Finite Group Databasebeta

← #37544927

Subgroups — #37544927

Order 23168.

324 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 121 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#26041836C211yesmaximal, characteristic
2#26041689C212yesmaximal, complemented
3#26041649C212yesmaximal, complemented
4#26041614C212yesmaximal
5#26041609C212yesmaximal
6#26041583C214yesmaximal, complemented
7#26041336C211yesmaximal, characteristic
8C2×#125×C181C211yesmaximal, characteristic
9#19153816C2211yescharacteristic
10#19153816C2211yescharacteristic
11#19153808—21no—
12#19153795—21no—
13#19153795C2212yes—
14C4×Dic362—21no—
15C4×Dic362C2212yes—
16#19153775—21no—
17#19153749C2214yes—
18#19153747C2214yes—
19C4⋊#13089678C2212yes—
20#19153739C2214yes—
21#19153739C2214yes—
22C22⋊#13089678C2212yes—
23#19153727C2212yes—
24#125×C181—21no—
25#125×C181—21no—
26#125×C181C2212yes—
27#125×C181C2212yes—
28C2×C4⋊C4×C181—21no—
29C2×C4⋊C4×C181—21no—
30C2×C4⋊C4×C181C2211yescharacteristic
31C2×C4⋊C4×C181C2211yescharacteristic
32C2×C42×C181C2211yescharacteristic
33C2×Dic362—21no—
34C2×Dic362C2312yes—
35C2×#13089678C2314yes—
36C4⋊Dic181—21no—
37C4⋊Dic181—21no—
38C4⋊Dic181—21no—
39C4⋊Dic181C2312yes—
40#15668428—22no—
41#15668428—22no—
42C22⋊Dic181—22no—
43C4×Dic181—22no—
44C22×C4×C181—21no—
45C22×C4×C181—21no—
46C22×C4×C181D411yescharacteristic
47C22×C4×C181D411yescharacteristic
48C22×C4×C181C2311yescharacteristic
49C4⋊C4×C181—22no—
50C4⋊C4×C181—22no—
51C4⋊C4×C181—22no—
52C4⋊C4×C181—22no—
53C4⋊C4×C181—21no—
54C4⋊C4×C181—21no—
55C4⋊C4×C181C2312yes—
56C4⋊C4×C181C2312yes—
57C42×C181D411yescharacteristic
58C42×C181D411yescharacteristic
59C42×C181C2311yescharacteristic
60C42×C181C2311yescharacteristic
61Dic362—24no—
62Dic362—42no—
63C2×Dic181—22no—
64C2×Dic181—22no—
65#13089678—24no—
66C23×C181C2×D411yescharacteristic
67C2×C4×C181—22no—
68C2×C4×C181—22no—
69C2×C4×C181—22no—
70C2×C4×C181—22no—
71C2×C4×C181—41no—
72C2×C4×C181—42no—
73C2×C4×C181—42no—
74C2×C4×C181C2×D411yescharacteristic
75C2×C4×C181C2×D411yescharacteristic
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×D411yescharacteristic
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2411yescharacteristic
80C22×C181—21no—
81C22×C181—21no—
82C22×C181#13712yes—
83C22×C181C22×D411yescharacteristic
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—21no—
87C4×C181—21no—
88C4×C181—21no—
89C4×C181—42no—
90C4×C181—42no—
91C4×C1812−1+412yes—
92Dic181—42no—
93Dic181—42no—
94C2×C181—22no—
95C2×C181#53611yescharacteristic
96C2×C181C2×#13711yescharacteristic
97C2×C181#57511yescharacteristic
98C181#323611yescharacteristic, complemented, Sylow
99#3236—1811nomaximal, Sylow
100#533—1811no—
101C2×#125D18111yescharacteristic
102#501—1812no—
103#491—1812no—
104#484—1812no—
105#483—1812no—
106#479—1814no—
107#432—1811no—
108C4⋊Q8—1811no—
109C4⋊Q8—1811no—
110#125—21no—
111#125—21no—
112#125—3621no—
113#125C2×D18112yes—
114#125C2×D18112yes—
115C22⋊Q8—3621no—
116C22⋊Q8—1812no—
117C4×Q8—3621no—
118C4×Q8—1812no—
119#117—3621no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D18111yescharacteristic
123C2×C4⋊C4C2×D18111yescharacteristic
124C2×C42C2×D18111yescharacteristic
125#107—1814no—
126#106—1814no—
127C4⋊C8—1812no—
128#103—1814no—
129#103—1814no—
130C22⋊C8—1812no—
131#97—1812no—
132C2×Q8—3621no—
133C2×Q8—1812no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4C22⋊D18111yescharacteristic
137C22×C4C22⋊D18111yescharacteristic
138C22×C4C22×D18111yescharacteristic
139C2×C8—1814no—
140C4⋊C4—22no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—22no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—3622no—
150C4⋊C4—3622no—
151C4⋊C4—1812no—
152C4⋊C4C22×D18112yes—
153C4⋊C4C22×D18112yes—
154C22⋊C4—3622no—
155C42—3622no—
156C42C22⋊D18111yescharacteristic
157C42C22⋊D18111yescharacteristic
158C42C22×D18111yescharacteristic
159C42C22×D18111yescharacteristic
160C23C2×C22⋊D18111yescharacteristic
161Q8—3624no—
162Q8—7242no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—3622no—
171C2×C4—3622no—
172C2×C4C2×C22⋊D18111yescharacteristic
173C2×C4C2×C22⋊D18111yescharacteristic
174C2×C4C2×C22⋊D18111yescharacteristic
175C2×C4C2×C22⋊D18111yescharacteristic
176C2×C4C2×C22⋊D18111yescharacteristic
177C2×C4C23×D18111yescharacteristic
178C8—3624no—
179C22—21no—
180C22—21no—
181C22#1915384612yes—
182C22C22×C22⋊D18111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—42no—
190C4—7242no—
191C4—7242no—
192C4#1915386412yes—
193C2—22no—
194C2#2604185311yescharacteristic
195C2C2×#1915384611yescharacteristic
196C2#2604207711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#125×C181C2
socleC22×C181C22×D4
prime radicalC23×C181C2×D4
hypercenterC2×#125D181
hypocenterC181#3236
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #26041689C2semidirect
3. #26041649C2semidirect
6. #26041583C2semidirect
98. C181#3236semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260416892
#260416492
#260416142
#260416092
#260415832
#260413362
C2×#125×C1812
#3236181