Finite Group Databasebeta

← #28389308

Subgroups — #28389308

Order 14464.

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

normal subgroups only

This group has 254 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#20299149C211yesmaximal, characteristic
2#20298620C212yesmaximal, complemented
3#20298347C211yesmaximal, characteristic, complemented
4#20298341C212yesmaximal, complemented
5#333×C113C211yesmaximal, characteristic, complemented
6C2×#14268648C412yes—
7C2×#14268630—22no—
8#16813619C2211yescharacteristic
9#16813611C412yes—
10#16813597—22no—
11#16813584—22no—
12C42×D113C2211yescharacteristic
13C4⋊#11744751C2212yes—
14#16813551—22no—
15C4⋊Q8×C113C2211yescharacteristic
16C4⋊C8×C113C2212yes—
17#14268648—44no—
18C2×D452—22no—
19C2×D452—22no—
20C2×D452C2×C412yes—
21C2×C4×D113—22no—
22C2×C4×D113C2×C411yescharacteristic
23C2×C4×D113D412yes—
24#14268630—44no—
25C2×#11744751—22no—
26#14268624—24no—
27C4×Dic113C2×C411yescharacteristic
28C4×Dic113D412yes—
29C2×Q8×C113C2×C412yes—
30C2×C8×C113—22no—
31C4⋊C4×C113—22no—
32C42×C113C2311yescharacteristic
33C22×D113—22no—
34C22×D113C22⋊C411yescharacteristic
35Q8×C113—42no—
36C2×C4×C113—22no—
37C2×C4×C113C22×C411yescharacteristic
38C2×C4×C113C2×D412yes—
39C2×Dic113C22⋊C412yes—
40C2×Dic113C22⋊C411yescharacteristic
41D452—42no—
42D452—44no—
43D452—42no—
44D452—42no—
45C4×D113—22no—
46C4×D113—22no—
47C4×D113—22no—
48C4×D113—44no—
49C8×C113—42no—
50#11744751—42no—
51C22×C113C2×C22⋊C411yescharacteristic
52C2×D113—21no—
53C2×D113—22no—
54C2×D113—42no—
55C2×D113—44no—
56C4×C113—21no—
57C4×C113—42no—
58C4×C113AGL(1,ℤ/8)12yes—
59C4×C113#13712yes—
60Dic113—22no—
61Dic113#10012yes—
62C2×C113C2×#10011yescharacteristic
63C2×C113#41712yes—
64D113—41no—
65D113—82no—
66#1560—1131nomaximal, Sylow
67C113#156011yescharacteristic, complemented, Sylow
68#532—1131no—
69#423—1132no—
70#333—1131no—
71#333D11311yescharacteristic, complemented
72#331—1132no—
73C2×#41—1132no—
74C2×M16—2262no—
75C4⋊Q8C2×D11311yescharacteristic
76#127—1131no—
77#124—1132no—
78#121—2262no—
79C4×D4—2262no—
80C2×C42—1131no—
81C4⋊C8—1132no—
82C4⋊C8—2262no—
83C4⋊C8C2×D11312yes—
84#41—4524no—
85C2×Q8C4×D11312yes—
86C2×D4—1132no—
87C2×D4—2262no—
88C2×D4—2262no—
89C22×C4—1131no—
90C22×C4—1132no—
91C22×C4—2262no—
92M16—4524no—
93C2×C8—22no—
94C2×C8—2262no—
95C4⋊C4—22no—
96C22⋊C4—2264no—
97C42—1131no—
98C42—1132no—
99C42C22×D11311yescharacteristic
100C23—1131no—
101C23—2262no—
102Q8—42no—
103D4—4522no—
104D4—4524no—
105D4—4522no—
106D4—4522no—
107C2×C4—22no—
108C2×C4—1131no—
109C2×C4—1132no—
110C2×C4—4524no—
111C2×C4—2262no—
112C2×C4—2262no—
113C2×C4—2262no—
114C2×C4C2×C4×D11311yescharacteristic
115C2×C4D4×D11312yes—
116C8—42no—
117C8—4522no—
118C22—4522no—
119C22—4524no—
120C22—2261no—
121C22—2262no—
122C22C22⋊C4×D11311yescharacteristic
123C4—21no—
124C4—42no—
125C4—1132no—
126C4—2262no—
127C4#1681364912yes—
128C4#1681365412yes—
129C2—9042no—
130C2—4521no—
131C2#100×D11311yescharacteristic
132C2#2029859812yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#333×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299149C2
cosocleC42×C113C23
hypercenter#333D113
hypocenterC113#1560
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20298620C2semidirect
3. #20298347C2semidirect
4. #20298341C2semidirect
5. #333×C113C2semidirect
67. C113#1560semidirect
71. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
#202986202
#202983472
#202983412
#333×C1132
#1560113