Finite Group Databasebeta

← #28389199

Subgroups — #28389199

Order 14464.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D113C211yesmaximal, characteristic
2#20298653C212yesmaximal
3#20298340C211yesmaximal, characteristic, complemented
4#20298339C212yesmaximal, complemented
5#330×C113C211yesmaximal, characteristic, complemented
6#16813614C2211yescharacteristic
7#16813613C412yes—
8#16813612—22no—
9C4⋊C4×D113—22no—
10C4⋊C4×D113C412yes—
11C42×D113C2211yescharacteristic
12#16813551—22no—
13#16813534—22no—
14#16813533C2212yes—
15#125×C113C2211yescharacteristic
16#97×C113C2212yes—
17C2×C4×D113—22no—
18C2×C4×D113C2×C411yescharacteristic
19C2×C4×D113D412yes—
20C2×#11744751—22no—
21C4⋊Dic113—22no—
22C4⋊Dic113C2×C412yes—
23#14268626—22no—
24#14268626—22no—
25#14268626—22no—
26C4×Dic113C2×C411yescharacteristic
27C4×Dic113D412yes—
28C2×C8×C113—22no—
29C4⋊C4×C113—22no—
30C4⋊C4×C113C2×C412yes—
31C42×C113C2311yescharacteristic
32C22×D113C22⋊C411yescharacteristic
33C2×C4×C113—22no—
34C2×C4×C113C22×C411yescharacteristic
35C2×C4×C113C2×D412yes—
36C2×Dic113—22no—
37C2×Dic113C22⋊C412yes—
38C2×Dic113C22⋊C411yescharacteristic
39C4×D113—22no—
40C4×D113—42no—
41C4×D113—44no—
42C8×C113—42no—
43#11744751—42no—
44C22×C113C2×C22⋊C411yescharacteristic
45C2×D113—22no—
46C2×D113#10112yes—
47C4×C113—21no—
48C4×C113—22no—
49C4×C113—42no—
50Dic113—21no—
51Dic113—22no—
52Dic113—42no—
53C2×C113C2×#10111yescharacteristic
54C2×C113#42112yes—
55D113—22no—
56#1534—1131nomaximal, Sylow
57C113#153411yescharacteristic, complemented, Sylow
58C2×#125—1131no—
59#432—1132no—
60#330—1131no—
61#330—1132no—
62#330D11311yescharacteristic, complemented
63#125—1132no—
64#125—1131no—
65#125—2262no—
66#125C2×D11311yescharacteristic
67C2×C4⋊C4—1132no—
68C2×C4⋊C4—2262no—
69C2×C42—1131no—
70C4⋊C8—2262no—
71C22⋊C8—2262no—
72#97—1132no—
73#97C2×D11312yes—
74C22×C4—1132no—
75C22×C4—1131no—
76C22×C4—2262no—
77C2×C8—22no—
78C2×C8—2262no—
79C4⋊C4—22no—
80C4⋊C4—1132no—
81C4⋊C4—2262no—
82C4⋊C4—2262no—
83C4⋊C4—2262no—
84C4⋊C4—2262no—
85C4⋊C4C4×D11312yes—
86C42—1131no—
87C42—1132no—
88C42C22×D11311yescharacteristic
89C23—1131no—
90C2×C4—22no—
91C2×C4—1131no—
92C2×C4—1132no—
93C2×C4—4522no—
94C2×C4—4524no—
95C2×C4—2262no—
96C2×C4—2262no—
97C2×C4C2×C4×D11311yescharacteristic
98C2×C4D4×D11312yes—
99C8—42no—
100C8—4522no—
101C22—1132no—
102C22—2262no—
103C22C22⋊C4×D11311yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—4522no—
108C4—2261no—
109C4—2262no—
110C2—2262no—
111C2#101×D11311yescharacteristic
112C2#2029861312yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#330×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C22⋊C4
cosocleC42×C113C23
hypercenter#330D113
hypocenterC113#1534
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20298340C2semidirect
4. #20298339C2semidirect
5. #330×C113C2semidirect
57. C113#1534semidirect
62. #330D113semidirect

Maximal subgroups

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

subgroupindex
#125×D1132
#202986532
#202983402
#202983392
#330×C1132
#1534113