Finite Group Databasebeta

← #20267940

Subgroups — #20267940

Order 6592.

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

normal subgroups only

This group has 188 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
2C2×#13110092C211yesmaximal, characteristic, complemented
3#15692997C211yesmaximal, characteristic, complemented
4#15692943C211yesmaximal, characteristic, complemented
5#15692942C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic, complemented
7C2×SD16×C103C211yesmaximal, characteristic, complemented
8C23×D103—21no—
9C2×D412C2211yescharacteristic
10C2×C22⋊D103—21no—
11D4×D103—22no—
12D4×D103—22no—
13C2×C4×D103C2211yescharacteristic
14#13110092—22no—
15C2×C103⋊C8C2211yescharacteristic, complemented
16C4⋊Dic103C2211yescharacteristic, complemented
17Dic103⋊C4—21no—
18(C2×D103)⋊C4—21no—
19C2×Q8×C103C2211yescharacteristic, complemented
20C2×D4×C103C2211yescharacteristic
21SD16×C103—22no—
22C2×C8×C103C2211yescharacteristic, complemented
23C23×C103—21no—
24C22×D103—24no—
25C22×D103—21no—
26C22×D103—42no—
27C22×D103—42no—
28C22×D103D411yescharacteristic
29Q8×C103—21no—
30Q8×C103—21no—
31D4×C103—21no—
32D4×C103D412yes—
33C2×C4×C103—21no—
34C2×C4×C103C2311yescharacteristic
35C22⋊D103—24no—
36C2×Dic103—21no—
37C2×Dic103D411yescharacteristic
38D412—21no—
39D412D412yes—
40C4×D103—21no—
41C4×D103—21no—
42C8×C103—21no—
43C103⋊C8—21no—
44C22×C103—22no—
45C22×C103—41no—
46C22×C103—41no—
47C22×C103C2×D411yescharacteristic
48C2×D103—21no—
49C2×D103—21no—
50C2×D103—22no—
51C2×D103—48no—
52C2×D103—41no—
53C2×D103—41no—
54C2×D103SD1612yescomplemented
55C4×C103—41no—
56C4×C103C2×D411yescharacteristic
57C4×C103C2×D411yescharacteristic
58Dic103—21no—
59Dic103—41no—
60C2×C103—42no—
61C2×C103#12011yescharacteristic
62C2×C103C2×SD1611yescharacteristic
63C2×C103AGL(1,ℤ/8)11yescharacteristic
64D103—22no—
65D103—42no—
66C103#45011yescharacteristic, complemented, Sylow
67#450—1031nomaximal, Sylow
68C22×D4—1031no—
69C2×SD16—1031no—
70C2×SD16D10311yescharacteristic, complemented
71C22⋊Q8—1031no—
72#102—1031no—
73#102—1031no—
74C22⋊C8—1031no—
75C24—2061no—
76C2×Q8C2×D10311yescharacteristic, complemented
77C2×D4—1031no—
78C2×D4—2061no—
79C2×D4—2062no—
80C2×D4—2062no—
81C2×D4C2×D10311yescharacteristic
82C22×C4—1031no—
83SD16—22no—
84SD16—2062no—
85C2×C8—1031no—
86C2×C8C2×D10311yescharacteristic, complemented
87C4⋊C4—1031no—
88C4⋊C4—2061no—
89C22⋊C4—2061no—
90C23—21no—
91C23—1031no—
92C23—4122no—
93C23—4122no—
94C23—2064no—
95C23—2061no—
96Q8—21no—
97Q8—21no—
98D4—21no—
99D4—1032no—
100D4—2064no—
101D4—2061no—
102D4C22⋊D10312yes—
103C2×C4—21no—
104C2×C4—1031no—
105C2×C4—2061no—
106C2×C4—2061no—
107C2×C4—2061no—
108C2×C4C22×D10311yescharacteristic
109C8—21no—
110C8—2061no—
111C22—22no—
112C22—41no—
113C22—41no—
114C22—1032no—
115C22—4128no—
116C22—4121no—
117C22—4121no—
118C22—2062no—
119C22—2061no—
120C22—2061no—
121C22D4×D10311yescharacteristic
122C4—41no—
123C4—4121no—
124C4—2061no—
125C4D4×D10311yescharacteristic
126C4C2×C22⋊D10311yescharacteristic
127C2—42no—
128C2—4122no—
129C2—2062no—
130C2#1569298911yescharacteristic
131C2SD16×D10311yescharacteristic
132C2#1569304811yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC2×SD16×C103C2
socleC22×C103C2×D4
hypercenterC2×SD16D103
hypocenterC103#450
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#13110092C2semidirect
3. #15692997C2semidirect
4. #15692943C2semidirect
5. #15692942C2semidirect
6. (C2×D103)⋊C8C2semidirect
7. C2×SD16×C103C2semidirect
15. C2×C103⋊C8C22semidirect
16. C4⋊Dic103C22semidirect
19. C2×Q8×C103C22semidirect
22. C2×C8×C103C22semidirect
54. C2×D103SD16semidirect
66. C103#450semidirect
70. C2×SD16D103semidirect
76. C2×Q8C2×D103semidirect
86. C2×C8C2×D103semidirect