Finite Group Databasebeta

← C22×C4⋊C4×D43 #19147754

Subgroups — C22×C4⋊C4×D43 #19147754

Order 5504.

2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.

normal subgroups only

This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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×C4×D43C212yesmaximal
2C23×C4×D43C211yesmaximal, characteristic
3C22×C4⋊Dic43C211yesmaximal, characteristic, complemented
4C22×Dic43⋊C4C212yesmaximal, complemented
5C2×C4⋊C4×D43C2124yesmaximal, direct product factor
6C22×C4⋊C4×C43C211yesmaximal, characteristic, complemented
7C24×D43C2211yescharacteristic
8C23×Dic43C2212yes—
9C23×Dic43C2211yescharacteristic
10C22×C4×D43—216no—
11C22×C4×D43C4116yescomplemented
12C22×C4×D43C22124yes—
13C22×C4×D43C22112yes—
14C2×C4⋊Dic43C22112yescomplemented
15C2×Dic43⋊C4C22124yescomplemented
16C4⋊C4×D43C22164yesdirect product factor
17C23×C4×C43C2212yes—
18C23×C4×C43C2211yescharacteristic
19C2×C4⋊C4×C43C22112yescomplemented
20C24×C43C2311yescharacteristic
21C23×D43C2×C418yes—
22C23×D43D418yes—
23C23×D43Q818yes—
24C23×D43C2316yes—
25C22×C4×C43—28no—
26C22×C4×C43C2×C418yescomplemented
27C22×C4×C43C23112yes—
28C22×C4×C43C2316yes—
29C22×Dic43—28no—
30C22×Dic43C2×C418yescomplemented
31C22×Dic43C23112yes—
32C22×Dic43C2316yes—
33C2×C4×D43—296no—
34C2×C4×D43C2×C4196yescomplemented
35C2×C4×D43C23132yes—
36C2×C4×D43C23116yes—
37C4⋊C4×C43C23116yescomplemented
38C4⋊Dic43C23116yescomplemented
39Dic43⋊C4C23132yescomplemented
40C23×C43C22×C414yes—
41C23×C43C2×D414yes—
42C23×C43C2×Q814yes—
43C23×C43C2413yes—
44C22×D43C4⋊C4164yesdirect product factor
45C22×D43C22×C4124yes—
46C22×D43C2×D4124yes—
47C22×D43C2×Q8124yes—
48C22×D43C2414yes—
49C2×C4×C43—224no—
50C2×C4×C43C22×C4124yescomplemented
51C2×C4×C43C2418yes—
52C2×C4×C43C2414yes—
53C2×Dic43—224no—
54C2×Dic43C22×C4124yescomplemented
55C2×Dic43C2418yes—
56C2×Dic43C2414yes—
57C4×D43—264no—
58C4×D43C22×C4164yescomplemented
59C22×C43C2×C4⋊C4116yescomplemented
60C22×C43C23×C416yes—
61C22×C43C22×D416yes—
62C22×C43C22×Q816yes—
63C22×C43C2511yescharacteristic
64C2×D43C2×C4⋊C4196yesdirect product factor
65C2×D43C23×C418yes—
66C2×D43C22×D418yes—
67C2×D43C22×Q818yes—
68C4×C43—28no—
69C4×C43C23×C418yescomplemented
70Dic43—28no—
71Dic43C23×C418yescomplemented
72C23×C4⋊C4—431nomaximal, Sylow
73C2×C43C22×C4⋊C4112yescomplemented
74C2×C43C24×C411yescharacteristic
75C2×C43C23×D411yescharacteristic
76C2×C43C23×Q811yescharacteristic
77D43C22×C4⋊C4116yesdirect product factor
78C24×C4—431no—
79C24×C4—432no—
80C22×C4⋊C4—432no—
81C22×C4⋊C4—431no—
82C22×C4⋊C4—4324no—
83C22×C4⋊C4D4311yescharacteristic, direct product factor
84C43C23×C4⋊C411yescharacteristic, complemented, Sylow
