Finite Group Databasebeta

← #37549844

Subgroups — #37549844

Order 23168.

396 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#19153883C211yesmaximal, characteristic, complemented
2C2×#19153873C212yesmaximal, complemented
3C2×C22⋊#13089685C212yesmaximal, complemented
4C2×C4×#13089685C211yesmaximal, characteristic, complemented
5C2×#19153776C211yesmaximal, characteristic
6C22×#13089685C2212yes—
7C22×#13089685C2212yes—
8#19153883—22no—
9#19153873—24no—
10C22⋊#13089685—24no—
11C4×#13089685—22no—
12C22×C22⋊D181C411yescharacteristic
13C23×Dic181C2211yescharacteristic
14C22×C4×D181C2211yescharacteristic
15#19153776—22no—
16#19153776—22no—
17C2×#15668428C411yescharacteristic
18C2×#15668426C411yescharacteristic
19C2×C4×Dic181C2211yescharacteristic
20C2×C22⋊C4×C181C411yescharacteristic
21C2×#13089685—22no—
22C2×#13089685—22no—
23C2×#13089685—22no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26C2×#13089685D414yescomplemented
27C23×D181C2×C411yescharacteristic
28C2×C22⋊D181—22no—
29C2×C22⋊D181—22no—
30C2×C22⋊D181C814yescomplemented
31C22×Dic181—21no—
32C22×Dic181—21no—
33C22×Dic181—22no—
34C22×Dic181—22no—
35C22×Dic181C2×C411yescharacteristic
36C22×Dic181C2×C411yescharacteristic
37C22×Dic181C2311yescharacteristic
38C2×C4×D181—21no—
39C2×C4×D181—21no—
40C2×C4×D181—22no—
41C2×C4×D181—22no—
42#15668428—22no—
43#15668426—22no—
44C4×Dic181D412yes—
45C4×Dic181D412yes—
46C24×C181C2×C411yescharacteristic
47C22×C4×C181C2×C411yescharacteristic
48C22×C4×C181C2×C411yescharacteristic
49C22⋊C4×C181—22no—
50#13089685—24no—
51#13089685—42no—
52C22×D181—21no—
53C22×D181—22no—
54C22×D181—21no—
55C22×D181—22no—
56C22×D181C2×C812yes—
57C22⋊D181—28no—
58C2×Dic181—21no—
59C2×Dic181—22no—
60C2×Dic181—42no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181C22⋊C412yes—
64C2×Dic181C2×C812yes—
65C2×Dic181M1612yes—
66C2×Dic181C2×D411yescharacteristic
67C2×Dic181C2×D412yes—
68C2×Dic181C2×D411yescharacteristic
69C2×Dic181#4112yes—
70C4×D181—42no—
71C4×D181—41no—
72C4×D181—41no—
73C23×C181—21no—
74C23×C181—22no—
75C23×C181—21no—
76C23×C181—22no—
77C23×C181C2×C812yes—
78C23×C181C22×C411yescharacteristic
79C2×C4×C181—22no—
80C2×C4×C181—21no—
81C2×C4×C181—22no—
82C2×C4×C181C22⋊C412yes—
83C22×C181—22no—
84C22×C181—24no—
85C22×C181—41no—
86C22×C181—41no—
87C22×C181—42no—
88C22×C181C2×C22⋊C411yescharacteristic
89C22×C181C4×D412yes—
90C22×C181C22×C811yescharacteristic
91C22×C181C2×M1611yescharacteristic
92C22×C181#13112yes—
93C2×D181—22no—
94C2×D181—24no—
95C2×D181—41no—
96C2×D181—41no—
97C2×D181—42no—
98C4×C181—22no—
99C4×C181—41no—
100Dic181—41no—
101Dic181C22⋊C814yescomplemented
102Dic181#12112yes—
103Dic181#12411yescharacteristic
104Dic181#12711yescharacteristic
105C2×C181—42no—
106C2×C181#39011yescharacteristic
107C2×C181C2×C22⋊C811yescharacteristic
108C2×C181#40811yescharacteristic
109C2×C181C8×D412yes—
110C2×C181#43612yes—
