Finite Group Databasebeta

← #34098298

Subgroups — #34098298

Order 20096.

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

normal subgroups only

This group has 120 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#23757649C211yesmaximal, characteristic
2#23757066C211yesmaximal, characteristic, complemented
3#353×C157C211yesmaximal, characteristic, complemented
4C2×#14578939—21no—
5C2×#14578939—21no—
6#19097768C411yescharacteristic, complemented
7#19097686—21no—
8C4×#11929434C411yescharacteristic, complemented
9#127×C157C2211yescharacteristic
10#99×C157—21no—
11C2×D628—21no—
12C2×D628—41no—
13#14578939—42no—
14#14578939—42no—
15C2×#11929434—21no—
16C22⋊Dic157—41no—
17C2×D4×C157—41no—
18C2×D4×C157D411yescharacteristic
19C2×D4×C157D411yescharacteristic
20C22⋊C4×C157—41no—
21C42×C157C2×C411yescharacteristic
22C22×D157—41no—
23D628—41no—
24D628—41no—
25D628—82no—
26C2×Dic157—81no—
27#11929434—22no—
28C23×C157—21no—
29C23×C157—21no—
30D4×C157—41no—
31D4×C157—41no—
32D4×C157—82no—
33C2×C4×C157—21no—
34C2×C4×C157—81no—
35C2×C4×C157C22⋊C411yescharacteristic
36C22×C157—41no—
37C22×C157—41no—
38C22×C157—81no—
39C22×C157—81no—
40C22×C157#9911yescharacteristic
41C2×D157—82no—
42C2×D157—81no—
43C4×C157—22no—
44C4×C157—21no—
45C4×C157—161no—
46Dic157—161no—
47C2×C157—21no—
48C2×C157—81no—
49C2×C157—81no—
50C2×C157#35311yescharacteristic
51D157—161no—
52C157#140811yescharacteristic, complemented, Sylow
53#1408—1571nomaximal, Sylow
54#493—1571no—
55#353—1571no—
56#353D15711yescharacteristic, complemented
57C2×D8—3141no—
58C2×D8—3141no—
59#127—1571no—
60#127C2×D15711yescharacteristic
61#99—21no—
62#99—3141no—
63C4×C8—1571no—
64C2×D4—41no—
65C2×D4—3141no—
66C2×D4—6281no—
67C2×D4C22⋊D15711yescharacteristic
68C2×D4D62811yescharacteristic
69D8—6282no—
70D8—6282no—
71C2×C8—3141no—
72C22⋊C4—41no—
73C22⋊C4—6281no—
74C42C4×D15711yescharacteristic
75C23—21no—
76C23—21no—
77C23—6281no—
78D4—41no—
79D4—41no—
80D4—82no—
81D4—6281no—
82D4—6281no—
83D4—12562no—
84C2×C4—21no—
85C2×C4—81no—
86C2×C4—12561no—
87C2×C4#1457893111yescharacteristic
88C8—3142no—
89C22—41no—
90C22—41no—
91C22—81no—
92C22—81no—
93C22—12562no—
94C22—12561no—
95C22#1909768511yescharacteristic
96C4—22no—
97C4—21no—
98C4—161no—
99C4—25121no—
100C2—21no—
101C2—81no—
102C2—81no—
103C2—25121no—
104C2#2375706511yescharacteristic
subgroupG/H
centerC2#23757065
commutatorC42×C157C2×C4
Frattini#127C2×D157
Fitting#353×C157C2
socleC2×C157#353
prime radical#23757649C2
cosocle#127×C157C22
hypercenter#353D157
hypocenterC157#1408
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
2. #23757066C2semidirect
3. #353×C157C2semidirect
6. #19097768C4semidirect
8. C4×#11929434C4semidirect
52. C157#1408semidirect
56. #353D157semidirect

Maximal subgroups

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

subgroupindex
#237576492
#237570662
#353×C1572
#1408157