Finite Group Databasebeta

← C2×#535 #3446

Subgroups — C2×#535 #3446

Order 128.

948 conjugacy classes of subgroups; only the 436 normal subgroups are shown.

normal subgroups only

This group has 948 conjugacy classes of subgroups — too many to draw. Only its 436 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×#41C211yesmaximal, characteristic, complemented
2C23×D4C211yesmaximal, characteristic, complemented
3#535C2116yesmaximal, direct product factor
4C2×#127C212yesmaximal, complemented
5C2×#124C212yesmaximal, complemented
6C2×#121C214yesmaximal, complemented
7C2×#120C214yesmaximal, complemented
8C2×#117C211yesmaximal, characteristic, complemented
9C25C2212yes—
10C2×#41—28no—
11C2×#41C2218yescomplemented
12C22×Q8C2211yescharacteristic, complemented
13C22×D4—28no—
14C22×D4C2212yes—
15C22×D4C2212yes—
16C22×D4C2212yes—
17C22×D4C2218yescomplemented
18C22×D4C2211yescharacteristic, complemented
19C22×D4C2218yescomplemented
20C23×C4C2211yescharacteristic
21C23×C4C2212yescomplemented
22#127C22116yescomplemented
23#124C22116yescomplemented
24#121C22132yescomplemented
25#120C22132yescomplemented
26#117C2218yescomplemented
27C2×C4⋊C4C2212yescomplemented
28C2×C22⋊C4C2212yes—
29C2×C22⋊C4C2218yescomplemented
30C2×C42C2212yescomplemented
31C24—28no—
32C24—48no—
33C24C2314yes—
34C24C2312yes—
35C24C2311yescharacteristic
36C24C2318yes—
37#41—232no—
38C2×Q8—24no—
39C2×Q8C2314yescomplemented
40C2×D4—28no—
41C2×D4—28no—
42C2×D4—28no—
43C2×D4—24no—
44C2×D4—232no—
45C2×D4—416no—
46C2×D4C2318yes—
47C2×D4C2318yes—
48C2×D4C2318yes—
49C2×D4C2314yescomplemented
50C2×D4C23132yescomplemented
51C22×C4—28no—
52C22×C4D418yescomplemented
53C22×C4C2314yes—
54C22×C4C2312yes—
55C22×C4C2311yescharacteristic
56C22×C4C2311yescharacteristic
57C22×C4C2314yes—
58C22×C4C2318yescomplemented
59C4⋊C4C2318yescomplemented
60C22⋊C4C2318yes—
61C22⋊C4C23132yescomplemented
62C42C2318yescomplemented
63C23—24no—
64C23—24no—
65C23—216no—
66C23—28no—
67C23—28no—
68C23—216no—
69C23—416no—
70C23—432no—
71C23C2×D414yes—
72C23C2418yes—
73C23C2414yes—
74C23C2412yes—
75C23C2411yescharacteristic
76Q8—28no—
77D4—216no—
78D4—216no—
79D4—216no—
80D4—28no—
81D4—432no—
82C2×C4—24no—
83C2×C4—28no—
84C2×C4—216no—
85C2×C4C2×D414yes—
86C2×C4C2×D414yes—
87C2×C4C2×D4116yescomplemented
88C2×C4C2418yes—
89C2×C4C2414yes—
90C2×C4C2412yes—
91C2×C4C2412yes—
92C22—28no—
93C22—24no—
94C22—24no—
95C22—28no—
96C22—28no—
97C22—216no—
98C22—432no—
99C22—48no—
100C22—416no—
101C22C22×D414yes—
102C22C22×D412yes—
103C22H(5,𝔽2)14yes—
104C22C2511yescharacteristic
105C4—24no—
106C4—28no—
107C4C22×D414yes—
108C4C22×D414yes—
109C2—24no—
110C2—44no—
111C2—48no—
112C2#53514yesdirect product factor
113C2C23×D411yescharacteristic
114C2C2×H(5,𝔽2)12yes—
subgroupG/H
center, socleC23C24
commutator, Frattini, cosocleC22C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#41C2semidirect
2. C23×D4C2semidirect
3. #535C2direct (N × H)
4. C2×#127C2semidirect
5. C2×#124C2semidirect
6. C2×#121C2semidirect
7. C2×#120C2semidirect
8. C2×#117C2semidirect
11. C2×#41C22semidirect
12. C22×Q8C22semidirect
17. C22×D4C22semidirect
18. C22×D4C22semidirect
19. C22×D4C22semidirect
21. C23×C4C22semidirect
22. #127C22semidirect
23. #124C22semidirect
24. #121C22semidirect
25. #120C22semidirect
26. #117C22semidirect
27. C2×C4⋊C4C22semidirect
29. C2×C22⋊C4C22semidirect
30. C2×C42C22semidirect
39. C2×Q8C23semidirect
49. C2×D4C23semidirect
50. C2×D4C23semidirect
52. C22×C4D4semidirect
58. C22×C4C23semidirect
59. C4⋊C4C23semidirect
61. C22⋊C4C23semidirect
62. C42C23semidirect
87. C2×C4C2×D4semidirect
112. C2#535direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#412
C23×D42
#5352
C2×#1272
C2×#1242
C2×#1212
C2×#1202
C2×#1172