Finite Group Databasebeta

← #46826005

Subgroups — #46826005

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#31770775C211yesmaximal, characteristic
4#22575520—21no—
5#22575512—21no—
6#22575498C411yescharacteristic, complemented
7#22575481—21no—
8#22575449C2211yescharacteristic
9#22575379—21no—
10#100×C269C411yescharacteristic, complemented
11C2×#14524137—41no—
12C22⋊#11761640—41no—
13#16864402—21no—
14#16864401—41no—
15C2×D1076D411yescharacteristic
16C2×C22⋊D269—41no—
17C2×C22⋊D269—41no—
18D4×D269—41no—
19#16864391—41no—
20D2152—41no—
21C4×Dic269D411yescharacteristic
22C2×D4×C269C2×C411yescharacteristic
23M16×C269—21no—
24C2×#11761640—81no—
25#14524137—81no—
26C22×D269—21no—
27C22×D269—41no—
28Dic538—21no—
29D1076—21no—
30D1076—41no—
31C22⋊D269—42no—
32C22⋊D269—41no—
33C22⋊D269—81no—
34C22⋊D269—81no—
35C2×Dic269—21no—
36C2×Dic269—41no—
37C4×D269—41no—
38C23×C269—21no—
39D4×C269—41no—
40C2×C4×C269C22⋊C411yescharacteristic
41C8×C269—41no—
42C22×C269—41no—
43C22×C269—81no—
44C22×C269#9911yescharacteristic
45C2×D269—41no—
46C2×D269—41no—
47C2×D269—81no—
48C2×D269—161no—
49#11761640—161no—
50C4×C269—21no—
51Dic269—21no—
52Dic269—21no—
53Dic269—41no—
54C2×C269—21no—
55C2×C269—81no—
56C2×C269AΣL(1,𝔽16)11yescharacteristic
57D269—81no—
58D269—81no—
59C269#140211yescharacteristic, complemented, Sylow
60#1402—2691nomaximal, Sylow
61#453—2691no—
62#353—2691no—
63#331—2691no—
64H(5,𝔽2)—2691no—
65AGL(1,ℤ/8)—5381no—
66#127—2691no—
67C4⋊C8—5381no—
68#104—5381no—
69#100#1176164011yescharacteristic, complemented
70#99—5381no—
71#41—5381no—
72#41—10761no—
73C2×D4—2691no—
74C2×D4—10761no—
75C2×D4—10761no—
76C2×D4—10761no—
77C2×D4C2×#1176164011yescharacteristic
78SD16—10761no—
79D8—10761no—
80M16—21no—
81C2×C8—10761no—
82C22⋊C4—10761no—
83C42—2691no—
84C23—21no—
85C23—5381no—
86C23—10761no—
87Q8—5381no—
88D4—41no—
89D4—5381no—
90D4—10761no—
91D4—10762no—
92D4—10761no—
93D4—21521no—
94D4—21521no—
95C2×C4—5381no—
96C2×C4—10761no—
97C2×C4—10761no—
98C2×C4—21521no—
99C2×C4C22⋊#1176164011yescharacteristic
100C8—41no—
101C8—21521no—
102C22—41no—
103C22—81no—
104C22—10761no—
105C22—10761no—
106C22—21521no—
107C22—43041no—
108C22#2257551211yescharacteristic
109C4—21no—
110C4—5381no—
111C4—5381no—
112C4—10761no—
113C4—43041no—
114C2—21no—
115C2—81no—
116C2—21521no—
117C2—21521no—
118C2#3177150611yescharacteristic
subgroupG/H
centerC2#31771506
commutatorC2×D4×C269C2×C4
FrattiniC2×D4C2×#11761640
Fitting#100×C269C4
socleC2×C269AΣL(1,𝔽16)
prime radical#31770775C2
cosocle#22575449C22
hypercenter#100#11761640
hypocenterC269#1402
LCSG ▷ C2×D4×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #31771509C2semidirect
2. #31771463C2semidirect
6. #22575498C4semidirect
10. #100×C269C4semidirect
59. C269#1402semidirect
69. #100#11761640semidirect

Maximal subgroups

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

subgroupindex
#317715092
#317714632
#317707752
#1402269