Finite Group Databasebeta

← #13109673

Subgroups — #13109673

Order 1632.

136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 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×#87972C211yesmaximal, characteristic
2#11717849C211yesmaximal, characteristic, complemented
3C3×#63247C211yesmaximal, characteristic, complemented
4#11717827C212yesmaximal, complemented
5#11717825C212yesmaximal, complemented
6D17⋊M16—31nomaximal, Hall
7C22×D51C411yescharacteristic
8C2×Dic3×C17C411yescharacteristic
9C2×C3×Dic17C2211yescharacteristic
10#87972C411yescharacteristic
11#87972C411yescharacteristic
12#87972C2211yescharacteristic
13#87972C2211yescharacteristic
14C3⋊#3624C2212yescomplemented
15C3×#3624C2212yescomplemented
16C2×C4×D17—31no—
17#63247—31no—
18#63247D311yescharacteristic, complemented
19#63243—32no—
20#63242—32no—
21C22×C3×C17C2×C411yescharacteristic
22C2×D51—22no—
23C2×D51C2×C411yescharacteristic
24C2×D51C2×C411yescharacteristic
25C3×Dic17C2×C411yescharacteristic
26C3×Dic17C2311yescharacteristic
27Dic3×C17C2×C411yescharacteristic
28Dic3×C17C2×C411yescharacteristic
29C22×D17—31no—
30C2×C4×C17—31no—
31C2×Dic17C2×D311yescharacteristic
32C4×D17—31no—
33C4×D17—31no—
34C4×D17—31no—
35C4×D17—31no—
36#3624—32no—
37#3624C2×D312yescomplemented
38C2×C3×C17—21no—
39C2×C3×C17C22×C411yescharacteristic
40D51—21no—
41D51M1612yescomplemented
42D3×M16—171nomaximal, Hall
43C22×C17C4×D311yescharacteristic
44C2×D17—31no—
45C2×D17—31no—
46C2×D17—62no—
47C4×C17—31no—
48C4×C17—31no—
49Dic17C4×D311yescharacteristic
50Dic17C22×D311yescharacteristic
51C3×C17C2×M1611yescharacteristic, complemented, Hall
52C2×C4×D3—171no—
53C3×M16—171no—
54#208—171no—
55ΓL(1,𝔽25)—172no—
56D3×C8—172no—
57C2×C17—21no—
58C2×C17C2×C4×D311yescharacteristic
59D17—32no—
60D17—61no—
61C2×M16—511noSylow
62C22×D3—171no—
63C2×C3×C4—171no—
64C2×Dic3#59511yescharacteristic
65C4×D3—171no—
66C4×D3—171no—
67C4×D3—171no—
68C4×D3—171no—
69C3×C8—172no—
70C3⋊C8—172no—
71C17D3×M1611yescharacteristic, complemented, Sylow
72C22×C4—511no—
73M16—171no—
74M16—512no—
75M16—511no—
76C2×C8—512no—
77C22×C3C2×#59511yescharacteristic
78C2×D3—171no—
79C2×D3—171no—
80C2×D3—342no—
81C3×C4—171no—
82C3×C4—171no—
83Dic3C2×#59511yescharacteristic
84Dic3C2×#59511yescharacteristic
85C23—511no—
86C2×C4—31no—
87C2×C4—171no—
88C2×C4—511no—
89C2×C4—511no—
90C2×C4—511no—
91C2×C4—511no—
92C8—172no—
93C8—512no—
94C2×C3—21no—
95C2×C3C22×#59511yescharacteristic
96D3—172no—
97D3—341no—
98C22—511no—
99C22—511no—
100C22—1022no—
101C22D3×#59511yescharacteristic
102C4—31no—
103C4—31no—
104C4—171no—
105C4—171no—
106C3D17⋊M1611yescharacteristic, complemented, Sylow
107C2—21no—
108C2—512no—
109C2—1021no—
110C2C2×D3×#59511yescharacteristic
subgroupG/H
center, FrattiniC2C2×D3×#595
commutator, socleC2×C3×C17C22×C4
FittingC22×C3×C17C2×C4
prime radicalC22×D51C4
cosocleC3×Dic17C23
hypercenterC22D3×#595
hypocenterC3×C17C2×M16
LCSG ▷ C2×C3×C17 ▷ C3×C17
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #11717849C2semidirect
3. C3×#63247C2semidirect
4. #11717827C2semidirect
5. #11717825C2semidirect
14. C3⋊#3624C22semidirect
15. C3×#3624C22semidirect
18. #63247D3semidirect
37. #3624C2×D3semidirect
41. D51M16semidirect
51. C3×C17C2×M16semidirect
71. C17D3×M16semidirect
106. C3D17⋊M16semidirect

Maximal subgroups

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

subgroupindex
C2×#879722
#117178492
C3×#632472
#117178272
#117178252
D17⋊M163
D3×M1617