Finite Group Databasebeta

← #34100579

Subgroups — #34100579

Order 20096.

442 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 101 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#23757784C211yesmaximal, characteristic
2C2×#19097699C212yesmaximal, complemented
3#23757237C211yesmaximal, characteristic, complemented
4#23757033C212yesmaximal, complemented
5C22×C42×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2211yescharacteristic
7C2×#14578938C2212yes—
8#19097754—21no—
9#19097750C412yescomplemented
10#19097745C412yescomplemented
11#19097740—21no—
12C4×C22⋊D157—22no—
13#19097730C2211yescharacteristic
14#19097699—24no—
15C22⋊#11929434—22no—
16C23×C4×C157—21no—
17C23×C4×C157C2211yescharacteristic
18C2×C42×C157—21no—
19C2×C42×C157—24no—
20C2×C42×C157C2212yes—
21#14578954—22no—
22#14578954—22no—
23C2×Dic314C2×C411yescharacteristic, complemented
24C2×D628C2×C411yescharacteristic, complemented
25C2×C22⋊D157—22no—
26C2×C22⋊D157—21no—
27C2×C4×D157—21no—
28#14578938—22no—
29#14578938—22no—
30C2×#11929434—22no—
31C4⋊Dic157C2×C412yescomplemented
32#14578933—22no—
33C22⋊Dic157—22no—
34C22⋊Dic157—21no—
35#14578931—22no—
36C4×Dic157—21no—
37C24×C157D411yescharacteristic
38C22×C4×C157—24no—
39C22×C4×C157—28no—
40C22×C4×C157—22no—
41C22×C4×C157—22no—
42C22×C4×C157—22no—
43C22×C4×C157C2×C412yes—
44C22×C4×C157D411yescharacteristic
45C22×C4×C157D412yes—
46C22×C4×C157C2311yescharacteristic
47C42×C157—24no—
48C42×C157—22no—
49C42×C157D414yescomplemented
50C22×D157—21no—
51Dic314—22no—
52D628—22no—
53C22⋊D157—44no—
54C22⋊D157—41no—
55C22⋊D157—41no—
56C2×Dic157—21no—
57C2×Dic157—22no—
58C4×D157—42no—
59#11929434—42no—
60C23×C157—24no—
61C23×C157—21no—
62C23×C157—21no—
63C23×C157C22⋊C412yes—
64C23×C157C2×D411yescharacteristic
65C2×C4×C157—216no—
66C2×C4×C157—28no—
67C2×C4×C157—21no—
68C2×C4×C157—24no—
69C2×C4×C157—21no—
70C2×C4×C157—24no—
71C2×C4×C157—24no—
72C2×C4×C157C22⋊C412yes—
73C2×C4×C157C22×C411yescharacteristic
74C2×C4×C157C2×D412yes—
75C2×C4×C157C2×D411yescharacteristic
76C2×C4×C157#4112yes—
77C22×C157—24no—
78C22×C157—24no—
79C22×C157—22no—
80C22×C157—22no—
81C22×C157—22no—
82C22×C157#10414yescomplemented
83C22×C157C2×C22⋊C411yescharacteristic
84C22×C157#12011yescharacteristic
85C22×C157#12311yescharacteristic
86C2×D157—41no—
87C2×D157—42no—
88C4×C157—28no—
89C4×C157—22no—
90C4×C157C4×D412yes—
91C4×C157#12112yes—
92Dic157—41no—
93Dic157—42no—
94C2×C157—21no—
95C2×C157—24no—
96C2×C157—21no—
97C2×C157#38611yescharacteristic
98C2×C157C2×#10412yes—
99D157—81no—
100C157#189611yescharacteristic, complemented, Sylow
101#1896—1571nomaximal, Sylow
102#525—1571no—
103C22×C42D15711yescharacteristic, complemented
104C2×#104—1572no—
105#407—1571no—
106#339—1572no—
107C2×#41—1571no—
108C23×C4—21no—
109C23×C4C2×D15711yescharacteristic
110C2×M16—1572no—
111#123—3141no—
112C22⋊Q8—1572no—
113#121—1572no—
114#120—3141no—
115C4×D4—3142no—
116#117—1571no—
117C2×C42—21no—
118C2×C42—24no—
119C2×C42C2×D15712yes—
120#104—3144no—
121C22⋊C8—3142no—
122C24C22⋊D15711yescharacteristic
123#41—3142no—
124#41—3142no—
125C2×Q8—1571no—
126C2×D4—3141no—
127C2×D4—3142no—
128C2×D4—1571no—
129C22×C4—24no—
130C22×C4—28no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—3141no—
135C22×C4C4×D15712yes—
136C22×C4C22⋊D15711yescharacteristic
137C22×C4D62812yes—
138C22×C4C22×D15711yescharacteristic
139M16—3142no—
140M16—3142no—
141C2×C8—3142no—
142C4⋊C4—3142no—
143C4⋊C4—1572no—
144C22⋊C4—3141no—
145C22⋊C4—3142no—
146C22⋊C4—3142no—
147C42—24no—
148C42—22no—
149C42—3141no—
150C42C22⋊D15714yescomplemented
151C23—24no—
152C23—21no—
153C23—21no—
154C23—3141no—
155C23#1457893112yes—
156C23C2×C22⋊D15711yescharacteristic
157Q8—3142no—
158D4—3142no—
159D4—6284no—
160D4—6281no—
161D4—6281no—
162C2×C4—216no—
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—24no—
168C2×C4—24no—
169C2×C4—3142no—
170C2×C4—3141no—
171C2×C4—6282no—
172C2×C4#1457893112yes—
173C2×C4C2×C4×D15711yescharacteristic
174C2×C4C2×C22⋊D15712yes—
175C2×C4C2×D62811yescharacteristic
176C2×C4#1457895412yes—
177C8—6282no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—6281no—
184C22—6282no—
185C22#1909769914yescomplemented
186C22C2×#1457893111yescharacteristic
187C22#1909774011yescharacteristic
188C22#1909775411yescharacteristic
189C4—28no—
190C4—22no—
191C4—6281no—
192C4—6282no—
193C4C4×C22⋊D15712yes—
194C4#1909774512yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—12561no—
199C2#2375715211yescharacteristic
200C2C2×#1909769912yes—
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC22×C42×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenterC22×C42D157
hypocenterC157#1896
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. C2×#19097699C2semidirect
3. #23757237C2semidirect
4. #23757033C2semidirect
5. C22×C42×C157C2semidirect
9. #19097750C4semidirect
10. #19097745C4semidirect
23. C2×Dic314C2×C4semidirect
24. C2×D628C2×C4semidirect
31. C4⋊Dic157C2×C4semidirect
49. C42×C157D4semidirect
82. C22×C157#104semidirect
100. C157#1896semidirect
103. C22×C42D157semidirect
150. C42C22⋊D157semidirect
185. C22#19097699semidirect

Maximal subgroups

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

subgroupindex
#237577842
C2×#190976992
#237572372
#237570332
C22×C42×C1572
#1896157