Finite Group Databasebeta

← #37549140

Subgroups — #37549140

Order 23168.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#26042224C211yesmaximal, characteristic, complemented
3#26042131C212yesmaximal, complemented
4#26042130C212yesmaximal, complemented
5#26041826C211yesmaximal, characteristic
6C4⋊#13089685—21no—
7#19153873C2212yes—
8#19153871—21no—
9(C2×#10624382)⋊C4—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—
25#15668449—44no—
26C2×Dic362—21no—
27C2×D724—21no—
28C2×D724C2×C411yescharacteristic
29C2×C22⋊D181—21no—
30C2×C22⋊D181—21no—
31C2×C22⋊D181—21no—
32C2×C4×D181—21no—
33C2×C4×D181D411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181C2311yescharacteristic
36C4⋊Dic181C2×C411yescharacteristic
37#15668428—21no—
38C22⋊Dic181—21no—
39#15668426—21no—
40#15668426—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C2×D4×C181C2×C411yescharacteristic
45C22×C4×C181—21no—
46C4⋊C4×C181C2×C411yescharacteristic
47C22⋊C4×C181—21no—
48C42×C181C2×C411yescharacteristic
49C2×#10624382—42no—
50C2×#10624382—42no—
51C2×#10624382—42no—
52#13089685—42no—
53C22×D181—21no—
54C22×D181C2×D411yescharacteristic
55Dic362—42no—
56D724—41no—
57D724—42no—
58C22⋊D181—42no—
59C22⋊D181—42no—
60C22⋊D181—42no—
61C2×Dic181—21no—
62C2×Dic181C22⋊C411yescharacteristic
63C2×Dic181C22⋊C411yescharacteristic
64C2×Dic181C2×D411yescharacteristic
65C4×D181—22no—
66C4×D181—41no—
67C4×D181—41no—
68C4×D181—42no—
69C23×C181—21no—
70D4×C181—41no—
71C2×C4×C181—21no—
72C2×C4×C181—42no—
73C2×C4×C181C22⋊C411yescharacteristic
74C2×C4×C181C22⋊C411yescharacteristic
75C2×C4×C181C22×C411yescharacteristic
76C22×C181—41no—
77C22×C181—41no—
78C22×C181—41no—
79C22×C181C2×C22⋊C411yescharacteristic
80C2×D181—21no—
81C2×D181—21no—
82C2×D181—41no—
83C2×D181—41no—
84C2×D181—41no—
85C2×D181AGL(1,ℤ/8)12yes—
86#10624382—82no—
87C4×C181—21no—
88C4×C181—21no—
89C4×C181—21no—
90C4×C181—41no—
91Dic181—21no—
92Dic181—21no—
93Dic181—21no—
94Dic181—41no—
95C2×C181—81no—
96C2×C181#41011yescharacteristic
97C2×C181#41811yescharacteristic
98C2×C181#42111yescharacteristic
99D181—22no—
100D181—81no—
101C181#151411yescharacteristic, complemented, Sylow
102#1514—1811nomaximal, Sylow
103#532—1811no—
104#432—1811no—
105#383—1811no—
106#327—1812no—
107#327—1812no—
108C2×#41—3621no—
109C4⋊Q8—1811no—
110#127—1811no—
111#124—3621no—
112#121—3621no—
113#121—1811no—
114#121—1811no—
115C4×D4—3621no—
116C4×D4—1811no—
117C4×D4#1062438211yescharacteristic, complemented
118C2×C42—1811no—
119C4⋊C8—3621no—
120C22⋊C8—1812no—
121#97—3621no—
122#95—3621no—
123#95—3621no—
124#95—1812no—
125#41—7244no—
126C2×Q8—3621no—
127C2×D4—3621no—
128C2×D4—3621no—
129C2×D4—3621no—
130C2×D4—3621no—
131C2×D4—1811no—
132C2×D4C2×#1062438211yescharacteristic
133C22×C4—21no—
134C22×C4—3621no—
135C22×C4—3622no—
136C22×C4—1811no—
137C22×C4—1811no—
138C22×C4—1811no—
139C2×C8—3622no—
140C4⋊C4—3621no—
141C4⋊C4—1811no—
142C4⋊C4C2×#1062438211yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3621no—
145C22⋊C4—3621no—
146C22⋊C4—3621no—
147C42—1811no—
148C42—1811no—
149C42—1811no—
150C42C2×#1062438211yescharacteristic
151C23—21no—
152C23—3621no—
153C23—1811no—
154Q8—7242no—
155D4—41no—
156D4—7241no—
157D4—7242no—
158D4—7242no—
159D4—7242no—
160D4—7242no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—3622no—
164C2×C4—3621no—
165C2×C4—1811no—
166C2×C4—1811no—
167C2×C4—1811no—
168C2×C4—7241no—
169C2×C4—7241no—
170C2×C4—7242no—
171C2×C4—7242no—
172C2×C4—7242no—
173C2×C4—7242no—
174C2×C4C22⋊#1062438211yescharacteristic
175C2×C4C22⋊#1062438211yescharacteristic
176C2×C4C22×#1062438211yescharacteristic
177C8—7242no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—3621no—
182C22—3621no—
183C22—1812no—
184C22—7241no—
185C22—7241no—
186C22—7241no—
187C22C2×C22⋊#1062438211yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—3621no—
193C4—3621no—
194C4—3621no—
195C4—14482no—
196C4—7241no—
197C2—81no—
198C2—3622no—
199C2—14481no—
200C2#2604225811yescharacteristic
201C2#2604227111yescharacteristic
202C2#2604227611yescharacteristic
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#1514
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. #26042301C2semidirect
2. #26042224C2semidirect
3. #26042131C2semidirect
4. #26042130C2semidirect
13. #19153815C4semidirect
14. #19153812C4semidirect
19. C4×D724C4semidirect
22. C4×D4×C181C4semidirect
101. C181#1514semidirect
117. C4×D4#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423012
#260422242
#260421312
#260421302
#260418262
#1514181