Finite Group Databasebeta

← C22×C4⋊C4×D103 #27208303

Subgroups — C22×C4⋊C4×D103 #27208303

Order 13184.

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×D103C212yesmaximal
2C23×C4×D103C211yesmaximal, characteristic
3C22×C4⋊Dic103C211yesmaximal, characteristic, complemented
4C22×Dic103⋊C4C212yesmaximal, complemented
5C2×C4⋊C4×D103C2124yesmaximal, direct product factor
6C22×C4⋊C4×C103C211yesmaximal, characteristic, complemented
7C24×D103C2211yescharacteristic
8C23×Dic103C2212yes—
9C23×Dic103C2211yescharacteristic
10C22×C4×D103—216no—
11C22×C4×D103C4116yescomplemented
12C22×C4×D103C22124yes—
13C22×C4×D103C22112yes—
14C2×C4⋊Dic103C22112yescomplemented
15C2×Dic103⋊C4C22124yescomplemented
16C4⋊C4×D103C22164yesdirect product factor
17C23×C4×C103C2212yes—
18C23×C4×C103C2211yescharacteristic
19C2×C4⋊C4×C103C22112yescomplemented
20C23×D103C2×C418yes—
21C23×D103D418yes—
22C23×D103Q818yes—
23C23×D103C2316yes—
24C22×Dic103—28no—
25C22×Dic103C2×C418yescomplemented
26C22×Dic103C23112yes—
27C22×Dic103C2316yes—
28C2×C4×D103—296no—
29C2×C4×D103C2×C4196yescomplemented
30C2×C4×D103C23132yes—
31C2×C4×D103C23116yes—
32C4⋊Dic103C23116yescomplemented
33Dic103⋊C4C23132yescomplemented
34C24×C103C2311yescharacteristic
35C22×C4×C103—28no—
36C22×C4×C103C2×C418yescomplemented
37C22×C4×C103C23112yes—
38C22×C4×C103C2316yes—
39C4⋊C4×C103C23116yescomplemented
40C23×C103C22×C414yes—
41C23×C103C2×D414yes—
42C23×C103C2×Q814yes—
43C23×C103C2413yes—
44C22×D103C4⋊C4164yesdirect product factor
45C22×D103C22×C4124yes—
46C22×D103C2×D4124yes—
47C22×D103C2×Q8124yes—
48C22×D103C2414yes—
49C2×C4×C103—224no—
50C2×C4×C103C22×C4124yescomplemented
51C2×C4×C103C2418yes—
52C2×C4×C103C2414yes—
53C2×Dic103—224no—
54C2×Dic103C22×C4124yescomplemented
55C2×Dic103C2418yes—
56C2×Dic103C2414yes—
57C4×D103—264no—
58C4×D103C22×C4164yescomplemented
59C22×C103C2×C4⋊C4116yescomplemented
60C22×C103C23×C416yes—
61C22×C103C22×D416yes—
62C22×C103C22×Q816yes—
63C22×C103C2511yescharacteristic
64C2×D103C2×C4⋊C4196yesdirect product factor
65C2×D103C23×C418yes—
66C2×D103C22×D418yes—
67C2×D103C22×Q818yes—
68C4×C103—28no—
69C4×C103C23×C418yescomplemented
70Dic103—28no—
71Dic103C23×C418yescomplemented
72C2×C103C22×C4⋊C4112yescomplemented
73C2×C103C24×C411yescharacteristic
74C2×C103C23×D411yescharacteristic
75C2×C103C23×Q811yescharacteristic
76D103C22×C4⋊C4116yesdirect product factor
77C23×C4⋊C4—1031nomaximal, Sylow
78C103C23×C4⋊C411yescharacteristic, complemented, Sylow
79C24×C4—1031no—
80C24×C4—1032no—
81C22×C4⋊C4—1032no—
82C22×C4⋊C4—1031no—
83C22×C4⋊C4—10324no—
84C22×C4⋊C4D10311yescharacteristic, direct product factor
85C25—1031no—
86C23×C4—1031no—
87C23×C4—10316no—
88C23×C4—10312no—
89C23×C4—1032no—
90C23×C4—10324no—
91C23×C4—20616no—
92C23×C4C2×D10312yes—
93C23×C4C2×D10311yescharacteristic
