Finite Group Databasebeta

← #28388729

Subgroups — #28388729

Order 14464.

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

normal subgroups only

This group has 106 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#20298780C211yesmaximal, characteristic
2#20298397C211yesmaximal, characteristic, complemented
3#333×C113C211yesmaximal, characteristic, complemented
4#16813670C411yescharacteristic
5#16813653—21no—
6#16813550—21no—
7#16813541—21no—
8#16813541C411yescharacteristic
9C4⋊Q8×C113C2211yescharacteristic
10C4⋊C8×C113—21no—
11#14268648—41no—
12#14268647—21no—
13#14268647—41no—
14Q8×D113—41no—
15#14268637—41no—
16#14268634—41no—
17#14268631—21no—
18#14268631—41no—
19C2×Q8×C113C2×C411yescharacteristic
20C2×Q8×C113D411yescharacteristic
21C2×C8×C113—41no—
22C4⋊C4×C113—41no—
23C42×C113D411yescharacteristic
24Q8×C113—41no—
25Q8×C113—41no—
26C2×C4×C113—21no—
27C2×C4×C113—21no—
28C2×C4×C113—21no—
29C2×C4×C113C22⋊C411yescharacteristic
30C22⋊D113—41no—
31D452—21no—
32D452—41no—
33C4×D113—41no—
34C4×D113—42no—
35Dic226—21no—
36Dic226—41no—
37C8×C113—81no—
38#11744751—41no—
39#11744751—81no—
40C22×C113#9911yescharacteristic
41C2×D113—41no—
42C4×C113—21no—
43C4×C113—21no—
44C4×C113—21no—
45C4×C113—41no—
46C4×C113—41no—
47Dic113—41no—
48C2×C113—21no—
49C2×C113AΣL(1,𝔽16)11yescharacteristic
50D113—81no—
51#1405—1131nomaximal, Sylow
52C113#140511yescharacteristic, complemented, Sylow
53#456—1131no—
54#356—1131no—
55#333D11311yescharacteristic, complemented
562−1+4—1131no—
57#137—2261no—
58C4⋊Q8C2×D11311yescharacteristic
59C4⋊C8—21no—
60#104—2261no—
61#101—1131no—
62#101—2261no—
63#41—4521no—
64#41—4521no—
65#41—2261no—
66C2×Q8—4521no—
67C2×Q8C4×D11311yescharacteristic
68C2×Q8D45211yescharacteristic
69Q16—4521no—
70SD16—4521no—
71M16—4521no—
72M16—2261no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D11311yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—4521no—
79Q8—2261no—
80D4—4521no—
81D4—4521no—
82D4—2261no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—4521no—
87C2×C4—4522no—
88C2×C4#1426862411yescharacteristic
89C8—81no—
90C8—9041no—
91C8—4521no—
92C22—4521no—
93C22#1681353611yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—4521no—
100C2—21no—
101C2—9041no—
102C2#2029838611yescharacteristic
subgroupG/H
centerC2#20298386
commutatorC2×Q8×C113C2×C4
FrattiniC4⋊Q8C2×D113
Fitting#333×C113C2
socleC2×C113AΣL(1,𝔽16)
prime radical#16813670C4
cosocleC4⋊Q8×C113C22
hypercenter#333D113
hypocenterC113#1405
LCSG ▷ C2×Q8×C113 ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #20298397C2semidirect
3. #333×C113C2semidirect
52. C113#1405semidirect
55. #333D113semidirect

Maximal subgroups

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

subgroupindex
#202987802
#202983972
#333×C1132
#1405113