Finite Group Databasebeta

← #16834770

Subgroups — #16834770

Order 3712.

270 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 64 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#14272134C211yesmaximal, characteristic
2D29⋊(C22⋊C8)C211yesmaximal, characteristic
3#14272008C214yesmaximal, complemented
4C2×#11745259C211yesmaximal, characteristic
5C22×C4×D29C2211yescharacteristic
6C22×Dic58C411yescharacteristic
7C2×#90796—21no—
8C2×D29⋊C8—21no—
9C2×C4⋊C4×C29C411yescharacteristic
10C2×#90781C412yes—
11C2×C4⋊Dic29C2212yes—
12#11745259—21no—
13#11745259—21no—
14#11745259—21no—
15#11745259—21no—
16C22⋊#6599C2212yes—
17C22⋊#6599C2212yes—
18#11745219—21no—
19#11745219—21no—
20C23×D29C2×C411yescharacteristic
21C22×C4×C29C2×C412yes—
22C22×C4×C29C2×C411yescharacteristic
23C22×Dic29C2×C412yes—
24C22×Dic29C2311yescharacteristic
25C2×C4×D29—42no—
26C2×C4×D29D411yescharacteristic
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×C4×D29D411yescharacteristic
30C2×Dic58—21no—
31C2×Dic58—21no—
32C2×Dic58—42no—
33C2×#6599—22no—
34C2×#6599—22no—
35#90796—42no—
36D29⋊C8—42no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29—21no—
39#90781—22no—
40#90781—22no—
41C4⋊Dic29—22no—
42C4⋊Dic29—22no—
43C23×C29C22×C411yescharacteristic
44C22×D29—22no—
45C22×D29—22no—
46C22×D29—41no—
47C22×D29C22⋊C411yescharacteristic
48C22×D29C22⋊C411yescharacteristic
49C2×C4×C29—22no—
50C2×C4×C29—22no—
51C2×C4×C29—24no—
52C2×C4×C29C22⋊C411yescharacteristic
53C2×C4×C29C22⋊C411yescharacteristic
54C2×Dic29—22no—
55C2×Dic29—41no—
56C2×Dic29—42no—
57C2×Dic29C2×D411yescharacteristic
58C2×Dic29C2×D411yescharacteristic
59C4×D29—22no—
60C4×D29—22no—
61C4×D29—41no—
62C4×D29—41no—
63Dic58—42no—
64Dic58—42no—
65#6599—42no—
66#6599—42no—
67#1472—291nomaximal, Sylow
68C22×C29—21no—
69C22×C29—21no—
70C22×C29C2×C22⋊C411yescharacteristic
71C22×C29#13112yes—
72C2×D29—21no—
73C2×D29—21no—
74C2×D29—21no—
75C2×D29—21no—
76C2×D29—21no—
77C2×D29—44no—
78C2×D29#10112yes—
79C4×C29—21no—
80C4×C29—42no—
81C4×C29#9912yes—
82Dic29—21no—
83Dic29—21no—
84Dic29—42no—
85C2×C22⋊Q8—291no—
86#407—291no—
87C2×C22⋊C8—291no—
88#324—294no—
89C2×C29—22no—
90C2×C29#40811yescharacteristic
91C2×C29C2×#9911yescharacteristic
92C2×C29C2×#10111yescharacteristic
93D29—22no—
94D29—41no—
95C22×Q8—291no—
96C23×C4—291no—
97C2×M16—581no—
98C22×C8—581no—
99C22⋊Q8—581no—
100C22⋊Q8—581no—
101C22⋊Q8—581no—
102C22⋊Q8—581no—
103C2×C4⋊C4—292no—
104C2×C4⋊C4#118111yescharacteristic
105C2×C22⋊C4—292no—
106C22⋊C8—292no—
107C22⋊C8—292no—
108C22⋊C8—581no—
109C22⋊C8—581no—
110C29#147211yescharacteristic, complemented, Sylow
111C24—291no—
112C2×Q8—581no—
113C2×Q8—581no—
114C2×Q8—1162no—
115C22×C4—291no—
116C22×C4—291no—
117C22×C4—291no—
118C22×C4—291no—
119C22×C4—291no—
120C22×C4—292no—
121C22×C4—1162no—
122C22×C4C2×#118112yes—
123C22×C4C2×#118111yescharacteristic
124M16—1162no—
125C2×C8—582no—
126C2×C8—582no—
127C2×C8—1162no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—582no—
131C4⋊C4—582no—
132C22⋊C4—582no—
133C22⋊C4—582no—
134C23—291no—
135C23—291no—
136C23—582no—
137C23—582no—
138C23—1161no—
139C23C22×#118111yescharacteristic
140Q8—1162no—
141Q8—1162no—
142C2×C4—22no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—291no—
146C2×C4—291no—
147C2×C4—582no—
148C2×C4—582no—
149C2×C4—582no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4—1162no—
154C2×C4C22⋊#118111yescharacteristic
155C2×C4C22⋊#118111yescharacteristic
156C8—1162no—
157C8—1162no—
158C22—21no—
159C22—21no—
160C22—292no—
161C22—581no—
162C22—581no—
163C22—581no—
164C22—581no—
165C22—581no—
166C22—1164no—
167C22#1174534612yes—
168C22C2×C22⋊#118111yescharacteristic
169C4—21no—
170C4—42no—
171C4—581no—
172C4—581no—
173C4—1162no—
174C4#1174521512yes—
175C2—22no—
176C2—582no—
177C2—1161no—
178C2#1427213711yescharacteristic
179C2C2×#1174521511yescharacteristic
180C2D29⋊#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#1472
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
3. #14272008C2semidirect
110. C29#1472semidirect

Maximal subgroups

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

subgroupindex
#142721342
D29⋊(C22⋊C8)2
#142720082
C2×#117452592
#147229