Finite Group Databasebeta

← C2×D4×#11759967 #30657801

Subgroups — C2×D4×#11759967 #30657801

Order 16448.

426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 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×#11759967C212yesmaximal, complemented
2D4×#11759967C218yesmaximal, direct product factor
3C2×C4⋊#11759967C211yesmaximal, characteristic, complemented
4C2×C22⋊#11759967C212yesmaximal, complemented
5C2×C4×#11759967C211yesmaximal, characteristic, complemented
6C2×D4×D257C211yesmaximal, characteristic
7C22×#11759967—28no—
8C22×#11759967C2211yescharacteristic
9C22×#11759967C2212yes—
10C22×#11759967C2211yescharacteristic
11C22×#11759967C2218yescomplemented
12C4⋊#11759967C2214yescomplemented
13C22⋊#11759967C2218yescomplemented
14C4×#11759967C2214yescomplemented
15C23×D257C2212yes—
16C2×D1028C411yescharacteristic, complemented
17C2×C22⋊D257C412yescomplemented
18D4×D257C414yescomplemented
19D4×D257C2214yes—
20C2×C4×D257C2211yescharacteristic
21C2×D4×C257C411yescharacteristic, complemented
22C2×#11759967—24no—
23C2×#11759967—22no—
24C2×#11759967—216no—
25C2×#11759967D414yesdirect product factor
26C2×#11759967C2312yes—
27C2×#11759967C2314yes—
28C2×#11759967C2312yes—
29C22×D257—24no—
30C22×D257—24no—
31C22×D257C2×C414yescomplemented
32C22×D257C2×C412yescomplemented
33C22×D257C2314yes—
34C22×D257C2311yescharacteristic
35D1028C2×C414yescomplemented
36C22⋊D257C2×C418yescomplemented
37C2×Dic257C2×C411yescharacteristic, complemented
38C4×D257C2×C412yescomplemented
39C4×D257C2312yes—
40C23×C257C2×C412yescomplemented
41D4×C257C2×C414yescomplemented
42C2×C4×C257C2×C411yescharacteristic, complemented
43C22×C257—24no—
44C22×C257C22×C411yescharacteristic
45C22×C257C22×C414yescomplemented
46C2×D257—24no—
47C2×D257—28no—
48C2×D257—24no—
49C2×D257—24no—
50C2×D257C22×C411yescharacteristic
51C2×D257C22×C414yescomplemented
52C2×D257C2×D412yes—
53C2×D257#4112yes—
54C2×D257C2411yescharacteristic
55#11759967—24no—
56#11759967—22no—
57#11759967C2×D414yesdirect product factor
58C4×C257C22×C412yescomplemented
59Dic257C22×C412yescomplemented
60C2×C257—24no—
61C2×C257C4×D412yescomplemented
62C2×C257C23×C411yescharacteristic
63D257—24no—
64D257C4×D412yescomplemented
65D257C22×D411yescharacteristic
66D257C2×#4111yescharacteristic
67C257C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—2571nomaximal, Sylow
69C22×D4—2571no—
70C23×C4—2572no—
71C4×D4—2578no—
72C2×C4⋊C4—2571no—
73C2×C22⋊C4—2572no—
74C2×C42—2571no—
75C24—2572no—
76C2×D4—2572no—
77C2×D4—2574no—
78C2×D4—2574no—
79C2×D4—2571no—
80C2×D4#1175996711yescharacteristic, direct product factor
81C22×C4—2571no—
82C22×C4—2571no—
83C22×C4—2571no—
84C22×C4—2572no—
85C22×C4—2578no—
86C22×C4—5148no—
87C4⋊C4—2574no—
88C22⋊C4—2578no—
89C42—2574no—
90C23—2571no—
91C23—2572no—
92C23—2574no—
93C23—2574no—
94C23—5144no—
95C23—5144no—
96C23C2×#1175996712yescomplemented
97D4—2578no—
98D4—2574no—
99D4C2×#1175996714yesdirect product factor
100C2×C4—2572no—
101C2×C4—2574no—
102C2×C4—2571no—
103C2×C4—2572no—
104C2×C4—2572no—
105C2×C4—2572no—
106C2×C4—2574no—
107C2×C4—51416no—
108C2×C4—5144no—
109C2×C4—5142no—
110C2×C4C2×#1175996711yescharacteristic, complemented
111C22—2572no—
112C22—2572no—
113C22—2571no—
114C22—2571no—
115C22—2574no—
116C22—24no—
117C22—5144no—
118C22—5144no—
119C22—5148no—
120C22—5144no—
121C22C22×#1175996711yescharacteristic
122C22C22×#1175996714yescomplemented
123C4—2574no—
124C4—2572no—
125C4—5144no—
126C4—5142no—
127C4C22×#1175996712yescomplemented
128C2—2571no—
129C2—2571no—
130C2—2572no—
131C2—24no—
132C2—5144no—
133C2D4×#1175996712yesdirect product factor
134C2C23×#1175996711yescharacteristic
subgroupG/H
centerC22C22×#11759967
commutatorC2×C257C23×C4
FrattiniC2C23×#11759967
FittingC2×D4×C257C4
socleC22×C257C22×C4
prime radicalC2×D4×D257C2
cosocleC2×D257C24
hypercenterC2×D4#11759967
hypocenterC257C2×C4×D4
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11759967C2semidirect
2. D4×#11759967C2direct (N × H)
3. C2×C4⋊#11759967C2semidirect
4. C2×C22⋊#11759967C2semidirect
5. C2×C4×#11759967C2semidirect
11. C22×#11759967C22semidirect
12. C4⋊#11759967C22semidirect
13. C22⋊#11759967C22semidirect
14. C4×#11759967C22semidirect
16. C2×D1028C4semidirect
17. C2×C22⋊D257C4semidirect
18. D4×D257C4semidirect
21. C2×D4×C257C4semidirect
25. C2×#11759967D4direct (N × H)
31. C22×D257C2×C4semidirect
32. C22×D257C2×C4semidirect
35. D1028C2×C4semidirect
36. C22⋊D257C2×C4semidirect
37. C2×Dic257C2×C4semidirect
38. C4×D257C2×C4semidirect
40. C23×C257C2×C4semidirect
41. D4×C257C2×C4semidirect
42. C2×C4×C257C2×C4semidirect
45. C22×C257C22×C4semidirect
51. C2×D257C22×C4semidirect
57. #11759967C2×D4direct (N × H)
58. C4×C257C22×C4semidirect
59. Dic257C22×C4semidirect
61. C2×C257C4×D4semidirect
64. D257C4×D4semidirect
67. C257C2×C4×D4semidirect
80. C2×D4#11759967direct (N × H)
96. C23C2×#11759967semidirect
99. D4C2×#11759967direct (N × H)
110. C2×C4C2×#11759967semidirect
122. C22C22×#11759967semidirect
127. C4C22×#11759967semidirect
133. C2D4×#11759967direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117599672
D4×#117599672
C2×C4⋊#117599672
C2×C22⋊#117599672
C2×C4×#117599672
C2×D4×D2572
C2×C4×D4257