85C25—431no—
86C23×C4—431no—
87C23×C4—4312no—
88C23×C4—4316no—
89C23×C4—432no—
90C23×C4—4324no—
91C23×C4—8616no—
92C23×C4C2×D4312yes—
93C23×C4C2×D4311yescharacteristic
94C2×C4⋊C4—4324no—
95C2×C4⋊C4—4312no—
96C2×C4⋊C4—4364no—
97C2×C4⋊C4C2×D43112yesdirect product factor
98C24—438no—
99C24—438no—
100C24—438no—
101C24—436no—
102C24C22×D4311yescharacteristic
103C22×C4—28no—
104C22×C4—438no—
105C22×C4—436no—
106C22×C4—4396no—
107C22×C4—4316no—
108C22×C4—4312no—
109C22×C4—4332no—
110C22×C4—8696no—
111C22×C4—868no—
112C22×C4C4×D4318yescomplemented
113C22×C4C22×D43112yes—
114C22×C4C22×D4316yes—
115C4⋊C4—4332no—
116C4⋊C4—4316no—
117C4⋊C4C22×D43116yesdirect product factor
118C23—4364no—
119C23—4324no—
120C23—4324no—
121C23—4324no—
122C23—434no—
123C23C2×C4×D4314yes—
124C23D4×D4314yes—
125C23Q8×D4314yes—
126C23C23×D4313yes—
127C2×C4—224no—
128C2×C4—4324no—
129C2×C4—434no—
130C2×C4—4364no—
131C2×C4—438no—
132C2×C4—8664no—
133C2×C4—8624no—
134C2×C4C2×C4×D43124yescomplemented
135C2×C4C23×D4318yes—
136C2×C4C23×D4314yes—
137C22—4396no—
138C22—438no—
139C22—438no—
140C22—438no—
141C22C4⋊C4×D43116yesdirect product factor
142C22C22×C4×D4316yes—
143C22C2×D4×D4316yes—
144C22C2×Q8×D4316yes—
145C22C24×D4311yescharacteristic
146C4—28no—
147C4—438no—
148C4—868no—
149C4C22×C4×D4318yescomplemented
150C2—4316no—
151C2C2×C4⋊C4×D43112yesdirect product factor
152C2C23×C4×D4311yescharacteristic
153C2C22×D4×D4311yescharacteristic
154C2C22×Q8×D4311yescharacteristic
subgroupG/H
centerC24C22×D43
commutatorC2×C43C24×C4
FrattiniC22C24×D43
FittingC22×C4⋊C4×C43C2
socleC24×C43C23
hypercenterC22×C4⋊C4D43
hypocenterC43C23×C4⋊C4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic43C2semidirect
4. C22×Dic43⋊C4C2semidirect
5. C2×C4⋊C4×D43C2direct (N × H)
6. C22×C4⋊C4×C43C2semidirect
11. C22×C4×D43C4semidirect
14. C2×C4⋊Dic43C22semidirect
15. C2×Dic43⋊C4C22semidirect
16. C4⋊C4×D43C22direct (N × H)
19. C2×C4⋊C4×C43C22semidirect
26. C22×C4×C43C2×C4semidirect
30. C22×Dic43C2×C4semidirect
34. C2×C4×D43C2×C4semidirect
37. C4⋊C4×C43C23semidirect
38. C4⋊Dic43C23semidirect
39. Dic43⋊C4C23semidirect
44. C22×D43C4⋊C4direct (N × H)
50. C2×C4×C43C22×C4semidirect
54. C2×Dic43C22×C4semidirect
58. C4×D43C22×C4semidirect
59. C22×C43C2×C4⋊C4semidirect
64. C2×D43C2×C4⋊C4direct (N × H)
69. C4×C43C23×C4semidirect
71. Dic43C23×C4semidirect
73. C2×C43C22×C4⋊C4semidirect
77. D43C22×C4⋊C4direct (N × H)
83. C22×C4⋊C4D43direct (N × H)
84. C43C23×C4⋊C4semidirect
97. C2×C4⋊C4C2×D43direct (N × H)
112. C22×C4C4×D43semidirect
117. C4⋊C4C22×D43direct (N × H)
134. C2×C4C2×C4×D43semidirect
141. C22C4⋊C4×D43direct (N × H)
149. C4C22×C4×D43semidirect
151. C2C2×C4⋊C4×D43direct (N × H)