Finite Group Databasebeta

← #46826010

Subgroups — #46826010

Order 34432.

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

normal subgroups only

This group has 106 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#31771515C211yesmaximal, characteristic, complemented
2#31771465C211yesmaximal, characteristic, complemented
3#31770788C211yesmaximal, characteristic
4#22575520—21no—
5#22575514—21no—
6#22575483—21no—
7#22575451C2211yescharacteristic
8#22575380—21no—
9#22575372C411yescharacteristic
102−1+4×C269C411yescharacteristic
11#16864411—41no—
12C2×#14524137—41no—
13C2×Dic538D411yescharacteristic
14#16864392—41no—
15#16864390—41no—
16#16864386—21no—
17#16864381—41no—
18C4×Dic269D411yescharacteristic
19#41×C269—21no—
20#41×C269—41no—
21#41×C269—41no—
22C2×Q8×C269—41no—
23C2×Q8×C269C2×C411yescharacteristic
24#14524137—81no—
25#14524137—81no—
26Dic538—41no—
27C2×Dic269—21no—
28C2×Dic269—21no—
29#14524130—41no—
30Q8×C269—21no—
31Q8×C269—41no—
32Q8×C269—41no—
33D4×C269—21no—
34D4×C269—41no—
35D4×C269—41no—
36C2×C4×C269—21no—
37C2×C4×C269—41no—
38C2×C4×C269—42no—
39C2×C4×C269C22⋊C411yescharacteristic
40C22×C269—41no—
41C22×C269#9911yescharacteristic
42C4×C269—21no—
43C4×C269—41no—
44C4×C269—41no—
45Dic269—21no—
46Dic269—21no—
47Dic269—41no—
48C2×C269—21no—
49C2×C269—81no—
50C2×C269AΣL(1,𝔽16)11yescharacteristic
51C269#140511yescharacteristic, complemented, Sylow
52#1405—2691nomaximal, Sylow
53#456—2691no—
54#356—2691no—
55#333—2691no—
562−1+4#1176164011yescharacteristic
57#137—5381no—
58C4⋊Q8—2691no—
59C4⋊C8—5381no—
60#104—5381no—
61#101—2691no—
62#101—5381no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—2691no—
68C2×Q8C2×#1176164011yescharacteristic
69Q16—10761no—
70SD16—10761no—
71M16—5381no—
72M16—10761no—
73C2×C8—10761no—
74C4⋊C4—10761no—
75C42—2691no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—10761no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—5381no—
87C2×C4—5381no—
88C2×C4C22⋊#1176164011yescharacteristic
89C8—10761no—
90C8—21521no—
91C8—21521no—
92C22—41no—
93C22#2257551111yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—5381no—
98C4—5381no—
99C4—10761no—
100C2—21no—
101C2—81no—
102C2#3177150511yescharacteristic
subgroupG/H
centerC2#31771505
commutatorC2×Q8×C269C2×C4
FrattiniC2×Q8C2×#11761640
Fitting, prime radical2−1+4×C269C4
socleC2×C269AΣL(1,𝔽16)
cosocle#22575451C22
hypercenter2−1+4#11761640
hypocenterC269#1405
LCSG ▷ C2×Q8×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #31771515C2semidirect
2. #31771465C2semidirect
51. C269#1405semidirect

Maximal subgroups

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

subgroupindex
#317715152
#317714652
#317707882
#1405269