Finite Group Databasebeta

← #30636887

Subgroups — #30636887

Order 16256.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22549673C211yesmaximal, characteristic, complemented
2#22549671C211yesmaximal, characteristic, complemented
3#496×C127C211yesmaximal, characteristic
4#16861128—21no—
5#16861124—21no—
6C2×SD16×C127—21no—
7C2×D8×C127—21no—
8#127×C127C411yescharacteristic, complemented
9#124×C127C2211yescharacteristic
10#97×C127C411yescharacteristic, complemented
11#14523232—41no—
12C22⋊Dic127—41no—
13C2×Q8×C127D411yescharacteristic
14C2×D4×C127—21no—
15C2×D4×C127—41no—
16C2×D4×C127D411yescharacteristic
17SD16×C127—42no—
18D8×C127—42no—
19C2×C8×C127—21no—
20C22⋊C4×C127—41no—
21C42×C127C2×C411yescharacteristic
22C2×Dic127—81no—
23C127⋊C8—81no—
24C23×C127—21no—
25C23×C127—41no—
26Q8×C127—41no—
27D4×C127—41no—
28D4×C127—41no—
29D4×C127—41no—
30D4×C127—82no—
31C2×C4×C127—21no—
32C2×C4×C127—21no—
33C2×C4×C127C22⋊C411yescharacteristic
34C8×C127—22no—
35C22×C127—41no—
36C22×C127—81no—
37C22×C127—82no—
38C22×C127—81no—
39C22×C127#9911yescharacteristic
40C4×C127—21no—
41C4×C127—41no—
42C4×C127—41no—
43Dic127—161no—
44C2×C127—21no—
45C2×C127—81no—
46C2×C127—161no—
47C2×C127#35311yescharacteristic
48#1406—1271nomaximal, Sylow
49C127#140611yescharacteristic, complemented, Sylow
50#496D12711yescharacteristic
51#355—1271no—
52#354—1271no—
53C2×SD16—21no—
54C2×D8—21no—
55#127Dic12711yescharacteristic, complemented
56#124C2×D12711yescharacteristic
57#101—2541no—
58#99—2541no—
59#97Dic12711yescharacteristic, complemented
60C2×Q8C22⋊D12711yescharacteristic
61C2×D4—21no—
62C2×D4—41no—
63C2×D4C22⋊D12711yescharacteristic
64SD16—42no—
65D8—42no—
66M16—5081no—
67C2×C8—21no—
68C22⋊C4—41no—
69C22⋊C4—5081no—
70C42C2×Dic12711yescharacteristic
71C23—21no—
72C23—41no—
73Q8—41no—
74D4—41no—
75D4—41no—
76D4—41no—
77D4—82no—
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—10161no—
81C2×C4C22⋊Dic12711yescharacteristic
82C8—22no—
83C8—10161no—
84C22—41no—
85C22—81no—
86C22—82no—
87C22—81no—
88C22#1686112411yescharacteristic
89C4—21no—
90C4—41no—
91C4—41no—
92C4—20321no—
93C2—21no—
94C2—81no—
95C2—161no—
96C2#2254966911yescharacteristic
subgroupG/H
centerC2#22549669
commutatorC42×C127C2×C4
Frattini#124C2×D127
Fitting, prime radical#496×C127C2
socleC2×C127#353
cosocle#124×C127C22
hypercenter#496D127
hypocenterC127#1406
LCSG ▷ C42×C127 ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #22549673C2semidirect
2. #22549671C2semidirect
8. #127×C127C4semidirect
10. #97×C127C4semidirect
49. C127#1406semidirect
55. #127Dic127semidirect
59. #97Dic127semidirect

Maximal subgroups

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

subgroupindex
#225496732
#225496712
#496×C1272
#1406127