Finite Group Databasebeta

← #28393170

Subgroups — #28393170

Order 14464.

672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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⋊Dic113C211yesmaximal, characteristic
2#20298492C214yesmaximal, complemented
3#20298486C214yesmaximal, complemented
4#20298456C212yesmaximal, complemented
5#20298454C211yesmaximal, characteristic
6C22⋊C4×Dic113C212yesmaximal, complemented
7#379×C113C211yesmaximal, characteristic
8C23×Dic113C2211yescharacteristic
9C23×Dic113C2211yescharacteristic
10C2×#14268626C2214yescomplemented
11C2×C22⋊Dic113C418yescomplemented
12C2×C22⋊Dic113C2212yes—
13C2×C22⋊Dic113C2212yes—
14C2×C22⋊Dic113C2212yes—
15C2×C22⋊Dic113C2212yes—
16C2×C22⋊Dic113C2212yes—
17C2×C4×Dic113C2214yescomplemented
18#16813529C2214yescomplemented
19#16813529C2214yescomplemented
20C25×C113C2211yescharacteristic
21C2×C22⋊C4×C113C2212yes—
22C2×C22⋊C4×C113C2212yes—
23C2×C22⋊C4×C113C2212yes—
24C22×Dic113—42no—
25C22×Dic113—42no—
26C22×Dic113C2×C414yes—
27C22×Dic113C2×C414yes—
28C22×Dic113C2314yes—
29C22×Dic113C2312yes—
30C22×Dic113C2312yes—
31#14268626—44no—
32C22⋊Dic113—24no—
33C22⋊Dic113—42no—
34C22⋊Dic113—42no—
35C22⋊Dic113C2×C418yes—
36C22⋊Dic113C2×C418yes—
37C4×Dic113—44no—
38C24×C113—24no—
39C24×C113—42no—
40C24×C113—42no—
41C24×C113C2×C414yes—
42C24×C113C2311yescharacteristic
43C24×C113C2311yescharacteristic
44C24×C113C2311yescharacteristic
45C22×C4×C113C2314yes—
46C22⋊C4×C113—24no—
47C22⋊C4×C113—42no—
48C22⋊C4×C113—42no—
49C23×C113—22no—
50C23×C113—22no—
51C23×C113—28no—
52C23×C113—22no—
53C23×C113—22no—
54C23×C113—22no—
55C23×C113—22no—
56C23×C113—22no—
57C23×C113—22no—
58C23×C113—44no—
59C23×C113—44no—
60C23×C113—416no—
61C23×C113C22×C412yes—
62C23×C113C22×C412yes—
63C23×C113C22×C412yes—
64C23×C113#4114yes—
65C23×C113C2411yescharacteristic
66C2×C4×C113—24no—
67C2×C4×C113—24no—
68C2×C4×C113—24no—
69C2×Dic113—24no—
70C2×Dic113—24no—
71C2×Dic113—24no—
72C2×Dic113—24no—
73C2×Dic113—24no—
74C2×Dic113—44no—
75C2×Dic113—44no—
76C2×Dic113C22×C414yes—
77C2×Dic113C22×C414yes—
78C22×C113—22no—
79C22×C113—22no—
80C22×C113—28no—
81C22×C113—22no—
82C22×C113—22no—
83C22×C113—22no—
84C22×C113—22no—
85C22×C113—22no—
86C22×C113—22no—
87C22×C113—416no—
88C22×C113—44no—
89C22×C113—44no—
90C22×C113#11714yes—
91C22×C113C23×C411yescharacteristic
92C22×C113C2×#4112yes—
93C22×C113H(5,𝔽2)12yes—
94C22×C113H(5,𝔽2)12yes—
95C4×C113—44no—
96Dic113—24no—
97Dic113—24no—
98Dic113—44no—
99C2×C113—24no—
100C2×C113—42no—
101C2×C113—42no—
102C2×C113C2×#11711yescharacteristic
103C2×C113#51811yescharacteristic
104C2×C113#51811yescharacteristic
105C2×C113#53814yes—
