Finite Group Databasebeta

← #34100589

Subgroups — #34100589

Order 20096.

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

normal subgroups only

This group has 598 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
1C2×#19097740C211yesmaximal, characteristic
2C2×#19097685C212yesmaximal, complemented
3#23757129C211yesmaximal, characteristic, complemented
4#23757039C212yesmaximal, complemented
5C22×C22⋊C4×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157C412yescomplemented
7C22×C22⋊D157C2211yescharacteristic
8#19097740—21no—
9#19097740—21no—
10#19097740—22no—
11C2×C22⋊Dic157—22no—
12C2×C22⋊Dic157C412yescomplemented
13C2×C22⋊Dic157C2212yes—
14C2×C22⋊Dic157C2211yescharacteristic
15#19097685—24no—
16C25×C157C2211yescharacteristic
17C23×C4×C157—21no—
18C2×C22⋊C4×C157—21no—
19C2×C22⋊C4×C157—24no—
20C2×C22⋊C4×C157C2212yes—
21C23×D157C2×C411yescharacteristic, complemented
22C2×C22⋊D157—22no—
23C2×C22⋊D157—22no—
24C2×C22⋊D157—22no—
25C2×C22⋊D157—21no—
26C2×C22⋊D157—21no—
27C2×C22⋊D157—22no—
28C2×C22⋊D157—44no—
29C22×Dic157—22no—
30C22×Dic157C2×C411yescharacteristic, complemented
31C22×Dic157C2×C412yescomplemented
32C22⋊Dic157—22no—
33C22⋊Dic157—22no—
34C22⋊Dic157—21no—
35C22⋊Dic157—21no—
36C22⋊Dic157—22no—
37C22⋊Dic157—22no—
38C22⋊Dic157—44no—
39C24×C157—22no—
40C24×C157—22no—
41C24×C157—44no—
42C24×C157C2×C412yes—
43C24×C157D411yescharacteristic
44C24×C157D411yescharacteristic
45C24×C157D412yes—
46C24×C157C2311yescharacteristic
47C22×C4×C157—24no—
48C22×C4×C157—22no—
49C22×C4×C157—44no—
50C22⋊C4×C157—24no—
51C22⋊C4×C157—22no—
52C22⋊C4×C157D414yescomplemented
53C22×D157—21no—
54C22×D157—22no—
55C22×D157—42no—
56C22⋊D157—44no—
57C22⋊D157—44no—
58C22⋊D157—41no—
59C22⋊D157—42no—
60C22⋊D157—41no—
61C2×Dic157—21no—
62C2×Dic157—22no—
63C2×Dic157—22no—
64C2×Dic157—42no—
65C2×Dic157—44no—
66C2×Dic157—42no—
67C23×C157—24no—
68C23×C157—21no—
69C23×C157—21no—
70C23×C157—24no—
71C23×C157—24no—
72C23×C157—24no—
73C23×C157—21no—
74C23×C157—24no—
75C23×C157—21no—
76C23×C157—42no—
77C23×C157—42no—
78C23×C157—42no—
79C23×C157—42no—
80C23×C157—48no—
81C23×C157—48no—
82C23×C157C22⋊C412yes—
83C23×C157C22⋊C412yes—
84C23×C157C22×C411yescharacteristic
85C23×C157C2×D411yescharacteristic
86C23×C157C2×D412yes—
87C23×C157C2×D411yescharacteristic
88C23×C157#4112yes—
89C2×C4×C157—24no—
90C2×C4×C157—48no—
91C2×C4×C157—44no—
92C22×C157—24no—
93C22×C157—24no—
94C22×C157—22no—
95C22×C157—22no—
96C22×C157—22no—
97C22×C157—22no—
98C22×C157—22no—
99C22×C157—22no—
100C22×C157—22no—
101C22×C157—22no—
102C22×C157—42no—
103C22×C157—42no—
104C22×C157—48no—
105C22×C157—48no—
106C22×C157—42no—
107C22×C157—42no—
108C22×C157#9914yescomplemented
109C22×C157C2×C22⋊C411yescharacteristic
110C22×C157C4×D412yes—
111C22×C157#12011yescharacteristic
112C22×C157#12112yes—
113C22×C157#12311yescharacteristic
114C2×D157—41no—
115C2×D157—42no—
116C2×D157—82no—
117C4×C157—44no—
118Dic157—41no—
119Dic157—42no—
120Dic157—82no—
121C2×C157—22no—
122C2×C157—21no—
123C2×C157—22no—
124C2×C157—24no—
125C2×C157—21no—
126C2×C157—42no—
127C2×C157#38611yescharacteristic
128C2×C157C2×#9912yes—
129D157—81no—
130C157#189811yescharacteristic, complemented, Sylow
