Finite Group Databasebeta

← #34098641

Subgroups — #34098641

Order 20096.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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×#19097678C211yesmaximal, characteristic, complemented
3#23757011C212yesmaximal, complemented
4#23757008C212yesmaximal, complemented
5#407×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C411yescharacteristic, complemented
7C23×Dic157—21no—
8#19097754—21no—
9#19097750C411yescharacteristic, complemented
10#19097750C2211yescharacteristic
11#19097745C411yescharacteristic, complemented
12#19097745C2211yescharacteristic
13#19097740—21no—
14C4×C22⋊D157—21no—
15C4×C22⋊D157—21no—
16#19097730C411yescharacteristic, complemented
17#19097678—21no—
18#19097678C2212yes—
19C23×C4×C157C2211yescharacteristic
20C2×M16×C157—21no—
21C22⋊C8×C157—21no—
22C22⋊C8×C157C2212yes—
23#14578954—42no—
24C2×Dic314C2×C411yescharacteristic, complemented
25C2×D628C2×C411yescharacteristic, complemented
26C2×C22⋊D157—21no—
27C2×C22⋊D157—21no—
28C2×C22⋊D157—21no—
29C22×Dic157—24no—
30C22×Dic157—22no—
31C22×Dic157—42no—
32C22×Dic157—42no—
33C2×C4×D157—21no—
34C4⋊Dic157C2×C411yescharacteristic, complemented
35C4⋊Dic157C2×C411yescharacteristic, complemented
36#14578933—21no—
37#14578933—21no—
38C22⋊Dic157—21no—
39C22⋊Dic157—21no—
40C22⋊Dic157—21no—
41#14578931—21no—
42#14578931—21no—
43C4×Dic157—21no—
44C24×C157D411yescharacteristic
45C22×C4×C157—42no—
46C22×C4×C157C2×C411yescharacteristic
47C22×C4×C157C2×C411yescharacteristic
48C22×C4×C157D411yescharacteristic
49C22×C4×C157D411yescharacteristic
50C22×C4×C157D411yescharacteristic
51C22×C4×C157C2311yescharacteristic
52M16×C157—42no—
53C2×C8×C157—22no—
54C22×D157—21no—
55Dic314—41no—
56D628—41no—
57C22⋊D157—42no—
58C22⋊D157—42no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C2×Dic157—24no—
62C2×Dic157—21no—
63C2×Dic157—21no—
64C2×Dic157—21no—
65C2×Dic157—48no—
66C2×Dic157—42no—
67C2×Dic157—42no—
68C4×D157—42no—
69C23×C157—22no—
70C23×C157—22no—
71C23×C157—21no—
72C23×C157—21no—
73C23×C157C22⋊C411yescharacteristic
74C23×C157C22⋊C411yescharacteristic
75C23×C157C2×D411yescharacteristic
76C2×C4×C157—22no—
77C2×C4×C157—22no—
78C2×C4×C157—41no—
79C2×C4×C157—41no—
80C2×C4×C157—41no—
81C2×C4×C157—41no—
82C2×C4×C157C22⋊C411yescharacteristic
83C2×C4×C157C22⋊C411yescharacteristic
84C2×C4×C157C22×C411yescharacteristic
85C2×C4×C157C2×D411yescharacteristic
86C8×C157—42no—
87C22×C157—24no—
88C22×C157—24no—
89C22×C157—21no—
90C22×C157—21no—
91C22×C157—21no—
92C22×C157—21no—
93C22×C157—21no—
94C22×C157—21no—
95C22×C157#9912yes—
96C22×C157#10412yes—
97C22×C157C2×C22⋊C411yescharacteristic
98C22×C157AGL(1,ℤ/8)11yescharacteristic
99C22×C157#13711yescharacteristic
100C2×D157—41no—
101C2×D157—41no—
102C2×D157—41no—
103C4×C157—21no—
104C4×C157—21no—
105C4×C157—21no—
106C4×C157—21no—
107Dic157—44no—
108Dic157—41no—
109Dic157—41no—
110Dic157—41no—
111C2×C157—21no—
112C2×C157—22no—
113C2×C157—22no—
114C2×C157—21no—
115C2×C157C2×#9911yescharacteristic
116C2×C157#41711yescharacteristic
117C2×C157C2×#10411yescharacteristic
