
1196#41—48no—
1197#41—48no—
1198#41—48no—
1199#41—48no—
1200#41—44no—
1201#41—44no—
1202#41—44no—
1203#41—44no—
1204#41C22×D418yes—
1205#41C22×D418yes—
1206#41C22×D418yes—
1207#41C22×D418yes—
1208C2×Q8—24no—
1209C2×Q8—24no—
1210C2×Q8—21no—
1211C2×Q8—21no—
1212C2×Q8—22no—
1213C2×Q8—24no—
1214C2×Q8—28no—
1215C2×Q8—22no—
1216C2×Q8—24no—
1217C2×Q8—21no—
1218C2×Q8—22no—
1219C2×Q8—21no—
1220C2×Q8—22no—
1221C2×Q8—22no—
1222C2×Q8—216no—
1223C2×Q8—28no—
1224C2×Q8—28no—
1225C2×Q8—24no—
1226C2×Q8—24no—
1227C2×Q8—24no—
1228C2×Q8—22no—
1229C2×Q8—22no—
1230C2×Q8—22no—
1231C2×Q8—24no—
1232C2×Q8—22no—
1233C2×Q8—24no—
1234C2×Q8—24no—
1235C2×Q8—48no—
1236C2×Q8—48no—
1237C2×Q8—44no—
1238C2×Q8—44no—
1239C2×Q8—416no—
1240C2×Q8—416no—
1241C2×Q8—416no—
1242C2×Q8—48no—
1243C2×Q8—48no—
1244C2×Q8—48no—
1245C2×Q8—48no—
1246C2×Q8—44no—
1247C2×Q8—44no—
1248C2×Q8—44no—
1249C2×Q8C22×D414yes—
1250C2×Q8C22×D414yes—
1251C2×Q8C22×D412yes—
1252C2×Q8C22×D412yes—
1253C2×Q8C22×D412yes—
1254C2×Q8C22×D412yes—
1255C2×Q8C2512yes—
1256C2×Q8C2514yes—
1257C2×Q8C2512yes—
1258C2×Q8C2512yes—
1259C2×Q8C2512yes—
1260C2×D4—28no—
1261C2×D4—28no—
1262C2×D4—28no—
1263C2×D4—28no—
1264C2×D4—22no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—28no—
1269C2×D4—28no—
1270C2×D4—216no—
1271C2×D4—22no—
1272C2×D4—24no—
1273C2×D4—22no—
1274C2×D4—28no—
1275C2×D4—22no—
1276C2×D4—24no—
1277C2×D4—22no—
1278C2×D4—24no—
1279C2×D4—28no—
1280C2×D4—24no—
1281C2×D4—28no—
1282C2×D4—216no—
1283C2×D4—28no—
1284C2×D4—24no—
1285C2×D4—24no—
1286C2×D4—21no—
1287C2×D4—21no—
1288C2×D4—24no—
1289C2×D4—22no—
1290C2×D4—22no—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—24no—
1294C2×D4—28no—
1295C2×D4—22no—
1296C2×D4—24no—
1297C2×D4—22no—
1298C2×D4—21no—
1299C2×D4—22no—
1300C2×D4—21no—
1301C2×D4—216no—
1302C2×D4—22no—
1303C2×D4—22no—
1304C2×D4—22no—
1305C2×D4—24no—
1306C2×D4—22no—
1307C2×D4—24no—
1308C2×D4—24no—
1309C2×D4—48no—
1310C2×D4—44no—
1311C2×D4—44no—
1312C2×D4—416no—
1313C2×D4—416no—
1314C2×D4—416no—
1315C2×D4—48no—
1316C2×D4—48no—
1317C2×D4—48no—
1318C2×D4—48no—
1319C2×D4—432no—
1320C2×D4—432no—
1321C2×D4—416no—
1322C2×D4—416no—
1323C2×D4—48no—
1324C2×D4—48no—
1325C2×D4—416no—
1326C2×D4—416no—
1327C2×D4—416no—
1328C2×D4—416no—
1329C2×D4—48no—
1330C2×D4—44no—
1331C2×D4—44no—
1332C2×D4—44no—
1333C2×D4—44no—
1334C2×D4—44no—
1335C2×D4—164no—
1336C2×D4—1616no—
1337C2×D4—164no—
1338C2×D4C22×D414yes—
1339C2×D4C22×D414yes—
1340C2×D4C22×D414yes—
1341C2×D4C22×D414yes—
1342C2×D4C22×D412yes—
1343C2×D4C22×D412yes—
1344C2×D4C22×D412yes—
1345C2×D4C22×D412yes—
1346C2×D4C22×D414yes—
1347C2×D4C22×D414yes—
1348C2×D4C22×D4116yes—
1349C2×D4C2512yes—
1350C2×D4C2514yes—
1351C2×D4C2512yes—
1352C2×D4C2512yes—
1353C2×D4C2512yes—
1354C22×C4—21no—
1355C22×C4—21no—
1356C22×C4—28no—
1357C22×C4—28no—
1358C22×C4—22no—
1359C22×C4—22no—
1360C22×C4—22no—
1361C22×C4—22no—
