Finite Group Databasebeta

← #36377978

Subgroups — #36377978

Order 22592.

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#26015037C211yesmaximal, characteristic
2#26014976C212yesmaximal, complemented
3#26014973C211yesmaximal, characteristic, complemented
4#26014906C212yesmaximal, complemented
5#99×C353C211yesmaximal, characteristic, complemented
6#19150737—21no—
7#19150736—22no—
8C2×C22⋊D353—21no—
9C2×C22⋊D353C2212yes—
10D4×D353—22no—
11C22×Dic353C2211yescharacteristic, complemented
12C4⋊Dic353—22no—
13#19150716—21no—
14C22⋊Dic353—21no—
15C22⋊Dic353C2211yescharacteristic, complemented
16#19150714—22no—
17C2×D4×C353C2211yescharacteristic
18C22⋊C4×C353C2212yescomplemented
19C22×D353—21no—
20C22×D353D412yes—
21Dic706—21no—
22D1412—21no—
23C22⋊D353—22no—
24C22⋊D353—22no—
25C22⋊D353—22no—
26C2×Dic353—21no—
27C2×Dic353—22no—
28C2×Dic353—21no—
29C2×Dic353—21no—
30C2×Dic353D412yes—
31C4×D353—22no—
32C23×C353D411yescharacteristic
33C23×C353C2311yescharacteristic
34D4×C353—22no—
35C2×C4×C353—22no—
36C2×C4×C353D411yescharacteristic
37C22×C353—21no—
38C22×C353—41no—
39C22×C353—41no—
40C22×C353C2×D412yes—
41C22×C353C2×D411yescharacteristic
42C2×D353—22no—
43C2×D353—42no—
44C2×D353—81no—
45C4×C353—21no—
46C4×C353—42no—
47Dic353—22no—
48Dic353—41no—
49Dic353—41no—
50C2×C353—21no—
51C2×C353—22no—
52C2×C353—41no—
53C2×C353#12011yescharacteristic
54D353—42no—
55C353#45811yescharacteristic, complemented, Sylow
56#458—3531nomaximal, Sylow
57H(5,𝔽2)—3531no—
58#123—3531no—
59#123—3532no—
60#99—3532no—
61#99D35311yescharacteristic, complemented
62#41—7062no—
63#41—7061no—
64C2×D4—3532no—
65C2×D4—7062no—
66C2×D4—7061no—
67C2×D4C2×D35311yescharacteristic
68C22×C4—3531no—
69C4⋊C4—7062no—
70C4⋊C4—7061no—
71C22⋊C4—3531no—
72C22⋊C4—7062no—
73C22⋊C4—7061no—
74C22⋊C4C2×D35312yescomplemented
75C23—3532no—
76C23—7061no—
77C23D141211yescharacteristic
78C23C22×D35311yescharacteristic
79Q8—7061no—
80D4—22no—
81D4—7061no—
82D4—7062no—
83D4—7062no—
84D4—7062no—
85C2×C4—22no—
86C2×C4—3532no—
87C2×C4—7062no—
88C2×C4—7062no—
89C2×C4—7061no—
90C2×C4—7061no—
91C2×C4—7061no—
92C2×C4D141211yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—28241no—
97C22—14122no—
98C22—7062no—
99C22D4×D35312yes—
100C22C2×D141211yescharacteristic
101C4—21no—
102C4—42no—
103C4—14121no—
104C4—14121no—
105C4—7062no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—14122no—
110C2#2601496211yescharacteristic
subgroupG/H
centerC2#26014962
commutator, cosocleC23×C353C23
FrattiniC23C22×D353
Fitting#99×C353C2
socleC2×C353#120
prime radical#26015037C2
hypercenter#99D353
hypocenterC353#458
LCSG ▷ C23×C353 ▷ C2×C353 ▷ C353
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #26014976C2semidirect
3. #26014973C2semidirect
4. #26014906C2semidirect
5. #99×C353C2semidirect
11. C22×Dic353C22semidirect
15. C22⋊Dic353C22semidirect
18. C22⋊C4×C353C22semidirect
55. C353#458semidirect
61. #99D353semidirect
74. C22⋊C4C2×D353semidirect

Maximal subgroups

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

subgroupindex
#260150372
#260149762
#260149732
#260149062
#99×C3532
#458353