Finite Group Databasebeta

← C22×#19153778 #37546891

Subgroups — C22×#19153778 #37546891

Order 23168.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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
1C23×D724C211yesmaximal, characteristic
2C23×C4×D181C212yesmaximal, complemented
3C2×#19153778C2124yesmaximal, direct product factor
4C22×#15668426C212yesmaximal, complemented
5C22×C4×Dic181C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C181C211yesmaximal, characteristic, complemented
7C24×D181C2212yes—
8C22×D724C4116yescomplemented
9C22×D724C22112yes—
10C23×Dic181C2211yescharacteristic
11C23×Dic181C2211yescharacteristic
12C22×C4×D181—216no—
13C22×C4×D181C22124yescomplemented
14#19153778C22164yesdirect product factor
15C2×#15668426C22124yescomplemented
16C2×C4×Dic181C22112yescomplemented
17C23×C4×C181C2212yes—
18C23×C4×C181C2211yescharacteristic
19C2×C4⋊C4×C181C22112yescomplemented
20C23×D181—28no—
21C23×D181—28no—
22C23×D181C2×C4116yescomplemented
23C23×D181C23112yes—
24C2×D724C2×C4196yescomplemented
25C2×D724C23116yes—
26C22×Dic181—24no—
27C22×Dic181D418yescomplemented
28C22×Dic181C2316yes—
29C22×Dic181C2316yes—
30C2×C4×D181—296no—
31C2×C4×D181C23132yescomplemented
32#15668426C23132yescomplemented
33C4×Dic181C23116yescomplemented
34C24×C181C2311yescharacteristic
35C22×C4×C181—28no—
36C22×C4×C181C2×C418yescomplemented
37C22×C4×C181C23112yes—
38C22×C4×C181C2316yes—
39C4⋊C4×C181C23116yescomplemented
40C22×D181—264no—
41C22×D181—224no—
42C22×D181—224no—
43C22×D181C22×C4148yescomplemented
44C22×D181C2418yes—
45D724C22×C4164yescomplemented
46C2×Dic181—212no—
47C2×Dic181C2×D4124yescomplemented
48C2×Dic181C2414yes—
49C2×Dic181C2414yes—
50C4×D181—264no—
51C23×C181C22×C414yes—
52C23×C181C2×D414yes—
53C23×C181#4114yes—
54C23×C181C2413yes—
55C2×C4×C181—224no—
56C2×C4×C181C22×C4124yescomplemented
57C2×C4×C181C2418yes—
58C2×C4×C181C2414yes—
59C22×C181C4×D4116yescomplemented
60C22×C181C23×C416yes—
61C22×C181C22×D416yes—
62C22×C181C2×#4116yes—
63C22×C181C2511yescharacteristic
64C2×D181—296no—
65C2×D181—28no—
66C2×D181—28no—
67C2×D181C23×C4116yescomplemented
68C4×C181—28no—
69C4×C181C23×C418yescomplemented
70Dic181—24no—
71Dic181C22×D418yescomplemented
72C2×C181C2×C4×D4112yescomplemented
73C2×C181C24×C411yescharacteristic
74C2×C181C23×D411yescharacteristic
75C2×C181C22×#4111yescharacteristic
76D181—216no—
77C181C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—1811nomaximal, Sylow
79C23×D4—1811no—
80C24×C4—1812no—
81C2×C4×D4—18124no—
82C22×C4⋊C4D18111yescharacteristic, complemented
83C22×C22⋊C4—1812no—
84C22×C42—1811no—
85C25—1812no—
86C22×D4—18116no—
87C22×D4—18112no—
88C23×C4—36216no—
89C23×C4—1811no—
90C23×C4—18124no—
91C23×C4—1811no—
92C23×C4C2×D18112yes—
93C23×C4C2×D18111yescharacteristic
94C4×D4—18164no—
