Finite Group Databasebeta

← #28393138

Subgroups — #28393138

Order 14464.

924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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×#16813618C211yesmaximal, characteristic
2C2×D4×Dic113C211yesmaximal, characteristic, complemented
3C2×#16813584C211yesmaximal, characteristic, complemented
4C2×#16813582C214yesmaximal, complemented
5#20298500C211yesmaximal, characteristic, complemented
6#20298498C214yesmaximal, complemented
7#20298467C211yesmaximal, characteristic, complemented
8C42×Dic113C211yesmaximal, characteristic, complemented
9#390×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11C22×C22⋊D113C2214yes—
12C23×Dic113C2212yes—
13C22×C4×D113C2212yes—
14#16813618C418yescomplemented
15D4×Dic113—24no—
16#16813584—24no—
17#16813582—216no—
18C2×C4⋊Dic113C2211yescharacteristic
19C2×#14268626C2214yes—
20C2×C22⋊Dic113C2212yes—
21C2×#14268624C2212yes—
22C2×#14268624C2214yes—
23C2×C4×Dic113C2212yes—
24C2×C4×Dic113C2211yescharacteristic
25C2×C4×Dic113C2212yes—
26C2×C4×Dic113C2211yescharacteristic
27C22×D4×C113C2211yescharacteristic
28C2×C4⋊C4×C113C2211yescharacteristic
29C2×C22⋊C4×C113C2214yes—
30C2×C42×C113C2211yescharacteristic
31C23×D113C2312yes—
32C2×D452—22no—
33C2×D452—22no—
34C2×D452C2×C414yescomplemented
35C2×C22⋊D113—28no—
36C2×C22⋊D113—28no—
37C2×C22⋊D113C2×C4116yescomplemented
38C22×Dic113—28no—
39C22×Dic113—24no—
40C22×Dic113C2312yes—
41C22×Dic113C2311yescharacteristic
42C22×Dic113C2312yes—
43C22×Dic113C2311yescharacteristic
44C2×C4×D113—28no—
45C2×C4×D113—24no—
46C4⋊Dic113—22no—
47#14268626—28no—
48C22⋊Dic113—24no—
49#14268624—28no—
50#14268624—24no—
51C4×Dic113—24no—
52C4×Dic113C2×C414yescomplemented
53C4×Dic113D418yescomplemented
54C4×Dic113D414yescomplemented
55C24×C113C2312yes—
56C2×D4×C113—22no—
57C2×D4×C113—22no—
58C2×D4×C113C2×C414yescomplemented
59C22×C4×C113C2312yes—
60C22×C4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62C4⋊C4×C113—22no—
63C22⋊C4×C113—28no—
64C42×C113—22no—
65C23×C113—24no—
66C23×C113—22no—
67C23×C113—22no—
68C23×C113—24no—
69C23×C113C22×C414yes—
70C23×C113C2411yescharacteristic
71C22×D113—24no—
72C22×D113—22no—
73C22×D113—24no—
74C22×D113—22no—
75C22×D113C22×C414yes—
76D4×C113—28no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113—24no—
80C2×C4×C113—22no—
81C2×C4×C113C22×C412yes—
82C2×C4×C113C2×D414yes—
83C2×C4×C113C2×D412yes—
84C2×C4×C113#4112yes—
85C22⋊D113—232no—
86C2×Dic113—22no—
87C2×Dic113—24no—
88C2×Dic113—22no—
89C2×Dic113—48no—
90C2×Dic113C22×C414yes—
91C2×Dic113C2×D412yes—
92C2×Dic113C2×D414yes—
93C2×Dic113C2×D414yes—
94C2×Dic113C2×D412yes—
95C2×Dic113#4114yes—
96D452—28no—
97C4×D113—48no—
98C22×C113—28no—
99C22×C113—24no—
100C22×C113—42no—
101C22×C113—44no—
102C22×C113—42no—
103C22×C113C23×C411yescharacteristic
104C22×C113C22×D412yes—
105C22×C113C22×D411yescharacteristic
106C22×C113C2×#4112yes—
107C22×C113C2×#4111yescharacteristic
108C2×D113—24no—
109C2×D113—28no—
110C2×D113—42no—
111C2×D113—44no—
112C2×D113—42no—
113C4×C113—24no—
114C4×C113—42no—
115C4×C113C4×D414yescomplemented
116Dic113—22no—
117Dic113—42no—
118Dic113C4×D418yescomplemented
119Dic113#12714yescomplemented
120C2×C113—44no—
121C2×C113C2×C4×D412yes—
122C2×C113C2×C4×D411yescharacteristic
123C2×C113C2×#12711yescharacteristic
124C2×C113#53212yes—
125C2×C113#53211yescharacteristic
126D113—44no—
127C4×#127—1131nomaximal, Sylow
128C113C4×#12711yescharacteristic, complemented, Sylow