118D157—81no—
119C157#150411yescharacteristic, complemented, Sylow
120#1504—1571nomaximal, Sylow
121#525—1571no—
122#407D15711yescharacteristic, complemented
123C2×#95—1571no—
124#328—1572no—
125#327—1572no—
126C2×#41—1571no—
127C23×C4—3141no—
128C23×C4C2×D15711yescharacteristic
129C2×M16—21no—
130#123—3141no—
131C22⋊Q8—1571no—
132C22⋊Q8—1571no—
133#121—1571no—
134#121—1571no—
135#120—3141no—
136C4×D4—3141no—
137C4×D4—3141no—
138#117—1571no—
139C22⋊C8—21no—
140C22⋊C8C2×D15712yes—
141#95—3141no—
142#95—1572no—
143C24D62811yescharacteristic
144#41—6282no—
145C2×Q8—1571no—
146C2×D4—3141no—
147C2×D4—3141no—
148C2×D4—3141no—
149C2×D4—1571no—
150C22×C4—42no—
151C22×C4—3144no—
152C22×C4—3142no—
153C22×C4—3141no—
154C22×C4—6282no—
155C22×C4—6282no—
156C22×C4C4×D15711yescharacteristic
157C22×C4C4×D15711yescharacteristic
158C22×C4C22⋊D15711yescharacteristic
159C22×C4C22⋊D15711yescharacteristic
160C22×C4D62811yescharacteristic
161C22×C4C22×D15711yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—3141no—
165C4⋊C4—3141no—
166C4⋊C4—1571no—
167C4⋊C4—1571no—
168C22⋊C4—3141no—
169C22⋊C4—3141no—
170C22⋊C4—3141no—
171C22⋊C4—3141no—
172C22⋊C4—3141no—
173C42—3141no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—3141no—
179C23#1457893111yescharacteristic
180C23#1457893111yescharacteristic
181C23C2×D62811yescharacteristic
182Q8—6281no—
183D4—6281no—
184D4—6282no—
185D4—6282no—
186D4—6281no—
187D4—6281no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—3144no—
195C2×C4—3141no—
196C2×C4—3141no—
197C2×C4—3141no—
198C2×C4—6282no—
199C2×C4—6288no—
200C2×C4—6282no—
201C2×C4—6282no—
202C2×C4#1457893111yescharacteristic
203C2×C4#1457893111yescharacteristic
204C2×C4C2×C4×D15711yescharacteristic
205C2×C4C2×C22⋊D15711yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—6281no—
216C22—6281no—
217C22—6281no—
218C22#1909768512yes—
219C22#1909769712yes—
220C22C2×#1457893111yescharacteristic
221C22#1909779911yescharacteristic
222C22#1909780411yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—6284no—
228C4—6281no—
229C4—6281no—
230C4—6281no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—12561no—
236C2C2×#1909768511yescharacteristic
237C2#2375727511yescharacteristic
238C2C2×#1909769711yescharacteristic
subgroupG/H
centerC22C2×#14578931
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#407×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757784C2
cosocleC22×C4×C157C23
hypercenter#407D157
hypocenterC157#1504
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#19097678C2semidirect
3. #23757011C2semidirect
4. #23757008C2semidirect
5. #407×C157C2semidirect
6. C2×#14578954C4semidirect
9. #19097750C4semidirect
11. #19097745C4semidirect
16. #19097730C4semidirect
24. C2×Dic314C2×C4semidirect
25. C2×D628C2×C4semidirect
34. C4⋊Dic157C2×C4semidirect
35. C4⋊Dic157C2×C4semidirect
119. C157#1504semidirect
122. #407D157semidirect

Maximal subgroups

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

subgroupindex
#237577842
C2×#190976782
#237570112
#237570082
#407×C1572
#1504157