Finite Group Databasebeta

← #20267935

Subgroups — #20267935

Order 6592.

162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#13110106C211yesmaximal, characteristic, complemented
2C2×#13110090C211yesmaximal, characteristic, complemented
3#15692992C211yesmaximal, characteristic, complemented
4#15692945C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8#13110106—22no—
9#13110106—22no—
10C2×D412—21no—
11C2×D412C2211yescharacteristic
12C2×C22⋊D103—21no—
13C2×C4×D103—21no—
14C2×C4×D103C2211yescharacteristic
15#13110090—22no—
16C2×C103⋊C8C2211yescharacteristic
17C4⋊Dic103C2211yescharacteristic
18C22⋊Dic103—21no—
19C2×Q8×C103C2211yescharacteristic
20C2×D4×C103C2211yescharacteristic
21SD16×C103—22no—
22C2×C8×C103C2211yescharacteristic
23C23×C103—21no—
24C22×D103—21no—
25C22×D103D411yescharacteristic
26Q8×C103—21no—
27Q8×C103D412yescomplemented
28D4×C103—21no—
29D4×C103—21no—
30C2×C4×C103—21no—
31C2×C4×C103C2311yescharacteristic
32C22⋊D103—42no—
33C2×Dic103—21no—
34C2×Dic103D411yescharacteristic
35D412—24no—
36D412—21no—
37D412D412yescomplemented
38C4×D103—24no—
39C4×D103—21no—
40C4×D103—21no—
41C8×C103—21no—
42C103⋊C8—21no—
43C22×C103—41no—
44C22×C103—41no—
45C22×C103—41no—
46C22×C103C2×D411yescharacteristic
47C2×D103—21no—
48C2×D103—22no—
49C2×D103—21no—
50C2×D103—21no—
51C2×D103—41no—
52C2×D103—41no—
53C4×C103—22no—
54C4×C103C2×D411yescharacteristic
55C4×C103C2×D411yescharacteristic
56Dic103—21no—
57Dic103—41no—
58C2×C103—81no—
59C2×C103#12011yescharacteristic
60C2×C103#13511yescharacteristic
61C2×C103AGL(1,ℤ/8)11yescharacteristic
62D103—41no—
63D103—42no—
64C103#44911yescharacteristic, complemented, Sylow
65#449—1031nomaximal, Sylow
66C2×#41—1031no—
67C2×SD16D10311yescharacteristic, complemented
68C2×D8—1031no—
69#121—1031no—
70#103—1031no—
71#102—1031no—
72C22⋊C8—1031no—
73#41—2062no—
74#41—2062no—
75C2×Q8C2×D10311yescharacteristic
76C2×D4—1031no—
77C2×D4—2061no—
78C2×D4—2061no—
79C2×D4C2×D10311yescharacteristic
80C22×C4—1031no—
81C22×C4—2061no—
82SD16—22no—
83D8—2062no—
84C2×C8—1031no—
85C2×C8C2×D10311yescharacteristic
86C4⋊C4—1031no—
87C22⋊C4—2061no—
88C23—21no—
89C23—1031no—
90C23—2061no—
91Q8—21no—
92Q8C22⋊D10312yescomplemented
93D4—21no—
94D4—21no—
95D4—1032no—
96D4—4122no—
97D4—2064no—
98D4—2061no—
99C2×C4—21no—
100C2×C4—1031no—
101C2×C4—2064no—
102C2×C4—2061no—
103C2×C4—2061no—
104C2×C4—2061no—
105C2×C4C22×D10311yescharacteristic
106C8—21no—
107C8—2061no—
108C22—41no—
109C22—41no—
110C22—41no—
111C22—4121no—
112C22—4121no—
113C22—2062no—
114C22—2061no—
115C22—2061no—
116C22—2061no—
117C22D4×D10311yescharacteristic
118C4—22no—
119C4—4121no—
120C4—2061no—
121C4D4×D10311yescharacteristic
122C4C2×C22⋊D10311yescharacteristic
123C2—81no—
124C2—4122no—
125C2—4121no—
126C2#1569298911yescharacteristic
127C2#1569304211yescharacteristic
128C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#449
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13110106C2semidirect
2. C2×#13110090C2semidirect
3. #15692992C2semidirect
4. #15692945C2semidirect
5. #15692943C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. C2×SD16×C103C2semidirect
27. Q8×C103D4semidirect
37. D412D4semidirect
64. C103#449semidirect
67. C2×SD16D103semidirect
92. Q8C22⋊D103semidirect