Finite Group Databasebeta

← #28392249

Subgroups — #28392249

Order 14464.

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

normal subgroups only

This group has 238 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#20298572C212yesmaximal
2#20298393C214yesmaximal, complemented
3#536×C113C211yesmaximal, characteristic
4#16813581—22no—
5#16813537—22no—
6#16813537C2214yes—
7C2×#41×C113C2211yescharacteristic
8C22×Q8×C113C411yescharacteristic, complemented
9C4⋊Q8×C113C412yescomplemented
10#124×C113C2212yes—
11#123×C113—22no—
12C22⋊Q8×C113—22no—
13#117×C113C411yescharacteristic, complemented
14C4⋊Dic113—42no—
15C22⋊Dic113—24no—
16C4×Dic113—42no—
17#41×C113—42no—
18C2×Q8×C113—21no—
19C2×Q8×C113—42no—
20C2×Q8×C113C2×C412yes—
21C2×Q8×C113C2×C411yescharacteristic
22C2×D4×C113D412yes—
23C2×D4×C113C2311yescharacteristic
24C22×C4×C113—21no—
25C22×C4×C113C2×C411yescharacteristic
26C22×C4×C113D412yes—
27C4⋊C4×C113—21no—
28C4⋊C4×C113—24no—
29C22⋊C4×C113—21no—
30C22⋊C4×C113—24no—
31C42×C113C2×C412yes—
32C23×C113C22⋊C411yescharacteristic
33C23×C113C2×D412yes—
34Q8×C113—41no—
35Q8×C113—42no—
36Q8×C113—42no—
37D4×C113—42no—
38D4×C113—41no—
39C2×C4×C113—22no—
40C2×C4×C113—22no—
41C2×C4×C113—22no—
42C2×C4×C113—22no—
43C2×C4×C113—22no—
44C2×C4×C113—42no—
45C2×C4×C113C22⋊C412yes—
46C2×C4×C113C22⋊C411yescharacteristic
47C2×C4×C113C22×C411yescharacteristic
48C2×Dic113—44no—
49C22×C113—22no—
50C22×C113—21no—
51C22×C113—41no—
52C22×C113—42no—
53C22×C113C2×C22⋊C411yescharacteristic
54C4×C113—22no—
55C4×C113—21no—
56C4×C113—42no—
57C4×C113—42no—
58C4×C113#9912yes—
59Dic113—84no—
60C2×C113—21no—
61C2×C113—42no—
62C2×C113—41no—
63C2×C113C2×#9911yescharacteristic
64#2129—1131nomaximal, Sylow
65C113#212911yescharacteristic, complemented, Sylow
66#536D11311yescharacteristic
67#410—1132no—
68#354—1134no—
69C2×#41C2×D11311yescharacteristic
70C22×Q8Dic11311yescharacteristic, complemented
71C4⋊Q8Dic11312yescomplemented
72#124C2×D11312yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—2262no—
76#117Dic11311yescharacteristic, complemented
77#99—1134no—
78#99—2262no—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×Dic11312yes—
83C2×Q8C2×Dic11311yescharacteristic
84C2×D4C22⋊D11312yes—
85C2×D4C22×D11311yescharacteristic
86C22×C4—21no—
87C22×C4C2×Dic11311yescharacteristic
88C22×C4C22⋊D11312yes—
89C4⋊C4—24no—
90C4⋊C4—21no—
91C4⋊C4—4522no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—2264no—
95C42—4522no—
96C42C2×Dic11312yes—
97C23C22⋊Dic11311yescharacteristic
98C23C2×C22⋊D11312yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—42no—
103D4—41no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—4524no—
111C2×C4C22⋊Dic11312yes—
112C2×C4C22⋊Dic11311yescharacteristic
113C2×C4C22×Dic11311yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊Dic11311yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—9044no—
124C4#1681353712yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#1681353711yescharacteristic
subgroupG/H
centerC2C2×#16813537
commutatorC2×C4×C113C22×C4
FrattiniC2×D4C22×D113
Fitting#536×C113C2
socleC2×C113C2×#99
prime radicalC2×#41×C113C22
cosocleC2×D4×C113C23
hypercenter#536D113
hypocenterC113#2129
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20298393C2semidirect
8. C22×Q8×C113C4semidirect
9. C4⋊Q8×C113C4semidirect
13. #117×C113C4semidirect
65. C113#2129semidirect
70. C22×Q8Dic113semidirect
71. C4⋊Q8Dic113semidirect
76. #117Dic113semidirect

Maximal subgroups

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

subgroupindex
#202985722
#202983932
#536×C1132
#2129113