Finite Group Databasebeta

← #28405693

Subgroups — #28405693

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#20298766C211yesmaximal, characteristic
4#16813689—21no—
5#16813681—21no—
6#16813647—21no—
7#16813618C2211yescharacteristic
8#16813549—21no—
9#16813539C411yescharacteristic, complemented
10H(5,𝔽2)×C113C411yescharacteristic, complemented
11C2×#11744753—41no—
12C22⋊#90673—41no—
13C2×D452D411yescharacteristic
14C2×C22⋊D113—41no—
15#14268634—41no—
16#14268632—41no—
17#14268631—21no—
18C4×Dic113D411yescharacteristic
19#41×C113—21no—
20#41×C113—41no—
21C2×D4×C113—41no—
22C2×D4×C113—41no—
23C2×D4×C113C2×C411yescharacteristic
24C23×C113—21no—
25C23×C113—41no—
26C22×D113—21no—
27C2×#90673—81no—
28Q8×C113—21no—
29D4×C113—21no—
30D4×C113—41no—
31D4×C113—42no—
32D4×C113—41no—
33C2×C4×C113—41no—
34C2×C4×C113—41no—
35C2×C4×C113C22⋊C411yescharacteristic
36C22⋊D113—81no—
37C22⋊D113—81no—
38C2×Dic113—21no—
39D452—41no—
40#11744753—81no—
41#11744751—41no—
42C22×C113—41no—
43C22×C113—41no—
44C22×C113—81no—
45C22×C113—161no—
46C22×C113#9911yescharacteristic
47C2×D113—41no—
48C2×D113—81no—
49#90673—161no—
50C4×C113—21no—
51C4×C113—41no—
52Dic113—21no—
53Dic113—21no—
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#331—1131no—
64H(5,𝔽2)#9067311yescharacteristic, complemented
65AGL(1,ℤ/8)—2261no—
66#127—1131no—
67C4⋊C8—2261no—
68#104—2261no—
69#100—1131no—
70#99—2261no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—1131no—
76C2×D4—4521no—
77C2×D4C2×#9067311yescharacteristic
78SD16—4521no—
79D8—4521no—
80M16—2261no—
81C2×C8—4521no—
82C22⋊C4—4521no—
83C42—1131no—
84C23—21no—
85C23—41no—
86C23—2261no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—9041no—
93D4—9041no—
94D4—4521no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—9041no—
98C2×C4—2261no—
99C2×C4C22⋊#9067311yescharacteristic
100C8—9041no—
101C8—4521no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—9041no—
107C22—4521no—
108C22#1681368011yescharacteristic
109C4—21no—
110C4—41no—
111C4—18081no—
112C4—2261no—
113C4—2261no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—9041no—
118C2#2029949811yescharacteristic
subgroupG/H
centerC2#20299498
commutatorC2×D4×C113C2×C4
FrattiniC2×D4C2×#90673
FittingH(5,𝔽2)×C113C4
socleC2×C113AΣL(1,𝔽16)
prime radical#20298766C2
cosocle#16813618C22
hypercenterH(5,𝔽2)#90673
hypocenterC113#1402
LCSG ▷ C2×D4×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #20299502C2semidirect
2. #20299456C2semidirect
9. #16813539C4semidirect
10. H(5,𝔽2)×C113C4semidirect
60. C113#1402semidirect
64. H(5,𝔽2)#90673semidirect

Maximal subgroups

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

subgroupindex
#202995022
#202994562
#202987662
#1402113