Finite Group Databasebeta

← C2×D4×#595 #11763873

Subgroups — C2×D4×#595 #11763873

Order 1088.

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×#595C212yesmaximal, complemented
2C2×D4×D17C211yesmaximal, characteristic
3C2×C22⋊#595C212yesmaximal, complemented
4D4×#595C218yesmaximal, direct product factor
5C2×C4⋊#595C211yesmaximal, characteristic, complemented
6C2×C4×#595C211yesmaximal, characteristic, complemented
7C23×D17C2212yes—
8C22×#595—28no—
9C22×#595C2211yescharacteristic
10C22×#595C2212yes—
11C22×#595C2211yescharacteristic
12C22×#595C2218yescomplemented
13C2×D4×C17C411yescharacteristic, complemented
14C2×C22⋊D17C412yescomplemented
15D4×D17C414yescomplemented
16D4×D17C2214yes—
17C2×D68C411yescharacteristic, complemented
18C2×C4×D17C2211yescharacteristic
19C22⋊#595C2218yescomplemented
20C4⋊#595C2214yescomplemented
21C4×#595C2214yescomplemented
22C23×C17C2×C412yescomplemented
23C22×D17—24no—
24C22×D17—24no—
25C22×D17C2×C414yescomplemented
26C22×D17C2×C412yescomplemented
27C22×D17C2314yes—
28C22×D17C2311yescharacteristic
29C2×#595—24no—
30C2×#595—22no—
31C2×#595—216no—
32C2×#595D414yesdirect product factor
33C2×#595C2312yes—
34C2×#595C2314yes—
35C2×#595C2312yes—
36D4×C17C2×C414yescomplemented
37C2×C4×C17C2×C411yescharacteristic, complemented
38C22⋊D17C2×C418yescomplemented
39C2×Dic17C2×C411yescharacteristic, complemented
40D68C2×C414yescomplemented
41C4×D17C2×C412yescomplemented
42C4×D17C2312yes—
43C22×C17—24no—
44C22×C17C22×C411yescharacteristic
45C22×C17C22×C414yescomplemented
46C2×D17—24no—
47C2×D17—28no—
48C2×D17—24no—
49C2×D17—24no—
50C2×D17C22×C411yescharacteristic
51C2×D17C22×C414yescomplemented
52C2×D17C2×D412yes—
53C2×D17#4112yes—
54C2×D17C2411yescharacteristic
55#595—24no—
56#595—22no—
57#595C2×D414yesdirect product factor
58C4×C17C22×C412yescomplemented
59Dic17C22×C412yescomplemented
60C2×C4×D4—171nomaximal, Sylow
61C2×C17—24no—
62C2×C17C4×D412yescomplemented
63C2×C17C23×C411yescharacteristic
64D17—24no—
65D17C4×D412yescomplemented
66D17C22×D411yescharacteristic
67D17C2×#4111yescharacteristic
68C22×D4—171no—
69C23×C4—172no—
70C4×D4—178no—
71C2×C4⋊C4—171no—
72C2×C22⋊C4—172no—
73C2×C42—171no—
74C17C2×C4×D411yescharacteristic, complemented, Sylow
75C24—172no—
76C2×D4—172no—
77C2×D4—174no—
78C2×D4—174no—
79C2×D4—171no—
80C2×D4#59511yescharacteristic, direct product factor
81C22×C4—171no—
82C22×C4—171no—
83C22×C4—171no—
84C22×C4—172no—
85C22×C4—178no—
86C22×C4—348no—
87C4⋊C4—174no—
88C22⋊C4—178no—
89C42—174no—
90C23—171no—
91C23—172no—
92C23—174no—
93C23—174no—
94C23—344no—
95C23—344no—
96C23C2×#59512yescomplemented
97D4—178no—
98D4—174no—
99D4C2×#59514yesdirect product factor
100C2×C4—172no—
101C2×C4—174no—
102C2×C4—171no—
103C2×C4—172no—
104C2×C4—172no—
105C2×C4—172no—
106C2×C4—174no—
107C2×C4—3416no—
108C2×C4—344no—
109C2×C4—342no—
110C2×C4C2×#59511yescharacteristic, complemented
111C22—24no—
112C22—172no—
113C22—172no—
114C22—171no—
115C22—171no—
116C22—174no—
117C22—344no—
118C22—344no—
119C22—348no—
120C22—344no—
121C22C22×#59511yescharacteristic
122C22C22×#59514yescomplemented
123C4—174no—
124C4—172no—
125C4—344no—
126C4—342no—
127C4C22×#59512yescomplemented
128C2—24no—
129C2—171no—
130C2—171no—
131C2—172no—
132C2—344no—
133C2D4×#59512yesdirect product factor
134C2C23×#59511yescharacteristic
subgroupG/H
centerC22C22×#595
commutatorC2×C17C23×C4
FrattiniC2C23×#595
FittingC2×D4×C17C4
socleC22×C17C22×C4
prime radicalC2×D4×D17C2
cosocleC2×D17C24
hypercenterC2×D4#595
hypocenterC17C2×C4×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#595C2semidirect
3. C2×C22⋊#595C2semidirect
4. D4×#595C2direct (N × H)
5. C2×C4⋊#595C2semidirect
6. C2×C4×#595C2semidirect
12. C22×#595C22semidirect
13. C2×D4×C17C4semidirect
14. C2×C22⋊D17C4semidirect
15. D4×D17C4semidirect
17. C2×D68C4semidirect
19. C22⋊#595C22semidirect
20. C4⋊#595C22semidirect
21. C4×#595C22semidirect
22. C23×C17C2×C4semidirect
25. C22×D17C2×C4semidirect
26. C22×D17C2×C4semidirect
32. C2×#595D4direct (N × H)
36. D4×C17C2×C4semidirect
37. C2×C4×C17C2×C4semidirect
38. C22⋊D17C2×C4semidirect
39. C2×Dic17C2×C4semidirect
40. D68C2×C4semidirect
41. C4×D17C2×C4semidirect
45. C22×C17C22×C4semidirect
51. C2×D17C22×C4semidirect
57. #595C2×D4direct (N × H)
58. C4×C17C22×C4semidirect
59. Dic17C22×C4semidirect
62. C2×C17C4×D4semidirect
65. D17C4×D4semidirect
74. C17C2×C4×D4semidirect
80. C2×D4#595direct (N × H)
96. C23C2×#595semidirect
99. D4C2×#595direct (N × H)
110. C2×C4C2×#595semidirect
122. C22C22×#595semidirect
127. C4C22×#595semidirect
133. C2D4×#595direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5952
C2×D4×D172
C2×C22⋊#5952
D4×#5952
C2×C4⋊#5952
C2×C4×#5952
C2×C4×D417