Finite Group Databasebeta

← #30636890

Subgroups — #30636890

Order 16256.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22549673C211yesmaximal, characteristic
2#22549671C211yesmaximal, characteristic
3#497×C127C211yesmaximal, characteristic
4#16861128—21no—
5#16861124—21no—
6C2×Q16×C127—21no—
7C2×SD16×C127—21no—
8C4⋊Q8×C127C411yescharacteristic, complemented
9#124×C127C2211yescharacteristic
10#97×C127C411yescharacteristic, complemented
11#14523232—41no—
12C22⋊Dic127—41no—
13C2×Q8×C127—21no—
14C2×Q8×C127D411yescharacteristic
15C2×D4×C127D411yescharacteristic
16Q16×C127—42no—
17SD16×C127—42no—
18C2×C8×C127—21no—
19C4⋊C4×C127—41no—
20C22⋊C4×C127—41no—
21C42×C127C2×C411yescharacteristic
22C2×Dic127—81no—
23C127⋊C8—81no—
24C23×C127—21no—
25Q8×C127—41no—
26Q8×C127—41no—
27Q8×C127—41no—
28D4×C127—41no—
29C2×C4×C127—21no—
30C2×C4×C127—21no—
31C2×C4×C127—41no—
32C2×C4×C127C22⋊C411yescharacteristic
33C8×C127—22no—
34C22×C127—41no—
35C22×C127—81no—
36C22×C127#9911yescharacteristic
37C4×C127—21no—
38C4×C127—41no—
39C4×C127—41no—
40C4×C127—81no—
41Dic127—161no—
42C2×C127—21no—
43C2×C127—81no—
44C2×C127#35311yescharacteristic
45#1407—1271nomaximal, Sylow
46C127#140711yescharacteristic, complemented, Sylow
47#497D12711yescharacteristic
48#355—1271no—
49#354—1271no—
50C2×Q16—21no—
51C2×SD16—21no—
52C4⋊Q8Dic12711yescharacteristic, complemented
53#124C2×D12711yescharacteristic
54#101—2541no—
55#99—2541no—
56#97Dic12711yescharacteristic, complemented
57C2×Q8—21no—
58C2×Q8C22⋊D12711yescharacteristic
59C2×D4C22⋊D12711yescharacteristic
60Q16—42no—
61SD16—42no—
62M16—5081no—
63C2×C8—21no—
64C4⋊C4—41no—
65C22⋊C4—41no—
66C22⋊C4—5081no—
67C42C2×Dic12711yescharacteristic
68C23—21no—
69Q8—41no—
70Q8—41no—
71Q8—41no—
72D4—41no—
73C2×C4—21no—
74C2×C4—21no—
75C2×C4—41no—
76C2×C4—10161no—
77C2×C4C22⋊Dic12711yescharacteristic
78C8—22no—
79C8—10161no—
80C22—41no—
81C22—81no—
82C22#1686112411yescharacteristic
83C4—21no—
84C4—41no—
85C4—41no—
86C4—81no—
87C4—20321no—
88C2—21no—
89C2—81no—
90C2#2254966911yescharacteristic
subgroupG/H
centerC2#22549669
commutatorC42×C127C2×C4
Frattini#124C2×D127
Fitting#497×C127C2
socleC2×C127#353
prime radicalC2×D4×C127D4
cosocle#124×C127C22
hypercenter#497D127
hypocenterC127#1407
LCSG ▷ C42×C127 ▷ C2×C4×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #497

Complements

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

NH ≅ G/Ntype
8. C4⋊Q8×C127C4semidirect
10. #97×C127C4semidirect
46. C127#1407semidirect
52. C4⋊Q8Dic127semidirect
56. #97Dic127semidirect

Maximal subgroups

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

subgroupindex
#225496732
#225496712
#497×C1272
#1407127