Finite Group Databasebeta

← C2×#483×C181 #37531029

Subgroups — C2×#483×C181 #37531029

Order 23168.

460 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 216 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×C22⋊Q8×C181C211yesmaximal, characteristic
2C22×C4⋊C4×C181C211yesmaximal, characteristic
3#483×C181C218yesmaximal, direct product factor
4C2×#106×C181C212yesmaximal, complemented
5C2×#103×C181C212yesmaximal, complemented
6C2×C22⋊C8×C181C211yesmaximal, characteristic
7C22×Q8×C181C2211yescharacteristic
8C23×C4×C181—21no—
9C23×C4×C181C2211yescharacteristic
10C22×C8×C181C2212yes—
11C22⋊Q8×C181—22no—
12C22⋊Q8×C181C2214yes—
13C2×C4⋊C4×C181—22no—
14C2×C4⋊C4×C181—21no—
15C2×C4⋊C4×C181—21no—
16C2×C4⋊C4×C181C2211yescharacteristic
17C2×C4⋊C4×C181C2212yes—
18C2×C4⋊C4×C181C2214yes—
19C2×C22⋊C4×C181—21no—
20#106×C181C2218yescomplemented
21#103×C181C2218yescomplemented
22C22⋊C8×C181C2214yes—
23C24×C181D411yescharacteristic
24C2×Q8×C181—21no—
25C2×Q8×C181—24no—
26C2×Q8×C181C2312yes—
27C22×C4×C181—24no—
28C22×C4×C181—24no—
29C22×C4×C181—21no—
30C22×C4×C181—21no—
31C22×C4×C181—22no—
32C22×C4×C181—44no—
33C22×C4×C181D412yes—
34C22×C4×C181D411yescharacteristic
35C22×C4×C181C2312yes—
36C22×C4×C181C2311yescharacteristic
37C2×C8×C181—24no—
38C2×C8×C181C2314yes—
39C4⋊C4×C181—24no—
40C4⋊C4×C181—22no—
41C4⋊C4×C181—24no—
42C4⋊C4×C181—21no—
43C4⋊C4×C181C2314yes—
44C4⋊C4×C181C2312yes—
45C22⋊C4×C181—24no—
46C23×C181—22no—
47C23×C181—22no—
48C23×C181SD1614yes—
49C23×C181C2×D412yes—
50C23×C181C2×D411yescharacteristic
51Q8×C181—24no—
52Q8×C181—42no—
53C2×C4×C181—22no—
54C2×C4×C181—24no—
55C2×C4×C181—24no—
56C2×C4×C181—22no—
57C2×C4×C181—22no—
58C2×C4×C181—24no—
59C2×C4×C181—42no—
60C2×C4×C181—48no—
61C2×C4×C181—44no—
62C2×C4×C181—42no—
63C2×C4×C181C2×D412yes—
64C2×C4×C181C2×D411yescharacteristic
65C2×C4×C181#4114yes—
66C2×C4×C181C2411yescharacteristic
67C8×C181—24no—
68C22×C181—22no—
69C22×C181—22no—
70C22×C181—28no—
71C22×C181#12312yes—
72C22×C181C2×SD1614yes—
73C22×C181C2×SD1612yes—
74C22×C181#13712yes—
75C22×C181C22×D411yescharacteristic
76C4×C181—22no—
77C4×C181—42no—
78C4×C181—44no—
79C4×C181—42no—
80C4×C181#12312yes—
81C4×C181C2×#4112yes—
82C2×C181—24no—
83C2×C181#48314yesdirect product factor
84C2×C181C2×#12311yescharacteristic
85C2×C181C22×SD1611yescharacteristic
86C2×C181C2×#13711yescharacteristic
87C181C2×#48311yescharacteristic, direct product factor, Sylow
88C2×#483C18111yesmaximal, characteristic, direct product factor, Sylow
89C2×C22⋊Q8C2×C18111yescharacteristic
90C22×C4⋊C4C2×C18111yescharacteristic
91#483C2×C18118yesdirect product factor
92C2×#106C2×C18112yescomplemented
93C2×#103C2×C18112yescomplemented
94C2×C22⋊C8C2×C18111yescharacteristic
95C22×Q8C22×C18111yescharacteristic
96C23×C4—21no—
97C23×C4C22×C18111yescharacteristic
98C22×C8C22×C18112yes—
99C22⋊Q8—22no—
100C22⋊Q8C22×C18114yes—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4C22×C18112yes—
105C2×C4⋊C4C22×C18114yes—
106C2×C4⋊C4C22×C18111yescharacteristic
107C2×C22⋊C4—21no—
108#106C22×C18118yescomplemented
109#103C22×C18118yescomplemented
110C22⋊C8C22×C18114yes—
111C24D4×C18111yescharacteristic
112C2×Q8—21no—
113C2×Q8—24no—
114C2×Q8C23×C18112yes—
115C22×C4—24no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—24no—
119C22×C4—22no—
120C22×C4—44no—
121C22×C4D4×C18111yescharacteristic
122C22×C4D4×C18112yes—
123C22×C4C23×C18112yes—
124C22×C4C23×C18111yescharacteristic
125C2×C8—24no—
126C2×C8C23×C18114yes—
127C4⋊C4—24no—
128C4⋊C4—22no—
129C4⋊C4—24no—
130C4⋊C4—21no—
131C4⋊C4C23×C18114yes—
132C4⋊C4C23×C18112yes—
133C22⋊C4—24no—
134C23—22no—
135C23—22no—
136C23SD16×C18114yes—
137C23C2×D4×C18112yes—
138C23C2×D4×C18111yescharacteristic
139Q8—24no—
140Q8—42no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—24no—
147C2×C4—42no—
148C2×C4—48no—
149C2×C4—44no—
150C2×C4—42no—
151C2×C4C2×D4×C18112yes—
152C2×C4C2×D4×C18111yescharacteristic
153C2×C4#41×C18114yes—
154C2×C4C24×C18111yescharacteristic
155C8—24no—
156C22—28no—
157C22—22no—
158C22—22no—
159C22#123×C18112yes—
160C22C2×SD16×C18114yes—
161C22C2×SD16×C18112yes—
162C22#137×C18112yes—
163C22C22×D4×C18111yescharacteristic
164C4—22no—
165C4—42no—
166C4—44no—
167C4—42no—
168C4#123×C18112yes—
169C4C2×#41×C18112yes—
170C2—24no—
171C2#483×C18114yesdirect product factor
172C2C2×#123×C18111yescharacteristic
173C2C22×SD16×C18111yescharacteristic
174C2C2×#137×C18111yescharacteristic
subgroupG/H
center, socleC23×C181C2×D4
commutator, Frattini, cosocleC2×C4C24×C181
prime radicalC24×C181D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C181 ◁ C23×C4×C181 ◁ G

Complements

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

NH ≅ G/Ntype
3. #483×C181C2direct (N × H)
4. C2×#106×C181C2semidirect
5. C2×#103×C181C2semidirect
20. #106×C181C22semidirect
21. #103×C181C22semidirect
83. C2×C181#483direct (N × H)
87. C181C2×#483direct (N × H)
88. C2×#483C181direct (N × H)
91. #483C2×C181direct (N × H)
92. C2×#106C2×C181semidirect
93. C2×#103C2×C181semidirect
108. #106C22×C181semidirect
109. #103C22×C181semidirect
171. C2#483×C181direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1812
C22×C4⋊C4×C1812
#483×C1812
C2×#106×C1812
C2×#103×C1812
C2×C22⋊C8×C1812
C2×#483181