Finite Group Databasebeta

← #37549128

Subgroups — #37549128

Order 23168.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#26042251C211yesmaximal, characteristic, complemented
2#26042222C211yesmaximal, characteristic, complemented
3#26042131C214yesmaximal, complemented
4C2×#19153791C211yesmaximal, characteristic
5C2×#15668458—21no—
6C2×C22⋊#10624382—21no—
7#19153873—21no—
8#19153873C2212yescomplemented
9(C2×#10624382)⋊C4—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—
21#15668458—42no—
22C2×#13089685—22no—
23C22⋊#10624382—42no—
24C23×D181—21no—
25C23×D181D411yescharacteristic
26C2×D724—22no—
27C2×D724—22no—
28C2×D724—21no—
29C2×D724—42no—
30C2×D724—44no—
31C2×D724C2×C412yes—
32C22×Dic181D411yescharacteristic
33C2×C4×D181—42no—
34C2×C4×D181C2×C411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C2×C4×D181D411yescharacteristic
37C2×C4×D181C2311yescharacteristic
38#15668426—22no—
39#15668426—22no—
40C22×C4×C181—21no—
41C22×C4×C181C2×C411yescharacteristic
42C4⋊C4×C181—21no—
43C4⋊C4×C181C2×C412yes—
44C2×#10624382—42no—
45C2×#10624382—42no—
46C2×#10624382—42no—
47#13089685—42no—
48C22×D181—22no—
49C22×D181—22no—
50C22×D181—22no—
51C22×D181—41no—
52C22×D181—42no—
53C22×D181—42no—
54C22×D181—42no—
55C22×D181C22⋊C411yescharacteristic
56C22×D181C2×D411yescharacteristic
57D724—42no—
58D724—42no—
59D724—44no—
60D724—44no—
61C2×Dic181—22no—
62C2×Dic181C22⋊C411yescharacteristic
63C2×Dic181C2×D411yescharacteristic
64C4×D181—41no—
65C4×D181—41no—
66C4×D181—41no—
67C4×D181—41no—
68C23×C181C22⋊C411yescharacteristic
69C2×C4×C181—22no—
70C2×C4×C181—22no—
71C2×C4×C181—42no—
72C2×C4×C181C22⋊C411yescharacteristic
73C2×C4×C181C22×C411yescharacteristic
74C22×C181—21no—
75C22×C181—21no—
76C22×C181#9912yes—
77C22×C181C2×C22⋊C411yescharacteristic
78C2×D181—21no—
79C2×D181—21no—
80C2×D181—21no—
81C2×D181—21no—
82C2×D181—21no—
83C2×D181—44no—
84C2×D181—42no—
85C2×D181—42no—
86C2×D181—42no—
87C2×D181—84no—
88C2×D181AGL(1,ℤ/8)12yes—
89#10624382—82no—
90C4×C181—21no—
91C4×C181—21no—
92C4×C181—42no—
93Dic181—21no—
94Dic181—21no—
95C2×C181—22no—
96C2×C181C2×#9911yescharacteristic
97C2×C181#41811yescharacteristic
98C2×C181#42111yescharacteristic
99D181—22no—
100D181—41no—
101D181—82no—
102C181#151011yescharacteristic, complemented, Sylow
103#1510—1811nomaximal, Sylow
104C2×#121—1811no—
105#407—1811no—
106#381—1811no—
107#327—1814no—
108C22×D4—3621no—
109C22×D4—1811no—
110C23×C4—1811no—
111C2×M16—3621no—
112#121—3621no—
113#121—3621no—
114#121—1812no—
115#121—1812no—
116C2×C4⋊C4#1062438211yescharacteristic, complemented
117C2×C22⋊C4—3621no—
118C2×C22⋊C4—3621no—
119C22⋊C8—3621no—
120C22⋊C8—1812no—
121#95—3621no—
122#95—1812no—
123C24—3621no—
124C24—1811no—
125C2×D4—3622no—
126C2×D4—3622no—
127C2×D4—3621no—
128C2×D4—1812no—
129C2×D4—7242no—
130C2×D4—7244no—
131C22×C4—21no—
132C22×C4—3622no—
133C22×C4—1811no—
134C22×C4—1811no—
135C22×C4—1811no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4—7242no—
139C22×C4C2×#1062438211yescharacteristic
140M16—7242no—
141C2×C8—3622no—
142C4⋊C4—21no—
143C4⋊C4C2×#1062438212yes—
144C22⋊C4—3622no—
145C22⋊C4—3622no—
146C22⋊C4—7242no—
147C23—3622no—
148C23—3622no—
149C23—3622no—
150C23—1811no—
151C23—1811no—
152C23—7241no—
153C23—7242no—
154C23—7242no—
155C23—7242no—
156C23C22⋊#1062438211yescharacteristic
157D4—7242no—
158D4—7242no—
159D4—7244no—
160D4—7244no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—3622no—
165C2×C4—1811no—
166C2×C4—1811no—
167C2×C4—7241no—
168C2×C4—7241no—
169C2×C4—7241no—
170C2×C4—7241no—
171C2×C4—7242no—
172C2×C4—7242no—
173C2×C4—7242no—
174C2×C4C22⋊#1062438211yescharacteristic
175C2×C4C22×#1062438211yescharacteristic
176C8—7242no—
177C22—21no—
178C22—21no—
179C22—3621no—
180C22—3621no—
181C22—3621no—
182C22—3621no—
183C22—3621no—
184C22—14484no—
185C22—1812no—
186C22—7244no—
187C22—7242no—
188C22—7242no—
189C22—7242no—
190C22#1915387512yes—
191C22C2×C22⋊#1062438211yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—3621no—
196C4—3621no—
197C4—14482no—
198C2—22no—
199C2—3622no—
200C2—14482no—
201C2—7241no—
202C2C2×#1915387511yescharacteristic
203C2#2604227111yescharacteristic
204C2#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#1510
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. #26042251C2semidirect
2. #26042222C2semidirect
3. #26042131C2semidirect
8. #19153873C22semidirect
10. (C2×#10624382)⋊C4C22semidirect
12. C22×D724C4semidirect
16. #19153791C4semidirect
19. C2×C4⋊C4×C181C4semidirect
102. C181#1510semidirect
116. C2×C4⋊C4#10624382semidirect

Maximal subgroups

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

subgroupindex
#260422512
#260422222
#260421312
C2×#191537912
#1510181