Finite Group Databasebeta

← D181⋊#324 #37548950

Subgroups — D181⋊#324 #37548950

Order 23168.

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

normal subgroups only

This group has 328 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)C212yesmaximal
2#26042125C212yesmaximal, complemented
3#26042124C212yesmaximal, complemented
4C2×C4⋊C4×D181C211yesmaximal, characteristic
5C2×D181⋊C8—22no—
6#19153873—22no—
7C22⋊#13089685C2214yes—
8C22×C4×D181C411yescharacteristic
9C22×C4×D181C411yescharacteristic
10C22×C4×D181C2211yescharacteristic
11C2×C4⋊Dic181C2211yescharacteristic
12C2×#15668428C411yescharacteristic
13C2×#15668428C2211yescharacteristic
14C4⋊C4×D181—22no—
15C4⋊C4×D181—22no—
16C2×C4⋊C4×C181C411yescharacteristic
17D181⋊C8—44no—
18C2×#13089685—24no—
19C23×D181C2×C411yescharacteristic
20C22×Dic181C2×C411yescharacteristic
21C22×Dic181C2×C411yescharacteristic
22C22×Dic181C2311yescharacteristic
23C2×C4×D181—21no—
24C2×C4×D181—21no—
25C2×C4×D181—22no—
26C2×C4×D181—21no—
27C2×C4×D181—21no—
28C2×C4×D181—42no—
29C2×C4×D181—42no—
30C2×C4×D181C814yescomplemented
31C2×C4×D181D412yes—
32C2×C4×D181D412yes—
33C4⋊Dic181—22no—
34#15668428—22no—
35#15668428—22no—
36C22×C4×C181C2×C411yescharacteristic
37C22×C4×C181C2×C411yescharacteristic
38C22×C4×C181C2×C411yescharacteristic
39C4⋊C4×C181—22no—
40#13089685—44no—
41C22×D181—22no—
42C22×D181—22no—
43C22×D181C22⋊C411yescharacteristic
44C22×D181C22⋊C411yescharacteristic
45C22×D181C2×C812yes—
46C22×D181M1612yes—
47C2×Dic181—21no—
48C2×Dic181—21no—
49C2×Dic181—21no—
50C2×Dic181—41no—
51C2×Dic181—41no—
52C2×Dic181C2×C812yescomplemented
53C2×Dic181C2×D412yes—
54C4×D181—24no—
55C4×D181—24no—
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—21no—
64C2×C4×C181—41no—
65C2×C4×C181—41no—
66C2×C4×C181C22⋊C412yes—
67C2×C4×C181C2×C812yescomplemented
68C22×C181—21no—
69C22×C181—21no—
70C22×C181C2×C22⋊C411yescharacteristic
71C22×C181C22×C811yescharacteristic
72C22×C181C2×M1611yescharacteristic
73C2×D181—21no—
74C2×D181—21no—
75C2×D181—24no—
76C2×D181—24no—
77C2×D181C22⋊C812yes—
78C2×D181C22⋊C812yes—
79C2×D181#9912yes—
80C2×D181#10112yes—
81C4×C181—22no—
82C4×C181—22no—
83C4×C181—41no—
84Dic181—22no—
85Dic181—22no—
86Dic181—41no—
87C2×C181—21no—
88C2×C181—21no—
89C2×C181C2×C22⋊C811yescharacteristic
90C2×C181C2×#9911yescharacteristic
91C2×C181C2×#10111yescharacteristic
92D181—22no—
93D181#32414yescomplemented
94C181C2×#32411yescharacteristic, complemented, Sylow
95C2×#324—1811nomaximal, Sylow
96C22×C4⋊C4—1811no—
97C2×C22⋊C8—1812no—
98#324—1812no—
99#324—1812no—
100C23×C4—1811no—
101C23×C4—1811no—
102C23×C4—1811no—
103C22×C8—3622no—
104C2×C4⋊C4—3622no—
105C2×C4⋊C4—3622no—
106C2×C4⋊C4—1811no—
107C2×C4⋊C4—1811no—
108C2×C4⋊C4—1811no—
109C2×C4⋊C4#1062438211yescharacteristic
110C22⋊C8—3622no—
111C22⋊C8—1814no—
112C24—1811no—
113C22×C4—3621no—
114C22×C4—3621no—
115C22×C4—3622no—
116C22×C4—3621no—
117C22×C4—3621no—
118C22×C4—1811no—
119C22×C4—1812no—
120C22×C4—1814no—
121C22×C4—1811no—
122C22×C4—1811no—
123C22×C4—1812no—
124C22×C4—7242no—
125C22×C4—7242no—
126C22×C4C2×#1062438211yescharacteristic
127C22×C4C2×#1062438211yescharacteristic
128C22×C4C2×#1062438211yescharacteristic
129C2×C8—3624no—
130C2×C8—7244no—
131C4⋊C4—22no—
132C4⋊C4—3622no—
133C4⋊C4—3622no—
134C4⋊C4—3622no—
135C23—3622no—
136C23—3622no—
137C23—1811no—
138C23—1812no—
139C23—1812no—
140C23—1811no—
141C23C22×#1062438211yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—3624no—
148C2×C4—3624no—
149C2×C4—3624no—
150C2×C4—3621no—
151C2×C4—3621no—
152C2×C4—3621no—
153C2×C4—1812no—
154C2×C4—1812no—
155C2×C4—7242no—
156C2×C4—7242no—
157C2×C4—7242no—
158C2×C4—7241no—
159C2×C4—7241no—
160C2×C4C22⋊#1062438212yes—
161C2×C4D181⋊C812yescomplemented
162C8—7244no—
163C22—21no—
164C22—21no—
165C22—3624no—
166C22—3624no—
167C22—3621no—
168C22—3621no—
169C22—1812no—
170C22—1812no—
171C22—1812no—
172C22—1812no—
173C22C2×C22⋊#1062438211yescharacteristic
174C22C2×D181⋊C811yescharacteristic
175C22D181⋊M1611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—3622no—
180C4—3622no—
181C4—7241no—
182C2—21no—
183C2—21no—
184C2—3622no—
185C2—1814no—
186C2D181⋊(C22⋊C8)11yescharacteristic
187C2D181⋊#9911yescharacteristic
188C2D181⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC22×C181C22×C8
FrattiniC23C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC23×D181C2×C4
cosocleC22×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181C2×#324
LCSG ▷ C22×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
2. #26042125C2semidirect
3. #26042124C2semidirect
30. C2×C4×D181C8semidirect
52. C2×Dic181C2×C8semidirect
67. C2×C4×C181C2×C8semidirect
93. D181#324semidirect
94. C181C2×#324semidirect
161. C2×C4D181⋊C8semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C22⋊C8)2
#260421252
#260421242
C2×C4⋊C4×D1812
C2×#324181