Finite Group Databasebeta

← #34102035

Subgroups — #34102035

Order 20096.

154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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#23757395C211yesmaximal, characteristic, complemented
2#23757385C211yesmaximal, characteristic, complemented
3#23757096C211yesmaximal, characteristic, complemented
4#23757086C211yesmaximal, characteristic, complemented
5#23757083C211yesmaximal, characteristic, complemented
6#23757050C211yesmaximal, characteristic, complemented
7#509×C157C211yesmaximal, characteristic
8#19097778—21no—
9D4×Dic157—21no—
10#19097711C2211yescharacteristic
11#19097707C2211yescharacteristic
12#19097703C2211yescharacteristic
13#19097698—21no—
14#19097692—21no—
15#19097681C2211yescharacteristic
16#135×C157C2211yescharacteristic
17C2×D8×C157C2211yescharacteristic
18SD32×C157C412yescomplemented
19D16×C157C412yescomplemented
20M32×C157C2211yescharacteristic
21C22×Dic157—41no—
22#14578938—21no—
23#14578938—41no—
24C2×#11929434—41no—
25C2×#11929434D411yescharacteristic
26C4⋊Dic157—21no—
27C22⋊Dic157—41no—
28C4×Dic157D411yescharacteristic
29#14578929—21no—
30#41×C157—21no—
31C2×D4×C157—21no—
32Q16×C157C2×C411yescharacteristic, complemented
33SD16×C157—21no—
34D8×C157—21no—
35D8×C157C2×C412yes—
36D8×C157C2×C411yescharacteristic, complemented
37C2×C8×C157C2311yescharacteristic
38C16×C157C2×C412yescomplemented
39C2×Dic157—21no—
40C2×Dic157—41no—
41C2×Dic157—82no—
42#11929434—21no—
43#11929434—41no—
44C23×C157—41no—
45Q8×C157—21no—
46D4×C157—22no—
47D4×C157—21no—
48D4×C157—41no—
49D4×C157—41no—
50C2×C4×C157—41no—
51C2×C4×C157C2×D411yescharacteristic
52C8×C157C22×C411yescharacteristic
53C8×C157#4111yescharacteristic
54C22×C157—41no—
55C22×C157—42no—
56C22×C157—81no—
57C22×C157—81no—
58C22×C157AGL(1,ℤ/8)11yescharacteristic
59C4×C157—41no—
60C4×C157C4×D411yescharacteristic
61C4×C157AGL(1,ℤ/8)11yescharacteristic
62Dic157—41no—
63Dic157—81no—
64C2×C157—21no—
65C2×C157—81no—
66C2×C157—82no—
67C2×C157#44211yescharacteristic
68C157AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
69AGL(1,ℤ/16)—1571nomaximal, Sylow
70#509D15711yescharacteristic
71#444—1571no—
72#442—1571no—
73#365—1571no—
74#361—1571no—
75#360—1571no—
76#347—1571no—
77#135C2×D15711yescharacteristic
78C2×D8C2×D15711yescharacteristic
79#131—3141no—
80C4×D4—3141no—
81SD32Dic15712yescomplemented
82D16Dic15712yescomplemented
83M32—1571no—
84M32C2×D15711yescharacteristic
85#108—1571no—
86#106—1571no—
87#104—3141no—
88#102—3141no—
89#97—1571no—
90#41—21no—
91C2×D4—21no—
92C22×C4—6281no—
93Q16C2×Dic15711yescharacteristic, complemented
94SD16—21no—
95D8—21no—
96D8C2×Dic15712yes—
97D8C2×Dic15711yescharacteristic, complemented
98M16—3141no—
99M16—6281no—
100C2×C8—6281no—
101C2×C8—1571no—
102C2×C8C22×D15711yescharacteristic
103C4⋊C4—3141no—
104C22⋊C4—6281no—
105C42—1571no—
106C16—3141no—
107C16C2×Dic15712yescomplemented
108C23—41no—
109Q8—21no—
110D4—22no—
111D4—21no—
112D4—41no—
113D4—41no—
114C2×C4—41no—
115C2×C4—3141no—
116C2×C4—6281no—
117C2×C4—12562no—
118C2×C4D4×D15711yescharacteristic
119C8—3141no—
120C8—6281no—
121C8C22×Dic15711yescharacteristic
122C8#1457895311yescharacteristic
123C22—41no—
124C22—42no—
125C22—81no—
126C22—81no—
127C22#1909779511yescharacteristic
128C4—41no—
129C4—6281no—
130C4—12561no—
131C4D4×Dic15711yescharacteristic
132C4#1909779511yescharacteristic
133C2—21no—
134C2—82no—
135C2—81no—
136C2#2375738511yescharacteristic
subgroupG/H
centerC2#23757385
commutatorC8×C157C22×C4
FrattiniC2×C8C22×D157
Fitting, prime radical#509×C157C2
socleC2×C157#442
cosocleC2×C8×C157C23
hypercenter#509D157
hypocenterC157AGL(1,ℤ/16)
LCSG ▷ C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23757395C2semidirect
2. #23757385C2semidirect
3. #23757096C2semidirect
4. #23757086C2semidirect
5. #23757083C2semidirect
6. #23757050C2semidirect
18. SD32×C157C4semidirect
19. D16×C157C4semidirect
32. Q16×C157C2×C4semidirect
36. D8×C157C2×C4semidirect
38. C16×C157C2×C4semidirect
68. C157AGL(1,ℤ/16)semidirect
81. SD32Dic157semidirect
82. D16Dic157semidirect
93. Q16C2×Dic157semidirect
97. D8C2×Dic157semidirect
107. C16C2×Dic157semidirect

Maximal subgroups

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

subgroupindex
#237573952
#237573852
#237570962
#237570862
#237570832
#237570502
#509×C1572
AGL(1,ℤ/16)157