Finite Group Databasebeta

← #20268136

Subgroups — #20268136

Order 6592.

118 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#15693020C211yesmaximal, characteristic, complemented
2#15693017C211yesmaximal, characteristic
3#15692943C211yesmaximal, characteristic, complemented
4#15692942C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6C8×Dic103C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×Dic206—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11C2×C22⋊D103—21no—
12C2×C103⋊C8C2211yescharacteristic
13C4⋊Dic103C2211yescharacteristic
14Dic103⋊C4—21no—
15C4×Dic103C2211yescharacteristic
16C2×D4×C103C2211yescharacteristic
17C2×C8×C103C2211yescharacteristic
18C4⋊C4×C103C2211yescharacteristic
19C23×C103—21no—
20C22×D103—21no—
21D4×C103—21no—
22D4×C103—21no—
23C2×C4×C103—21no—
24C2×C4×C103C2311yescharacteristic
25C22⋊D103—42no—
26C22⋊D103—42no—
27C2×Dic103—21no—
28C2×Dic103D411yescharacteristic
29C2×Dic103D411yescharacteristic
30D412—21no—
31D412—21no—
32Dic206—42no—
33C8×C103—21no—
34C103⋊C8—21no—
35C22×C103—41no—
36C22×C103—41no—
37C22×C103—41no—
38C22×C103C2×D411yescharacteristic
39C2×D103—41no—
40C2×D103—41no—
41C2×D103—41no—
42C4×C103—41no—
43C4×C103#4111yescharacteristic
44C4×C103#4111yescharacteristic
45Dic103—41no—
46Dic103D812yes—
47Dic103SD1612yes—
48C2×C103—81no—
49C2×C103#12411yescharacteristic
50C2×C103C2×D811yescharacteristic
51C2×C103C2×SD1611yescharacteristic
52D103—81no—
53C103#48611yescharacteristic, complemented, Sylow
54#486—1031nomaximal, Sylow
55C4⋊Q8—1031no—
56#127—1031no—
57#102—1031no—
58#102—1031no—
59#102—1031no—
60#102D10311yescharacteristic, complemented
61C4×C8—1031no—
62C2×Q8—2061no—
63C2×D4—1031no—
64C2×D4—2061no—
65C2×D4—2061no—
66C2×D4C2×D10311yescharacteristic
67C2×C8—1031no—
68C2×C8C2×D10311yescharacteristic
69C4⋊C4—1031no—
70C4⋊C4—2061no—
71C4⋊C4C2×D10311yescharacteristic
72C42—1031no—
73C23—21no—
74C23—2061no—
75Q8—4122no—
76D4—21no—
77D4—21no—
78D4—4122no—
79D4—4122no—
80D4—2061no—
81D4—2061no—
82C2×C4—21no—
83C2×C4—1031no—
84C2×C4—1031no—
85C2×C4—2061no—
86C2×C4C22×D10311yescharacteristic
87C8—21no—
88C8—2061no—
89C22—41no—
90C22—41no—
91C22—41no—
92C22—4121no—
93C22—4121no—
94C22—4121no—
95C22D4×D10311yescharacteristic
96C4—41no—
97C4—1032no—
98C4—1032no—
99C4—4121no—
100C4#1311010411yescharacteristic
101C4#1311010511yescharacteristic
102C2—81no—
103C2—8241no—
104C2#1569300711yescharacteristic
105C2D8×D10311yescharacteristic
106C2SD16×D10311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#486
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #15693020C2semidirect
3. #15692943C2semidirect
4. #15692942C2semidirect
5. #15692941C2semidirect
6. C8×Dic103C2semidirect
7. #102×C103C2semidirect
53. C103#486semidirect
60. #102D103semidirect