Finite Group Databasebeta

← #28388604

Subgroups — #28388604

Order 14464.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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#20298367C211yesmaximal, characteristic
2#20298324C211yesmaximal, characteristic
3#395×C113C211yesmaximal, characteristic
4C2×#14268631—21no—
5C22⋊#11744751—21no—
6C22×Q8×C113C411yescharacteristic
7C2×C4⋊C4×C113—21no—
8C2×C4⋊C4×C113C2211yescharacteristic
9#95×C113—21no—
10#95×C113C411yescharacteristic
11#14268631—22no—
12#14268631—41no—
13C2×#11744751—41no—
14C2×#11744751—41no—
15C2×Q8×C113—42no—
16C2×Q8×C113—41no—
17C22×C4×C113—21no—
18C22×C4×C113—21no—
19C22×C4×C113C2×C411yescharacteristic
20C22×C4×C113D411yescharacteristic
21C22×C4×C113D411yescharacteristic
22C4⋊C4×C113—41no—
23C4⋊C4×C113—42no—
24C23×C113C22⋊C411yescharacteristic
25Q8×C113—42no—
26Q8×C113—42no—
27C2×C4×C113—21no—
28C2×C4×C113—21no—
29C2×C4×C113—22no—
30C2×C4×C113—22no—
31C2×C4×C113—21no—
32C2×C4×C113—21no—
33C2×C4×C113—41no—
34C2×C4×C113—41no—
35C2×C4×C113—41no—
36C2×C4×C113—41no—
37C2×C4×C113—41no—
38C2×C4×C113—41no—
39C2×C4×C113SD1611yescharacteristic
40C2×C4×C113Q1611yescharacteristic
41#11744751—42no—
42#11744751—81no—
43C22×C113—21no—
44C22×C113—21no—
45C22×C113#9911yescharacteristic
46C22×C113#10311yescharacteristic
47C22×C113#10411yescharacteristic
48C4×C113—21no—
49C4×C113—21no—
50C4×C113—42no—
51C4×C113—41no—
52C4×C113—42no—
53C4×C113—41no—
54C2×C113—21no—
55C2×C113—21no—
56C2×C113#32811yescharacteristic
57C2×C113AΣL(1,𝔽16)11yescharacteristic
58C2×C113#35611yescharacteristic
59#1354—1131nomaximal, Sylow
60C113#135411yescharacteristic, complemented, Sylow
61#395D11311yescharacteristic
62#343—1131no—
63#324—1131no—
64C22×Q8Dic11311yescharacteristic
65C2×M16—2261no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D11311yescharacteristic
68C22⋊C8—2261no—
69#95—21no—
70#95Dic11311yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic11311yescharacteristic
76C22×C4C22⋊D11311yescharacteristic
77C22×C4C22⋊D11311yescharacteristic
78M16—4521no—
79M16—2262no—
80C2×C8—4521no—
81C2×C8—4521no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic11311yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1426863411yescharacteristic
100C2×C4#1426863711yescharacteristic
101C8—9041no—
102C8—4522no—
103C22—21no—
104C22—21no—
105C22#1681353711yescharacteristic
106C22#1681354611yescharacteristic
107C22#1681354911yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#2029833511yescharacteristic
117C2#2029838511yescharacteristic
118C2#2029839711yescharacteristic
subgroupG/H
centerC22#16813537
commutatorC22×C4×C113C2×C4
FrattiniC2×C4⋊C4C2×D113
Fitting#395×C113C2
socleC22×C113#99
prime radicalC23×C113C22⋊C4
cosocleC2×C4⋊C4×C113C22
hypercenter#395D113
hypocenterC113#1354
LCSG ▷ C22×C4×C113 ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
60. C113#1354semidirect

Maximal subgroups

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

subgroupindex
#202983672
#202983242
#395×C1132
#1354113