Finite Group Databasebeta

← #28407053

Subgroups — #28407053

Order 14464.

816 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 210 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
1C22×C22⋊#90673C212yesmaximal
2#20299545C218yesmaximal, complemented
3#20299540C214yesmaximal, complemented
4C2×C22⋊C4×D113C211yesmaximal, characteristic
5C23×#90673C2214yes—
6C2×C4⋊#90673C2218yescomplemented
7C2×C22⋊#90673—28no—
8C2×C22⋊#90673C2214yes—
9C2×C22⋊#90673C2214yes—
10(C2×#90673)⋊C4C2218yescomplemented
11C24×D113C2211yescharacteristic
12C22×C4×D113C2212yes—
13C2×C22⋊Dic113C411yescharacteristic, complemented
14C2×#14268624C412yescomplemented
15C22⋊C4×D113C414yescomplemented
16C22⋊C4×D113C2214yes—
17C2×C22⋊C4×C113C411yescharacteristic, complemented
18C22×#90673—28no—
19C22×#90673—48no—
20C22×#90673C2318yes—
21C4⋊#90673—48no—
22C22⋊#90673—28no—
23C22⋊#90673—28no—
24C23×D113—44no—
25C23×D113C2×C412yes—
26C23×D113C2×C411yescharacteristic
27C23×D113D414yes—
28C23×D113Q814yes—
29C23×D113C2312yes—
30C23×D113C2311yescharacteristic
31C22×Dic113C2×C412yescomplemented
32C2×C4×D113—44no—
33C2×C4×D113C2×C414yescomplemented
34C2×C4×D113C2314yes—
35C22⋊Dic113C2×C414yescomplemented
36#14268624C2×C418yescomplemented
37C24×C113C2×C411yescharacteristic
38C22×C4×C113C2×C412yescomplemented
39C22⋊C4×C113C2×C414yescomplemented
40C23×C113—42no—
41C23×C113C4⋊C414yescomplemented
42C23×C113C22×C412yes—
43C23×C113C22×C411yescharacteristic
44C22×D113—24no—
45C22×D113—28no—
46C22×D113—48no—
47C22×D113—48no—
48C22×D113—44no—
49C22×D113—42no—
50C22×D113C4⋊C418yescomplemented
51C22×D113C4⋊C414yescomplemented
52C22×D113C22×C412yes—
53C22×D113C22×C411yescharacteristic
54C22×D113C2×D412yes—
55C22×D113C2×D414yes—
56C22×D113C2×Q814yes—
57C22×D113C2×Q812yes—
58C22×D113C2411yescharacteristic
59C2×#90673—28no—
60C2×#90673—216no—
61C2×#90673—416no—
62C2×C4×C113—42no—
63C2×C4×C113C22×C414yes—
64C2×Dic113—42no—
65C2×Dic113C22×C414yes—
66C4×D113—28no—
67C4×D113—44no—
68C22×C113—22no—
69C22×C113—24no—
70C22×C113—44no—
71C22×C113C2×C4⋊C412yes—
72C22×C113C2×C4⋊C414yes—
73C22×C113C23×C411yescharacteristic
74C2×D113—22no—
75C2×D113—24no—
76C2×D113—28no—
77C2×D113—24no—
78C2×D113—24no—
79C2×D113—28no—
80C2×D113—48no—
81C2×D113—44no—
82C2×D113C2×C4⋊C414yes—
83C2×D113C2×C4⋊C412yes—
84C2×D113C22×D411yescharacteristic
85C2×D113C22×Q811yescharacteristic
86C2×D113H(5,𝔽2)14yes—
87#90673—48no—
88C4×C113—24no—
89Dic113—24no—
90C2×C113—24no—
91C2×C113—22no—
92C2×C113C22×C4⋊C411yescharacteristic
93C2×C113#51812yes—
94D113—22no—
95D113—24no—
96D113#53412yes—
97D113#54312yes—
98#2315—1131nomaximal, Sylow
99C113#231511yescharacteristic, complemented, Sylow
100C22×C22⋊C4—1131no—
101C22×C22⋊C4—1132no—
