Finite Group Databasebeta

← #28389081

Subgroups — #28389081

Order 14464.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#20299148C211yesmaximal, characteristic
2#20298655C211yesmaximal, characteristic, complemented
3#20298331C214yesmaximal, complemented
4#376×C113C211yesmaximal, characteristic, complemented
5C2×#14268647—21no—
6#16813622C411yescharacteristic, complemented
7#16813619C411yescharacteristic, complemented
8#16813610—21no—
9#16813596—21no—
10#16813596C2212yes—
11C4×D452—21no—
12C4×D452C412yescomplemented
13C4⋊#11744751—21no—
14C22⋊#11744751C2212yes—
15#16813533—21no—
16C2×C42×C113—21no—
17C2×C42×C113C2211yescharacteristic
18#95×C113—21no—
19#95×C113C2212yes—
20#14268647—44no—
21C2×Dic226—21no—
22C2×D452—21no—
23C2×D452—21no—
24C2×D452C2×C412yes—
25C2×C22⋊D113—22no—
26C2×C4×D113—22no—
27C2×#11744751—22no—
28C4⋊Dic113—21no—
29C4⋊Dic113C2×C412yes—
30#14268624—22no—
31#14268624—22no—
32C22×C4×C113—22no—
33C22×C4×C113D411yescharacteristic
34C22×C4×C113D411yescharacteristic
35C22×C4×C113C2311yescharacteristic
36C42×C113—24no—
37C42×C113C2×C411yescharacteristic
38C42×C113C2×C411yescharacteristic
39C42×C113D411yescharacteristic
40C42×C113D411yescharacteristic
41C23×C113C2×D411yescharacteristic
42C22×D113—22no—
43C2×C4×C113—22no—
44C2×C4×C113—22no—
45C2×C4×C113—24no—
46C2×C4×C113—41no—
47C2×C4×C113—42no—
48C2×C4×C113—42no—
49C2×C4×C113C22⋊C411yescharacteristic
50C2×C4×C113C22⋊C411yescharacteristic
51C2×C4×C113C22⋊C411yescharacteristic
52C2×C4×C113C22⋊C411yescharacteristic
53C2×C4×C113C22×C411yescharacteristic
54C2×C4×C113C2×D411yescharacteristic
55C22⋊D113—44no—
56C2×Dic113—22no—
57D452—42no—
58D452—42no—
59D452—42no—
60C4×D113—44no—
61Dic226—42no—
62#11744751—42no—
63C22×C113—21no—
64C22×C113—21no—
65C22×C113C2×C22⋊C411yescharacteristic
66C22×C113AGL(1,ℤ/8)12yes—
67C2×D113—42no—
68C2×D113—42no—
69C2×D113—42no—
70C4×C113—21no—
71C4×C113—21no—
72C4×C113—21no—
73C4×C113—21no—
74C4×C113—21no—
75C4×C113—44no—
76C4×C113#10412yes—
77Dic113—42no—
78C2×C113—22no—
79C2×C113#41011yescharacteristic
80C2×C113#41811yescharacteristic
81C2×C113C2×#10411yescharacteristic
82D113—82no—
83#1505—1131nomaximal, Sylow
84C113#150511yescharacteristic, complemented, Sylow
85#532—1131no—
86#432—1131no—
87#376D11311yescharacteristic, complemented
88#327—1134no—
89C2×#41—2261no—
90C4⋊Q8—1131no—
91#127—1131no—
92#124—2261no—
93#121—1132no—
94#121—2261no—
95C4×D4—1132no—
96C4×D4—2261no—
97C2×C42—21no—
98C2×C42C2×D11311yescharacteristic
99C4⋊C8—2261no—
100C22⋊C8—1132no—
101#97—2261no—
102#95—21no—
103#95C2×D11312yes—
104#41—4524no—
105C2×Q8—2261no—
106C2×D4—1132no—
107C2×D4—2262no—
108C2×D4—2261no—
109C2×D4—2261no—
110C22×C4—22no—
111C22×C4—2262no—
112C22×C4C22⋊D11311yescharacteristic
113C22×C4C22⋊D11311yescharacteristic
114C22×C4C22×D11311yescharacteristic
115C2×C8—2262no—
116C4⋊C4—1132no—
117C4⋊C4—2261no—
118C22⋊C4—2262no—
119C22⋊C4—2262no—
120C42—24no—
121C42C4×D11311yescharacteristic
122C42C4×D11311yescharacteristic
123C42D45211yescharacteristic
124C42D45211yescharacteristic
125C23—2262no—
126C23C2×C22⋊D11311yescharacteristic
127Q8—4522no—
128D4—4522no—
129D4—4522no—
130D4—4524no—
131D4—4522no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—4524no—
139C2×C4—2262no—
140C2×C4#1426862411yescharacteristic
141C2×C4#1426862411yescharacteristic
142C2×C4#1426862411yescharacteristic
143C2×C4#1426862411yescharacteristic
144C2×C4C2×C4×D11311yescharacteristic
145C2×C4C2×D45211yescharacteristic
146C8—4522no—
147C22—21no—
148C22—21no—
149C22—4522no—
150C22—4522no—
151C22—4522no—
152C22C2×#1426862411yescharacteristic
153C22#1681364712yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—4522no—
161C4#1681355012yes—
162C2—22no—
163C2—9042no—
164C2#2029857111yescharacteristic
165C2#2029860211yescharacteristic
166C2C2×#1681355011yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#376×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299148C2
cosocleC22×C4×C113C23
hypercenter#376D113
hypocenterC113#1505
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #20298655C2semidirect
3. #20298331C2semidirect
4. #376×C113C2semidirect
6. #16813622C4semidirect
7. #16813619C4semidirect
12. C4×D452C4semidirect
84. C113#1505semidirect
87. #376D113semidirect

Maximal subgroups

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

subgroupindex
#202991482
#202986552
#202983312
#376×C1132
#1505113