Finite Group Databasebeta

← #488×D157 #34110449

Subgroups — #488×D157 #34110449

Order 20096.

412 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 125 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#125×D157C211yesmaximal, characteristic, complemented
2#124×D157C211yesmaximal, characteristic
3#23757630C211yesmaximal, characteristic, complemented
4#23757629C212yesmaximal, complemented
5#23757628C211yesmaximal, characteristic, complemented
6#23757627C211yesmaximal, characteristic, complemented
7#23757626C212yesmaximal, complemented
8#103×D157C212yesmaximal, complemented
9#102×D157C212yesmaximal
10C4×C8×D157C211yesmaximal, characteristic, complemented
11#488×C157C211yesmaximal, characteristic, complemented
12C2×Q8×D157C2211yescharacteristic
13C2×D4×D157C2211yescharacteristic
14C2×C8×D157C2212yes—
15#19097763C2211yescharacteristic, complemented
16#19097762C2212yescomplemented
17#19097761—22no—
18#19097760C2211yescharacteristic
19#19097759C2211yescharacteristic
20#19097758C2211yescharacteristic
21#19097757—22no—
22C4⋊C4×D157—22no—
23C4⋊C4×D157C2212yes—
24C22⋊C4×D157—22no—
25C42×D157C2211yescharacteristic
26#19097696C2212yescomplemented
27#19097695C2212yescomplemented
28#19097694C2212yescomplemented
29#19097693C2212yes—
30#19097692C2212yes—
31#19097691C2212yes—
32C4×#11929434C2211yescharacteristic, complemented
33C8×Dic157C2212yescomplemented
34#125×C157C2211yescharacteristic, complemented
35#124×C157C2211yescharacteristic
36#103×C157C2212yescomplemented
37#102×C157C2212yes—
38C4×C8×C157C2211yescharacteristic, complemented
39C23×D157—21no—
40C2×Dic314—21no—
41C2×Dic314C2311yescharacteristic
42Q8×D157—24no—
43C2×D628C2311yescharacteristic
44C2×C22⋊D157—21no—
45D4×D157—24no—
46C2×C4×D157—21no—
47C2×C4×D157—22no—
48C2×C4×D157D412yes—
49C2×C4×D157C2311yescharacteristic
50C2×#11929434C2312yes—
51C8×D157—24no—
52C4⋊Dic157—22no—
53C4⋊Dic157C2312yes—
54#14578933—22no—
55#14578933—22no—
56#14578933—22no—
57C22⋊Dic157—22no—
58#14578931—22no—
59#14578931—22no—
60C4×Dic157D412yes—
61C4×Dic157C2311yescharacteristic
62C2×Q8×C157C2311yescharacteristic
63C2×D4×C157C2311yescharacteristic
64C2×C8×C157C2312yes—
65C4⋊C4×C157—22no—
66C4⋊C4×C157C2312yes—
67C22⋊C4×C157—22no—
68C42×C157C2311yescharacteristic
69C22×D157—21no—
70C22×D157—42no—
71C22×D157—44no—
72C22×D157C2×D411yescharacteristic
73Dic314—22no—
74Dic314—42no—
75D628—22no—
76C22⋊D157—42no—
77C2×Dic157—21no—
78C2×Dic157—22no—
79C2×Dic157C2×D412yes—
80C2×Dic157C2×D411yescharacteristic
81C4×D157—24no—
82C4×D157—42no—
83C4×D157—44no—
84C4×D157#4114yes—
85#11929434—22no—
86C23×C157—21no—
87Q8×C157—22no—
88D4×C157—22no—
89C2×C4×C157—21no—
90C2×C4×C157—22no—
91C2×C4×C157C2×D412yes—
92C2×C4×C157C2411yescharacteristic
93C8×C157—22no—
94C22×C157—41no—
95C22×C157—42no—
96C22×C157C22×D411yescharacteristic
97C2×D157—41no—
98C2×D157—42no—
99C2×D157—84no—
100C2×D157#12412yes—
101C2×D157#13514yes—
102C4×C157—22no—
103C4×C157—41no—
104C4×C157—42no—
105C4×C157C2×#4112yes—
106Dic157—22no—
107Dic157—41no—
108Dic157—42no—
109Dic157#12412yes—
110C2×C157—81no—
111C2×C157C2×#12411yescharacteristic
112C2×C157C2×#13512yes—
113D157—81no—
114D157#48814yesdirect product factor
115C157C2×#48811yescharacteristic, complemented, Sylow
