Finite Group Databasebeta

← #20267923

Subgroups — #20267923

Order 6592.

198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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, complemented
2C2×#13110090C211yesmaximal, characteristic, complemented
3#15692992C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7C2×D8×C103C211yesmaximal, characteristic, complemented
8C23×D103—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11C2×C22⋊D103—21no—
12D4×D103—22no—
13D4×D103—22no—
14C2×C4×D103C2211yescharacteristic
15#13110090—22no—
16C2×C103⋊C8C2211yescharacteristic, complemented
17C4⋊Dic103C2211yescharacteristic, complemented
18C22⋊Dic103—21no—
19C2×D4×C103C2211yescharacteristic
20C2×D4×C103C2211yescharacteristic, complemented
21D8×C103—22no—
22C2×C8×C103C2211yescharacteristic, complemented
23C23×C103—21no—
24C23×C103—21no—
25C22×D103—24no—
26C22×D103—21no—
27C22×D103—42no—
28C22×D103—42no—
29C22×D103D411yescharacteristic
30D4×C103—21no—
31D4×C103—21no—
32D4×C103—21no—
33D4×C103D412yescomplemented
34C2×C4×C103C2311yescharacteristic
35C22⋊D103—24no—
36C22⋊D103—42no—
37C2×Dic103—21no—
38C2×Dic103D411yescharacteristic
39D412—21no—
40D412D412yescomplemented
41C4×D103—21no—
42C4×D103—21no—
43C8×C103—21no—
44C103⋊C8—21no—
45C22×C103—22no—
46C22×C103—41no—
47C22×C103—41no—
48C22×C103—41no—
49C22×C103—41no—
50C22×C103—41no—
51C22×C103C2×D411yescharacteristic
52C2×D103—21no—
53C2×D103—21no—
54C2×D103—22no—
55C2×D103—48no—
56C2×D103—41no—
57C2×D103—41no—
58C2×D103D812yescomplemented
59C4×C103C2×D411yescharacteristic
60C4×C103C2×D411yescharacteristic
61Dic103—21no—
62Dic103—41no—
63C2×C103—42no—
64C2×C103—81no—
65C2×C103#12011yescharacteristic
66C2×C103C2×D811yescharacteristic
67C2×C103AGL(1,ℤ/8)11yescharacteristic
68D103—22no—
69D103—42no—
70C103#44711yescharacteristic, complemented, Sylow
71#447—1031nomaximal, Sylow
72C22×D4—1031no—
73C2×D8—1031no—
74C2×D8D10311yescharacteristic, complemented
75#121—1031no—
76#102—1031no—
77#102—1031no—
78C22⋊C8—1031no—
79C24—2061no—
80C2×D4—1031no—
81C2×D4—2061no—
82C2×D4—2062no—
83C2×D4—2061no—
84C2×D4—2062no—
85C2×D4C2×D10311yescharacteristic
86C2×D4C2×D10311yescharacteristic, complemented
87C22×C4—1031no—
88D8—22no—
89D8—2062no—
90C2×C8—1031no—
91C2×C8C2×D10311yescharacteristic, complemented
92C4⋊C4—1031no—
93C22⋊C4—2061no—
94C23—21no—
95C23—21no—
96C23—1031no—
97C23—4122no—
98C23—4122no—
99C23—2064no—
100C23—2061no—
101D4—21no—
102D4—21no—
103D4—21no—
104D4—1032no—
105D4—4122no—
106D4—2064no—
107D4—2061no—
108D4C22⋊D10312yescomplemented
109C2×C4—1031no—
110C2×C4—2061no—
111C2×C4—2061no—
112C2×C4—2061no—
113C2×C4C22×D10311yescharacteristic
114C8—21no—
115C8—2061no—
116C22—22no—
117C22—41no—
118C22—41no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—1032no—
123C22—4128no—
124C22—4121no—
125C22—4121no—
126C22—2062no—
127C22—2061no—
128C22—2061no—
129C22D4×D10311yescharacteristic
130C4—4121no—
131C4—2061no—
132C4D4×D10311yescharacteristic
133C4C2×C22⋊D10311yescharacteristic
134C2—42no—
135C2—81no—
136C2—4122no—
137C2—2062no—
138C2#1569298911yescharacteristic
139C2D8×D10311yescharacteristic
140C2#1569304511yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×D8×C103C2
socleC22×C103C2×D4
hypercenterC2×D8D103
hypocenterC103#447
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×D4×D103C2semidirect
2. C2×#13110090C2semidirect
3. #15692992C2semidirect
4. #15692943C2semidirect
5. #15692942C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. C2×D8×C103C2semidirect
16. C2×C103⋊C8C22semidirect
17. C4⋊Dic103C22semidirect
20. C2×D4×C103C22semidirect
22. C2×C8×C103C22semidirect
33. D4×C103D4semidirect
40. D412D4semidirect
58. C2×D103D8semidirect
70. C103#447semidirect
74. C2×D8D103semidirect
86. C2×D4C2×D103semidirect
91. C2×C8C2×D103semidirect
108. D4C22⋊D103semidirect