Finite Group Databasebeta

← #20267995

Subgroups — #20267995

Order 6592.

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

normal subgroups only

This group has 120 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
2C2×#13110092C211yesmaximal, characteristic
3#15693019C211yesmaximal, characteristic, complemented
4#15692983C211yesmaximal, characteristic
5Dic103⋊C8C211yesmaximal, characteristic, complemented
6#15692944C211yesmaximal, characteristic, complemented
7#103×C103C211yesmaximal, characteristic, complemented
8C2×Dic206C2211yescharacteristic
9C2×D412C2211yescharacteristic
10C2×C4×D103—21no—
11#13110094—22no—
12#13110092—22no—
13C2×C103⋊C8C2211yescharacteristic
14Dic103⋊C4—21no—
15Dic103⋊C4—21no—
16(C2×D103)⋊C4—21no—
17C4×Dic103C2211yescharacteristic
18C2×Q8×C103C2211yescharacteristic
19C2×C8×C103C2211yescharacteristic
20C4⋊C4×C103C2211yescharacteristic
21C22×D103—21no—
22Q8×C103—21no—
23Q8×C103—21no—
24C2×C4×C103—21no—
25C2×C4×C103—21no—
26C2×C4×C103C2311yescharacteristic
27C2×Dic103—21no—
28C2×Dic103D411yescharacteristic
29C2×Dic103D411yescharacteristic
30D412—21no—
31D412D412yes—
32C4×D103—42no—
33Dic206—21no—
34Dic206—21no—
35C8×C103—21no—
36C103⋊C8—21no—
37C22×C103C2×D411yescharacteristic
38C2×D103—22no—
39C2×D103—41no—
40C2×D103—41no—
41C4×C103—41no—
42C4×C103—41no—
43C4×C103C2×D411yescharacteristic
44C4×C103#4111yescharacteristic
45Dic103—21no—
46Dic103—41no—
47Dic103SD1612yescomplemented
48C2×C103#12111yescharacteristic
49C2×C103C2×SD1611yescharacteristic
50C2×C103#13711yescharacteristic
51D103—42no—
52C103#46111yescharacteristic, complemented, Sylow
53#461—1031nomaximal, Sylow
54C2×SD16—1031no—
55C2×SD16—1031no—
56C4⋊Q8—1031no—
57C4×D4—1031no—
58C4⋊C8—1031no—
59#103—1031no—
60#103D10311yescharacteristic, complemented
61C2×Q8—1031no—
62C2×Q8C2×D10311yescharacteristic
63C2×D4—1031no—
64C22×C4—2061no—
65SD16—2062no—
66SD16—2062no—
67C2×C8—1031no—
68C2×C8C2×D10311yescharacteristic
69C4⋊C4—2061no—
70C4⋊C4—2061no—
71C4⋊C4C2×D10311yescharacteristic
72C22⋊C4—2061no—
73C42—1031no—
74C23—2061no—
75Q8—21no—
76Q8—21no—
77Q8—2061no—
78Q8—2061no—
79D4—1032no—
80D4—2061no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—1031no—
84C2×C4—1031no—
85C2×C4—4122no—
86C2×C4—2061no—
87C2×C4C22×D10311yescharacteristic
88C8—21no—
89C8—2061no—
90C22—4121no—
91C22—4121no—
92C22—2062no—
93C22D4×D10311yescharacteristic
94C4—41no—
95C4—41no—
96C4—1032no—
97C4—4121no—
98C4—2061no—
99C4D4×D10311yescharacteristic
100C4#1311010511yescharacteristic
101C2—4122no—
102C2#1569299411yescharacteristic
103C2SD16×D10311yescharacteristic
104C2#1569305311yescharacteristic
subgroupG/H
centerC22D4×D103
commutatorC2×C4×C103C23
FrattiniC2×C4C22×D103
Fitting#103×C103C2
socleC22×C103C2×D4
hypercenter#103D103
hypocenterC103#461
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
3. #15693019C2semidirect
5. Dic103⋊C8C2semidirect
6. #15692944C2semidirect
7. #103×C103C2semidirect
47. Dic103SD16semidirect
52. C103#461semidirect
60. #103D103semidirect