Finite Group Databasebeta

← #30636715

Subgroups — #30636715

Order 16256.

114 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 33 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#22549658C211yesmaximal, characteristic, complemented
2#22549633C211yesmaximal, characteristic, complemented
3#469×C127C211yesmaximal, characteristic
4#16861168—21no—
5#16861149—21no—
6C2×D8×C127C411yescharacteristic, complemented
7C2×M16×C127C2211yescharacteristic
8#121×C127—21no—
9#106×C127C411yescharacteristic, complemented
10#102×C127—21no—
11C4⋊Dic127—41no—
12C22⋊Dic127—41no—
13C4×Dic127—22no—
14C127⋊C16—41no—
15C2×D4×C127—21no—
16C2×D4×C127—41no—
17C22×C4×C127D411yescharacteristic
18D8×C127—41no—
19M16×C127—41no—
20C2×C8×C127C2×C411yescharacteristic
21C2×C8×C127D411yescharacteristic
22C4⋊C4×C127—21no—
23C22⋊C4×C127—41no—
24C2×Dic127—42no—
25C23×C127—41no—
26C23×C127D811yescharacteristic
27D4×C127—41no—
28D4×C127—41no—
29D4×C127—82no—
30C2×C4×C127—21no—
31C2×C4×C127—21no—
32C2×C4×C127—41no—
33C2×C4×C127C22⋊C411yescharacteristic
34C2×C4×C127SD1611yescharacteristic
35C8×C127—21no—
36C8×C127—21no—
37C22×C127—21no—
38C22×C127—41no—
39C22×C127—81no—
40C22×C127—81no—
41C22×C127—81no—
42C22×C127#10211yescharacteristic
43C4×C127—21no—
44C4×C127—81no—
45C4×C127#9911yescharacteristic
46C4×C127#10411yescharacteristic
47Dic127—82no—
48C2×C127—21no—
49C2×C127—41no—
50C2×C127—161no—
51C2×C127#32711yescharacteristic
52#1339—1271nomaximal, Sylow
53C127#133911yescharacteristic, complemented, Sylow
54#469D12711yescharacteristic
55#349—1271no—
56H(3,ℤ/4)—1271no—
57C2×D8Dic12711yescharacteristic, complemented
58C2×M16C2×D12711yescharacteristic
59#121—21no—
60#117—2541no—
61M32—2541no—
62#106Dic12711yescharacteristic, complemented
63#102—21no—
64C2×D4—21no—
65C2×D4—41no—
66C22×C4C22⋊D12711yescharacteristic
67D8—41no—
68M16—41no—
69C2×C8C2×Dic12711yescharacteristic
70C2×C8C22⋊D12711yescharacteristic
71C4⋊C4—21no—
72C4⋊C4—5081no—
73C22⋊C4—41no—
74C22⋊C4—5081no—
75C42—2542no—
76C16—5081no—
77C23—41no—
78C23#1452323311yescharacteristic
79D4—41no—
80D4—41no—
81D4—82no—
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—5082no—
86C2×C4C22⋊Dic12711yescharacteristic
87C2×C4#1452323611yescharacteristic
88C8—21no—
89C8—21no—
90C22—21no—
91C22—41no—
92C22—81no—
93C22—81no—
94C22—81no—
95C22#1686113011yescharacteristic
96C4—21no—
97C4—81no—
98C4—10162no—
99C4#1686112411yescharacteristic
100C4#1686113611yescharacteristic
101C2—21no—
102C2—41no—
103C2—161no—
104C2#2254961011yescharacteristic
subgroupG/H
centerC2#22549610
commutatorC2×C8×C127C2×C4
FrattiniC2×M16C2×D127
Fitting, prime radical#469×C127C2
socleC2×C127#327
cosocleC2×M16×C127C22
hypercenter#469D127
hypocenterC127#1339
LCSG ▷ C2×C8×C127 ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #22549658C2semidirect
2. #22549633C2semidirect
6. C2×D8×C127C4semidirect
9. #106×C127C4semidirect
53. C127#1339semidirect
57. C2×D8Dic127semidirect
62. #106Dic127semidirect

Maximal subgroups

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

subgroupindex
#225496582
#225496332
#469×C1272
#1339127