Finite Group Databasebeta

← #28402256

Subgroups — #28402256

Order 14464.

526 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813645C211yesmaximal, characteristic, complemented
2C22×D904C211yesmaximal, characteristic, complemented
3#20299239C212yesmaximal, complemented
4#20298983C211yesmaximal, characteristic, complemented
5#20298835C211yesmaximal, characteristic, complemented
6#20298816C212yesmaximal, complemented
7#20298748C212yesmaximal, complemented
8#20298746C212yesmaximal, complemented
9#20298680C211yesmaximal, characteristic, complemented
10C8×C22⋊D113C211yesmaximal, characteristic, complemented
11#467×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yescomplemented
13C22×D452C2212yes—
14#16813645—24no—
15C2×#14268634C2212yescomplemented
16C2×#14268634C2212yescomplemented
17C2×D904—24no—
18C2×D904C2212yes—
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic, complemented
22#16813611C2212yescomplemented
23#16813607—22no—
24#16813597—22no—
25#16813597C2212yescomplemented
26#16813592—22no—
27#16813584C2212yescomplemented
28C4×C22⋊D113C2211yescharacteristic
29C22⋊C4×D113—22no—
30#16813551C2211yescharacteristic, complemented
31#16813542C2212yescomplemented
32#16813542C2212yescomplemented
33C22⋊#11744751C2211yescharacteristic
34#16813534C2211yescharacteristic, complemented
35C8×Dic113C2211yescharacteristic, complemented
36C2×Q16×C113C2211yescharacteristic, complemented
37C22×C8×C113C2211yescharacteristic
38C22⋊Q8×C113C2212yes—
39#107×C113C2211yescharacteristic, complemented
40#103×C113C2212yescomplemented
41C23×D113—22no—
42#14268648—24no—
43#14268648—42no—
44C2×D452—24no—
45C2×D452—22no—
46C2×D452—22no—
47C2×D452—22no—
48C2×D452—42no—
49C2×D452C2312yes—
50C2×D452C2312yes—
51C2×C22⋊D113D411yescharacteristic
52C2×C4×D113—22no—
53C2×C4×D113—22no—
54C2×C4×D113C2311yescharacteristic
55#14268634—24no—
56#14268634—42no—
57D904—24no—
58D904—22no—
59D904D414yescomplemented
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C8×D113—22no—
63#14268626D411yescharacteristic
64C22⋊Dic113D411yescharacteristic
65#14268624—22no—
66#14268624—22no—
67#14268624—22no—
68#14268624—22no—
69#14268624D411yescharacteristic
70C4×Dic113C2311yescharacteristic
71C2×Q8×C113C2312yes—
72C22×C4×C113C2311yescharacteristic
73Q16×C113—22no—
74C2×C8×C113—22no—
75C2×C8×C113C2311yescharacteristic
76C2×C8×C113C2311yescharacteristic
77C4⋊C4×C113—22no—
78C4⋊C4×C113C2312yes—
79C22⋊C4×C113—22no—
80C23×C113C2×D411yescharacteristic
81C22×D113—22no—
82C22×D113—22no—
83C22×D113—44no—
84C22×D113—44no—
85C22×D113—82no—
86C22×D113C2×D411yescharacteristic
87Q8×C113—22no—
88Q8×C113—22no—
89C2×C4×C113—21no—
90C2×C4×C113—21no—
91C2×C4×C113—22no—
92C2×C4×C113—22no—
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C22⋊D113—22no—
96C2×Dic113C2×D411yescharacteristic
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99D452—22no—
100D452—22no—
101D452—22no—
102D452—44no—
103D452—44no—
104D452—82no—
105D452C2×D414yes—
106C4×D113—21no—
107C4×D113—21no—
108C4×D113—44no—
109C4×D113—82no—
110C8×C113—21no—
111C8×C113C2×D412yes—
112#11744751—21no—
113#11744751—21no—
114C22×C113—21no—
115C22×C113—21no—
116C22×C113#13512yescomplemented
117C22×C113C22×D411yescharacteristic
118C2×D113—21no—
119C2×D113—24no—
120C2×D113—21no—
121C2×D113—21no—
122C2×D113—42no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—42no—
127C2×D113—88no—
128C4×C113—21no—
129C4×C113—42no—
130C4×C113—42no—
131C4×C113C22×D411yescharacteristic
132C4×C113H(5,𝔽2)11yescharacteristic
133Dic113—21no—
134Dic113—21no—
135Dic113—21no—
136C2×C113—22no—
137C2×C113D4211yescharacteristic
138C2×C113C2×#13511yescharacteristic
139C2×C113#57611yescharacteristic
140D113—41no—
141D113—44no—
142D113—82no—
143#3280—1131nomaximal, Sylow
144C113#328011yescharacteristic, complemented, Sylow
145C2×#135—1131no—
146C22×D8—1131no—
147#546—1132no—
148#495—1131no—
