Finite Group Databasebeta

← #31795934

Subgroups — #31795934

Order 17536.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22578312C211yesmaximal, characteristic
2#22578310C211yesmaximal, characteristic
3#22577760C211yesmaximal, characteristic
4#17984149—21no—
5#17984147—21no—
6#17984076C2211yescharacteristic
7#17984011—21no—
8#17984008—21no—
9C4×#11764040C411yescharacteristic, complemented
10#125×C137C411yescharacteristic, complemented
11#14555519—41no—
12C22⋊#10587739—41no—
13C2×Dic274D411yescharacteristic
14C2×D548D411yescharacteristic
15C2×#11764040—21no—
16#14555487—41no—
17C4⋊C4×C137—21no—
18C4⋊C4×C137—41no—
19C42×C137C2×C411yescharacteristic
20C2×#10587739—81no—
21#11764047—81no—
22C22×D137—21no—
23Dic274—41no—
24D548—41no—
25C2×Dic137—21no—
26#11764040—41no—
27C2×C4×C137—21no—
28C2×C4×C137—41no—
29C2×C4×C137C22⋊C411yescharacteristic
30C22×C137#9911yescharacteristic
31C2×D137—41no—
32C2×D137—81no—
33#10587739—161no—
34C4×C137—21no—
35C4×C137—41no—
36C4×C137—81no—
37Dic137—41no—
38C2×C137—21no—
39C2×C137#35411yescharacteristic
40D137—81no—
41C137#141411yescharacteristic, complemented, Sylow
42#1414—1371nomaximal, Sylow
43#488—1371no—
44#355—1371no—
45#354—1371no—
46#125#1058773911yescharacteristic, complemented
47#124—1371no—
48#103—2741no—
49#102—2741no—
50#101—2741no—
51#99—2741no—
52C4×C8—1371no—
53C2×Q8—1371no—
54C2×D4—1371no—
55M16—5481no—
56C2×C8—2741no—
57C4⋊C4—21no—
58C4⋊C4—41no—
59C22⋊C4—5481no—
60C22⋊C4—5481no—
61C42C2×#1058773911yescharacteristic
62C23—2741no—
63Q8—5481no—
64D4—5481no—
65C2×C4—21no—
66C2×C4—41no—
67C2×C4—2741no—
68C2×C4—10961no—
69C2×C4C22⋊#1058773911yescharacteristic
70C8—5481no—
71C8—10961no—
72C22—5481no—
73C22—10961no—
74C22#1798414611yescharacteristic
75C4—21no—
76C4—41no—
77C4—81no—
78C4—5481no—
79C4—21921no—
80C2—21no—
81C2—10961no—
82C2#2257830911yescharacteristic
subgroupG/H
centerC2#22578309
commutatorC42×C137C2×C4
FrattiniC42C2×#10587739
Fitting#125×C137C4
socleC2×C137#354
prime radicalC2×D548D4
cosocle#17984076C22
hypercenter#125#10587739
hypocenterC137#1414
LCSG ▷ C42×C137 ▷ C2×C4×C137 ▷ C22×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C4×#11764040C4semidirect
10. #125×C137C4semidirect
41. C137#1414semidirect
46. #125#10587739semidirect

Maximal subgroups

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

subgroupindex
#225783122
#225783102
#225777602
#1414137