Finite Group Databasebeta

← #16835239

Subgroups — #16835239

Order 3712.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#11745227C212yesmaximal
2C4×C22⋊#1181C212yesmaximal, complemented
3#14272041C212yesmaximal, complemented
4C2×#11745243C211yesmaximal, characteristic
5C22×C22⋊D29C2211yescharacteristic
6C23×Dic29C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181C2214yes—
9C2×C4×#1181—22no—
10C2×C22⋊C4×C29C411yescharacteristic, complemented
11C2×#90781C2211yescharacteristic
12C2×#90779C411yescharacteristic, complemented
13C2×C4×Dic29C411yescharacteristic, complemented
14#11745243—22no—
15#11745243—22no—
16#11745227C418yescomplemented
17(C2×#1181)⋊C4—22no—
18C24×C29C2×C411yescharacteristic
19C23×D29C2311yescharacteristic
20C22×#1181—24no—
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2×C411yescharacteristic
23C2×C22⋊D29—22no—
24C2×C22⋊D29—22no—
25C2×C22⋊D29C2×C414yes—
26C22×Dic29—21no—
27C22×Dic29—21no—
28C22×Dic29—42no—
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29C2×C411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C2×C4×D29—42no—
33C2×C4×D29D412yes—
34C2×C4×D29D412yes—
35C22⋊#1181—24no—
36C22⋊#1181C2×C418yescomplemented
37C4×#1181—44no—
38C22⋊C4×C29—22no—
39#90781—22no—
40#90779—22no—
41C4×Dic29—21no—
42C4×Dic29—21no—
43C23×C29—21no—
44C23×C29—21no—
45C23×C29—41no—
46C23×C29—41no—
47C23×C29C4212yescomplemented
48C23×C29C22×C411yescharacteristic
49C22×D29—41no—
50C22×D29—41no—
51C22×D29C22×C412yes—
52C22×D29C2×D412yes—
53C22×D29#4112yes—
54C2×#1181—28no—
55C2×#1181—44no—
56C2×#1181—44no—
57C2×C4×C29—21no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C22⋊C412yes—
61C22⋊D29—28no—
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—22no—
65C2×Dic29—21no—
66C2×Dic29—42no—
67C2×Dic29—42no—
68C2×Dic29—41no—
69C2×Dic29C4212yescomplemented
70C2×Dic29C22⋊C411yescharacteristic
71C2×Dic29C22⋊C411yescharacteristic
72C4×D29—24no—
73C4×D29—42no—
74C4×#99—291nomaximal, Sylow
75C22×C29—21no—
76C22×C29—21no—
77C22×C29—22no—
78C22×C29—42no—
79C22×C29—42no—
80C22×C29—41no—
81C22×C29—41no—
82C22×C29C2×C4211yescharacteristic
83C22×C29C2×C22⋊C411yescharacteristic
84C22×C29#11711yescharacteristic
85C2×D29—22no—
86C2×D29—22no—
87C2×D29—42no—
88C2×D29—42no—
89C2×D29C4×D414yes—
90#1181—48no—
91C4×C29—22no—
92C4×C29—41no—
93Dic29—22no—
94Dic29—21no—
95Dic29—41no—
96Dic29#9912yescomplemented
97C2×C4×D4—291no—
98C2×#99—292no—
99C4×C22⋊C4—292no—
100#342—292no—
101C2×C29—21no—
102C2×C29—21no—
103C2×C29—42no—
104C2×C29C4×C22⋊C411yescharacteristic
105C2×C29C2×#9911yescharacteristic
106C2×C29#41011yescharacteristic
107D29—24no—
108C22×D4—291no—
109C23×C4—291no—
110C23×C4—291no—
111C4×D4—582no—
112C4×D4—582no—
113C2×C4⋊C4—291no—
114C2×C22⋊C4—294no—
115C2×C22⋊C4—291no—
116C2×C22⋊C4#118111yescharacteristic, complemented
117C2×C42—291no—
118C2×C42—582no—
119#99—298no—
120#95—582no—
121C29C4×#9911yescharacteristic, complemented, Sylow
122C24—291no—
123C24C2×#118111yescharacteristic
124C2×D4—294no—
125C2×D4—582no—
126C2×D4—582no—
127C22×C4—291no—
128C22×C4—291no—
129C22×C4—292no—
130C22×C4—292no—
131C22×C4—291no—
132C22×C4—581no—
133C22×C4—581no—
134C22×C4—584no—
135C22×C4—1162no—
136C22×C4—1162no—
137C22×C4C2×#118111yescharacteristic
138C22×C4C2×#118111yescharacteristic
139C4⋊C4—582no—
140C22⋊C4—22no—
141C22⋊C4—298no—
142C22⋊C4—582no—
143C22⋊C4—584no—
144C42—581no—
145C42—581no—
146C42—1164no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—292no—
152C23—292no—
153C23—292no—
154C23—1161no—
155C23—1161no—
156C23C4×#118112yescomplemented
157C23C22×#118111yescharacteristic
158D4—588no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—291no—
163C2×C4—292no—
164C2×C4—291no—
165C2×C4—584no—
166C2×C4—582no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—588no—
170C2×C4—581no—
171C2×C4—1162no—
172C2×C4—1162no—
173C2×C4—1162no—
174C2×C4—1164no—
175C2×C4—1164no—
176C2×C4—1161no—
177C2×C4C22⋊#118112yes—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—294no—
186C22—582no—
187C22—582no—
188C22—1162no—
189C22—1162no—
190C22C2×C4×#118111yescharacteristic
191C22#1174534511yescharacteristic
192C22C2×C22⋊#118111yescharacteristic
193C4—22no—
194C4—41no—
195C4—292no—
196C4—582no—
197C4—581no—
198C4—1168no—
199C4—1161no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2—584no—
204C2C4×C22⋊#118111yescharacteristic
205C2D29⋊#9911yescharacteristic
206C2#1427214311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC22×C29C2×C42
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC22×C22⋊D29C22
cosocleC23×D29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29C4×#99
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#1181C2semidirect
3. #14272041C2semidirect
6. C23×Dic29C4semidirect
10. C2×C22⋊C4×C29C4semidirect
12. C2×#90779C4semidirect
13. C2×C4×Dic29C4semidirect
16. #11745227C4semidirect
36. C22⋊#1181C2×C4semidirect
47. C23×C29C42semidirect
69. C2×Dic29C42semidirect
96. Dic29#99semidirect
116. C2×C22⋊C4#1181semidirect
121. C29C4×#99semidirect
156. C23C4×#1181semidirect

Maximal subgroups

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

subgroupindex
C2×#117452272
C4×C22⋊#11812
#142720412
C2×#117452432
C4×#9929