Finite Group Databasebeta

← #20268154

Subgroups — #20268154

Order 6592.

110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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#15693017C211yesmaximal, characteristic
2#15693012C211yesmaximal, characteristic, complemented
3#15692943C211yesmaximal, characteristic, complemented
4#15692942C211yesmaximal, characteristic, complemented
5#15692941C211yesmaximal, characteristic, complemented
6#15692931C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C2×C22⋊D103—21no—
10C2×C22⋊D103—21no—
11C2×C103⋊C8C2211yescharacteristic
12C4⋊Dic103—21no—
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—
32C8×C103—21no—
33C103⋊C8—21no—
34C22×C103—41no—
35C22×C103—41no—
36C22×C103—41no—
37C22×C103C2×D411yescharacteristic
38C2×D103—41no—
39C2×D103—41no—
40C2×D103—41no—
41C4×C103—41no—
42C4×C103#4111yescharacteristic
43C4×C103#4111yescharacteristic
44Dic103—21no—
45Dic103—21no—
46Dic103—41no—
47C2×C103—81no—
48C2×C103#12411yescharacteristic
49C2×C103AGL(1,ℤ/8)11yescharacteristic
50C2×C103AGL(1,ℤ/8)11yescharacteristic
51D103—81no—
52C103#49011yescharacteristic, complemented, Sylow
53#490—1031nomaximal, Sylow
54#127—1031no—
55#125—1031no—
56#102—1031no—
57#102—1031no—
58#102—1031no—
59#102D10311yescharacteristic, complemented
60#97—1031no—
61C2×D4—1031no—
62C2×D4—2061no—
63C2×D4—2061no—
64C2×D4C2×D10311yescharacteristic
65C2×C8—1031no—
66C2×C8C2×D10311yescharacteristic
67C4⋊C4—1031no—
68C4⋊C4—2061no—
69C4⋊C4—2061no—
70C4⋊C4C2×D10311yescharacteristic
71C42—1031no—
72C23—21no—
73C23—2061no—
74D4—21no—
75D4—21no—
76D4—4122no—
77D4—4122no—
78D4—2061no—
79D4—2061no—
80C2×C4—21no—
81C2×C4—1031no—
82C2×C4—1031no—
83C2×C4—2061no—
84C2×C4C22×D10311yescharacteristic
85C8—21no—
86C8—2061no—
87C22—41no—
88C22—41no—
89C22—41no—
90C22—4121no—
91C22—4121no—
92C22—4121no—
93C22D4×D10311yescharacteristic
94C4—41no—
95C4—4121no—
96C4—2061no—
97C4—2061no—
98C4#1311010411yescharacteristic
99C4#1311010511yescharacteristic
100C2—81no—
101C2—8241no—
102C2#1569300711yescharacteristic
103C2#1569304511yescharacteristic
104C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#490
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
2. #15693012C2semidirect
3. #15692943C2semidirect
4. #15692942C2semidirect
5. #15692941C2semidirect
6. #15692931C2semidirect
7. #102×C103C2semidirect
52. C103#490semidirect
59. #102D103semidirect