1362C22×C4—24no—
1363C22×C4—24no—
1364C22×C4—24no—
1365C22×C4—24no—
1366C22×C4—21no—
1367C22×C4—22no—
1368C22×C4—22no—
1369C22×C4—21no—
1370C22×C4—24no—
1371C22×C4—28no—
1372C22×C4—24no—
1373C22×C4—22no—
1374C22×C4—22no—
1375C22×C4—22no—
1376C22×C4—24no—
1377C22×C4—28no—
1378C22×C4—24no—
1379C22×C4—24no—
1380C22×C4—22no—
1381C22×C4—28no—
1382C22×C4—24no—
1383C22×C4—22no—
1384C22×C4—22no—
1385C22×C4—22no—
1386C22×C4—28no—
1387C22×C4—28no—
1388C22×C4—48no—
1389C22×C4—416no—
1390C22×C4—416no—
1391C22×C4—48no—
1392C22×C4—48no—
1393C22×C4—44no—
1394C22×C4—44no—
1395C22×C4—44no—
1396C22×C4C22×D412yes—
1397C22×C4C22×D414yes—
1398C22×C4C22×D414yes—
1399C22×C4C22×D412yes—
1400C22×C4C22×D414yes—
1401C22×C4C22×D411yescharacteristic
1402C22×C4C22×D411yescharacteristic
1403C22×C4C22×D411yescharacteristic
1404C22×C4C22×D414yes—
1405C22×C4H(5,𝔽2)14yes—
1406C22×C4C2514yes—
1407C22×C4C2514yes—
1408C22×C4C2511yescharacteristic
1409C22×C4C2511yescharacteristic
1410C22×C4C2511yescharacteristic
1411Q16—216no—
1412Q16—28no—
1413Q16—28no—
1414Q16—24no—
1415Q16—24no—
1416Q16—48no—
1417Q16C22×D418yes—
1418Q16C22×D418yes—
1419SD16—216no—
1420SD16—28no—
1421SD16—28no—
1422SD16—216no—
1423SD16—28no—
1424SD16—28no—
1425SD16—28no—
1426SD16—28no—
1427SD16—24no—
1428SD16—24no—
1429SD16—28no—
1430SD16—28no—
1431SD16—24no—
1432SD16—24no—
1433SD16—48no—
1434SD16—48no—
1435SD16C22×D418yes—
1436SD16C22×D418yes—
1437SD16C22×D418yes—
1438SD16C22×D418yes—
1439D8—28no—
1440D8—28no—
1441D8—216no—
1442D8—24no—
1443D8—24no—
1444D8—48no—
1445D8C22×D418yes—
1446D8C22×D418yes—
1447M16—24no—
1448M16—24no—
1449M16—24no—
1450M16—24no—
1451M16—24no—
1452M16—24no—
1453M16—28no—
1454M16—28no—
1455M16—28no—
1456M16—28no—
1457C2×C8—24no—
1458C2×C8—24no—
1459C2×C8—24no—
1460C2×C8—28no—
1461C2×C8—28no—
1462C2×C8—28no—
1463C2×C8—28no—
1464C2×C8C22×D414yes—
1465C2×C8C22×D414yes—
1466C2×C8C22×D414yes—
1467C2×C8C22×D414yes—
1468C2×C8C22×D414yes—
1469C2×C8C22×D414yes—
1470C2×C8C2514yes—
1471C2×C8C2514yes—
1472C2×C8C2514yes—
1473C2×C8C2511yescharacteristic
1474C2×C8C2511yescharacteristic
1475C2×C8C2511yescharacteristic
1476C2×C8C2511yescharacteristic
1477C4⋊C4—22no—
1478C4⋊C4—22no—
1479C4⋊C4—216no—
1480C4⋊C4—216no—
1481C4⋊C4—28no—
1482C4⋊C4—28no—
1483C4⋊C4—28no—
1484C4⋊C4—28no—
1485C4⋊C4C22×D414yes—
1486C4⋊C4C22×D4116yes—
1487C4⋊C4C22×D414yes—
1488C4⋊C4C2514yes—
1489C4⋊C4C2514yes—
1490C22⋊C4—22no—
1491C22⋊C4—22no—
1492C22⋊C4—28no—
1493C22⋊C4—216no—
1494C22⋊C4—22no—
1495C22⋊C4—22no—
1496C22⋊C4—28no—
1497C22⋊C4—216no—
1498C22⋊C4—216no—
1499C22⋊C4—216no—
1500C22⋊C4—28no—
1501C22⋊C4—28no—
1502C22⋊C4—28no—
1503C22⋊C4—28no—
1504C22⋊C4C22×D414yes—
1505C22⋊C4C22×D4116yes—
1506C22⋊C4C22×D4116yes—
1507C22⋊C4C22×D414yes—
1508C42—22no—
1509C42—22no—
1510C42—28no—
1511C42—28no—
1512C42—22no—
1513C42—22no—
1514C42C22×D414yes—
1515C42C2514yes—
