Finite Group Databasebeta

← #20267979

Subgroups — #20267979

Order 6592.

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

normal subgroups only

This group has 198 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
1#15693066C211yesmaximal, characteristic, complemented
2#15692991C212yesmaximal, complemented
3#15692989C211yesmaximal, characteristic, complemented
4#15692935C212yesmaximal, complemented
5#99×C103C211yesmaximal, characteristic, complemented
6C23×D103C2211yescharacteristic, complemented
7#13110105—21no—
8#13110104—22no—
9C2×D412—22no—
10C2×C22⋊D103—21no—
11C2×C22⋊D103—21no—
12C2×C22⋊D103C2212yes—
13D4×D103—22no—
14C22⋊Dic103C2211yescharacteristic, complemented
15(C2×D103)⋊C4—21no—
16(C2×D103)⋊C4—22no—
17C2×D4×C103C2211yescharacteristic
18C22⋊C4×C103C2212yescomplemented
19C23×C103D411yescharacteristic, complemented
20C23×C103C2311yescharacteristic
21C22×D103—21no—
22C22×D103—22no—
23C22×D103—21no—
24C22×D103—42no—
25C22×D103D412yescomplemented
26D4×C103—22no—
27C2×C4×C103—22no—
28C2×C4×C103D411yescharacteristic, complemented
29C22⋊D103—22no—
30C22⋊D103—22no—
31C22⋊D103—22no—
32C22⋊D103—42no—
33C2×Dic103—21no—
34C2×Dic103—21no—
35C2×Dic103D412yescomplemented
36D412—21no—
37D412—44no—
38C4×D103—22no—
39Dic206—21no—
40C22×C103—21no—
41C22×C103—41no—
42C22×C103—41no—
43C22×C103C2×D412yes—
44C22×C103C2×D411yescharacteristic
45C2×D103—24no—
46C2×D103—22no—
47C2×D103—22no—
48C2×D103—41no—
49C2×D103—42no—
50C2×D103—41no—
51C2×D103—42no—
52C2×D103—81no—
53C4×C103—21no—
54C4×C103—42no—
55Dic103—22no—
56Dic103—41no—
57C2×C103—21no—
58C2×C103—22no—
59C2×C103—41no—
60C2×C103#12011yescharacteristic
61D103—42no—
62D103—42no—
63C103B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—1031nomaximal, Sylow
65H(5,𝔽2)—1031no—
66#120—1031no—
67#120—1032no—
68#99—1032no—
69#99D10311yescharacteristic, complemented
70C24—1031no—
71#41—2062no—
72#41—2061no—
73C2×D4—1032no—
74C2×D4—2062no—
75C2×D4—2062no—
76C2×D4—2061no—
77C2×D4—2061no—
78C2×D4C2×D10311yescharacteristic
79C22⋊C4—1031no—
80C22⋊C4—2062no—
81C22⋊C4—2061no—
82C22⋊C4C2×D10312yescomplemented
83C23—1032no—
84C23—4122no—
85C23—2061no—
86C23—2062no—
87C23—2061no—
88C23D41211yescharacteristic, complemented
89C23C22×D10311yescharacteristic
90Q8—2061no—
91D4—22no—
92D4—4124no—
93D4—4122no—
94D4—2061no—
95D4—2062no—
96D4—2062no—
97D4—2062no—
98C2×C4—22no—
99C2×C4—1032no—
100C2×C4—2062no—
101C2×C4—2061no—
102C2×C4—2061no—
103C2×C4D41211yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—8241no—
108C22—4122no—
109C22—4122no—
110C22—4121no—
111C22—4121no—
112C22—2064no—
113C22—2062no—
114C22—2062no—
115C22D4×D10312yes—
116C22C2×D41211yescharacteristic
117C4—21no—
118C4—42no—
119C4—4121no—
120C4—2062no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—4122no—
125C2—4122no—
126C2#1569299111yescharacteristic
subgroupG/H
centerC2#15692991
commutatorC23×C103C23
FrattiniC23C22×D103
Fitting#99×C103C2
socleC2×C103#120
hypercenter#99D103
hypocenterC103B(4,𝔽2)
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #15693066C2semidirect
2. #15692991C2semidirect
3. #15692989C2semidirect
4. #15692935C2semidirect
5. #99×C103C2semidirect
6. C23×D103C22semidirect
14. C22⋊Dic103C22semidirect
18. C22⋊C4×C103C22semidirect
19. C23×C103D4semidirect
25. C22×D103D4semidirect
28. C2×C4×C103D4semidirect
35. C2×Dic103D4semidirect
63. C103B(4,𝔽2)semidirect
69. #99D103semidirect
82. C22⋊C4C2×D103semidirect
88. C23D412semidirect
103. C2×C4D412semidirect