Finite Group Databasebeta

← #14271354

Subgroups — #14271354

Order 1856.

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#11745359C211yesmaximal, characteristic
2#11745297C211yesmaximal, characteristic, complemented
3#11745248C212yesmaximal, complemented
4C29×#99C211yesmaximal, characteristic, complemented
5#11745154C212yesmaximal, complemented
6C2×D4×C29C2211yescharacteristic
7C2×C22⋊D29—21no—
8C2×C22⋊D29C2212yes—
9C22×Dic29C2211yescharacteristic, complemented
10#90807—22no—
11D4×D29—22no—
12#90805—21no—
13C22⋊C4×C29C2212yescomplemented
14C22⋊Dic29—21no—
15C22⋊Dic29C2211yescharacteristic, complemented
16#90781—22no—
17C4⋊Dic29—22no—
18#90779—21no—
19C23×C29D411yescharacteristic
20C23×C29C2311yescharacteristic
21C22×D29—21no—
22C22×D29D412yes—
23D4×C29—22no—
24C2×C4×C29—22no—
25C2×C4×C29D411yescharacteristic
26C22⋊D29—22no—
27C22⋊D29—22no—
28C22⋊D29—22no—
29C2×Dic29—21no—
30C2×Dic29—21no—
31C2×Dic29—21no—
32C2×Dic29—22no—
33C2×Dic29D412yes—
34D116—21no—
35C4×D29—22no—
36Dic58—21no—
37C22×C29—21no—
38C22×C29—41no—
39C22×C29—41no—
40C22×C29C2×D411yescharacteristic
41C22×C29C2×D412yes—
42C2×D29—22no—
43C2×D29—42no—
44C2×D29—81no—
45C4×C29—21no—
46C4×C29—42no—
47Dic29—22no—
48Dic29—41no—
49Dic29—41no—
50#458—291nomaximal, Sylow
51C2×C29—21no—
52C2×C29—22no—
53C2×C29—41no—
54C2×C29#12011yescharacteristic
55D29—42no—
56H(5,𝔽2)—291no—
57#123—291no—
58#123—292no—
59#99—292no—
60#99D2911yescharacteristic, complemented
61C29#45811yescharacteristic, complemented, Sylow
62#41—582no—
63#41—581no—
64C2×D4—292no—
65C2×D4—582no—
66C2×D4—581no—
67C2×D4C2×D2911yescharacteristic
68C22×C4—291no—
69C4⋊C4—582no—
70C4⋊C4—581no—
71C22⋊C4—291no—
72C22⋊C4—582no—
73C22⋊C4—581no—
74C22⋊C4C2×D2912yescomplemented
75C23—292no—
76C23—581no—
77C23D11611yescharacteristic
78C23C22×D2911yescharacteristic
79Q8—581no—
80D4—22no—
81D4—581no—
82D4—582no—
83D4—582no—
84D4—582no—
85C2×C4—22no—
86C2×C4—292no—
87C2×C4—582no—
88C2×C4—581no—
89C2×C4—581no—
90C2×C4—581no—
91C2×C4—582no—
92C2×C4D11611yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—582no—
97C22—1162no—
98C22—2321no—
99C22C2×D11611yescharacteristic
100C22D4×D2912yes—
101C4—21no—
102C4—42no—
103C4—582no—
104C4—1161no—
105C4—1161no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—1162no—
110C2#1174524411yescharacteristic
subgroupG/H
centerC2#11745244
commutator, cosocleC23×C29C23
FrattiniC23C22×D29
FittingC29×#99C2
socleC2×C29#120
prime radical#11745359C2
hypercenter#99D29
hypocenterC29#458
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #11745297C2semidirect
3. #11745248C2semidirect
4. C29×#99C2semidirect
5. #11745154C2semidirect
9. C22×Dic29C22semidirect
13. C22⋊C4×C29C22semidirect
15. C22⋊Dic29C22semidirect
60. #99D29semidirect
61. C29#458semidirect
74. C22⋊C4C2×D29semidirect

Maximal subgroups

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

subgroupindex
#117453592
#117452972
#117452482
C29×#992
#117451542
#45829