Finite Group Databasebeta

← #34108985

Subgroups — #34108985

Order 20096.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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
2#23757745C212yesmaximal, complemented
3#23757386C211yesmaximal, characteristic, complemented
4#23757385C211yesmaximal, characteristic, complemented
5#23757384C211yesmaximal, characteristic, complemented
6C4×#14578939C212yesmaximal, complemented
7#23757353C212yesmaximal, complemented
8#23757308C211yesmaximal, characteristic, complemented
9#23757276C212yesmaximal, complemented
10#23757230C211yesmaximal, characteristic, complemented
11#442×C157C211yesmaximal, characteristic, complemented
12C2×D4×D157C2212yes—
13C2×D1256C2211yescharacteristic
14C2×#14578939C2212yes—
15D8×D157C418yescomplemented
16C2×#14578937C2211yescharacteristic
17C2×C8×D157C2211yescharacteristic
18C4×D628C2212yescomplemented
19D4×Dic157C2212yescomplemented
20#19097733C2212yescomplemented
21C4×C22⋊D157—22no—
22#19097731—22no—
23#19097729C2212yes—
24#19097728C2211yescharacteristic
25C2×#14578931—22no—
26C22⋊C4×D157—22no—
27#19097704C2212yescomplemented
28#19097703C2211yescharacteristic, complemented
29#19097693C2212yescomplemented
30#19097692C2212yescomplemented
31#19097691C2212yescomplemented
32#19097681C2211yescharacteristic, complemented
33C4×#11929434C2211yescharacteristic, complemented
34C8×Dic157C2211yescharacteristic, 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×D157C2311yescharacteristic
49D1256C2×C414yescomplemented
50#14578939C2×C418yescomplemented
51#14578937—22no—
52C2×#11929434C2311yescharacteristic
53C2×#11929434C2311yescharacteristic
54C8×D157C2×C414yescomplemented
55C4⋊Dic157C2312yes—
56#14578933D412yes—
57C22⋊Dic157—22no—
58#14578931—22no—
59#14578931—22no—
60#14578931—22no—
61#14578931D412yes—
62C4×Dic157—22no—
63C4×Dic157C2311yescharacteristic
64C2×D4×C157C2312yes—
65C22×C4×C157—22no—
66D8×C157C2×C414yescomplemented
67C2×C8×C157C2311yescharacteristic
68C2×C8×C157C2311yescharacteristic
69C4⋊C4×C157C2312yes—
70C22⋊C4×C157—22no—
71C42×C157C2311yescharacteristic
72C22×D157—22no—
73C22×D157—28no—
74C22×D157—82no—
75C22×D157—82no—
76C22×D157C2×D411yescharacteristic
77D628—22no—
78D628C22×C414yes—
79C22⋊D157—28no—
80C2×Dic157—22no—
81C2×Dic157—82no—
82C2×Dic157C2×D412yes—
83C2×Dic157C2×D411yescharacteristic
84C4×D157—82no—
85C4×D157—82no—
86C4×D157C22×C412yes—
87C4×D157#4112yes—
88#11929434—21no—
89#11929434C22×C412yes—
90C23×C157—22no—
91D4×C157—22no—
92D4×C157C22×C414yes—
93C2×C4×C157—22no—
94C2×C4×C157—82no—
95C2×C4×C157C2×D412yes—
96C2×C4×C157C2411yescharacteristic
97C8×C157—21no—
98C8×C157C22×C412yes—
99C22×C157—24no—
100C22×C157—42no—
101C22×C157—42no—
102C22×C157C22×D411yescharacteristic
103C2×D157—22no—
104C2×D157—24no—
105C2×D157—42no—
106C2×D157—42no—
107C2×D157—88no—
108C2×D157C4×D412yes—
109C4×C157—22no—
110C4×C157—42no—
111C4×C157C23×C411yescharacteristic
112C4×C157C2×#4111yescharacteristic
113Dic157—22no—
114Dic157—42no—
115Dic157C4×D412yes—
116C2×C157—44no—
117C2×C157C2×C4×D411yescharacteristic
118C2×C157#57612yes—
119D157—22no—
120D157—44no—
121C157#294811yescharacteristic, complemented, Sylow
122#2948—1571nomaximal, Sylow
123C22×D8—1571no—
124#518—1572no—
125#442—1571no—
126#442—1571no—
127#442—1571no—
128#442D15711yescharacteristic, complemented
129C4×D8—1572no—
130C4×D8—1572no—
131#427—1571no—
132#418—1572no—
133#405—1571no—
