Finite Group Databasebeta

← #28399423

Subgroups — #28399423

Order 14464.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D113C211yesmaximal, characteristic
2#20299070C212yesmaximal, complemented
3#20298711C211yesmaximal, characteristic, complemented
4#20298710C211yesmaximal, characteristic, complemented
5#20298709C211yesmaximal, characteristic, complemented
6C4×#14268632C212yesmaximal, complemented
7#20298678C212yesmaximal, complemented
8#20298633C211yesmaximal, characteristic, complemented
9#20298601C212yesmaximal, complemented
10#20298555C211yesmaximal, characteristic, complemented
11#442×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113C2212yes—
13C2×D904C2211yescharacteristic
14C2×#14268632C2212yes—
15D8×D113C418yescomplemented
16C2×#14268630C2211yescharacteristic
17C2×C8×D113C2211yescharacteristic
18C4×D452C2212yescomplemented
19D4×Dic113C2212yescomplemented
20#16813584C2212yescomplemented
21C4×C22⋊D113—22no—
22#16813582—22no—
23#16813580C2212yes—
24#16813579C2211yescharacteristic
25C2×#14268624—22no—
26C22⋊C4×D113—22no—
27#16813555C2212yescomplemented
28#16813554C2211yescharacteristic, complemented
29#16813544C2212yescomplemented
30#16813543C2212yescomplemented
31#16813542C2212yescomplemented
32#16813532C2211yescharacteristic, complemented
33C4×#11744751C2211yescharacteristic, complemented
34C8×Dic113C2211yescharacteristic, complemented
35C2×D8×C113C2211yescharacteristic
36C4×D4×C113C2212yescomplemented
37#106×C113C2211yescharacteristic, complemented
38#102×C113C2212yescomplemented
39#97×C113C2211yescharacteristic, complemented
40C23×D113—22no—
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43D4×D113—24no—
44D4×D113C2×C418yescomplemented
45C22×Dic113—22no—
46C2×C4×D113—22no—
47C2×C4×D113—22no—
48C2×C4×D113C2311yescharacteristic
49D904C2×C414yescomplemented
50#14268632C2×C418yescomplemented
51#14268630—22no—
52C2×#11744751C2311yescharacteristic
53C2×#11744751C2311yescharacteristic
54C8×D113C2×C414yescomplemented
55C4⋊Dic113C2312yes—
56#14268626D412yes—
57C22⋊Dic113—22no—
58#14268624—22no—
59#14268624—22no—
60#14268624—22no—
61#14268624D412yes—
62C4×Dic113—22no—
63C4×Dic113C2311yescharacteristic
64C2×D4×C113C2312yes—
65C22×C4×C113—22no—
66D8×C113C2×C414yescomplemented
67C2×C8×C113C2311yescharacteristic
68C2×C8×C113C2311yescharacteristic
69C4⋊C4×C113C2312yes—
70C22⋊C4×C113—22no—
71C42×C113C2311yescharacteristic
72C23×C113—22no—
73C22×D113—22no—
74C22×D113—28no—
75C22×D113—82no—
76C22×D113—82no—
77C22×D113C2×D411yescharacteristic
78D4×C113—22no—
79D4×C113C22×C414yes—
80C2×C4×C113—22no—
81C2×C4×C113—82no—
82C2×C4×C113C2×D412yes—
83C2×C4×C113C2411yescharacteristic
84C22⋊D113—28no—
85C2×Dic113—22no—
86C2×Dic113—82no—
87C2×Dic113C2×D412yes—
88C2×Dic113C2×D411yescharacteristic
89D452—22no—
90D452C22×C414yes—
91C4×D113—82no—
92C4×D113—82no—
93C4×D113C22×C412yes—
94C4×D113#4112yes—
95C8×C113—21no—
96C8×C113C22×C412yes—
97#11744751—21no—
98#11744751C22×C412yes—
99C22×C113—24no—
100C22×C113—42no—
101C22×C113—42no—
102C22×C113C22×D411yescharacteristic
103C2×D113—22no—
104C2×D113—24no—
105C2×D113—42no—
106C2×D113—42no—
107C2×D113—88no—
108C2×D113C4×D412yes—
109C4×C113—22no—
110C4×C113—42no—
111C4×C113C23×C411yescharacteristic
112C4×C113C2×#4111yescharacteristic
113Dic113—22no—
114Dic113—42no—
115Dic113C4×D412yes—
116C2×C113—44no—
117C2×C113C2×C4×D411yescharacteristic
118C2×C113#57612yes—
119D113—22no—
120D113—44no—
121#2948—1131nomaximal, Sylow
122C113#294811yescharacteristic, complemented, Sylow
123C22×D8—1131no—
124#518—1132no—
125#442—1131no—
126#442—1131no—
127#442—1131no—
