Finite Group Databasebeta

← #37543820

Subgroups — #37543820

Order 23168.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#26041836C211yesmaximal, characteristic, complemented
2#26041614C212yesmaximal, complemented
3#26041559C212yesmaximal, complemented
4#26041484C212yesmaximal, complemented
5#26041430C212yesmaximal
6#26041379C214yesmaximal, complemented
7#26041336C211yesmaximal, characteristic, complemented
8C2×C4×D4×C181C211yesmaximal, characteristic
9C2×#15668437C2214yes—
10#19153816C2211yescharacteristic, complemented
11#19153816C2211yescharacteristic, complemented
12#19153808—21no—
13#19153795—21no—
14#19153795C2212yes—
15C4×Dic362—21no—
16C4×Dic362C2212yescomplemented
17#19153775—21no—
18#19153749C2214yescomplemented
19C4⋊#13089678C2212yescomplemented
20#19153739C2214yescomplemented
21#19153737C2214yes—
22C22⋊#13089678C2212yes—
23#19153727C2212yescomplemented
24C22×D4×C181C2211yescharacteristic
25C23×C4×C181—21no—
26C4×D4×C181—21no—
27C4×D4×C181—21no—
28C4×D4×C181C2212yes—
29C4×D4×C181C2212yes—
30C2×C4⋊C4×C181C2211yescharacteristic
31C2×C22⋊C4×C181—21no—
32C2×C42×C181C2211yescharacteristic
33C2×Dic362—21no—
34C2×Dic362C2312yes—
35#15668437—28no—
36C2×#13089678C2314yes—
37C4⋊Dic181—21no—
38C4⋊Dic181—21no—
39C4⋊Dic181—21no—
40C4⋊Dic181C2312yes—
41#15668428—22no—
42#15668428—22no—
43C22⋊Dic181—22no—
44C4×Dic181—22no—
45C24×C181—21no—
46C2×D4×C181—24no—
47C2×D4×C181—21no—
48C2×D4×C181C2312yes—
49C22×C4×C181—21no—
50C22×C4×C181—22no—
51C22×C4×C181—22no—
52C22×C4×C181—44no—
53C22×C4×C181D411yescharacteristic
54C22×C4×C181D411yescharacteristic
55C22×C4×C181C2311yescharacteristic
56C4⋊C4×C181—21no—
57C4⋊C4×C181C2312yes—
58C22⋊C4×C181—22no—
59C22⋊C4×C181—22no—
60C42×C181D411yescharacteristic
61C42×C181D411yescharacteristic
62C42×C181C2311yescharacteristic
63C42×C181C2311yescharacteristic
64Dic362—24no—
65Dic362—42no—
66C2×Dic181—22no—
67C2×Dic181—22no—
68#13089678—24no—
69C23×C181—24no—
70C23×C181—22no—
71C23×C181—42no—
72C23×C181—42no—
73C23×C181C2×D411yescharacteristic
74D4×C181—24no—
75D4×C181—22no—
76D4×C181#4114yes—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181—22no—
81C2×C4×C181—44no—
82C2×C4×C181—42no—
83C2×C4×C181—44no—
84C2×C4×C181C2×D411yescharacteristic
85C2×C4×C181C2×D411yescharacteristic
86C2×C4×C181C2×D411yescharacteristic
87C2×C4×C181C2×D411yescharacteristic
88C2×C4×C181C2×D411yescharacteristic
89C2×C4×C181C2411yescharacteristic
90C22×C181—21no—
91C22×C181—21no—
92C22×C181—24no—
93C22×C181—48no—
94C22×C181—42no—
95C22×C181—42no—
96C22×C181#13712yes—
97C22×C181C22×D411yescharacteristic
98C4×C181—21no—
99C4×C181—21no—
100C4×C181—21no—
101C4×C181—21no—
102C4×C181—42no—
103C4×C181AGL(1,ℤ/8)12yes—
104C4×C181C2×#4112yes—
105Dic181—42no—
106Dic181—42no—
107C2×C181—22no—
108C2×C181—44no—
109C2×C181#52511yescharacteristic
110C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C181C2×#13711yescharacteristic
112C181#311011yescharacteristic, complemented, Sylow
113#3110—1811nomaximal, Sylow
114#533—1811no—
115C2×C4×D4D18111yescharacteristic
116#484—1812no—
117#474—1812no—
118#461—1812no—
119#450—1812no—
120#440—1814no—
121#432—1811no—
122C22×D4C2×D18111yescharacteristic
123C23×C4—21no—
124C2×SD16—1814no—
125C4⋊Q8—1811no—
126C4⋊Q8—1811no—
127#125—3621no—
128C22⋊Q8—3621no—
129C22⋊Q8—1812no—
130C4×Q8—3621no—
131C4×Q8—1812no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D18112yes—
135C4×D4C2×D18112yes—
136#117—3621no—
137C2×C4⋊C4C2×D18111yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D18111yescharacteristic
140#107—1814no—
141C4⋊C8—1812no—
142#103—1814no—
143#102—1814no—
144C22⋊C8—1812no—
145#97—1812no—
146C24—21no—
147C2×Q8—3621no—
148C2×Q8—1812no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D18112yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D18111yescharacteristic
157C22×C4C22⋊D18111yescharacteristic
158C22×C4C22×D18111yescharacteristic
159SD16—3628no—
160C2×C8—1814no—
161C4⋊C4—21no—
162C4⋊C4—3621no—
163C4⋊C4—3621no—
164C4⋊C4—3621no—
165C4⋊C4—3622no—
166C4⋊C4—3622no—
167C4⋊C4—1812no—
168C4⋊C4C22×D18112yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—3622no—
172C42—3622no—
173C42C22⋊D18111yescharacteristic
174C42C22⋊D18111yescharacteristic
175C42C22×D18111yescharacteristic
176C42C22×D18111yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D18111yescharacteristic
182Q8—3624no—
183Q8—7242no—
184D4—24no—
185D4—22no—
186D4#1566844914yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—3622no—
195C2×C4—3622no—
196C2×C4C2×C22⋊D18111yescharacteristic
197C2×C4C2×C22⋊D18111yescharacteristic
198C2×C4C2×C22⋊D18111yescharacteristic
199C2×C4C2×C22⋊D18111yescharacteristic
200C2×C4C2×C22⋊D18111yescharacteristic
201C2×C4C23×D18111yescharacteristic
202C8—3624no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1915384612yes—
210C22C22×C22⋊D18111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—7242no—
217C4—7242no—
218C4#1915384212yes—
219C4C2×#1566844912yes—
220C2—22no—
221C2—44no—
222C2#2604179011yescharacteristic
223C2C2×#1915384211yescharacteristic
224C2C2×#1915384611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×C4×D4×C181C2
socleC22×C181C22×D4
prime radicalC22×D4×C181C22
hypercenterC2×C4×D4D181
hypocenterC181#3110
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #26041836C2semidirect
2. #26041614C2semidirect
3. #26041559C2semidirect
4. #26041484C2semidirect
6. #26041379C2semidirect
7. #26041336C2semidirect
10. #19153816C22semidirect
11. #19153816C22semidirect
16. C4×Dic362C22semidirect
18. #19153749C22semidirect
19. C4⋊#13089678C22semidirect
20. #19153739C22semidirect
23. #19153727C22semidirect
112. C181#3110semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260416142
#260415592
#260414842
#260414302
#260413792
#260413362
C2×C4×D4×C1812
#3110181