Finite Group Databasebeta

← C22×D8×D181 #37548435

Subgroups — C22×D8×D181 #37548435

Order 23168.

1976 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 565 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×D4×D181C212yesmaximal, complemented
2C22×D1448C211yesmaximal, characteristic, complemented
3C22×#15668434C212yesmaximal, complemented
4C2×D8×D181C2124yesmaximal, direct product factor
5C22×C8×D181C211yesmaximal, characteristic, complemented
6C22×D8×C181C211yesmaximal, characteristic, complemented
7C24×D181—22no—
8C22×D724C2212yescomplemented
9C22×C22⋊D181—22no—
10C2×D4×D181—212no—
11C2×D4×D181C22124yescomplemented
12C22×C4×D181C2211yescharacteristic
13C2×D1448C22112yescomplemented
14C2×#15668434C22124yescomplemented
15D8×D181C22164yesdirect product factor
16C22×#13089678C2211yescharacteristic, complemented
17C2×C8×D181C22112yescomplemented
18C22×D4×C181C2212yescomplemented
19C2×D8×C181C22112yescomplemented
20C22×C8×C181C2211yescharacteristic, complemented
21C23×D181—224no—
22C23×D181—22no—
23C23×D181—416no—
24C23×D181D411yescharacteristic
25C2×D724—26no—
26C2×D724C23112yescomplemented
27C2×C22⋊D181—224no—
28D4×D181—248no—
29D4×D181C23132yescomplemented
30C22×Dic181D411yescharacteristic
31C2×C4×D181D416yes—
32C2×C4×D181C2316yes—
33D1448C23116yescomplemented
34#15668434C23132yescomplemented
35C2×#13089678C2316yescomplemented
36C8×D181C23116yescomplemented
37C24×C181—22no—
38C2×D4×C181—26no—
39C2×D4×C181C23112yescomplemented
40C22×C4×C181C2311yescharacteristic
41D8×C181C23116yescomplemented
42C2×C8×C181C2316yescomplemented
43C22×D181—212no—
44C22×D181—232no—
45C22×D181—48no—
46C22×D181—496no—
47C22×D181D818yesdirect product factor
48C22×D181C2×D416yes—
49D724—212no—
50D724C2418yescomplemented
51C22⋊D181—232no—
52C2×Dic181C2×D416yes—
53C4×D181C2×D4112yes—
54C4×D181C2414yes—
55#13089678C2414yescomplemented
56C23×C181—212no—
57C23×C181—48no—
58C23×C181C2×D411yescharacteristic
59D4×C181—212no—
60D4×C181C2418yescomplemented
61C2×C4×C181C2×D413yes—
62C2×C4×C181C2413yes—
63C8×C181C2414yescomplemented
64C22×C181—28no—
65C22×C181—424no—
66C22×C181C2×D814yescomplemented
67C22×C181C22×D413yes—
68C2×D181—28no—
69C2×D181—424no—
70C2×D181—464no—
71C2×D181C2×D8124yesdirect product factor
72C2×D181C22×D414yes—
73C4×C181C22×D413yes—
74C4×C181C2511yescharacteristic
75Dic181C22×D414yes—
76C2×C181—48no—
77C2×C181C22×D816yescomplemented
78C2×C181C23×D411yescharacteristic
79D181—48no—
80D181C22×D818yesdirect product factor
81C181C23×D811yescharacteristic, complemented, Sylow
82C23×D8—1811nomaximal, Sylow
83C23×D4—1812no—
84C22×D8—1812no—
85C22×D8—18124no—
86C22×D8—1811no—
87C22×D8D18111yescharacteristic, direct product factor
88C23×C8—1811no—
89C25—3622no—
90C22×D4—36212no—
91C22×D4—3622no—
92C22×D4—18124no—
93C22×D4—1812no—
94C22×D4C2×D18112yescomplemented
95C23×C4—1811no—
96C2×D8—18124no—
97C2×D8—18164no—
98C2×D8—18112no—
99C2×D8C2×D181112yesdirect product factor
