Finite Group Databasebeta

← #20268021

Subgroups — #20268021

Order 6592.

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

normal subgroups only

This group has 124 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×#13110094C211yesmaximal, characteristic, complemented
2C2×C8×D103C211yesmaximal, characteristic, complemented
3#15693001C211yesmaximal, characteristic, complemented
4#15692996C211yesmaximal, characteristic
5#15692944C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#106×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412—21no—
10C2×D412C2211yescharacteristic
11C2×C4×D103C2211yescharacteristic
12#13110094—22no—
13C2×C103⋊C8C2211yescharacteristic
14C8×D103—22no—
15C4⋊Dic103—21no—
16(C2×D103)⋊C4—21no—
17(C2×D103)⋊C4—21no—
18C2×C8×C103C2211yescharacteristic
19C4⋊C4×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C22×D103—21no—
22C22×D103D411yescharacteristic
23C2×C4×C103—21no—
24C2×C4×C103—21no—
25C2×C4×C103C2311yescharacteristic
26C2×Dic103—21no—
27C2×Dic103D411yescharacteristic
28D412—21no—
29D412—21no—
30D412—42no—
31C4×D103—21no—
32C4×D103—21no—
33Dic206—21no—
34Dic206—21no—
35C8×C103D412yescomplemented
36C103⋊C8—21no—
37C22×C103C2×D411yescharacteristic
38C2×D103—21no—
39C2×D103—21no—
40C2×D103—41no—
41C2×D103—41no—
42C2×D103—41no—
43C2×D103SD1612yescomplemented
44C4×C103—41no—
45C4×C103—41no—
46C4×C103C2×D411yescharacteristic
47C4×C103#4111yescharacteristic
48Dic103—21no—
49Dic103—41no—
50C2×C103#12111yescharacteristic
51C2×C103C2×SD1611yescharacteristic
52C2×C103#13511yescharacteristic
53D103—22no—
54D103—81no—
55C103#46511yescharacteristic, complemented, Sylow
56#465—1031nomaximal, Sylow
57C2×SD16—1031no—
58C22×C8—1031no—
59C22⋊Q8—1031no—
60#121—1031no—
61#106D10311yescharacteristic, complemented
62#103—1031no—
63#102—1031no—
64C2×Q8—1031no—
65C2×D4—1031no—
66C2×D4—2061no—
67C22×C4—1031no—
68SD16—2062no—
69C2×C8—1031no—
70C2×C8—2062no—
71C2×C8C2×D10311yescharacteristic
72C4⋊C4—2061no—
73C4⋊C4C2×D10311yescharacteristic
74C4⋊C4C2×D10311yescharacteristic
75C22⋊C4—2061no—
76C22⋊C4—2061no—
77C23—1031no—
78C23—2061no—
79Q8—2061no—
80Q8—2061no—
81D4—4122no—
82D4—2061no—
83D4—2061no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—1031no—
87C2×C4—2061no—
88C2×C4—2061no—
89C2×C4—2061no—
90C2×C4C22×D10311yescharacteristic
91C8—2061no—
92C8D41212yescomplemented
93C22—1032no—
94C22—4121no—
95C22—4121no—
96C22—4121no—
97C22—2061no—
98C22—2061no—
99C22D4×D10311yescharacteristic
100C4—41no—
101C4—41no—
102C4—4121no—
103C4—2061no—
104C4C2×D41211yescharacteristic
105C4#1311010611yescharacteristic
106C2—8241no—
107C2—2062no—
108C2#1569299611yescharacteristic
109C2SD16×D10311yescharacteristic
110C2#1569304211yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#106×C103C2
socleC22×C103C2×D4
hypercenter#106D103
hypocenterC103#465
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. C2×#13110094C2semidirect
2. C2×C8×D103C2semidirect
3. #15693001C2semidirect
5. #15692944C2semidirect
6. #15692941C2semidirect
7. #106×C103C2semidirect
35. C8×C103D4semidirect
43. C2×D103SD16semidirect
55. C103#465semidirect
61. #106D103semidirect
92. C8D412semidirect