Finite Group Databasebeta

← #37549122

Subgroups — #37549122

Order 23168.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#26042302C211yesmaximal, characteristic, complemented
2C4×C4⋊#10624382C211yesmaximal, characteristic, complemented
3#26042133C212yesmaximal, complemented
4#26042130C212yesmaximal
5#26041808C211yesmaximal, characteristic
6C2×C4⋊#10624382—21no—
7C2×C4×#10624382—21no—
8#19153883—21no—
9#19153873C2212yes—
10#19153871—21no—
11(C2×#10624382)⋊C4C2212yes—
12#19153809—21no—
13#19153808C411yescharacteristic, complemented
14#19153798—21no—
15#19153792C2211yescharacteristic
16#19153787C2211yescharacteristic
17Q8×Dic181C411yescharacteristic, complemented
18D4×Dic181C411yescharacteristic, complemented
19#19153776—21no—
20#19153772—21no—
21C42×D181C2211yescharacteristic
22#124×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4⋊#10624382—24no—
26C4×#10624382—42no—
27C2×C22⋊D181—21no—
28C22×Dic181—21no—
29C2×C4×D181D411yescharacteristic
30C2×C4×D181D411yescharacteristic
31C2×C4×D181C2311yescharacteristic
32C4⋊Dic181—21no—
33C4⋊Dic181C2×C411yescharacteristic
34C4⋊Dic181C2×C411yescharacteristic
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38C22⋊Dic181—21no—
39C22⋊Dic181—21no—
40#15668426—21no—
41C4×Dic181—21no—
42C4×Dic181C2×C411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181D411yescharacteristic
45C2×Q8×C181C2×C411yescharacteristic
46C2×D4×C181C2×C411yescharacteristic
47C22⋊C4×C181—21no—
48C22⋊C4×C181—21no—
49C42×C181C2×C411yescharacteristic
50C2×#10624382—24no—
51C2×#10624382—42no—
52C2×#10624382—42no—
53#13089685—42no—
54C22×D181C2×D411yescharacteristic
55C22⋊D181—41no—
56C22⋊D181—41no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—42no—
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C22⋊C411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C4×D181—21no—
64C4×D181—21no—
65C4×D181—22no—
66C4×D181—41no—
67C23×C181—21no—
68Q8×C181—41no—
69D4×C181—41no—
70C2×C4×C181—21no—
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22⋊C411yescharacteristic
73C2×C4×C181C22×C411yescharacteristic
74C22×C181—41no—
75C22×C181—41no—
76C22×C181—41no—
77C22×C181C2×C22⋊C411yescharacteristic
78C2×D181—21no—
79C2×D181—21no—
80C2×D181AGL(1,ℤ/8)11yescharacteristic
81C2×D181#13711yescharacteristic
82#10624382—44no—
83C4×C181—21no—
84C4×C181—21no—
85C4×C181—21no—
86C4×C181—41no—
87Dic181—21no—
88Dic181—21no—
89Dic181—41no—
90Dic181—41no—
91Dic181#10412yes—
92C2×C181—81no—
93C2×C181#41011yescharacteristic
94C2×C181#41711yescharacteristic
95C2×C181C2×#10411yescharacteristic
96D181—21no—
97D181—21no—
98C181#150911yescharacteristic, complemented, Sylow
99#1509—1811nomaximal, Sylow
100#529—1811no—
101#432—1811no—
102C4×C4⋊C4—1811no—
103#328—1812no—
104#327—1812no—
105#126—3621no—
106#125—1811no—
107#124#1062438211yescharacteristic, complemented
108#123—3621no—
109C22⋊Q8—1811no—
110#121—1811no—
111C4×Q8—1811no—
112C4×D4—3621no—
113C4×D4—1811no—
114#117—3621no—
115C2×C4⋊C4—3621no—
116C2×C42—3621no—
117C2×C42—1811no—
118C4⋊C8—3621no—
119C22⋊C8—1812no—
120#97—3621no—
121#95—1812no—
122C2×Q8C2×#1062438211yescharacteristic
123C2×D4—3621no—
124C2×D4C2×#1062438211yescharacteristic
125C22×C4—3622no—
126C22×C4—3621no—
127C22×C4—1811no—
128C22×C4—1811no—
129C22×C4—1811no—
130C2×C8—3622no—
131C4⋊C4—3621no—
132C4⋊C4—3621no—
133C4⋊C4—3624no—
134C4⋊C4—3621no—
135C4⋊C4—3621no—
136C4⋊C4—1811no—
137C4⋊C4—1811no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—3621no—
141C22⋊C4—3621no—
142C22⋊C4—3621no—
143C42—3621no—
144C42—1811no—
145C42—1811no—
146C42—1811no—
147C42—7242no—
148C42C2×#1062438211yescharacteristic
149C23—21no—
150C23—1811no—
151Q8—41no—
152D4—41no—
153D4—7241no—
154D4—7241no—
155C2×C4—21no—
156C2×C4—3621no—
157C2×C4—3621no—
158C2×C4—3622no—
159C2×C4—3624no—
160C2×C4—3621no—
161C2×C4—3621no—
162C2×C4—1811no—
163C2×C4—1811no—
164C2×C4—1811no—
165C2×C4—7241no—
166C2×C4—7242no—
167C2×C4—7242no—
168C2×C4—7242no—
169C2×C4C22⋊#1062438211yescharacteristic
170C2×C4C22⋊#1062438211yescharacteristic
171C2×C4C22×#1062438211yescharacteristic
172C8—7242no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—3621no—
177C22—3621no—
178C22—1811no—
179C22—1811no—
180C22C2×C22⋊#1062438211yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—3621no—
186C4—3621no—
187C4—1812no—
188C4—7244no—
189C4—7241no—
190C4—7241no—
191C2—81no—
192C2—3621no—
193C2—3621no—
194C2#2604225911yescharacteristic
195C2#2604227011yescharacteristic
196C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#124×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153787C22
cosocleC2×C4×D181C23
hypercenter#124#10624382
hypocenterC181#1509
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. C4×C4⋊#10624382C2semidirect
3. #26042133C2semidirect
13. #19153808C4semidirect
17. Q8×Dic181C4semidirect
18. D4×Dic181C4semidirect
22. #124×C181C4semidirect
98. C181#1509semidirect
107. #124#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423022
C4×C4⋊#106243822
#260421332
#260421302
#260418082
#1509181