Finite Group Databasebeta

← #46809031

Subgroups — #46809031

Order 34432.

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

normal subgroups only

This group has 122 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#31770772C211yesmaximal, characteristic
2#31770398C211yesmaximal, characteristic, complemented
3#331×C269C211yesmaximal, characteristic, complemented
4#22575498C411yescharacteristic, complemented
5#22575479—21no—
6#22575381—21no—
7#22575370C411yescharacteristic, complemented
8#22575368—21no—
9#127×C269C2211yescharacteristic
10C4⋊C8×C269—21no—
11#16864402—21no—
12#16864401—41no—
13C2×C22⋊D269—41no—
14D4×D269—41no—
15#16864390—41no—
16#16864387—41no—
17#16864386—21no—
18C22⋊Dic269—41no—
19C2×D4×C269—41no—
20C2×D4×C269C2×C411yescharacteristic
21C2×D4×C269D411yescharacteristic
22C2×C8×C269—41no—
23C42×C269D411yescharacteristic
24C22×D269—41no—
25Dic538—21no—
26D1076—21no—
27C22⋊D269—42no—
28C22⋊D269—41no—
29C2×Dic269—41no—
30C2×Dic269—81no—
31C4×D269—41no—
32#14524130—41no—
33C23×C269—21no—
34C23×C269—21no—
35D4×C269—41no—
36D4×C269—41no—
37D4×C269—81no—
38D4×C269—81no—
39C2×C4×C269—21no—
40C2×C4×C269C22⋊C411yescharacteristic
41C8×C269—81no—
42C22×C269—41no—
43C22×C269—41no—
44C22×C269—81no—
45C22×C269—81no—
46C22×C269#9911yescharacteristic
47C2×D269—41no—
48C2×D269—161no—
49C4×C269—21no—
50C4×C269—21no—
51C4×C269—21no—
52Dic269—41no—
53Dic269—161no—
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#331D26911yescharacteristic, complemented
64H(5,𝔽2)—2691no—
65AGL(1,ℤ/8)—5381no—
66#127C2×D26911yescharacteristic
67C4⋊C8—21no—
68#104—5381no—
69#100—2691no—
70#99—5381no—
71#41—5381no—
72#41—10761no—
73C2×D4—41no—
74C2×D4—10761no—
75C2×D4—10761no—
76C2×D4C4×D26911yescharacteristic
77C2×D4D107611yescharacteristic
78SD16—10761no—
79D8—10761no—
80M16—5381no—
81C2×C8—41no—
82C22⋊C4—10761no—
83C42C22⋊D26911yescharacteristic
84C23—21no—
85C23—21no—
86C23—10761no—
87Q8—5381no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—5381no—
93D4—10762no—
94D4—10761no—
95C2×C4—21no—
96C2×C4—10761no—
97C2×C4—10761no—
98C2×C4—21521no—
99C2×C4#1686437911yescharacteristic
100C8—81no—
101C8—10761no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—10761no—
107C22—43041no—
108C22#2257536711yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—10761no—
113C4—43041no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—21521no—
118C2#3177039311yescharacteristic
subgroupG/H
centerC2#31770393
commutatorC2×D4×C269C2×C4
Frattini#127C2×D269
Fitting#331×C269C2
socleC2×C269AΣL(1,𝔽16)
prime radical#31770772C2
cosocle#127×C269C22
hypercenter#331D269
hypocenterC269#1402
LCSG ▷ C2×D4×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31770398C2semidirect
3. #331×C269C2semidirect
4. #22575498C4semidirect
7. #22575370C4semidirect
59. C269#1402semidirect
63. #331D269semidirect

Maximal subgroups

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

subgroupindex
#317707722
#317703982
#331×C2692
#1402269