Finite Group Databasebeta

← C22×#13063287 #19147765

Subgroups — C22×#13063287 #19147765

Order 5504.

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×D172C211yesmaximal, characteristic
2C23×C4×D43C212yesmaximal, complemented
3C2×#13063287C2124yesmaximal, direct product factor
4C22×(C2×D43)⋊C4C212yesmaximal, complemented
5C22×C4×Dic43C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
7C24×D43C2212yes—
8C22×D172C4116yescomplemented
9C22×D172C22112yes—
10C23×Dic43C2211yescharacteristic
11C23×Dic43C2211yescharacteristic
12C22×C4×D43—216no—
13C22×C4×D43C22124yescomplemented
14#13063287C22164yesdirect product factor
15C2×(C2×D43)⋊C4C22124yescomplemented
16C2×C4×Dic43C22112yescomplemented
17C23×C4×C43C2212yes—
18C23×C4×C43C2211yescharacteristic
19C2×C4⋊C4×C43C22112yescomplemented
20C24×C43C2311yescharacteristic
21C23×D43—28no—
22C23×D43—28no—
23C23×D43C2×C4116yescomplemented
24C23×D43C23112yes—
25C22×C4×C43—28no—
26C22×C4×C43C2×C418yescomplemented
27C22×C4×C43C23112yes—
28C22×C4×C43C2316yes—
29C22×Dic43—24no—
30C22×Dic43D418yescomplemented
31C22×Dic43C2316yes—
32C22×Dic43C2316yes—
33C2×D172C2×C4196yescomplemented
34C2×D172C23116yes—
35C2×C4×D43—296no—
36C2×C4×D43C23132yescomplemented
37C4⋊C4×C43C23116yescomplemented
38(C2×D43)⋊C4C23132yescomplemented
39C4×Dic43C23116yescomplemented
40C23×C43C22×C414yes—
41C23×C43C2×D414yes—
42C23×C43#4114yes—
43C23×C43C2413yes—
44C22×D43—264no—
45C22×D43—224no—
46C22×D43—224no—
47C22×D43C22×C4148yescomplemented
48C22×D43C2418yes—
49C2×C4×C43—224no—
50C2×C4×C43C22×C4124yescomplemented
51C2×C4×C43C2418yes—
52C2×C4×C43C2414yes—
53C2×Dic43—212no—
54C2×Dic43C2×D4124yescomplemented
55C2×Dic43C2414yes—
56C2×Dic43C2414yes—
57D172C22×C4164yescomplemented
58C4×D43—264no—
59C22×C43C4×D4116yescomplemented
60C22×C43C23×C416yes—
61C22×C43C22×D416yes—
62C22×C43C2×#4116yes—
63C22×C43C2511yescharacteristic
64C2×D43—296no—
65C2×D43—28no—
66C2×D43—28no—
67C2×D43C23×C4116yescomplemented
68C4×C43—28no—
69C4×C43C23×C418yescomplemented
70Dic43—24no—
71Dic43C22×D418yescomplemented
72C22×C4×D4—431nomaximal, Sylow
73C2×C43C2×C4×D4112yescomplemented
74C2×C43C24×C411yescharacteristic
75C2×C43C23×D411yescharacteristic
76C2×C43C22×#4111yescharacteristic
77D43—216no—
78C23×D4—431no—
79C24×C4—432no—
80C2×C4×D4—4324no—
81C22×C4⋊C4D4311yescharacteristic, complemented
82C22×C22⋊C4—432no—
83C22×C42—431no—
84C43C22×C4×D411yescharacteristic, complemented, Sylow
85C25—432no—
86C22×D4—4312no—
87C22×D4—4316no—
88C23×C4—431no—
89C23×C4—431no—
90C23×C4—4324no—
91C23×C4—8616no—
92C23×C4C2×D4312yes—
