Finite Group Databasebeta

← #37549240

Subgroups — #37549240

Order 23168.

252 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 62 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#26042299C211yesmaximal, characteristic, complemented
2C2×#19153883C211yesmaximal, characteristic, complemented
3#26042139C212yesmaximal, complemented
4#26042137C212yesmaximal, complemented
5#26041825C211yesmaximal, characteristic
6C22×#13089685—21no—
7#19153883—21no—
8#19153883C2212yes—
9#19153883C2212yes—
10C22⋊#13089685—21no—
11#19153871—21no—
12C2×#15668449C411yescharacteristic
13#19153814C2211yescharacteristic
14#19153812C2211yescharacteristic
15#19153805C411yescharacteristic
16#19153803C411yescharacteristic
17#19153788—21no—
18#19153788—21no—
19C4×C22⋊D181—21no—
20C4×C22⋊D181—21no—
21C2×C4×Dic181C2211yescharacteristic
22C2×#41×C181C411yescharacteristic
23C2×#13089685—22no—
24C2×#13089685—22no—
25C2×#13089685—42no—
26#15668449—42no—
27C2×Dic362C2×C411yescharacteristic
28C2×D724C2×C411yescharacteristic
29C2×C22⋊D181—21no—
30C2×C22⋊D181—21no—
31C2×C22⋊D181—21no—
32C22×Dic181D411yescharacteristic
33C22×Dic181D411yescharacteristic
34C2×C4×D181—21no—
35#15668428—21no—
36#15668428—21no—
37C22⋊Dic181—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40#15668426—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181C2311yescharacteristic
45#41×C181—42no—
46C2×Q8×C181C2×C411yescharacteristic
47C2×D4×C181—21no—
48C2×D4×C181C2×C411yescharacteristic
49C22×C4×C181—21no—
50C22×C4×C181C2×C411yescharacteristic
51#13089685—42no—
52#13089685—42no—
53C22×D181—21no—
54Dic362—41no—
55D724—41no—
56C22⋊D181—42no—
57C22⋊D181—42no—
58C22⋊D181—41no—
59C22⋊D181—41no—
60C2×Dic181—22no—
61C2×Dic181—21no—
62C2×Dic181—21no—
63C2×Dic181—21no—
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C22⋊C411yescharacteristic
66C2×Dic181C2×D411yescharacteristic
67C2×Dic181C2×D411yescharacteristic
68C4×D181—42no—
69C23×C181—21no—
70C23×C181C22⋊C411yescharacteristic
71Q8×C181—41no—
72D4×C181—41no—
73D4×C181—42no—
74C2×C4×C181—22no—
75C2×C4×C181—21no—
76C2×C4×C181—42no—
77C2×C4×C181C22⋊C411yescharacteristic
78C2×C4×C181C22×C411yescharacteristic
79C22×C181—21no—
80C22×C181—21no—
81C22×C181—41no—
82C22×C181—41no—
83C22×C181—41no—
84C22×C181#10012yes—
85C22×C181C2×C22⋊C411yescharacteristic
86C2×D181—41no—
87C2×D181—41no—
88C2×D181—41no—
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—41no—
92Dic181—21no—
93Dic181—21no—
94Dic181—41no—
95Dic181#13512yes—
96Dic181AGL(1,ℤ/8)11yescharacteristic
97Dic181#13711yescharacteristic
98C2×C181—22no—
99C2×C181—81no—
100C2×C181C2×#10011yescharacteristic
101C2×C181#41611yescharacteristic
102C2×C181#41711yescharacteristic
103D181—81no—
104C181#155111yescharacteristic, complemented, Sylow
105#1551—1811nomaximal, Sylow
106#532—1811no—
107#432—1811no—
108C2×C4⋊C8—1811no—
109#333—1812no—
110#331—1812no—
111C2×#41—1811no—
112C2×#41#1062438211yescharacteristic
113C22×C8—3621no—
114C4⋊Q8—1811no—
115#127—1811no—
116#124—1811no—
117#124—1811no—
118#121—3621no—
119#121—3621no—
120C4×D4—3621no—
121C4×D4—3621no—
122C2×C42—1811no—
123C4⋊C8—3621no—
124C4⋊C8—1812no—
125C4⋊C8—1812no—
126C22⋊C8—3621no—
127#97—3621no—
128#41—42no—
129#41—7242no—
130C2×Q8—1811no—
131C2×Q8C2×#1062438211yescharacteristic
132C2×D4—21no—
133C2×D4—3621no—
134C2×D4—3621no—
135C2×D4—3621no—
136C2×D4—1811no—
137C2×D4C2×#1062438211yescharacteristic
138C22×C4—21no—
139C22×C4—3621no—
140C22×C4—1811no—
141C22×C4—1811no—
142C22×C4C2×#1062438211yescharacteristic
143C2×C8—3622no—
144C2×C8—3622no—
145C2×C8—7242no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C22⋊C4—3621no—
149C22⋊C4—3621no—
150C22⋊C4—3621no—
151C22⋊C4—3621no—
152C42—1811no—
153C42—1811no—
154C42—1811no—
155C42—1811no—
156C23—21no—
157C23—3621no—
158C23C22⋊#1062438211yescharacteristic
159Q8—41no—
160Q8—7241no—
161D4—41no—
162D4—42no—
163D4—7241no—
164D4—7242no—
165D4—7241no—
166D4—7241no—
167D4—7242no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—3621no—
172C2×C4—3622no—
173C2×C4—3621no—
174C2×C4—3621no—
175C2×C4—1811no—
176C2×C4—1811no—
177C2×C4—1811no—
178C2×C4—1811no—
179C2×C4—7242no—
180C2×C4C22⋊#1062438211yescharacteristic
181C2×C4C22×#1062438211yescharacteristic
182C8—7242no—
183C8—7242no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—7241no—
190C22—7241no—
191C22—7241no—
192C22#1915387612yes—
193C22C2×C22⋊#1062438211yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—3621no—
198C4—3621no—
199C4—1812no—
200C4—1811no—
201C4—1811no—
202C4—7241no—
203C2—22no—
204C2—81no—
205C2—14481no—
206C2C2×#1915387611yescharacteristic
207C2#2604226911yescharacteristic
208C2#2604227011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×#41×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041825C2
cosocleC4×Dic181C23
hypercenterC2×#41#10624382
hypocenterC181#1551
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26042299C2semidirect
2. C2×#19153883C2semidirect
3. #26042139C2semidirect
4. #26042137C2semidirect
104. C181#1551semidirect

Maximal subgroups

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

subgroupindex
#260422992
C2×#191538832
#260421392
#260421372
#260418252
#1551181