Finite Group Databasebeta

← #28401410

Subgroups — #28401410

Order 14464.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#20299108C212yesmaximal, complemented
2#20298942C212yesmaximal, complemented
3#20298921C212yesmaximal, complemented
4#20298856C211yesmaximal, characteristic, complemented
5#20298842C212yesmaximal, complemented
6#20298761C212yesmaximal, complemented
7#20298740C212yesmaximal, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#469×C113C211yesmaximal, characteristic, complemented
10C2×#14268646C2212yes—
11C22×C4×D113C2211yescharacteristic
12C2×Dic452C2211yescharacteristic, complemented
13C2×#14268635C2212yescomplemented
14C2×#14268631C2211yescharacteristic
15#16813604—22no—
16#16813602C2212yes—
17#16813601C2212yes—
18#16813593C2212yes—
19#16813590—22no—
20D4×Dic113—22no—
21#16813582—22no—
22#16813580C2212yes—
23#16813555C2212yescomplemented
24#16813554C2211yescharacteristic, complemented
25#16813547C2212yescomplemented
26#16813545C2212yescomplemented
27#16813543C2212yescomplemented
28#16813534C2212yes—
29#16813534C2212yes—
30C2×D8×C113C2211yescharacteristic, complemented
31C2×M16×C113C2211yescharacteristic
32#121×C113C2212yes—
33#106×C113C2211yescharacteristic, complemented
34#102×C113C2212yescomplemented
35C23×D113D411yescharacteristic
36#14268646—42no—
37#14268646—42no—
38C2×Dic226C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C22×Dic113—22no—
42C22×Dic113D411yescharacteristic
43C2×C4×D113—41no—
44C2×C4×D113—41no—
45C2×C4×D113D412yes—
46C2×C4×D113C2312yes—
47Dic452—41no—
48#14268635—42no—
49#14268631—41no—
50C2×#11744751C2312yes—
51C4⋊Dic113—22no—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54C22⋊Dic113—22no—
55C22⋊Dic113—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C2×D4×C113—22no—
60C2×D4×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62D8×C113—41no—
63M16×C113—41no—
64C2×C8×C113C2311yescharacteristic
65C2×C8×C113C2311yescharacteristic
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C23×C113—22no—
69C23×C113C2×D411yescharacteristic
70C22×D113—41no—
71C22×D113—42no—
72C22×D113C2×D412yes—
73D4×C113—22no—
74D4×C113—22no—
75D4×C113—44no—
76C2×C4×C113—21no—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2411yescharacteristic
81C22⋊D113—44no—
82C22⋊D113—44no—
83C2×Dic113—22no—
84C2×Dic113—22no—
85C2×Dic113—41no—
86C2×Dic113—44no—
87C2×Dic113C2×D412yes—
88C4×D113—22no—
89C4×D113—22no—
90C4×D113—42no—
91Dic226—22no—
92Dic226—22no—
93C8×C113—21no—
94C8×C113—21no—
95#11744751—22no—
96C22×C113—21no—
97C22×C113—22no—
98C22×C113—42no—
99C22×C113—42no—
100C22×C113—42no—
101C22×C113C22×D411yescharacteristic
102C2×D113—22no—
103C2×D113—22no—
104C2×D113—22no—
105C2×D113—44no—
106C4×C113—21no—
107C4×C113—42no—
108C4×C113H(5,𝔽2)11yescharacteristic
109C4×C113H(5,𝔽2)11yescharacteristic
110Dic113—22no—
111Dic113—42no—
112Dic113—42no—
113C2×C113—41no—
114C2×C113—82no—
115C2×C113#53411yescharacteristic
116C2×C113#57512yes—
117D113—42no—
118#3197—1131nomaximal, Sylow
119C113#319711yescharacteristic, complemented, Sylow
120#525—1132no—
121#485—1132no—
122#482—1132no—