100C22×C8—1811no—
101C22×C8—18112no—
102C22×C8C2×D18111yescharacteristic, complemented
103C24—22no—
104C24—36224no—
105C24—3622no—
106C24—1811no—
107C24—72416no—
108C2×D4—26no—
109C2×D4—36248no—
110C2×D4—36224no—
111C2×D4—3626no—
112C2×D4—18132no—
113C2×D4—18112no—
114C2×D4C22×D181112yescomplemented
115C22×C4—1811no—
116C22×C4—1816no—
117C22×C4—1816no—
118C22×C4C22×D18111yescharacteristic
119D8—18132no—
120D8—18116no—
121D8C22×D181116yesdirect product factor
122C2×C8—1816no—
123C2×C8—18116no—
124C2×C8C22×D18116yescomplemented
125C23—212no—
126C23—48no—
127C23—36232no—
128C23—36212no—
129C23—1818no—
130C23—1816no—
131C23—72496no—
132C23—7248no—
133C23D4×D18111yescharacteristic
134D4—212no—
135D4—36232no—
136D4—36212no—
137D4—1818no—
138D4C23×D18118yescomplemented
139C2×C4—1816no—
140C2×C4—18112no—
141C2×C4—1814no—
142C2×C4D4×D18113yes—
143C2×C4C23×D18113yes—
144C8—1814no—
145C8C23×D18114yescomplemented
146C22—28no—
147C22—424no—
148C22—3628no—
149C22—18124no—
150C22—1814no—
151C22—72464no—
152C22—72424no—
153C22D8×D18114yesdirect product factor
154C22C2×D4×D18113yes—
155C4—1814no—
156C4C2×D4×D18113yes—
157C4C24×D18111yescharacteristic
158C2—48no—
159C2—1818no—
160C2—7248no—
161C2C2×D8×D18116yesdirect product factor
162C2C22×D4×D18111yescharacteristic
subgroupG/H
centerC23D4×D181
commutator, cosocleC4×C181C25
FrattiniC4C24×D181
FittingC22×D8×C181C2
socleC23×C181C2×D4
hypercenterC22×D8D181
hypocenterC181C23×D8
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×D4×D181C2semidirect
2. C22×D1448C2semidirect
3. C22×#15668434C2semidirect
4. C2×D8×D181C2direct (N × H)
5. C22×C8×D181C2semidirect
6. C22×D8×C181C2semidirect
8. C22×D724C22semidirect
11. C2×D4×D181C22semidirect
13. C2×D1448C22semidirect
14. C2×#15668434C22semidirect
15. D8×D181C22direct (N × H)
16. C22×#13089678C22semidirect
17. C2×C8×D181C22semidirect
18. C22×D4×C181C22semidirect
19. C2×D8×C181C22semidirect
20. C22×C8×C181C22semidirect
26. C2×D724C23semidirect
29. D4×D181C23semidirect
33. D1448C23semidirect
34. #15668434C23semidirect
35. C2×#13089678C23semidirect
36. C8×D181C23semidirect
39. C2×D4×C181C23semidirect
41. D8×C181C23semidirect
42. C2×C8×C181C23semidirect
47. C22×D181D8direct (N × H)
50. D724C24semidirect
55. #13089678C24semidirect
60. D4×C181C24semidirect
63. C8×C181C24semidirect
66. C22×C181C2×D8semidirect
71. C2×D181C2×D8direct (N × H)
77. C2×C181C22×D8semidirect
80. D181C22×D8direct (N × H)
81. C181C23×D8semidirect
87. C22×D8D181direct (N × H)
94. C22×D4C2×D181semidirect
99. C2×D8C2×D181direct (N × H)
102. C22×C8C2×D181semidirect
114. C2×D4C22×D181semidirect
121. D8C22×D181direct (N × H)
124. C2×C8C22×D181semidirect
138. D4C23×D181semidirect
145. C8C23×D181semidirect
153. C22D8×D181direct (N × H)
161. C2C2×D8×D181direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D1812
C22×D14482
C22×#156684342
C2×D8×D1812
C22×C8×D1812
C22×D8×C1812
C23×D8181