Finite Group Databasebeta

← #46826006

Subgroups — #46826006

Order 34432.

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

normal subgroups only

This group has 112 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#31771513C211yesmaximal, characteristic, complemented
2#31771460C211yesmaximal, characteristic, complemented
3#31770783C211yesmaximal, characteristic
4#22575514—21no—
5#22575508—21no—
6#22575483—21no—
7#22575440C2211yescharacteristic
8#22575380—21no—
9#22575370C411yescharacteristic
10H(5,𝔽2)×C269C411yescharacteristic
11#16864411—41no—
12C2×#14524137—41no—
13C2×Dic538D411yescharacteristic
14#16864392—41no—
15#16864390—41no—
16#16864386—21no—
17C22⋊Dic269—41no—
18C4×Dic269D411yescharacteristic
19#41×C269—21no—
20#41×C269—41no—
21C2×D4×C269—41no—
22C2×D4×C269—41no—
23C2×D4×C269C2×C411yescharacteristic
24#14524137—42no—
25#14524137—81no—
26Dic538—41no—
27C2×Dic269—21no—
28C2×Dic269—21no—
29#14524130—41no—
30C23×C269—21no—
31C23×C269—41no—
32Q8×C269—21no—
33D4×C269—21no—
34D4×C269—41no—
35D4×C269—42no—
36D4×C269—41no—
37C2×C4×C269—41no—
38C2×C4×C269—41no—
39C2×C4×C269C22⋊C411yescharacteristic
40C22×C269—41no—
41C22×C269—41no—
42C22×C269—81no—
43C22×C269—161no—
44C22×C269#9911yescharacteristic
45C4×C269—21no—
46C4×C269—41no—
47Dic269—41no—
48Dic269—41no—
49C2×C269—21no—
50C2×C269—81no—
51C2×C269—81no—
52C2×C269AΣL(1,𝔽16)11yescharacteristic
53C269#140311yescharacteristic, complemented, Sylow
54#1403—2691nomaximal, Sylow
55#455—2691no—
56#355—2691no—
57#329—2691no—
58H(5,𝔽2)#1176164011yescharacteristic
59#137—5381no—
60#124—2691no—
61#104—5381no—
62#101—5381no—
63#100—2691no—
64#97—5381no—
65#41—21no—
66#41—41no—
67C2×Q8—2691no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#1176164011yescharacteristic
71Q16—10761no—
72SD16—10761no—
73M16—5381no—
74M16—10761no—
75C2×C8—10761no—
76C22⋊C4—10761no—
77C42—2691no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—10761no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—5381no—
89C2×C4—5381no—
90C2×C4C22⋊#1176164011yescharacteristic
91C8—10761no—
92C8—10762no—
93C8—21521no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#2257551111yescharacteristic
99C4—21no—
100C4—41no—
101C4—10761no—
102C4—10761no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#3177150511yescharacteristic
subgroupG/H
centerC2#31771505
commutatorC2×D4×C269C2×C4
FrattiniC2×D4C2×#11761640
Fitting, prime radicalH(5,𝔽2)×C269C4
socleC2×C269AΣL(1,𝔽16)
cosocle#22575440C22
hypercenterH(5,𝔽2)#11761640
hypocenterC269#1403
LCSG ▷ C2×D4×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
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. #31771513C2semidirect
2. #31771460C2semidirect
53. C269#1403semidirect

Maximal subgroups

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

subgroupindex
#317715132
#317714602
#317707832
#1403269