Finite Group Databasebeta

← #34102203

Subgroups — #34102203

Order 20096.

154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 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#23757713C211yesmaximal, characteristic, complemented
2#23757656C211yesmaximal, characteristic, complemented
3#23757390C211yesmaximal, characteristic, complemented
4#23757093C211yesmaximal, characteristic, complemented
5#23757090C211yesmaximal, characteristic, complemented
6#23757086C211yesmaximal, characteristic, complemented
7#509×C157C211yesmaximal, characteristic
8C2×Dic628C2211yescharacteristic
9C2×#14578942—21no—
10#19097778—21no—
11#19097758—21no—
12#19097717—21no—
13#19097715—21no—
14#19097711C2211yescharacteristic
15#19097707C2211yescharacteristic
16#19097698—21no—
17C8×Dic157C2211yescharacteristic
18#135×C157C2211yescharacteristic
19C2×D8×C157C2211yescharacteristic
20SD32×C157—21no—
21D16×C157—21no—
22M32×C157C2211yescharacteristic
23C2×Dic314—21no—
24Dic628—21no—
25Dic628—21no—
26#14578942—41no—
27#14578942—41no—
28#14578938—21no—
29#14578938—41no—
30C2×#11929434—41no—
31C2×#11929434D411yescharacteristic
32C22⋊Dic157—42no—
33C4×Dic157D411yescharacteristic
34#14578929—21no—
35#41×C157—21no—
36C2×D4×C157—21no—
37Q16×C157D411yescharacteristic
38SD16×C157—21no—
39D8×C157—21no—
40D8×C157—21no—
41D8×C157D411yescharacteristic
42C2×C8×C157C2311yescharacteristic
43C16×C157—21no—
44Dic314—41no—
45Dic314—41no—
46C2×Dic157—21no—
47C2×Dic157—41no—
48#11929434—41no—
49#11929434D811yescharacteristic
50#11929434D811yescharacteristic
51C23×C157—41no—
52Q8×C157—21no—
53D4×C157—21no—
54D4×C157—41no—
55D4×C157—41no—
56D4×C157—41no—
57C2×C4×C157—41no—
58C2×C4×C157C2×D411yescharacteristic
59C8×C157C2×D411yescharacteristic
60C8×C157#4111yescharacteristic
61C22×C157—41no—
62C22×C157—82no—
63C22×C157—81no—
64C22×C157AGL(1,ℤ/8)11yescharacteristic
65C4×C157—41no—
66C4×C157#12111yescharacteristic
67C4×C157C2×D811yescharacteristic
68Dic157—41no—
69Dic157—81no—
70C2×C157—21no—
71C2×C157—81no—
72C2×C157—161no—
73C2×C157#45911yescharacteristic
74C157#221211yescharacteristic, complemented, Sylow
75#2212—1571nomaximal, Sylow
76#510—1571no—
77#509D15711yescharacteristic
78#495—1571no—
79#443—1571no—
80#364—1571no—
81#362—1571no—
82#361—1571no—
83#135C2×D15711yescharacteristic
84C2×Q16—1571no—
85C2×SD16—3141no—
86C2×D8C2×D15711yescharacteristic
87#131—3141no—
88#124—3141no—
89Q32—3141no—
90SD32—21no—
91SD32—3141no—
92D16—21no—
93M32—1571no—
94M32C2×D15711yescharacteristic
95#108—1571no—
96#104—3141no—
97C4×C8—1571no—
98#41—21no—
99C2×Q8—3141no—
100C2×D4—21no—
101Q16—3141no—
102Q16—3141no—
103Q16C22⋊D15711yescharacteristic
104SD16—21no—
105SD16—6281no—
106SD16—6281no—
107D8—21no—
108D8—21no—
109D8C22⋊D15711yescharacteristic
110M16—3141no—
111M16—6281no—
112C2×C8—6281no—
113C2×C8—1571no—
114C2×C8C22×D15711yescharacteristic
115C22⋊C4—6282no—
116C42—1571no—
117C16—21no—
118C16—3141no—
119C23—41no—
120Q8—21no—
121Q8—6281no—
122Q8—6281no—
123D4—21no—
124D4—41no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—3141no—
129C2×C4—6281no—
130C2×C4D4×D15711yescharacteristic
131C8—6281no—
132C8—1571no—
133C8—1571no—
134C8C2×C22⋊D15711yescharacteristic
135C8#1457895311yescharacteristic
136C22—41no—
137C22—82no—
138C22—81no—
139C22#1909779511yescharacteristic
140C4—41no—
141C4—6281no—
142C4—12561no—
143C4#1909774311yescharacteristic
144C4D8×D15711yescharacteristic
145C2—21no—
146C2—81no—
147C2—161no—
148C2#2375746611yescharacteristic
subgroupG/H
centerC2#23757466
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting, prime radical#509×C157C2
socleC2×C157#459
hypercenter#509D157
hypocenterC157#2212
LCSG ▷ C2×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. #23757713C2semidirect
2. #23757656C2semidirect
3. #23757390C2semidirect
4. #23757093C2semidirect
5. #23757090C2semidirect
6. #23757086C2semidirect
74. C157#2212semidirect

Maximal subgroups

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

subgroupindex
#237577132
#237576562
#237573902
#237570932
#237570902
#237570862
#509×C1572
#2212157