Finite Group Databasebeta

← C2×#15692996 #20268284

Subgroups — C2×#15692996 #20268284

Order 6592.

426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 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×D412C212yesmaximal, complemented
2C22×D412C211yesmaximal, characteristic, complemented
3C22×C4×D103C211yesmaximal, characteristic, complemented
4#15692996C218yesmaximal, direct product factor
5C2×(C2×D103)⋊C4C212yesmaximal, complemented
6C2×C4⋊C4×C103C211yesmaximal, characteristic, complemented
7C23×D103C2212yes—
8C23×D103C2211yescharacteristic
9C2×D412—28no—
10C2×D412—24no—
11C2×D412C2218yescomplemented
12C2×D412C2214yescomplemented
13C22×Dic103C2211yescharacteristic
14C2×C4×D103—24no—
15C2×C4×D103C2214yescomplemented
16(C2×D103)⋊C4C2218yescomplemented
17C22×C4×C103C2212yes—
18C22×C4×C103C2211yescharacteristic
19C4⋊C4×C103C2214yescomplemented
20C23×C103C2311yescharacteristic
21C22×D103—22no—
22C22×D103—22no—
23C22×D103—24no—
24C22×D103—24no—
25C22×D103—24no—
26C22×D103D414yescomplemented
27C22×D103C2314yes—
28C22×D103C2312yes—
29C2×C4×C103—24no—
30C2×C4×C103D414yescomplemented
31C2×C4×C103C2314yes—
32C2×C4×C103C2312yes—
33C2×Dic103—22no—
34C2×Dic103C2312yes—
35D412—216no—
36D412—28no—
37C4×D103—28no—
38C22×C103C2×D412yes—
39C22×C103C2×D412yes—
40C22×C103#4112yes—
41C22×C103C2411yescharacteristic
42C2×D103—28no—
43C2×D103—22no—
44C2×D103—22no—
45C2×D103—24no—
46C2×D103—24no—
47C2×D103—24no—
48C2×D103—48no—
49C2×D103C2×D414yescomplemented
50C4×C103—24no—
51C4×C103C2×D414yescomplemented
52Dic103—22no—
53C2×C103#12114yescomplemented
54C2×C103C22×D411yescharacteristic
55C2×C103C22×D411yescharacteristic
56C2×C103C2×#4111yescharacteristic
57D103—24no—
58D103—44no—
59C103C2×#12111yescharacteristic, complemented, Sylow
60C2×#121—1031nomaximal, Sylow
61C22×D4—1032no—
62C22×D4—1031no—
63C23×C4—1031no—
64#121—1038no—
65C2×C4⋊C4D10311yescharacteristic, complemented
66C2×C22⋊C4—1032no—
67C24—1031no—
68C24—1032no—
69C2×D4—1038no—
70C2×D4—1034no—
71C2×D4—2068no—
72C2×D4—2064no—
73C22×C4—1031no—
74C22×C4—1034no—
75C22×C4—2064no—
76C22×C4C2×D10312yes—
77C22×C4C2×D10311yescharacteristic
78C4⋊C4C2×D10314yescomplemented
79C22⋊C4—1038no—
80C23—1034no—
81C23—1032no—
82C23—1034no—
83C23—2064no—
84C23—2064no—
85C23—2064no—
86C23—2062no—
87C23—2062no—
88C23C22×D10311yescharacteristic
89D4—20616no—
90D4—2068no—
91C2×C4—24no—
92C2×C4—1032no—
93C2×C4—2062no—
94C2×C4—2068no—
95C2×C4D41214yescomplemented
96C2×C4C22×D10314yes—
97C2×C4C22×D10312yes—
98C22—1034no—
99C22—4128no—
100C22—2064no—
101C22—2064no—
102C22—2064no—
103C22—2062no—
104C22—2062no—
105C22—2068no—
106C22D4×D10312yes—
107C22C2×D41212yes—
108C22#1311010612yes—
109C22C23×D10311yescharacteristic
110C4—24no—
111C4—2062no—
112C4C2×D41214yescomplemented
113C2—4124no—
114C2—2064no—
115C2#1569299614yesdirect product factor
116C2C2×D4×D10311yescharacteristic
117C2C22×D41211yescharacteristic
118C2C2×#1311010611yescharacteristic
subgroupG/H
centerC23C22×D103
commutatorC22×C103C24
FrattiniC22C23×D103
FittingC2×C4⋊C4×C103C2
socleC23×C103C23
hypercenterC2×C4⋊C4D103
hypocenterC103C2×#121
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D412C2semidirect
2. C22×D412C2semidirect
3. C22×C4×D103C2semidirect
4. #15692996C2direct (N × H)
5. C2×(C2×D103)⋊C4C2semidirect
6. C2×C4⋊C4×C103C2semidirect
11. C2×D412C22semidirect
12. C2×D412C22semidirect
15. C2×C4×D103C22semidirect
16. (C2×D103)⋊C4C22semidirect
19. C4⋊C4×C103C22semidirect
26. C22×D103D4semidirect
30. C2×C4×C103D4semidirect
49. C2×D103C2×D4semidirect
51. C4×C103C2×D4semidirect
53. C2×C103#121semidirect
59. C103C2×#121semidirect
65. C2×C4⋊C4D103semidirect
78. C4⋊C4C2×D103semidirect
95. C2×C4D412semidirect
112. C4C2×D412semidirect
115. C2#15692996direct (N × H)