111D181—42no—
112C181#195411yescharacteristic, complemented, Sylow
113#1954—1811nomaximal, Sylow
114C2×C4×D4—1811no—
115C2×C4⋊C8—1811no—
116C2×C22⋊C8—1812no—
117C2×C22⋊C8—1812no—
118C2×C4×C8—1811no—
119C22×D4—1811no—
120C23×C4—1811no—
121C23×C4—1811no—
122C22×C8—1812no—
123C22×C8—1812no—
124C4×D4—3622no—
125C4×D4—3622no—
126C2×C4⋊C4—1811no—
127C2×C22⋊C4—1811no—
128C2×C22⋊C4#1062438211yescharacteristic
129C2×C42—1811no—
130C4⋊C8—3622no—
131C22⋊C8—3624no—
132C22⋊C8—3624no—
133C4×C8—3622no—
134C24—1811no—
135C24C2×#1062438211yescharacteristic
136C2×D4—3622no—
137C2×D4—3622no—
138C2×D4—1814no—
139C22×C4—3622no—
140C22×C4—3621no—
141C22×C4—3621no—
142C22×C4—3622no—
143C22×C4—3622no—
144C22×C4—3621no—
145C22×C4—3621no—
146C22×C4—3622no—
147C22×C4—1811no—
148C22×C4—1811no—
149C22×C4—1811no—
150C22×C4C2×#1062438211yescharacteristic
151C22×C4C2×#1062438211yescharacteristic
152C2×C8—3622no—
153C2×C8—3622no—
154C2×C8—3622no—
155C2×C8—3622no—
156C2×C8—3622no—
157C2×C8—1814no—
158C4⋊C4—3622no—
159C22⋊C4—22no—
160C22⋊C4—3622no—
161C42—1812no—
162C42—1812no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—3621no—
168C23—3622no—
169C23—3621no—
170C23—3622no—
171C23—1812no—
172C23D181⋊C812yes—
173C23C22×#1062438211yescharacteristic
174D4—3628no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—3621no—
179C2×C4—3622no—
180C2×C4—1812no—
181C2×C4—1811no—
182C2×C4—1811no—
183C2×C4—1812no—
184C2×C4—1812no—
185C2×C4—1812no—
186C2×C4—1812no—
187C2×C4—7242no—
188C2×C4—7241no—
189C2×C4—7241no—
190C2×C4—7242no—
191C2×C4—7241no—
192C2×C4—7241no—
193C2×C4C22⋊#1062438212yes—
194C8—3624no—
195C8—7242no—
196C22—22no—
197C22—24no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—3622no—
202C22—3624no—
203C22—7241no—
204C22—7241no—
205C22—7242no—
206C22C2×C22⋊#1062438211yescharacteristic
207C22D4×#1062438212yes—
208C22C2×D181⋊C811yescharacteristic
209C22D181⋊M1611yescharacteristic
210C22#1915390312yes—
211C4—22no—
212C4—41no—
213C4—1812no—
214C4—1811no—
215C4—1811no—
216C4—1814no—
217C4—7241no—
218C2—42no—
219C2—7242no—
220C2#2604223111yescharacteristic
221C2D181⋊(C22⋊C8)11yescharacteristic
222C2#2604225211yescharacteristic
223C2#2604230612yes—
224C2#2604231212yes—
subgroupG/H
center, FrattiniC23C22×#10624382
commutatorC22×C181C22×C8
FittingC2×C22⋊C4×C181C4
socleC23×C181C22×C4
prime radicalC22×C22⋊D181C4
cosocleC22×Dic181C23
hypercenterC2×C22⋊C4#10624382
hypocenterC181#1954
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#19153883C2semidirect
2. C2×#19153873C2semidirect
3. C2×C22⋊#13089685C2semidirect
4. C2×C4×#13089685C2semidirect
26. C2×#13089685D4semidirect
30. C2×C22⋊D181C8semidirect
101. Dic181C22⋊C8semidirect
112. C181#1954semidirect

Maximal subgroups

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

subgroupindex
C2×#191538832
C2×#191538732
C2×C22⋊#130896852
C2×C4×#130896852
C2×#191537762
#1954181