95C2×C4⋊C4C2×D181112yescomplemented
96C2×C22⋊C4—18124no—
97C2×C42—18112no—
98C24—3628no—
99C24—3628no—
100C24—18116no—
101C24—18112no—
102C24C22×D18111yescharacteristic
103C2×D4—18196no—
104C2×D4—18116no—
105C22×C4—28no—
106C22×C4—36296no—
107C22×C4—3624no—
108C22×C4—1816no—
109C22×C4—18132no—
110C22×C4—1818no—
111C22×C4—1816no—
112C22×C4C4×D18118yescomplemented
113C22×C4C22×D181112yes—
114C22×C4C22×D18116yes—
115C4⋊C4C22×D181116yescomplemented
116C22⋊C4—18132no—
117C42—18116no—
118C23—36264no—
119C23—36224no—
120C23—36224no—
121C23—18148no—
122C23—1818no—
123C23C2×C4×D18114yes—
124C23D4×D18114yes—
125C23#1566845014yes—
126C23C23×D18113yes—
127D4—18164no—
128C2×C4—224no—
129C2×C4—36264no—
130C2×C4—36212no—
131C2×C4—1814no—
132C2×C4—18124no—
133C2×C4—1814no—
134C2×C4C2×C4×D181124yescomplemented
135C2×C4C23×D18118yes—
136C2×C4C23×D18114yes—
137C22—36296no—
138C22—3628no—
139C22—3628no—
140C22—18116no—
141C22#19153778116yesdirect product factor
142C22C22×C4×D18116yes—
143C22C2×D4×D18116yes—
144C22C2×#1566845016yes—
145C22C24×D18111yescharacteristic
146C4—28no—
147C4—3624no—
148C4—1818no—
149C4C22×C4×D18118yescomplemented
150C2—36216no—
151C2C2×#19153778112yesdirect product factor
152C2C23×C4×D18111yescharacteristic
153C2C22×D4×D18111yescharacteristic
154C2C22×#1566845011yescharacteristic
subgroupG/H
centerC24C22×D181
commutatorC2×C181C24×C4
FrattiniC22C24×D181
FittingC22×C4⋊C4×C181C2
socleC24×C181C23
prime radicalC23×D724C2
cosocleC22×C181C25
hypercenterC22×C4⋊C4D181
hypocenterC181C22×C4×D4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D181C2semidirect
3. C2×#19153778C2direct (N × H)
4. C22×#15668426C2semidirect
5. C22×C4×Dic181C2semidirect
6. C22×C4⋊C4×C181C2semidirect
8. C22×D724C4semidirect
13. C22×C4×D181C22semidirect
14. #19153778C22direct (N × H)
15. C2×#15668426C22semidirect
16. C2×C4×Dic181C22semidirect
19. C2×C4⋊C4×C181C22semidirect
22. C23×D181C2×C4semidirect
24. C2×D724C2×C4semidirect
27. C22×Dic181D4semidirect
31. C2×C4×D181C23semidirect
32. #15668426C23semidirect
33. C4×Dic181C23semidirect
36. C22×C4×C181C2×C4semidirect
39. C4⋊C4×C181C23semidirect
43. C22×D181C22×C4semidirect
45. D724C22×C4semidirect
47. C2×Dic181C2×D4semidirect
56. C2×C4×C181C22×C4semidirect
59. C22×C181C4×D4semidirect
67. C2×D181C23×C4semidirect
69. C4×C181C23×C4semidirect
71. Dic181C22×D4semidirect
72. C2×C181C2×C4×D4semidirect
77. C181C22×C4×D4semidirect
82. C22×C4⋊C4D181semidirect
95. C2×C4⋊C4C2×D181semidirect
112. C22×C4C4×D181semidirect
115. C4⋊C4C22×D181semidirect
134. C2×C4C2×C4×D181semidirect
141. C22#19153778direct (N × H)
149. C4C22×C4×D181semidirect
151. C2C2×#19153778direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D7242
C23×C4×D1812
C2×#191537782
C22×#156684262
C22×C4×Dic1812
C22×C4⋊C4×C1812
C22×C4×D4181