102#385—1138no—
103#380—1134no—
104C25—1131no—
105C23×C4—1132no—
106C23×C4—1134no—
107C2×C4⋊C4—1138no—
108C2×C22⋊C4—1131no—
109C2×C22⋊C4—1132no—
110C2×C22⋊C4—1134no—
111C2×C22⋊C4—1134no—
112C2×C22⋊C4—1134no—
113C2×C22⋊C4—1134no—
114C2×C22⋊C4—2268no—
115C2×C22⋊C4#9067311yescharacteristic, complemented
116#95—1138no—
117C24—1134no—
118C24—1134no—
119C24—1131no—
120C24—1132no—
121C24—1131no—
122C24—1132no—
123C24—4524no—
124C24C2×#9067311yescharacteristic
125C22×C4—1132no—
126C22×C4—1134no—
127C22×C4—1134no—
128C22×C4—1138no—
129C22×C4—4524no—
130C22×C4—4528no—
131C22×C4—2268no—
132C22×C4C2×#9067312yescomplemented
133C4⋊C4—4528no—
134C22⋊C4—1134no—
135C22⋊C4—1138no—
136C22⋊C4—2268no—
137C22⋊C4—2268no—
138C22⋊C4C2×#9067314yescomplemented
139C23—42no—
140C23—1131no—
141C23—1138no—
142C23—1134no—
143C23—1132no—
144C23—1134no—
145C23—1132no—
146C23—1134no—
147C23—1132no—
148C23—1131no—
149C23—4522no—
150C23—4524no—
151C23—4528no—
152C23—4528no—
153C23—2264no—
154C23—2268no—
155C23C4⋊#9067314yescomplemented
156C23C22×#9067312yes—
157C23C22×#9067311yescharacteristic
158C2×C4—42no—
159C2×C4—1134no—
160C2×C4—4524no—
161C2×C4—45216no—
162C2×C4—4522no—
163C2×C4—2268no—
164C2×C4—2268no—
165C2×C4—22616no—
166C2×C4C22×#9067314yes—
167C22—22no—
168C22—24no—
169C22—44no—
170C22—1131no—
171C22—1131no—
172C22—1134no—
173C22—1132no—
174C22—1134no—
175C22—4524no—
176C22—4528no—
177C22—2268no—
178C22—2264no—
179C22—2264no—
180C22—2268no—
181C22—2262no—
182C22—2264no—
183C22C2×C4⋊#9067312yes—
184C22C2×C4⋊#9067314yes—
185C22C23×#9067311yescharacteristic
186C4—24no—
187C4—4528no—
188C4—2264no—
189C2—22no—
190C2—24no—
191C2—1132no—
192C2—1132no—
193C2—2264no—
194C2—2262no—
195C2C22×C4⋊#9067311yescharacteristic
196C2#2029966512yes—
subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
FittingC2×C22⋊C4×C113C4
prime radicalC24×D113C22
cosocleC22×D113C24
hypercenterC2×C22⋊C4#90673
hypocenterC113#2315
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20299545C2semidirect
3. #20299540C2semidirect
6. C2×C4⋊#90673C22semidirect
10. (C2×#90673)⋊C4C22semidirect
13. C2×C22⋊Dic113C4semidirect
14. C2×#14268624C4semidirect
15. C22⋊C4×D113C4semidirect
17. C2×C22⋊C4×C113C4semidirect
31. C22×Dic113C2×C4semidirect
33. C2×C4×D113C2×C4semidirect
35. C22⋊Dic113C2×C4semidirect
36. #14268624C2×C4semidirect
38. C22×C4×C113C2×C4semidirect
39. C22⋊C4×C113C2×C4semidirect
41. C23×C113C4⋊C4semidirect
50. C22×D113C4⋊C4semidirect
51. C22×D113C4⋊C4semidirect
99. C113#2315semidirect
115. C2×C22⋊C4#90673semidirect
132. C22×C4C2×#90673semidirect
138. C22⋊C4C2×#90673semidirect
155. C23C4⋊#90673semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#906732
#202995452
#202995402
C2×C22⋊C4×D1132
#2315113