Finite Group Databasebeta

← #37532244

Subgroups — #37532244

Order 23168.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#26041813C211yesmaximal, characteristic
2#26041336C211yesmaximal, characteristic, complemented
3#26041015C212yesmaximal, complemented
4#26041012C212yesmaximal
5C4×C4⋊C4×C181C211yesmaximal, characteristic, complemented
6#19153810—21no—
7#19153808C411yescharacteristic, complemented
8#19153804C411yescharacteristic, complemented
9#19153799—21no—
10#19153795C2211yescharacteristic
11#19153790C2211yescharacteristic
12C4×Dic362C411yescharacteristic, complemented
13C4×D724C411yescharacteristic, complemented
14C4×C22⋊D181—21no—
15#19153773—21no—
16C4⋊#13089678—21no—
17C22⋊#13089678C2212yes—
18#19153727—21no—
19C2×C4⋊C4×C181—21no—
20C2×C42×C181—21no—
21C2×C42×C181C2211yescharacteristic
22#95×C181C2212yes—
23C2×Dic362C2×C411yescharacteristic
24C2×D724C2×C411yescharacteristic
25C2×C22⋊D181—21no—
26C2×C4×D181—21no—
27C2×#13089678—22no—
28C4⋊Dic181C2×C411yescharacteristic
29C4⋊Dic181C2×C411yescharacteristic
30#15668428—21no—
31#15668428—21no—
32#15668428—21no—
33#15668428—21no—
34C22⋊Dic181—21no—
35#15668426—21no—
36#15668426—21no—
37#15668426—21no—
38#15668426—21no—
39C4×Dic181—21no—
40C22×C4×C181—22no—
41C22×C4×C181D411yescharacteristic
42C22×C4×C181D411yescharacteristic
43C22×C4×C181C2311yescharacteristic
44C4⋊C4×C181—24no—
45C42×C181—42no—
46C42×C181C2×C411yescharacteristic
47C42×C181C2×C411yescharacteristic
48C42×C181D411yescharacteristic
49C42×C181D411yescharacteristic
50C22×D181—21no—
51Dic362—41no—
52D724—41no—
53C22⋊D181—41no—
54C22⋊D181—41no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C4×D181—42no—
59#13089678—42no—
60C23×C181C2×D411yescharacteristic
61C2×C4×C181—21no—
62C2×C4×C181—21no—
63C2×C4×C181—22no—
64C2×C4×C181—24no—
65C2×C4×C181—41no—
66C2×C4×C181—42no—
67C2×C4×C181—42no—
68C2×C4×C181C22⋊C411yescharacteristic
69C2×C4×C181C22⋊C411yescharacteristic
70C2×C4×C181C22⋊C411yescharacteristic
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22×C411yescharacteristic
73C2×C4×C181C2×D411yescharacteristic
74C22×C181—21no—
75C22×C181—21no—
76C22×C181C2×C22⋊C411yescharacteristic
77C22×C181AGL(1,ℤ/8)11yescharacteristic
78C22×C181#13711yescharacteristic
79C2×D181—41no—
80C2×D181—41no—
81C2×D181—41no—
82C4×C181—21no—
83C4×C181—21no—
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—21no—
87C4×C181—44no—
88C4×C181#10412yes—
89Dic181—41no—
90Dic181—41no—
91Dic181—41no—
92C2×C181—21no—
93C2×C181—21no—
94C2×C181#41011yescharacteristic
95C2×C181#41711yescharacteristic
96C2×C181C2×#10411yescharacteristic
97D181—81no—
98C181#150911yescharacteristic, complemented, Sylow
99#1509—1811nomaximal, Sylow
100#529—1811no—
101#432—1811no—
102C4×C4⋊C4D18111yescharacteristic, complemented
103#328—1812no—
104#327—1812no—
105#126—3621no—
106#125—1811no—
107#124—1811no—
108#123—3621no—
109C22⋊Q8—1811no—
110#121—1811no—
111C4×Q8—1811no—
112C4×D4—3621no—
113C4×D4—1811no—
114#117—3621no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C2×D18111yescharacteristic
118C4⋊C8—3621no—
119C22⋊C8—1812no—
120#97—3621no—
121#95C2×D18112yes—
122C2×Q8—1811no—
123C2×D4—3621no—
124C2×D4—1811no—
125C22×C4—22no—
126C22×C4—3621no—
127C22×C4C22⋊D18111yescharacteristic
128C22×C4C22⋊D18111yescharacteristic
129C22×C4C22×D18111yescharacteristic
130C2×C8—3622no—
131C4⋊C4—24no—
132C4⋊C4—3621no—
133C4⋊C4—3621no—
134C4⋊C4—3621no—
135C4⋊C4—3621no—
136C4⋊C4—1811no—
137C4⋊C4—1811no—
138C22⋊C4—3621no—
139C22⋊C4—3621no—
140C22⋊C4—3621no—
141C22⋊C4—3621no—
142C22⋊C4—3621no—
143C42—42no—
144C42—3621no—
145C42C4×D18111yescharacteristic
146C42C4×D18111yescharacteristic
147C42D72411yescharacteristic
148C42D72411yescharacteristic
149C23—3621no—
150C23C2×C22⋊D18111yescharacteristic
151Q8—7241no—
152D4—7241no—
153D4—7241no—
154D4—7241no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—3621no—
163C2×C4—3621no—
164C2×C4—3621no—
165C2×C4—7242no—
166C2×C4#1566842611yescharacteristic
167C2×C4#1566842611yescharacteristic
168C2×C4#1566842611yescharacteristic
169C2×C4#1566842611yescharacteristic
170C2×C4C2×C4×D18111yescharacteristic
171C2×C4C2×D72411yescharacteristic
172C8—7242no—
173C22—21no—
174C22—21no—
175C22—7241no—
176C22—7241no—
177C22—7241no—
178C22C2×#1566842611yescharacteristic
179C22#1915384211yescharacteristic
180C22#1915384711yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—7241no—
188C4—7241no—
189C4—7241no—
190C4#1915374412yes—
191C2—21no—
192C2—21no—
193C2—14481no—
194C2#2604125211yescharacteristic
195C2#2604127811yescharacteristic
196C2C2×#1915374411yescharacteristic
subgroupG/H
centerC22C2×#15668426
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
FittingC4×C4⋊C4×C181C2
socleC22×C181C2×C22⋊C4
prime radical#19153790C22
cosocleC22×C4×C181C23
hypercenterC4×C4⋊C4D181
hypocenterC181#1509
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #26041336C2semidirect
3. #26041015C2semidirect
5. C4×C4⋊C4×C181C2semidirect
7. #19153808C4semidirect
8. #19153804C4semidirect
12. C4×Dic362C4semidirect
13. C4×D724C4semidirect
98. C181#1509semidirect
102. C4×C4⋊C4D181semidirect

Maximal subgroups

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

subgroupindex
#260418132
#260413362
#260410152
#260410122
C4×C4⋊C4×C1812
#1509181