131#1898—1571nomaximal, Sylow
132C2×#120—1571no—
133C22×C22⋊C4D15711yescharacteristic, complemented
134C2×#99—1572no—
135#379—1571no—
136#342—1572no—
137C25C2×D15711yescharacteristic
138C22×D4—1571no—
139C22×D4—1572no—
140C23×C4—21no—
141#120—3141no—
142#120—3141no—
143#120—3142no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—24no—
146C2×C22⋊C4—3142no—
147C2×C22⋊C4—1572no—
148C2×C22⋊C4—1572no—
149C2×C22⋊C4—1571no—
150C2×C22⋊C4C2×D15712yes—
151#99—3144no—
152C24—22no—
153C24—22no—
154C24—44no—
155C24—1571no—
156C24C4×D15712yes—
157C24C22⋊D15711yescharacteristic
158C24C22⋊D15711yescharacteristic
159C24D62812yes—
160C24C22×D15711yescharacteristic
161C2×D4—3142no—
162C2×D4—3141no—
163C2×D4—3141no—
164C2×D4—3142no—
165C2×D4—3142no—
166C2×D4—3142no—
167C2×D4—6284no—
168C22×C4—24no—
169C22×C4—22no—
170C22×C4—44no—
171C22×C4—3142no—
172C22×C4—1571no—
173C22×C4—1572no—
174C22⋊C4—24no—
175C22⋊C4—22no—
176C22⋊C4—3141no—
177C22⋊C4—3141no—
178C22⋊C4—3142no—
179C22⋊C4—3142no—
180C22⋊C4—3142no—
181C22⋊C4—3142no—
182C22⋊C4—6284no—
183C22⋊C4C22⋊D15714yescomplemented
184C23—24no—
185C23—21no—
186C23—21no—
187C23—24no—
188C23—24no—
189C23—24no—
190C23—21no—
191C23—24no—
192C23—21no—
193C23—42no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—48no—
198C23—48no—
199C23—3141no—
200C23—3142no—
201C23—6282no—
202C23#1457893112yes—
203C23#1457893112yes—
204C23C2×C4×D15711yescharacteristic
205C23C2×C22⋊D15711yescharacteristic
206C23C2×C22⋊D15712yes—
207C23C2×D62811yescharacteristic
208C23#1457895412yes—
209D4—6284no—
210D4—6284no—
211D4—6281no—
212D4—6282no—
213D4—6281no—
214C2×C4—24no—
215C2×C4—48no—
216C2×C4—44no—
217C2×C4—3141no—
218C2×C4—3142no—
219C2×C4—3142no—
220C2×C4—6282no—
221C2×C4—6284no—
222C2×C4—6282no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—42no—
234C22—42no—
235C22—48no—
236C22—48no—
237C22—42no—
238C22—42no—
239C22—6281no—
240C22—6282no—
241C22—12562no—
242C22#1909768514yescomplemented
243C22C2×#1457893111yescharacteristic
244C22C4×C22⋊D15712yes—
245C22#1909774011yescharacteristic
246C22#1909774512yes—
247C22#1909775411yescharacteristic
248C4—44no—
249C4—6281no—
250C4—6282no—
251C4—12562no—
252C2—21no—
253C2—22no—
254C2—24no—
255C2—21no—
256C2—22no—
257C2—42no—
258C2—12561no—
259C2#2375715211yescharacteristic
260C2C2×#1909768512yes—
subgroupG/H
centerC22C2×#14578931
commutatorC23×C157C22×C4
FrattiniC24C22×D157
FittingC22×C22⋊C4×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC2×#19097740C2
cosocleC24×C157C23
hypercenterC22×C22⋊C4D157
hypocenterC157#1898
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19097685C2semidirect
3. #23757129C2semidirect
4. #23757039C2semidirect
5. C22×C22⋊C4×C157C2semidirect
6. C22×C22⋊D157C4semidirect
12. C2×C22⋊Dic157C4semidirect
21. C23×D157C2×C4semidirect
30. C22×Dic157C2×C4semidirect
31. C22×Dic157C2×C4semidirect
52. C22⋊C4×C157D4semidirect
108. C22×C157#99semidirect
130. C157#1898semidirect
133. C22×C22⋊C4D157semidirect
183. C22⋊C4C22⋊D157semidirect
242. C22#19097685semidirect

Maximal subgroups

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

subgroupindex
C2×#190977402
C2×#190976852
#237571292
#237570392
C22×C22⋊C4×C1572
#1898157