Finite Group Databasebeta

← #99×D103 #20267760

Subgroups — #99×D103 #20267760

Order 6592.

210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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×D4×D103C211yesmaximal, characteristic
2C22⋊C4×D103C212yesmaximal, complemented
3#15692936C211yesmaximal, characteristic, complemented
4#15692935C212yesmaximal, complemented
5#99×C103C211yesmaximal, characteristic, complemented
6C23×D103C411yescharacteristic, complemented
7C23×D103C2211yescharacteristic
8C2×D412C411yescharacteristic, complemented
9C2×C22⋊D103C411yescharacteristic, complemented
10C2×C22⋊D103C2211yescharacteristic
11D4×D103—22no—
12D4×D103—22no—
13C2×C4×D103—22no—
14C2×C4×D103C411yescharacteristic, complemented
15C22⋊Dic103C2212yescomplemented
16(C2×D103)⋊C4—22no—
17C2×D4×C103C2211yescharacteristic
18C22⋊C4×C103C2212yescomplemented
19C23×C103C2×C411yescharacteristic, complemented
20C23×C103C2311yescharacteristic
21C22×D103—21no—
22C22×D103—21no—
23C22×D103—42no—
24C22×D103—42no—
25C22×D103C2×C411yescharacteristic
26C22×D103C2×C411yescharacteristic
27C22×D103C2×C411yescharacteristic, complemented
28C22×D103D412yes—
29C22×D103D412yes—
30D4×C103—22no—
31C2×C4×C103—22no—
32C2×C4×C103C2×C411yescharacteristic, complemented
33C22⋊D103—22no—
34C22⋊D103—22no—
35C2×Dic103—22no—
36C2×Dic103C2×C411yescharacteristic, complemented
37D412—22no—
38C4×D103—21no—
39C4×D103—21no—
40C4×D103—44no—
41C22×C103—21no—
42C22×C103—41no—
43C22×C103—41no—
44C22×C103C22×C411yescharacteristic
45C22×C103C2×D412yes—
46C2×D103—24no—
47C2×D103—22no—
48C2×D103—21no—
49C2×D103—41no—
50C2×D103—42no—
51C2×D103—42no—
52C2×D103—42no—
53C2×D103—41no—
54C2×D103C22⋊C411yescharacteristic
55C2×D103C22⋊C412yes—
56C2×D103C22⋊C411yescharacteristic
57C4×C103—21no—
58C4×C103—42no—
59Dic103—21no—
60Dic103—42no—
61C2×C103—22no—
62C2×C103—21no—
63C2×C103—41no—
64C2×C103C2×C22⋊C411yescharacteristic
65D103—21no—
66D103—22no—
67D103—41no—
68D103#9912yesdirect product factor
69C103C2×#9911yescharacteristic, complemented, Sylow
70C2×#99—1031nomaximal, Sylow
71C22×D4—1031no—
72C2×C22⋊C4—1032no—
73#99—1031no—
74#99—1032no—
75#99D10311yescharacteristic, direct product factor
76C24—1031no—
77C24—1031no—
78C2×D4—1031no—
79C2×D4—1031no—
80C2×D4—1031no—
81C2×D4—2062no—
82C2×D4—2062no—
83C2×D4C2×D10311yescharacteristic
84C22×C4—1031no—
85C22×C4—2062no—
86C22⋊C4—1032no—
87C22⋊C4—2062no—
88C22⋊C4C2×D10312yescomplemented
89C23—1031no—
90C23—1032no—
91C23—1031no—
92C23—1032no—
93C23—1031no—
94C23—4122no—
95C23—4122no—
96C23—2061no—
97C23—2061no—
98C23C4×D10311yescharacteristic, complemented
99C23C22×D10311yescharacteristic
100D4—22no—
101D4—2062no—
102D4—2062no—
103D4—2062no—
104C2×C4—22no—
105C2×C4—1031no—
106C2×C4—4124no—
107C2×C4—2061no—
108C2×C4—2061no—
109C2×C4—2062no—
110C2×C4C4×D10311yescharacteristic, complemented
111C22—21no—
112C22—41no—
113C22—41no—
114C22—1031no—
115C22—1031no—
116C22—1032no—
117C22—4121no—
118C22—4122no—
119C22—4121no—
120C22—4122no—
121C22—4122no—
122C22—2064no—
123C22—2062no—
124C22—2061no—
125C22C2×C4×D10311yescharacteristic
126C22D4×D10312yes—
127C4—21no—
128C4—42no—
129C4—4122no—
130C4—2061no—
131C2—22no—
132C2—21no—
133C2—41no—
134C2—1032no—
135C2—4121no—
136C2—2061no—
137C2—2062no—
138C2C22⋊C4×D10311yescharacteristic
subgroupG/H
centerC2C22⋊C4×D103
commutatorC22×C103C22×C4
FrattiniC23C22×D103
Fitting#99×C103C2
socleC2×C103C2×C22⋊C4
hypercenter#99D103
hypocenterC103C2×#99
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×D103C2semidirect
3. #15692936C2semidirect
4. #15692935C2semidirect
5. #99×C103C2semidirect
6. C23×D103C4semidirect
8. C2×D412C4semidirect
9. C2×C22⋊D103C4semidirect
14. C2×C4×D103C4semidirect
15. C22⋊Dic103C22semidirect
18. C22⋊C4×C103C22semidirect
19. C23×C103C2×C4semidirect
27. C22×D103C2×C4semidirect
32. C2×C4×C103C2×C4semidirect
36. C2×Dic103C2×C4semidirect
68. D103#99direct (N × H)
69. C103C2×#99semidirect
75. #99D103direct (N × H)
88. C22⋊C4C2×D103semidirect
98. C23C4×D103semidirect
110. C2×C4C4×D103semidirect