Finite Group Databasebeta

← #23757454

Subgroups — #23757454

Order 10048.

142 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 39 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#19097818C211yesmaximal, characteristic
2#19097802C211yesmaximal, characteristic, complemented
3#19097769C211yesmaximal, characteristic, complemented
4#19097698C211yesmaximal, characteristic, complemented
5#19097697C211yesmaximal, characteristic, complemented
6#19097689C211yesmaximal, characteristic, complemented
7#137×C157C211yesmaximal, characteristic, complemented
8#14578954—21no—
9#14578954C2211yescharacteristic
10#14578953—22no—
11#14578953—21no—
12C2×Dic314—21no—
13C2×Dic314C2211yescharacteristic
14Q8×D157—21no—
15#14578944—21no—
16#14578941—21no—
17#14578938C2211yescharacteristic
18#14578933—22no—
19C4×Dic157C2211yescharacteristic
20#41×C157C2211yescharacteristic
21C2×Q8×C157C2211yescharacteristic
22Q16×C157—21no—
23SD16×C157—21no—
24M16×C157C2211yescharacteristic
25Dic314—22no—
26Dic314—21no—
27Dic314—21no—
28Dic314D411yescharacteristic
29D628D411yescharacteristic
30C22⋊D157—22no—
31C22⋊D157—21no—
32C2×Dic157—22no—
33C2×Dic157—21no—
34C2×Dic157D412yes—
35C4×D157—22no—
36C4×D157—21no—
37#11929434—21no—
38Q8×C157—21no—
39Q8×C157—21no—
40Q8×C157D411yescharacteristic
41D4×C157—21no—
42D4×C157D411yescharacteristic
43C2×C4×C157—21no—
44C2×C4×C157—21no—
45C2×C4×C157C2311yescharacteristic
46C8×C157—21no—
47C22×C157—21no—
48C22×C157C2×D411yescharacteristic
49C2×D157—21no—
50C4×C157—21no—
51C4×C157—41no—
52C4×C157C2×D411yescharacteristic
53C4×C157C2×D411yescharacteristic
54Dic157—22no—
55Dic157—21no—
56Dic157—22no—
57C2×C157—21no—
58C2×C157—41no—
59C2×C157#12011yescharacteristic
60D157—41no—
61C157#45611yescharacteristic, complemented, Sylow
62#456—1571nomaximal, Sylow
632−1+4—1571no—
64#137—1571no—
65#137D15711yescharacteristic, complemented
66C4⋊Q8—1571no—
67#104—1571no—
68#104—1571no—
69#101—1571no—
70#41—3141no—
71#41—3141no—
72#41—3142no—
73#41—1571no—
74#41C2×D15711yescharacteristic
75C2×Q8—3141no—
76C2×Q8—3141no—
77C2×Q8—1571no—
78C2×Q8C2×D15711yescharacteristic
79Q16—21no—
80Q16—3141no—
81SD16—21no—
82SD16—3141no—
83M16—1571no—
84M16C2×D15711yescharacteristic
85C4⋊C4—3142no—
86C42—1571no—
87Q8—21no—
88Q8—21no—
89Q8—3142no—
90Q8—3141no—
91Q8—3141no—
92Q8—1571no—
93Q8C22⋊D15711yescharacteristic
94D4—21no—
95D4—3142no—
96D4—3141no—
97D4—1571no—
98D4C22⋊D15711yescharacteristic
99C2×C4—21no—
100C2×C4—21no—
101C2×C4—3142no—
102C2×C4—3142no—
103C2×C4—3141no—
104C2×C4—3141no—
105C2×C4—1572no—
106C2×C4C22×D15711yescharacteristic
107C8—21no—
108C8—3141no—
109C22—21no—
110C22—3141no—
111C22D4×D15711yescharacteristic
112C4—21no—
113C4—41no—
114C4—3142no—
115C4—3141no—
116C4—3142no—
117C4D4×D15711yescharacteristic
118C4C2×C22⋊D15711yescharacteristic
119C2—21no—
120C2—41no—
121C2—6281no—
122C2#1909773911yescharacteristic
subgroupG/H
centerC2#19097739
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#137×C157C2
socleC2×C157#120
prime radical#19097818C2
hypercenter#137D157
hypocenterC157#456
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. #19097802C2semidirect
3. #19097769C2semidirect
4. #19097698C2semidirect
5. #19097697C2semidirect
6. #19097689C2semidirect
7. #137×C157C2semidirect
61. C157#456semidirect
65. #137D157semidirect