Finite Group Databasebeta

← #34098283

Subgroups — #34098283

Order 20096.

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

normal subgroups only

This group has 112 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#23757450C211yesmaximal, characteristic
2#23757013C211yesmaximal, characteristic, complemented
3#355×C157C211yesmaximal, characteristic, complemented
4#19097816C411yescharacteristic
5#19097802—21no—
6#19097699—21no—
7#19097688C411yescharacteristic
8#19097682—21no—
9#124×C157C2211yescharacteristic
10#101×C157—21no—
11#14578954—21no—
12#14578953—41no—
13C2×C22⋊D157—41no—
14D4×D157—41no—
15#14578944—41no—
16#14578941—41no—
17#14578938—21no—
18C2×#11929434—41no—
19C2×Q8×C157D411yescharacteristic
20C2×D4×C157C2×C411yescharacteristic
21M16×C157—41no—
22C22⋊C4×C157—41no—
23C42×C157D411yescharacteristic
24C22×D157—41no—
25Dic314—21no—
26D628—21no—
27C22⋊D157—42no—
28C22⋊D157—41no—
29C2×Dic157—41no—
30C4×D157—41no—
31#11929434—41no—
32#11929434—42no—
33C23×C157—21no—
34Q8×C157—41no—
35D4×C157—41no—
36C2×C4×C157—21no—
37C2×C4×C157—21no—
38C2×C4×C157C22⋊C411yescharacteristic
39C8×C157—81no—
40C22×C157—41no—
41C22×C157—81no—
42C22×C157#9911yescharacteristic
43C2×D157—41no—
44C2×D157—161no—
45C4×C157—21no—
46C4×C157—41no—
47C4×C157—41no—
48Dic157—41no—
49C2×C157—21no—
50C2×C157—81no—
51C2×C157AΣL(1,𝔽16)11yescharacteristic
52D157—81no—
53C157#140311yescharacteristic, complemented, Sylow
54#1403—1571nomaximal, Sylow
55#455—1571no—
56#355D15711yescharacteristic, complemented
57#329—1571no—
58H(5,𝔽2)—1571no—
59#137—3141no—
60#124C2×D15711yescharacteristic
61#104—3141no—
62#101—21no—
63#100—1571no—
64#97—3141no—
65#41—3141no—
66#41—6281no—
67C2×Q8C22⋊D15711yescharacteristic
68C2×D4—6281no—
69C2×D4—6281no—
70C2×D4C4×D15711yescharacteristic
71Q16—6281no—
72SD16—6281no—
73M16—41no—
74M16—3141no—
75C2×C8—6281no—
76C22⋊C4—41no—
77C42D62811yescharacteristic
78C23—21no—
79C23—6281no—
80Q8—41no—
81Q8—3141no—
82D4—41no—
83D4—3141no—
84D4—6282no—
85D4—6281no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—6281no—
89C2×C4—6281no—
90C2×C4#1457893111yescharacteristic
91C8—81no—
92C8—6281no—
93C8—6282no—
94C22—41no—
95C22—81no—
96C22—6281no—
97C22—25121no—
98C22#1909768511yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—6281no—
103C2—21no—
104C2—81no—
105C2—12561no—
106C2#2375705911yescharacteristic
subgroupG/H
centerC2#23757059
commutatorC2×D4×C157C2×C4
Frattini#124C2×D157
Fitting#355×C157C2
socleC2×C157AΣL(1,𝔽16)
prime radical#19097816C4
cosocle#124×C157C22
hypercenter#355D157
hypocenterC157#1403
LCSG ▷ C2×D4×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #23757013C2semidirect
3. #355×C157C2semidirect
53. C157#1403semidirect
56. #355D157semidirect

Maximal subgroups

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

subgroupindex
#237574502
#237570132
#355×C1572
#1403157