Finite Group Databasebeta

← C22×C3×#1141 #13061140

Subgroups — C22×C3×#1141 #13061140

Order 1344.

676 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 254 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×C3×C7×D4C211yesmaximal, characteristic, complemented
2C22×C3×D28C211yesmaximal, characteristic, complemented
3C2×C3×#1141C2112yesmaximal, direct product factor
4C22×C3×C7⋊C8C211yesmaximal, characteristic, complemented
5C22×#1141C311yesmaximal, characteristic, direct product factor, Hall
6C24×C3×C7—21no—
7C23×C3×D7—21no—
8C2×C3×C7×D4—23no—
9C2×C3×C7×D4C2216yescomplemented
10C22×C3×C4×C7C2211yescharacteristic
11C2×C3×D28—23no—
12C2×C3×D28C2216yescomplemented
13C3×#1141C22116yesdirect product factor
14C2×C3×C7⋊C8C2216yescomplemented
15C22×C7×D4C2×C311yescharacteristic, complemented
16C22×D28C2×C311yescharacteristic, complemented
17C2×#1141C2×C3112yesdirect product factor
18C22×C7⋊C8C2×C311yescharacteristic, complemented
19C22×C3×D8—71nomaximal, Hall
20C23×C3×C7—26no—
21C23×C3×C7—44no—
22C23×C3×C7D411yescharacteristic
23C22×C3×D7—26no—
24C22×C3×D7—44no—
25C3×C7×D4—26no—
26C3×C7×D4C2314yescomplemented
27C2×C3×C4×C7D413yes—
28C2×C3×C4×C7C2313yes—
29C3×D28—26no—
30C3×D28C2314yescomplemented
31C3×C7⋊C8C2314yescomplemented
32C24×C7—21no—
33C23×D7—21no—
34C2×C7×D4—23no—
35C2×C7×D4C22×C316yescomplemented
36C22×C4×C7C22×C311yescharacteristic
37C2×D28—23no—
38C2×D28C22×C316yescomplemented
39#1141C22×C3116yesdirect product factor
40C2×C7⋊C8C22×C316yescomplemented
41C22×C3×D4—71no—
42C22×C3×D4D711yescharacteristic, complemented
43C2×C3×D8—712no—
44C22×C3×C8—71no—
45C22×C3×C7—24no—
46C22×C3×C7—412no—
47C22×C3×C7D814yescomplemented
48C22×C3×C7C2×D413yes—
49C2×C3×D7—24no—
50C2×C3×D7—412no—
51C3×C4×C7C2×D413yes—
52C3×C4×C7C2411yescharacteristic
53C22×D8—71noSylow
54C23×C7—26no—
55C23×C7—44no—
56C23×C7C3×D411yescharacteristic
57C22×D7—26no—
58C22×D7—44no—
59C7×D4—26no—
60C7×D4C23×C314yescomplemented
61C2×C4×C7C3×D413yes—
62C2×C4×C7C23×C313yes—
63D28—26no—
64D28C23×C314yescomplemented
65C7⋊C8C23×C314yescomplemented
66C24×C3—21no—
67C24×C3—141no—
68C2×C3×D4—23no—
69C2×C3×D4—76no—
70C2×C3×D4—143no—
71C2×C3×D4C2×D716yescomplemented
72C22×C3×C4C2×D711yescharacteristic
73C3×D8—716no—
74C2×C3×C8—76no—
75C2×C3×C7—44no—
76C2×C3×C7C2×D816yescomplemented
77C2×C3×C7C22×D411yescharacteristic
78C3×D7—44no—
79C22×D4—71no—
80C22×D4C3×D711yescharacteristic, complemented
81C2×D8—712no—
82C22×C8—71no—
83C22×C7—24no—
84C22×C7—412no—
85C22×C7C3×D814yescomplemented
86C22×C7C2×C3×D413yes—
87C2×D7—24no—
88C2×D7—412no—
89C4×C7C2×C3×D413yes—
90C4×C7C24×C311yescharacteristic
91C23×C3—26no—
92C23×C3—44no—
93C23×C3—146no—
94C23×C3—284no—
95C23×C3C22⋊D711yescharacteristic
96C3×D4—26no—
97C3×D4—74no—
98C3×D4—146no—
99C3×D4C22×D714yescomplemented