106#2312—1131nomaximal, Sylow
107C113#231211yescharacteristic, complemented, Sylow
108C22×C22⋊C4—1131no—
109#388—1134no—
110#388—1134no—
111#380—1132no—
112#379—1131no—
113#379D11311yescharacteristic
114C4×C22⋊C4—1132no—
115C25C2×D11311yescharacteristic
116C23×C4—1131no—
117C23×C4—1131no—
118C2×C4⋊C4—1134no—
119C2×C22⋊C4—1138no—
120C2×C22⋊C4—1132no—
121C2×C22⋊C4—1132no—
122C2×C22⋊C4—1132no—
123C2×C22⋊C4—1132no—
124C2×C22⋊C4—1132no—
125C2×C22⋊C4C2×D11312yes—
126C2×C22⋊C4C2×D11312yes—
127C2×C22⋊C4C2×D11312yes—
128C2×C42—1134no—
129#95—1134no—
130#95—1134no—
131C24—24no—
132C24—42no—
133C24—42no—
134C24C4×D11314yes—
135C24C22×D11311yescharacteristic
136C24C22×D11311yescharacteristic
137C24C22×D11311yescharacteristic
138C22×C4—1134no—
139C22×C4—1134no—
140C22×C4—1132no—
141C22×C4—1132no—
142C22×C4—1134no—
143C22×C4—4522no—
144C22×C4—4522no—
145C22×C4C22×D11314yes—
146C4⋊C4—4524no—
147C22⋊C4—24no—
148C22⋊C4—42no—
149C22⋊C4—42no—
150C22⋊C4—1138no—
151C22⋊C4—1138no—
152C22⋊C4—4522no—
153C22⋊C4—4522no—
154C22⋊C4—2264no—
155C42—4524no—
156C23—22no—
157C23—22no—
158C23—28no—
159C23—22no—
160C23—22no—
161C23—22no—
162C23—22no—
163C23—22no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—416no—
168C23C2×C4×D11312yes—
169C23C2×C4×D11312yes—
170C23C2×C4×D11312yes—
171C23#1426864614yes—
172C23C23×D11311yescharacteristic
173C2×C4—24no—
174C2×C4—24no—
175C2×C4—24no—
176C2×C4—1134no—
177C2×C4—1134no—
178C2×C4—4524no—
179C2×C4—4524no—
180C2×C4—2264no—
181C2×C4—2264no—
182C2×C4—2264no—
183C2×C4—2264no—
184C2×C4—2264no—
185C22—22no—
186C22—22no—
187C22—28no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—416no—
195C22—44no—
196C22—44no—
197C22#1681357814yes—
198C22C22×C4×D11311yescharacteristic
199C22C2×#1426864612yes—
200C22#1681366712yes—
201C22#1681366712yes—
202C4—44no—
203C4—4524no—
204C4—2264no—
205C4—2264no—
206C2—24no—
207C2—42no—
208C2—42no—
209C2C2×#1681357811yescharacteristic
210C2#2029907111yescharacteristic
211C2#2029907111yescharacteristic
212C2#2029918314yes—
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#379×C113C2
socle, cosocleC23×C113C24
prime radicalC25×C113C22
hypercenter#379D113
hypocenterC113#2312
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. #20298492C2semidirect
3. #20298486C2semidirect
4. #20298456C2semidirect
6. C22⋊C4×Dic113C2semidirect
10. C2×#14268626C22semidirect
11. C2×C22⋊Dic113C4semidirect
17. C2×C4×Dic113C22semidirect
18. #16813529C22semidirect
19. #16813529C22semidirect
107. C113#2312semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Dic1132
#202984922
#202984862
#202984562
#202984542
C22⋊C4×Dic1132
#379×C1132
#2312113