149#467D11311yescharacteristic, complemented
150#466—1131no—
151#463—1132no—
152#450—1132no—
153#449—1132no—
154C4×D8—1131no—
155C8×D4—1131no—
156C2×#41—1132no—
157C22×D4—1132no—
158#135—2264no—
159C2×Q16C2×D11311yescharacteristic, complemented
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×D8—1131no—
163C2×D8—1132no—
164C2×D8—1131no—
165C2×D8—2264no—
166C22×C8—1131no—
167C22×C8C2×D11311yescharacteristic
168#124—1132no—
169#123—2262no—
170C22⋊Q8C2×D11312yes—
171#121—1132no—
172#121—2262no—
173#120—2262no—
174C4×D4—1131no—
175C4×D4—1132no—
176C2×C22⋊C4—2262no—
177#107C2×D11311yescharacteristic, complemented
178C4⋊C8—1131no—
179#103C2×D11312yescomplemented
180#102—1132no—
181#102—1132no—
182C22⋊C8—1131no—
183C22⋊C8—1131no—
184C4×C8—1131no—
185C24—2262no—
186#41—4522no—
187#41—2264no—
188C2×Q8C22×D11312yes—
189C2×D4—1131no—
190C2×D4—1132no—
191C2×D4—1132no—
192C2×D4—4522no—
193C2×D4—2264no—
194C2×D4—2262no—
195C2×D4—2262no—
196C2×D4—2262no—
197C22×C4—1131no—
198C22×C4—2262no—
199C22×C4—2262no—
200C22×C4C22×D11311yescharacteristic
201Q16—22no—
202SD16—4522no—
203SD16—2264no—
204D8—1134no—
205D8—2264no—
206D8—2262no—
207C2×C8—22no—
208C2×C8—1131no—
209C2×C8—1131no—
210C2×C8—2262no—
211C2×C8C22×D11311yescharacteristic
212C2×C8C22×D11311yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—1131no—
215C4⋊C4C22×D11312yes—
216C22⋊C4—22no—
217C22⋊C4—1131no—
218C22⋊C4—1131no—
219C22⋊C4—2262no—
220C22⋊C4—2262no—
221C22⋊C4—2262no—
222C22⋊C4—2262no—
223C42—1131no—
224C23—1131no—
225C23—9042no—
226C23—4524no—
227C23—4524no—
228C23—2262no—
229C23—2262no—
230C23D4×D11311yescharacteristic
231Q8—22no—
232Q8—22no—
233D4—1134no—
234D4—9042no—
235D4—4524no—
236D4—4524no—
237D4—2262no—
238D4—2262no—
239D4—2262no—
240D4—2262no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—1131no—
246C2×C4—1131no—
247C2×C4—1131no—
248C2×C4—9042no—
249C2×C4—4524no—
250C2×C4—2261no—
251C2×C4—2261no—
252C2×C4D4×D11311yescharacteristic
253C2×C4C23×D11311yescharacteristic
254C8—21no—
255C8—2261no—
256C8—2261no—
257C8D4×D11312yes—
258C22—21no—
259C22—21no—
260C22—9048no—
261C22—4522no—
262C22—4522no—
263C22—4522no—
264C22—4522no—
265C22—4522no—
266C22—2261no—
267C22—2261no—
268C22—2264no—
269C22—2261no—
270C22#1681364512yescomplemented
271C22C2×D4×D11311yescharacteristic
272C4—21no—
273C4—42no—
274C4—42no—
275C4—2261no—
276C4—2261no—
277C4—2261no—
278C4C2×D4×D11311yescharacteristic
279C4#1681366811yescharacteristic
280C2—22no—
281C2—9042no—
282C2—4524no—
283C2—4521no—
284C2#2029923211yescharacteristic
285C2C2×#1681364511yescharacteristic
286C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#467×C113C2
socleC22×C113C22×D4
hypercenter#467D113
hypocenterC113#3280
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#16813645C2semidirect
2. C22×D904C2semidirect
3. #20299239C2semidirect
4. #20298983C2semidirect
5. #20298835C2semidirect
6. #20298816C2semidirect
7. #20298748C2semidirect
8. #20298746C2semidirect
9. #20298680C2semidirect
10. C8×C22⋊D113C2semidirect
11. #467×C113C2semidirect
12. C2×#14268648C22semidirect
15. C2×#14268634C22semidirect
16. C2×#14268634C22semidirect
21. C2×C8×D113C22semidirect
22. #16813611C22semidirect
25. #16813597C22semidirect
27. #16813584C22semidirect
30. #16813551C22semidirect
31. #16813542C22semidirect
32. #16813542C22semidirect
34. #16813534C22semidirect
35. C8×Dic113C22semidirect
36. C2×Q16×C113C22semidirect
39. #107×C113C22semidirect
40. #103×C113C22semidirect
59. D904D4semidirect
116. C22×C113#135semidirect
144. C113#3280semidirect
149. #467D113semidirect
159. C2×Q16C2×D113semidirect
177. #107C2×D113semidirect
179. #103C2×D113semidirect
270. C22#16813645semidirect

Maximal subgroups

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

subgroupindex
C2×#168136452
C22×D9042
#202992392
#202989832
#202988352
#202988162
#202987482
#202987462
#202986802
C8×C22⋊D1132
#467×C1132
#3280113