94C2×C4⋊C4—10324no—
95C2×C4⋊C4—10312no—
96C2×C4⋊C4—10364no—
97C2×C4⋊C4C2×D103112yesdirect product factor
98C24—1038no—
99C24—1038no—
100C24—1038no—
101C24—1036no—
102C24C22×D10311yescharacteristic
103C22×C4—28no—
104C22×C4—1038no—
105C22×C4—1036no—
106C22×C4—10396no—
107C22×C4—10316no—
108C22×C4—10312no—
109C22×C4—10332no—
110C22×C4—20696no—
111C22×C4—2068no—
112C22×C4C4×D10318yescomplemented
113C22×C4C22×D103112yes—
114C22×C4C22×D10316yes—
115C4⋊C4—10332no—
116C4⋊C4—10316no—
117C4⋊C4C22×D103116yesdirect product factor
118C23—10324no—
119C23—10324no—
120C23—1034no—
121C23—10364no—
122C23—10324no—
123C23C2×C4×D10314yes—
124C23D4×D10314yes—
125C23Q8×D10314yes—
126C23C23×D10313yes—
127C2×C4—224no—
128C2×C4—1034no—
129C2×C4—10324no—
130C2×C4—10364no—
131C2×C4—1038no—
132C2×C4—20664no—
133C2×C4—20624no—
134C2×C4C2×C4×D103124yescomplemented
135C2×C4C23×D10318yes—
136C2×C4C23×D10314yes—
137C22—1038no—
138C22—1038no—
139C22—1038no—
140C22—10396no—
141C22C4⋊C4×D103116yesdirect product factor
142C22C22×C4×D10316yes—
143C22C2×D4×D10316yes—
144C22C2×Q8×D10316yes—
145C22C24×D10311yescharacteristic
146C4—28no—
147C4—1038no—
148C4—2068no—
149C4C22×C4×D10318yescomplemented
150C2—10316no—
151C2C2×C4⋊C4×D103112yesdirect product factor
152C2C23×C4×D10311yescharacteristic
153C2C22×D4×D10311yescharacteristic
154C2C22×Q8×D10311yescharacteristic
subgroupG/H
centerC24C22×D103
commutatorC2×C103C24×C4
FrattiniC22C24×D103
FittingC22×C4⋊C4×C103C2
socleC24×C103C23
prime radicalC24×D103C22
cosocleC22×C103C25
hypercenterC22×C4⋊C4D103
hypocenterC103C23×C4⋊C4
LCSG ▷ C2×C103 ▷ C103
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic103C2semidirect
4. C22×Dic103⋊C4C2semidirect
5. C2×C4⋊C4×D103C2direct (N × H)
6. C22×C4⋊C4×C103C2semidirect
11. C22×C4×D103C4semidirect
14. C2×C4⋊Dic103C22semidirect
15. C2×Dic103⋊C4C22semidirect
16. C4⋊C4×D103C22direct (N × H)
19. C2×C4⋊C4×C103C22semidirect
25. C22×Dic103C2×C4semidirect
29. C2×C4×D103C2×C4semidirect
32. C4⋊Dic103C23semidirect
33. Dic103⋊C4C23semidirect
36. C22×C4×C103C2×C4semidirect
39. C4⋊C4×C103C23semidirect
44. C22×D103C4⋊C4direct (N × H)
50. C2×C4×C103C22×C4semidirect
54. C2×Dic103C22×C4semidirect
58. C4×D103C22×C4semidirect
59. C22×C103C2×C4⋊C4semidirect
64. C2×D103C2×C4⋊C4direct (N × H)
69. C4×C103C23×C4semidirect
71. Dic103C23×C4semidirect
72. C2×C103C22×C4⋊C4semidirect
76. D103C22×C4⋊C4direct (N × H)
78. C103C23×C4⋊C4semidirect
84. C22×C4⋊C4D103direct (N × H)
97. C2×C4⋊C4C2×D103direct (N × H)
112. C22×C4C4×D103semidirect
117. C4⋊C4C22×D103direct (N × H)
134. C2×C4C2×C4×D103semidirect
141. C22C4⋊C4×D103direct (N × H)
149. C4C22×C4×D103semidirect
151. C2C2×C4⋊C4×D103direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4×D1032
C22×C4⋊Dic1032
C22×Dic103⋊C42
C2×C4⋊C4×D1032
C22×C4⋊C4×C1032
C23×C4⋊C4103