Finite Group Databasebeta

← #28401416

Subgroups — #28401416

Order 14464.

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

normal subgroups only

This group has 418 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#20299109C212yesmaximal, complemented
2#20298940C212yesmaximal, complemented
3#20298923C212yesmaximal, complemented
4#20298856C211yesmaximal, characteristic, complemented
5#20298851C211yesmaximal, characteristic, complemented
6#20298844C212yesmaximal, complemented
7#20298762C212yesmaximal, complemented
8#20298745C212yesmaximal, complemented
9#407×C113C211yesmaximal, characteristic, complemented
10C2×#14268647C2212yes—
11C2×Dic452C2211yescharacteristic, complemented
12C2×#14268636C2212yescomplemented
13C2×D904C2211yescharacteristic, complemented
14#16813605—22no—
15#16813601C2212yes—
16#16813601C2212yes—
17#16813596C2212yes—
18#16813596C2212yes—
19#16813591—22no—
20C4×C22⋊D113—22no—
21C4×C22⋊D113—22no—
22#16813581C2212yes—
23#16813556C2212yescomplemented
24#16813554C2211yescharacteristic, complemented
25#16813554C2211yescharacteristic, complemented
26#16813547C2212yescomplemented
27#16813547C2212yescomplemented
28#16813544C2212yescomplemented
29#16813544C2212yescomplemented
30C23×C4×C113C2211yescharacteristic
31C2×M16×C113C2211yescharacteristic
32C2×M16×C113C2211yescharacteristic
33C22⋊C8×C113C2212yes—
34C22⋊C8×C113C2212yes—
35#14268647—42no—
36#14268647—42no—
37C2×Dic226C2312yes—
38C2×D452C2312yes—
39C2×C22⋊D113—22no—
40C2×C22⋊D113—22no—
41C2×C22⋊D113—22no—
42C2×C4×D113—22no—
43Dic452—41no—
44#14268636—42no—
45D904—41no—
46C4⋊Dic113C2312yes—
47C4⋊Dic113C2312yes—
48#14268626—22no—
49#14268626—22no—
50C22⋊Dic113—22no—
51C22⋊Dic113—22no—
52C22⋊Dic113—22no—
53#14268624—22no—
54#14268624—22no—
55C4×Dic113—22no—
56C24×C113D411yescharacteristic
57C22×C4×C113—41no—
58C22×C4×C113—41no—
59C22×C4×C113D411yescharacteristic
60C22×C4×C113D412yes—
61C22×C4×C113C2312yes—
62C22×C4×C113C2311yescharacteristic
63M16×C113—41no—
64M16×C113—41no—
65C2×C8×C113C2311yescharacteristic
66C2×C8×C113C2312yes—
67C2×C8×C113C2311yescharacteristic
68C23×C113—41no—
69C23×C113—42no—
70C23×C113C2×D412yes—
71C23×C113C2×D411yescharacteristic
72C22×D113—22no—
73C2×C4×C113—21no—
74C2×C4×C113—21no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113—41no—
78C2×C4×C113—42no—
79C2×C4×C113C2×D412yes—
80C2×C4×C113C2×D411yescharacteristic
81C2×C4×C113C2411yescharacteristic
82C22⋊D113—44no—
83C22⋊D113—44no—
84C22⋊D113—44no—
85C2×Dic113—22no—
86C2×Dic113—22no—
87C2×Dic113—22no—
88D452—22no—
89D452—22no—
90C4×D113—44no—
91Dic226—22no—
92Dic226—22no—
93C8×C113—21no—
94C8×C113—22no—
95C8×C113—21no—
96C22×C113—22no—
97C22×C113—21no—
98C22×C113—22no—
99C22×C113—22no—
100C22×C113—22no—
101C22×C113—44no—
102C22×C113C22×D411yescharacteristic
103C2×D113—42no—
104C2×D113—42no—
105C2×D113—42no—
106C4×C113—22no—
107C4×C113—21no—
108C4×C113H(5,𝔽2)11yescharacteristic
109C4×C113H(5,𝔽2)11yescharacteristic
110Dic113—42no—
111Dic113—42no—
112Dic113—42no—
113C2×C113—42no—
114C2×C113—41no—
