Finite Group Databasebeta

← #34101262

Subgroups — #34101262

Order 20096.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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#23757835C211yesmaximal, characteristic, complemented
2C2×#19097740C212yesmaximal, complemented
3C2×#19097685C212yesmaximal, complemented
4#23757040C211yesmaximal, characteristic, complemented
5#379×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157—22no—
7C22×C22⋊D157C2212yes—
8#19097755—22no—
9#19097745—22no—
10#19097741—22no—
11#19097740—24no—
12#19097740—24no—
13C2×C22⋊Dic157—22no—
14C2×C22⋊Dic157C2212yes—
15#19097685—24no—
16C25×C157C2211yescharacteristic
17C2×C22⋊C4×C157—22no—
18C2×C22⋊C4×C157C2211yescharacteristic
19C2×C22⋊C4×C157C2211yescharacteristic
20C23×D157D412yescomplemented
21C2×D628—22no—
22C2×C22⋊D157—28no—
23C2×C22⋊D157—22no—
24C2×C22⋊D157—22no—
25C2×C22⋊D157—22no—
26C2×C22⋊D157—22no—
27C2×C22⋊D157—22no—
28C2×C22⋊D157—22no—
29C2×C22⋊D157—48no—
30C22×Dic157—22no—
31C22×Dic157D412yescomplemented
32C4⋊Dic157—22no—
33C22⋊Dic157—28no—
34C22⋊Dic157—22no—
35C22⋊Dic157D414yescomplemented
36#14578931—24no—
37C24×C157—21no—
38C24×C157—22no—
39C24×C157—22no—
40C24×C157—21no—
41C24×C157—44no—
42C24×C157D412yescomplemented
43C24×C157C2311yescharacteristic
44C22×C4×C157—21no—
45C22×C4×C157D412yescomplemented
46C22⋊C4×C157—22no—
47C22⋊C4×C157—22no—
48C22⋊C4×C157—44no—
49C22×D157—22no—
50C22×D157—22no—
51C22×D157—22no—
52C22×D157—44no—
53D628—82no—
54C22⋊D157—416no—
55C22⋊D157—42no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C22⋊D157—42no—
59C2×Dic157—24no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—44no—
64C23×C157—28no—
65C23×C157—24no—
66C23×C157—24no—
67C23×C157—22no—
68C23×C157—44no—
69C23×C157—42no—
70C23×C157—42no—
71C23×C157—44no—
72C23×C157—44no—
73C23×C157—48no—
74C23×C157—41no—
75C23×C157—42no—
76C23×C157—41no—
77C23×C157C2×D412yes—
78C23×C157C2×D412yes—
79C23×C157C2×D411yescharacteristic
80C23×C157C2×D411yescharacteristic
81C23×C157#4111yescharacteristic
82C2×C4×C157—22no—
83C2×C4×C157—42no—
84C2×C4×C157—42no—
85C2×C4×C157—41no—
86C22×C157—22no—
87C22×C157—24no—
88C22×C157—24no—
89C22×C157—28no—
90C22×C157—42no—
91C22×C157—41no—
92C22×C157—41no—
93C22×C157—44no—
94C22×C157—44no—
95C22×C157—48no—
96C22×C157—42no—
97C22×C157—42no—
98C22×C157—44no—
99C22×C157#12011yescharacteristic
100C22×C157#12012yes—
101C22×C157#12112yes—
102C22×C157#12111yescharacteristic
103C22×C157#12711yescharacteristic
104C2×D157—44no—
105C2×D157—42no—
106C2×D157—44no—
107C2×D157—82no—
108C4×C157—42no—
109C4×C157—81no—
110Dic157—44no—
111Dic157—42no—
112C2×C157—22no—
113C2×C157—21no—
114C2×C157—22no—
115C2×C157—21no—
116C2×C157—44no—
117C2×C157#39211yescharacteristic
118C2×C157B(4,𝔽2)12yes—
119D157—82no—
120C157#202111yescharacteristic, complemented, Sylow
121#2021—1571nomaximal, Sylow
122#534—1571no—
123C2×#120—1572no—
124C2×#99—1572no—
125#379D15711yescharacteristic, complemented
126#342—1571no—
127C25C2×D15711yescharacteristic
128C22×D4—3142no—
129C22×D4—1572no—
130#123—3142no—
131#121—3142no—
132#120—3142no—
133#120—3144no—
134#120—3144no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—3142no—
137C2×C22⋊C4—1572no—
138C2×C22⋊C4C2×D15711yescharacteristic
139C2×C22⋊C4C2×D15711yescharacteristic
140#99—3144no—
141C24—22no—
142C24—21no—
143C24—22no—
144C24—21no—
145C24—44no—
146C24—1572no—
147C24D62812yescomplemented
148C24C22×D15711yescharacteristic
149C2×D4—3142no—
150C2×D4—3148no—
151C2×D4—3142no—
152C2×D4—3142no—
153C2×D4—3142no—
154C2×D4—3142no—
155C2×D4—3142no—
156C2×D4—3142no—
157C2×D4—6288no—
158C22×C4—21no—
159C22×C4—3142no—
160C22×C4—1572no—
161C22×C4C22⋊D15712yescomplemented
162C4⋊C4—3142no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—3144no—
167C22⋊C4—3148no—
168C22⋊C4—3142no—
169C22⋊C4—1574no—
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—42no—
182C23—41no—
183C23—3142no—
184C23—3142no—
185C23—3142no—
186C23—6284no—
187C23D4×D15712yes—
188C23D4×D15712yes—
189C23C2×C22⋊D15711yescharacteristic
190C23C2×D62811yescharacteristic
191C23#1457895411yescharacteristic
192D4—62816no—
193D4—6282no—
194D4—6282no—
195D4—6282no—
196D4—6282no—
197D4—12562no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—3142no—
203C2×C4—3142no—
204C2×C4—3144no—
205C2×C4—3142no—
206C2×C4—6284no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—6284no—
221C22—6282no—
222C22—6284no—
223C22—12562no—
224C22#1909773911yescharacteristic
225C22#1909774112yes—
226C22#1909774412yes—
227C22#1909774511yescharacteristic
228C22#1909776711yescharacteristic
229C4—42no—
230C4—81no—
231C4—6284no—
232C4—6282no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—12562no—
239C2#2375718211yescharacteristic
240C2#2375745912yes—
subgroupG/H
centerC22#19097739
commutator, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#379×C157C2
socleC22×C157#120
hypercenter#379D157
hypocenterC157#2021
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #23757835C2semidirect
2. C2×#19097740C2semidirect
3. C2×#19097685C2semidirect
4. #23757040C2semidirect
5. #379×C157C2semidirect
20. C23×D157D4semidirect
31. C22×Dic157D4semidirect
35. C22⋊Dic157D4semidirect
42. C24×C157D4semidirect
45. C22×C4×C157D4semidirect
120. C157#2021semidirect
125. #379D157semidirect
147. C24D628semidirect
161. C22×C4C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
#237578352
C2×#190977402
C2×#190976852
#237570402
#379×C1572
#2021157