Finite Group Databasebeta

← C2×#22627669 #34036959

Subgroups — C2×#22627669 #34036959

Order 18752.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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
1#22627669C2116yesmaximal, direct product factor
2C2×#17989802C212yesmaximal, complemented
3C2×#17989801C214yesmaximal, complemented
4C22×C22⋊D293C214yesmaximal, complemented
5C2×D4×D293C214yesmaximal, complemented
6C22×D4×C293C211yesmaximal, characteristic, complemented
7C23×D293C2214yescomplemented
8#17989802C22116yescomplemented
9#17989801C22132yescomplemented
10C2×Dic586C2212yescomplemented
11C2×D1172C2212yescomplemented
12C2×C22⋊D293C2218yescomplemented
13C2×C22⋊D293C2214yescomplemented
14C2×C22⋊D293C22132yescomplemented
15D4×D293C22132yescomplemented
16C22×Dic293C2214yescomplemented
17C2×C4×D293C2214yescomplemented
18C24×C293C2212yescomplemented
19C2×D4×C293C2214yescomplemented
20C2×D4×C293C2218yescomplemented
21C22×C4×C293C2211yescharacteristic, complemented
22C22×D293—48no—
23C22×D293C2314yes—
24C22×D293C23116yescomplemented
25Dic586C2318yescomplemented
26D1172C2318yescomplemented
27C22⋊D293C23132yescomplemented
28C22⋊D293C23116yescomplemented
29C2×Dic293C2314yes—
30C2×Dic293C23116yescomplemented
31C4×D293C23116yescomplemented
32C23×C293—44no—
33C23×C293C2311yescharacteristic
34C23×C293C2314yes—
35C23×C293C2318yescomplemented
36D4×C293C23116yescomplemented
37C2×C4×C293C2312yes—
38C2×C4×C293C2314yescomplemented
39C22×C293—22no—
40C22×C293—28no—
41C22×C293—48no—
42C22×C293C2412yes—
43C22×C293C2418yes—
44C22×C293C2411yescharacteristic
45C2×D293—28no—
46C2×D293—416no—
47C2×D293C2418yes—
48C4×C293C2414yes—
49Dic293C2418yes—
50C2×C293—28no—
51C2×C293—22no—
52C2×C293H(5,𝔽2)12yescomplemented
53C2×C293C2511yescharacteristic
54D293—28no—
55C293C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
56C2×H(5,𝔽2)—2931nomaximal, Sylow
57H(5,𝔽2)—29316no—
58C2×#41—2934no—
59C2×#41—2932no—
60C22×D4—2934no—
61C22×D4—2934no—
62C22×D4D29311yescharacteristic, complemented
63C24—2934no—
64C24C2×D29312yescomplemented
65#41—29332no—
66#41—29316no—
67C2×Q8—2932no—
68C2×D4—2938no—
69C2×D4—2934no—
70C2×D4—29332no—
71C2×D4—29332no—
72C2×D4—2932no—
73C2×D4C2×D29314yescomplemented
74C2×D4C2×D29318yescomplemented
75C22×C4—2934no—
76C22×C4—2934no—
77C22×C4C2×D29311yescharacteristic, complemented
78C23—44no—
79C23—2934no—
80C23—29316no—
81C23—11728no—
82C23C22×D29314yes—
83C23C22×D29311yescharacteristic
84C23C22×D29318yescomplemented
85Q8—2938no—
86D4—29332no—
87D4—29316no—
88D4—2938no—
89D4C22×D293116yescomplemented
90C2×C4—29316no—
91C2×C4—2934no—
92C2×C4—29316no—
93C2×C4C22×D29312yes—
94C2×C4C22×D29314yescomplemented
95C22—22no—
96C22—28no—
97C22—48no—
98C22—2938no—
99C22—5868no—
100C22—117216no—
101C22C23×D29318yes—
102C22C23×D29312yes—
103C22C23×D29311yescharacteristic
104C4—2938no—
105C4C23×D29314yes—
106C2—22no—
107C2—28no—
108C2—5868no—
109C2#2262766912yesdirect product factor
110C2C24×D29311yescharacteristic
subgroupG/H
centerC22C23×D293
commutator, cosocleC2×C293C25
FrattiniC2C24×D293
FittingC22×D4×C293C2
socleC22×C293C24
hypercenterC22×D4D293
hypocenterC293C2×H(5,𝔽2)
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #22627669C2direct (N × H)
2. C2×#17989802C2semidirect
3. C2×#17989801C2semidirect
4. C22×C22⋊D293C2semidirect
5. C2×D4×D293C2semidirect
6. C22×D4×C293C2semidirect
7. C23×D293C22semidirect
8. #17989802C22semidirect
9. #17989801C22semidirect
10. C2×Dic586C22semidirect
11. C2×D1172C22semidirect
12. C2×C22⋊D293C22semidirect
13. C2×C22⋊D293C22semidirect
14. C2×C22⋊D293C22semidirect
15. D4×D293C22semidirect
16. C22×Dic293C22semidirect
17. C2×C4×D293C22semidirect
18. C24×C293C22semidirect
19. C2×D4×C293C22semidirect
20. C2×D4×C293C22semidirect
21. C22×C4×C293C22semidirect
24. C22×D293C23semidirect
25. Dic586C23semidirect
26. D1172C23semidirect
27. C22⋊D293C23semidirect
28. C22⋊D293C23semidirect
30. C2×Dic293C23semidirect
31. C4×D293C23semidirect
35. C23×C293C23semidirect
36. D4×C293C23semidirect
38. C2×C4×C293C23semidirect
52. C2×C293H(5,𝔽2)semidirect
55. C293C2×H(5,𝔽2)semidirect
62. C22×D4D293semidirect
64. C24C2×D293semidirect
73. C2×D4C2×D293semidirect
74. C2×D4C2×D293semidirect
77. C22×C4C2×D293semidirect
84. C23C22×D293semidirect
89. D4C22×D293semidirect
94. C2×C4C22×D293semidirect
109. C2#22627669direct (N × H)

Maximal subgroups

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

subgroupindex
#226276692
C2×#179898022
C2×#179898012
C22×C22⋊D2932
C2×D4×D2932
C22×D4×C2932
C2×H(5,𝔽2)293