Finite Group Databasebeta

← #46826004

Subgroups — #46826004

Order 34432.

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#31771509C211yesmaximal, characteristic, complemented
2#31771463C211yesmaximal, characteristic, complemented
3#31770773C211yesmaximal, characteristic
4#22575520—21no—
5#22575512—21no—
6#22575478—21no—
7#22575449C2211yescharacteristic
8#22575380—21no—
9#22575370C411yescharacteristic, complemented
10H(5,𝔽2)×C269C411yescharacteristic, complemented
11C2×#14524137—41no—
12C22⋊#11761640—41no—
13C2×D1076D411yescharacteristic
14C2×C22⋊D269—41no—
15#16864389—41no—
16#16864387—41no—
17#16864386—21no—
18C4×Dic269D411yescharacteristic
19#41×C269—21no—
20#41×C269—41no—
21C2×D4×C269—41no—
22C2×D4×C269—41no—
23C2×D4×C269C2×C411yescharacteristic
24C2×#11761640—81no—
25#14524137—81no—
26C22×D269—21no—
27D1076—41no—
28C22⋊D269—81no—
29C22⋊D269—81no—
30C2×Dic269—21no—
31#14524130—41no—
32C23×C269—21no—
33C23×C269—41no—
34Q8×C269—21no—
35D4×C269—21no—
36D4×C269—41no—
37D4×C269—42no—
38D4×C269—41no—
39C2×C4×C269—41no—
40C2×C4×C269—41no—
41C2×C4×C269C22⋊C411yescharacteristic
42C22×C269—41no—
43C22×C269—41no—
44C22×C269—81no—
45C22×C269—161no—
46C22×C269#9911yescharacteristic
47C2×D269—41no—
48C2×D269—81no—
49#11761640—161no—
50C4×C269—21no—
51C4×C269—41no—
52Dic269—21no—
53Dic269—21no—
54C2×C269—21no—
55C2×C269—81no—
56C2×C269—81no—
57C2×C269AΣL(1,𝔽16)11yescharacteristic
58D269—81no—
59C269#140211yescharacteristic, complemented, Sylow
60#1402—2691nomaximal, Sylow
61#453—2691no—
62#353—2691no—
63#331—2691no—
64H(5,𝔽2)#1176164011yescharacteristic, complemented
65AGL(1,ℤ/8)—5381no—
66#127—2691no—
67C4⋊C8—5381no—
68#104—5381no—
69#100—2691no—
70#99—5381no—
71#41—21no—
72#41—41no—
73C2×D4—41no—
74C2×D4—41no—
75C2×D4—2691no—
76C2×D4—10761no—
77C2×D4C2×#1176164011yescharacteristic
78SD16—10761no—
79D8—10761no—
80M16—5381no—
81C2×C8—10761no—
82C22⋊C4—10761no—
83C42—2691no—
84C23—21no—
85C23—41no—
86C23—5381no—
87Q8—21no—
88D4—21no—
89D4—41no—
90D4—42no—
91D4—41no—
92D4—10761no—
93D4—21521no—
94D4—21521no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—5381no—
98C2×C4—21521no—
99C2×C4C22⋊#1176164011yescharacteristic
100C8—10761no—
101C8—21521no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—161no—
106C22—10761no—
107C22—21521no—
108C22#2257551111yescharacteristic
109C4—21no—
110C4—41no—
111C4—5381no—
112C4—5381no—
113C4—43041no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—21521no—
118C2#3177150511yescharacteristic
subgroupG/H
centerC2#31771505
commutatorC2×D4×C269C2×C4
FrattiniC2×D4C2×#11761640
FittingH(5,𝔽2)×C269C4
socleC2×C269AΣL(1,𝔽16)
prime radical#31770773C2
cosocle#22575449C22
hypercenterH(5,𝔽2)#11761640
hypocenterC269#1402
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. #31771509C2semidirect
2. #31771463C2semidirect
9. #22575370C4semidirect
10. H(5,𝔽2)×C269C4semidirect
59. C269#1402semidirect
64. H(5,𝔽2)#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715092
#317714632
#317707732
#1402269