Finite Group Databasebeta

← #37543652

Subgroups — #37543652

Order 23168.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#26041790C211yesmaximal, characteristic
2#26041620C214yesmaximal, complemented
3#26041603C214yesmaximal, complemented
4#26041319C212yesmaximal, complemented
5#26041278C212yesmaximal, complemented
6#26041243C211yesmaximal, characteristic, complemented
7C2×#117×C181C211yesmaximal, characteristic, complemented
8C2×#15668449C2211yescharacteristic
9C2×#15668433C2212yes—
10#19153799—21no—
11#19153795C2212yes—
12#19153790C2212yes—
13#19153785—21no—
14C4×C22⋊D181—22no—
15#19153775C2211yescharacteristic
16#19153749C2214yescomplemented
17#19153747C2214yescomplemented
18#19153739C2214yescomplemented
19#19153736C2214yescomplemented
20C22⋊#13089678C2214yes—
21C23×C4×C181C2211yescharacteristic
22#117×C181—22no—
23#117×C181C2214yes—
24C2×C4⋊C4×C181C2212yes—
25C2×C22⋊C4×C181—21no—
26C2×C42×C181—21no—
27#15668449—24no—
28C2×Dic362C2311yescharacteristic
29C2×D724C2311yescharacteristic
30C2×C22⋊D181—22no—
31C2×C22⋊D181—21no—
32C2×C4×D181—21no—
33#15668433—24no—
34C2×#13089678C2314yes—
35C4⋊Dic181C2312yes—
36#15668428—22no—
37C22⋊Dic181—21no—
38C22⋊Dic181—22no—
39#15668426—22no—
40C4×Dic181—21no—
41C24×C181D411yescharacteristic
42C22×C4×C181—24no—
43C22×C4×C181—22no—
44C22×C4×C181D411yescharacteristic
45C22×C4×C181D412yes—
46C22×C4×C181C2312yes—
47C22×C4×C181C2311yescharacteristic
48C4⋊C4×C181—22no—
49C4⋊C4×C181C2314yes—
50C22⋊C4×C181—24no—
51C42×C181—24no—
52C22×D181—21no—
53Dic362—22no—
54D724—22no—
55C22⋊D181—44no—
56C22⋊D181—42no—
57C2×Dic181—22no—
58C2×Dic181—21no—
59C4×D181—42no—
60#13089678—24no—
61C23×C181—22no—
62C23×C181—42no—
63C23×C181C2×D412yes—
64C23×C181C2×D411yescharacteristic
65C2×C4×C181—22no—
66C2×C4×C181—24no—
67C2×C4×C181—24no—
68C2×C4×C181—24no—
69C2×C4×C181—44no—
70C2×C4×C181C2×D412yes—
71C2×C4×C181C2×D411yescharacteristic
72C2×C4×C181#4114yes—
73C2×C4×C181C2411yescharacteristic
74C22×C181—22no—
75C22×C181—22no—
76C22×C181—22no—
77C22×C181—22no—
78C22×C181—44no—
79C22×C181#12312yes—
80C22×C181C22×D411yescharacteristic
81C2×D181—41no—
82C2×D181—42no—
83C4×C181—22no—
84C4×C181—44no—
85C4×C181#12312yes—
86C4×C181C2×#4112yes—
87Dic181—41no—
88Dic181—42no—
89C2×C181—22no—
90C2×C181—42no—
91C2×C181C2×#12311yescharacteristic
92C2×C181#57512yes—
93D181—81no—
94C181#309311yescharacteristic, complemented, Sylow
95#3093—1811nomaximal, Sylow
96#525—1811no—
97C2×#117D18111yescharacteristic, complemented
98#485—1814no—
99#482—1814no—
100#428—1812no—
101#417—1812no—
102#407—1811no—
103C2×#41—1811no—
104C23×C4C2×D18111yescharacteristic
105C2×M16—1812no—
106#123—3621no—
107C22⋊Q8—1812no—
108#121—1812no—
109#120—3621no—
110C4×D4—3622no—
111#117—22no—
112#117—1811no—
113#117C2×D18114yes—
114C2×C4⋊C4C2×D18112yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107—1814no—
118#106—1814no—
119#103—1814no—
120#102—1814no—
121C22⋊C8—1814no—
122C24C22⋊D18111yescharacteristic
123#41—3624no—
124C2×Q8—1811no—
125C2×D4—3622no—
126C2×D4—3621no—
127C2×D4—1811no—
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—3621no—
131C22×C4C22⋊D18111yescharacteristic
132C22×C4C22⋊D18112yes—
133C22×C4C22×D18112yes—
134C22×C4C22×D18111yescharacteristic
135M16—3624no—
136C2×C8—1814no—
137C4⋊C4—22no—
138C4⋊C4—3622no—
139C4⋊C4—1812no—
140C4⋊C4C22×D18114yes—
141C22⋊C4—24no—
142C22⋊C4—3621no—
143C22⋊C4—3622no—
144C22⋊C4—3622no—
145C42—24no—
146C42—3621no—
147C23—22no—
148C23—42no—
149C23—3621no—
150C23C2×C22⋊D18112yes—
151C23C2×C22⋊D18111yescharacteristic
152Q8—3622no—
153D4—3622no—
154D4—7244no—
155D4—7242no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—44no—
161C2×C4—3622no—
162C2×C4—3621no—
163C2×C4—7242no—
164C2×C4C2×C22⋊D18112yes—
165C2×C4C2×C22⋊D18111yescharacteristic
166C2×C4#1566844914yes—
167C2×C4C23×D18111yescharacteristic
168C8—3624no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—7241no—
175C22—7242no—
176C22#1915379912yes—
177C22C22×C22⋊D18111yescharacteristic
178C4—22no—
179C4—44no—
180C4—7241no—
181C4—7242no—
182C4#1915379912yes—
183C4C2×#1566844912yes—
184C2—22no—
185C2—42no—
186C2—14481no—
187C2C2×#1915379911yescharacteristic
188C2#2604207712yes—
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#117×C181C2
socleC22×C181C22×D4
prime radical#26041790C2
hypercenterC2×#117D181
hypocenterC181#3093
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #26041620C2semidirect
3. #26041603C2semidirect
4. #26041319C2semidirect
5. #26041278C2semidirect
6. #26041243C2semidirect
7. C2×#117×C181C2semidirect
16. #19153749C22semidirect
17. #19153747C22semidirect
18. #19153739C22semidirect
19. #19153736C22semidirect
94. C181#3093semidirect
97. C2×#117D181semidirect

Maximal subgroups

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

subgroupindex
#260417902
#260416202
#260416032
#260413192
#260412782
#260412432
C2×#117×C1812
#3093181