134C22×D4—1572no—
135C2×D8—1572no—
136C2×D8—1578no—
137C2×D8—1571no—
138C2×D8C2×D15711yescharacteristic
139C2×M16—1571no—
140C22×C8—1571no—
141C4×D4—3142no—
142C4×D4—3142no—
143C4×D4—1572no—
144C4×D4—1572no—
145C4×D4—1572no—
146C4×D4C2×D15712yescomplemented
147#117—1572no—
148#117—1571no—
149C2×C22⋊C4—3142no—
150C2×C22⋊C4—3142no—
151#107—1572no—
152#106—1571no—
153#106C2×D15711yescharacteristic, complemented
154#102—1572no—
155#102—1572no—
156#102—1572no—
157#102C2×D15712yescomplemented
158#97—1571no—
159#97C2×D15711yescharacteristic, complemented
160C4×C8—1571no—
161C4×C8—1571no—
162C24—3142no—
163C2×D4—3144no—
164C2×D4—3142no—
165C2×D4—1578no—
166C2×D4—1572no—
167C2×D4C22×D15712yes—
168C22×C4—22no—
169C22×C4—3142no—
170C22×C4—3142no—
171C22×C4—3142no—
172C22×C4—1571no—
173D8—1578no—
174D8—1574no—
175D8C4×D15714yescomplemented
176M16—3142no—
177C2×C8—1571no—
178C2×C8—1571no—
179C2×C8—1574no—
180C2×C8C22×D15711yescharacteristic
181C2×C8C22×D15711yescharacteristic
182C4⋊C4—1572no—
183C4⋊C4—1572no—
184C4⋊C4C22×D15712yes—
185C22⋊C4—22no—
186C22⋊C4—3142no—
187C22⋊C4—3142no—
188C22⋊C4—3142no—
189C22⋊C4—3142no—
190C22⋊C4—1572no—
191C42—3142no—
192C42—1571no—
193C42C22×D15711yescharacteristic
194C23—22no—
195C23—3148no—
196C23—3142no—
197C23—1571no—
198C23—12562no—
199C23—12562no—
200D4—22no—
201D4—3148no—
202D4—3142no—
203D4—1574no—
204D4C2×C4×D15714yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—3142no—
208C2×C4—1572no—
209C2×C4—1571no—
210C2×C4—1572no—
211C2×C4—1572no—
212C2×C4—12562no—
213C2×C4—12562no—
214C2×C4—12562no—
215C2×C4D4×D15712yes—
216C2×C4C23×D15711yescharacteristic
217C8—21no—
218C8—3141no—
219C8—1572no—
220C8C2×C4×D15712yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—3142no—
225C22—3144no—
226C22—6282no—
227C22—6282no—
228C22—1572no—
229C22—12568no—
230C22C2×D4×D15711yescharacteristic
231C4—22no—
232C4—42no—
233C4—3142no—
234C4—6282no—
235C4—1572no—
236C4C22×C4×D15711yescharacteristic
237C4#41×D15711yescharacteristic
238C2—44no—
239C2—3142no—
240C2—6284no—
241C2C4×D4×D15711yescharacteristic
242C2#2375807712yes—
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
hypocenterC157#2948
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. #23757745C2semidirect
3. #23757386C2semidirect
4. #23757385C2semidirect
5. #23757384C2semidirect
6. C4×#14578939C2semidirect
7. #23757353C2semidirect
8. #23757308C2semidirect
9. #23757276C2semidirect
10. #23757230C2semidirect
11. #442×C157C2semidirect
15. D8×D157C4semidirect
18. C4×D628C22semidirect
19. D4×Dic157C22semidirect
20. #19097733C22semidirect
27. #19097704C22semidirect
28. #19097703C22semidirect
29. #19097693C22semidirect
30. #19097692C22semidirect
31. #19097691C22semidirect
32. #19097681C22semidirect
33. C4×#11929434C22semidirect
34. C8×Dic157C22semidirect
36. C4×D4×C157C22semidirect
37. #106×C157C22semidirect
38. #102×C157C22semidirect
39. #97×C157C22semidirect
44. D4×D157C2×C4semidirect
49. D1256C2×C4semidirect
50. #14578939C2×C4semidirect
54. C8×D157C2×C4semidirect
66. D8×C157C2×C4semidirect
121. C157#2948semidirect
128. #442D157semidirect
146. C4×D4C2×D157semidirect
153. #106C2×D157semidirect
157. #102C2×D157semidirect
159. #97C2×D157semidirect
175. D8C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1572
#237577452
#237573862
#237573852
#237573842
C4×#145789392
#237573532
#237573082
#237572762
#237572302
#442×C1572
#2948157