Finite Group Databasebeta

← #34098639

Subgroups — #34098639

Order 20096.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#23757786C211yesmaximal, characteristic
2#23757235C211yesmaximal, characteristic, complemented
3#95×D157C211yesmaximal, characteristic, complemented
4#23757010C211yesmaximal, characteristic, complemented
5#23757008C211yesmaximal, characteristic, complemented
6#23757006C211yesmaximal, characteristic, complemented
7#328×C157C211yesmaximal, characteristic, complemented
8C2×#14578955C411yescharacteristic, complemented
9C22×C4×D157—21no—
10C22×C4×D157C2211yescharacteristic
11C2×#14578937—21no—
12#19097756—21no—
13#19097747C411yescharacteristic, complemented
14#19097746C411yescharacteristic, complemented
15#19097745C2211yescharacteristic
16#19097741—21no—
17#19097733—21no—
18#19097731—21no—
19#19097729C411yescharacteristic, complemented
20C22⋊#11929434C2211yescharacteristic
21#19097683—21no—
22#19097678—21no—
23#19097678C2211yescharacteristic
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C23×D157D411yescharacteristic
28#14578955—42no—
29C2×D628—21no—
30C2×D628—21no—
31C2×D628C2×C411yescharacteristic, complemented
32C2×C22⋊D157—21no—
33C22×Dic157—21no—
34C22×Dic157D411yescharacteristic
35C2×C4×D157—24no—
36C2×C4×D157—21no—
37C2×C4×D157—42no—
38C2×C4×D157—42no—
39C2×C4×D157—42no—
40C2×C4×D157C2×C411yescharacteristic
41C2×C4×D157C2×C411yescharacteristic
42C2×C4×D157D411yescharacteristic
43C2×C4×D157D411yescharacteristic
44#14578937—42no—
45C2×#11929434—21no—
46C4⋊Dic157C2×C411yescharacteristic, complemented
47#14578933—21no—
48#14578931—21no—
49#14578931—21no—
50#14578931—21no—
51#14578931—21no—
52C4×Dic157—21no—
53C2×Q8×C157C2×C411yescharacteristic, complemented
54C22×C4×C157—21no—
55C22×C4×C157C2311yescharacteristic
56C2×C8×C157—21no—
57C4⋊C4×C157—21no—
58C4⋊C4×C157C2×C411yescharacteristic, complemented
59C22⋊C4×C157—21no—
60C22×D157—21no—
61C22×D157—21no—
62C22×D157—22no—
63C22×D157—22no—
64C22×D157—21no—
65C22×D157C22⋊C411yescharacteristic
66C22×D157C22⋊C411yescharacteristic
67D628—41no—
68D628—42no—
69D628—42no—
70C22⋊D157—41no—
71C22⋊D157—41no—
72C2×Dic157—22no—
73C2×Dic157—21no—
74C2×Dic157—41no—
75C2×Dic157—41no—
76C2×Dic157—41no—
77C2×Dic157C22⋊C411yescharacteristic
78C2×Dic157C22⋊C411yescharacteristic
79C4×D157—22no—
80C4×D157—22no—
81C4×D157—41no—
82C4×D157—41no—
83C4×D157—42no—
84C4×D157—48no—
85#11929434—41no—
86C23×C157C2×D411yescharacteristic
87Q8×C157—41no—
88C2×C4×C157—22no—
89C2×C4×C157—21no—
90C2×C4×C157—21no—
91C2×C4×C157—41no—
92C2×C4×C157—41no—
93C2×C4×C157—41no—
94C2×C4×C157C22×C411yescharacteristic
95C2×C4×C157C2×D411yescharacteristic
96C8×C157—41no—
97C22×C157—21no—
98C22×C157—21no—
99C22×C157C2×C22⋊C411yescharacteristic
100C22×C157AGL(1,ℤ/8)11yescharacteristic
101C22×C157#13711yescharacteristic
102C2×D157—24no—
103C2×D157—24no—
104C2×D157—21no—
105C2×D157—21no—
106C2×D157—21no—
107C2×D157—21no—
108C2×D157—41no—
109C2×D157—41no—
110C2×D157—41no—
111C2×D157#9912yes—
112C2×D157#10412yes—
113C4×C157—21no—
114C4×C157—21no—
115C4×C157—42no—
116C4×C157—41no—
117C4×C157—41no—
118Dic157—21no—
119Dic157—21no—
120Dic157—42no—
121Dic157—41no—
122C2×C157—21no—
123C2×C157—21no—
124C2×C157C2×#9911yescharacteristic
125C2×C157#41711yescharacteristic
