Finite Group Databasebeta

← #34100584

Subgroups — #34100584

Order 20096.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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
5C2×#117×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×C157C2211yescharacteristic
17#117×C157—24no—
18C2×C4⋊C4×C157—21no—
19C2×C22⋊C4×C157—21no—
20C2×C42×C157C2212yes—
21#14578954—22no—
22#14578954—22no—
23C2×Dic314C2×C411yescharacteristic
24C2×D628C2×C411yescharacteristic
25C2×C22⋊D157—22no—
26C2×C22⋊D157—21no—
27C2×C4×D157—21no—
28#14578938—22no—
29#14578938—22no—
30C2×#11929434—22no—
31C4⋊Dic157C2×C412yes—
32#14578933—22no—
33C22⋊Dic157—22no—
34C22⋊Dic157—21no—
35#14578931—22no—
36C4×Dic157—21no—
37C24×C157D411yescharacteristic
38C22×C4×C157—22no—
39C22×C4×C157—22no—
40C22×C4×C157—22no—
41C22×C4×C157C2×C412yes—
42C22×C4×C157D411yescharacteristic
43C22×C4×C157D412yes—
44C22×C4×C157C2311yescharacteristic
45C4⋊C4×C157—24no—
46C22⋊C4×C157—24no—
47C42×C157—22no—
48C42×C157D414yescomplemented
49C22×D157—21no—
50Dic314—22no—
51D628—22no—
52C22⋊D157—44no—
53C22⋊D157—41no—
54C22⋊D157—41no—
55C2×Dic157—21no—
56C2×Dic157—22no—
57C4×D157—42no—
58#11929434—42no—
59C23×C157—21no—
60C23×C157—21no—
61C23×C157—42no—
62C23×C157C22⋊C412yes—
63C23×C157C2×D411yescharacteristic
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157—24no—
67C2×C4×C157—24no—
68C2×C4×C157—24no—
69C2×C4×C157—44no—
70C2×C4×C157C22⋊C412yes—
71C2×C4×C157C22×C411yescharacteristic
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D411yescharacteristic
74C2×C4×C157#4112yes—
75C22×C157—22no—
76C22×C157—22no—
77C22×C157—22no—
78C22×C157—22no—
79C22×C157—42no—
80C22×C157—42no—
81C22×C157C2×C22⋊C411yescharacteristic
82C22×C157#12011yescharacteristic
83C22×C157#12311yescharacteristic
84C2×D157—41no—
85C2×D157—42no—
86C4×C157—22no—
87C4×C157—44no—
88C4×C157C4×D412yes—
89C4×C157#12112yes—
90Dic157—41no—
91Dic157—42no—
92C2×C157—21no—
93C2×C157—21no—
94C2×C157—42no—
95C2×C157#38611yescharacteristic
96C2×C157#42112yes—
97D157—81no—
98C157#189711yescharacteristic, complemented, Sylow
99#1897—1571nomaximal, Sylow
100#525—1571no—
101C2×#117D15711yescharacteristic, complemented
102C2×#104—1572no—
103#407—1571no—
104#339—1572no—
105C2×#41—1571no—
106C23×C4C2×D15711yescharacteristic
107C2×M16—1572no—
108#123—3141no—
109C22⋊Q8—1572no—
110#121—1572no—
111#120—3141no—
112C4×D4—3142no—
113#117—24no—
114#117—1571no—
115C2×C4⋊C4—21no—
116C2×C22⋊C4—21no—
117C2×C42C2×D15712yes—
118#104—3144no—
119C22⋊C8—3142no—
120C24C22⋊D15711yescharacteristic
121#41—3142no—
122#41—3142no—
123C2×Q8—1571no—
124C2×D4—3141no—
125C2×D4—3142no—
126C2×D4—1571no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—3141no—
131C22×C4C4×D15712yes—
132C22×C4C22⋊D15711yescharacteristic
133C22×C4D62812yes—
134C22×C4C22×D15711yescharacteristic
135M16—3142no—
136M16—3142no—
137C2×C8—3142no—
138C4⋊C4—24no—
139C4⋊C4—3142no—
140C4⋊C4—1572no—
141C22⋊C4—24no—
142C22⋊C4—3141no—
143C22⋊C4—3142no—
144C22⋊C4—3142no—
145C42—22no—
146C42—3141no—
147C42C22⋊D15714yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3141no—
152C23#1457893112yes—
153C23C2×C22⋊D15711yescharacteristic
154Q8—3142no—
155D4—3142no—
156D4—6284no—
157D4—6281no—
158D4—6281no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—3142no—
166C2×C4—3141no—
167C2×C4—6282no—
168C2×C4#1457893112yes—
169C2×C4C2×C4×D15711yescharacteristic
170C2×C4C2×C22⋊D15712yes—
171C2×C4C2×D62811yescharacteristic
172C2×C4#1457895412yes—
173C8—6282no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—6281no—
181C22—6282no—
182C22C2×#1457893111yescharacteristic
183C22#1909774011yescharacteristic
184C22#1909775411yescharacteristic
185C4—22no—
186C4—44no—
187C4—6281no—
188C4—6282no—
189C4C4×C22⋊D15712yes—
190C4#1909774512yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—12561no—
195C2#2375715211yescharacteristic
196C2#2375729112yes—
subgroupG/H
centerC2×C4C2×D628
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#117×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenterC2×#117D157
hypocenterC157#1897
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#19097699C2semidirect
3. #23757237C2semidirect
4. #23757033C2semidirect
5. C2×#117×C157C2semidirect
9. #19097750C4semidirect
10. #19097745C4semidirect
48. C42×C157D4semidirect
98. C157#1897semidirect
101. C2×#117D157semidirect
147. C42C22⋊D157semidirect

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
C2×#117×C1572
#1897157