Finite Group Databasebeta

← #37548978

Subgroups — #37548978

Order 23168.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#26042250C212yesmaximal, complemented
2#26042124C212yesmaximal, complemented
3#26042123C212yesmaximal, complemented
4C2×C4×D724C211yesmaximal, characteristic
5C2×#15668459—22no—
6#19153873—22no—
7C22⋊#13089685C2214yes—
8C22×D724C411yescharacteristic
9C22×C4×D181C411yescharacteristic
10C22×C4×D181C2211yescharacteristic
11C4×D724—22no—
12C4×D724—22no—
13C2×C4⋊Dic181C2211yescharacteristic
14C2×#15668426C411yescharacteristic
15C2×#15668426C2211yescharacteristic
16C2×C42×C181C411yescharacteristic
17#15668459—44no—
18C2×#13089685—24no—
19C23×D181C2×C411yescharacteristic
20C23×D181C2×C411yescharacteristic
21C2×D724—22no—
22C2×D724—22no—
23C2×D724—22no—
24C22×Dic181C2×C411yescharacteristic
25C22×Dic181C2311yescharacteristic
26C2×C4×D181—21no—
27C2×C4×D181—21no—
28C2×C4×D181—42no—
29C2×C4×D181—42no—
30C2×C4×D181D412yes—
31C2×C4×D181D412yes—
32C4⋊Dic181—22no—
33#15668426—22no—
34#15668426—22no—
35C22×C4×C181C2×C411yescharacteristic
36C22×C4×C181C2×C411yescharacteristic
37C22×C4×C181C2×C411yescharacteristic
38C42×C181—21no—
39C42×C181—21no—
40#13089685—44no—
41C22×D181—21no—
42C22×D181—21no—
43C22×D181—21no—
44C22×D181—21no—
45C22×D181—41no—
46C22×D181—41no—
47C22×D181—41no—
48C22×D181—41no—
49C22×D181C22⋊C412yes—
50C22×D181M1612yescomplemented
51D724—28no—
52C2×Dic181—21no—
53C2×Dic181—41no—
54C2×Dic181—41no—
55C2×Dic181C2×D412yes—
56C4×D181—24no—
57C4×D181—42no—
58C4×D181—42no—
59C4×D181—42no—
60C23×C181C22×C411yescharacteristic
61C2×C4×C181—21no—
62C2×C4×C181—21no—
63C2×C4×C181—22no—
64C2×C4×C181—21no—
65C2×C4×C181—41no—
66C2×C4×C181C22⋊C411yescharacteristic
67C2×C4×C181C22⋊C411yescharacteristic
68C2×C4×C181M1612yescomplemented
69C22×C181—21no—
70C22×C181—21no—
71C22×C181C2×C22⋊C411yescharacteristic
72C22×C181C2×M1611yescharacteristic
73C22×C181C2×M1611yescharacteristic
74C2×D181—22no—
75C2×D181—22no—
76C2×D181—22no—
77C2×D181—22no—
78C2×D181—42no—
79C2×D181—42no—
80C2×D181—42no—
81C2×D181—41no—
82C2×D181—41no—
83C2×D181—42no—
84C4×C181—22no—
85C4×C181—21no—
86C4×C181—41no—
87C4×C181#9912yes—
88Dic181—22no—
89Dic181—41no—
90C2×C181—21no—
91C2×C181—21no—
92C2×C181#40711yescharacteristic
93C2×C181C2×#9911yescharacteristic
94C2×C181#41311yescharacteristic
95D181—42no—
96D181—42no—
97C181#146511yescharacteristic, complemented, Sylow
98#1465—1811nomaximal, Sylow
99C2×C4×D4—1811no—
100#407—1812no—
101#324—1812no—
102#323—1812no—
103C22×D4—1811no—
104C23×C4—1811no—
105C23×C4—1811no—
106C2×M16—3622no—
107C4×D4—3622no—
108C4×D4—3622no—
109C2×C4⋊C4—1811no—
110C2×C22⋊C4—1811no—
111C2×C22⋊C4—1811no—
112C2×C42#1062438211yescharacteristic
113C22⋊C8—3622no—
114C22⋊C8—1814no—
115C24—1811no—
116C24—1811no—
117C2×D4—3622no—
118C2×D4—3622no—
119C2×D4—3622no—
120C22×C4—3621no—
121C22×C4—3621no—
122C22×C4—1812no—
123C22×C4—1811no—
124C22×C4—1811no—
125C22×C4—1812no—
126C22×C4—7242no—
127C22×C4—7242no—
128C22×C4C2×#1062438211yescharacteristic
129C22×C4C2×#1062438211yescharacteristic
130C22×C4C2×#1062438211yescharacteristic
131M16—7244no—
132C2×C8—3624no—
133C4⋊C4—3622no—
134C22⋊C4—3622no—
135C22⋊C4—3622no—
136C42—21no—
137C42—21no—
138C23—3621no—
139C23—3621no—
140C23—3621no—
141C23—3621no—
142C23—1812no—
143C23—1812no—
144C23—7241no—
145C23—7241no—
146C23—7241no—
147C23—7241no—
148C23C22×#1062438211yescharacteristic
149D4—3628no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—3624no—
156C2×C4—3621no—
157C2×C4—1812no—
158C2×C4—7242no—
159C2×C4—7242no—
160C2×C4—7241no—
161C2×C4—7242no—
162C2×C4—7241no—
163C2×C4C22⋊#1062438211yescharacteristic
164C2×C4C22⋊#1062438211yescharacteristic
165C2×C4#1566845912yescomplemented
166C8—7244no—
167C22—21no—
168C22—21no—
169C22—3622no—
170C22—3622no—
171C22—3622no—
172C22—3622no—
173C22—7242no—
174C22—7242no—
175C22—7242no—
176C22—7242no—
177C22—7241no—
178C22—7241no—
179C22C2×C22⋊#1062438211yescharacteristic
180C22D181⋊M1611yescharacteristic
181C22C2×#1566845911yescharacteristic
182C4—22no—
183C4—21no—
184C4—41no—
185C4—3622no—
186C4—7241no—
187C4#1915387512yes—
188C2—21no—
189C2—21no—
190C2—7242no—
191C2—7242no—
192C2#2604225011yescharacteristic
193C2C2×#1915387511yescharacteristic
194C2#2604226511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C42×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D724C4
cosocleC22×Dic181C23
hypercenterC2×C42#10624382
hypocenterC181#1465
LCSG ▷ C23×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #26042250C2semidirect
2. #26042124C2semidirect
3. #26042123C2semidirect
50. C22×D181M16semidirect
68. C2×C4×C181M16semidirect
97. C181#1465semidirect
165. C2×C4#15668459semidirect

Maximal subgroups

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

subgroupindex
#260422502
#260421242
#260421232
C2×C4×D7242
#1465181