Finite Group Databasebeta

← #28401417

Subgroups — #28401417

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#20299111C212yesmaximal, complemented
2#20298937C212yesmaximal, complemented
3#20298924C212yesmaximal, complemented
4#20298851C211yesmaximal, characteristic, complemented
5#20298846C212yesmaximal, complemented
6#20298759C212yesmaximal, complemented
7#20298746C212yesmaximal, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#470×C113C211yesmaximal, characteristic, complemented
10C2×#14268648C2212yes—
11C22×C4×D113C2211yescharacteristic
12C2×#14268634C2212yescomplemented
13C2×D904C2211yescharacteristic, complemented
14C2×#14268631C2211yescharacteristic
15#16813607—22no—
16#16813598C2212yes—
17#16813597C2212yes—
18#16813596C2212yes—
19#16813592—22no—
20#16813584—22no—
21#16813582—22no—
22#16813580C2212yes—
23#16813555C2212yescomplemented
24#16813554C2211yescharacteristic, complemented
25#16813546C2212yescomplemented
26#16813544C2212yescomplemented
27#16813542C2212yescomplemented
28#16813534C2212yes—
29#16813534C2212yes—
30C2×Q16×C113C2211yescharacteristic, complemented
31C2×M16×C113C2211yescharacteristic
32C22⋊Q8×C113C2212yes—
33#106×C113C2211yescharacteristic, complemented
34#103×C113C2212yescomplemented
35C23×D113D411yescharacteristic
36#14268648—42no—
37#14268648—42no—
38C2×D452—22no—
39C2×D452—22no—
40C2×D452C2312yes—
41C2×C22⋊D113—22no—
42C22×Dic113D411yescharacteristic
43C2×C4×D113—22no—
44C2×C4×D113—41no—
45C2×C4×D113—41no—
46C2×C4×D113D412yes—
47C2×C4×D113C2312yes—
48#14268634—42no—
49D904—41no—
50#14268631—41no—
51C2×#11744751C2312yes—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54#14268624—22no—
55#14268624—22no—
56#14268624—22no—
57#14268624—22no—
58C4×Dic113—22no—
59C2×Q8×C113C2312yes—
60C22×C4×C113C2311yescharacteristic
61Q16×C113—41no—
62M16×C113—41no—
63C2×C8×C113C2311yescharacteristic
64C2×C8×C113C2311yescharacteristic
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C23×C113C2×D411yescharacteristic
69C22×D113—22no—
70C22×D113—41no—
71C22×D113—42no—
72C22×D113C2×D412yes—
73Q8×C113—22no—
74Q8×C113—22no—
75C2×C4×C113—21no—
76C2×C4×C113—21no—
77C2×C4×C113—22no—
78C2×C4×C113—22no—
79C2×C4×C113C2×D411yescharacteristic
80C2×C4×C113C2411yescharacteristic
81C22⋊D113—44no—
82C2×Dic113—22no—
83C2×Dic113—41no—
84C2×Dic113C2×D412yes—
85D452—22no—
86D452—22no—
87D452—44no—
88D452—44no—
89C4×D113—22no—
90C4×D113—22no—
91C4×D113—42no—
92C4×D113—44no—
93C8×C113—21no—
94C8×C113—21no—
95#11744751—22no—
96C22×C113—21no—
97C22×C113—22no—
98C22×C113C22×D411yescharacteristic
99C2×D113—22no—
100C2×D113—22no—
101C2×D113—22no—
102C2×D113—44no—
103C2×D113—42no—
104C2×D113—42no—
105C2×D113—42no—
106C4×C113—21no—
107C4×C113—42no—
108C4×C113—42no—
109C4×C113H(5,𝔽2)11yescharacteristic
110C4×C113H(5,𝔽2)11yescharacteristic
111Dic113—22no—
112Dic113—42no—
113C2×C113—41no—
114C2×C113#53411yescharacteristic
115C2×C113#57512yes—
116D113—42no—
117D113—82no—
118#3197—1131nomaximal, Sylow
119C113#319711yescharacteristic, complemented, Sylow
120#525—1132no—
121#485—1132no—
122#482—1132no—
123#470D11311yescharacteristic, complemented
124#469—1131no—
125#468—1132no—
126#452—1132no—
127#449—1132no—
128#407—1131no—
129C2×#41—1132no—
130C23×C4—1131no—
131C2×Q16C2×D11311yescharacteristic, complemented
132C2×SD16—1132no—
133C2×D8—1131no—
134C2×M16—1131no—
135C2×M16C2×D11311yescharacteristic
136#123—2262no—
137C22⋊Q8—1132no—
138C22⋊Q8C2×D11312yes—
139#121—1132no—
140#121—1132no—
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#103C2×D11312yescomplemented
150#102—1132no—
151#102—1132no—
152C22⋊C8—1132no—
153C22⋊C8—1132no—
154C24—1131no—
155#41—4522no—
156#41—4522no—
157C2×Q8C22×D11312yes—
158C2×D4—1132no—
159C2×D4—2262no—
160C2×D4—2262no—
161C2×D4—2262no—
162C22×C4—1131no—
163C22×C4—1132no—
164C22×C4—1132no—
165C22×C4—4521no—
166C22×C4—4521no—
167C22×C4—2262no—
168C22×C4C22×D11311yescharacteristic
169Q16—41no—
170SD16—4522no—
171D8—4521no—
172M16—41no—
173M16—4521no—
174C2×C8—1132no—
175C2×C8C22×D11311yescharacteristic
176C2×C8C22×D11311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—1132no—
179C4⋊C4—2262no—
180C4⋊C4C22×D11312yes—
181C22⋊C4—22no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C22⋊C4—2262no—
185C22⋊C4—2262no—
186C42—2262no—
187C23—1132no—
188C23—4521no—
189C23—4522no—
190C23—2262no—
191C23D4×D11311yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—4524no—
195D4—4524no—
196D4—4524no—
197D4—2262no—
198D4—2262no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—1132no—
204C2×C4—4522no—
205C2×C4—4524no—
206C2×C4—4521no—
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—4524no—
218C22—4522no—
219C22—4522no—
220C22—4522no—
221C22—2262no—
222C22—2262no—
223C22—2262no—
224C22C2×D4×D11311yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—4522no—
229C4—2262no—
230C4#1681366711yescharacteristic
231C4#1681366811yescharacteristic
232C2—41no—
233C2—9042no—
234C2—4522no—
235C2#2029915611yescharacteristic
236C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
hypercenter#470D113
hypocenterC113#3197
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20299111C2semidirect
2. #20298937C2semidirect
3. #20298924C2semidirect
4. #20298851C2semidirect
5. #20298846C2semidirect
6. #20298759C2semidirect
7. #20298746C2semidirect
8. #20298561C2semidirect
9. #470×C113C2semidirect
12. C2×#14268634C22semidirect
13. C2×D904C22semidirect
23. #16813555C22semidirect
24. #16813554C22semidirect
25. #16813546C22semidirect
26. #16813544C22semidirect
27. #16813542C22semidirect
30. C2×Q16×C113C22semidirect
33. #106×C113C22semidirect
34. #103×C113C22semidirect
119. C113#3197semidirect
123. #470D113semidirect
131. C2×Q16C2×D113semidirect
147. #106C2×D113semidirect
149. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991112
#202989372
#202989242
#202988512
#202988462
#202987592
#202987462
#202985612
#470×C1132
#3197113