Finite Group Databasebeta

← #34116547

Subgroups — #34116547

Order 20096.

154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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#23758319C211yesmaximal, characteristic, complemented
2#23758314C211yesmaximal, characteristic, complemented
3#23758198C211yesmaximal, characteristic, complemented
4#23758191C211yesmaximal, characteristic, complemented
5#23758190C211yesmaximal, characteristic, complemented
6#23758163C211yesmaximal, characteristic, complemented
7#23757710C211yesmaximal, characteristic
8#19097859—21no—
9D4×#10597845—21no—
10#19097846C2211yescharacteristic
11#19097841C2211yescharacteristic
12#19097839C2211yescharacteristic
13#19097836—21no—
14#19097833—21no—
15#19097825C2211yescharacteristic
16#19097794C2211yescharacteristic
17D8×D157C2211yescharacteristic
18#19097714C411yescharacteristic, complemented
19D2512C411yescharacteristic, complemented
20#19097712C411yescharacteristic, complemented
21#19097710C2211yescharacteristic
22SD32×C157C411yescharacteristic, complemented
23C22×#10597845—41no—
24#14578964—21no—
25#14578964—41no—
26D157⋊C8—41no—
27D157⋊C8D411yescharacteristic
28C4⋊#10597845—21no—
29C22⋊#10597845—41no—
30C4×#10597845D411yescharacteristic
31#14578957—21no—
32#14578955—21no—
33D4×D157—21no—
34#14578941—21no—
35D1256C2×C411yescharacteristic
36D1256C2×C411yescharacteristic, complemented
37#14578939—21no—
38C8×D157C2311yescharacteristic
39#14578929C2×C411yescharacteristic, complemented
40Q16×C157C2×C411yescharacteristic, complemented
41D8×C157C2×C411yescharacteristic
42C16×C157C2×C411yescharacteristic, complemented
43C2×#10597845—21no—
44C2×#10597845—41no—
45C2×#10597845—82no—
46#11929441—21no—
47#11929441—41no—
48C22×D157—41no—
49D628—21no—
50D628—21no—
51D628—41no—
52C22⋊D157—41no—
53C4×D157—41no—
54C4×D157C2×D411yescharacteristic
55#11929434#4111yescharacteristic
56Q8×C157—21no—
57D4×C157—21no—
58C8×C157C22×C411yescharacteristic
59C22×C157—41no—
60C2×D157—41no—
61C2×D157—41no—
62C2×D157—81no—
63C2×D157—81no—
64C2×D157AGL(1,ℤ/8)11yescharacteristic
65#10597845—41no—
66#10597845—81no—
67C4×C157—41no—
68C4×C157C4×D411yescharacteristic
69Dic157AGL(1,ℤ/8)11yescharacteristic
70C2×C157—81no—
71C2×C157#44211yescharacteristic
72D157—21no—
73D157—81no—
74D157—81no—
75C157AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
76AGL(1,ℤ/16)—1571nomaximal, Sylow
77#509—1571no—
78#444—1571no—
79#442—1571no—
80#365—1571no—
81#361—1571no—
82#360—1571no—
83#347—1571no—
84#135—1571no—
85C2×D8—1571no—
86#131—3141no—
87C4×D4—3141no—
88SD32—1571no—
89SD32#1059784511yescharacteristic, complemented
90D16—1571no—
91D16—1571no—
92M32—1571no—
93M32—1571no—
94#108—1571no—
95#106—1571no—
96#104—3141no—
97#102—3141no—
98#97—1571no—
99#41—3141no—
100C2×D4—3141no—
101C22×C4—6281no—
102Q16C2×#1059784511yescharacteristic, complemented
103SD16—3141no—
104D8—3141no—
105D8—1571no—
106D8—1571no—
107D8C2×#1059784511yescharacteristic
108M16—3141no—
109M16—6281no—
110C2×C8—6281no—
111C2×C8—1571no—
112C2×C8—1571no—
113C4⋊C4—3141no—
114C22⋊C4—6281no—
115C42—1571no—
116C16—3141no—
117C16—1571no—
118C16C2×#1059784511yescharacteristic, complemented
119C23—6281no—
120Q8—21no—
121D4—21no—
122D4—3141no—
123D4—3141no—
124D4—6281no—
125D4—6281no—
126C2×C4—3141no—
127C2×C4—6281no—
128C2×C4—6281no—
129C2×C4—1571no—
130C2×C4—12562no—
131C8—3141no—
132C8—6281no—
133C8—1571no—
134C8C22×#1059784511yescharacteristic
135C22—41no—
136C22—6281no—
137C22—6281no—
138C22—1571no—
139C22—12561no—
140C22—12561no—
141C4—41no—
142C4—6281no—
143C4—1571no—
144C4—12561no—
145C4D4×#1059784511yescharacteristic
146C2—81no—
147C2—3141no—
148C2—12561no—
149C2—12561no—
150C2#2375831411yescharacteristic
subgroupG/H
centerC2#23758314
commutatorC8×C157C22×C4
FrattiniC8C22×#10597845
FittingSD32×C157C4
socleC2×C157#442
prime radical#23757710C2
cosocleC8×D157C23
hypercenterSD32#10597845
hypocenterC157AGL(1,ℤ/16)
LCSG ▷ C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #23758319C2semidirect
2. #23758314C2semidirect
3. #23758198C2semidirect
4. #23758191C2semidirect
5. #23758190C2semidirect
6. #23758163C2semidirect
18. #19097714C4semidirect
19. D2512C4semidirect
20. #19097712C4semidirect
22. SD32×C157C4semidirect
36. D1256C2×C4semidirect
39. #14578929C2×C4semidirect
40. Q16×C157C2×C4semidirect
42. C16×C157C2×C4semidirect
75. C157AGL(1,ℤ/16)semidirect
89. SD32#10597845semidirect
102. Q16C2×#10597845semidirect
118. C16C2×#10597845semidirect

Maximal subgroups

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

subgroupindex
#237583192
#237583142
#237581982
#237581912
#237581902
#237581632
#237577102
AGL(1,ℤ/16)157