Finite Group Databasebeta

← #28400709

Subgroups — #28400709

Order 14464.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#20299129C211yesmaximal, characteristic, complemented
2C2×#16813584C211yesmaximal, characteristic, complemented
3#20298928C211yesmaximal, characteristic, complemented
4#20298901C212yesmaximal, complemented
5#20298812C212yesmaximal, complemented
6#20298751C211yesmaximal, characteristic, complemented
7#20298731C211yesmaximal, characteristic
8#20298707C212yesmaximal, complemented
9#20298697C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#480×C113C211yesmaximal, characteristic, complemented
12C22×D452C2211yescharacteristic
13C22×C4×D113—21no—
14C2×#14268636C2212yes—
15C2×#14268632C2212yes—
16#16813615—21no—
17#16813613C2211yescharacteristic, complemented
18#16813609C2211yescharacteristic, complemented
19#16813603—21no—
20#16813601C2211yescharacteristic
21#16813587C2211yescharacteristic, complemented
22D4×Dic113—21no—
23D4×Dic113C2211yescharacteristic, complemented
24#16813584—21no—
25#16813584—21no—
26#16813584C2212yes—
27#16813584C2212yes—
28#16813578—21no—
29C2×#14268624—21no—
30C2×C4×Dic113C2211yescharacteristic
31#16813553C2212yescomplemented
32#16813551C2212yescomplemented
33#16813545C2212yescomplemented
34#16813544C2212yes—
35#16813542C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yescomplemented
38#121×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41#102×C113C2212yescomplemented
42C22⋊C8×C113C2211yescharacteristic
43C23×D113—21no—
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—24no—
47C2×D452C2312yes—
48C22×Dic113—21no—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51C2×C4×D113—22no—
52C2×C4×D113—22no—
53C2×C4×D113—44no—
54#14268636—24no—
55#14268632—24no—
56C2×#11744751C2312yes—
57C4⋊Dic113—21no—
58C4⋊Dic113C2311yescharacteristic
59#14268626—21no—
60#14268626—21no—
61#14268626—21no—
62C22⋊Dic113—21no—
63C22⋊Dic113—21no—
64C22⋊Dic113—21no—
65C22⋊Dic113—21no—
66#14268624—22no—
67#14268624—22no—
68C4×Dic113—21no—
69C4×Dic113D411yescharacteristic
70C4×Dic113D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C4×Dic113C2311yescharacteristic
73C2×D4×C113—21no—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113C2311yescharacteristic
77C2×C8×C113C2312yes—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2312yes—
80C4⋊C4×C113C2311yescharacteristic
81C22⋊C4×C113—21no—
82C23×C113—21no—
83C23×C113C2×D411yescharacteristic
84C22×D113—24no—
85C22×D113—22no—
86C22×D113—42no—
87C22×D113—42no—
88D4×C113—22no—
89D4×C113—42no—
90C2×C4×C113—22no—
91C2×C4×C113—21no—
92C2×C4×C113—22no—
93C2×C4×C113—42no—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—41no—
100C2×Dic113—42no—
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105D452—24no—
106D452—22no—
107D452#4114yes—
108C4×D113—44no—
109C4×D113—44no—
110Dic226—22no—
111C8×C113—22no—
112#11744751—22no—
113C22×C113—21no—
114C22×C113—21no—
115C22×C113—41no—
116C22×C113—41no—
117C22×C113—41no—
118C22×C113AGL(1,ℤ/8)12yes—
119C22×C113C22×D411yescharacteristic
120C2×D113—24no—
121C2×D113—48no—
122C2×D113—42no—
123C2×D113—42no—
124C4×C113—21no—
125C4×C113—42no—
126C4×C113—41no—
127C4×C113C2×#4112yes—
128Dic113—21no—
129Dic113—21no—
130Dic113—21no—
131Dic113—21no—
132Dic113—41no—
133Dic113—41no—
134C2×C113—22no—
135C2×C113—81no—
136C2×C113#52511yescharacteristic
137C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C113#57511yescharacteristic
139D113—44no—
140#3114—1131nomaximal, Sylow
