Finite Group Databasebeta

← #20267900

Subgroups — #20267900

Order 6592.

132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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
2D4×Dic103C211yesmaximal, characteristic, complemented
3#15692983C211yesmaximal, characteristic, complemented
4#15692952C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic, complemented
6#15692931C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C22×Dic103—21no—
10C2×C4×D103—21no—
11#13110090C414yescomplemented
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14C22⋊Dic103—21no—
15(C2×D103)⋊C4—21no—
16C4×Dic103C2211yescharacteristic
17C2×D4×C103C2211yescharacteristic
18C2×C8×C103C2211yescharacteristic
19C4⋊C4×C103C2211yescharacteristic
20C23×C103—21no—
21C22×D103—21no—
22D4×C103—21no—
23D4×C103C2×C412yescomplemented
24C2×C4×C103—21no—
25C2×C4×C103C2311yescharacteristic
26C2×Dic103—21no—
27C2×Dic103—42no—
28C2×Dic103D411yescharacteristic
29C2×Dic103D411yescharacteristic
30D412—21no—
31D412C2×C412yescomplemented
32C4×D103—42no—
33C8×C103—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—41no—
43C4×C103C22×C411yescharacteristic
44C4×C103#4111yescharacteristic
45Dic103—21no—
46Dic103—21no—
47Dic103—41no—
48C2×C103—42no—
49C2×C103C4×D411yescharacteristic
50C2×C103AGL(1,ℤ/8)11yescharacteristic
51C2×C103AGL(1,ℤ/8)11yescharacteristic
52D103—42no—
53C103#44211yescharacteristic, complemented, Sylow
54#442—1031nomaximal, Sylow
55C2×D8—1031no—
56C4×D4—1031no—
57C4×D4—1031no—
58#106—1031no—
59#102—1031no—
60#102D10311yescharacteristic, complemented
61#97—1031no—
62C2×D4—1031no—
63C2×D4C2×D10311yescharacteristic
64C22×C4—2061no—
65C22×C4—2061no—
66D8—1034no—
67C2×C8—1031no—
68C2×C8C2×D10311yescharacteristic
69C4⋊C4—1031no—
70C4⋊C4C2×D10311yescharacteristic
71C22⋊C4—2061no—
72C22⋊C4—2061no—
73C42—1031no—
74C23—21no—
75C23—2061no—
76D4—21no—
77D4—1032no—
78D4—2061no—
79D4C4×D10312yescomplemented
80C2×C4—21no—
81C2×C4—1031no—
82C2×C4—1031no—
83C2×C4—4122no—
84C2×C4—4122no—
85C2×C4—2061no—
86C2×C4C22×D10311yescharacteristic
87C8—21no—
88C8—1032no—
89C22—22no—
90C22—41no—
91C22—41no—
92C22—4121no—
93C22—4121no—
94C22—2062no—
95C22D4×D10311yescharacteristic
96C4—41no—
97C4—4121no—
98C4—2061no—
99C4—2061no—
100C4C2×C4×D10311yescharacteristic
101C4#1311010411yescharacteristic
102C2—42no—
103C2—4122no—
104C2(C22⋊D103)⋊C411yescharacteristic
105C2#1569304511yescharacteristic
106C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#442
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D4×Dic103C2semidirect
3. #15692983C2semidirect
4. #15692952C2semidirect
5. #15692943C2semidirect
6. #15692931C2semidirect
7. #102×C103C2semidirect
11. #13110090C4semidirect
23. D4×C103C2×C4semidirect
31. D412C2×C4semidirect
34. C103⋊C8C2×C4semidirect
53. C103#442semidirect
60. #102D103semidirect
79. D4C4×D103semidirect