Finite Group Databasebeta

← C127×#20689 #44584362

Subgroups — C127×#20689 #44584362

Order 32512.

1602 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C127C211yesmaximal, characteristic
2C127×#2308C212yesmaximal
3C127×#1820C214yesmaximal, complemented
4C127×#1819C214yesmaximal, complemented
5C2×#342×C127C214yesmaximal, complemented
6C23×D4×C127C2211yescharacteristic
7#518×C127—28no—
8C2×C4×D4×C127C418yescomplemented
9C2×#117×C127C2212yes—
10C22×C22⋊C4×C127C2214yes—
11C22×C22⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2212yes—
13#386×C127—28no—
14#381×C127C2214yes—
15#379×C127C2214yes—
16#342×C127C22116yes—
17C25×C127C2311yescharacteristic
18C25×C127C2311yescharacteristic
19C22×D4×C127—28no—
20C22×D4×C127C2×C414yes—
21C22×D4×C127D418yes—
22C23×C4×C127—24no—
23C23×C4×C127C2×C414yes—
24C23×C4×C127C2×C414yescomplemented
25C23×C4×C127C2311yescharacteristic
26C4×D4×C127—232no—
27#117×C127—28no—
28C2×C4⋊C4×C127C2×C414yescomplemented
29C2×C22⋊C4×C127—28no—
30C2×C22⋊C4×C127—28no—
31C2×C22⋊C4×C127—216no—
32C2×C22⋊C4×C127—24no—
33C2×C22⋊C4×C127—28no—
34C2×C22⋊C4×C127C2×C414yes—
35C2×C22⋊C4×C127C2×C414yescomplemented
36C2×C22⋊C4×C127C2318yes—
37C2×C22⋊C4×C127C2314yes—
38C2×C42×C127C2×C414yescomplemented
39#95×C127—28no—
40C24×C127—24no—
41C24×C127—82no—
42C24×C127—82no—
43C24×C127C22×C412yes—
44C24×C127C22×C412yes—
45C24×C127C2×D414yes—
46C24×C127C2×D414yes—
47C24×C127#4118yes—
48C24×C127C2411yescharacteristic
49C2×D4×C127—216no—
50C2×D4×C127—216no—
51C2×D4×C127—216no—
52C2×D4×C127C22⋊C4116yes—
53C22×C4×C127—24no—
54C22×C4×C127—28no—
55C22×C4×C127—28no—
56C22×C4×C127—28no—
57C22×C4×C127—48no—
58C22×C4×C127—88no—
59C22×C4×C127—84no—
60C22×C4×C127—84no—
61C22×C4×C127C22×C412yes—
62C22×C4×C127C22×C418yes—
63C22×C4×C127C2×D414yes—
64C4⋊C4×C127—28no—
65C22⋊C4×C127—28no—
66C22⋊C4×C127—28no—
67C22⋊C4×C127—28no—
68C22⋊C4×C127—216no—
69C22⋊C4×C127—48no—
70C22⋊C4×C127—88no—
71C42×C127—28no—
72C23×C127—24no—
73C23×C127—28no—
74C23×C127—44no—
75C23×C127—44no—
76C23×C127—48no—
77C23×C127—42no—
78C23×C127—48no—
79C23×C127—88no—
80C23×C127—88no—
81C23×C127C2×C22⋊C414yes—
82C23×C127C2×C22⋊C414yes—
83C23×C127#11718yes—
84C23×C127#12318yes—
85C23×C127#12318yes—
86C23×C127C23×C411yescharacteristic
87C23×C127C22×D412yes—
88C23×C127C2×#4114yes—
89D4×C127—232no—
90C2×C4×C127—24no—
91C2×C4×C127—28no—
92C2×C4×C127—28no—
93C2×C4×C127—48no—
94C2×C4×C127—416no—
95C2×C4×C127—48no—
96C2×C4×C127—88no—
97C2×C4×C127—88no—
98C2×C4×C127—816no—
99C2×C4×C127C2×C22⋊C414yes—
100C22×C127—22no—
101C22×C127—24no—
102C22×C127—28no—
103C22×C127—28no—
104C22×C127—24no—
105C22×C127—48no—
106C22×C127—44no—
107C22×C127—48no—
108C22×C127—48no—
109C22×C127—48no—
110C22×C127—88no—
111C22×C127#38118yes—
112C22×C127C22×C22⋊C411yescharacteristic
113C22×C127C2×#11712yes—
114C22×C127C2×#12314yes—
115C4×C127—24no—
116C4×C127—48no—
117C4×C127—88no—
