Finite Group Databasebeta

← #28388720

Subgroups — #28388720

Order 14464.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#20298765C211yesmaximal, characteristic
2#20298391C211yesmaximal, characteristic, complemented
3#331×C113C211yesmaximal, characteristic, complemented
4#16813667C411yescharacteristic, complemented
5#16813648—21no—
6#16813550—21no—
7#16813539C411yescharacteristic, complemented
8#16813537—21no—
9#127×C113C2211yescharacteristic
10C4⋊C8×C113—21no—
11#14268647—21no—
12#14268646—41no—
13C2×C22⋊D113—41no—
14D4×D113—41no—
15#14268635—41no—
16#14268632—41no—
17#14268631—21no—
18C22⋊Dic113—41no—
19C2×D4×C113—41no—
20C2×D4×C113C2×C411yescharacteristic
21C2×D4×C113D411yescharacteristic
22C2×C8×C113—41no—
23C42×C113D411yescharacteristic
24C23×C113—21no—
25C23×C113—21no—
26C22×D113—41no—
27D4×C113—41no—
28D4×C113—41no—
29D4×C113—81no—
30D4×C113—81no—
31C2×C4×C113—21no—
32C2×C4×C113C22⋊C411yescharacteristic
33C22⋊D113—42no—
34C22⋊D113—41no—
35C2×Dic113—41no—
36C2×Dic113—81no—
37D452—21no—
38C4×D113—41no—
39Dic226—21no—
40C8×C113—81no—
41#11744751—41no—
42C22×C113—41no—
43C22×C113—41no—
44C22×C113—81no—
45C22×C113—81no—
46C22×C113#9911yescharacteristic
47C2×D113—41no—
48C2×D113—161no—
49C4×C113—21no—
50C4×C113—21no—
51C4×C113—21no—
52Dic113—41no—
53Dic113—161no—
54C2×C113—21no—
55C2×C113—81no—
56C2×C113—81no—
57C2×C113AΣL(1,𝔽16)11yescharacteristic
58D113—81no—
59#1402—1131nomaximal, Sylow
60C113#140211yescharacteristic, complemented, Sylow
61#453—1131no—
62#353—1131no—
63#331D11311yescharacteristic, complemented
64H(5,𝔽2)—1131no—
65AGL(1,ℤ/8)—2261no—
66#127C2×D11311yescharacteristic
67C4⋊C8—21no—
68#104—2261no—
69#100—1131no—
70#99—2261no—
71#41—4521no—
72#41—2261no—
73C2×D4—41no—
74C2×D4—4521no—
75C2×D4—4521no—
76C2×D4C4×D11311yescharacteristic
77C2×D4D45211yescharacteristic
78SD16—4521no—
79D8—4521no—
80M16—2261no—
81C2×C8—41no—
82C22⋊C4—4521no—
83C42C22⋊D11311yescharacteristic
84C23—21no—
85C23—21no—
86C23—4521no—
87Q8—2261no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—4522no—
93D4—4521no—
94D4—2261no—
95C2×C4—21no—
96C2×C4—9041no—
97C2×C4—4521no—
98C2×C4—4521no—
99C2×C4#1426862411yescharacteristic
100C8—81no—
101C8—4521no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—18081no—
107C22—4521no—
108C22#1681353611yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—18081no—
113C4—4521no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—9041no—
118C2#2029838611yescharacteristic
subgroupG/H
centerC2#20298386
commutatorC2×D4×C113C2×C4
Frattini#127C2×D113
Fitting#331×C113C2
socleC2×C113AΣL(1,𝔽16)
prime radical#20298765C2
cosocle#127×C113C22
hypercenter#331D113
hypocenterC113#1402
LCSG ▷ C2×D4×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20298391C2semidirect
3. #331×C113C2semidirect
4. #16813667C4semidirect
7. #16813539C4semidirect
60. C113#1402semidirect
63. #331D113semidirect

Maximal subgroups

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

subgroupindex
#202987652
#202983912
#331×C1132
#1402113