Finite Group Databasebeta

← #29601073

Subgroups — #29601073

Order 15616.

134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#21448128C211yesmaximal, characteristic, complemented
2C2×D1952C211yesmaximal, characteristic, complemented
3#21444035C212yesmaximal, complemented
4D3904C212yesmaximal, complemented
5C61×M128C211yesmaximal, characteristic, complemented
6#16840194—21no—
7C2×D976—21no—
8Dic976C2211yescharacteristic, complemented
9#16839601—21no—
10D1952—21no—
11D1952C2212yes—
12D1952C2211yescharacteristic, complemented
13C2×C32×C61C2211yescharacteristic
14C61×C64C2212yescomplemented
15#14519799—41no—
16C2×D488—41no—
17Dic488—21no—
18#14519722—41no—
19D976—21no—
20D976—22no—
21D976—41no—
22C2×C16×C61D411yescharacteristic
23C32×C61D411yescharacteristic
24C32×C61C2311yescharacteristic
25#11758222—81no—
26C2×D244—81no—
27C2×C8×C61D811yescharacteristic
28Dic244—41no—
29D488—42no—
30D488—41no—
31D488—81no—
32#11758190—81no—
33C16×C61D811yescharacteristic
34C16×C61C2×D411yescharacteristic
35C22×D61—161no—
36C2×C4×C61D1611yescharacteristic
37C22⋊D61—161no—
38D244—81no—
39D244—82no—
40D244—161no—
41C4×D61—161no—
42Dic122—81no—
43C8×C61D1611yescharacteristic
44C8×C61C2×D811yescharacteristic
45#13742—611nomaximal, Sylow
46C22×C61D3211yescharacteristic
47C2×D61—161no—
48C2×D61—162no—
49C2×D61—322no—
50C4×C61D3211yescharacteristic
51C4×C61C2×D1611yescharacteristic
52Dic61—161no—
53#2262—611no—
54C2×D32—611no—
55SD128—612no—
56D64—612no—
57M128D6111yescharacteristic, complemented
58C2×C61—21no—
59C2×C61C2×D3211yescharacteristic
60D61—321no—
61D61—322no—
62#508—1221no—
63C2×D16—1221no—
64Q64—611no—
65SD64—1221no—
66D32—611no—
67D32—612no—
68D32—1221no—
69C2×C32C2×D6111yescharacteristic
70C64C2×D6112yescomplemented
71C61#1374211yescharacteristic, complemented, Sylow
72#135—2441no—
73C2×D8—2441no—
74Q32—1221no—
75SD32—2441no—
76D16—1222no—
77D16—1221no—
78D16—2441no—
79C2×C16D24411yescharacteristic
80C32D24411yescharacteristic
81C32C22×D6111yescharacteristic
82#41—4881no—
83C2×D4—4881no—
84Q16—2441no—
85SD16—4881no—
86D8—4881no—
87D8—2442no—
88D8—2441no—
89C2×C8D48811yescharacteristic
90C16D48811yescharacteristic
91C16C2×D24411yescharacteristic
92C23—9761no—
93Q8—4881no—
94D4—9761no—
95D4—9761no—
96D4—4882no—
97D4—4881no—
98C2×C4—9761no—
99C2×C4D97611yescharacteristic
100C8D97611yescharacteristic
101C8C2×D48811yescharacteristic
102C22—19522no—
103C22—9761no—
104C22—9762no—
105C22D195211yescharacteristic
106C4—9761no—
107C4D195211yescharacteristic
108C4C2×D97611yescharacteristic
109C2—21no—
110C2—19522no—
111C2—19521no—
112C2C2×D195211yescharacteristic
subgroupG/H
centerC2C2×D1952
commutator, cosocleC32×C61C23
FrattiniC32C22×D61
FittingC61×M128C2
socleC2×C61C2×D32
hypercenterM128D61
hypocenterC61#13742
LCSG ▷ C32×C61 ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ M128

Complements

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

NH ≅ G/Ntype
1. #21448128C2semidirect
2. C2×D1952C2semidirect
3. #21444035C2semidirect
4. D3904C2semidirect
5. C61×M128C2semidirect
8. Dic976C22semidirect
12. D1952C22semidirect
14. C61×C64C22semidirect
57. M128D61semidirect
70. C64C2×D61semidirect
71. C61#13742semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214481282
C2×D19522
#214440352
D39042
C61×M1282
#1374261