1516C23—22no—
1517C23—22no—
1518C23—24no—
1519C23—24no—
1520C23—24no—
1521C23—24no—
1522C23—22no—
1523C23—24no—
1524C23—22no—
1525C23—42no—
1526C23—44no—
1527C23—44no—
1528C23—48no—
1529C23—48no—
1530C23—416no—
1531C23—44no—
1532C23—42no—
1533C23—42no—
1534C23—44no—
1535C23—44no—
1536C23—82no—
1537C23—82no—
1538C23—84no—
1539C23—82no—
1540C23—88no—
1541C23—84no—
1542C23—84no—
1543C23—816no—
1544C23—82no—
1545C23—88no—
1546C23—168no—
1547C23—1616no—
1548C23D4214yes—
1549C23C23×D414yes—
1550C23C23×D414yes—
1551C23C23×D411yescharacteristic
1552C23C23×D411yescharacteristic
1553C23C23×D411yescharacteristic
1554Q8—22no—
1555Q8—22no—
1556Q8—24no—
1557Q8—24no—
1558Q8—24no—
1559Q8—24no—
1560Q8—24no—
1561Q8—24no—
1562Q8—24no—
1563Q8—22no—
1564Q8—22no—
1565Q8—22no—
1566Q8—24no—
1567Q8—22no—
1568Q8—416no—
1569Q8—48no—
1570Q8—48no—
1571Q8—44no—
1572Q8—44no—
1573Q8—44no—
1574Q8—42no—
1575Q8—42no—
1576Q8C23×D414yes—
1577Q8C23×D414yes—
1578D4—28no—
1579D4—28no—
1580D4—28no—
1581D4—28no—
1582D4—28no—
1583D4—28no—
1584D4—28no—
1585D4—28no—
1586D4—22no—
1587D4—22no—
1588D4—24no—
1589D4—22no—
1590D4—22no—
1591D4—22no—
1592D4—24no—
1593D4—22no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—24no—
1599D4—24no—
1600D4—416no—
1601D4—416no—
1602D4—48no—
1603D4—48no—
1604D4—416no—
1605D4—48no—
1606D4—48no—
1607D4—48no—
1608D4—48no—
1609D4—416no—
1610D4—44no—
1611D4—44no—
1612D4—44no—
1613D4—44no—
1614D4—44no—
1615D4—44no—
1616D4—44no—
1617D4—42no—
1618D4—42no—
1619D4—816no—
1620D4—88no—
1621D4—88no—
1622D4—816no—
1623D4C23×D414yes—
1624D4C23×D414yes—
1625C2×C4—22no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—24no—
1633C2×C4—24no—
1634C2×C4—24no—
1635C2×C4—28no—
1636C2×C4—28no—
1637C2×C4—28no—
1638C2×C4—28no—
1639C2×C4—28no—
1640C2×C4—28no—
1641C2×C4—24no—
1642C2×C4—24no—
1643C2×C4—22no—
1644C2×C4—24no—
1645C2×C4—22no—
1646C2×C4—44no—
1647C2×C4—416no—
1648C2×C4—48no—
1649C2×C4—48no—
1650C2×C4—48no—
1651C2×C4—48no—
1652C2×C4—48no—
1653C2×C4—48no—
1654C2×C4—416no—
1655C2×C4—416no—
1656C2×C4—44no—
1657C2×C4—42no—
1658C2×C4—42no—
1659C2×C4—44no—
1660C2×C4—44no—
1661C2×C4—44no—
1662C2×C4—44no—
1663C2×C4—44no—
1664C2×C4—44no—
1665C2×C4—88no—
1666C2×C4—88no—
1667C2×C4—82no—
1668C2×C4—82no—
1669C2×C4D4214yes—
1670C2×C4D4214yes—
1671C2×C4D4214yes—
1672C2×C4C23×D418yes—
1673C2×C4C23×D414yes—
1674C2×C4C23×D414yes—
1675C2×C4C23×D412yes—
1676C2×C4C23×D412yes—
1677C2×C4C23×D412yes—
1678C2×C4C23×D411yescharacteristic
1679C2×C4C23×D411yescharacteristic
1680C2×C4C23×D411yescharacteristic
1681C2×C4C2×H(5,𝔽2)12yes—
1682C2×C4C2×H(5,𝔽2)12yes—
1683C2×C4C2×H(5,𝔽2)12yes—
1684C2×C4C2611yescharacteristic
1685C8—24no—
1686C8—24no—
1687C8—24no—
1688C8C23×D412yes—
1689C8C23×D412yes—
1690C8C23×D412yes—
1691C8C23×D412yes—
1692C22—22no—
1693C22—22no—
1694C22—22no—
1695C22—28no—
1696C22—28no—
1697C22—24no—
