Finite Group Databasebeta

← #34102037

Subgroups — #34102037

Order 20096.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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#23757709C211yesmaximal, characteristic
2#23757394C211yesmaximal, characteristic, complemented
3#23757385C211yesmaximal, characteristic, complemented
4#23757097C211yesmaximal, characteristic, complemented
5#23757084C211yesmaximal, characteristic, complemented
6#23757050C211yesmaximal, characteristic, complemented
7#361×C157C211yesmaximal, characteristic, complemented
8#19097793C2211yescharacteristic
9#19097779—21no—
10D4×Dic157—21no—
11#19097715C412yescomplemented
12#19097712C412yescomplemented
13#19097711C2211yescharacteristic
14#19097703C2211yescharacteristic
15#19097697—21no—
16#19097692—21no—
17#19097681C2211yescharacteristic
18C2×D8×C157C2211yescharacteristic
19M32×C157C2211yescharacteristic
20#108×C157C2211yescharacteristic
21#14578954—21no—
22C22×Dic157—41no—
23Dic628C2×C411yescharacteristic, complemented
24#14578943—21no—
25D1256C2×C411yescharacteristic, complemented
26#14578937—41no—
27C2×#11929434D411yescharacteristic
28C8×D157—41no—
29C4⋊Dic157—21no—
30C22⋊Dic157—41no—
31C4×Dic157D411yescharacteristic
32#14578929C2×C412yescomplemented
33C2×D4×C157—21no—
34D8×C157—21no—
35D8×C157C2×C412yes—
36M16×C157—21no—
37C2×C8×C157C2311yescharacteristic
38C16×C157—21no—
39Dic314—21no—
40D628—21no—
41C22⋊D157—41no—
42C2×Dic157—21no—
43C2×Dic157—41no—
44C2×Dic157—82no—
45C4×D157—41no—
46#11929434—21no—
47C23×C157—41no—
48D4×C157—22no—
49D4×C157—41no—
50C2×C4×C157C2×D411yescharacteristic
51C8×C157—41no—
52C8×C157C22×C411yescharacteristic
53C8×C157#4111yescharacteristic
54C22×C157—42no—
55C22×C157—81no—
56C22×C157—81no—
57C22×C157AGL(1,ℤ/8)11yescharacteristic
58C2×D157—41no—
59C4×C157C4×D411yescharacteristic
60C4×C157AGL(1,ℤ/8)11yescharacteristic
61Dic157—41no—
62Dic157—41no—
63Dic157—81no—
64C2×C157—21no—
65C2×C157—82no—
66C2×C157#44211yescharacteristic
67D157—81no—
68C157AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
69AGL(1,ℤ/16)—1571nomaximal, Sylow
70#509—1571no—
71#444—1571no—
72#442—1571no—
73#365—1571no—
74#361D15711yescharacteristic, complemented
75#360—1571no—
76#347—1571no—
77#135—1571no—
78C2×D8C2×D15711yescharacteristic
79#131—3141no—
80C4×D4—3141no—
81SD32—1572no—
82D16—1572no—
83M32—1571no—
84M32C2×D15711yescharacteristic
85#108C2×D15711yescharacteristic
86#106—1571no—
87#104—3141no—
88#102—3141no—
89#97—1571no—
90#41—3141no—
91C2×D4—21no—
92C22×C4—6281no—
93Q16—1571no—
94SD16—3141no—
95D8—21no—
96D8—1571no—
97D8C4×D15712yes—
98M16—21no—
99M16—6281no—
100C2×C8—6281no—
101C2×C8—1571no—
102C2×C8C22×D15711yescharacteristic
103C4⋊C4—3141no—
104C22⋊C4—6281no—
105C42—1571no—
106C16—21no—
107C16—1572no—
108C23—41no—
109Q8—3141no—
110D4—22no—
111D4—41no—
112D4—3141no—
113D4—6281no—
114C2×C4—3141no—
115C2×C4—6281no—
116C2×C4—6281no—
117C2×C4—12562no—
118C2×C4D4×D15711yescharacteristic
119C8—41no—
120C8—3141no—
121C8C2×C4×D15711yescharacteristic
122C8#1457895311yescharacteristic
123C22—42no—
124C22—81no—
125C22—81no—
126C22—6281no—
127C22#1909779811yescharacteristic
128C4—6281no—
129C4—6281no—
130C4—12561no—
131C4#1909773111yescharacteristic
132C4#1909779511yescharacteristic
133C2—21no—
134C2—82no—
135C2—12561no—
136C2#2375738211yescharacteristic
subgroupG/H
centerC2#23757382
commutatorC8×C157C22×C4
FrattiniC2×C8C22×D157
Fitting#361×C157C2
socleC2×C157#442
prime radical#23757709C2
cosocleC2×C8×C157C23
hypercenter#361D157
hypocenterC157AGL(1,ℤ/16)
LCSG ▷ C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #23757394C2semidirect
3. #23757385C2semidirect
4. #23757097C2semidirect
5. #23757084C2semidirect
6. #23757050C2semidirect
7. #361×C157C2semidirect
11. #19097715C4semidirect
12. #19097712C4semidirect
23. Dic628C2×C4semidirect
25. D1256C2×C4semidirect
32. #14578929C2×C4semidirect
68. C157AGL(1,ℤ/16)semidirect
74. #361D157semidirect

Maximal subgroups

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

subgroupindex
#237577092
#237573942
#237573852
#237570972
#237570842
#237570502
#361×C1572
AGL(1,ℤ/16)157