Finite Group Databasebeta

← #20267948

Subgroups — #20267948

Order 6592.

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

normal subgroups only

This group has 148 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×Q8×D103C211yesmaximal, characteristic
2C2×Dic412C211yesmaximal, characteristic, complemented
3C2×#13110095C211yesmaximal, characteristic, complemented
4#15693001C211yesmaximal, characteristic
5#15692944C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C8C211yesmaximal, characteristic
7#103×C103C211yesmaximal, characteristic, complemented
8C2×Dic206—21no—
9C2×Dic206C2211yescharacteristic
10C2×Dic206C2211yescharacteristic
11Q8×D103—22no—
12Q8×D103—22no—
13C2×C4×D103—21no—
14C2×C4×D103C2211yescharacteristic
15Dic412—22no—
16#13110095—22no—
17C2×C103⋊C8C2211yescharacteristic
18C4⋊Dic103—21no—
19(C2×D103)⋊C4—21no—
20C2×Q8×C103C2211yescharacteristic
21C2×C8×C103C2211yescharacteristic
22C4⋊C4×C103C2211yescharacteristic
23C22×D103D411yescharacteristic
24Q8×C103—21no—
25Q8×C103D412yes—
26C2×C4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103C2311yescharacteristic
29C2×Dic103—21no—
30C2×Dic103—21no—
31C2×Dic103D411yescharacteristic
32C4×D103—24no—
33C4×D103—21no—
34C4×D103—21no—
35Dic206—24no—
36Dic206—21no—
37Dic206—21no—
38Dic206—21no—
39Dic206D412yes—
40C8×C103—21no—
41C103⋊C8—21no—
42C22×C103C2×D411yescharacteristic
43C2×D103—21no—
44C2×D103—21no—
45C2×D103Q1612yescomplemented
46C4×C103—22no—
47C4×C103—41no—
48C4×C103C2×D411yescharacteristic
49C4×C103C2×D411yescharacteristic
50Dic103—21no—
51Dic103—22no—
52Dic103—41no—
53C2×C103#12011yescharacteristic
54C2×C103C2×Q1611yescharacteristic
55C2×C103#13711yescharacteristic
56D103—22no—
57C103#45111yescharacteristic, complemented, Sylow
58#451—1031nomaximal, Sylow
59C22×Q8—1031no—
60C2×Q16—1031no—
61C2×Q16—1031no—
62C22⋊Q8—1031no—
63#103—1031no—
64#103D10311yescharacteristic, complemented
65C22⋊C8—1031no—
66C2×Q8—1031no—
67C2×Q8—1031no—
68C2×Q8—2061no—
69C2×Q8—2062no—
70C2×Q8—2062no—
71C2×Q8C2×D10311yescharacteristic
72C22×C4—1031no—
73C22×C4—2061no—
74Q16—2062no—
75Q16—2062no—
76C2×C8—1031no—
77C2×C8C2×D10311yescharacteristic
78C4⋊C4—2061no—
79C4⋊C4C2×D10311yescharacteristic
80C22⋊C4—2061no—
81C23—1031no—
82Q8—21no—
83Q8—1032no—
84Q8—2064no—
85Q8—2061no—
86Q8—2061no—
87Q8—2061no—
88Q8D41212yes—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—1031no—
92C2×C4—2064no—
93C2×C4—2061no—
94C2×C4—2061no—
95C2×C4—2061no—
96C2×C4—2061no—
97C2×C4C22×D10311yescharacteristic
98C8—21no—
99C8—2061no—
100C22—1032no—
101C22—2061no—
102C22—2061no—
103C22D4×D10311yescharacteristic
104C4—22no—
105C4—41no—
106C4—4121no—
107C4—2061no—
108C4—2062no—
109C4D4×D10311yescharacteristic
110C4C2×D41211yescharacteristic
111C2—2062no—
112C2#1569299111yescharacteristic
113C2Q16×D10311yescharacteristic
114C2#1569305011yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#451
LCSG ▷ C2×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×Dic412C2semidirect
3. C2×#13110095C2semidirect
5. #15692944C2semidirect
7. #103×C103C2semidirect
45. C2×D103Q16semidirect
57. C103#451semidirect
64. #103D103semidirect