Finite Group Databasebeta

← #30636905

Subgroups — #30636905

Order 16256.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22549673C211yesmaximal, characteristic
2#22549671C211yesmaximal, characteristic
3#488×C127C211yesmaximal, characteristic
4#16861128—21no—
5#16861124—21no—
6#125×C127C411yescharacteristic, complemented
7#124×C127C2211yescharacteristic
8#103×C127—21no—
9#102×C127—21no—
10C4×C8×C127C411yescharacteristic, complemented
11#14523232—41no—
12C22⋊Dic127—41no—
13C2×Q8×C127D411yescharacteristic
14C2×D4×C127D411yescharacteristic
15C2×C8×C127—21no—
16C4⋊C4×C127—21no—
17C4⋊C4×C127—41no—
18C22⋊C4×C127—41no—
19C42×C127C2×C411yescharacteristic
20C2×Dic127—81no—
21C127⋊C8—81no—
22C23×C127—21no—
23Q8×C127—41no—
24D4×C127—41no—
25C2×C4×C127—21no—
26C2×C4×C127—21no—
27C2×C4×C127—41no—
28C2×C4×C127C22⋊C411yescharacteristic
29C8×C127—41no—
30C22×C127—41no—
31C22×C127—81no—
32C22×C127#9911yescharacteristic
33C4×C127—21no—
34C4×C127—41no—
35C4×C127—41no—
36C4×C127—81no—
37Dic127—161no—
38C2×C127—21no—
39C2×C127—81no—
40C2×C127#35411yescharacteristic
41#1414—1271nomaximal, Sylow
42C127#141411yescharacteristic, complemented, Sylow
43#488D12711yescharacteristic
44#355—1271no—
45#354—1271no—
46#125Dic12711yescharacteristic, complemented
47#124C2×D12711yescharacteristic
48#103—21no—
49#102—21no—
50#101—2541no—
51#99—2541no—
52C4×C8Dic12711yescharacteristic, complemented
53C2×Q8C22⋊D12711yescharacteristic
54C2×D4C22⋊D12711yescharacteristic
55M16—5081no—
56C2×C8—21no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—41no—
60C22⋊C4—5081no—
61C42C2×Dic12711yescharacteristic
62C23—21no—
63Q8—41no—
64D4—41no—
65C2×C4—21no—
66C2×C4—21no—
67C2×C4—41no—
68C2×C4—10161no—
69C2×C4C22⋊Dic12711yescharacteristic
70C8—41no—
71C8—10161no—
72C22—41no—
73C22—81no—
74C22#1686112411yescharacteristic
75C4—21no—
76C4—41no—
77C4—41no—
78C4—81no—
79C4—20321no—
80C2—21no—
81C2—81no—
82C2#2254967111yescharacteristic
subgroupG/H
centerC2#22549671
commutatorC42×C127C2×C4
Frattini#124C2×D127
Fitting#488×C127C2
socleC2×C127#354
prime radicalC2×D4×C127D4
cosocle#124×C127C22
hypercenter#488D127
hypocenterC127#1414
LCSG ▷ C42×C127 ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
6. #125×C127C4semidirect
10. C4×C8×C127C4semidirect
42. C127#1414semidirect
46. #125Dic127semidirect
52. C4×C8Dic127semidirect

Maximal subgroups

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

subgroupindex
#225496732
#225496712
#488×C1272
#1414127