116C2×#488—1571nomaximal, Sylow
117C2×#125—1571no—
118C2×#124—1571no—
119#488—1571no—
120#488—1571no—
121#488—1572no—
122#488—1572no—
123#488—1571no—
124#488D15711yescharacteristic, direct product factor
125C2×#103—1572no—
126C2×#102—1572no—
127C2×C4×C8—1571no—
128C22×Q8—1571no—
129C22×D4—1571no—
130C22×C8—1572no—
131#125—3142no—
132#125—1572no—
133#125—1571no—
134#125C2×D15711yescharacteristic, complemented
135#124—3142no—
136#124—1571no—
137#124—1571no—
138#124—1571no—
139#124C2×D15711yescharacteristic
140C2×C4⋊C4—3142no—
141C2×C4⋊C4—1572no—
142C2×C22⋊C4—3142no—
143C2×C42—1571no—
144#103—1572no—
145#103—1572no—
146#103—1572no—
147#103C2×D15712yescomplemented
148#102—1572no—
149#102—1572no—
150#102—1572no—
151#102C2×D15712yes—
152C4×C8—1572no—
153C4×C8—1571no—
154C4×C8C2×D15711yescharacteristic, complemented
155C24—3141no—
156C2×Q8—3141no—
157C2×Q8—3144no—
158C2×Q8—1571no—
159C2×Q8C22×D15711yescharacteristic
160C2×D4—3144no—
161C2×D4—3141no—
162C2×D4—1571no—
163C2×D4C22×D15711yescharacteristic
164C22×C4—3141no—
165C22×C4—3142no—
166C22×C4—1572no—
167C22×C4—1571no—
168C2×C8—3144no—
169C2×C8—1572no—
170C2×C8C22×D15712yes—
171C4⋊C4—22no—
172C4⋊C4—3142no—
173C4⋊C4—3142no—
174C4⋊C4—3142no—
175C4⋊C4—3142no—
176C4⋊C4—1572no—
177C4⋊C4C22×D15712yes—
178C22⋊C4—22no—
179C22⋊C4—3142no—
180C22⋊C4—3142no—
181C22⋊C4—3142no—
182C42—1572no—
183C42—1571no—
184C42C22×D15711yescharacteristic
185C23—21no—
186C23—3141no—
187C23—6282no—
188C23—6284no—
189C23—1571no—
190Q8—22no—
191Q8—3142no—
192Q8—6282no—
193D4—22no—
194D4—3142no—
195D4—6282no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—3144no—
199C2×C4—3141no—
200C2×C4—3142no—
201C2×C4—6282no—
202C2×C4—6284no—
203C2×C4—1572no—
204C2×C4—1571no—
205C2×C4—1574no—
206C2×C4D4×D15712yes—
207C2×C4C23×D15711yescharacteristic
208C8—22no—
209C8—3142no—
210C22—41no—
211C22—42no—
212C22—6281no—
213C22—6282no—
214C22—1572no—
215C22—1574no—
216C22—12564no—
217C22C2×D4×D15711yescharacteristic
218C4—22no—
219C4—41no—
220C4—42no—
221C4—3142no—
222C4—6281no—
223C4—6282no—
224C4—1572no—
225C4#41×D15712yes—
226C2—81no—
227C2—1574no—
228C2—12561no—
229C2#124×D15711yescharacteristic
230C2#135×D15712yes—
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#488×C157C2
socleC22×C157C22×D4
prime radicalC2×D4×D157C22
hypercenter#488D157
hypocenterC157C2×#488
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #125×D157C2semidirect
3. #23757630C2semidirect
4. #23757629C2semidirect
5. #23757628C2semidirect
6. #23757627C2semidirect
7. #23757626C2semidirect
8. #103×D157C2semidirect
10. C4×C8×D157C2semidirect
11. #488×C157C2semidirect
15. #19097763C22semidirect
16. #19097762C22semidirect
26. #19097696C22semidirect
27. #19097695C22semidirect
28. #19097694C22semidirect
32. C4×#11929434C22semidirect
33. C8×Dic157C22semidirect
34. #125×C157C22semidirect
36. #103×C157C22semidirect
38. C4×C8×C157C22semidirect
114. D157#488direct (N × H)
115. C157C2×#488semidirect
124. #488D157direct (N × H)
134. #125C2×D157semidirect
147. #103C2×D157semidirect
154. C4×C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#125×D1572
#124×D1572
#237576302
#237576292
#237576282
#237576272
#237576262
#103×D1572
#102×D1572
C4×C8×D1572
#488×C1572
C2×#488157