129C2×#127—1131no—
130C2×C4×D4—1131no—
131C2×C4×D4—1131no—
132C2×C4×D4—1134no—
133#390—1134no—
134#390—1131no—
135#390D11311yescharacteristic, complemented
136#384—1131no—
137C43—1131no—
138C22×D4—1134no—
139C22×D4—1131no—
140C22×D4C2×D11311yescharacteristic
141C23×C4—1132no—
142C23×C4—1132no—
143#127—1138no—
144C4×D4—22616no—
145C4×D4—2264no—
146C4×D4—2264no—
147C2×C4⋊C4—1134no—
148C2×C4⋊C4—1131no—
149C2×C4⋊C4C2×D11311yescharacteristic
150C2×C22⋊C4—1132no—
151C2×C22⋊C4—1132no—
152C2×C22⋊C4—1134no—
153C2×C22⋊C4C2×D11314yes—
154C2×C42—1132no—
155C2×C42—1131no—
156C2×C42—1131no—
157C2×C42—1132no—
158C2×C42C2×D11311yescharacteristic
159C24—1132no—
160C24C22×D11312yes—
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—11316no—
164C2×D4—1134no—
165C2×D4—2268no—
166C2×D4—2268no—
167C2×D4—2262no—
168C2×D4—2262no—
169C2×D4C4×D11314yescomplemented
170C22×C4—1132no—
171C22×C4—1131no—
172C22×C4—1131no—
173C22×C4—1132no—
174C22×C4—2268no—
175C22×C4—2264no—
176C22×C4—2268no—
177C22×C4—2264no—
178C22×C4C22×D11312yes—
179C22×C4C22×D11312yes—
180C22×C4C22×D11311yescharacteristic
181C4⋊C4—22no—
182C4⋊C4—2268no—
183C4⋊C4—2262no—
184C22⋊C4—28no—
185C22⋊C4—2264no—
186C22⋊C4—2264no—
187C22⋊C4—2268no—
188C42—22no—
189C42—1134no—
190C42—1138no—
191C42—1134no—
192C42—2264no—
193C23—24no—
194C23—22no—
195C23—24no—
196C23—22no—
197C23—1134no—
198C23—2264no—
199C23—2262no—
200C23—2264no—
201C23—2262no—
202C23C2×C4×D11314yes—
203C23C23×D11311yescharacteristic
204D4—28no—
205D4—22632no—
206D4—2268no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—1134no—
212C2×C4—1134no—
213C2×C4—1134no—
214C2×C4—1132no—
215C2×C4—1134no—
216C2×C4—1132no—
217C2×C4—4528no—
218C2×C4—4528no—
219C2×C4—2264no—
220C2×C4—2262no—
221C2×C4—2262no—
222C2×C4C2×C4×D11312yes—
223C2×C4D4×D11314yes—
224C2×C4D4×D11312yes—
225C2×C4#1426864612yes—
226C22—28no—
227C22—24no—
228C22—42no—
229C22—44no—
230C22—42no—
231C22—4522no—
232C22—4524no—
233C22—4522no—
234C22—2268no—
235C22—2264no—
236C22C22×C4×D11311yescharacteristic
237C22C2×D4×D11312yes—
238C22C2×D4×D11311yescharacteristic
239C22#41×D11312yes—
240C22C2×#1426864611yescharacteristic
241C4—24no—
242C4—42no—
243C4—1138no—
244C4—1134no—
245C4—4522no—
246C4—2262no—
247C4#1681358214yescomplemented
248C2—44no—
249C2—4524no—
250C2C4×D4×D11312yes—
251C2C2×#1681358211yescharacteristic
252C2#127×D11311yescharacteristic
253C2#2029914312yes—
254C2#2029914711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#390×C113C2
socle, cosocleC23×C113C24
prime radicalC2×#16813618C2
hypercenter#390D113
hypocenterC113C4×#127
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic113C2semidirect
3. C2×#16813584C2semidirect
4. C2×#16813582C2semidirect
5. #20298500C2semidirect
6. #20298498C2semidirect
7. #20298467C2semidirect
8. C42×Dic113C2semidirect
9. #390×C113C2semidirect
14. #16813618C4semidirect
34. C2×D452C2×C4semidirect
37. C2×C22⋊D113C2×C4semidirect
52. C4×Dic113C2×C4semidirect
53. C4×Dic113D4semidirect
54. C4×Dic113D4semidirect
58. C2×D4×C113C2×C4semidirect
115. C4×C113C4×D4semidirect
118. Dic113C4×D4semidirect
119. Dic113#127semidirect
128. C113C4×#127semidirect
135. #390D113semidirect
169. C2×D4C4×D113semidirect
247. C4#16813582semidirect

Maximal subgroups

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

subgroupindex
C2×#168136182
C2×D4×Dic1132
C2×#168135842
C2×#168135822
#202985002
#202984982
#202984672
C42×Dic1132
#390×C1132
C4×#127113