Finite Group Databasebeta

← #46826007

Subgroups — #46826007

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#31770785C211yesmaximal, characteristic
4#22575514—21no—
5#22575508—21no—
6#22575498C411yescharacteristic
7#22575486—21no—
8#22575440C2211yescharacteristic
9#22575379—21no—
10#100×C269C411yescharacteristic
11#16864411—41no—
12C2×#14524137—41no—
13#16864402—21no—
14#16864401—41no—
15C2×Dic538D411yescharacteristic
16C2×C22⋊D269—41no—
17D4×D269—41no—
18Dic1076—41no—
19#16864391—41no—
20C22⋊Dic269—41no—
21C4×Dic269D411yescharacteristic
22C2×D4×C269C2×C411yescharacteristic
23M16×C269—21no—
24#14524137—42no—
25#14524137—81no—
26C22×D269—41no—
27Dic538—21no—
28Dic538—41no—
29D1076—21no—
30C22⋊D269—42no—
31C22⋊D269—41no—
32C2×Dic269—21no—
33C2×Dic269—21no—
34C2×Dic269—41no—
35C4×D269—41no—
36C23×C269—21no—
37D4×C269—41no—
38C2×C4×C269C22⋊C411yescharacteristic
39C8×C269—41no—
40C22×C269—41no—
41C22×C269—81no—
42C22×C269#9911yescharacteristic
43C2×D269—41no—
44C2×D269—161no—
45C4×C269—21no—
46Dic269—41no—
47Dic269—41no—
48Dic269—41no—
49C2×C269—21no—
50C2×C269—81no—
51C2×C269AΣL(1,𝔽16)11yescharacteristic
52D269—81no—
53C269#140311yescharacteristic, complemented, Sylow
54#1403—2691nomaximal, Sylow
55#455—2691no—
56#355—2691no—
57#329—2691no—
58H(5,𝔽2)—2691no—
59#137—5381no—
60#124—2691no—
61#104—5381no—
62#101—5381no—
63#100#1176164011yescharacteristic
64#97—5381no—
65#41—5381no—
66#41—10761no—
67C2×Q8—2691no—
68C2×D4—10761no—
69C2×D4—10761no—
70C2×D4C2×#1176164011yescharacteristic
71Q16—10761no—
72SD16—10761no—
73M16—21no—
74M16—10761no—
75C2×C8—10761no—
76C22⋊C4—10761no—
77C42—2691no—
78C23—21no—
79C23—10761no—
80Q8—5381no—
81Q8—10761no—
82D4—41no—
83D4—5381no—
84D4—10762no—
85D4—10761no—
86C2×C4—5381no—
87C2×C4—5381no—
88C2×C4—10761no—
89C2×C4—10761no—
90C2×C4C22⋊#1176164011yescharacteristic
91C8—41no—
92C8—10762no—
93C8—21521no—
94C22—41no—
95C22—81no—
96C22—10761no—
97C22—43041no—
98C22#2257551211yescharacteristic
99C4—21no—
100C4—10761no—
101C4—10761no—
102C4—10761no—
103C2—21no—
104C2—81no—
105C2—21521no—
106C2#3177150611yescharacteristic
subgroupG/H
centerC2#31771506
commutatorC2×D4×C269C2×C4
FrattiniC2×D4C2×#11761640
Fitting#100×C269C4
socleC2×C269AΣL(1,𝔽16)
prime radical#22575498C4
cosocle#22575440C22
hypercenter#100#11761640
hypocenterC269#1403
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. #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
#317707852
#1403269