Finite Group Databasebeta

← C4×#13110090 #20267872

Subgroups — C4×#13110090 #20267872

Order 6592.

134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#13110090C211yesmaximal, characteristic
2C4×D412C211yesmaximal, characteristic, complemented
3#15692954C211yesmaximal, characteristic, complemented
4#15692942C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6C4×C103⋊C8C211yesmaximal, characteristic, complemented
7C4×D4×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C2×C4×D103—21no—
10#13110090C414yesdirect product factor
11C2×C103⋊C8C2211yescharacteristic
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14(C2×D103)⋊C4—21no—
15C2×D4×C103C2211yescharacteristic
16C22×C4×C103—21no—
17C4⋊C4×C103C2211yescharacteristic
18C22⋊C4×C103—21no—
19C42×C103C2211yescharacteristic
20C23×C103—21no—
21C22×D103—21no—
22D4×C103—21no—
23D4×C103C2×C412yescomplemented
24C2×C4×C103—21no—
25C2×C4×C103—42no—
26C2×C4×C103D411yescharacteristic
27C2×C4×C103D411yescharacteristic
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30D412—21no—
31D412C2×C412yescomplemented
32C4×D103—42no—
33C103⋊C8—21no—
34C103⋊C8C2×C412yescomplemented
35C22×C103—22no—
36C22×C103—41no—
37C22×C103—41no—
38C22×C103C2×D411yescharacteristic
39C2×D103—22no—
40C2×D103—41no—
41C2×D103—41no—
42C4×C103—21no—
43C4×C103—41no—
44C4×C103D812yescomplemented
45C4×C103C22×C411yescharacteristic
46C4×C103#4111yescharacteristic
47Dic103—41no—
48C2×C103—42no—
49C2×C103C4×D411yescharacteristic
50C2×C103C2×D811yescharacteristic
51C2×C103#13511yescharacteristic
52D103—42no—
53C103C4×D811yescharacteristic, complemented, Sylow
54C4×D8—1031nomaximal, Sylow
55C2×D8—1031no—
56C4×D4—1031no—
57C4×D4D10311yescharacteristic, complemented
58#107—1031no—
59#102—1031no—
60#102—1031no—
61C4×C8—1031no—
62C2×D4—1031no—
63C2×D4C2×D10311yescharacteristic
64C22×C4—21no—
65C22×C4—2061no—
66D8—1034no—
67C2×C8—1031no—
68C2×C8—1031no—
69C4⋊C4—1031no—
70C4⋊C4C2×D10311yescharacteristic
71C22⋊C4—21no—
72C22⋊C4—2061no—
73C42C2×D10311yescharacteristic
74C23—21no—
75C23—2061no—
76D4—21no—
77D4—1032no—
78D4—2061no—
79D4C4×D10312yescomplemented
80C2×C4—21no—
81C2×C4—42no—
82C2×C4—4122no—
83C2×C4—2061no—
84C2×C4C22⋊D10311yescharacteristic
85C2×C4C22⋊D10311yescharacteristic
86C2×C4C22×D10311yescharacteristic
87C8—1032no—
88C8—2061no—
89C22—22no—
90C22—41no—
91C22—41no—
92C22—4121no—
93C22—4121no—
94C22—2062no—
95C22C2×C22⋊D10311yescharacteristic
96C4—21no—
97C4—41no—
98C4—4121no—
99C4#1311009012yesdirect product factor
100C4C2×C4×D10311yescharacteristic
101C4#1311010511yescharacteristic
102C2—42no—
103C2—4122no—
104C2C4×C22⋊D10311yescharacteristic
105C2C2×#1311009011yescharacteristic
106C2#1569304111yescharacteristic
subgroupG/H
centerC2×C4C22⋊D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
FittingC4×D4×C103C2
socleC22×C103C2×D4
hypercenterC4×D4D103
hypocenterC103C4×D8
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D412C2semidirect
3. #15692954C2semidirect
4. #15692942C2semidirect
5. #15692941C2semidirect
6. C4×C103⋊C8C2semidirect
7. C4×D4×C103C2semidirect
10. #13110090C4direct (N × H)
23. D4×C103C2×C4semidirect
31. D412C2×C4semidirect
34. C103⋊C8C2×C4semidirect
44. C4×C103D8semidirect
53. C103C4×D8semidirect
57. C4×D4D103semidirect
79. D4C4×D103semidirect
99. C4#13110090direct (N × H)