Finite Group Databasebeta

← #20268007

Subgroups — #20268007

Order 6592.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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×#13110094C211yesmaximal, characteristic, complemented
2C2×D824C211yesmaximal, characteristic
3#15693009C211yesmaximal, characteristic, complemented
4C4×D412C211yesmaximal, characteristic, complemented
5#15692946C211yesmaximal, characteristic, complemented
6#15692943C211yesmaximal, characteristic, complemented
7C4⋊C8×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×D412C2211yescharacteristic
11C2×C4×D103—21no—
12#13110094—22no—
13D824—22no—
14C4⋊Dic103C2211yescharacteristic
15(C2×D103)⋊C4—21no—
16(C2×D103)⋊C4—21no—
17(C2×D103)⋊C4—21no—
18C2×C8×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C42×C103C2211yescharacteristic
21C22×D103—21no—
22C22×D103—21no—
23C2×C4×C103D411yescharacteristic
24C2×C4×C103D411yescharacteristic
25C2×C4×C103C2311yescharacteristic
26C2×Dic103—21no—
27C2×Dic103—21no—
28D412—21no—
29D412—21no—
30D412—21no—
31D412D412yes—
32C4×D103—42no—
33Dic206—21no—
34Dic206—21no—
35C8×C103—21no—
36C8×C103—21no—
37C22×C103C2×D411yescharacteristic
38C2×D103—22no—
39C2×D103—41no—
40C2×D103—41no—
41C2×D103—41no—
42C2×D103—41no—
43C2×D103—41no—
44C4×C103—21no—
45C4×C103—21no—
46C4×C103C2×D411yescharacteristic
47C4×C103#4111yescharacteristic
48Dic103—41no—
49Dic103—41no—
50C2×C103#12111yescharacteristic
51C2×C103#13511yescharacteristic
52C2×C103AGL(1,ℤ/8)11yescharacteristic
53D103—42no—
54D103—81no—
55C103#46311yescharacteristic, complemented, Sylow
56#463—1031nomaximal, Sylow
57C2×SD16—1031no—
58C2×D8—1031no—
59#124—1031no—
60C4×D4—1031no—
61C4⋊C8D10311yescharacteristic, complemented
62#103—1031no—
63#102—1031no—
64C2×Q8—1031no—
65C2×D4—1031no—
66C2×D4—1031no—
67C22×C4—2061no—
68SD16—2062no—
69D8—2062no—
70C2×C8C2×D10311yescharacteristic
71C2×C8C2×D10311yescharacteristic
72C4⋊C4—1031no—
73C22⋊C4—2061no—
74C22⋊C4—2061no—
75C22⋊C4—2061no—
76C42C2×D10311yescharacteristic
77C23—2061no—
78C23—2061no—
79Q8—2061no—
80Q8—2061no—
81D4—1032no—
82D4—2061no—
83D4—2061no—
84D4—2061no—
85C2×C4—4122no—
86C2×C4—2061no—
87C2×C4—2061no—
88C2×C4D41211yescharacteristic
89C2×C4D41211yescharacteristic
90C2×C4C22×D10311yescharacteristic
91C8—21no—
92C8—21no—
93C22—4121no—
94C22—4121no—
95C22—4121no—
96C22—4121no—
97C22—4121no—
98C22—2062no—
99C22C2×D41211yescharacteristic
100C4—21no—
101C4—21no—
102C4—4121no—
103C4—4121no—
104C4D4×D10311yescharacteristic
105C4#1311010611yescharacteristic
106C2—8241no—
107C2—4122no—
108C2#1569299611yescharacteristic
109C2#1569304311yescharacteristic
110C2#1569304911yescharacteristic
subgroupG/H
centerC22C2×D412
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
FittingC4⋊C8×C103C2
socleC22×C103C2×D4
hypercenterC4⋊C8D103
hypocenterC103#463
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#13110094C2semidirect
3. #15693009C2semidirect
4. C4×D412C2semidirect
5. #15692946C2semidirect
6. #15692943C2semidirect
7. C4⋊C8×C103C2semidirect
55. C103#463semidirect
61. C4⋊C8D103semidirect