Finite Group Databasebeta

← #102×D103 #20267776

Subgroups — #102×D103 #20267776

Order 6592.

202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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×D4×D103C211yesmaximal, characteristic
2C2×C8×D103C211yesmaximal, characteristic, complemented
3C4⋊C4×D103C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C23×D103—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11D4×D103—22no—
12D4×D103C414yescomplemented
13C2×C4×D103—21no—
14C2×C4×D103C2211yescharacteristic
15C2×C103⋊C8C2211yescharacteristic, complemented
16C8×D103—22no—
17C4⋊Dic103C2211yescharacteristic, complemented
18Dic103⋊C4—21no—
19C2×D4×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic, complemented
21C4⋊C4×C103C2211yescharacteristic, complemented
22C23×C103—21no—
23C22×D103—21no—
24C22×D103—24no—
25C22×D103—42no—
26C22×D103—42no—
27C22×D103D411yescharacteristic
28D4×C103—21no—
29D4×C103C2×C412yescomplemented
30C2×C4×C103—21no—
31C2×C4×C103C2311yescharacteristic
32C22⋊D103—24no—
33C2×Dic103—21no—
34C2×Dic103D411yescharacteristic
35D412—21no—
36D412C2×C412yescomplemented
37C4×D103—42no—
38C4×D103C2×C412yes—
39C4×D103D412yes—
40C8×C103—21no—
41C103⋊C8—21no—
42C22×C103—22no—
43C22×C103—41no—
44C22×C103—41no—
45C22×C103C2×D411yescharacteristic
46C2×D103—22no—
47C2×D103—41no—
48C2×D103—41no—
49C2×D103—48no—
50C2×D103C22⋊C412yes—
51C2×D103D812yes—
52C2×D103SD1612yes—
53C4×C103—41no—
54C4×C103C22×C411yescharacteristic
55C4×C103C2×D411yescharacteristic
56Dic103—41no—
57Dic103C22⋊C412yes—
58C2×C103—42no—
59C2×C103C2×C22⋊C411yescharacteristic
60C2×C103C2×D811yescharacteristic
61C2×C103C2×SD1611yescharacteristic
62D103—42no—
63D103#10214yesdirect product factor
64C103C2×#10211yescharacteristic, complemented, Sylow
65C2×#102—1031nomaximal, Sylow
66C22×D4—1031no—
67C22×C8—1031no—
68C2×C4⋊C4—1031no—
69#102—1031no—
70#102—1031no—
71#102—1031no—
72#102D10311yescharacteristic, direct product factor
73C24—2061no—
74C2×D4—1034no—
75C2×D4—1031no—
76C2×D4—2062no—
77C2×D4—2061no—
78C2×D4C2×D10311yescharacteristic
79C22×C4—1031no—
80C22×C4—2061no—
81C2×C8—1031no—
82C2×C8—2062no—
83C2×C8C2×D10311yescharacteristic, complemented
84C4⋊C4—1031no—
85C4⋊C4—2061no—
86C4⋊C4C2×D10311yescharacteristic, complemented
87C23—21no—
88C23—1031no—
89C23—4122no—
90C23—4122no—
91C23—2064no—
92C23—2061no—
93D4—21no—
94D4—1032no—
95D4—2064no—
96D4—2061no—
97D4C4×D10312yescomplemented
98C2×C4—21no—
99C2×C4—1031no—
100C2×C4—1032no—
101C2×C4—1032no—
102C2×C4—4122no—
103C2×C4—2061no—
104C2×C4C22×D10311yescharacteristic
105C8—21no—
106C8—2061no—
107C22—22no—
108C22—41no—
109C22—41no—
110C22—1032no—
111C22—1032no—
112C22—1032no—
113C22—4128no—
114C22—4121no—
115C22—4121no—
116C22—2062no—
117C22D4×D10311yescharacteristic
118C4—41no—
119C4—1032no—
120C4—4121no—
121C4C2×C4×D10311yescharacteristic
122C4D4×D10311yescharacteristic
123C2—42no—
124C2—1034no—
125C2—4122no—
126C2C22⋊C4×D10311yescharacteristic
127C2D8×D10311yescharacteristic
128C2SD16×D10311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103C2×#102
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. C2×C8×D103C2semidirect
3. C4⋊C4×D103C2semidirect
4. #15692943C2semidirect
5. #15692942C2semidirect
6. #15692941C2semidirect
7. #102×C103C2semidirect
12. D4×D103C4semidirect
15. C2×C103⋊C8C22semidirect
17. C4⋊Dic103C22semidirect
20. C2×C8×C103C22semidirect
21. C4⋊C4×C103C22semidirect
29. D4×C103C2×C4semidirect
36. D412C2×C4semidirect
63. D103#102direct (N × H)
64. C103C2×#102semidirect
72. #102D103direct (N × H)
83. C2×C8C2×D103semidirect
86. C4⋊C4C2×D103semidirect
97. D4C4×D103semidirect