123#470—1131no—
124#469D11311yescharacteristic, complemented
125#468—1132no—
126#452—1132no—
127#449—1132no—
128#407—1131no—
129C2×#41—1132no—
130C23×C4—1131no—
131C2×Q16—1131no—
132C2×SD16—1132no—
133C2×D8C2×D11311yescharacteristic, complemented
134C2×M16—1131no—
135C2×M16C2×D11311yescharacteristic
136#123—2262no—
137C22⋊Q8—1132no—
138C22⋊Q8—1132no—
139#121—1132no—
140#121C2×D11312yes—
141#120—2262no—
142C4×D4—2262no—
143C4×D4—2262no—
144#117—1132no—
145#107—1132no—
146#106—1131no—
147#106C2×D11311yescharacteristic, complemented
148#103—1132no—
149#103—1132no—
150#102—1132no—
151#102C2×D11312yescomplemented
152C22⋊C8—1132no—
153C22⋊C8—1132no—
154C24—1131no—
155#41—4522no—
156#41—4522no—
157C2×Q8—1132no—
158C2×D4—22no—
159C2×D4—2262no—
160C2×D4—2262no—
161C2×D4C22×D11312yes—
162C22×C4—1131no—
163C22×C4—1132no—
164C22×C4—1132no—
165C22×C4—4521no—
166C22×C4—4521no—
167C22×C4—2262no—
168C22×C4C22×D11311yescharacteristic
169Q16—4521no—
170SD16—4522no—
171D8—41no—
172M16—41no—
173M16—4521no—
174C2×C8—1132no—
175C2×C8C22×D11311yescharacteristic
176C2×C8C22×D11311yescharacteristic
177C4⋊C4—1132no—
178C4⋊C4—2262no—
179C4⋊C4—2262no—
180C4⋊C4C22×D11312yes—
181C22⋊C4—22no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C22⋊C4—2262no—
185C22⋊C4—2262no—
186C42—2262no—
187C23—22no—
188C23—1132no—
189C23—4521no—
190C23—4522no—
191C23D4×D11311yescharacteristic
192Q8—2262no—
193Q8—2262no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—4524no—
198D4—4524no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—1132no—
203C2×C4—4522no—
204C2×C4—4524no—
205C2×C4—4521no—
206C2×C4—2262no—
207C2×C4—2262no—
208C2×C4—2262no—
209C2×C4—2262no—
210C2×C4D4×D11311yescharacteristic
211C2×C4C23×D11311yescharacteristic
212C8—21no—
213C8—21no—
214C8—2262no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—4524no—
221C22—2262no—
222C22—2262no—
223C22—2262no—
224C22C2×D4×D11311yescharacteristic
225C4—21no—
226C4—42no—
227C4—4522no—
228C4—4522no—
229C4—2262no—
230C4#1681366711yescharacteristic
231C4#1681366811yescharacteristic
232C2—41no—
233C2—82no—
234C2—4522no—
235C2#2029915611yescharacteristic
236C2#2029939412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#469×C113C2
socleC22×C113C22×D4
hypercenter#469D113
hypocenterC113#3197
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20299108C2semidirect
2. #20298942C2semidirect
3. #20298921C2semidirect
4. #20298856C2semidirect
5. #20298842C2semidirect
6. #20298761C2semidirect
7. #20298740C2semidirect
8. #20298561C2semidirect
9. #469×C113C2semidirect
12. C2×Dic452C22semidirect
13. C2×#14268635C22semidirect
23. #16813555C22semidirect
24. #16813554C22semidirect
25. #16813547C22semidirect
26. #16813545C22semidirect
27. #16813543C22semidirect
30. C2×D8×C113C22semidirect
33. #106×C113C22semidirect
34. #102×C113C22semidirect
119. C113#3197semidirect
124. #469D113semidirect
133. C2×D8C2×D113semidirect
147. #106C2×D113semidirect
151. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991082
#202989422
#202989212
#202988562
#202988422
#202987612
#202987402
#202985612
#469×C1132
#3197113