Finite Group Databasebeta

← #28405694

Subgroups — #28405694

Order 14464.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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#20299502C211yesmaximal, characteristic, complemented
2#20299456C211yesmaximal, characteristic, complemented
3#20298768C211yesmaximal, characteristic
4#16813689—21no—
5#16813681—21no—
6#16813667C411yescharacteristic, complemented
7#16813650—21no—
8#16813618C2211yescharacteristic
9#16813548—21no—
10#100×C113C411yescharacteristic, complemented
11C2×#11744753—41no—
12C22⋊#90673—41no—
13#14268647—21no—
14#14268646—41no—
15C2×D452D411yescharacteristic
16C2×C22⋊D113—41no—
17C2×C22⋊D113—41no—
18D4×D113—41no—
19#14268636—41no—
20D904—41no—
21C4×Dic113D411yescharacteristic
22C2×D4×C113C2×C411yescharacteristic
23M16×C113—21no—
24C23×C113—21no—
25C22×D113—21no—
26C22×D113—41no—
27C2×#90673—81no—
28D4×C113—41no—
29C2×C4×C113C22⋊C411yescharacteristic
30C22⋊D113—42no—
31C22⋊D113—41no—
32C22⋊D113—81no—
33C22⋊D113—81no—
34C2×Dic113—21no—
35C2×Dic113—41no—
36D452—21no—
37D452—41no—
38C4×D113—41no—
39Dic226—21no—
40#11744753—81no—
41C8×C113—41no—
42C22×C113—41no—
43C22×C113—81no—
44C22×C113#9911yescharacteristic
45C2×D113—41no—
46C2×D113—41no—
47C2×D113—81no—
48C2×D113—161no—
49#90673—161no—
50C4×C113—21no—
51Dic113—21no—
52Dic113—21no—
53Dic113—41no—
54C2×C113—21no—
55C2×C113—81no—
56C2×C113AΣL(1,𝔽16)11yescharacteristic
57D113—81no—
58D113—81no—
59#1402—1131nomaximal, Sylow
60C113#140211yescharacteristic, complemented, Sylow
61#453—1131no—
62#353—1131no—
63#331—1131no—
64H(5,𝔽2)—1131no—
65AGL(1,ℤ/8)—2261no—
66#127—1131no—
67C4⋊C8—2261no—
68#104—2261no—
69#100#9067311yescharacteristic, complemented
70#99—2261no—
71#41—4521no—
72#41—2261no—
73C2×D4—1131no—
74C2×D4—4521no—
75C2×D4—4521no—
76C2×D4—4521no—
77C2×D4C2×#9067311yescharacteristic
78SD16—4521no—
79D8—4521no—
80M16—21no—
81C2×C8—4521no—
82C22⋊C4—4521no—
83C42—1131no—
84C23—21no—
85C23—4521no—
86C23—2261no—
87Q8—2261no—
88D4—41no—
89D4—9041no—
90D4—9041no—
91D4—4521no—
92D4—4522no—
93D4—4521no—
94D4—2261no—
95C2×C4—9041no—
96C2×C4—4521no—
97C2×C4—4521no—
98C2×C4—2261no—
99C2×C4C22⋊#9067311yescharacteristic
100C8—41no—
101C8—9041no—
102C22—41no—
103C22—81no—
104C22—18081no—
105C22—9041no—
106C22—4521no—
107C22—4521no—
108C22#1681368111yescharacteristic
109C4—21no—
110C4—18081no—
111C4—4521no—
112C4—2261no—
113C4—2261no—
114C2—21no—
115C2—81no—
116C2—9041no—
117C2—9041no—
118C2#2029949911yescharacteristic
subgroupG/H
centerC2#20299499
commutatorC2×D4×C113C2×C4
FrattiniC2×D4C2×#90673
Fitting#100×C113C4
socleC2×C113AΣL(1,𝔽16)
prime radical#20298768C2
cosocle#16813618C22
hypercenter#100#90673
hypocenterC113#1402
LCSG ▷ C2×D4×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #20299502C2semidirect
2. #20299456C2semidirect
6. #16813667C4semidirect
10. #100×C113C4semidirect
60. C113#1402semidirect
69. #100#90673semidirect

Maximal subgroups

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

subgroupindex
#202995022
#202994562
#202987682
#1402113