Finite Group Databasebeta

← #16835392

Subgroups — #16835392

Order 3712.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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#14272135C212yesmaximal
2#14272043C214yesmaximal, complemented
3C2×C4⋊C4×D29C211yesmaximal, characteristic
4C22×C4×D29C412yes—
5C22×C4×D29C2211yescharacteristic
6C2×#90800C2214yes—
7C2×C4⋊C4×C29C411yescharacteristic
8C2×C4⋊Dic29C411yescharacteristic
9C2×#90779C2212yes—
10C4⋊C4×D29—22no—
11C4⋊C4×D29—22no—
12#11745219—22no—
13#11745219—22no—
14C23×D29C2×C411yescharacteristic
15C22×C4×C29C2×C412yes—
16C22×C4×C29C2×C411yescharacteristic
17C22×Dic29C2×C412yes—
18C22×Dic29C2311yescharacteristic
19C2×C4×D29—24no—
20C2×C4×D29—22no—
21C2×C4×D29—22no—
22C2×C4×D29—44no—
23C2×C4×D29D412yes—
24C2×C4×D29D412yes—
25#90800—28no—
26C2×#6599—24no—
27C4⋊C4×C29—22no—
28C4⋊Dic29—22no—
29#90779—24no—
30C23×C29C22×C411yescharacteristic
31C22×D29—22no—
32C22×D29—22no—
33C22×D29—22no—
34C22×D29C22⋊C411yescharacteristic
35C22×D29C22⋊C411yescharacteristic
36C2×C4×C29—22no—
37C2×C4×C29—22no—
38C2×C4×C29—42no—
39C2×C4×C29C22⋊C412yes—
40C2×Dic29—22no—
41C2×Dic29—42no—
42C2×Dic29C2×D412yes—
43C2×Dic29#4114yes—
44C4×D29—24no—
45C4×D29—24no—
46C4×D29—44no—
47C4×D29—44no—
48#6599—44no—
49#1821—291nomaximal, Sylow
50C22×C29—21no—
51C22×C29—21no—
52C22×C29C2×C22⋊C411yescharacteristic
53C22×C29#11712yes—
54C2×D29—28no—
55C2×D29—21no—
56C2×D29—21no—
57C2×D29—21no—
58C2×D29—21no—
59C2×D29#10012yes—
60C2×D29#10112yes—
61C4×C29—22no—
62C4×C29—42no—
63Dic29—42no—
64Dic29#12314yes—
65C22×C4⋊C4—291no—
66#407—292no—
67#343—294no—
68C2×C29—22no—
69C2×C29#38111yescharacteristic
70C2×C29C2×#10011yescharacteristic
71C2×C29C2×#10111yescharacteristic
72D29—22no—
73D29—22no—
74C23×C4—291no—
75C23×C4—292no—
76C2×M16—294no—
77C2×C4⋊C4—292no—
78C2×C4⋊C4—291no—
79C2×C4⋊C4—582no—
80C2×C4⋊C4—582no—
81C2×C4⋊C4#118111yescharacteristic
82C22⋊C8—582no—
83C22⋊C8—582no—
84C29#182111yescharacteristic, complemented, Sylow
85C24—291no—
86C22×C4—291no—
87C22×C4—292no—
88C22×C4—292no—
89C22×C4—292no—
90C22×C4—584no—
91C22×C4—582no—
92C22×C4—582no—
93C22×C4—1164no—
94C22×C4C2×#118112yes—
95C22×C4C2×#118111yescharacteristic
96M16—588no—
97C2×C8—584no—
98C4⋊C4—22no—
99C4⋊C4—584no—
100C4⋊C4—582no—
101C23—291no—
102C23—291no—
103C23—582no—
104C23—582no—
105C23—582no—
106C23C22×#118111yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—294no—
111C2×C4—292no—
112C2×C4—584no—
113C2×C4—584no—
114C2×C4—582no—
115C2×C4—1164no—
116C2×C4—1164no—
117C2×C4—1162no—
118C2×C4C22⋊#118112yes—
119C8—1164no—
120C22—21no—
121C22—21no—
122C22—292no—
123C22—292no—
124C22—588no—
125C22—581no—
126C22—581no—
127C22—581no—
128C22—581no—
129C22#1174534512yes—
130C22C2×C22⋊#118111yescharacteristic
131C4—22no—
132C4—42no—
133C4—294no—
134C4—1162no—
135C2—22no—
136C2—582no—
137C2—582no—
138C2#1427210611yescharacteristic
139C2D29⋊#10011yescharacteristic
140C2D29⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC23×D29C2×C4
cosocleC22×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1821
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14272043C2semidirect
84. C29#1821semidirect

Maximal subgroups

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

subgroupindex
#142721352
#142720432
C2×C4⋊C4×D292
#182129