Finite Group Databasebeta

← #37541906

Subgroups — #37541906

Order 23168.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C181⋊#401C212yesmaximal, complemented
2#26041215C211yesmaximal, characteristic
3#26041213C212yesmaximal, complemented
4#26041211C212yesmaximal, complemented
5#26041209C212yesmaximal, complemented
6#26041207C212yesmaximal
7#26041154C212yesmaximal
8#26041151C211yesmaximal, characteristic
9#397×C181C211yesmaximal, characteristic
10C23×Dic181C2211yescharacteristic
11C2×C4⋊Dic181C2212yes—
12C2×C4⋊Dic181C2212yes—
13C2×C4⋊Dic181C2211yescharacteristic
14C2×#15668428C2212yes—
15C2×#15668428C2212yes—
16C2×#15668428C2212yes—
17C2×C22⋊Dic181C2211yescharacteristic
18C2×C22⋊Dic181C2212yes—
19#19153723C2212yes—
20#19153723C2212yes—
21#19153723C2212yes—
22#19153723C2212yes—
23#19153723C2212yes—
24#19153723C2212yes—
25#19153723C2211yescharacteristic
26C2×C4⋊C4×C181C2211yescharacteristic
27C2×C22⋊C4×C181C2212yes—
28C2×C22⋊C4×C181C2211yescharacteristic
29#95×C181C2212yes—
30#95×C181C2211yescharacteristic
31C22×Dic181—41no—
32C22×Dic181—42no—
33C22×Dic181C2312yes—
34C22×Dic181C2312yes—
35C22×Dic181C2312yes—
36C22×Dic181C2312yes—
37C4⋊Dic181—41no—
38C4⋊Dic181—42no—
39C4⋊Dic181—42no—
40#15668428—42no—
41#15668428—42no—
42#15668428—42no—
43C22⋊Dic181—22no—
44C22⋊Dic181—42no—
45C24×C181C2311yescharacteristic
46C22×C4×C181C2311yescharacteristic
47C22×C4×C181C2312yes—
48C22×C4×C181C2312yes—
49C22×C4×C181C2311yescharacteristic
50C4⋊C4×C181—41no—
51C22⋊C4×C181—24no—
52C22⋊C4×C181—41no—
53C2×Dic181—22no—
54C2×Dic181—22no—
55C2×Dic181—22no—
56C2×Dic181—22no—
57C2×Dic181—22no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—22no—
61C2×Dic181—22no—
62C2×Dic181—22no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65C2×Dic181—44no—
66C23×C181—21no—
67C23×C181—22no—
68C23×C181—22no—
69C23×C181—21no—
70C23×C181#4112yes—
71C23×C181C2411yescharacteristic
72C2×C4×C181—22no—
73C2×C4×C181—22no—
74C2×C4×C181—21no—
75C2×C4×C181—21no—
76C2×C4×C181—22no—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181—22no—
81C2×C4×C181—22no—
82C22×C181—24no—
83C22×C181—22no—
84C22×C181—41no—
85C22×C181—41no—
86C22×C181—42no—
87C22×C181C2×#4111yescharacteristic
88C22×C181H(5,𝔽2)11yescharacteristic
89C22×C181H(5,𝔽2)12yes—
90C22×C1812−1+412yes—
91C22×C1812−1+411yescharacteristic
92C4×C181—42no—
93C4×C181—42no—
94C4×C181—41no—
95C4×C181—41no—
96Dic181—42no—
97Dic181—42no—
98Dic181—42no—
99Dic181—42no—
100C2×C181—42no—
101C2×C181#53912yes—
102C2×C181#53911yescharacteristic
103C2×C181#56011yescharacteristic
104C2×C181#56311yescharacteristic
105C2×C181#56312yes—
106C181#283411yescharacteristic, complemented, Sylow
107#2834—1811nomaximal, Sylow
108#401—1812no—
109#399—1811no—
110#398—1812no—
111#398—1812no—
112#398—1812no—
113#397—1812no—
114#397D18111yescharacteristic
115#385—1811no—
116#385—1812no—
117C23×C4—1811no—
118C2×C4⋊C4—1812no—
119C2×C4⋊C4—1812no—
120C2×C4⋊C4—1812no—
121C2×C4⋊C4—1812no—
122C2×C4⋊C4—1812no—
123C2×C4⋊C4—1811no—
124C2×C4⋊C4C2×D18111yescharacteristic
125C2×C22⋊C4—1811no—
126C2×C22⋊C4—1812no—
127C2×C22⋊C4C2×D18112yes—
128C2×C22⋊C4C2×D18111yescharacteristic
129#95—1812no—
130#95—1812no—
131#95—1812no—
132#95—1812no—
133#95—1812no—
134#95—1812no—
135#95—1811no—
136#95C2×D18111yescharacteristic
137#95C2×D18112yes—
138C24C22×D18111yescharacteristic
139C22×C4—1812no—
140C22×C4—1812no—
141C22×C4—1812no—
142C22×C4—1812no—
143C22×C4—7241no—
144C22×C4—7242no—
145C22×C4C22×D18111yescharacteristic
146C22×C4C22×D18112yes—
147C22×C4C22×D18112yes—
148C22×C4C22×D18111yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—7242no—
151C4⋊C4—7242no—
152C4⋊C4—7242no—
153C4⋊C4—7241no—
154C4⋊C4—7242no—
155C4⋊C4—7242no—
156C22⋊C4—24no—
157C22⋊C4—41no—
158C22⋊C4—3622no—
159C22⋊C4—7242no—
160C23—21no—
161C23—22no—
162C23—22no—
163C23—21no—
164C23#1566844812yes—
165C23C23×D18111yescharacteristic
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—3622no—
177C2×C4—3622no—
178C2×C4—3622no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4—3622no—
182C2×C4—3622no—
183C2×C4—3622no—
184C2×C4—3622no—
185C2×C4—3622no—
186C2×C4—3622no—
187C2×C4—3622no—
188C2×C4—7244no—
189C22—24no—
190C22—22no—
191C22—41no—
192C22—41no—
193C22—42no—
194C22C2×#1566844811yescharacteristic
195C22#1915386111yescharacteristic
196C22#1915386212yes—
197C22#1915386312yes—
198C22#1915386311yescharacteristic
199C4—42no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—7242no—
204C4—7242no—
205C4—7242no—
206C4—7242no—
207C2—42no—
208C2#2604187312yes—
209C2#2604187411yescharacteristic
210C2#2604201911yescharacteristic
211C2#2604202911yescharacteristic
212C2#2604203112yes—
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#397×C181C2
prime radicalC24×C181C23
hypercenter#397D181
hypocenterC181#2834
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C181⋊#401C2semidirect
3. #26041213C2semidirect
4. #26041211C2semidirect
5. #26041209C2semidirect
106. C181#2834semidirect

Maximal subgroups

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

subgroupindex
C181⋊#4012
#260412152
#260412132
#260412112
#260412092
#260412072
#260411542
#260411512
#397×C1812
#2834181