Finite Group Databasebeta

← #34101387

Subgroups — #34101387

Order 20096.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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
2C2×#19097685C212yesmaximal, complemented
3#23757152C212yesmaximal, complemented
4#23757040C211yesmaximal, characteristic, complemented
5#385×C157C211yesmaximal, characteristic, complemented
6C22×C22⋊D157C2212yes—
7#19097755—22no—
8#19097745—21no—
9#19097745—21no—
10#19097741—22no—
11C2×C22⋊Dic157C2212yes—
12C2×#14578931—22no—
13#19097685—24no—
14#19097678—22no—
15C23×C4×C157C2211yescharacteristic
16C2×C4⋊C4×C157—21no—
17C2×C22⋊C4×C157C2211yescharacteristic
18C2×C22⋊C4×C157C2211yescharacteristic
19#95×C157—21no—
20C23×D157D412yes—
21C2×D628—21no—
22C2×D628—21no—
23C2×C22⋊D157—22no—
24C2×C22⋊D157—22no—
25C2×C22⋊D157—22no—
26C2×C22⋊D157—22no—
27C2×C22⋊D157—22no—
28C2×C22⋊D157—22no—
29C22×Dic157—22no—
30C22×Dic157D412yes—
31C4⋊Dic157—21no—
32C4⋊Dic157—21no—
33C22⋊Dic157—22no—
34C22⋊Dic157—22no—
35#14578931—22no—
36#14578931—22no—
37#14578931—44no—
38C24×C157C2311yescharacteristic
39C22×C4×C157—21no—
40C22×C4×C157—21no—
41C22×C4×C157—22no—
42C22×C4×C157—42no—
43C22×C4×C157D411yescharacteristic
44C22×C4×C157D411yescharacteristic
45C4⋊C4×C157—42no—
46C22⋊C4×C157—22no—
47C22⋊C4×C157—21no—
48C22⋊C4×C157D412yescomplemented
49C22×D157—22no—
50C22×D157—22no—
51C22×D157—22no—
52C22×D157—42no—
53C22×D157—42no—
54D628—81no—
55D628—81no—
56C22⋊D157—42no—
57C22⋊D157—42no—
58C22⋊D157—42no—
59C22⋊D157—42no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—42no—
64C2×Dic157—42no—
65C2×Dic157—42no—
66C23×C157—41no—
67C23×C157—41no—
68C23×C157C2×D412yes—
69C23×C157C2×D411yescharacteristic
70C23×C157C2×D411yescharacteristic
71C23×C157#4111yescharacteristic
72C23×C157#4112yes—
73C2×C4×C157—22no—
74C2×C4×C157—24no—
75C2×C4×C157—21no—
76C2×C4×C157—21no—
77C2×C4×C157—22no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157—42no—
82C2×C4×C157—41no—
83C2×C4×C157—41no—
84C2×C4×C157—41no—
85C22×C157—21no—
86C22×C157—22no—
87C22×C157—21no—
88C22×C157—22no—
89C22×C157—41no—
90C22×C157—41no—
91C22×C157—42no—
92C22×C157#12011yescharacteristic
93C22×C157#12111yescharacteristic
94C22×C157#12112yes—
95C22×C157#12312yes—
96C22×C157#12411yescharacteristic
97C2×D157—44no—
98C2×D157—42no—
99C2×D157—42no—
100C2×D157—42no—
101C2×D157—82no—
102C4×C157—42no—
103C4×C157—42no—
104C4×C157—41no—
105C4×C157—41no—
106Dic157—42no—
107Dic157—82no—
108C2×C157—22no—
109C2×C157—21no—
110C2×C157—22no—
111C2×C157—21no—
112C2×C157#39411yescharacteristic
113C2×C157B(4,𝔽2)11yescharacteristic
114C2×C157#45811yescharacteristic
115D157—82no—
116C157#204411yescharacteristic, complemented, Sylow
117#2044—1571nomaximal, Sylow
118#534—1571no—
119C2×#99—1572no—
120#386—1572no—
121#385D15711yescharacteristic, complemented
122#342—1571no—
123C22×D4—1572no—
124C23×C4C2×D15711yescharacteristic
125#123—3142no—
126#121—3141no—
127#121—3141no—
128#120—3142no—
129C2×C4⋊C4—21no—
130C2×C22⋊C4—3142no—
131C2×C22⋊C4—1572no—
132C2×C22⋊C4C2×D15711yescharacteristic
133C2×C22⋊C4C2×D15711yescharacteristic
134#99—3144no—
135#95—21no—
136#95—3142no—
137C24—1572no—
138C24C22×D15711yescharacteristic
139C2×D4—3141no—
140C2×D4—3141no—
141C2×D4—3142no—
142C2×D4—3142no—
143C2×D4—3142no—
144C2×D4—3142no—
145C2×D4—3142no—
146C2×D4—3142no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—42no—
151C22×C4—3142no—
152C22×C4—1572no—
153C22×C4C22⋊D15711yescharacteristic
154C22×C4C22⋊D15711yescharacteristic
155C4⋊C4—42no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C22⋊C4—22no—
159C22⋊C4—21no—
160C22⋊C4—3142no—
161C22⋊C4—3142no—
162C22⋊C4—3142no—
163C22⋊C4—3142no—
164C22⋊C4—6284no—
165C22⋊C4D62812yescomplemented
166C23—41no—
167C23—41no—
168C23—3142no—
169C23—3142no—
170C23—3142no—
171C23—6282no—
172C23—6282no—
173C23D4×D15712yes—
174C23C2×C22⋊D15711yescharacteristic
175C23C2×D62811yescharacteristic
176C23#1457895411yescharacteristic
177C23#1457895512yes—
178D4—6282no—
179D4—6282no—
180D4—6282no—
181D4—6282no—
182D4—12561no—
183D4—12561no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—3142no—
197C2×C4—3142no—
198C2×C4—3142no—
199C2×C4—6282no—
200C2×C4—6282no—
201C2×C4—6282no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—6284no—
210C22—6282no—
211C22—6282no—
212C22—6282no—
213C22—12562no—
214C22#1909773911yescharacteristic
215C22#1909774511yescharacteristic
216C22#1909774612yes—
217C22#1909775612yes—
218C22#1909776011yescharacteristic
219C4—42no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—6282no—
224C4—12562no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—12562no—
230C2#2375719011yescharacteristic
231C2#2375745911yescharacteristic
232C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC24×C157C23
FrattiniC24C22×D157
Fitting#385×C157C2
socleC22×C157#120
prime radical#23757835C2
hypercenter#385D157
hypocenterC157#2044
LCSG ▷ C24×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#19097685C2semidirect
3. #23757152C2semidirect
4. #23757040C2semidirect
5. #385×C157C2semidirect
48. C22⋊C4×C157D4semidirect
116. C157#2044semidirect
121. #385D157semidirect
165. C22⋊C4D628semidirect

Maximal subgroups

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

subgroupindex
#237578352
C2×#190976852
#237571522
#237570402
#385×C1572
#2044157