Finite Group Databasebeta

← #37548989

Subgroups — #37548989

Order 23168.

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

normal subgroups only

This group has 280 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#26042250C211yesmaximal, characteristic, complemented
2D181⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#26042125C212yesmaximal, complemented
4#26042123C212yesmaximal, complemented
5C2×#19153801C211yesmaximal, characteristic
6C2×#15668459—21no—
7C2×D181⋊C8—21no—
8#19153873—21no—
9#19153873—21no—
10C22⋊#13089685C2212yes—
11C22⋊#13089685C2212yes—
12C22×D724C411yescharacteristic
13C22×C4×D181C2211yescharacteristic
14#19153801—21no—
15#19153801—21no—
16#19153801—21no—
17#19153801—21no—
18C2×#15668428C2211yescharacteristic
19C2×#15668426C411yescharacteristic
20C2×#15668426C411yescharacteristic
21C2×#15668426C2211yescharacteristic
22C2×C4⋊C4×C181C411yescharacteristic
23#15668459—42no—
24D181⋊C8—42no—
25C2×#13089685—22no—
26C2×#13089685—22no—
27C23×D181C2×C411yescharacteristic
28C23×D181C2×C411yescharacteristic
29C2×D724—21no—
30C2×D724—21no—
31C2×D724—42no—
32C22×Dic181C2×C411yescharacteristic
33C22×Dic181C2311yescharacteristic
34C2×C4×D181—42no—
35C2×C4×D181D411yescharacteristic
36C2×C4×D181D411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39#15668428—21no—
40#15668428—21no—
41#15668426—21no—
42#15668426—21no—
43#15668426—21no—
44#15668426—21no—
45#15668426—21no—
46#15668426—21no—
47C22×C4×C181C2×C411yescharacteristic
48C22×C4×C181C2×C411yescharacteristic
49C22×C4×C181C2×C411yescharacteristic
50C4⋊C4×C181—21no—
51C4⋊C4×C181—21no—
52#13089685—42no—
53#13089685—42no—
54C22×D181—22no—
55C22×D181—22no—
56C22×D181—21no—
57C22×D181—22no—
58C22×D181—41no—
59C22×D181—41no—
60C22×D181—41no—
61C22×D181C22⋊C411yescharacteristic
62C22×D181C22⋊C411yescharacteristic
63D724—42no—
64D724—42no—
65C2×Dic181—21no—
66C2×Dic181—22no—
67C2×Dic181—41no—
68C2×Dic181C2×D411yescharacteristic
69C2×Dic181C2×D411yescharacteristic
70C4×D181—22no—
71C4×D181—22no—
72C4×D181—41no—
73C4×D181—41no—
74C23×C181C22×C411yescharacteristic
75C2×C4×C181—21no—
76C2×C4×C181—21no—
77C2×C4×C181—41no—
78C2×C4×C181—41no—
79C2×C4×C181—41no—
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22⋊C411yescharacteristic
82C22×C181—21no—
83C22×C181—21no—
84C22×C181C2×C22⋊C411yescharacteristic
85C22×C181#13112yes—
86C2×D181—21no—
87C2×D181—21no—
88C2×D181—21no—
89C2×D181—21no—
90C2×D181—21no—
91C2×D181—44no—
92C2×D181—41no—
93C2×D181—41no—
94C2×D181—41no—
95C2×D181—82no—
96C2×D181#9912yes—
97C4×C181—21no—
98C4×C181—21no—
99C4×C181—41no—
100C4×C181—41no—
101Dic181—21no—
102Dic181—21no—
103Dic181—41no—
104C2×C181—22no—
105C2×C181#40811yescharacteristic
106C2×C181C2×#9911yescharacteristic
107C2×C181#41311yescharacteristic
108D181—22no—
109D181—41no—
110D181—81no—
111C181#146811yescharacteristic, complemented, Sylow
112#1468—1811nomaximal, Sylow
113C2×#123—1811no—
114#407—1811no—
115C2×C22⋊C8—1811no—
116#324—1812no—
117#323—1812no—
118C22×D4—1811no—
119C23×C4—1811no—
120C2×M16—3621no—
121C22×C8—3621no—
122#123—3621no—
123#123—3621no—
124#123—3621no—
125#123—3621no—
126C2×C4⋊C4—1811no—
127C2×C4⋊C4#1062438211yescharacteristic
128C2×C22⋊C4—1811no—
129C2×C22⋊C4—1811no—
130C2×C22⋊C4—1811no—
131C22⋊C8—3621no—
132C22⋊C8—3621no—
133C22⋊C8—1812no—
134C22⋊C8—1812no—
135C24—1811no—
136C24—1811no—
137C2×D4—3621no—
138C2×D4—3621no—
139C2×D4—7242no—
140C22×C4—1811no—
141C22×C4—1811no—
142C22×C4—1811no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—1811no—
146C22×C4—7242no—
147C22×C4C2×#1062438211yescharacteristic
148C22×C4C2×#1062438211yescharacteristic
149C22×C4C2×#1062438211yescharacteristic
150M16—7242no—
151C2×C8—3622no—
152C2×C8—3622no—
153C2×C8—7242no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—3621no—
157C4⋊C4—3621no—
158C22⋊C4—3621no—
159C22⋊C4—3621no—
160C22⋊C4—3621no—
161C22⋊C4—3621no—
162C22⋊C4—3621no—
163C22⋊C4—3621no—
164C23—3622no—
165C23—3622no—
166C23—3622no—
167C23—3621no—
168C23—1811no—
169C23—1811no—
170C23—7241no—
171C23—7241no—
172C23—7241no—
173C23C22×#1062438211yescharacteristic
174D4—7242no—
175D4—7242no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—3622no—
182C2×C4—3622no—
183C2×C4—3621no—
184C2×C4—3622no—
185C2×C4—1811no—
186C2×C4—1811no—
187C2×C4—7241no—
188C2×C4—7241no—
189C2×C4—7241no—
190C2×C4C22⋊#1062438211yescharacteristic
191C2×C4C22⋊#1062438211yescharacteristic
192C8—7242no—
193C8—7242no—
194C22—21no—
195C22—21no—
196C22—3621no—
197C22—3621no—
198C22—3621no—
199C22—3621no—
200C22—3621no—
201C22—14482no—
202C22—1812no—
203C22—7244no—
204C22—7241no—
205C22—7241no—
206C22—7241no—
207C22C2×C22⋊#1062438211yescharacteristic
208C22#1915390412yes—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—3621no—
214C4—3621no—
215C4—7241no—
216C2—22no—
217C2—3622no—
218C2—14481no—
219C2—7241no—
220C2#2604225411yescharacteristic
221C2D181⋊#9911yescharacteristic
222C2#2604226511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC23×C181C22×C4
FrattiniC23C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D724C4
cosocleC22×Dic181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181#1468
LCSG ▷ C23×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
1. #26042250C2semidirect
2. D181⋊(C22⋊C8)C2semidirect
3. #26042125C2semidirect
4. #26042123C2semidirect
111. C181#1468semidirect

Maximal subgroups

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

subgroupindex
#260422502
D181⋊(C22⋊C8)2
#260421252
#260421232
C2×#191538012
#1468181