126C2×C157C2×#10411yescharacteristic
127D157—22no—
128D157—22no—
129D157—81no—
130C157#150411yescharacteristic, complemented, Sylow
131#1504—1571nomaximal, Sylow
132#525—1571no—
133#407—1571no—
134C2×#95—1571no—
135#328—1571no—
136#328D15711yescharacteristic, complemented
137#327—1571no—
138#327—1571no—
139C2×#41—1571no—
140C23×C4—3141no—
141C23×C4—1571no—
142C2×M16—3141no—
143#123—3141no—
144C22⋊Q8—1571no—
145C22⋊Q8C2×D15711yescharacteristic
146#121—1571no—
147#121—1571no—
148#120—3141no—
149C4×D4—3141no—
150C4×D4—3141no—
151#117—1571no—
152C22⋊C8—3141no—
153C22⋊C8—1571no—
154C22⋊C8C2×D15711yescharacteristic
155#95—3141no—
156#95—1571no—
157#95C2×D15711yescharacteristic
158C24—1571no—
159#41—6282no—
160C2×Q8C4×D15711yescharacteristic, complemented
161C2×D4—3141no—
162C2×D4—3141no—
163C2×D4—3141no—
164C2×D4—1571no—
165C22×C4—21no—
166C22×C4—3144no—
167C22×C4—3141no—
168C22×C4—3141no—
169C22×C4—6282no—
170C22×C4—6282no—
171C22×C4—6282no—
172C22×C4—1571no—
173C22×C4—1571no—
174C22×C4—1571no—
175C22×C4—1571no—
176C22×C4—1571no—
177C22×C4C22×D15711yescharacteristic
178M16—6282no—
179C2×C8—21no—
180C2×C8—3141no—
181C4⋊C4—21no—
182C4⋊C4—3141no—
183C4⋊C4—1571no—
184C4⋊C4C4×D15711yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—3141no—
187C22⋊C4—3141no—
188C22⋊C4—3141no—
189C22⋊C4—3141no—
190C42—3141no—
191C23—3142no—
192C23—3142no—
193C23—3141no—
194C23—3141no—
195C23—3141no—
196C23—1571no—
197C23—1571no—
198C23D4×D15711yescharacteristic
199Q8—41no—
200D4—6281no—
201D4—6282no—
202D4—6282no—
203D4—6281no—
204D4—6281no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—3142no—
212C2×C4—3142no—
213C2×C4—3142no—
214C2×C4—3141no—
215C2×C4—6281no—
216C2×C4—6281no—
217C2×C4—6282no—
218C2×C4—6288no—
219C2×C4—6281no—
220C2×C4—6281no—
221C2×C4—6281no—
222C2×C4—1571no—
223C2×C4—1571no—
224C2×C4C2×C4×D15711yescharacteristic
225C2×C4D4×D15711yescharacteristic
226C8—41no—
227C8—6281no—
228C22—21no—
229C22—21no—
230C22—3144no—
231C22—3144no—
232C22—3141no—
233C22—3141no—
234C22—3141no—
235C22—3141no—
236C22—6281no—
237C22—6281no—
238C22—6281no—
239C22—1572no—
240C22—1572no—
241C22C22⋊C4×D15711yescharacteristic
242C22#1909779811yescharacteristic
243C22#1909780311yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—41no—
249C4—3141no—
250C4—3141no—
251C4—6282no—
252C4—6281no—
253C2—21no—
254C2—21no—
255C2—3142no—
256C2—3142no—
257C2—12561no—
258C2#99×D15711yescharacteristic
259C2#2375727311yescharacteristic
260C2#104×D15711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757786C2
cosocleC22×C4×C157C23
hypercenter#328D157
hypocenterC157#1504
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23757235C2semidirect
3. #95×D157C2semidirect
4. #23757010C2semidirect
5. #23757008C2semidirect
6. #23757006C2semidirect
7. #328×C157C2semidirect
8. C2×#14578955C4semidirect
13. #19097747C4semidirect
14. #19097746C4semidirect
19. #19097729C4semidirect
31. C2×D628C2×C4semidirect
46. C4⋊Dic157C2×C4semidirect
53. C2×Q8×C157C2×C4semidirect
58. C4⋊C4×C157C2×C4semidirect
130. C157#1504semidirect
136. #328D157semidirect
160. C2×Q8C4×D157semidirect
184. C4⋊C4C4×D157semidirect

Maximal subgroups

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

subgroupindex
#237577862
#237572352
#95×D1572
#237570102
#237570082
#237570062
#328×C1572
#1504157