Finite Group Databasebeta

← #28402246

Subgroups — #28402246

Order 14464.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×D113C212yesmaximal, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20299233C211yesmaximal, characteristic, complemented
4#20298974C211yesmaximal, characteristic, complemented
5#20298833C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298733C212yesmaximal, complemented
8#20298730C212yesmaximal, complemented
9C4×#14268632C211yesmaximal, characteristic, complemented
10#20298663C211yesmaximal, characteristic, complemented
11#459×C113C211yesmaximal, characteristic, complemented
12C22×D452—21no—
13C2×D4×D113—21no—
14C2×D4×D113C2212yescomplemented
15C2×D4×D113C2212yescomplemented
16C2×D904C2212yescomplemented
17C2×#14268632C2211yescharacteristic
18C2×#14268632C2212yescomplemented
19C2×#14268632C2212yescomplemented
20D8×D113—28no—
21C2×C8×D113C2212yescomplemented
22#16813619C2211yescharacteristic, complemented
23#16813597C2212yescomplemented
24#16813596—21no—
25#16813593—21no—
26#16813593C2212yescomplemented
27#16813592—22no—
28#16813590—22no—
29C4×D452C2211yescharacteristic
30C4×D452C2211yescharacteristic, complemented
31#16813555C2211yescharacteristic, complemented
32#16813544C2212yescomplemented
33#16813543C2211yescharacteristic, complemented
34#16813542C2211yescharacteristic, complemented
35#16813534C2212yescomplemented
36C4×#11744751C2211yescharacteristic, complemented
37C2×D8×C113C2212yescomplemented
38#127×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic, complemented
40C4⋊C8×C113C2211yescharacteristic, complemented
41#102×C113C2212yescomplemented
42C23×D113—22no—
43C23×D113—22no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—44no—
48C2×D452D411yescharacteristic
49C2×D452C2312yes—
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—22no—
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54D4×D113—24no—
55D4×D113—24no—
56D4×D113—42no—
57D4×D113—42no—
58D4×D113—44no—
59C2×C4×D113—21no—
60C2×C4×D113C2312yes—
61D904—24no—
62#14268632—24no—
63#14268632—42no—
64#14268632D414yescomplemented
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C8×D113—24no—
68C4⋊Dic113D411yescharacteristic
69C4⋊Dic113C2311yescharacteristic
70C22⋊Dic113—22no—
71#14268624—21no—
72#14268624—22no—
73#14268624D412yes—
74C2×D4×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113C2312yes—
77C2×D4×C113C2311yescharacteristic
78C22×C4×C113—21no—
79D8×C113—24no—
80C2×C8×C113C2312yes—
81C4⋊C4×C113C2311yescharacteristic
82C22⋊C4×C113—21no—
83C42×C113C2311yescharacteristic
84C23×C113—21no—
85C23×C113—22no—
86C22×D113—21no—
87C22×D113—22no—
88C22×D113—44no—
89C22×D113—44no—
90C22×D113—44no—
91C22×D113—44no—
92C22×D113—82no—
93C22×D113—82no—
94C22×D113C2×D412yes—
95D4×C113—22no—
96D4×C113—21no—
97D4×C113—22no—
98D4×C113—42no—
99D4×C113—81no—
100D4×C113C2×D412yescomplemented
101C2×C4×C113—21no—
102C2×C4×C113—42no—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D411yescharacteristic
105C2×C4×C113C2411yescharacteristic
106C22⋊D113—44no—
107C22⋊D113—44no—
108C22⋊D113—44no—
109C2×Dic113—21no—
110C2×Dic113C2×D412yes—
111D452—22no—
112D452—21no—
113D452—22no—
114D452—44no—
115D452—42no—
116D452—81no—
117D452D814yescomplemented
118D452C2×D412yescomplemented
119C4×D113—22no—
120C4×D113—22no—
121C4×D113—42no—
122C8×C113—22no—
123#11744751—21no—
124#11744751C2×D412yescomplemented
125C22×C113—22no—
126C22×C113—41no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113—42no—
130C22×C113—42no—
131C22×C113C22×D411yescharacteristic
132C2×D113—22no—
133C2×D113—22no—
134C2×D113—22no—
135C2×D113—41no—
136C2×D113—41no—
137C2×D113—42no—
138C2×D113—42no—
139C2×D113—42no—
140C2×D113—88no—
141C2×D113—88no—
142C2×D113C2×D814yescomplemented
143C4×C113—21no—
144C4×C113—41no—
145C4×C113C2×D812yescomplemented
146C4×C113C22×D411yescharacteristic
147C4×C113H(5,𝔽2)11yescharacteristic
148Dic113—22no—
149Dic113—41no—
150C2×C113—42no—
151C2×C113—82no—
152C2×C113D4211yescharacteristic
153C2×C113C22×D811yescharacteristic
154C2×C113#57611yescharacteristic
155D113—24no—
156D113—42no—
157D113—82no—
158D4×D8—1131nomaximal, Sylow
159C113D4×D811yescharacteristic, complemented, Sylow
160C22×D8—1132no—
161D42—1131no—
162D42—1131no—
163#493—1131no—
164#466—1132no—
165#459—1131no—
