Finite Group Databasebeta

← #442×D157 #34108925

Subgroups — #442×D157 #34108925

Order 20096.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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×D8×D157C211yesmaximal, characteristic
2C4×D4×D157C212yesmaximal, complemented
3#23757386C211yesmaximal, characteristic, complemented
4#23757385C211yesmaximal, characteristic, complemented
5#23757384C211yesmaximal, characteristic, complemented
6#23757383C212yesmaximal, complemented
7#23757382C212yesmaximal, complemented
8#106×D157C211yesmaximal, characteristic, complemented
9#102×D157C212yesmaximal, complemented
10#97×D157C211yesmaximal, characteristic, complemented
11#442×C157C211yesmaximal, characteristic, complemented
12C2×D4×D157C2212yes—
13C22×C4×D157—22no—
14C2×D1256C2211yescharacteristic
15C2×#14578939C2212yes—
16D8×D157C418yescomplemented
17C2×C8×D157C2211yescharacteristic
18C2×C8×D157C2211yescharacteristic
19C4×D628C2212yescomplemented
20D4×Dic157C2212yescomplemented
21#19097733C2212yescomplemented
22C4×C22⋊D157—22no—
23#19097731—22no—
24C4⋊C4×D157C2212yes—
25C22⋊C4×D157—22no—
26C42×D157C2211yescharacteristic
27#19097703C2211yescharacteristic, complemented
28#19097702C2212yescomplemented
29#19097693C2212yescomplemented
30#19097692C2212yescomplemented
31#19097691C2212yescomplemented
32#19097682C2211yescharacteristic, complemented
33#19097681C2211yescharacteristic, complemented
34#19097681C2211yescharacteristic, complemented
35C2×D8×C157C2211yescharacteristic
36C4×D4×C157C2212yescomplemented
37#106×C157C2211yescharacteristic, complemented
38#102×C157C2212yescomplemented
39#97×C157C2211yescharacteristic, complemented
40C23×D157—22no—
41C2×D628C2312yes—
42C2×C22⋊D157—22no—
43D4×D157—24no—
44D4×D157C2×C418yescomplemented
45C22×Dic157—22no—
46C2×C4×D157—22no—
47C2×C4×D157—22no—
48C2×C4×D157—22no—
49C2×C4×D157—48no—
50C2×C4×D157D412yes—
51C2×C4×D157C2311yescharacteristic
52D1256C2×C414yescomplemented
53#14578939C2×C418yescomplemented
54C2×#11929434C2311yescharacteristic
55C2×#11929434C2311yescharacteristic
56C8×D157—22no—
57C8×D157C2×C414yescomplemented
58C4⋊Dic157C2312yes—
59#14578933—22no—
60C22⋊Dic157—22no—
61#14578931—22no—
62#14578931—22no—
63C4×Dic157D412yes—
64C4×Dic157C2311yescharacteristic
65C2×D4×C157C2312yes—
66C22×C4×C157—22no—
67D8×C157C2×C414yescomplemented
68C2×C8×C157C2311yescharacteristic
69C2×C8×C157C2311yescharacteristic
70C4⋊C4×C157C2312yes—
71C22⋊C4×C157—22no—
72C42×C157C2311yescharacteristic
73C22×D157—22no—
74C22×D157—28no—
75C22×D157—44no—
76C22×D157—44no—
77C22×D157C2×D411yescharacteristic
78D628—22no—
79D628C22×C414yescomplemented
80C22⋊D157—28no—
81C2×Dic157—22no—
82C2×Dic157—44no—
83C2×Dic157C2×D412yes—
84C2×Dic157C2×D411yescharacteristic
85C4×D157—24no—
86C4×D157—44no—
87C4×D157—44no—
88C4×D157—44no—
89C4×D157C22×C412yes—
90C4×D157#4112yes—
91#11929434—21no—
92#11929434C22×C412yescomplemented
93C23×C157—22no—
94D4×C157—22no—
95D4×C157C22×C414yescomplemented
96C2×C4×C157—22no—
97C2×C4×C157—44no—
98C2×C4×C157C2×D412yes—
99C2×C4×C157C2411yescharacteristic
100C8×C157—21no—
101C8×C157C22×C412yescomplemented
102C22×C157—24no—
103C22×C157—42no—
104C22×C157—42no—
105C22×C157C22×D411yescharacteristic
106C2×D157—24no—
107C2×D157—42no—
108C2×D157—42no—
109C2×D157—416no—
110C2×D157C4×D412yes—
111C2×D157AGL(1,ℤ/8)14yes—
112C4×C157—22no—
113C4×C157—42no—
114C4×C157C23×C411yescharacteristic
115C4×C157C2×#4111yescharacteristic
116Dic157—22no—
117Dic157—42no—
118Dic157C4×D412yes—
119C2×C157—44no—
120C2×C157C2×C4×D411yescharacteristic
121C2×C157C2×AGL(1,ℤ/8)12yes—
122D157—44no—
123D157#44214yesdirect product factor
124C157C2×#44211yescharacteristic, complemented, Sylow
125C2×#442—1571nomaximal, Sylow
126C22×D8—1571no—
127C2×C4×D4—1572no—
128#442—1571no—
129#442—1572no—
130#442—1571no—
131#442—1572no—
132#442—1571no—