128#442D11311yescharacteristic, complemented
129C4×D8—1132no—
130C4×D8—1132no—
131#427—1131no—
132#418—1132no—
133#405—1131no—
134C22×D4—1132no—
135C2×D8—1132no—
136C2×D8—1138no—
137C2×D8—1131no—
138C2×D8C2×D11311yescharacteristic
139C2×M16—1131no—
140C22×C8—1131no—
141C4×D4—1132no—
142C4×D4—1132no—
143C4×D4—1132no—
144C4×D4—2262no—
145C4×D4—2262no—
146C4×D4C2×D11312yescomplemented
147#117—1131no—
148#117—1132no—
149C2×C22⋊C4—2262no—
150C2×C22⋊C4—2262no—
151#107—1132no—
152#106—1131no—
153#106C2×D11311yescharacteristic, complemented
154#102—1132no—
155#102—1132no—
156#102—1132no—
157#102C2×D11312yescomplemented
158#97—1131no—
159#97C2×D11311yescharacteristic, complemented
160C4×C8—1131no—
161C4×C8—1131no—
162C24—2262no—
163C2×D4—1138no—
164C2×D4—1132no—
165C2×D4—2264no—
166C2×D4—2262no—
167C2×D4C22×D11312yes—
168C22×C4—22no—
169C22×C4—1131no—
170C22×C4—2262no—
171C22×C4—2262no—
172C22×C4—2262no—
173D8—1138no—
174D8—1134no—
175D8C4×D11314yescomplemented
176M16—2262no—
177C2×C8—1131no—
178C2×C8—1134no—
179C2×C8—1131no—
180C2×C8C22×D11311yescharacteristic
181C2×C8C22×D11311yescharacteristic
182C4⋊C4—1132no—
183C4⋊C4—1132no—
184C4⋊C4C22×D11312yes—
185C22⋊C4—22no—
186C22⋊C4—1132no—
187C22⋊C4—2262no—
188C22⋊C4—2262no—
189C22⋊C4—2262no—
190C22⋊C4—2262no—
191C42—1131no—
192C42—2262no—
193C42C22×D11311yescharacteristic
194C23—22no—
195C23—1131no—
196C23—9042no—
197C23—9042no—
198C23—2268no—
199C23—2262no—
200D4—22no—
201D4—1134no—
202D4—2268no—
203D4—2262no—
204D4C2×C4×D11314yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—1131no—
208C2×C4—1132no—
209C2×C4—1132no—
210C2×C4—1132no—
211C2×C4—9042no—
212C2×C4—9042no—
213C2×C4—9042no—
214C2×C4—2262no—
215C2×C4D4×D11312yes—
216C2×C4C23×D11311yescharacteristic
217C8—21no—
218C8—1132no—
219C8—2261no—
220C8C2×C4×D11312yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—1132no—
225C22—9048no—
226C22—4522no—
227C22—4522no—
228C22—2264no—
229C22—2262no—
230C22C2×D4×D11311yescharacteristic
231C4—22no—
232C4—42no—
233C4—1132no—
234C4—4522no—
235C4—2262no—
236C4C22×C4×D11311yescharacteristic
237C4#41×D11311yescharacteristic
238C2—44no—
239C2—4524no—
240C2—2262no—
241C2C4×D4×D11311yescharacteristic
242C2#2029940212yes—
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#442×C113C2
socleC22×C113C22×D4
prime radicalC2×D8×D113C2
cosocleC2×C4×C113C24
hypercenter#442D113
hypocenterC113#2948
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #20299070C2semidirect
3. #20298711C2semidirect
4. #20298710C2semidirect
5. #20298709C2semidirect
6. C4×#14268632C2semidirect
7. #20298678C2semidirect
8. #20298633C2semidirect
9. #20298601C2semidirect
10. #20298555C2semidirect
11. #442×C113C2semidirect
15. D8×D113C4semidirect
18. C4×D452C22semidirect
19. D4×Dic113C22semidirect
20. #16813584C22semidirect
27. #16813555C22semidirect
28. #16813554C22semidirect
29. #16813544C22semidirect
30. #16813543C22semidirect
31. #16813542C22semidirect
32. #16813532C22semidirect
33. C4×#11744751C22semidirect
34. C8×Dic113C22semidirect
36. C4×D4×C113C22semidirect
37. #106×C113C22semidirect
38. #102×C113C22semidirect
39. #97×C113C22semidirect
44. D4×D113C2×C4semidirect
49. D904C2×C4semidirect
50. #14268632C2×C4semidirect
54. C8×D113C2×C4semidirect
66. D8×C113C2×C4semidirect
122. C113#2948semidirect
128. #442D113semidirect
146. C4×D4C2×D113semidirect
153. #106C2×D113semidirect
157. #102C2×D113semidirect
159. #97C2×D113semidirect
175. D8C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1132
#202990702
#202987112
#202987102
#202987092
C4×#142686322
#202986782
#202986332
#202986012
#202985552
#442×C1132
#2948113