Finite Group Databasebeta

← #26011682

Subgroups — #26011682

Order 11072.

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#19149724C211yesmaximal, characteristic
2#19149663C212yesmaximal, complemented
3#19149660C211yesmaximal, characteristic, complemented
4#19149593C212yesmaximal, complemented
5#99×C173C211yesmaximal, characteristic, complemented
6#14583826—21no—
7#14583825—22no—
8C2×C22⋊D173—21no—
9C2×C22⋊D173C2212yes—
10D4×D173—22no—
11C22×Dic173C2211yescharacteristic, complemented
12C4⋊Dic173—22no—
13#14583805—21no—
14C22⋊Dic173—21no—
15C22⋊Dic173C2211yescharacteristic, complemented
16#14583803—22no—
17C2×D4×C173C2211yescharacteristic
18C22⋊C4×C173C2212yescomplemented
19C22×D173—21no—
20C22×D173D412yes—
21Dic346—21no—
22D692—21no—
23C22⋊D173—22no—
24C22⋊D173—22no—
25C22⋊D173—22no—
26C2×Dic173—21no—
27C2×Dic173—22no—
28C2×Dic173—21no—
29C2×Dic173—21no—
30C2×Dic173D412yes—
31C4×D173—22no—
32C23×C173D411yescharacteristic
33C23×C173C2311yescharacteristic
34D4×C173—22no—
35C2×C4×C173—22no—
36C2×C4×C173D411yescharacteristic
37C22×C173—21no—
38C22×C173—41no—
39C22×C173—41no—
40C22×C173C2×D412yes—
41C22×C173C2×D411yescharacteristic
42C2×D173—22no—
43C2×D173—42no—
44C2×D173—81no—
45C4×C173—21no—
46C4×C173—42no—
47Dic173—22no—
48Dic173—41no—
49Dic173—41no—
50C2×C173—21no—
51C2×C173—22no—
52C2×C173—41no—
53C2×C173#12011yescharacteristic
54D173—42no—
55C173#45811yescharacteristic, complemented, Sylow
56#458—1731nomaximal, Sylow
57H(5,𝔽2)—1731no—
58#123—1731no—
59#123—1732no—
60#99—1732no—
61#99D17311yescharacteristic, complemented
62#41—3462no—
63#41—3461no—
64C2×D4—3462no—
65C2×D4—3461no—
66C2×D4—1732no—
67C2×D4C2×D17311yescharacteristic
68C22×C4—1731no—
69C4⋊C4—3462no—
70C4⋊C4—3461no—
71C22⋊C4—3462no—
72C22⋊C4—3461no—
73C22⋊C4—1731no—
74C22⋊C4C2×D17312yescomplemented
75C23—3461no—
76C23—1732no—
77C23D69211yescharacteristic
78C23C22×D17311yescharacteristic
79Q8—3461no—
80D4—22no—
81D4—3461no—
82D4—3462no—
83D4—3462no—
84D4—3462no—
85C2×C4—22no—
86C2×C4—3462no—
87C2×C4—3461no—
88C2×C4—3462no—
89C2×C4—3461no—
90C2×C4—3461no—
91C2×C4—1732no—
92C2×C4D69211yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—3462no—
97C22—13841no—
98C22—6922no—
99C22D4×D17312yes—
100C22C2×D69211yescharacteristic
101C4—21no—
102C4—42no—
103C4—3462no—
104C4—6921no—
105C4—6921no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—6922no—
110C2#1914964911yescharacteristic
subgroupG/H
centerC2#19149649
commutator, cosocleC23×C173C23
FrattiniC23C22×D173
Fitting#99×C173C2
socleC2×C173#120
prime radical#19149724C2
hypercenter#99D173
hypocenterC173#458
LCSG ▷ C23×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #19149663C2semidirect
3. #19149660C2semidirect
4. #19149593C2semidirect
5. #99×C173C2semidirect
11. C22×Dic173C22semidirect
15. C22⋊Dic173C22semidirect
18. C22⋊C4×C173C22semidirect
55. C173#458semidirect
61. #99D173semidirect
74. C22⋊C4C2×D173semidirect

Maximal subgroups

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

subgroupindex
#191497242
#191496632
#191496602
#191495932
#99×C1732
#458173