Finite Group Databasebeta

← C22×#19153880 #37550344

Subgroups — C22×#19153880 #37550344

Order 23168.

856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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
1C22×#15668459C211yesmaximal, characteristic, complemented
2C22×C4×#10624382C211yesmaximal, characteristic, complemented
3C2×#19153880C2112yesmaximal, direct product factor
4C22×#15668448C211yesmaximal, characteristic
5C23×#10624382—21no—
6C2×#15668459—23no—
7C2×#15668459C2216yescomplemented
8C22×#13089685—21no—
9C2×C4×#10624382—23no—
10C2×C4×#10624382C2216yescomplemented
11#19153880C22116yesdirect product factor
12C2×#15668448—23no—
13C2×#15668448—23no—
14C2×#15668448C416yescomplemented
15C2×#15668448C2216yes—
16C22×Dic362C411yescharacteristic, complemented
17C22×C22⋊D181—21no—
18C23×Dic181—21no—
19C22×C4×D181C2211yescharacteristic
20C22×D4×C181C411yescharacteristic, complemented
21C22×#10624382—28no—
22C22×#10624382—26no—
23#15668459—26no—
24#15668459C2314yescomplemented
25C2×#13089685—26no—
26C4×#10624382—26no—
27C4×#10624382C2314yescomplemented
28C23×D181D411yescharacteristic
29#15668448—212no—
30#15668448—26no—
31#15668448—26no—
32#15668448C2×C4112yescomplemented
33#15668448C2314yes—
34C2×Dic362—23no—
35C2×Dic362C2×C416yescomplemented
36C2×C22⋊D181—26no—
37C2×C22⋊D181—26no—
38C22×Dic181—26no—
39C22×Dic181—26no—
40C22×Dic181—21no—
41C22×Dic181D411yescharacteristic
42C2×C4×D181C2×C413yes—
43C2×C4×D181D413yes—
44C2×C4×D181D413yes—
45C2×C4×D181C2313yes—
46C24×C181—21no—
47C2×D4×C181—23no—
48C2×D4×C181C2×C416yescomplemented
49C22×C4×C181C2×C411yescharacteristic
50C2×#10624382—224no—
51C2×#10624382—24no—
52#13089685—24no—
53C22×D181—24no—
54C22×D181C22⋊C413yes—
55C22×D181C2×D413yes—
56Dic362—26no—
57Dic362C22×C414yescomplemented
58C22⋊D181—212no—
59C22⋊D181—24no—
60C2×Dic181—26no—
61C2×Dic181—212no—
62C2×Dic181—24no—
63C2×Dic181C22⋊C413yes—
64C2×Dic181C2×D413yes—
65C4×D181C22⋊C416yes—
66C4×D181C22×C413yes—
67C4×D181C2×D413yes—
68C4×D181C2×D413yes—
69C4×D181C2411yescharacteristic
70C23×C181—26no—
71C23×C181—44no—
72C23×C181C22⋊C411yescharacteristic
73D4×C181—26no—
74D4×C181C22×C414yescomplemented
75C2×C4×C181C22⋊C413yes—
76C2×C4×C181C22×C413yes—
77C22×C181—24no—
78C22×C181—412no—
79C22×C181#10414yescomplemented
80C22×C181C2×C22⋊C413yes—
81C2×D181—26no—
82C2×D181—26no—
83C2×D181C2×C22⋊C413yes—
84C2×D181C22×D411yescharacteristic
85#10624382—28no—
86C4×C181C2×C22⋊C413yes—
87C4×C181C23×C411yescharacteristic
88Dic181—24no—
89Dic181C2×C22⋊C413yes—
90Dic181C22×D411yescharacteristic
91C2×C181—44no—
92C2×C181C2×#10416yescomplemented
93C2×C181C22×C22⋊C411yescharacteristic
94D181—21no—
95D181—23no—
96C181C22×#10411yescharacteristic, complemented, Sylow
97C22×#104—1811nomaximal, Sylow
98C22×#41—1811no—
99C22×M16—1811no—
100C22×C42—1811no—
101C2×#104—18112no—
102C2×#41—3623no—
