Finite Group Databasebeta

← #37549111

Subgroups — #37549111

Order 23168.

272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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#26042302C211yesmaximal, characteristic, complemented
2#26042215C211yesmaximal, characteristic, complemented
3#26042131C212yesmaximal, complemented
4#26042130C212yesmaximal, complemented
5#26041826C211yesmaximal, characteristic
6C2×C4×#10624382—21no—
7#19153883—21no—
8#19153873C2212yes—
9#19153871—21no—
10(C2×#10624382)⋊C4—21no—
11(C2×#10624382)⋊C4C2212yes—
12C2×#15668449—21no—
13#19153815C411yescharacteristic, complemented
14#19153812C411yescharacteristic, complemented
15#19153802—21no—
16#19153791C2211yescharacteristic
17#19153789—21no—
18#19153787C2211yescharacteristic
19C4×D724C411yescharacteristic, complemented
20C4×C22⋊D181—21no—
21C42×D181C2211yescharacteristic
22C4×D4×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24C2×#13089685—22no—
25C4×#10624382—24no—
26#15668449—44no—
27C2×Dic362—21no—
28C2×D724—21no—
29C2×D724C2×C411yescharacteristic
30C2×C22⋊D181—21no—
31C2×C22⋊D181—21no—
32C2×C22⋊D181—21no—
33C2×C4×D181—21no—
34C2×C4×D181D411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C2×C4×D181C2311yescharacteristic
37C4⋊Dic181C2×C411yescharacteristic
38#15668428—21no—
39C22⋊Dic181—21no—
40#15668426—21no—
41#15668426—21no—
42C4×Dic181C2×C411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181D411yescharacteristic
45C2×D4×C181C2×C411yescharacteristic
46C22×C4×C181—21no—
47C4⋊C4×C181C2×C411yescharacteristic
48C22⋊C4×C181—21no—
49C42×C181C2×C411yescharacteristic
50C2×#10624382—24no—
51C2×#10624382—42no—
52C2×#10624382—42no—
53#13089685—42no—
54C22×D181—21no—
55C22×D181C2×D411yescharacteristic
56Dic362—42no—
57D724—41no—
58D724—42no—
59C22⋊D181—42no—
60C22⋊D181—42no—
61C22⋊D181—42no—
62C2×Dic181—21no—
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C22⋊C411yescharacteristic
65C2×Dic181C2×D411yescharacteristic
66C4×D181—22no—
67C4×D181—22no—
68C4×D181—41no—
69C4×D181—42no—
70C23×C181—21no—
71D4×C181—41no—
72C2×C4×C181—21no—
73C2×C4×C181—42no—
74C2×C4×C181C22⋊C411yescharacteristic
75C2×C4×C181C22⋊C411yescharacteristic
76C2×C4×C181C22×C411yescharacteristic
77C22×C181—41no—
78C22×C181—41no—
79C22×C181—41no—
80C22×C181C2×C22⋊C411yescharacteristic
81C2×D181—21no—
82C2×D181—21no—
83C2×D181—41no—
84C2×D181—41no—
85C2×D181—41no—
86C2×D181AGL(1,ℤ/8)12yes—
87#10624382—44no—
88C4×C181—21no—
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—41no—
92Dic181—21no—
93Dic181—21no—
94Dic181—41no—
95Dic181#10412yes—
96C2×C181—81no—
97C2×C181#41011yescharacteristic
98C2×C181#41811yescharacteristic
99C2×C181C2×#10411yescharacteristic
100D181—22no—
101D181—81no—
102C181#150511yescharacteristic, complemented, Sylow
103#1505—1811nomaximal, Sylow
104#532—1811no—
105#432—1811no—
106#376—1811no—
107#327—1812no—
108#327—1812no—
109C2×#41—3621no—
110C4⋊Q8—1811no—
111#127—1811no—
112#124—3621no—
113#121—3621no—
114#121—1811no—
115#121—1811no—
116C4×D4—3621no—
117C4×D4—1811no—
118C4×D4#1062438211yescharacteristic, complemented
119C2×C42—3621no—
120C2×C42—1811no—
121C4⋊C8—3621no—
122C22⋊C8—1812no—
123#97—3621no—
124#95—3621no—
125#95—1812no—
126#41—7244no—
127C2×Q8—3621no—
128C2×D4—3621no—
129C2×D4—3621no—
130C2×D4—3621no—
131C2×D4—3621no—
132C2×D4—1811no—
133C2×D4C2×#1062438211yescharacteristic
134C22×C4—21no—
135C22×C4—3622no—
136C22×C4—3621no—
137C22×C4—1811no—
138C22×C4—1811no—
139C22×C4—1811no—
140C2×C8—3622no—
141C4⋊C4—3621no—
142C4⋊C4—1811no—
143C4⋊C4C2×#1062438211yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—3621no—
146C22⋊C4—3621no—
147C22⋊C4—3621no—
148C42—3624no—
149C42—1811no—
150C42—1811no—
151C42—1811no—
152C42C2×#1062438211yescharacteristic
153C23—21no—
154C23—3621no—
155C23—1811no—
156Q8—7242no—
157D4—41no—
158D4—7241no—
159D4—7242no—
160D4—7242no—
161D4—7242no—
162D4—7242no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—3622no—
166C2×C4—3622no—
167C2×C4—3624no—
168C2×C4—3621no—
169C2×C4—1811no—
170C2×C4—1811no—
171C2×C4—1811no—
172C2×C4—7241no—
173C2×C4—7242no—
174C2×C4—7242no—
175C2×C4—7242no—
176C2×C4C22⋊#1062438211yescharacteristic
177C2×C4C22⋊#1062438211yescharacteristic
178C2×C4C22×#1062438211yescharacteristic
179C8—7242no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—3621no—
184C22—3621no—
185C22—1812no—
186C22—7241no—
187C22—7241no—
188C22—7241no—
189C22C2×C22⋊#1062438211yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—3621no—
195C4—3621no—
196C4—1812no—
197C4—7244no—
198C4—7241no—
199C2—81no—
200C2—3622no—
201C2—14481no—
202C2#2604225811yescharacteristic
203C2#2604227111yescharacteristic
204C2D181⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×D4×C181C4
socleC22×C181C2×C22⋊C4
prime radical#26041826C2
cosocleC2×C4×D181C23
hypercenterC4×D4#10624382
hypocenterC181#1505
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #26042302C2semidirect
2. #26042215C2semidirect
3. #26042131C2semidirect
4. #26042130C2semidirect
13. #19153815C4semidirect
14. #19153812C4semidirect
19. C4×D724C4semidirect
22. C4×D4×C181C4semidirect
102. C181#1505semidirect
118. C4×D4#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423022
#260422152
#260421312
#260421302
#260418262
#1505181