Finite Group Databasebeta

← #30636736

Subgroups — #30636736

Order 16256.

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

normal subgroups only

This group has 124 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#22549645C211yesmaximal, characteristic
2#22549602C211yesmaximal, characteristic
3#398×C127C211yesmaximal, characteristic
4C2×#14523232—21no—
5C22⋊(C127⋊C8)—21no—
6C2×C4⋊C4×C127—21no—
7C2×C4⋊C4×C127C411yescharacteristic
8C2×C4⋊C4×C127C2211yescharacteristic
9#95×C127—21no—
10#95×C127C411yescharacteristic
11#14523232—22no—
12#14523232—41no—
13C2×C127⋊C8—41no—
14C2×C127⋊C8—41no—
15C22×C4×C127—21no—
16C22×C4×C127—21no—
17C22×C4×C127C2×C411yescharacteristic
18C22×C4×C127D411yescharacteristic
19C22×C4×C127D411yescharacteristic
20C4⋊C4×C127—41no—
21C4⋊C4×C127—41no—
22C4⋊C4×C127—41no—
23C4⋊C4×C127—41no—
24C127⋊C8—42no—
25C127⋊C8—81no—
26C23×C127C22⋊C411yescharacteristic
27C2×C4×C127—21no—
28C2×C4×C127—21no—
29C2×C4×C127—22no—
30C2×C4×C127—21no—
31C2×C4×C127—21no—
32C2×C4×C127—41no—
33C2×C4×C127—41no—
34C2×C4×C127—41no—
35C2×C4×C127—41no—
36C2×C4×C127—41no—
37C2×C4×C127—41no—
38C2×C4×C127—41no—
39C2×C4×C127D811yescharacteristic
40C2×C4×C127SD1611yescharacteristic
41C22×C127—21no—
42C22×C127—21no—
43C22×C127#9911yescharacteristic
44C22×C127#10211yescharacteristic
45C22×C127#10411yescharacteristic
46C4×C127—21no—
47C4×C127—21no—
48C4×C127—42no—
49C4×C127—41no—
50C4×C127—41no—
51C4×C127—81no—
52C2×C127—21no—
53C2×C127—21no—
54C2×C127#32711yescharacteristic
55C2×C127#35211yescharacteristic
56C2×C127#35611yescharacteristic
57#1346—1271nomaximal, Sylow
58C127#134611yescharacteristic, complemented, Sylow
59#398D12711yescharacteristic
60#343—1271no—
61#324—1271no—
62C2×M16—2541no—
63C2×C4⋊C4—21no—
64C2×C4⋊C4Dic12711yescharacteristic
65C2×C4⋊C4C2×D12711yescharacteristic
66C22⋊C8—2541no—
67#95—21no—
68#95Dic12711yescharacteristic
69C22×C4—21no—
70C22×C4—21no—
71C22×C4C2×Dic12711yescharacteristic
72C22×C4C22⋊D12711yescharacteristic
73C22×C4C22⋊D12711yescharacteristic
74M16—5081no—
75M16—2542no—
76C2×C8—5081no—
77C2×C8—5081no—
78C4⋊C4—41no—
79C4⋊C4—41no—
80C4⋊C4—41no—
81C4⋊C4—41no—
82C23C22⋊Dic12711yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—41no—
89C2×C4—41no—
90C2×C4—41no—
91C2×C4—41no—
92C2×C4—41no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4#1452323311yescharacteristic
96C2×C4#1452323611yescharacteristic
97C8—10161no—
98C8—5082no—
99C22—21no—
100C22—21no—
101C22#1686112411yescharacteristic
102C22#1686113011yescharacteristic
103C22#1686113611yescharacteristic
104C4—21no—
105C4—21no—
106C4—42no—
107C4—41no—
108C4—41no—
109C4—81no—
110C2—21no—
111C2—21no—
112C2#2254961011yescharacteristic
113C2#2254966611yescharacteristic
114C2#2254967511yescharacteristic
subgroupG/H
centerC22#16861124
commutatorC22×C4×C127C2×C4
FrattiniC2×C4⋊C4C2×D127
Fitting#398×C127C2
socleC22×C127#99
prime radicalC23×C127C22⋊C4
cosocleC2×C4⋊C4×C127C22
hypercenter#398D127
hypocenterC127#1346
LCSG ▷ C22×C4×C127 ▷ C23×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C127#1346semidirect

Maximal subgroups

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

subgroupindex
#225496452
#225496022
#398×C1272
#1346127