Finite Group Databasebeta

← #46830366

Subgroups — #46830366

Order 34624.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#31772673C211yesmaximal, characteristic
2#31772612C212yesmaximal, complemented
3#31772609C211yesmaximal, characteristic, complemented
4#31772542C212yesmaximal, complemented
5#99×C541C211yesmaximal, characteristic, complemented
6#22575836—21no—
7#22575835—22no—
8C2×C22⋊D541—21no—
9C2×C22⋊D541C2212yes—
10D4×D541—22no—
11C22×Dic541C2211yescharacteristic, complemented
12C4⋊Dic541—22no—
13#22575815—21no—
14C22⋊Dic541—21no—
15C22⋊Dic541C2211yescharacteristic, complemented
16#22575813—22no—
17C2×D4×C541C2211yescharacteristic
18C22⋊C4×C541C2212yescomplemented
19C22×D541—21no—
20C22×D541D412yes—
21Dic1082—21no—
22D2164—21no—
23C22⋊D541—22no—
24C22⋊D541—22no—
25C22⋊D541—22no—
26C2×Dic541—21no—
27C2×Dic541—22no—
28C2×Dic541—21no—
29C2×Dic541—21no—
30C2×Dic541D412yes—
31C4×D541—22no—
32C23×C541D411yescharacteristic
33C23×C541C2311yescharacteristic
34D4×C541—22no—
35C2×C4×C541—22no—
36C2×C4×C541D411yescharacteristic
37C22×C541—21no—
38C22×C541—41no—
39C22×C541—41no—
40C22×C541C2×D412yes—
41C22×C541C2×D411yescharacteristic
42C2×D541—22no—
43C2×D541—42no—
44C2×D541—81no—
45C4×C541—21no—
46C4×C541—42no—
47Dic541—22no—
48Dic541—41no—
49Dic541—41no—
50C2×C541—21no—
51C2×C541—22no—
52C2×C541—41no—
53C2×C541#12011yescharacteristic
54D541—42no—
55C541#45811yescharacteristic, complemented, Sylow
56#458—5411nomaximal, Sylow
57H(5,𝔽2)—5411no—
58#123—5411no—
59#123—5412no—
60#99—5412no—
61#99D54111yescharacteristic, complemented
62#41—10822no—
63#41—10821no—
64C2×D4—5412no—
65C2×D4—10822no—
66C2×D4—10821no—
67C2×D4C2×D54111yescharacteristic
68C22×C4—5411no—
69C4⋊C4—10822no—
70C4⋊C4—10821no—
71C22⋊C4—5411no—
72C22⋊C4—10822no—
73C22⋊C4—10821no—
74C22⋊C4C2×D54112yescomplemented
75C23—5412no—
76C23—10821no—
77C23D216411yescharacteristic
78C23C22×D54111yescharacteristic
79Q8—10821no—
80D4—22no—
81D4—10821no—
82D4—10822no—
83D4—10822no—
84D4—10822no—
85C2×C4—22no—
86C2×C4—5412no—
87C2×C4—10822no—
88C2×C4—10821no—
89C2×C4—10822no—
90C2×C4—10821no—
91C2×C4—10821no—
92C2×C4D216411yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—10822no—
97C22—21642no—
98C22—43281no—
99C22D4×D54112yes—
100C22C2×D216411yescharacteristic
101C4—21no—
102C4—42no—
103C4—10822no—
104C4—21641no—
105C4—21641no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—21642no—
110C2#3177259811yescharacteristic
subgroupG/H
centerC2#31772598
commutator, cosocleC23×C541C23
FrattiniC23C22×D541
Fitting#99×C541C2
socleC2×C541#120
prime radical#31772673C2
hypercenter#99D541
hypocenterC541#458
LCSG ▷ C23×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #31772612C2semidirect
3. #31772609C2semidirect
4. #31772542C2semidirect
5. #99×C541C2semidirect
11. C22×Dic541C22semidirect
15. C22⋊Dic541C22semidirect
18. C22⋊C4×C541C22semidirect
55. C541#458semidirect
61. #99D541semidirect
74. C22⋊C4C2×D541semidirect

Maximal subgroups

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

subgroupindex
#317726732
#317726122
#317726092
#317725422
#99×C5412
#458541