Finite Group Databasebeta

← #28389266

Subgroups — #28389266

Order 14464.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#20299146C211yesmaximal, characteristic
2#20298654C211yesmaximal, characteristic, complemented
3C4⋊C8×D113C211yesmaximal, characteristic, complemented
4#20298346C211yesmaximal, characteristic, complemented
5#20298346C211yesmaximal, characteristic, complemented
6#20298342C211yesmaximal, characteristic, complemented
7#331×C113C211yesmaximal, characteristic, complemented
8C2×#14268646C412yes—
9C2×C8×D113—21no—
10#16813622C2211yescharacteristic
11#16813609C412yes—
12#16813593—21no—
13#16813593—21no—
14D4×Dic113—21no—
15D4×Dic113—21no—
16C42×D113C2211yescharacteristic
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813551—21no—
20#16813534—21no—
21#16813532—21no—
22#127×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25#14268646—44no—
26C2×Dic226C2×C412yes—
27C2×C22⋊D113—22no—
28C22×Dic113—22no—
29C2×C4×D113C2×C411yescharacteristic
30C2×C4×D113D411yescharacteristic
31C2×C4×D113D411yescharacteristic
32C2×#11744751—21no—
33C2×#11744751—21no—
34C8×D113—42no—
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37C22⋊Dic113—22no—
38C22⋊Dic113—22no—
39C4×Dic113C2×C411yescharacteristic
40C4×Dic113D411yescharacteristic
41C4×Dic113D411yescharacteristic
42C2×D4×C113—21no—
43C2×D4×C113—21no—
44C2×D4×C113C2×C412yes—
45C2×C8×C113—21no—
46C2×C8×C113—21no—
47C42×C113C2311yescharacteristic
48C23×C113—22no—
49C22×D113C22⋊C411yescharacteristic
50D4×C113—42no—
51D4×C113—41no—
52D4×C113—41no—
53D4×C113—41no—
54D4×C113—41no—
55C2×C4×C113C22×C411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C22⋊D113—44no—
59C2×Dic113—22no—
60C2×Dic113—44no—
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C22⋊C411yescharacteristic
64C4×D113—22no—
65C4×D113—21no—
66C4×D113—21no—
67C4×D113—21no—
68C4×D113—21no—
69Dic226—42no—
70C8×C113—41no—
71C8×C113—41no—
72#11744751—41no—
73#11744751—41no—
74C22×C113—42no—
75C22×C113—42no—
76C22×C113—42no—
77C22×C113C2×C22⋊C411yescharacteristic
78C2×D113—21no—
79C2×D113—21no—
80C2×D113#10012yes—
81C4×C113—21no—
82C4×C113#13511yescharacteristic
83C4×C113#13511yescharacteristic
84C4×C113AGL(1,ℤ/8)11yescharacteristic
85C4×C113#13711yescharacteristic
86Dic113—21no—
87Dic113—21no—
88Dic113—21no—
89Dic113—42no—
90C2×C113—82no—
91C2×C113C2×#10011yescharacteristic
92C2×C113#41611yescharacteristic
93C2×C113#41711yescharacteristic
94D113—22no—
95#1551—1131nomaximal, Sylow
96C113#155111yescharacteristic, complemented, Sylow
97#532—1131no—
98#432—1131no—
99C2×C4⋊C8—1131no—
100#333—1131no—
101#333—1131no—
102#331—1131no—
103#331D11311yescharacteristic, complemented
104C2×#41—1132no—
105C22×C8—2261no—
106C4⋊Q8—1131no—
107#127C2×D11311yescharacteristic
108#124—1132no—
109#121—2261no—
110#121—2261no—
111C4×D4—2261no—
112C4×D4—2261no—
113C2×C42—1131no—
114C4⋊C8—1131no—
115C4⋊C8—1131no—
116C4⋊C8—2261no—
117C4⋊C8C2×D11311yescharacteristic
118C4⋊C8C2×D11311yescharacteristic
119C22⋊C8—2261no—
120#97—2261no—
121#41—4524no—
122C2×Q8—1132no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—2262no—
126C2×D4C4×D11312yes—
127C22×C4—1131no—
128C22×C4—1131no—
129C22×C4—1131no—
130C22×C4—2262no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4522no—
134C2×C8—2261no—
135C2×C8—2261no—
136C4⋊C4—2261no—
137C4⋊C4—2261no—
138C22⋊C4—2262no—
139C22⋊C4—2262no—
140C42—1131no—
141C42—1131no—
142C42—1131no—
143C42C22×D11311yescharacteristic
144C23—22no—
145C23—1131no—
146Q8—4522no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—4524no—
153C2×C4—1131no—
154C2×C4—1131no—
155C2×C4—1131no—
156C2×C4—4524no—
157C2×C4—2262no—
158C2×C4—2262no—
159C2×C4—2261no—
160C2×C4—2261no—
161C2×C4—2261no—
162C2×C4—2261no—
163C2×C4C2×C4×D11311yescharacteristic
164C2×C4D4×D11311yescharacteristic
165C2×C4D4×D11311yescharacteristic
166C8—41no—
167C8—41no—
168C8—4521no—
169C8—4521no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—1132no—
174C22—2261no—
175C22—2261no—
176C22C22⋊C4×D11311yescharacteristic
177C4—21no—
178C4—4522no—
179C4—2261no—
180C4—2261no—
181C4—2261no—
182C4#1681364111yescharacteristic
183C4#1681364311yescharacteristic
184C4#1681364611yescharacteristic
185C4#1681365111yescharacteristic
186C2—82no—
187C2—2262no—
188C2#100×D11311yescharacteristic
189C2#2029859111yescharacteristic
190C2#2029859611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#331×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299146C2
cosocleC42×C113C23
hypercenter#331D113
hypocenterC113#1551
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20298654C2semidirect
3. C4⋊C8×D113C2semidirect
4. #20298346C2semidirect
5. #20298346C2semidirect
6. #20298342C2semidirect
7. #331×C113C2semidirect
96. C113#1551semidirect
103. #331D113semidirect

Maximal subgroups

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

subgroupindex
#202991462
#202986542
C4⋊C8×D1132
#202983462
#202983422
#331×C1132
#1551113