Finite Group Databasebeta

← #23757883

Subgroups — #23757883

Order 10048.

192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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#19097769C211yesmaximal, characteristic, complemented
2#19097764C212yesmaximal
3#19097764C212yesmaximal
4#19097762C211yesmaximal, characteristic, complemented
5#19097762C212yesmaximal, complemented
6#19097761C212yesmaximal, complemented
7#19097750C211yesmaximal, characteristic
8Q8×Dic157C211yesmaximal, characteristic, complemented
9#19097736C211yesmaximal, characteristic, complemented
10#19097730C211yesmaximal, characteristic
11C22⋊Q8×C157C211yesmaximal, characteristic
12C2×Dic314C2211yescharacteristic
13C4⋊Dic157C2211yescharacteristic
14C4⋊Dic157C2211yescharacteristic
15C4⋊Dic157C2211yescharacteristic
16C4⋊Dic157C2212yes—
17C4⋊Dic157C2212yes—
18#14578933C2212yes—
19#14578933C2212yes—
20#14578933C2212yes—
21#14578933C2212yes—
22#14578933C2212yes—
23C22⋊Dic157C2211yescharacteristic
24C22⋊Dic157C2211yescharacteristic
25C22⋊Dic157C2212yes—
26C4×Dic157C2211yescharacteristic
27C4×Dic157C2211yescharacteristic
28C4×Dic157C2212yes—
29C4×Dic157C2212yes—
30C2×Q8×C157C2211yescharacteristic
31C22×C4×C157C2211yescharacteristic
32C4⋊C4×C157C2211yescharacteristic
33C4⋊C4×C157C2212yes—
34C22⋊C4×C157C2212yes—
35Dic314—22no—
36C2×Dic157C2312yes—
37C2×Dic157C2311yescharacteristic
38C2×Dic157C2311yescharacteristic
39C2×Dic157C2311yescharacteristic
40C2×Dic157C2311yescharacteristic
41C2×Dic157C2312yes—
42C23×C157C2311yescharacteristic
43Q8×C157—22no—
44C2×C4×C157—22no—
45C2×C4×C157C2312yes—
46C2×C4×C157C2312yes—
47C2×C4×C157C2311yescharacteristic
48C2×C4×C157C2311yescharacteristic
49C22×C157—21no—
50C22×C157—21no—
51C22×C157—21no—
52C22×C157C2411yescharacteristic
53C4×C157—21no—
54C4×C157—22no—
55C4×C157—22no—
56C4×C157#4112yes—
57Dic157—22no—
58Dic157—21no—
59Dic157—21no—
60Dic157—21no—
61Dic157—21no—
62Dic157—22no—
63C2×C157—41no—
64C2×C157C2×#4111yescharacteristic
65C2×C1572−1+411yescharacteristic
66C2×C1572−1+411yescharacteristic
67C157#54111yescharacteristic, complemented, Sylow
68#541—1571nomaximal, Sylow
69C4⋊Q8—1571no—
70#126—1572no—
71#126—1572no—
72#125—1572no—
73#125—1571no—
74#125—1572no—
75C22⋊Q8—1571no—
76C22⋊Q8D15711yescharacteristic
77C4×Q8—1571no—
78C4×Q8—1571no—
79#117—1571no—
80C2×Q8—1571no—
81C2×Q8C2×D15711yescharacteristic
82C22×C4C2×D15711yescharacteristic
83C4⋊C4—1571no—
84C4⋊C4—1571no—
85C4⋊C4—1571no—
86C4⋊C4—1572no—
87C4⋊C4—1572no—
88C4⋊C4—1572no—
89C4⋊C4—1572no—
90C4⋊C4—1572no—
91C4⋊C4—1572no—
92C4⋊C4—1572no—
93C4⋊C4C2×D15711yescharacteristic
94C4⋊C4C2×D15712yes—
95C22⋊C4—1571no—
96C22⋊C4—1571no—
97C22⋊C4—1572no—
98C22⋊C4C2×D15712yes—
99C42—1571no—
100C42—1571no—
101C42—1572no—
102C42—1572no—
103C23C22×D15711yescharacteristic
104Q8—22no—
105Q8—3142no—
106C2×C4—22no—
107C2×C4—1571no—
108C2×C4—1571no—
109C2×C4—1571no—
110C2×C4—1571no—
111C2×C4—1572no—
112C2×C4—1572no—
113C2×C4C22×D15712yes—
114C2×C4C22×D15712yes—
115C2×C4C22×D15711yescharacteristic
116C2×C4C22×D15711yescharacteristic
117C22—21no—
118C22—21no—
119C22—21no—
120C22C23×D15711yescharacteristic
121C4—21no—
122C4—22no—
123C4—22no—
124C4—3142no—
125C4—3141no—
126C4—3141no—
127C4—3141no—
128C4—3141no—
129C4—3142no—
130C4#1457895312yes—
131C2—41no—
132C2C2×#1457895311yescharacteristic
133C2#1909781811yescharacteristic
134C2#1909781911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, cosocleC22×C157C24
FittingC22⋊Q8×C157C2
prime radicalC23×C157C23
hypercenterC22⋊Q8D157
hypocenterC157#541
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #19097769C2semidirect
4. #19097762C2semidirect
5. #19097762C2semidirect
6. #19097761C2semidirect
8. Q8×Dic157C2semidirect
9. #19097736C2semidirect
67. C157#541semidirect