Finite Group Databasebeta

← #23757444

Subgroups — #23757444

Order 10048.

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

normal subgroups only

This group has 146 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, complemented
2#19097797C211yesmaximal, characteristic, complemented
3#19097758C211yesmaximal, characteristic, complemented
4#19097698C211yesmaximal, characteristic, complemented
5#19097697C211yesmaximal, characteristic, complemented
6#19097689C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C157C211yesmaximal, characteristic, complemented
8#14578954—21no—
9#14578954C2211yescharacteristic
10#14578953—22no—
11#14578953—21no—
12C2×Dic314—21no—
13C2×Dic314C2211yescharacteristic
14Q8×D157—21no—
15#14578942—21no—
16#14578939—21no—
17#14578938C2211yescharacteristic
18C22⋊Dic157—22no—
19C4×Dic157C2211yescharacteristic
20#41×C157C2211yescharacteristic
21C2×D4×C157C2211yescharacteristic
22SD16×C157—21no—
23D8×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—
38C23×C157—21no—
39Q8×C157D411yescharacteristic
40D4×C157—21no—
41D4×C157—21no—
42D4×C157—21no—
43D4×C157D411yescharacteristic
44C2×C4×C157—21no—
45C2×C4×C157C2311yescharacteristic
46C8×C157—21no—
47C22×C157—21no—
48C22×C157—42no—
49C22×C157—41no—
50C22×C157C2×D411yescharacteristic
51C2×D157—21no—
52C4×C157—21no—
53C4×C157C2×D411yescharacteristic
54C4×C157C2×D411yescharacteristic
55Dic157—21no—
56Dic157—22no—
57Dic157—41no—
58C2×C157—21no—
59C2×C157—41no—
60C2×C157—81no—
61C2×C157#12011yescharacteristic
62D157—41no—
63C157#45411yescharacteristic, complemented, Sylow
64#454—1571nomaximal, Sylow
652−1+4—1571no—
66AGL(1,ℤ/8)—1571no—
67AGL(1,ℤ/8)D15711yescharacteristic, complemented
68#124—1571no—
69#104—1571no—
70#104—1571no—
71#101—1571no—
72#41—3141no—
73#41—3141no—
74#41—3142no—
75#41—1571no—
76#41C2×D15711yescharacteristic
77C2×Q8—3141no—
78C2×Q8—3141no—
79C2×Q8—1571no—
80C2×D4C2×D15711yescharacteristic
81SD16—21no—
82SD16—3141no—
83D8—21no—
84D8—3141no—
85M16—1571no—
86M16C2×D15711yescharacteristic
87C22⋊C4—3142no—
88C42—1571no—
89C23—21no—
90Q8—3142no—
91Q8—3141no—
92Q8—3141no—
93Q8—1571no—
94Q8C22⋊D15711yescharacteristic
95D4—21no—
96D4—21no—
97D4—21no—
98D4—3142no—
99D4—3141no—
100D4—1571no—
101D4C22⋊D15711yescharacteristic
102C2×C4—21no—
103C2×C4—3142no—
104C2×C4—3142no—
105C2×C4—3141no—
106C2×C4—3141no—
107C2×C4—1572no—
108C2×C4C22×D15711yescharacteristic
109C8—21no—
110C8—3141no—
111C22—21no—
112C22—42no—
113C22—41no—
114C22—3141no—
115C22D4×D15711yescharacteristic
116C4—21no—
117C4—3141no—
118C4—3142no—
119C4—6281no—
120C4D4×D15711yescharacteristic
121C4C2×C22⋊D15711yescharacteristic
122C2—21no—
123C2—41no—
124C2—81no—
125C2—6281no—
126C2#1909773911yescharacteristic
subgroupG/H
centerC2#19097739
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingAGL(1,ℤ/8)×C157C2
socleC2×C157#120
hypercenterAGL(1,ℤ/8)D157
hypocenterC157#454
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19097818C2semidirect
2. #19097797C2semidirect
3. #19097758C2semidirect
4. #19097698C2semidirect
5. #19097697C2semidirect
6. #19097689C2semidirect
7. AGL(1,ℤ/8)×C157C2semidirect
63. C157#454semidirect
67. AGL(1,ℤ/8)D157semidirect