1698C22—24no—
1699C22—24no—
1700C22—24no—
1701C22—44no—
1702C22—48no—
1703C22—44no—
1704C22—44no—
1705C22—44no—
1706C22—48no—
1707C22—44no—
1708C22—42no—
1709C22—42no—
1710C22—44no—
1711C22—84no—
1712C22—84no—
1713C22—84no—
1714C22—88no—
1715C22—162no—
1716C22—162no—
1717C22—164no—
1718C22—164no—
1719C22—168no—
1720C22—168no—
1721C22—1616no—
1722C22C2×D4212yes—
1723C22C2×D4212yes—
1724C22C2×D4212yes—
1725C22C24×D411yescharacteristic
1726C4—28no—
1727C4—24no—
1728C4—24no—
1729C4—24no—
1730C4—24no—
1731C4—44no—
1732C4—44no—
1733C4—42no—
1734C4—42no—
1735C4—44no—
1736C4C2×D4212yes—
1737C4C2×D4212yes—
1738C4C2×D4212yes—
1739C4C24×D411yescharacteristic
1740C4C22×H(5,𝔽2)11yescharacteristic
1741C2—22no—
1742C2—22no—
1743C2—22no—
1744C2—44no—
1745C2—44no—
1746C2—44no—
1747C2—44no—
1748C2—84no—
1749C2—82no—
1750C2—82no—
1751C2C22×D4211yescharacteristic
1752C2#6309212yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3449 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3584C2semidirect
2. C22×#577C2semidirect
3. #62859C2semidirect
4. #62852C2semidirect
5. #61088C2semidirect
6. #61087C2semidirect
7. #61083C2semidirect
8. #61082C2semidirect
9. #61062C2semidirect
10. #61061C2semidirect
11. #61058C2semidirect
12. #61055C2semidirect
13. #61052C2semidirect
14. #61050C2semidirect
15. C2×#3154C2semidirect
16. #60450C2semidirect
17. C2×#3057C2semidirect
18. #60427C2semidirect
19. #60426C2semidirect
20. #60370C2semidirect
21. #60369C2semidirect
22. #60368C2semidirect
23. #60367C2semidirect
24. #60167C2semidirect
25. #60140C2semidirect
27. C2×#585C22semidirect
28. C22×2−1+4C22semidirect
29. C22×H(5,𝔽2)C22semidirect
31. C2×#578C22semidirect
32. C2×#578C22semidirect
34. C2×#577C22semidirect
35. C2×#577C22semidirect
36. C2×#577C22semidirect
37. C2×#577C22semidirect
38. C2×#577C22semidirect
39. C2×#577C22semidirect
40. C2×#577C22semidirect
41. C2×#577C22semidirect
42. C2×#576C22semidirect
43. C2×#576C22semidirect
45. C2×#575C22semidirect
46. C2×#575C22semidirect
47. C22×#137C22semidirect
48. C22×#137C22semidirect
49. C22×#137C22semidirect
50. C22×AGL(1,ℤ/8)C22semidirect
51. C22×AGL(1,ℤ/8)C22semidirect
52. C22×AGL(1,ℤ/8)C22semidirect
54. C22×#135C22semidirect
55. C22×#135C22semidirect
56. C22×#135C22semidirect
57. C23×SD16C22semidirect
58. C23×SD16C22semidirect
59. C22×#131C22semidirect
60. C22×#131C22semidirect
63. #3500C22semidirect
64. #3500C22semidirect
66. #3499C22semidirect
68. #3498C22semidirect
70. #3489C22semidirect
72. #3488C22semidirect
73. #3487C22semidirect
74. #3486C22semidirect
76. #3485C22semidirect
78. #3484C22semidirect
82. #3449C22semidirect
83. #3449C22semidirect
85. C2×#536C22semidirect
86. C2×#536C22semidirect
89. C2×#535C22semidirect
90. #3428C22semidirect
91. #3428C22semidirect
92. #3284C22semidirect
93. #3282C22semidirect
94. #3282C22semidirect
95. D4×SD16C22semidirect