166#459D11311yescharacteristic, complemented
167#447—1132no—
168#447—1132no—
169C4×D8—1131no—
170C8×D4—1131no—
171C22×D4—1132no—
172C22×D4—1132no—
173C22×D4—2261no—
174C22×D4—2261no—
175C2×D8—1131no—
176C2×D8—1132no—
177C2×D8—1132no—
178C2×D8—1132no—
179C2×D8—2268no—
180C2×D8C2×D11312yescomplemented
181C22×C8—1132no—
182#127—1131no—
183#127C2×D11311yescharacteristic, complemented
184#121—1132no—
185#121—1132no—
186#121—2261no—
187#121—2261no—
188#120—2262no—
189#120—2262no—
190C4×D4—1131no—
191C4×D4—1131no—
192C4×D4C2×D11311yescharacteristic, complemented
193#107—1131no—
194C4⋊C8C2×D11311yescharacteristic, complemented
195#102—1131no—
196#102—1132no—
197#102—1131no—
198#102C2×D11312yescomplemented
199C22⋊C8—1132no—
200C4×C8—1131no—
201C24—2262no—
202C24—2262no—
203C2×D4—21no—
204C2×D4—21no—
205C2×D4—1131no—
206C2×D4—1131no—
207C2×D4—1132no—
208C2×D4—4524no—
209C2×D4—4524no—
210C2×D4—4522no—
211C2×D4—4522no—
212C2×D4—2262no—
213C2×D4—2262no—
214C2×D4—2262no—
215C2×D4—2264no—
216C2×D4—2262no—
217C2×D4—2264no—
218C2×D4—2261no—
219C2×D4—2261no—
220C2×D4C22×D11312yes—
221C2×D4C22×D11311yescharacteristic
222C22×C4—21no—
223C22×C4—1132no—
224C22×C4—2261no—
225D8—24no—
226D8—1134no—
227D8—4522no—
228D8—2264no—
229D8—2264no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—2264no—
233C2×C8C22×D11312yes—
234C4⋊C4—1131no—
235C4⋊C4—1131no—
236C4⋊C4C22×D11311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—1132no—
239C22⋊C4—2262no—
240C22⋊C4—2262no—
241C22⋊C4—2261no—
242C42C22×D11311yescharacteristic
243C23—21no—
244C23—22no—
245C23—1132no—
246C23—9042no—
247C23—9042no—
248C23—4524no—
249C23—4524no—
250C23—4524no—
251C23—4524no—
252C23—2262no—
253C23—2261no—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—42no—
258D4—81no—
259D4—1134no—
260D4—1132no—
261D4—9041no—
262D4—4524no—
263D4—4524no—
264D4—4524no—
265D4—4524no—
266D4—4522no—
267D4—2262no—
268D4—2262no—
269D4—2261no—
270D4D4×D11312yescomplemented
271C2×C4—21no—
272C2×C4—42no—
273C2×C4—1132no—
274C2×C4—4522no—
275C2×C4—2261no—
276C2×C4—2262no—
277C2×C4—2262no—
278C2×C4D4×D11311yescharacteristic
279C2×C4D4×D11311yescharacteristic
280C2×C4C23×D11311yescharacteristic
281C8—22no—
282C8—1132no—
283C8—2261no—
284C22—22no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—1134no—
291C22—9048no—
292C22—9048no—
293C22—4522no—
294C22—4522no—
295C22—4522no—
296C22—4521no—
297C22—4521no—
298C22—2262no—
299C22—2262no—
300C22—2262no—
301C22C2×D4×D11311yescharacteristic
302C4—21no—
303C4—41no—
304C4—4521no—
305C4—2262no—
306C4D8×D11312yescomplemented
307C4C2×D4×D11311yescharacteristic
308C4#1681366811yescharacteristic
309C2—42no—
310C2—82no—
311C2—9042no—
312C2—4522no—
313C2—2264no—
314C2#2029923211yescharacteristic
315C2C2×D8×D11311yescharacteristic
316C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×D8×D113C2semidirect
2. D4×D452C2semidirect
3. #20299233C2semidirect
4. #20298974C2semidirect
5. #20298833C2semidirect
6. #20298794C2semidirect
7. #20298733C2semidirect
8. #20298730C2semidirect
9. C4×#14268632C2semidirect
10. #20298663C2semidirect
11. #459×C113C2semidirect
14. C2×D4×D113C22semidirect
15. C2×D4×D113C22semidirect
16. C2×D904C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268632C22semidirect
21. C2×C8×D113C22semidirect
22. #16813619C22semidirect
23. #16813597C22semidirect
26. #16813593C22semidirect
30. C4×D452C22semidirect
31. #16813555C22semidirect
32. #16813544C22semidirect
33. #16813543C22semidirect
34. #16813542C22semidirect
35. #16813534C22semidirect
36. C4×#11744751C22semidirect
37. C2×D8×C113C22semidirect
38. #127×C113C22semidirect
39. C4×D4×C113C22semidirect
40. C4⋊C8×C113C22semidirect
41. #102×C113C22semidirect
64. #14268632D4semidirect
100. D4×C113C2×D4semidirect
117. D452D8semidirect
118. D452C2×D4semidirect
124. #11744751C2×D4semidirect
142. C2×D113C2×D8semidirect
145. C4×C113C2×D8semidirect
159. C113D4×D8semidirect
166. #459D113semidirect
180. C2×D8C2×D113semidirect
183. #127C2×D113semidirect
192. C4×D4C2×D113semidirect
194. C4⋊C8C2×D113semidirect
198. #102C2×D113semidirect
270. D4D4×D113semidirect
306. C4D8×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
D4×D4522
#202992332
#202989742
#202988332
#202987942
#202987332
#202987302
C4×#142686322
#202986632
#459×C1132
D4×D8113