Finite Group Databasebeta

← #28393549

Subgroups — #28393549

Order 14464.

560 conjugacy classes of subgroups; only the 193 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 193 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
1C2×C4×D452C211yesmaximal, characteristic
2#20298499C212yesmaximal
3#20298490C214yesmaximal, complemented
4#20298460C212yesmaximal, complemented
5C4⋊C4×Dic113C212yesmaximal, complemented
6C4×C4⋊Dic113C211yesmaximal, characteristic, complemented
7#20298445C212yesmaximal, complemented
8#382×C113C211yesmaximal, characteristic, complemented
9C22×D452C2211yescharacteristic
10C22×C4×D113C2212yes—
11C4×D452C418yescomplemented
12C2×C4⋊Dic113C2212yes—
13C2×C4⋊Dic113C2211yescharacteristic
14C2×#14268624C2214yes—
15C2×#14268624C2214yes—
16C2×#14268624C2212yes—
17C2×C4×Dic113C2212yes—
18C2×C4×Dic113C2214yes—
19#16813529C2211yescharacteristic
20#16813529C2211yescharacteristic
21#16813529C2214yes—
22C2×C4⋊C4×C113C2212yes—
23C2×C42×C113C2211yescharacteristic
24#95×C113C2212yes—
25#95×C113C2212yes—
26C23×D113C2312yes—
27C2×D452—22no—
28C2×D452—22no—
29C2×D452C2×C414yes—
30C22×Dic113C2312yes—
31C22×Dic113C2312yes—
32C22×Dic113C2312yes—
33C2×C4×D113—44no—
34C2×C4×D113C2×C418yes—
35C4⋊Dic113—24no—
36C4⋊Dic113C2×C414yes—
37#14268624—28no—
38#14268624—44no—
39#14268624C2×C418yes—
40C4×Dic113—24no—
41C4×Dic113—44no—
42C22×C4×C113C2314yes—
43C22×C4×C113C2311yescharacteristic
44C22×C4×C113C2311yescharacteristic
45C22×C4×C113C2311yescharacteristic
46C4⋊C4×C113—24no—
47C42×C113C2×C414yes—
48C23×C113C2411yescharacteristic
49C22×D113—24no—
50C22×D113—22no—
51C22×D113—22no—
52C22×D113—24no—
53C22×D113C22×C414yes—
54C2×C4×C113—22no—
55C2×C4×C113—22no—
56C2×C4×C113—24no—
57C2×C4×C113—24no—
58C2×C4×C113—24no—
59C2×C4×C113C22×C412yes—
60C2×C4×C113C22×C412yes—
61C2×C4×C113C22×C412yes—
62C2×C4×C113#4112yes—
63C2×C4×C113#4112yes—
64C2×Dic113—22no—
65C2×Dic113—22no—
66C2×Dic113—24no—
67C2×Dic113—22no—
68C2×Dic113—22no—
69C2×Dic113—22no—
70C2×Dic113C22×C414yes—
71C2×Dic113#4114yes—
72D452—28no—
73C4×D113—48no—
74C22×C113C23×C411yescharacteristic
75C22×C113C2×#4112yes—
76C22×C113C2×#4111yescharacteristic
77C22×C113C2×#4111yescharacteristic
78C22×C113H(5,𝔽2)12yes—
79C2×D113—24no—
80C2×D113—24no—
81C2×D113—24no—
82C2×D113—44no—
83C2×D113—44no—
84C4×C113—22no—
85C4×C113—22no—
86C4×C113—44no—
87C4×C113#11714yes—
88Dic113—24no—
89Dic113—24no—
90Dic113—42no—
91C2×C113C2×#11711yescharacteristic
92C2×C113C4×#4111yescharacteristic
93C2×C113#51811yescharacteristic
94C2×C113#55312yes—
95C2×C113#55912yes—
96D113—44no—
97#2357—1131nomaximal, Sylow
98C113#235711yescharacteristic, complemented, Sylow
99C2×C4×D4—1131no—
100#390—1132no—
101#388—1134no—
102#382D11311yescharacteristic, complemented
103#381—1132no—
104C4×C4⋊C4—1132no—
105C4×C4⋊C4—1131no—
106C4×C22⋊C4—1132no—
107C22×D4—1131no—
108C23×C4—1132no—
109C4×D4—1138no—
110C2×C4⋊C4—1131no—
111C2×C4⋊C4—1132no—
112C2×C4⋊C4C2×D11312yes—
113C2×C22⋊C4—1132no—
114C2×C22⋊C4—1134no—
115C2×C22⋊C4—1134no—
116C2×C42—1134no—
117C2×C42—1132no—
118C2×C42C2×D11311yescharacteristic
119#95—1131no—
120#95—1131no—
121#95—1134no—
122#95C2×D11312yes—
123#95C2×D11312yes—
124C24—1132no—
125C2×D4—1134no—
126C2×D4—2262no—
127C2×D4—2262no—
128C22×C4—1132no—
129C22×C4—1132no—
130C22×C4—1138no—
131C22×C4—1132no—
132C22×C4—4524no—
133C22×C4C22×D11314yes—
134C22×C4C22×D11311yescharacteristic
135C22×C4C22×D11311yescharacteristic
136C22×C4C22×D11311yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—1134no—
139C4⋊C4—2264no—
140C22⋊C4—1138no—
141C22⋊C4—4524no—
142C22⋊C4—2268no—
143C42—4524no—
144C42—2264no—
145C42C4×D11314yes—
146C23—1134no—
147C23—2264no—
148C23—2262no—
149C23—2262no—
150C23—2264no—
151C23C23×D11311yescharacteristic
152D4—2268no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—24no—
157C2×C4—24no—
158C2×C4—1134no—
159C2×C4—1134no—
160C2×C4—4528no—
161C2×C4—2262no—
162C2×C4—2262no—
163C2×C4—2262no—
164C2×C4—2262no—
165C2×C4—2262no—
166C2×C4—2264no—
167C2×C4C2×C4×D11312yes—
168C2×C4C2×C4×D11312yes—
169C2×C4C2×C4×D11312yes—
170C2×C4#1426864612yes—
171C2×C4#1426864812yes—
172C22—4524no—
173C22—4524no—
174C22—2264no—
175C22—2264no—
176C22—2264no—
177C22C22×C4×D11311yescharacteristic
178C22#41×D11312yes—
179C22C2×#1426864611yescharacteristic
180C22C2×#1426864811yescharacteristic
181C22#1681366812yes—
182C4—22no—
183C4—22no—
184C4—44no—
185C4—4522no—
186C4—2264no—
187C4—2264no—
188C4#1681358014yes—
189C2—4524no—
190C2C2×#1681358011yescharacteristic
191C2#2029906611yescharacteristic
192C2#2029907211yescharacteristic
193C2#2029930112yes—
194C2#2029933012yes—
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#382×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D452C22
hypercenter#382D113
hypocenterC113#2357
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
3. #20298490C2semidirect
4. #20298460C2semidirect
5. C4⋊C4×Dic113C2semidirect
6. C4×C4⋊Dic113C2semidirect
7. #20298445C2semidirect
8. #382×C113C2semidirect
11. C4×D452C4semidirect
98. C113#2357semidirect
102. #382D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4522
#202984992
#202984902
#202984602
C4⋊C4×Dic1132
C4×C4⋊Dic1132
#202984452
#382×C1132
#2357113