Finite Group Databasebeta

← C2×#26042132 #37549089

Subgroups — C2×#26042132 #37549089

Order 23168.

336 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×#19153873C211yesmaximal, characteristic
2C2×(C2×#10624382)⋊C4C211yesmaximal, characteristic
3#26042132C214yesmaximal, direct product factor
4C2×#19153796C211yesmaximal, characteristic
5C23×#10624382—21no—
6C22×#13089685—21no—
7#19153873—21no—
8#19153873C2212yes—
9(C2×#10624382)⋊C4—21no—
10(C2×#10624382)⋊C4C2212yes—
11C22×Dic362C411yescharacteristic, complemented
12C22×C4×D181C2211yescharacteristic
13#19153796—21no—
14#19153796—21no—
15#19153796C412yescomplemented
16#19153796C2212yes—
17C2×C4⋊Dic181—21no—
18C2×#15668426—21no—
19C2×C4⋊C4×C181C411yescharacteristic, complemented
20C22×#10624382—24no—
21C22×#10624382—22no—
22C22×#10624382—42no—
23C22×#10624382—42no—
24C2×#13089685—22no—
25C2×#13089685—42no—
26C23×D181D411yescharacteristic
27C2×Dic362—21no—
28C2×Dic362—42no—
29C2×Dic362C2×C412yescomplemented
30C22×Dic181—21no—
31C22×Dic181D411yescharacteristic
32C2×C4×D181—42no—
33C2×C4×D181C2×C411yescharacteristic
34C2×C4×D181D411yescharacteristic
35C2×C4×D181D411yescharacteristic
36C2×C4×D181C2311yescharacteristic
37C4⋊Dic181—22no—
38C4⋊Dic181—22no—
39#15668426—22no—
40#15668426—22no—
41C22×C4×C181—21no—
42C22×C4×C181C2×C411yescharacteristic
43C4⋊C4×C181—21no—
44C4⋊C4×C181C2×C412yescomplemented
45C2×#10624382—24no—
46C2×#10624382—48no—
47C2×#10624382—42no—
48C2×#10624382—42no—
49#13089685—42no—
50C22×D181—22no—
51C22×D181—22no—
52C22×D181C22⋊C411yescharacteristic
53C22×D181SD1612yes—
54C22×D181Q1612yes—
55C22×D181C2×D411yescharacteristic
56Dic362—42no—
57Dic362—42no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—42no—
61C2×Dic181C22⋊C411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C4×D181—41no—
64C4×D181—41no—
65C4×D181—41no—
66C4×D181—41no—
67C23×C181C22⋊C411yescharacteristic
68C2×C4×C181—22no—
69C2×C4×C181—22no—
70C2×C4×C181—42no—
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22×C411yescharacteristic
73C22×C181#9912yes—
74C22×C181#10312yes—
75C22×C181#10412yes—
76C22×C181C2×C22⋊C411yescharacteristic
77C2×D181—24no—
78C2×D181—24no—
79C2×D181—21no—
80C2×D181—21no—
81C2×D181—21no—
82C2×D181—21no—
83C2×D181#10312yes—
84C2×D181C2×SD1611yescharacteristic
85C2×D181C2×Q1611yescharacteristic
86#10624382—44no—
87C4×C181—21no—
88C4×C181—21no—
89C4×C181—42no—
90Dic181—21no—
91Dic181—21no—
92Dic181—42no—
93C2×C181#32814yescomplemented
94C2×C181C2×#9911yescharacteristic
95C2×C181C2×#10311yescharacteristic
96C2×C181C2×#10411yescharacteristic
97D181—21no—
98D181—22no—
99D181—21no—
100C181C2×#32811yescharacteristic, complemented, Sylow
101C2×#328—1811nomaximal, Sylow
102C2×C22⋊Q8—1811no—
103C2×C22⋊C8—1811no—
104C2×#95—1811no—
105#328—1814no—
106C22×Q8—1811no—
107C23×C4—3621no—
108C23×C4—1811no—
109C22×C8—3621no—
110C22⋊Q8—3621no—
111C22⋊Q8—3621no—
112C22⋊Q8—1812no—
113C22⋊Q8—1812no—
114C2×C4⋊C4—3621no—
115C2×C4⋊C4#1062438211yescharacteristic, complemented
116C2×C22⋊C4—3621no—
117C22⋊C8—3621no—
118C22⋊C8—1812no—
119#95—3621no—
120#95—1812no—
121C24—1811no—
122C2×Q8—3621no—
123C2×Q8—1812no—
124C2×Q8—7242no—
125C22×C4—21no—
126C22×C4—3624no—
127C22×C4—3622no—
128C22×C4—3621no—
129C22×C4—1811no—
130C22×C4—1811no—
131C22×C4—1811no—
132C22×C4—1811no—
133C22×C4—1811no—
134C22×C4—7242no—
135C22×C4—7242no—
136C22×C4—7242no—
137C22×C4C2×#1062438211yescharacteristic
138C2×C8—3622no—
139C2×C8—7242no—
140C4⋊C4—21no—
141C4⋊C4—3622no—
142C4⋊C4—3622no—
143C4⋊C4C2×#1062438212yescomplemented
144C22⋊C4—3622no—
145C22⋊C4—3622no—
146C23—3622no—
147C23—3622no—
148C23—1812no—
149C23—1812no—
150C23—1811no—
151C23—1811no—
152C23C22⋊#1062438211yescharacteristic
153Q8—7242no—
154Q8—7242no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—3622no—
159C2×C4—3624no—
160C2×C4—3622no—
161C2×C4—1811no—
162C2×C4—1811no—
163C2×C4—7241no—
164C2×C4—7241no—
165C2×C4—7241no—
166C2×C4—7241no—
167C2×C4—7248no—
168C2×C4—7242no—
169C2×C4—7242no—
170C2×C4—7242no—
171C2×C4C22⋊#1062438211yescharacteristic
172C2×C4C22×#1062438211yescharacteristic
173C8—7242no—
174C22—3624no—
175C22—3624no—
176C22—3621no—
177C22—3621no—
178C22—3621no—
179C22—3621no—
180C22—1811no—
181C22—1812no—
182C22—1811no—
183C22#1915387512yes—
184C22#1915387912yes—
185C22#1915388012yes—
186C22C2×C22⋊#1062438211yescharacteristic
187C4—21no—
188C4—21no—
189C4—42no—
190C4—3621no—
191C4—3621no—
192C4—7244no—
193C4—7242no—
194C2—3621no—
195C2—3622no—
196C2—3621no—
197C2#2604213214yesdirect product factor
198C2C2×#1915387511yescharacteristic
199C2C2×#1915387911yescharacteristic
200C2C2×#1915388011yescharacteristic
subgroupG/H
centerC23C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×C4⋊C4×C181C4
socleC23×C181C22⋊C4
prime radicalC23×D181D4
cosocleC2×C4×D181C23
hypercenterC2×C4⋊C4#10624382
hypocenterC181C2×#328
LCSG ▷ C2×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #26042132C2direct (N × H)
11. C22×Dic362C4semidirect
15. #19153796C4semidirect
19. C2×C4⋊C4×C181C4semidirect
29. C2×Dic362C2×C4semidirect
44. C4⋊C4×C181C2×C4semidirect
93. C2×C181#328semidirect
100. C181C2×#328semidirect
115. C2×C4⋊C4#10624382semidirect
143. C4⋊C4C2×#10624382semidirect
197. C2#26042132direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191538732
C2×(C2×#10624382)⋊C42
#260421322
C2×#191537962
C2×#328181