Finite Group Databasebeta

← #34098291

Subgroups — #34098291

Order 20096.

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

normal subgroups only

This group has 106 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#23757455C211yesmaximal, characteristic
2#23757072C211yesmaximal, characteristic, complemented
3#333×C157C211yesmaximal, characteristic, complemented
4#19097819C411yescharacteristic
5#19097802—21no—
6#19097699—21no—
7#19097690—21no—
8#19097690C411yescharacteristic
9C4⋊Q8×C157C2211yescharacteristic
10C4⋊C8×C157—21no—
11#14578955—41no—
12#14578954—21no—
13#14578954—41no—
14Q8×D157—41no—
15#14578944—41no—
16#14578941—41no—
17#14578938—21no—
18#14578938—41no—
19C2×Q8×C157C2×C411yescharacteristic
20C2×Q8×C157D411yescharacteristic
21C2×C8×C157—41no—
22C4⋊C4×C157—41no—
23C42×C157D411yescharacteristic
24Dic314—21no—
25Dic314—41no—
26D628—21no—
27D628—41no—
28C22⋊D157—41no—
29C4×D157—41no—
30C4×D157—42no—
31#11929434—41no—
32#11929434—81no—
33Q8×C157—41no—
34Q8×C157—41no—
35C2×C4×C157—21no—
36C2×C4×C157—21no—
37C2×C4×C157—21no—
38C2×C4×C157C22⋊C411yescharacteristic
39C8×C157—81no—
40C22×C157#9911yescharacteristic
41C2×D157—41no—
42C4×C157—21no—
43C4×C157—21no—
44C4×C157—21no—
45C4×C157—41no—
46C4×C157—41no—
47Dic157—41no—
48C2×C157—21no—
49C2×C157AΣL(1,𝔽16)11yescharacteristic
50D157—81no—
51C157#140511yescharacteristic, complemented, Sylow
52#1405—1571nomaximal, Sylow
53#456—1571no—
54#356—1571no—
55#333D15711yescharacteristic, complemented
562−1+4—1571no—
57#137—3141no—
58C4⋊Q8C2×D15711yescharacteristic
59C4⋊C8—21no—
60#104—3141no—
61#101—3141no—
62#101—1571no—
63#41—3141no—
64#41—6281no—
65#41—6281no—
66C2×Q8—6281no—
67C2×Q8C4×D15711yescharacteristic
68C2×Q8D62811yescharacteristic
69Q16—6281no—
70SD16—6281no—
71M16—3141no—
72M16—6281no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D15711yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—3141no—
79Q8—6281no—
80D4—3141no—
81D4—6281no—
82D4—6281no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—6281no—
87C2×C4—6282no—
88C2×C4#1457893111yescharacteristic
89C8—81no—
90C8—6281no—
91C8—12561no—
92C22—6281no—
93C22#1909768511yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—6281no—
100C2—21no—
101C2—12561no—
102C2#2375706111yescharacteristic
subgroupG/H
centerC2#23757061
commutatorC2×Q8×C157C2×C4
FrattiniC4⋊Q8C2×D157
Fitting#333×C157C2
socleC2×C157AΣL(1,𝔽16)
prime radical#19097819C4
cosocleC4⋊Q8×C157C22
hypercenter#333D157
hypocenterC157#1405
LCSG ▷ C2×Q8×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23757072C2semidirect
3. #333×C157C2semidirect
51. C157#1405semidirect
55. #333D157semidirect

Maximal subgroups

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

subgroupindex
#237574552
#237570722
#333×C1572
#1405157