133#442D15711yescharacteristic, direct product factor
134C2×#106—1571no—
135C2×#102—1572no—
136C2×#97—1571no—
137C22×D4—1572no—
138C23×C4—3142no—
139C2×D8—1572no—
140C2×D8—1578no—
141C2×D8—1571no—
142C2×D8C2×D15711yescharacteristic
143C22×C8—1571no—
144C22×C8—1571no—
145C4×D4—3142no—
146C4×D4—3142no—
147C4×D4—1572no—
148C4×D4—1572no—
149C4×D4—1572no—
150C4×D4C2×D15712yescomplemented
151C2×C4⋊C4—1572no—
152C2×C22⋊C4—3142no—
153C2×C42—1571no—
154#106—1571no—
155#106—1572no—
156#106C2×D15711yescharacteristic, complemented
157#102—1572no—
158#102—1572no—
159#102—1572no—
160#102C2×D15712yescomplemented
161#97—1571no—
162#97—1571no—
163#97—1571no—
164#97C2×D15711yescharacteristic, complemented
165C24—3142no—
166C2×D4—3144no—
167C2×D4—3142no—
168C2×D4—1578no—
169C2×D4—1572no—
170C2×D4C22×D15712yes—
171C22×C4—22no—
172C22×C4—3142no—
173C22×C4—3142no—
174C22×C4—3142no—
175C22×C4—3142no—
176C22×C4—6288no—
177C22×C4—1572no—
178C22×C4—1571no—
179D8—1578no—
180D8—1574no—
181D8C4×D15714yescomplemented
182C2×C8—3142no—
183C2×C8—1571no—
184C2×C8—1571no—
185C2×C8—1574no—
186C2×C8C22×D15711yescharacteristic
187C2×C8C22×D15711yescharacteristic
188C4⋊C4—3142no—
189C4⋊C4—1572no—
190C4⋊C4C22×D15712yes—
191C22⋊C4—22no—
192C22⋊C4—3142no—
193C22⋊C4—3142no—
194C22⋊C4—3142no—
195C42—1572no—
196C42—1571no—
197C42C22×D15711yescharacteristic
198C23—22no—
199C23—3148no—
200C23—3142no—
201C23—6284no—
202C23—6284no—
203C23—1571no—
204D4—22no—
205D4—3148no—
206D4—3142no—
207D4—1574no—
208D4C2×C4×D15714yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—3144no—
212C2×C4—3142no—
213C2×C4—6284no—
214C2×C4—6284no—
215C2×C4—6284no—
216C2×C4—6284no—
217C2×C4—1572no—
218C2×C4—1571no—
219C2×C4—1572no—
220C2×C4—1572no—
221C2×C4D4×D15712yes—
222C2×C4C23×D15711yescharacteristic
223C8—21no—
224C8—3141no—
225C8—1572no—
226C8C2×C4×D15712yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—3144no—
231C22—62816no—
232C22—6282no—
233C22—6282no—
234C22—1572no—
235C22—1574no—
236C22C2×D4×D15711yescharacteristic
237C4—22no—
238C4—42no—
239C4—3142no—
240C4—6282no—
241C4—1572no—
242C4C22×C4×D15711yescharacteristic
243C4#41×D15711yescharacteristic
244C2—44no—
245C2—6284no—
246C2—1574no—
247C2C4×D4×D15711yescharacteristic
248C2AGL(1,ℤ/8)×D15712yes—
subgroupG/H
centerC22C2×D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
Fitting#442×C157C2
socleC22×C157C22×D4
prime radicalC2×D8×D157C2
cosocleC2×C4×C157C24
hypercenter#442D157
hypocenterC157C2×#442
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D157C2semidirect
3. #23757386C2semidirect
4. #23757385C2semidirect
5. #23757384C2semidirect
6. #23757383C2semidirect
7. #23757382C2semidirect
8. #106×D157C2semidirect
9. #102×D157C2semidirect
10. #97×D157C2semidirect
11. #442×C157C2semidirect
16. D8×D157C4semidirect
19. C4×D628C22semidirect
20. D4×Dic157C22semidirect
21. #19097733C22semidirect
27. #19097703C22semidirect
28. #19097702C22semidirect
29. #19097693C22semidirect
30. #19097692C22semidirect
31. #19097691C22semidirect
32. #19097682C22semidirect
33. #19097681C22semidirect
34. #19097681C22semidirect
36. C4×D4×C157C22semidirect
37. #106×C157C22semidirect
38. #102×C157C22semidirect
39. #97×C157C22semidirect
44. D4×D157C2×C4semidirect
52. D1256C2×C4semidirect
53. #14578939C2×C4semidirect
57. C8×D157C2×C4semidirect
67. D8×C157C2×C4semidirect
79. D628C22×C4semidirect
92. #11929434C22×C4semidirect
95. D4×C157C22×C4semidirect
101. C8×C157C22×C4semidirect
123. D157#442direct (N × H)
124. C157C2×#442semidirect
133. #442D157direct (N × H)
150. C4×D4C2×D157semidirect
156. #106C2×D157semidirect
160. #102C2×D157semidirect
164. #97C2×D157semidirect
181. D8C4×D157semidirect
208. D4C2×C4×D157semidirect
226. C8C2×C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1572
C4×D4×D1572
#237573862
#237573852
#237573842
#237573832
#237573822
#106×D1572
#102×D1572
#97×D1572
#442×C1572
C2×#442157