Finite Group Databasebeta

← #16834833

Subgroups — #16834833

Order 3712.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#14272184C211yesmaximal, characteristic, complemented
2C4×#90800C211yesmaximal, characteristic, complemented
3#14272011C214yesmaximal, complemented
4C2×#11745255C211yesmaximal, characteristic
5C22×D116C411yescharacteristic
6C22×C4×D29—21no—
7C2×#90800—21no—
8C2×C4⋊C4×C29C411yescharacteristic
9C2×#90781—21no—
10C2×C4×Dic29C2211yescharacteristic
11#11745255—21no—
12#11745255—21no—
13#11745255C412yes—
14#11745255C2212yes—
15C22⋊#6599—21no—
16#11745218—21no—
17#11745218—21no—
18C4⋊#6599C2212yescomplemented
19C4×#6599C2212yescomplemented
20C23×D29—21no—
21C22×C4×C29—21no—
22C22×C4×C29C2×C411yescharacteristic
23C22×Dic29D411yescharacteristic
24C22×Dic29D411yescharacteristic
25C2×D116—21no—
26C2×D116—24no—
27C2×D116C2×C412yes—
28C2×C4×D29—22no—
29C2×C4×D29—22no—
30C2×C4×D29—44no—
31#90800—24no—
32C2×#6599—22no—
33C2×#6599—22no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29C2×C412yes—
36#90781—22no—
37#90781—22no—
38C4×Dic29C2×C411yescharacteristic
39C4×Dic29D411yescharacteristic
40C4×Dic29D411yescharacteristic
41C4×Dic29C2311yescharacteristic
42C23×C29C22⋊C411yescharacteristic
43C22×D29—24no—
44C22×D29—22no—
45C22×D29—42no—
46C22×D29—42no—
47C2×C4×C29—22no—
48C2×C4×C29—22no—
49C2×C4×C29—42no—
50C2×C4×C29C22⋊C411yescharacteristic
51C2×C4×C29C22×C411yescharacteristic
52C2×Dic29—22no—
53C2×Dic29—22no—
54C2×Dic29C22⋊C411yescharacteristic
55C2×Dic29C22⋊C411yescharacteristic
56C2×Dic29C2×D411yescharacteristic
57C2×Dic29C2×D411yescharacteristic
58D116—24no—
59D116—22no—
60D116M1614yescomplemented
61C4×D29—44no—
62C4×D29—44no—
63#6599—24no—
64#6599—42no—
65#1490—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—21no—
68C22×C29#10412yes—
69C22×C29C2×C22⋊C411yescharacteristic
70C2×D29—24no—
71C2×D29—48no—
72C2×D29—42no—
73C2×D29—42no—
74C4×C29—21no—
75C4×C29—42no—
76C4×C29C2×M1612yes—
77Dic29—21no—
78Dic29—21no—
79Dic29—21no—
80Dic29AGL(1,ℤ/8)12yes—
81C2×C4×D4—291no—
82#432—291no—
83C4×M16—291no—
84D4⋊C8—294no—
85C2×C29—22no—
86C2×C29#40711yescharacteristic
87C2×C29#41811yescharacteristic
88C2×C29C2×#10411yescharacteristic
89D29—44no—
90C22×D4—291no—
91C23×C4—581no—
92C2×M16—581no—
93C4×D4—292no—
94C4×D4—292no—
95C4×D4—581no—
96C4×D4—581no—
97C2×C4⋊C4#118111yescharacteristic
98C2×C22⋊C4—581no—
99C2×C42—291no—
100C4⋊C8—292no—
101C22⋊C8—581no—
102#97—581no—
103#97—581no—
104C4×C8—292no—
105C29#149011yescharacteristic, complemented, Sylow
106C24—581no—
107C2×D4—292no—
108C2×D4—584no—
109C2×D4—581no—
110C22×C4—21no—
111C22×C4—291no—
112C22×C4—291no—
113C22×C4—582no—
114C22×C4—582no—
115C22×C4—1164no—
116C22×C4C2×#118111yescharacteristic
117M16—584no—
118C2×C8—582no—
119C2×C8—582no—
120C4⋊C4—21no—
121C4⋊C4C2×#118112yes—
122C22⋊C4—582no—
123C22⋊C4—582no—
124C42—291no—
125C42—291no—
126C42—291no—
127C42—291no—
128C23—584no—
129C23—582no—
130C23—1162no—
131C23—1162no—
132C23C22⋊#118111yescharacteristic
133D4—294no—
134D4—584no—
135D4—582no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—291no—
140C2×C4—291no—
141C2×C4—291no—
142C2×C4—291no—
143C2×C4—582no—
144C2×C4—582no—
145C2×C4—1164no—
146C2×C4—1164no—
147C2×C4C22⋊#118111yescharacteristic
148C2×C4C22×#118111yescharacteristic
149C8—584no—
150C8—1162no—
151C22—21no—
152C22—21no—
153C22—584no—
154C22—1168no—
155C22—1162no—
156C22—1162no—
157C22#1174522612yes—
158C22C2×C22⋊#118111yescharacteristic
159C4—21no—
160C4—42no—
161C4—292no—
162C4—581no—
163C4—581no—
164C4—581no—
165C4D29⋊M1612yes—
166C2—22no—
167C2—1164no—
168C2#1427213511yescharacteristic
169C2#1427215511yescharacteristic
170C2C2×#1174522611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D116C4
cosocleC4×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1490
LCSG ▷ C2×C4×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
1. #14272184C2semidirect
2. C4×#90800C2semidirect
3. #14272011C2semidirect
18. C4⋊#6599C22semidirect
19. C4×#6599C22semidirect
60. D116M16semidirect
105. C29#1490semidirect

Maximal subgroups

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

subgroupindex
#142721842
C4×#908002
#142720112
C2×#117452552
#149029