Finite Group Databasebeta

← #20268043

Subgroups — #20268043

Order 6592.

130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 39 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×#13110090C211yesmaximal, characteristic, complemented
2C2×#13110088C211yesmaximal, characteristic, complemented
3#15692996C211yesmaximal, characteristic, complemented
4#15692992C211yesmaximal, characteristic, complemented
5#15692952C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic, complemented
7#102×C103C211yesmaximal, characteristic, complemented
8C2×D412—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11C2×C4×D103C2211yescharacteristic
12#13110090—22no—
13#13110088—22no—
14C2×C103⋊C8C2211yescharacteristic
15C4⋊Dic103C2211yescharacteristic
16C22⋊Dic103—21no—
17(C2×D103)⋊C4—21no—
18C2×D4×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C23×C103—21no—
22C22×D103—21no—
23C22×D103D411yescharacteristic
24D4×C103—21no—
25D4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103C2311yescharacteristic
28C22⋊D103—42no—
29C2×Dic103—21no—
30C2×Dic103D411yescharacteristic
31D412—21no—
32D412—21no—
33D412—42no—
34C4×D103—21no—
35C4×D103—21no—
36C8×C103—21no—
37C103⋊C8D412yescomplemented
38C22×C103—41no—
39C22×C103—41no—
40C22×C103—41no—
41C22×C103C2×D411yescharacteristic
42C2×D103—21no—
43C2×D103—21no—
44C2×D103—21no—
45C2×D103—41no—
46C2×D103—41no—
47C2×D103—41no—
48C4×C103—41no—
49C4×C103C2×D411yescharacteristic
50C4×C103#4111yescharacteristic
51Dic103—21no—
52Dic103—41no—
53C2×C103—81no—
54C2×C103#12111yescharacteristic
55C2×C103AGL(1,ℤ/8)11yescharacteristic
56C2×C103AGL(1,ℤ/8)11yescharacteristic
57D103—41no—
58D103—81no—
59C103#46911yescharacteristic, complemented, Sylow
60#469—1031nomaximal, Sylow
61C2×D8—1031no—
62C2×M16—1031no—
63#121—1031no—
64#121—1031no—
65#106—1031no—
66#102—1031no—
67#102D10311yescharacteristic, complemented
68C2×D4—1031no—
69C2×D4—2061no—
70C2×D4—2061no—
71C2×D4C2×D10311yescharacteristic
72C22×C4—1031no—
73D8—2062no—
74M16—2062no—
75C2×C8—1031no—
76C2×C8C2×D10311yescharacteristic
77C4⋊C4—1031no—
78C4⋊C4C2×D10311yescharacteristic
79C22⋊C4—2061no—
80C22⋊C4—2061no—
81C23—21no—
82C23—1031no—
83C23—2061no—
84D4—21no—
85D4—21no—
86D4—4122no—
87D4—4122no—
88D4—2061no—
89D4—2061no—
90C2×C4—21no—
91C2×C4—1031no—
92C2×C4—2061no—
93C2×C4—2061no—
94C2×C4—2061no—
95C2×C4C22×D10311yescharacteristic
96C8—21no—
97C8—1032no—
98C22—41no—
99C22—41no—
100C22—41no—
101C22—4121no—
102C22—4121no—
103C22—4121no—
104C22—2061no—
105C22—2061no—
106C22—2061no—
107C22D4×D10311yescharacteristic
108C4—41no—
109C4—4121no—
110C4—2061no—
111C4D4×D10311yescharacteristic
112C4#1311010511yescharacteristic
113C2—81no—
114C2—8241no—
115C2—4121no—
116C2#1569299411yescharacteristic
117C2#1569304511yescharacteristic
118C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#102×C103C2
socleC22×C103C2×D4
hypercenter#102D103
hypocenterC103#469
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. C2×#13110090C2semidirect
2. C2×#13110088C2semidirect
3. #15692996C2semidirect
4. #15692992C2semidirect
5. #15692952C2semidirect
6. #15692943C2semidirect
7. #102×C103C2semidirect
37. C103⋊C8D4semidirect
59. C103#469semidirect
67. #102D103semidirect