Finite Group Databasebeta

← #30636675

Subgroups — #30636675

Order 16256.

134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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#22549745C211yesmaximal, characteristic
2#22549602C211yesmaximal, characteristic
3#324×C127C211yesmaximal, characteristic
4C2×C4⋊Dic127C411yescharacteristic
5C2×Dic127⋊C4—21no—
6C2×Dic127⋊C4—21no—
7C2×C4×Dic127C411yescharacteristic
8C22⋊(C127⋊C8)—21no—
9C2×C4⋊C4×C127C2211yescharacteristic
10C22⋊C8×C127—21no—
11C22×Dic127—21no—
12C22×Dic127—21no—
13C2×C127⋊C8—41no—
14C4⋊Dic127—41no—
15Dic127⋊C4—42no—
16Dic127⋊C4—42no—
17C4×Dic127—21no—
18C4×Dic127C812yescomplemented
19C22×C4×C127C2×C411yescharacteristic
20C22×C4×C127D411yescharacteristic
21C22×C4×C127D411yescharacteristic
22C2×C8×C127—41no—
23C4⋊C4×C127—41no—
24C2×Dic127—22no—
25C2×Dic127—22no—
26C2×Dic127—22no—
27C2×Dic127—41no—
28C2×Dic127—41no—
29C2×Dic127—41no—
30C127⋊C8—81no—
31C23×C127C22⋊C411yescharacteristic
32C2×C4×C127—21no—
33C2×C4×C127—21no—
34C2×C4×C127—21no—
35C2×C4×C127—21no—
36C2×C4×C127—41no—
37C2×C4×C127—41no—
38C2×C4×C127C2×C811yescharacteristic
39C2×C4×C127M1611yescharacteristic
40C8×C127—81no—
41C22×C127—21no—
42C22×C127—21no—
43C22×C127C22⋊C811yescharacteristic
44C22×C127#9911yescharacteristic
45C22×C127#10111yescharacteristic
46C4×C127—21no—
47C4×C127—21no—
48C4×C127—41no—
49C4×C127—41no—
50Dic127—24no—
51Dic127—81no—
52C2×C127—21no—
53C2×C127—21no—
54C2×C127#32411yescharacteristic
55C2×C127#35311yescharacteristic
56C2×C127#35611yescharacteristic
57#1325—1271nomaximal, Sylow
58C127#132511yescharacteristic, complemented, Sylow
59#384—1271no—
60#324—1271no—
61#324D12711yescharacteristic
62C2×C4⋊C4—1271no—
63C2×C4⋊C4—2541no—
64C2×C4⋊C4—2541no—
65C2×C4⋊C4C2×D12711yescharacteristic
66C2×C42—1271no—
67C22⋊C8—21no—
68C22⋊C8—2541no—
69C22×C4—2541no—
70C22×C4—2541no—
71C22×C4C4×D12711yescharacteristic
72C22×C4C22⋊D12711yescharacteristic
73C22×C4D50811yescharacteristic
74C2×C8—41no—
75C2×C8—5081no—
76C4⋊C4—41no—
77C4⋊C4—5081no—
78C4⋊C4—5082no—
79C4⋊C4—5082no—
80C42—1272no—
81C42—2541no—
82C23(C2×D127)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—5081no—
90C2×C4—5081no—
91C2×C4—5081no—
92C2×C4—2542no—
93C2×C4—2542no—
94C2×C4—2542no—
95C2×C4C8×D12711yescharacteristic
96C2×C4#1452323111yescharacteristic
97C8—81no—
98C8—10161no—
99C22—21no—
100C22—21no—
101C22(C2×D127)⋊C811yescharacteristic
102C22#1686112311yescharacteristic
103C22#1686112711yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—10161no—
109C4—2544no—
110C2—21no—
111C2—21no—
112C2#2254960111yescharacteristic
113C2#2254966811yescharacteristic
114C2#2254967411yescharacteristic
subgroupG/H
centerC22#16861123
commutatorC2×C4×C127C2×C8
FrattiniC2×C4⋊C4C2×D127
Fitting#324×C127C2
socleC22×C127#99
prime radicalC23×C127C22⋊C4
cosocleC2×C4⋊C4×C127C22
hypercenter#324D127
hypocenterC127#1325
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
18. C4×Dic127C8semidirect
58. C127#1325semidirect

Maximal subgroups

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

subgroupindex
#225497452
#225496022
#324×C1272
#1325127