Finite Group Databasebeta

← #37549061

Subgroups — #37549061

Order 23168.

316 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 68 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#26042301C211yesmaximal, characteristic, complemented
2C4×#15668459C211yesmaximal, characteristic, complemented
3#26042127C212yesmaximal, complemented
4D4⋊#13089685C212yesmaximal, complemented
5C4×D4×D181C211yesmaximal, characteristic
6C2×#15668459—21no—
7C4⋊#13089685C2212yescomplemented
8#19153873—21no—
9#19153871—21no—
10#19153871—21no—
11C4×#13089685C2212yescomplemented
12C2×D4×D181C411yescharacteristic
13C22×C4×D181—21no—
14C4×D724C411yescharacteristic
15D4×Dic181C2211yescharacteristic
16#19153778C2211yescharacteristic
17C4×C22⋊D181—21no—
18#19153776—21no—
19C4⋊C4×D181C411yescharacteristic
20C22⋊C4×D181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic
23#15668459—24no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26C23×D181—21no—
27C2×D724C2×C411yescharacteristic
28C2×C22⋊D181—21no—
29D4×D181—22no—
30D4×D181—22no—
31C22×Dic181—21no—
32C2×C4×D181—21no—
33C2×C4×D181—21no—
34C2×C4×D181—21no—
35C2×C4×D181—44no—
36C2×C4×D181C2×C411yescharacteristic
37C2×C4×D181D411yescharacteristic
38C2×C4×D181D411yescharacteristic
39C4⋊Dic181C2×C411yescharacteristic
40#15668428—21no—
41C22⋊Dic181—21no—
42#15668426—21no—
43#15668426—21no—
44C4×Dic181D411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181C2311yescharacteristic
47C2×D4×C181C2×C411yescharacteristic
48C22×C4×C181—21no—
49C4⋊C4×C181C2×C411yescharacteristic
50C22⋊C4×C181—21no—
51C42×C181C2×C411yescharacteristic
52#13089685—24no—
53#13089685—42no—
54C22×D181—24no—
55C22×D181—21no—
56C22×D181—42no—
57C22×D181—42no—
58C22×D181C22⋊C411yescharacteristic
59D724—21no—
60D724M1612yescomplemented
61C22⋊D181—24no—
62C2×Dic181—21no—
63C2×Dic181—42no—
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C2×Dic181C2×D411yescharacteristic
67C4×D181—22no—
68C4×D181—21no—
69C4×D181—21no—
70C4×D181—22no—
71C4×D181—42no—
72C4×D181—42no—
73C4×D181—42no—
74C23×C181—21no—
75D4×C181—21no—
76D4×C181M1612yescomplemented
77C2×C4×C181—21no—
78C2×C4×C181—42no—
79C2×C4×C181C22⋊C411yescharacteristic
80C2×C4×C181C22⋊C411yescharacteristic
81C2×C4×C181C22×C411yescharacteristic
82C22×C181—22no—
83C22×C181—41no—
84C22×C181—41no—
85C22×C181C2×C22⋊C411yescharacteristic
86C2×D181—21no—
87C2×D181—21no—
88C2×D181—22no—
89C2×D181—48no—
90C2×D181—41no—
91C2×D181—41no—
92C2×D181#10412yes—
93C4×C181—21no—
94C4×C181—21no—
95C4×C181—41no—
96C4×C181C2×M1611yescharacteristic
97C4×C181C2×M1611yescharacteristic
98Dic181—21no—
99Dic181—21no—
100Dic181—41no—
101Dic181AGL(1,ℤ/8)12yes—
102C2×C181—42no—
103C2×C181#40711yescharacteristic
104C2×C181#41811yescharacteristic
105C2×C181C2×#10411yescharacteristic
106D181—22no—
107D181—42no—
108C181#149011yescharacteristic, complemented, Sylow
109#1490—1811nomaximal, Sylow
110C2×C4×D4—1811no—
111#432—1811no—
112C4×M16—1811no—
113D4⋊C8—1812no—
114D4⋊C8—1812no—
115C22×D4—1811no—
116C23×C4—3621no—
117C2×M16—3621no—
118C4×D4—3621no—
119C4×D4—3621no—
120C4×D4—1811no—
121C4×D4—1811no—
122C4×D4—1811no—
123C4×D4#1062438211yescharacteristic
124C2×C4⋊C4—1811no—
125C2×C22⋊C4—3621no—
126C2×C42—1811no—
127C4⋊C8—1812no—
128C22⋊C8—3621no—
129#97—3621no—
130#97—3621no—
131C4×C8—1812no—
132C24—3621no—
133C2×D4—3622no—
134C2×D4—3622no—
135C2×D4—3621no—
136C2×D4—1811no—
137C2×D4C2×#1062438211yescharacteristic
138C22×C4—21no—
139C22×C4—3621no—
140C22×C4—3621no—
141C22×C4—3621no—
142C22×C4—3621no—
143C22×C4—1811no—
144C22×C4—1811no—
145C22×C4—1811no—
146C22×C4—7244no—
147M16—3624no—
148C2×C8—3622no—
149C2×C8—3622no—
150C4⋊C4—3621no—
151C4⋊C4—1811no—
152C4⋊C4C2×#1062438211yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—3621no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C42—1811no—
158C42—1811no—
159C42—1811no—
160C42C2×#1062438211yescharacteristic
161C23—21no—
162C23—3624no—
163C23—3621no—
164C23—1811no—
165C23—7242no—
166C23—7242no—
167D4—21no—
168D4—3624no—
169D4—3621no—
170D4—1812no—
171D4#1566845912yescomplemented
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—3622no—
175C2×C4—3622no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—3621no—
179C2×C4—1811no—
180C2×C4—1811no—
181C2×C4—1811no—
182C2×C4—7242no—
183C2×C4—7242no—
184C2×C4—7242no—
185C2×C4—7242no—
186C2×C4C22⋊#1062438211yescharacteristic
187C2×C4C22⋊#1062438211yescharacteristic
188C2×C4C22×#1062438211yescharacteristic
189C8—3624no—
190C8—7242no—
191C22—22no—
192C22—41no—
193C22—41no—
194C22—3621no—
195C22—3621no—
196C22—3622no—
197C22—1812no—
198C22—7248no—
199C22—7241no—
200C22—7241no—
201C22C2×C22⋊#1062438211yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—3621no—
206C4—3621no—
207C4—1812no—
208C4—7241no—
209C4D181⋊M1611yescharacteristic
210C4C2×#1566845911yescharacteristic
211C2—42no—
212C2—3622no—
213C2—7242no—
214C2#2604225011yescharacteristic
215C2#2604227111yescharacteristic
216C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×D4×D181C4
cosocleC4×Dic181C23
hypercenterC4×D4#10624382
hypocenterC181#1490
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042301C2semidirect
2. C4×#15668459C2semidirect
3. #26042127C2semidirect
4. D4⋊#13089685C2semidirect
7. C4⋊#13089685C22semidirect
11. C4×#13089685C22semidirect
60. D724M16semidirect
76. D4×C181M16semidirect
108. C181#1490semidirect
171. D4#15668459semidirect

Maximal subgroups

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

subgroupindex
#260423012
C4×#156684592
#260421272
D4⋊#130896852
C4×D4×D1812
#1490181