115C2×C113#53411yescharacteristic
116C2×C113#57512yes—
117D113—82no—
118#3197—1131nomaximal, Sylow
119C113#319711yescharacteristic, complemented, Sylow
120#525—1132no—
121#485—1132no—
122#482—1132no—
123#470—1131no—
124#469—1131no—
125#468—1132no—
126#452—1132no—
127#449—1132no—
128#407D11311yescharacteristic, complemented
129C2×#41—1132no—
130C23×C4C2×D11311yescharacteristic
131C2×Q16—1131no—
132C2×SD16—1132no—
133C2×D8—1131no—
134C2×M16C2×D11311yescharacteristic
135C2×M16C2×D11311yescharacteristic
136#123—2262no—
137C22⋊Q8—1132no—
138C22⋊Q8—1132no—
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#106—1131no—
148#103—1132no—
149#103—1132no—
150#102—1132no—
151#102—1132no—
152C22⋊C8C2×D11312yes—
153C22⋊C8C2×D11312yes—
154C24D45211yescharacteristic
155#41—4522no—
156#41—4522no—
157C2×Q8—1132no—
158C2×D4—1132no—
159C2×D4—2262no—
160C2×D4—2262no—
161C2×D4—2262no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—2262no—
165C22×C4D45211yescharacteristic
166C22×C4D45212yes—
167C22×C4C22×D11312yes—
168C22×C4C22×D11311yescharacteristic
169Q16—4521no—
170SD16—4522no—
171D8—4521no—
172M16—41no—
173M16—41no—
174C2×C8C22×D11311yescharacteristic
175C2×C8C22×D11312yes—
176C2×C8C22×D11311yescharacteristic
177C4⋊C4—1132no—
178C4⋊C4—1132no—
179C4⋊C4—2262no—
180C4⋊C4—2262no—
181C22⋊C4—2262no—
182C22⋊C4—2262no—
183C22⋊C4—2262no—
184C22⋊C4—2262no—
185C22⋊C4—2262no—
186C42—2262no—
187C23—41no—
188C23—42no—
189C23—2262no—
190C23C2×D45211yescharacteristic
191C23C2×D45212yes—
192Q8—2262no—
193Q8—2262no—
194D4—4524no—
195D4—4524no—
196D4—4524no—
197D4—2262no—
198D4—2262no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—4524no—
206C2×C4—2262no—
207C2×C4—2262no—
208C2×C4—2262no—
209C2×C4C2×D45212yes—
210C2×C4C2×D45211yescharacteristic
211C2×C4C23×D11311yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—4522no—
222C22—4522no—
223C22—4522no—
224C22C22×D45211yescharacteristic
225C4—22no—
226C4—21no—
227C4—4522no—
228C4—4522no—
229C4—4522no—
230C4#1681366711yescharacteristic
231C4#1681366711yescharacteristic
232C2—41no—
233C2—42no—
234C2—9042no—
235C2#2029916011yescharacteristic
236C2#2029939812yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#407×C113C2
socleC22×C113C22×D4
hypercenter#407D113
hypocenterC113#3197
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #20299109C2semidirect
2. #20298940C2semidirect
3. #20298923C2semidirect
4. #20298856C2semidirect
5. #20298851C2semidirect
6. #20298844C2semidirect
7. #20298762C2semidirect
8. #20298745C2semidirect
9. #407×C113C2semidirect
11. C2×Dic452C22semidirect
12. C2×#14268636C22semidirect
13. C2×D904C22semidirect
23. #16813556C22semidirect
24. #16813554C22semidirect
25. #16813554C22semidirect
26. #16813547C22semidirect
27. #16813547C22semidirect
28. #16813544C22semidirect
29. #16813544C22semidirect
119. C113#3197semidirect
128. #407D113semidirect

Maximal subgroups

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

subgroupindex
#202991092
#202989402
#202989232
#202988562
#202988512
#202988442
#202987622
#202987452
#407×C1132
#3197113