103C2×#41—3623no—
104C2×#41—1816no—
105C2×#41—1816no—
106C22×Q8—1811no—
107C22×D4—3621no—
108C22×D4#1062438211yescharacteristic, complemented
109C23×C4—3621no—
110C23×C4—3621no—
111C23×C4—1811no—
112C2×M16—3623no—
113C2×M16—1816no—
114C22×C8—3621no—
115C2×C42—3623no—
116C2×C42—1816no—
117#104—18116no—
118C24—21no—
119C24—1811no—
120#41—3626no—
121#41—3626no—
122#41—36212no—
123#41—1814no—
124#41—18112no—
125C2×Q8—3623no—
126C2×Q8—1816no—
127C2×D4—23no—
128C2×D4—3626no—
129C2×D4—3626no—
130C2×D4C2×#1062438216yescomplemented
131C22×C4—3628no—
132C22×C4—3626no—
133C22×C4—3621no—
134C22×C4—3626no—
135C22×C4—3626no—
136C22×C4—1811no—
137C22×C4—1813no—
138C22×C4—1813no—
139C22×C4—1813no—
140C22×C4—1813no—
141C22×C4C2×#1062438211yescharacteristic
142M16—3626no—
143M16—1814no—
144C2×C8—3626no—
145C42—3626no—
146C42—1814no—
147C23—26no—
148C23—44no—
149C23—3624no—
150C23—1813no—
151C23—1813no—
152C23C22⋊#1062438211yescharacteristic
153Q8—3626no—
154Q8—1814no—
155D4—26no—
156D4—3624no—
157D4—36212no—
158D4C22×#1062438214yescomplemented
159C2×C4—36224no—
160C2×C4—3624no—
161C2×C4—3626no—
162C2×C4—3624no—
163C2×C4—36212no—
164C2×C4—1813no—
165C2×C4—1813no—
166C2×C4—1813no—
167C2×C4—1813no—
168C2×C4—1816no—
169C2×C4—1811no—
170C2×C4—1813no—
171C2×C4C22⋊#1062438213yes—
172C2×C4C22×#1062438213yes—
173C8—3624no—
174C22—24no—
175C22—412no—
176C22—3626no—
177C22—3626no—
178C22—1811no—
179C22—1813no—
180C22#1915388014yesdirect product factor
181C22C2×C22⋊#1062438213yes—
182C4—3628no—
183C4—3624no—
184C4—1811no—
185C4—1813no—
186C4C2×C22⋊#1062438213yes—
187C4C23×#1062438211yescharacteristic
188C2—44no—
189C2—3621no—
190C2—3623no—
191C2C2×#1915388016yesdirect product factor
192C2C22×C22⋊#1062438211yescharacteristic
subgroupG/H
centerC23C22⋊#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingC22×D4×C181C4
socleC23×C181C22⋊C4
prime radicalC22×#15668448C2
cosocleC4×D181C24
hypercenterC22×D4#10624382
hypocenterC181C22×#104
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#15668459C2semidirect
2. C22×C4×#10624382C2semidirect
3. C2×#19153880C2direct (N × H)
7. C2×#15668459C22semidirect
10. C2×C4×#10624382C22semidirect
11. #19153880C22direct (N × H)
14. C2×#15668448C4semidirect
16. C22×Dic362C4semidirect
20. C22×D4×C181C4semidirect
24. #15668459C23semidirect
27. C4×#10624382C23semidirect
32. #15668448C2×C4semidirect
35. C2×Dic362C2×C4semidirect
48. C2×D4×C181C2×C4semidirect
57. Dic362C22×C4semidirect
74. D4×C181C22×C4semidirect
79. C22×C181#104semidirect
92. C2×C181C2×#104semidirect
96. C181C22×#104semidirect
108. C22×D4#10624382semidirect
130. C2×D4C2×#10624382semidirect
158. D4C22×#10624382semidirect
180. C22#19153880direct (N × H)
191. C2C2×#19153880direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156684592
C22×C4×#106243822
C2×#191538802
C22×#156684482
C22×#104181