Finite Group Databasebeta

← #37549624

Subgroups — #37549624

Order 23168.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
2#26042221C211yesmaximal, characteristic
3#26042152C214yesmaximal, complemented
4C2×C4⋊C4×D181C211yesmaximal, characteristic
5C2×D181⋊C8C2212yes—
6C2×C4⋊#10624382C2212yes—
7C2×C22⋊#10624382—21no—
8#19153873—21no—
9C22⋊#13089685—21no—
10(C2×#10624382)⋊C4—21no—
11C22×C4×D181—21no—
12C22×C4×D181C2211yescharacteristic
13C2×C4⋊Dic181C411yescharacteristic, complemented
14C2×#15668428—21no—
15C4⋊C4×D181—21no—
16C4⋊C4×D181—21no—
17C4⋊C4×D181C412yescomplemented
18C4⋊C4×D181C2212yes—
19C2×C4⋊C4×C181C411yescharacteristic, complemented
20C22×#10624382—22no—
21D181⋊C8—24no—
22C2×#13089685—22no—
23C4⋊#10624382—24no—
24C22⋊#10624382—42no—
25C23×D181D411yescharacteristic
26C22×Dic181—21no—
27C22×Dic181D411yescharacteristic
28C2×C4×D181—24no—
29C2×C4×D181—22no—
30C2×C4×D181—22no—
31C2×C4×D181—42no—
32C2×C4×D181—42no—
33C2×C4×D181C2×C411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C2×C4×D181C2311yescharacteristic
37C4⋊Dic181—21no—
38C4⋊Dic181C2×C412yes—
39#15668428—22no—
40#15668428—22no—
41C22×C4×C181—21no—
42C22×C4×C181C2×C411yescharacteristic
43C4⋊C4×C181—21no—
44C4⋊C4×C181C2×C412yes—
45C2×#10624382—42no—
46C2×#10624382—42no—
47C2×#10624382—42no—
48#13089685—42no—
49C22×D181—22no—
50C22×D181—22no—
51C22×D181C22⋊C411yescharacteristic
52C22×D181D812yes—
53C22×D181SD1612yes—
54C22×D181C2×D411yescharacteristic
55C2×Dic181—22no—
56C2×Dic181—22no—
57C2×Dic181—42no—
58C2×Dic181C22⋊C411yescharacteristic
59C2×Dic181C2×D411yescharacteristic
60C4×D181—22no—
61C4×D181—22no—
62C4×D181—22no—
63C4×D181—44no—
64C4×D181—42no—
65C4×D181—42no—
66C4×D181#4114yes—
67C23×C181C22⋊C411yescharacteristic
68C2×C4×C181—22no—
69C2×C4×C181—22no—
70C2×C4×C181—42no—
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22×C411yescharacteristic
73C22×C181—21no—
74C22×C181—21no—
75C22×C181#10212yes—
76C22×C181C2×C22⋊C411yescharacteristic
77C2×D181—21no—
78C2×D181—21no—
79C2×D181—24no—
80C2×D181—24no—
81C2×D181#10212yes—
82C2×D181#12312yes—
83C2×D181C2×D811yescharacteristic
84C2×D181C2×SD1611yescharacteristic
85C2×D181#13712yes—
86#10624382—82no—
87C4×C181—21no—
88C4×C181—42no—
89C4×C181#11712yes—
90Dic181—21no—
91Dic181—42no—
92Dic181#12312yes—
93C2×C181—22no—
94C2×C181#38111yescharacteristic
95C2×C181C2×#10211yescharacteristic
96C2×C181#41911yescharacteristic
97D181—22no—
98D181#48012yes—
99D181#48312yes—
100C181#182311yescharacteristic, complemented, Sylow
101#1823—1811nomaximal, Sylow
102C22×C4⋊C4—1811no—
103C2×C22⋊C8—1811no—
104#380—1811no—
105#340—1814no—
106C23×C4—3621no—
107C23×C4—1811no—
108C22×C8—1812no—
109C2×C4⋊C4—3621no—
110C2×C4⋊C4—3621no—
111C2×C4⋊C4—3621no—
112C2×C4⋊C4—1812no—
113C2×C4⋊C4—1811no—
114C2×C4⋊C4—1812no—
115C2×C4⋊C4—1812no—
116C2×C4⋊C4#1062438211yescharacteristic, complemented
117C2×C22⋊C4—3621no—
118C22⋊C8—3621no—
119C22⋊C8—3621no—
120#95—3621no—
121C24—1811no—
122C22×C4—21no—
123C22×C4—3624no—
124C22×C4—3622no—
125C22×C4—3622no—
126C22×C4—3621no—
127C22×C4—3622no—
128C22×C4—1811no—
129C22×C4—1811no—
130C22×C4—1811no—
131C22×C4—1811no—
132C22×C4—1811no—
133C22×C4—7242no—
134C22×C4—7242no—
135C22×C4C2×#1062438211yescharacteristic
136C2×C8—3622no—
137C2×C8—3624no—
138C4⋊C4—21no—
139C4⋊C4—3622no—
140C4⋊C4—3622no—
141C4⋊C4—3621no—
142C4⋊C4—3624no—
143C4⋊C4—1812no—
144C4⋊C4C2×#1062438212yes—
145C22⋊C4—7242no—
146C23—3622no—
147C23—3622no—
148C23—1812no—
149C23—1812no—
150C23—1811no—
151C23—1811no—
152C23C22⋊#1062438211yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—3622no—
157C2×C4—3622no—
158C2×C4—3622no—
159C2×C4—3622no—
160C2×C4—3622no—
161C2×C4—1811no—
162C2×C4—1811no—
163C2×C4—1814no—
164C2×C4—7244no—
165C2×C4—7242no—
166C2×C4—7242no—
167C2×C4—7242no—
168C2×C4—7242no—
169C2×C4—7242no—
170C2×C4—7242no—
171C2×C4C22⋊#1062438211yescharacteristic
172C2×C4C22×#1062438211yescharacteristic
173C8—7242no—
174C22—21no—
175C22—21no—
176C22—3624no—
177C22—3624no—
178C22—3621no—
179C22—3621no—
180C22—1812no—
181C22—1812no—
182C22—1811no—
183C22—1811no—
184C22—1812no—
185C22#1915387812yes—
186C22C2×C22⋊#1062438211yescharacteristic
187C4—21no—
188C4—42no—
189C4—3621no—
190C4—14482no—
191C4—1812no—
192C4—7242no—
193C4#1915389512yes—
194C2—22no—
195C2—3622no—
196C2—1812no—
197C2—1812no—
198C2#2604222211yescharacteristic
199C2C2×#1915387811yescharacteristic
200C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181D4
cosocleC2×C4×D181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1823
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #26042152C2semidirect
13. C2×C4⋊Dic181C4semidirect
17. C4⋊C4×D181C4semidirect
19. C2×C4⋊C4×C181C4semidirect
100. C181#1823semidirect
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
D181⋊(C22⋊C8)2
#260422212
#260421522
C2×C4⋊C4×D1812
#1823181