Finite Group Databasebeta

← C2×D4×#11761640 #31771669

Subgroups — C2×D4×#11761640 #31771669

Order 17216.

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×#11761640C212yesmaximal, complemented
2D4×#11761640C218yesmaximal, direct product factor
3C2×C4⋊#11761640C211yesmaximal, characteristic, complemented
4C2×C22⋊#11761640C212yesmaximal, complemented
5C2×C4×#11761640C211yesmaximal, characteristic, complemented
6C2×D4×D269C211yesmaximal, characteristic
7C22×#11761640—28no—
8C22×#11761640C2211yescharacteristic
9C22×#11761640C2212yes—
10C22×#11761640C2211yescharacteristic
11C22×#11761640C2218yescomplemented
12C4⋊#11761640C2214yescomplemented
13C22⋊#11761640C2218yescomplemented
14C4×#11761640C2214yescomplemented
15C23×D269C2212yes—
16C2×D1076C411yescharacteristic, complemented
17C2×C22⋊D269C412yescomplemented
18D4×D269C414yescomplemented
19D4×D269C2214yes—
20C2×C4×D269C2211yescharacteristic
21C2×D4×C269C411yescharacteristic, complemented
22C2×#11761640—24no—
23C2×#11761640—22no—
24C2×#11761640—216no—
25C2×#11761640D414yesdirect product factor
26C2×#11761640C2312yes—
27C2×#11761640C2314yes—
28C2×#11761640C2312yes—
29C22×D269—24no—
30C22×D269—24no—
31C22×D269C2×C414yescomplemented
32C22×D269C2×C412yescomplemented
33C22×D269C2314yes—
34C22×D269C2311yescharacteristic
35D1076C2×C414yescomplemented
36C22⋊D269C2×C418yescomplemented
37C2×Dic269C2×C411yescharacteristic, complemented
38C4×D269C2×C412yescomplemented
39C4×D269C2312yes—
40C23×C269C2×C412yescomplemented
41D4×C269C2×C414yescomplemented
42C2×C4×C269C2×C411yescharacteristic, complemented
43C22×C269—24no—
44C22×C269C22×C411yescharacteristic
45C22×C269C22×C414yescomplemented
46C2×D269—24no—
47C2×D269—28no—
48C2×D269—24no—
49C2×D269—24no—
50C2×D269C22×C411yescharacteristic
51C2×D269C22×C414yescomplemented
52C2×D269C2×D412yes—
53C2×D269#4112yes—
54C2×D269C2411yescharacteristic
55#11761640—24no—
56#11761640—22no—
57#11761640C2×D414yesdirect product factor
58C4×C269C22×C412yescomplemented
59Dic269C22×C412yescomplemented
60C2×C269—24no—
61C2×C269C4×D412yescomplemented
62C2×C269C23×C411yescharacteristic
63D269—24no—
64D269C4×D412yescomplemented
65D269C22×D411yescharacteristic
66D269C2×#4111yescharacteristic
67C269C2×C4×D411yescharacteristic, complemented, Sylow
68C2×C4×D4—2691nomaximal, Sylow
69C22×D4—2691no—
70C23×C4—2692no—
71C4×D4—2698no—
72C2×C4⋊C4—2691no—
73C2×C22⋊C4—2692no—
74C2×C42—2691no—
75C24—2692no—
76C2×D4—2692no—
77C2×D4—2694no—
78C2×D4—2694no—
79C2×D4—2691no—
80C2×D4#1176164011yescharacteristic, direct product factor
81C22×C4—2691no—
82C22×C4—2691no—
83C22×C4—2691no—
84C22×C4—2692no—
85C22×C4—2698no—
86C22×C4—5388no—
87C4⋊C4—2694no—
88C22⋊C4—2698no—
89C42—2694no—
90C23—2691no—
91C23—2692no—
92C23—2694no—
93C23—2694no—
94C23—5384no—
95C23—5384no—
96C23C2×#1176164012yescomplemented
97D4—2698no—
98D4—2694no—
99D4C2×#1176164014yesdirect product factor
100C2×C4—2692no—
101C2×C4—2694no—
102C2×C4—2691no—
103C2×C4—2692no—
104C2×C4—2692no—
105C2×C4—2692no—
106C2×C4—2694no—
107C2×C4—53816no—
108C2×C4—5384no—
109C2×C4—5382no—
110C2×C4C2×#1176164011yescharacteristic, complemented
111C22—24no—
112C22—2692no—
113C22—2692no—
114C22—2691no—
115C22—2691no—
116C22—2694no—
117C22—5384no—
118C22—5384no—
119C22—5388no—
120C22—5384no—
121C22C22×#1176164011yescharacteristic
122C22C22×#1176164014yescomplemented
123C4—2694no—
124C4—2692no—
125C4—5384no—
126C4—5382no—
127C4C22×#1176164012yescomplemented
128C2—24no—
129C2—2691no—
130C2—2691no—
131C2—2692no—
132C2—5384no—
133C2D4×#1176164012yesdirect product factor
134C2C23×#1176164011yescharacteristic
subgroupG/H
centerC22C22×#11761640
commutatorC2×C269C23×C4
FrattiniC2C23×#11761640
FittingC2×D4×C269C4
socleC22×C269C22×C4
prime radicalC2×D4×D269C2
cosocleC2×D269C24
hypercenterC2×D4#11761640
hypocenterC269C2×C4×D4
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#11761640C2semidirect
2. D4×#11761640C2direct (N × H)
3. C2×C4⋊#11761640C2semidirect
4. C2×C22⋊#11761640C2semidirect
5. C2×C4×#11761640C2semidirect
11. C22×#11761640C22semidirect
12. C4⋊#11761640C22semidirect
13. C22⋊#11761640C22semidirect
14. C4×#11761640C22semidirect
16. C2×D1076C4semidirect
17. C2×C22⋊D269C4semidirect
18. D4×D269C4semidirect
21. C2×D4×C269C4semidirect
25. C2×#11761640D4direct (N × H)
31. C22×D269C2×C4semidirect
32. C22×D269C2×C4semidirect
35. D1076C2×C4semidirect
36. C22⋊D269C2×C4semidirect
37. C2×Dic269C2×C4semidirect
38. C4×D269C2×C4semidirect
40. C23×C269C2×C4semidirect
41. D4×C269C2×C4semidirect
42. C2×C4×C269C2×C4semidirect
45. C22×C269C22×C4semidirect
51. C2×D269C22×C4semidirect
57. #11761640C2×D4direct (N × H)
58. C4×C269C22×C4semidirect
59. Dic269C22×C4semidirect
61. C2×C269C4×D4semidirect
64. D269C4×D4semidirect
67. C269C2×C4×D4semidirect
80. C2×D4#11761640direct (N × H)
96. C23C2×#11761640semidirect
99. D4C2×#11761640direct (N × H)
110. C2×C4C2×#11761640semidirect
122. C22C22×#11761640semidirect
127. C4C22×#11761640semidirect
133. C2D4×#11761640direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117616402
D4×#117616402
C2×C4⋊#117616402
C2×C22⋊#117616402
C2×C4×#117616402
C2×D4×D2692
C2×C4×D4269