Finite Group Databasebeta

← #20267984

Subgroups — #20267984

Order 6592.

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

normal subgroups only

This group has 140 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×#13110090C211yesmaximal, characteristic, complemented
2#15693017C211yesmaximal, characteristic, complemented
3D4×Dic103C211yesmaximal, characteristic, complemented
4Dic103⋊C8C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic, complemented
6#15692942C211yesmaximal, characteristic, complemented
7C2×D8×C103C211yesmaximal, characteristic, complemented
8C2×D412C2211yescharacteristic
9C2×C22⋊D103—21no—
10C2×C22⋊D103—21no—
11C22×Dic103—21no—
12#13110090—22no—
13C2×C103⋊C8C2211yescharacteristic
14C4⋊Dic103C2211yescharacteristic
15C22⋊Dic103—21no—
16C4×Dic103C2211yescharacteristic
17C2×D4×C103C2211yescharacteristic
18C2×D4×C103C2211yescharacteristic
19D8×C103—22no—
20C2×C8×C103C2211yescharacteristic
21C23×C103—21no—
22C23×C103—21no—
23C22×D103—21no—
24D4×C103—21no—
25D4×C103—21no—
26D4×C103—21no—
27D4×C103D412yescomplemented
28C2×C4×C103C2311yescharacteristic
29C22⋊D103—42no—
30C22⋊D103—42no—
31C2×Dic103—21no—
32C2×Dic103—42no—
33C2×Dic103D411yescharacteristic
34C2×Dic103D411yescharacteristic
35D412—21no—
36D412—21no—
37C8×C103—21no—
38C103⋊C8—21no—
39C22×C103—22no—
40C22×C103—41no—
41C22×C103—41no—
42C22×C103—41no—
43C22×C103—41no—
44C22×C103—41no—
45C22×C103C2×D411yescharacteristic
46C2×D103—41no—
47C2×D103—41no—
48C2×D103—41no—
49C4×C103C2×D411yescharacteristic
50C4×C103#4111yescharacteristic
51Dic103—21no—
52Dic103—41no—
53Dic103D812yescomplemented
54C2×C103—42no—
55C2×C103—81no—
56C2×C103#12111yescharacteristic
57C2×C103C2×D811yescharacteristic
58C2×C103AGL(1,ℤ/8)11yescharacteristic
59D103—81no—
60C103#45911yescharacteristic, complemented, Sylow
61#459—1031nomaximal, Sylow
62C2×D8—1031no—
63C2×D8D10311yescharacteristic, complemented
64#127—1031no—
65C4×D4—1031no—
66C4⋊C8—1031no—
67#102—1031no—
68#102—1031no—
69C2×D4—1031no—
70C2×D4—2061no—
71C2×D4—2061no—
72C2×D4C2×D10311yescharacteristic
73C2×D4C2×D10311yescharacteristic
74C22×C4—2061no—
75D8—22no—
76D8—2062no—
77C2×C8—1031no—
78C2×C8C2×D10311yescharacteristic
79C4⋊C4—1031no—
80C22⋊C4—2061no—
81C42—1031no—
82C23—21no—
83C23—21no—
84C23—2061no—
85D4—21no—
86D4—21no—
87D4—21no—
88D4—4122no—
89D4—4122no—
90D4—2061no—
91D4—2061no—
92D4C22⋊D10312yescomplemented
93C2×C4—1031no—
94C2×C4—1031no—
95C2×C4—4122no—
96C2×C4—2061no—
97C2×C4C22×D10311yescharacteristic
98C8—21no—
99C8—2061no—
100C22—22no—
101C22—41no—
102C22—41no—
103C22—41no—
104C22—41no—
105C22—41no—
106C22—4121no—
107C22—4121no—
108C22—4121no—
109C22D4×D10311yescharacteristic
110C4—1032no—
111C4—4121no—
112C4—2061no—
113C4C2×C22⋊D10311yescharacteristic
114C4#1311010411yescharacteristic
115C2—42no—
116C2—81no—
117C2—8241no—
118C2#1569299311yescharacteristic
119C2D8×D10311yescharacteristic
120C2#1569304511yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×D8×C103C2
socleC22×C103C2×D4
hypercenterC2×D8D103
hypocenterC103#459
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13110090C2semidirect
2. #15693017C2semidirect
3. D4×Dic103C2semidirect
4. Dic103⋊C8C2semidirect
5. #15692943C2semidirect
6. #15692942C2semidirect
7. C2×D8×C103C2semidirect
27. D4×C103D4semidirect
53. Dic103D8semidirect
60. C103#459semidirect
63. C2×D8D103semidirect
92. D4C22⋊D103semidirect