Finite Group Databasebeta

← #30636739

Subgroups — #30636739

Order 16256.

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

normal subgroups only

This group has 126 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
1C22⋊(C127⋊C16)C211yesmaximal, characteristic, complemented
2#22549639C211yesmaximal, characteristic, complemented
3#466×C127C211yesmaximal, characteristic
4C2×C4⋊Dic127—21no—
5C2×C127⋊C16—21no—
6C2×D8×C127C411yescharacteristic, complemented
7C22×C8×C127C2211yescharacteristic
8#121×C127—21no—
9#107×C127C411yescharacteristic, complemented
10#102×C127—21no—
11C22×Dic127—41no—
12C4⋊Dic127—22no—
13C4⋊Dic127—41no—
14C127⋊C16—41no—
15C2×D4×C127—21no—
16C2×D4×C127—41no—
17C22×C4×C127D411yescharacteristic
18D8×C127—41no—
19C2×C8×C127—41no—
20C2×C8×C127C2×C411yescharacteristic
21C2×C8×C127D411yescharacteristic
22C4⋊C4×C127—21no—
23C22⋊C4×C127—41no—
24C2×Dic127—42no—
25C2×Dic127—81no—
26C2×Dic127—81no—
27C23×C127—41no—
28C23×C127D811yescharacteristic
29D4×C127—41no—
30D4×C127—41no—
31D4×C127—81no—
32D4×C127—81no—
33C2×C4×C127—21no—
34C2×C4×C127—21no—
35C2×C4×C127—41no—
36C2×C4×C127C22⋊C411yescharacteristic
37C2×C4×C127SD1611yescharacteristic
38C8×C127—21no—
39C8×C127—21no—
40C22×C127—21no—
41C22×C127—21no—
42C22×C127—81no—
43C22×C127—81no—
44C22×C127—81no—
45C22×C127#10211yescharacteristic
46C22×C127D1611yescharacteristic
47C22×C127SD3211yescharacteristic
48C4×C127—21no—
49C4×C127—81no—
50C4×C127#9911yescharacteristic
51C4×C127#10411yescharacteristic
52Dic127—82no—
53C2×C127—21no—
54C2×C127—21no—
55C2×C127—161no—
56C2×C127#32711yescharacteristic
57C2×C127#35711yescharacteristic
58C2×C127#36011yescharacteristic
59#1347—1271nomaximal, Sylow
60C127#134711yescharacteristic, complemented, Sylow
61#466D12711yescharacteristic
62C22⋊C16—1271no—
63#340—1271no—
64C2×D8Dic12711yescharacteristic, complemented
65C22×C8C2×D12711yescharacteristic
66#121—21no—
67C2×C4⋊C4—2541no—
68C2×C16—2541no—
69#107Dic12711yescharacteristic, complemented
70#102—21no—
71C2×D4—21no—
72C2×D4—41no—
73C22×C4—5081no—
74C22×C4C22⋊D12711yescharacteristic
75D8—41no—
76C2×C8—41no—
77C2×C8C2×Dic12711yescharacteristic
78C2×C8C22⋊D12711yescharacteristic
79C4⋊C4—21no—
80C4⋊C4—5081no—
81C4⋊C4—2542no—
82C22⋊C4—41no—
83C16—5081no—
84C23—41no—
85C23#1452323311yescharacteristic
86D4—41no—
87D4—41no—
88D4—81no—
89D4—81no—
90C2×C4—21no—
91C2×C4—21no—
92C2×C4—41no—
93C2×C4—10161no—
94C2×C4—10161no—
95C2×C4—5082no—
96C2×C4C22⋊Dic12711yescharacteristic
97C2×C4#1452323611yescharacteristic
98C8—21no—
99C8—21no—
100C22—21no—
101C22—21no—
102C22—81no—
103C22—81no—
104C22—81no—
105C22#1686113011yescharacteristic
106C22#1686115011yescharacteristic
107C22#1686115311yescharacteristic
108C4—21no—
109C4—81no—
110C4—10162no—
111C4#1686112411yescharacteristic
112C4#1686113611yescharacteristic
113C2—21no—
114C2—21no—
115C2—161no—
116C2#2254961011yescharacteristic
117C2#2254967711yescharacteristic
118C2#2254968611yescharacteristic
subgroupG/H
centerC22#16861130
commutatorC2×C8×C127C2×C4
FrattiniC22×C8C2×D127
Fitting, prime radical#466×C127C2
socleC22×C127#102
cosocleC22×C8×C127C22
hypercenter#466D127
hypocenterC127#1347
LCSG ▷ C2×C8×C127 ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22⋊(C127⋊C16)C2semidirect
2. #22549639C2semidirect
6. C2×D8×C127C4semidirect
9. #107×C127C4semidirect
60. C127#1347semidirect
64. C2×D8Dic127semidirect
69. #107Dic127semidirect

Maximal subgroups

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

subgroupindex
C22⋊(C127⋊C16)2
#225496392
#466×C1272
#1347127