96. #3278C22semidirect
97. #3277C22semidirect
98. #3273C22semidirect
99. #3272C22semidirect
100. #3271C22semidirect
101. #3270C22semidirect
102. #3269C22semidirect
103. #3268C22semidirect
104. #3267C22semidirect
105. #3266C22semidirect
106. #3265C22semidirect
107. #3264C22semidirect
108. #3154C22semidirect
109. #3154C22semidirect
110. #3154C22semidirect
111. #3154C22semidirect
112. C2×#497C22semidirect
113. C2×#496C22semidirect
114. C2×#495C22semidirect
115. C2×#492C22semidirect
116. #3061C22semidirect
117. #3060C22semidirect
118. #3059C22semidirect
119. #3058C22semidirect
120. #3057C22semidirect
121. #3057C22semidirect
122. #3057C22semidirect
123. #3057C22semidirect
124. #3057C22semidirect
125. #3057C22semidirect
126. #3054C22semidirect
127. C2×#468C22semidirect
128. #3050C22semidirect
129. C2×#465C22semidirect
130. #3046C22semidirect
131. #3045C22semidirect
132. #3044C22semidirect
133. #3043C22semidirect
134. #3042C22semidirect
135. #3041C22semidirect
136. #3040C22semidirect
137. #3040C22semidirect
138. #3039C22semidirect
139. #3038C22semidirect
140. #3013C22semidirect
141. #3012C22semidirect
142. #3011C22semidirect
143. #3011C22semidirect
144. #3011C22semidirect
145. #3010C22semidirect
146. #3010C22semidirect
147. #3010C22semidirect
148. #3009C22semidirect
149. #3009C22semidirect
150. #3009C22semidirect
151. #3008C22semidirect
152. #3008C22semidirect
153. #3008C22semidirect
154. #3007C22semidirect
155. #3006C22semidirect
156. #3005C22semidirect
157. #3005C22semidirect
158. #3004C22semidirect
159. #3003C22semidirect
160. #2952C22semidirect
161. #2951C22semidirect
162. #2950C22semidirect
163. #2949C22semidirect
164. #2949C22semidirect
165. #2948C22semidirect
166. #2943C22semidirect
167. C4×#135C22semidirect
168. #2932C22semidirect
169. #2931C22semidirect
170. #2930C22semidirect
171. #2930C22semidirect
172. #2929C22semidirect
173. #2929C22semidirect
174. C2×#427C22semidirect
175. #2905C22semidirect
176. #2896C22semidirect
177. #2896C22semidirect
178. #2896C22semidirect
179. #2896C22semidirect
180. C2×#419C22semidirect
181. C2×#418C22semidirect
182. #2879C22semidirect
183. #2879C22semidirect
184. C2×#405C22semidirect
200. C2×2−1+4C23semidirect
214. C2×H(5,𝔽2)C23semidirect
231. C22×#41C23semidirect
265. C2×#137C23semidirect
266. C2×#137C23semidirect
267. C2×#137C23semidirect
268. C2×#137C23semidirect
269. C2×#137C23semidirect
270. C2×#137C23semidirect
283. C2×AGL(1,ℤ/8)C23semidirect
284. C2×AGL(1,ℤ/8)C23semidirect
285. C2×AGL(1,ℤ/8)C23semidirect
286. C2×AGL(1,ℤ/8)C23semidirect
287. C2×AGL(1,ℤ/8)C23semidirect
291. C2×#135D4semidirect
301. C2×#135C23semidirect
302. C2×#135C23semidirect
303. C2×#135C23semidirect
304. C2×#135C23semidirect
305. C2×#135C23semidirect
306. C2×#135C23semidirect
307. C2×#135C23semidirect
310. C22×Q16C23semidirect
311. C22×Q16C23semidirect
