Finite Group Databasebeta

← #34098300

Subgroups — #34098300

Order 20096.

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#23757645C211yesmaximal, characteristic
2#23757066C211yesmaximal, characteristic
3#353×C157C211yesmaximal, characteristic
4C2×#14578942—21no—
5C2×#14578942—21no—
6#19097771C411yescharacteristic, complemented
7#19097686—21no—
8C4×#11929434C411yescharacteristic, complemented
9#127×C157C2211yescharacteristic
10#99×C157—21no—
11C2×Dic314—21no—
12#14578942—42no—
13#14578942—42no—
14C2×#11929434—21no—
15C4⋊Dic157—41no—
16C22⋊Dic157—41no—
17C2×D4×C157—41no—
18C2×D4×C157D411yescharacteristic
19C2×D4×C157D411yescharacteristic
20C22⋊C4×C157—41no—
21C42×C157C2×C411yescharacteristic
22Dic314—41no—
23Dic314—41no—
24C2×Dic157—41no—
25C2×Dic157—81no—
26#11929434—22no—
27C23×C157—21no—
28C23×C157—21no—
29D4×C157—41no—
30D4×C157—41no—
31D4×C157—82no—
32C2×C4×C157—21no—
33C2×C4×C157—81no—
34C2×C4×C157C22⋊C411yescharacteristic
35C22×C157—41no—
36C22×C157—41no—
37C22×C157—81no—
38C22×C157—81no—
39C22×C157#9911yescharacteristic
40C4×C157—22no—
41C4×C157—21no—
42C4×C157—161no—
43Dic157—81no—
44Dic157—161no—
45C2×C157—21no—
46C2×C157—81no—
47C2×C157—81no—
48C2×C157#35311yescharacteristic
49C157#140911yescharacteristic, complemented, Sylow
50#1409—1571nomaximal, Sylow
51#492—1571no—
52#353—1571no—
53#353D15711yescharacteristic
54C2×SD16—3141no—
55C2×SD16—3141no—
56C4⋊Q8—1571no—
57#127C2×D15711yescharacteristic
58#99—21no—
59#99—3141no—
60C4×C8—1571no—
61C2×Q8—3141no—
62C2×D4—41no—
63C2×D4C22⋊D15711yescharacteristic
64C2×D4D62811yescharacteristic
65SD16—6282no—
66SD16—6282no—
67C2×C8—3141no—
68C4⋊C4—6281no—
69C22⋊C4—41no—
70C22⋊C4—6281no—
71C42C4×D15711yescharacteristic
72C23—21no—
73C23—21no—
74Q8—6281no—
75Q8—6281no—
76D4—41no—
77D4—41no—
78D4—82no—
79C2×C4—21no—
80C2×C4—81no—
81C2×C4—6281no—
82C2×C4—12561no—
83C2×C4#1457893111yescharacteristic
84C8—3142no—
85C22—41no—
86C22—41no—
87C22—81no—
88C22—81no—
89C22#1909768511yescharacteristic
90C4—22no—
91C4—21no—
92C4—161no—
93C4—25121no—
94C4—12561no—
95C2—21no—
96C2—81no—
97C2—81no—
98C2#2375706511yescharacteristic
subgroupG/H
centerC2#23757065
commutatorC42×C157C2×C4
Frattini#127C2×D157
Fitting#353×C157C2
socleC2×C157#353
prime radical, cosocle#127×C157C22
hypercenter#353D157
hypocenterC157#1409
LCSG ▷ C42×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
6. #19097771C4semidirect
8. C4×#11929434C4semidirect
49. C157#1409semidirect

Maximal subgroups

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

subgroupindex
#237576452
#237570662
#353×C1572
#1409157