Finite Group Databasebeta

← #442×D127 #30647519

Subgroups — #442×D127 #30647519

Order 16256.

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×D127C211yesmaximal, characteristic
2C4×D4×D127C212yesmaximal, complemented
3#22549989C211yesmaximal, characteristic, complemented
4#22549988C211yesmaximal, characteristic, complemented
5#22549987C211yesmaximal, characteristic, complemented
6#22549986C212yesmaximal, complemented
7#22549985C212yesmaximal, complemented
8#106×D127C211yesmaximal, characteristic, complemented
9#102×D127C212yesmaximal, complemented
10#97×D127C211yesmaximal, characteristic, complemented
11#442×C127C211yesmaximal, characteristic, complemented
12C2×D4×D127C2212yes—
13C22×C4×D127—22no—
14C2×D1016C2211yescharacteristic
15C2×#14523233C2212yes—
16D8×D127C418yescomplemented
17C2×C8×D127C2211yescharacteristic
18C2×C8×D127C2211yescharacteristic
19C4×D508C2212yescomplemented
20D4×Dic127C2212yescomplemented
21#16861171C2212yescomplemented
22C4×C22⋊D127—22no—
23(C22⋊D127)⋊C4—22no—
24C4⋊C4×D127C2212yes—
25C22⋊C4×D127—22no—
26C42×D127C2211yescharacteristic
27#16861141C2211yescharacteristic, complemented
28#16861140C2212yescomplemented
29#16861131C2212yescomplemented
30#16861130C2212yescomplemented
31#16861129C2212yescomplemented
32#16861120C2211yescharacteristic, complemented
33#16861119C2211yescharacteristic, complemented
34#16861119C2211yescharacteristic, complemented
35C2×D8×C127C2211yescharacteristic
36C4×D4×C127C2212yescomplemented
37#106×C127C2211yescharacteristic, complemented
38#102×C127C2212yescomplemented
39#97×C127C2211yescharacteristic, complemented
40C23×D127—22no—
41C2×D508C2312yes—
42C2×C22⋊D127—22no—
43D4×D127—24no—
44D4×D127C2×C418yescomplemented
45C22×Dic127—22no—
46C2×C4×D127—22no—
47C2×C4×D127—22no—
48C2×C4×D127—22no—
49C2×C4×D127—48no—
50C2×C4×D127D412yes—
51C2×C4×D127C2311yescharacteristic
52D1016C2×C414yescomplemented
53#14523233C2×C418yescomplemented
54C2×C127⋊C8C2311yescharacteristic
55C2×C127⋊C8C2311yescharacteristic
56C8×D127—22no—
57C8×D127C2×C414yescomplemented
58C4⋊Dic127C2312yes—
59Dic127⋊C4—22no—
60C22⋊Dic127—22no—
61(C2×D127)⋊C4—22no—
62(C2×D127)⋊C4—22no—
63C4×Dic127D412yes—
64C4×Dic127C2311yescharacteristic
65C2×D4×C127C2312yes—
66C22×C4×C127—22no—
67D8×C127C2×C414yescomplemented
68C2×C8×C127C2311yescharacteristic
69C2×C8×C127C2311yescharacteristic
70C4⋊C4×C127C2312yes—
71C22⋊C4×C127—22no—
72C42×C127C2311yescharacteristic
73C22×D127—22no—
74C22×D127—28no—
75C22×D127—44no—
76C22×D127—44no—
77C22×D127C2×D411yescharacteristic
78D508—22no—
79D508C22×C414yescomplemented
80C22⋊D127—28no—
81C2×Dic127—22no—
82C2×Dic127—44no—
83C2×Dic127C2×D412yes—
84C2×Dic127C2×D411yescharacteristic
85C4×D127—24no—
86C4×D127—44no—
87C4×D127—44no—
88C4×D127—44no—
89C4×D127C22×C412yes—
90C4×D127#4112yes—
91C127⋊C8—21no—
92C127⋊C8C22×C412yescomplemented
93C23×C127—22no—
94D4×C127—22no—
95D4×C127C22×C414yescomplemented
96C2×C4×C127—22no—
97C2×C4×C127—44no—
98C2×C4×C127C2×D412yes—
99C2×C4×C127C2411yescharacteristic
100C8×C127—21no—
101C8×C127C22×C412yescomplemented
102C22×C127—24no—
103C22×C127—42no—
104C22×C127—42no—
105C22×C127C22×D411yescharacteristic
106C2×D127—24no—
107C2×D127—42no—
108C2×D127—42no—
109C2×D127—416no—
110C2×D127C4×D412yes—
111C2×D127AGL(1,ℤ/8)14yes—
112C4×C127—22no—
113C4×C127—42no—
114C4×C127C23×C411yescharacteristic
115C4×C127C2×#4111yescharacteristic
116Dic127—22no—
117Dic127—42no—
118Dic127C4×D412yes—
119C2×C127—44no—
120C2×C127C2×C4×D411yescharacteristic
121C2×C127C2×AGL(1,ℤ/8)12yes—
122D127—44no—
123D127#44214yesdirect product factor
124C2×#442—1271nomaximal, Sylow
125C127C2×#44211yescharacteristic, complemented, Sylow
126C22×D8—1271no—
127C2×C4×D4—1272no—
128#442—1271no—
129#442—1272no—
130#442—1271no—
131#442—1272no—
132#442—1271no—
133#442D12711yescharacteristic, direct product factor
