Finite Group Databasebeta

← #30636894

Subgroups — #30636894

Order 16256.

110 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 23 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#22550248C211yesmaximal, characteristic
2#22549669C211yesmaximal, characteristic
3#353×C127C211yesmaximal, characteristic
4C2×#14523236—21no—
5C2×#14523236—21no—
6#16861209C411yescharacteristic, complemented
7#16861124—21no—
8C4×C127⋊C8C411yescharacteristic, complemented
9#127×C127C2211yescharacteristic
10#99×C127—21no—
11C2×Dic254—21no—
12#14523236—42no—
13#14523236—42no—
14C2×C127⋊C8—21no—
15C4⋊Dic127—41no—
16C22⋊Dic127—41no—
17C2×D4×C127—41no—
18C2×D4×C127D411yescharacteristic
19C2×D4×C127D411yescharacteristic
20C22⋊C4×C127—41no—
21C42×C127C2×C411yescharacteristic
22Dic254—41no—
23Dic254—41no—
24C2×Dic127—41no—
25C2×Dic127—81no—
26C127⋊C8—22no—
27C23×C127—21no—
28C23×C127—21no—
29D4×C127—41no—
30D4×C127—41no—
31D4×C127—82no—
32C2×C4×C127—21no—
33C2×C4×C127—81no—
34C2×C4×C127C22⋊C411yescharacteristic
35C22×C127—41no—
36C22×C127—41no—
37C22×C127—81no—
38C22×C127—81no—
39C22×C127#9911yescharacteristic
40C4×C127—22no—
41C4×C127—21no—
42C4×C127—161no—
43Dic127—81no—
44Dic127—161no—
45C2×C127—21no—
46C2×C127—81no—
47C2×C127—81no—
48C2×C127#35311yescharacteristic
49#1409—1271nomaximal, Sylow
50C127#140911yescharacteristic, complemented, Sylow
51#492—1271no—
52#353—1271no—
53#353D12711yescharacteristic
54C2×SD16—2541no—
55C2×SD16—2541no—
56C4⋊Q8—1271no—
57#127C2×D12711yescharacteristic
58#99—21no—
59#99—2541no—
60C4×C8—1271no—
61C2×Q8—2541no—
62C2×D4—41no—
63C2×D4C22⋊D12711yescharacteristic
64C2×D4D50811yescharacteristic
65SD16—5082no—
66SD16—5082no—
67C2×C8—2541no—
68C4⋊C4—5081no—
69C22⋊C4—41no—
70C22⋊C4—5081no—
71C42C4×D12711yescharacteristic
72C23—21no—
73C23—21no—
74Q8—5081no—
75Q8—5081no—
76D4—41no—
77D4—41no—
78D4—82no—
79C2×C4—21no—
80C2×C4—81no—
81C2×C4—10161no—
82C2×C4—5081no—
83C2×C4(C2×D127)⋊C411yescharacteristic
84C8—2542no—
85C22—41no—
86C22—41no—
87C22—81no—
88C22—81no—
89C22#1686112311yescharacteristic
90C4—22no—
91C4—21no—
92C4—161no—
93C4—20321no—
94C4—10161no—
95C2—21no—
96C2—81no—
97C2—81no—
98C2#2254966811yescharacteristic
subgroupG/H
centerC2#22549668
commutatorC42×C127C2×C4
Frattini#127C2×D127
Fitting#353×C127C2
socleC2×C127#353
prime radical, cosocle#127×C127C22
hypercenter#353D127
hypocenterC127#1409
LCSG ▷ C42×C127 ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #16861209C4semidirect
8. C4×C127⋊C8C4semidirect
50. C127#1409semidirect

Maximal subgroups

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

subgroupindex
#225502482
#225496692
#353×C1272
#1409127