141C113#311411yescharacteristic, complemented, Sylow
142#529—1131no—
143C2×C4×D4—1131no—
144#483—1131no—
145#480D11311yescharacteristic, complemented
146#478—1132no—
147#463—1132no—
148#450—1131no—
149#447—1131no—
150#442—1132no—
151#440—1132no—
152#432—1131no—
153C22×D4—1131no—
154C23×C4—2261no—
155C2×SD16—1132no—
156C2×D8—1132no—
157#126—2261no—
158#125—1131no—
159#124—1131no—
160#123—2261no—
161C22⋊Q8—1131no—
162#121C2×D11311yescharacteristic
163C4×Q8—1131no—
164C4×D4—1131no—
165C4×D4—1132no—
166C4×D4—1132no—
167C4×D4—2261no—
168C4×D4—2261no—
169C4×D4—2261no—
170#117—2261no—
171C2×C4⋊C4C2×D11311yescharacteristic
172C2×C22⋊C4—2261no—
173C2×C42—1131no—
174#107C2×D11312yescomplemented
175#106—1132no—
176C4⋊C8—1132no—
177#103—1132no—
178#102—1132no—
179#102—1132no—
180#102C2×D11312yescomplemented
181C22⋊C8—1131no—
182C22⋊C8C2×D11311yescharacteristic
183#97—1132no—
184C24—2261no—
185C2×Q8—1131no—
186C2×D4—21no—
187C2×D4—1132no—
188C2×D4—2264no—
189C2×D4—2261no—
190C2×D4C22×D11311yescharacteristic
191C22×C4—21no—
192C22×C4—1131no—
193C22×C4—1131no—
194C22×C4—4524no—
195C22×C4—2262no—
196C22×C4—2262no—
197C22×C4—2261no—
198C22×C4C22×D11311yescharacteristic
199SD16—2264no—
200D8—2264no—
201C2×C8—1132no—
202C2×C8C22×D11312yes—
203C4⋊C4—21no—
204C4⋊C4—1131no—
205C4⋊C4—2261no—
206C4⋊C4—2261no—
207C4⋊C4—2261no—
208C4⋊C4—2261no—
209C4⋊C4C22×D11311yescharacteristic
210C4⋊C4C22×D11312yes—
211C22⋊C4—21no—
212C22⋊C4—2262no—
213C22⋊C4—2262no—
214C22⋊C4—2261no—
215C22⋊C4—2261no—
216C22⋊C4—2261no—
217C22⋊C4—2261no—
218C42—1131no—
219C42—1131no—
220C42—1131no—
221C42—1131no—
222C42—2261no—
223C23—21no—
224C23—4522no—
225C23—4522no—
226C23—2264no—
227C23—2262no—
228C23D4×D11311yescharacteristic
229Q8—2262no—
230D4—22no—
231D4—42no—
232D4—1134no—
233D4—2264no—
234D4—2262no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—1131no—
240C2×C4—1131no—
241C2×C4—1131no—
242C2×C4—1131no—
243C2×C4—4524no—
244C2×C4—4524no—
245C2×C4—4522no—
246C2×C4—4521no—
247C2×C4—2261no—
248C2×C4—2261no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4C23×D11311yescharacteristic
252C8—22no—
253C8—2262no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—4528no—
260C22—4522no—
261C22—4522no—
262C22—2264no—
263C22#1681364612yes—
264C22C2×D4×D11311yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—4521no—
269C4—4521no—
270C4—2261no—
271C4—2261no—
272C4—2261no—
273C4—2261no—
274C4#41×D11312yes—
275C2—22no—
276C2—81no—
277C2—4524no—
278C2#2029910611yescharacteristic
279C2C2×#1681364611yescharacteristic
280C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#480×C113C2
socleC22×C113C22×D4
prime radical#20298731C2
hypercenter#480D113
hypocenterC113#3114
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #20299129C2semidirect
2. C2×#16813584C2semidirect
3. #20298928C2semidirect
4. #20298901C2semidirect
5. #20298812C2semidirect
6. #20298751C2semidirect
8. #20298707C2semidirect
9. #20298697C2semidirect
10. #20298652C2semidirect
11. #480×C113C2semidirect
17. #16813613C22semidirect
18. #16813609C22semidirect
21. #16813587C22semidirect
23. D4×Dic113C22semidirect
31. #16813553C22semidirect
32. #16813551C22semidirect
33. #16813545C22semidirect
37. #16813532C22semidirect
40. #107×C113C22semidirect
41. #102×C113C22semidirect
141. C113#3114semidirect
145. #480D113semidirect
174. #107C2×D113semidirect
180. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991292
C2×#168135842
#202989282
#202989012
#202988122
#202987512
#202987312
#202987072
#202986972
#202986522
#480×C1132
#3114113