Finite Group Databasebeta

← #20267955

Subgroups — #20267955

Order 6592.

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

normal subgroups only

This group has 152 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×#13110105C211yesmaximal, characteristic
2C2×Dic412C211yesmaximal, characteristic, complemented
3C2×#13110094C211yesmaximal, characteristic, complemented
4#15693000C211yesmaximal, characteristic, complemented
5#15692946C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic, complemented
7C22⋊C8×C103C211yesmaximal, characteristic, complemented
8#13110105—22no—
9#13110105—22no—
10C2×Dic206C2211yescharacteristic
11C2×Dic206C2211yescharacteristic
12C2×D412C2211yescharacteristic
13C2×C22⋊D103—21no—
14C2×C4×D103—21no—
15Dic412—22no—
16#13110094—22no—
17C4⋊Dic103C2211yescharacteristic
18Dic103⋊C4—21no—
19C22⋊Dic103—21no—
20C22×C4×C103C2211yescharacteristic
21C2×C8×C103C2211yescharacteristic
22C2×C8×C103C2211yescharacteristic
23C23×C103D411yescharacteristic
24C22×D103—21no—
25C2×C4×C103—21no—
26C2×C4×C103—21no—
27C2×C4×C103D411yescharacteristic
28C2×C4×C103C2311yescharacteristic
29C22⋊D103—24no—
30C2×Dic103—21no—
31C2×Dic103—21no—
32C2×Dic103—21no—
33D412—21no—
34D412D412yes—
35C4×D103—24no—
36Dic206—21no—
37Dic206—21no—
38Dic206—21no—
39Dic206D412yes—
40C8×C103—21no—
41C8×C103—21no—
42C22×C103—21no—
43C22×C103—21no—
44C22×C103—21no—
45C22×C103C2×D411yescharacteristic
46C2×D103—22no—
47C2×D103—41no—
48C2×D103—41no—
49C4×C103—21no—
50C4×C103C2×D411yescharacteristic
51C4×C103C2×D411yescharacteristic
52Dic103—22no—
53Dic103—41no—
54Dic103—41no—
55C2×C103—41no—
56C2×C103#12011yescharacteristic
57C2×C103#13511yescharacteristic
58C2×C103#13711yescharacteristic
59D103—42no—
60C103#45211yescharacteristic, complemented, Sylow
61#452—1031nomaximal, Sylow
62C2×#41—1031no—
63C2×Q16—1031no—
64C2×SD16—1031no—
65C22⋊Q8—1031no—
66#103—1031no—
67#102—1031no—
68C22⋊C8D10311yescharacteristic, complemented
69#41—2062no—
70#41—2062no—
71C2×Q8—1031no—
72C2×Q8—1031no—
73C2×D4—1031no—
74C2×D4—2061no—
75C22×C4—2061no—
76C22×C4C2×D10311yescharacteristic
77Q16—2062no—
78SD16—2062no—
79C2×C8C2×D10311yescharacteristic
80C2×C8C2×D10311yescharacteristic
81C4⋊C4—1031no—
82C4⋊C4—2061no—
83C22⋊C4—2061no—
84C23—2061no—
85C23D41211yescharacteristic
86Q8—1032no—
87Q8—2061no—
88Q8—2061no—
89Q8—2061no—
90D4—1032no—
91D4—2064no—
92D4—2061no—
93C2×C4—21no—
94C2×C4—21no—
95C2×C4—2064no—
96C2×C4—2061no—
97C2×C4—2061no—
98C2×C4—2061no—
99C2×C4D41211yescharacteristic
100C2×C4C22×D10311yescharacteristic
101C8—21no—
102C8—21no—
103C22—21no—
104C22—21no—
105C22—21no—
106C22—4121no—
107C22—4121no—
108C22—2062no—
109C22C2×D41211yescharacteristic
110C4—21no—
111C4—4121no—
112C4—4121no—
113C4—2062no—
114C4D4×D10311yescharacteristic
115C4D4×D10311yescharacteristic
116C2—41no—
117C2—4122no—
118C2#1569299111yescharacteristic
119C2#1569304311yescharacteristic
120C2#1569305411yescharacteristic
subgroupG/H
centerC22C2×D412
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC22⋊C8×C103C2
socleC22×C103C2×D4
hypercenterC22⋊C8D103
hypocenterC103#452
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic412C2semidirect
3. C2×#13110094C2semidirect
4. #15693000C2semidirect
5. #15692946C2semidirect
6. #15692943C2semidirect
7. C22⋊C8×C103C2semidirect
60. C103#452semidirect
68. C22⋊C8D103semidirect