Finite Group Databasebeta

← #20267928

Subgroups — #20267928

Order 6592.

158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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×Q8×D103C211yesmaximal, characteristic, complemented
2C2×#13110093C211yesmaximal, characteristic, complemented
3#15692992C211yesmaximal, characteristic
4#15692946C211yesmaximal, characteristic, complemented
5#15692945C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8C2×Dic206—21no—
9C2×Dic206C2211yescharacteristic
10Q8×D103—22no—
11Q8×D103—22no—
12C2×C22⋊D103—21no—
13C2×C4×D103—21no—
14C2×C4×D103C2211yescharacteristic
15#13110093—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×D103D411yescharacteristic
25Q8×C103—21no—
26Q8×C103D412yescomplemented
27D4×C103—21no—
28D4×C103—21no—
29C2×C4×C103—21no—
30C2×C4×C103C2311yescharacteristic
31C22⋊D103—42no—
32C2×Dic103—21no—
33C2×Dic103—21no—
34C2×Dic103D411yescharacteristic
35C4×D103—24no—
36C4×D103—21no—
37C4×D103—21no—
38Dic206—24no—
39Dic206—21no—
40Dic206D412yescomplemented
41C8×C103—21no—
42C103⋊C8—21no—
43C22×C103—41no—
44C22×C103—41no—
45C22×C103—41no—
46C22×C103C2×D411yescharacteristic
47C2×D103—21no—
48C2×D103—21no—
49C2×D103SD1612yescomplemented
50C4×C103—22no—
51C4×C103C2×D411yescharacteristic
52C4×C103C2×D411yescharacteristic
53Dic103—21no—
54Dic103—22no—
55Dic103—41no—
56C2×C103—81no—
57C2×C103#12011yescharacteristic
58C2×C103C2×SD1611yescharacteristic
59C2×C103#13711yescharacteristic
60D103—22no—
61C103#44811yescharacteristic, complemented, Sylow
62#448—1031nomaximal, Sylow
63C22×Q8—1031no—
64C2×SD16—1031no—
65C2×SD16D10311yescharacteristic, complemented
66#121—1031no—
67#103—1031no—
68#103—1031no—
69C22⋊C8—1031no—
70C2×Q8—1031no—
71C2×Q8—2061no—
72C2×Q8—2062no—
73C2×Q8—2062no—
74C2×Q8C2×D10311yescharacteristic
75C2×D4—2061no—
76C2×D4C2×D10311yescharacteristic
77C22×C4—1031no—
78C22×C4—2061no—
79SD16—22no—
80SD16—2062no—
81C2×C8—1031no—
82C2×C8C2×D10311yescharacteristic
83C4⋊C4—1031no—
84C22⋊C4—2061no—
85C23—21no—
86C23—1031no—
87Q8—21no—
88Q8—1032no—
89Q8—2064no—
90Q8—2061no—
91Q8C22⋊D10312yescomplemented
92D4—21no—
93D4—21no—
94D4—4122no—
95C2×C4—21no—
96C2×C4—1031no—
97C2×C4—2064no—
98C2×C4—2061no—
99C2×C4—2061no—
100C2×C4—2061no—
101C2×C4—2061no—
102C2×C4C22×D10311yescharacteristic
103C8—21no—
104C8—2061no—
105C22—41no—
106C22—41no—
107C22—41no—
108C22—1032no—
109C22—2061no—
110C22—2061no—
111C22D4×D10311yescharacteristic
112C4—22no—
113C4—4121no—
114C4—2061no—
115C4—2062no—
116C4D4×D10311yescharacteristic
117C4C2×C22⋊D10311yescharacteristic
118C2—81no—
119C2—2062no—
120C2#1569298911yescharacteristic
121C2SD16×D10311yescharacteristic
122C2#1569305011yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#448
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×Q8×D103C2semidirect
2. C2×#13110093C2semidirect
4. #15692946C2semidirect
5. #15692945C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. C2×SD16×C103C2semidirect
26. Q8×C103D4semidirect
40. Dic206D4semidirect
49. C2×D103SD16semidirect
61. C103#448semidirect
65. C2×SD16D103semidirect
91. Q8C22⋊D103semidirect