Finite Group Databasebeta

← #37549158

Subgroups — #37549158

Order 23168.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D181⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#26042221C211yesmaximal, characteristic, complemented
3#26042131C214yesmaximal, complemented
4C2×#19153791C211yesmaximal, characteristic
5C2×D181⋊C8—21no—
6C2×C4⋊#10624382—21no—
7C2×C22⋊#10624382—21no—
8#19153873C2212yescomplemented
9C22⋊#13089685—21no—
10(C2×#10624382)⋊C4C2212yescomplemented
11C22×D724—21no—
12C22×D724C411yescharacteristic, complemented
13C22×C4×D181C2211yescharacteristic
14#19153791—21no—
15#19153791—21no—
16#19153791C412yescomplemented
17#19153791C2212yes—
18C2×#15668426—21no—
19C2×C4⋊C4×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21D181⋊C8—42no—
22C2×#13089685—22no—
23C4⋊#10624382—42no—
24C22⋊#10624382—42no—
25C23×D181—21no—
26C23×D181D411yescharacteristic
27C2×D724—22no—
28C2×D724—22no—
29C2×D724—21no—
30C2×D724—42no—
31C2×D724—42no—
32C2×D724—42no—
33C2×D724C2×C412yes—
34C22×Dic181D411yescharacteristic
35C2×C4×D181—42no—
36C2×C4×D181C2×C411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39C2×C4×D181C2311yescharacteristic
40#15668426—22no—
41#15668426—22no—
42C22×C4×C181—21no—
43C22×C4×C181C2×C411yescharacteristic
44C4⋊C4×C181—21no—
45C4⋊C4×C181C2×C412yes—
46C2×#10624382—42no—
47C2×#10624382—42no—
48C2×#10624382—42no—
49#13089685—42no—
50C22×D181—22no—
51C22×D181—41no—
52C22×D181—41no—
53C22×D181—42no—
54C22×D181—42no—
55C22×D181—42no—
56C22×D181C22⋊C411yescharacteristic
57C22×D181D812yes—
58C22×D181SD1612yes—
59C22×D181C2×D411yescharacteristic
60D724—42no—
61D724—44no—
62D724—42no—
63D724—42no—
64D724—42no—
65C2×Dic181—41no—
66C2×Dic181C22⋊C411yescharacteristic
67C2×Dic181C2×D411yescharacteristic
68C4×D181—22no—
69C4×D181—22no—
70C4×D181—41no—
71C4×D181—41no—
72C23×C181C22⋊C411yescharacteristic
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—42no—
76C2×C4×C181C22⋊C411yescharacteristic
77C2×C4×C181C22×C411yescharacteristic
78C22×C181—21no—
79C22×C181—21no—
80C22×C181#10212yes—
81C22×C181C2×C22⋊C411yescharacteristic
82C2×D181—21no—
83C2×D181—21no—
84C2×D181—21no—
85C2×D181—21no—
86C2×D181—42no—
87C2×D181—42no—
88C2×D181—42no—
89C2×D181—42no—
90C2×D181—42no—
91C2×D181—84no—
92C2×D181#10212yes—
93C2×D181C2×D811yescharacteristic
94C2×D181C2×SD1611yescharacteristic
95#10624382—82no—
96C4×C181—21no—
97C4×C181—42no—
98C4×C181#9912yes—
99Dic181—21no—
100Dic181—21no—
101C2×C181—22no—
102C2×C181C2×#9911yescharacteristic
103C2×C181C2×#10211yescharacteristic
104C2×C181#42111yescharacteristic
105D181—21no—
106D181—22no—
107D181—21no—
108D181—82no—
109C181#151911yescharacteristic, complemented, Sylow
110#1519—1811nomaximal, Sylow
111C2×#121—1811no—
112C2×C22⋊C8—1811no—
113#380—1811no—
114#327—1814no—
115C22×D4—3621no—
116C22×D4—1811no—
117C23×C4—1811no—
118C22×C8—3621no—
119#121—3621no—
120#121—3621no—
121#121—1812no—
122#121—1812no—
123C2×C4⋊C4—3621no—
124C2×C4⋊C4#1062438211yescharacteristic, complemented
125C2×C22⋊C4—3621no—
126C2×C22⋊C4—3621no—
127C22⋊C8—3621no—
128C22⋊C8—1812no—
129#95—1812no—
130C24—3621no—
131C24—1811no—
132C2×D4—3622no—
133C2×D4—3622no—
134C2×D4—3621no—
135C2×D4—1812no—
136C2×D4—7242no—
137C2×D4—7242no—
138C2×D4—7242no—
139C22×C4—21no—
140C22×C4—3622no—
141C22×C4—1811no—
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—1811no—
146C22×C4—7242no—
147C22×C4C2×#1062438211yescharacteristic
148C2×C8—3622no—
149C2×C8—7242no—
150C4⋊C4—21no—
151C4⋊C4—7242no—
152C4⋊C4C2×#1062438212yes—
153C22⋊C4—3622no—
154C22⋊C4—3622no—
155C22⋊C4—7242no—
156C23—3622no—
157C23—1811no—
158C23—1811no—
159C23—1812no—
160C23—1812no—
161C23—7241no—
162C23—7241no—
163C23—7242no—
164C23—7242no—
165C23—7242no—
166C23C22⋊#1062438211yescharacteristic
167D4—7242no—
168D4—7242no—
169D4—7244no—
170D4—7242no—
171D4—7242no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—3622no—
176C2×C4—3622no—
177C2×C4—1811no—
178C2×C4—1811no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4—7241no—
182C2×C4—7242no—
183C2×C4—7242no—
184C2×C4—7242no—
185C2×C4C22⋊#1062438211yescharacteristic
186C2×C4C22×#1062438211yescharacteristic
187C8—7242no—
188C22—21no—
189C22—21no—
190C22—3621no—
191C22—3621no—
192C22—3621no—
193C22—3621no—
194C22—14484no—
195C22—1811no—
196C22—1812no—
197C22—1811no—
198C22—7242no—
199C22—7242no—
200C22—7242no—
201C22—7242no—
202C22—7242no—
203C22#1915387812yes—
204C22C2×C22⋊#1062438211yescharacteristic
205C4—21no—
206C4—42no—
207C4—3621no—
208C4—3621no—
209C4—14482no—
210C4#1915387512yes—
211C2—22no—
212C2—3621no—
213C2—3621no—
214C2—3622no—
215C2—14482no—
216C2C2×#1915387511yescharacteristic
217C2C2×#1915387811yescharacteristic
218C2#2604227811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#19153791C2
cosocleC2×C4×D181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1519
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D181⋊(C22⋊C8)C2semidirect
2. #26042221C2semidirect
3. #26042131C2semidirect
8. #19153873C22semidirect
10. (C2×#10624382)⋊C4C22semidirect
12. C22×D724C4semidirect
16. #19153791C4semidirect
19. C2×C4⋊C4×C181C4semidirect
109. C181#1519semidirect
124. C2×C4⋊C4#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C22⋊C8)2
#260422212
#260421312
C2×#191537912
#1519181