100C2×C3×C4C22⋊D713yes—
101C2×C3×C4C22×D713yes—
102C3×C8—74no—
103C3×C7C22×D811yescharacteristic, complemented, Hall
104C24—21no—
105C24—141no—
106C2×D4—23no—
107C2×D4—76no—
108C2×D4—143no—
109C2×D4C2×C3×D716yescomplemented
110C22×C4C2×C3×D711yescharacteristic
111D8—716no—
112C2×C8—76no—
113C2×C7—44no—
114C2×C7C2×C3×D816yescomplemented
115C2×C7C22×C3×D411yescharacteristic
116D7—44no—
117C22×C3—24no—
118C22×C3—412no—
119C22×C3—144no—
120C22×C3—2812no—
121C22×C3#114114yesdirect product factor
122C22×C3C2×C22⋊D713yes—
123C3×C4C2×C22⋊D713yes—
124C3×C4C23×D711yescharacteristic
125C23—26no—
126C23—44no—
127C23—146no—
128C23—284no—
129C23C3×C22⋊D711yescharacteristic
130D4—26no—
131D4—74no—
132D4—146no—
133D4C22×C3×D714yescomplemented
134C2×C4C3×C22⋊D713yes—
135C2×C4C22×C3×D713yes—
136C8—74no—
137C7C22×C3×D811yescharacteristic, complemented, Sylow
138C2×C3—44no—
139C2×C3—284no—
140C2×C3C2×#114116yesdirect product factor
141C2×C3C22×C22⋊D711yescharacteristic
142C22—24no—
143C22—412no—
144C22—144no—
145C22—2812no—
146C22C3×#114114yesdirect product factor
147C22C2×C3×C22⋊D713yes—
148C4C2×C3×C22⋊D713yes—
149C4C23×C3×D711yescharacteristic
150C3C22×#114111yescharacteristic, direct product factor, Sylow
151C2—44no—
152C2—284no—
153C2C2×C3×#114116yesdirect product factor
154C2C22×C3×C22⋊D711yescharacteristic
subgroupG/H
centerC23×C3C22⋊D7
commutator, cosocleC4×C7C24×C3
FrattiniC4C23×C3×D7
FittingC22×C3×C7×D4C2
socleC23×C3×C7D4
hypercenterC22×C3×D4D7
hypocenterC7C22×C3×D8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C7×D4C2semidirect
2. C22×C3×D28C2semidirect
3. C2×C3×#1141C2direct (N × H)
4. C22×C3×C7⋊C8C2semidirect
5. C22×#1141C3direct (N × H)
9. C2×C3×C7×D4C22semidirect
12. C2×C3×D28C22semidirect
13. C3×#1141C22direct (N × H)
14. C2×C3×C7⋊C8C22semidirect
15. C22×C7×D4C2×C3semidirect
16. C22×D28C2×C3semidirect
17. C2×#1141C2×C3direct (N × H)
18. C22×C7⋊C8C2×C3semidirect
26. C3×C7×D4C23semidirect
30. C3×D28C23semidirect
31. C3×C7⋊C8C23semidirect
35. C2×C7×D4C22×C3semidirect
38. C2×D28C22×C3semidirect
39. #1141C22×C3direct (N × H)
40. C2×C7⋊C8C22×C3semidirect
42. C22×C3×D4D7semidirect
47. C22×C3×C7D8semidirect
60. C7×D4C23×C3semidirect
64. D28C23×C3semidirect
65. C7⋊C8C23×C3semidirect
71. C2×C3×D4C2×D7semidirect
76. C2×C3×C7C2×D8semidirect
80. C22×D4C3×D7semidirect
85. C22×C7C3×D8semidirect
99. C3×D4C22×D7semidirect
103. C3×C7C22×D8semidirect
109. C2×D4C2×C3×D7semidirect
114. C2×C7C2×C3×D8semidirect
121. C22×C3#1141direct (N × H)
133. D4C22×C3×D7semidirect
137. C7C22×C3×D8semidirect
140. C2×C3C2×#1141direct (N × H)
146. C22C3×#1141direct (N × H)
150. C3C22×#1141direct (N × H)
153. C2C2×C3×#1141direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C7×D42
C22×C3×D282
C2×C3×#11412
C22×C3×C7⋊C82
C22×#11413
C22×C3×D87