134C2×#106—1271no—
135C2×#102—1272no—
136C2×#97—1271no—
137C22×D4—1272no—
138C23×C4—2542no—
139C2×D8—1272no—
140C2×D8—1278no—
141C2×D8—1271no—
142C2×D8C2×D12711yescharacteristic
143C22×C8—1271no—
144C22×C8—1271no—
145C4×D4—1272no—
146C4×D4—1272no—
147C4×D4—1272no—
148C4×D4—2542no—
149C4×D4—2542no—
150C4×D4C2×D12712yescomplemented
151C2×C4⋊C4—1272no—
152C2×C22⋊C4—2542no—
153C2×C42—1271no—
154#106—1271no—
155#106—1272no—
156#106C2×D12711yescharacteristic, complemented
157#102—1272no—
158#102—1272no—
159#102—1272no—
160#102C2×D12712yescomplemented
161#97—1271no—
162#97—1271no—
163#97—1271no—
164#97C2×D12711yescharacteristic, complemented
165C24—2542no—
166C2×D4—1278no—
167C2×D4—1272no—
168C2×D4—2544no—
169C2×D4—2542no—
170C2×D4C22×D12712yes—
171C22×C4—22no—
172C22×C4—1271no—
173C22×C4—1272no—
174C22×C4—5088no—
175C22×C4—2542no—
176C22×C4—2542no—
177C22×C4—2542no—
178C22×C4—2542no—
179D8—1278no—
180D8—1274no—
181D8C4×D12714yescomplemented
182C2×C8—1271no—
183C2×C8—1274no—
184C2×C8—1271no—
185C2×C8—2542no—
186C2×C8C22×D12711yescharacteristic
187C2×C8C22×D12711yescharacteristic
188C4⋊C4—1272no—
189C4⋊C4—2542no—
190C4⋊C4C22×D12712yes—
191C22⋊C4—22no—
192C22⋊C4—2542no—
193C22⋊C4—2542no—
194C22⋊C4—2542no—
195C42—1272no—
196C42—1271no—
197C42C22×D12711yescharacteristic
198C23—22no—
199C23—1271no—
200C23—5084no—
201C23—5084no—
202C23—2548no—
203C23—2542no—
204D4—22no—
205D4—1274no—
206D4—2548no—
207D4—2542no—
208D4C2×C4×D12714yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—1271no—
212C2×C4—1272no—
213C2×C4—1272no—
214C2×C4—1272no—
215C2×C4—5084no—
216C2×C4—5084no—
217C2×C4—5084no—
218C2×C4—5084no—
219C2×C4—2544no—
220C2×C4—2542no—
221C2×C4D4×D12712yes—
222C2×C4C23×D12711yescharacteristic
223C8—21no—
224C8—1272no—
225C8—2541no—
226C8C2×C4×D12712yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—1272no—
231C22—1274no—
232C22—50816no—
233C22—5082no—
234C22—5082no—
235C22—2544no—
236C22C2×D4×D12711yescharacteristic
237C4—22no—
238C4—42no—
239C4—1272no—
240C4—5082no—
241C4—2542no—
242C4C22×C4×D12711yescharacteristic
243C4#41×D12711yescharacteristic
244C2—44no—
245C2—1274no—
246C2—5084no—
247C2C4×D4×D12711yescharacteristic
248C2AGL(1,ℤ/8)×D12712yes—
subgroupG/H
centerC22C2×D4×D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
Fitting#442×C127C2
socleC22×C127C22×D4
prime radicalC2×D8×D127C2
cosocleC2×C4×C127C24
hypercenter#442D127
hypocenterC127C2×#442
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D127C2semidirect
3. #22549989C2semidirect
4. #22549988C2semidirect
5. #22549987C2semidirect
6. #22549986C2semidirect
7. #22549985C2semidirect
8. #106×D127C2semidirect
9. #102×D127C2semidirect
10. #97×D127C2semidirect
11. #442×C127C2semidirect
16. D8×D127C4semidirect
19. C4×D508C22semidirect
20. D4×Dic127C22semidirect
21. #16861171C22semidirect
27. #16861141C22semidirect
28. #16861140C22semidirect
29. #16861131C22semidirect
30. #16861130C22semidirect
31. #16861129C22semidirect
32. #16861120C22semidirect
33. #16861119C22semidirect
34. #16861119C22semidirect
36. C4×D4×C127C22semidirect
37. #106×C127C22semidirect
38. #102×C127C22semidirect
39. #97×C127C22semidirect
44. D4×D127C2×C4semidirect
52. D1016C2×C4semidirect
53. #14523233C2×C4semidirect
57. C8×D127C2×C4semidirect
67. D8×C127C2×C4semidirect
79. D508C22×C4semidirect
92. C127⋊C8C22×C4semidirect
95. D4×C127C22×C4semidirect
101. C8×C127C22×C4semidirect
123. D127#442direct (N × H)
125. C127C2×#442semidirect
133. #442D127direct (N × H)
150. C4×D4C2×D127semidirect
156. #106C2×D127semidirect
160. #102C2×D127semidirect
164. #97C2×D127semidirect
181. D8C4×D127semidirect
208. D4C2×C4×D127semidirect
226. C8C2×C4×D127semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1272
C4×D4×D1272
#225499892
#225499882
#225499872
#225499862
#225499852
#106×D1272
#102×D1272
#97×D1272
#442×C1272
C2×#442127