Finite Group Databasebeta

← #34099394

Subgroups — #34099394

Order 20096.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757993C211yesmaximal, characteristic
2#23757678C211yesmaximal, characteristic, complemented
3#23757559C211yesmaximal, characteristic, complemented
4#23757478C211yesmaximal, characteristic
5#23757018C211yesmaximal, characteristic, complemented
6#23757005C211yesmaximal, characteristic, complemented
7D4⋊C8×C157C211yesmaximal, characteristic
8C2×#14578942—21no—
9#19097771C2211yescharacteristic
10#19097771C2211yescharacteristic
11#19097764—22no—
12#19097758—21no—
13#19097750—21no—
14C4×Dic314C2211yescharacteristic
15#19097736—21no—
16#19097730—21no—
17#19097705—22no—
18#19097703—21no—
19C4⋊#11929434C2211yescharacteristic
20#19097696—21no—
21#19097694—21no—
22C4×D4×C157C2211yescharacteristic
23C4⋊C8×C157C2211yescharacteristic
24C4×C8×C157C2211yescharacteristic
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314D411yescharacteristic
28#14578942—42no—
29C2×#11929434—21no—
30C4⋊Dic157—21no—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C4⋊Dic157D411yescharacteristic
34C4⋊Dic157D412yes—
35#14578933—22no—
36#14578933—21no—
37C22⋊Dic157—22no—
38C22⋊Dic157—22no—
39C4×Dic157—22no—
40C4×Dic157—21no—
41C2×D4×C157D411yescharacteristic
42C22×C4×C157—21no—
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C4⋊C4×C157D411yescharacteristic
46C22⋊C4×C157—21no—
47C42×C157C2311yescharacteristic
48Dic314—21no—
49Dic314—21no—
50Dic314—41no—
51Dic314—41no—
52Dic314—41no—
53Dic314—41no—
54C2×Dic157—22no—
55C2×Dic157—21no—
56C2×Dic157—21no—
57C2×Dic157—41no—
58#11929434—41no—
59C23×C157—21no—
60D4×C157—21no—
61D4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—41no—
64C2×C4×C157—41no—
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157C2×D411yescharacteristic
67C2×C4×C157C2×D411yescharacteristic
68C8×C157—22no—
69C8×C157—41no—
70C22×C157—41no—
71C22×C157—41no—
72C22×C157—41no—
73C22×C157#12011yescharacteristic
74C4×C157—21no—
75C4×C157—41no—
76C4×C157#13511yescharacteristic
77C4×C157#13511yescharacteristic
78C4×C157AGL(1,ℤ/8)11yescharacteristic
79C4×C157#13711yescharacteristic
80Dic157—42no—
81Dic157—41no—
82Dic157—41no—
83Dic157—81no—
84C2×C157—81no—
85C2×C157#44911yescharacteristic
86C2×C157#45211yescharacteristic
87C2×C157#45611yescharacteristic
88C157#165011yescharacteristic, complemented, Sylow
89#1650—1571nomaximal, Sylow
90#556—1571no—
91#500—1571no—
92#475—1571no—
93#461—1571no—
94#332—1571no—
95Q8⋊C8—1571no—
96D4⋊C8D15711yescharacteristic
97C2×SD16—3141no—
98C4⋊Q8—1571no—
99C4⋊Q8—1571no—
100#126—3142no—
101#124—3141no—
102C22⋊Q8—3141no—
103C4×Q8—3141no—
104C4×Q8—1571no—
105C4×D4C2×D15711yescharacteristic
106#117—3141no—
107#107—3142no—
108#106—3141no—
109C4⋊C8—1571no—
110C4⋊C8C2×D15711yescharacteristic
111#103—3141no—
112#103—3141no—
113C4×C8C2×D15711yescharacteristic
114C2×Q8—3141no—
115C2×Q8—3141no—
116C2×Q8—1571no—
117C2×D4D62811yescharacteristic
118C22×C4—21no—
119SD16—6282no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—3141no—
123C4⋊C4—3142no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—1571no—
129C4⋊C4—1572no—
130C4⋊C4D62811yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—3142no—
133C22⋊C4—3142no—
134C42—3142no—
135C42—3141no—
136C42C22×D15711yescharacteristic
137C23—21no—
138Q8—3141no—
139Q8—3141no—
140Q8—6281no—
141Q8—6281no—
142Q8—6281no—
143Q8—6281no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3141no—
150C2×C4—3141no—
151C2×C4—3142no—
152C2×C4—6281no—
153C2×C4D4×D15711yescharacteristic
154C2×C4D4×D15711yescharacteristic
155C2×C4C2×D62811yescharacteristic
156C8—22no—
157C8—41no—
158C8—6281no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1909774111yescharacteristic
163C4—21no—
164C4—41no—
165C4—6282no—
166C4—6281no—
167C4—6281no—
168C4—12561no—
169C4#1909779011yescharacteristic
170C4#1909779311yescharacteristic
171C4#1909779911yescharacteristic
172C4#1909780011yescharacteristic
173C2—81no—
174C2#2375742011yescharacteristic
175C2#2375743611yescharacteristic
176C2#2375745711yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
FittingD4⋊C8×C157C2
socleC22×C157#120
prime radicalC2×D4×C157D4
hypercenterD4⋊C8D157
hypocenterC157#1650
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23757678C2semidirect
3. #23757559C2semidirect
5. #23757018C2semidirect
6. #23757005C2semidirect
88. C157#1650semidirect

Maximal subgroups

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

subgroupindex
#237579932
#237576782
#237575592
#237574782
#237570182
#237570052
D4⋊C8×C1572
#1650157