312. C22×Q16C23semidirect
328. C22×SD16C23semidirect
329. C22×SD16C23semidirect
330. C22×SD16C23semidirect
331. C22×SD16C23semidirect
332. C22×SD16C23semidirect
336. C22×D8C23semidirect
337. C22×D8C23semidirect
346. C2×#131C23semidirect
347. C2×#131C23semidirect
352. C22×M16C23semidirect
355. C23×C8C23semidirect
359. D4×Q8C23semidirect
363. #548C23semidirect
367. #547C23semidirect
375. #546C23semidirect
403. #536C23semidirect
404. #536C23semidirect
439. C2×C4⋊Q8C23semidirect
448. C2×#124C23semidirect
464. C2×C22⋊Q8C23semidirect
474. #520C23semidirect
484. C4×#41C23semidirect
490. #497C23semidirect
491. #497C23semidirect
492. #496C23semidirect
493. #496C23semidirect
494. #495C23semidirect
495. #495C23semidirect
496. #492C23semidirect
497. #492C23semidirect
498. #470C23semidirect
499. #469C23semidirect
500. #468C23semidirect
501. #468C23semidirect
502. #468C23semidirect
503. #468C23semidirect
504. #467C23semidirect
505. #466C23semidirect
506. #465C23semidirect
507. #465C23semidirect
508. #465C23semidirect
509. #465C23semidirect
510. #464C23semidirect
511. #464C23semidirect
512. #463C23semidirect
513. #463C23semidirect
514. #462C23semidirect
515. #461C23semidirect
516. #460C23semidirect
517. #459C23semidirect
519. #452C23semidirect
520. #452C23semidirect
521. #452C23semidirect
522. #451C23semidirect
523. #451C23semidirect
525. #450C23semidirect
527. #449C23semidirect
528. #449C23semidirect
529. #449C23semidirect
530. #448C23semidirect
531. #448C23semidirect
533. #447C23semidirect
534. #442C23semidirect
535. #441C23semidirect
536. #440C23semidirect
537. #440C23semidirect
538. C4×Q16C23semidirect
539. C4×SD16C23semidirect
540. C4×SD16C23semidirect
541. C4×D8C23semidirect
542. #436C23semidirect
543. #435C23semidirect
544. #435C23semidirect
545. C8×D4C23semidirect
548. #427C23semidirect
549. #427C23semidirect
550. C2×#107C23semidirect
551. C2×#106C23semidirect
553. #424C23semidirect
554. #423C23semidirect
558. #419C23semidirect
559. #419C23semidirect
560. #419C23semidirect
565. #418C23semidirect
566. #418C23semidirect
568. #417C23semidirect
569. #417C23semidirect
570. #417C23semidirect
574. #416C23semidirect
575. C2×#103C23semidirect
580. #408C23semidirect
582. #407C23semidirect
585. #405C23semidirect
586. #405C23semidirect
587. C2×#97C23semidirect
588. C2×C4×C8C23semidirect
687. C2×#41C2×D4semidirect
835. #135C2×D4semidirect
836. #135C2×D4semidirect
837. #135C2×D4semidirect
838. #135C2×D4semidirect
843. C2×Q16C2×D4semidirect
868. C2×SD16C2×D4semidirect
869. C2×SD16C2×D4semidirect
894. C2×D8C2×D4semidirect
928. C22×C8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35842
C22×#5772
#628592
#628522
#610882
#610872
#610832
#610822
#610622
#610612
#610582
#610552
#610522
#610502
C2×#31542
#604502
C2×#30572
#604272
#604262
#603702
#603692
#603682
#603672
#601672
#601402