93C23×C4C2×D4311yescharacteristic
94C4×D4—4364no—
95C2×C4⋊C4C2×D43112yescomplemented
96C2×C22⋊C4—4324no—
97C2×C42—4312no—
98C24—4316no—
99C24—4312no—
100C24—868no—
101C24—868no—
102C24C22×D4311yescharacteristic
103C2×D4—4396no—
104C2×D4—4316no—
105C22×C4—28no—
106C22×C4—438no—
107C22×C4—436no—
108C22×C4—436no—
109C22×C4—4332no—
110C22×C4—8696no—
111C22×C4—864no—
112C22×C4C4×D4318yescomplemented
113C22×C4C22×D43112yes—
114C22×C4C22×D4316yes—
115C4⋊C4C22×D43116yescomplemented
116C22⋊C4—4332no—
117C42—4316no—
118C23—4348no—
119C23—438no—
120C23—8664no—
121C23—8624no—
122C23—8624no—
123C23C2×C4×D4314yes—
124C23D4×D4314yes—
125C23#1062190214yes—
126C23C23×D4313yes—
127D4—4364no—
128C2×C4—224no—
129C2×C4—4324no—
130C2×C4—434no—
131C2×C4—434no—
132C2×C4—8664no—
133C2×C4—8612no—
134C2×C4C2×C4×D43124yescomplemented
135C2×C4C23×D4318yes—
136C2×C4C23×D4314yes—
137C22—4316no—
138C22—8696no—
139C22—868no—
140C22—868no—
141C22#13063287116yesdirect product factor
142C22C22×C4×D4316yes—
143C22C2×D4×D4316yes—
144C22C2×#1062190216yes—
145C22C24×D4311yescharacteristic
146C4—28no—
147C4—438no—
148C4—864no—
149C4C22×C4×D4318yescomplemented
150C2—8616no—
151C2C2×#13063287112yesdirect product factor
152C2C23×C4×D4311yescharacteristic
153C2C22×D4×D4311yescharacteristic
154C2C22×#1062190211yescharacteristic
subgroupG/H
centerC24C22×D43
commutatorC2×C43C24×C4
FrattiniC22C24×D43
FittingC22×C4⋊C4×C43C2
socleC24×C43C23
hypercenterC22×C4⋊C4D43
hypocenterC43C22×C4×D4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D43C2semidirect
3. C2×#13063287C2direct (N × H)
4. C22×(C2×D43)⋊C4C2semidirect
5. C22×C4×Dic43C2semidirect
6. C22×C4⋊C4×C43C2semidirect
8. C22×D172C4semidirect
13. C22×C4×D43C22semidirect
14. #13063287C22direct (N × H)
15. C2×(C2×D43)⋊C4C22semidirect
16. C2×C4×Dic43C22semidirect
19. C2×C4⋊C4×C43C22semidirect
23. C23×D43C2×C4semidirect
26. C22×C4×C43C2×C4semidirect
30. C22×Dic43D4semidirect
33. C2×D172C2×C4semidirect
36. C2×C4×D43C23semidirect
37. C4⋊C4×C43C23semidirect
38. (C2×D43)⋊C4C23semidirect
39. C4×Dic43C23semidirect
47. C22×D43C22×C4semidirect
50. C2×C4×C43C22×C4semidirect
54. C2×Dic43C2×D4semidirect
57. D172C22×C4semidirect
59. C22×C43C4×D4semidirect
67. C2×D43C23×C4semidirect
69. C4×C43C23×C4semidirect
71. Dic43C22×D4semidirect
73. C2×C43C2×C4×D4semidirect
81. C22×C4⋊C4D43semidirect
84. C43C22×C4×D4semidirect
95. C2×C4⋊C4C2×D43semidirect
112. C22×C4C4×D43semidirect
115. C4⋊C4C22×D43semidirect
134. C2×C4C2×C4×D43semidirect
141. C22#13063287direct (N × H)
149. C4C22×C4×D43semidirect
151. C2C2×#13063287direct (N × H)