Finite Group Databasebeta

← #20267791

Subgroups — #20267791

Order 6592.

162 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 55 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×#13110106C211yesmaximal, characteristic
2C2×#13110088C211yesmaximal, characteristic, complemented
3C4⋊C4×D103C211yesmaximal, characteristic, complemented
4#15692945C211yesmaximal, characteristic, complemented
5#15692943C211yesmaximal, characteristic, complemented
6#15692941C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8#13110106—22no—
9#13110106C414yescomplemented
10C2×D412—21no—
11C2×D412C2211yescharacteristic
12C2×C4×D103—21no—
13C2×C4×D103—21no—
14C2×C4×D103C2211yescharacteristic
15#13110088—22no—
16C2×C103⋊C8C2211yescharacteristic
17C4⋊Dic103C2211yescharacteristic
18Dic103⋊C4—21no—
19C2×Q8×C103C2211yescharacteristic
20C2×C8×C103C2211yescharacteristic
21C4⋊C4×C103C2211yescharacteristic
22C22×D103—21no—
23C22×D103D411yescharacteristic
24Q8×C103—21no—
25Q8×C103C2×C412yescomplemented
26C2×C4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30C2×Dic103D411yescharacteristic
31D412—24no—
32D412—21no—
33D412C2×C412yescomplemented
34C4×D103—24no—
35C4×D103—42no—
36C4×D103C2×C412yes—
37C4×D103D412yes—
38C8×C103—21no—
39C103⋊C8—21no—
40C22×C103C2×D411yescharacteristic
41C2×D103—21no—
42C2×D103—21no—
43C2×D103—22no—
44C2×D103—41no—
45C2×D103—41no—
46C2×D103C22⋊C412yes—
47C4×C103—22no—
48C4×C103—41no—
49C4×C103C22×C411yescharacteristic
50C4×C103C2×D411yescharacteristic
51Dic103—41no—
52Dic103C22⋊C412yes—
53C2×C103C2×C22⋊C411yescharacteristic
54C2×C103AGL(1,ℤ/8)11yescharacteristic
55C2×C103#13711yescharacteristic
56D103—22no—
57D103—42no—
58C103#41711yescharacteristic, complemented, Sylow
59#417—1031nomaximal, Sylow
60C2×#41—1031no—
61C2×M16—1031no—
62C2×C4⋊C4—1031no—
63#103—1031no—
64#103D10311yescharacteristic, complemented
65#102—1031no—
66#102—1031no—
67#41—1034no—
68#41—2062no—
69C2×Q8C2×D10311yescharacteristic
70C2×D4—1031no—
71C2×D4—2061no—
72C22×C4—1031no—
73C22×C4—2061no—
74C22×C4—2061no—
75M16—2062no—
76C2×C8—1031no—
77C2×C8C2×D10311yescharacteristic
78C4⋊C4—1031no—
79C4⋊C4—2061no—
80C4⋊C4C2×D10311yescharacteristic
81C23—1031no—
82C23—2061no—
83Q8—21no—
84Q8C4×D10312yescomplemented
85D4—1032no—
86D4—2064no—
87D4—2061no—
88C2×C4—21no—
89C2×C4—21no—
90C2×C4—1031no—
91C2×C4—1032no—
92C2×C4—1032no—
93C2×C4—4122no—
94C2×C4—2064no—
95C2×C4—2061no—
96C2×C4C22×D10311yescharacteristic
97C8—21no—
98C8—2061no—
99C22—1032no—
100C22—4121no—
101C22—4121no—
102C22—2062no—
103C22—2061no—
104C22—2061no—
105C22D4×D10311yescharacteristic
106C4—22no—
107C4—41no—
108C4—1032no—
109C4—4121no—
110C4C2×C4×D10311yescharacteristic
111C4D4×D10311yescharacteristic
112C2—4122no—
113C2—2062no—
114C2C22⋊C4×D10311yescharacteristic
115C2#1569304811yescharacteristic
116C2#1569305311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC4×C103C22×C4
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#417
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#13110088C2semidirect
3. C4⋊C4×D103C2semidirect
4. #15692945C2semidirect
5. #15692943C2semidirect
6. #15692941C2semidirect
7. #103×C103C2semidirect
9. #13110106C4semidirect
25. Q8×C103C2×C4semidirect
33. D412C2×C4semidirect
58. C103#417semidirect
64. #103D103semidirect
84. Q8C4×D103semidirect