118#20689C12711yesmaximal, characteristic, direct product factor, Sylow
119C2×C127—24no—
120C2×C127—22no—
121C2×C127—28no—
122C2×C127—44no—
123C2×C127C2×#38111yescharacteristic
124C2×C127#288312yes—
125C2×#518C2×C12711yescharacteristic
126#2308C2×C12712yes—
127#1820C2×C12714yescomplemented
128#1819C2×C12714yescomplemented
129C2×#342C2×C12714yescomplemented
130C127#2068911yescharacteristic, direct product factor, Sylow
131C23×D4C22×C12711yescharacteristic
132#518—28no—
133C2×C4×D4C4×C12718yescomplemented
134C2×#117C22×C12712yes—
135C22×C22⋊C4C22×C12714yes—
136C22×C22⋊C4C22×C12712yes—
137C22×C22⋊C4C22×C12712yes—
138#386—28no—
139#381C22×C12714yes—
140#379C22×C12714yes—
141#342C22×C127116yes—
142C25C23×C12711yescharacteristic
143C25C23×C12711yescharacteristic
144C22×D4—28no—
145C22×D4C2×C4×C12714yes—
146C22×D4D4×C12718yes—
147C23×C4—24no—
148C23×C4C2×C4×C12714yes—
149C23×C4C2×C4×C12714yescomplemented
150C23×C4C23×C12711yescharacteristic
151C4×D4—232no—
152#117—28no—
153C2×C4⋊C4C2×C4×C12714yescomplemented
154C2×C22⋊C4—28no—
155C2×C22⋊C4—28no—
156C2×C22⋊C4—216no—
157C2×C22⋊C4—24no—
158C2×C22⋊C4—28no—
159C2×C22⋊C4C2×C4×C12714yes—
160C2×C22⋊C4C2×C4×C12714yescomplemented
161C2×C22⋊C4C23×C12718yes—
162C2×C22⋊C4C23×C12714yes—
163C2×C42C2×C4×C12714yescomplemented
164#95—28no—
165C24—24no—
166C24—82no—
167C24—82no—
168C24C22×C4×C12712yes—
169C24C22×C4×C12712yes—
170C24C2×D4×C12714yes—
171C24C2×D4×C12714yes—
172C24#41×C12718yes—
173C24C24×C12711yescharacteristic
174C2×D4—216no—
175C2×D4—216no—
176C2×D4—216no—
177C2×D4C22⋊C4×C127116yes—
178C22×C4—24no—
179C22×C4—28no—
180C22×C4—28no—
181C22×C4—28no—
182C22×C4—48no—
183C22×C4—88no—
184C22×C4—84no—
185C22×C4—84no—
186C22×C4C22×C4×C12712yes—
187C22×C4C22×C4×C12718yes—
188C22×C4C2×D4×C12714yes—
189C4⋊C4—28no—
190C22⋊C4—28no—
191C22⋊C4—28no—
192C22⋊C4—28no—
193C22⋊C4—216no—
194C22⋊C4—48no—
195C22⋊C4—88no—
196C42—28no—
197C23—24no—
198C23—28no—
199C23—44no—
200C23—44no—
201C23—48no—
202C23—42no—
203C23—48no—
204C23—88no—
205C23—88no—
206C23C2×C22⋊C4×C12714yes—
207C23C2×C22⋊C4×C12714yes—
208C23#117×C12718yes—
209C23#123×C12718yes—
210C23#123×C12718yes—
211C23C23×C4×C12711yescharacteristic
212C23C22×D4×C12712yes—
213C23C2×#41×C12714yes—
214D4—232no—
215C2×C4—24no—
216C2×C4—28no—
217C2×C4—28no—
218C2×C4—48no—
219C2×C4—416no—
220C2×C4—48no—
221C2×C4—88no—
222C2×C4—88no—
223C2×C4—816no—
224C2×C4C2×C22⋊C4×C12714yes—
225C22—22no—
226C22—24no—
227C22—28no—
228C22—28no—
229C22—24no—
230C22—48no—
231C22—44no—
232C22—48no—
233C22—48no—
234C22—48no—
235C22—88no—
236C22#381×C12718yes—
237C22C22×C22⋊C4×C12711yescharacteristic
238C22C2×#117×C12712yes—
239C22C2×#123×C12714yes—
240C4—24no—
241C4—48no—
242C4—88no—
243C2—24no—
244C2—22no—
245C2—28no—
246C2—44no—
247C2C2×#381×C12711yescharacteristic
248C2C127×#288312yes—
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1820C2semidirect
4. C127×#1819C2semidirect
5. C2×#342×C127C2semidirect
8. C2×C4×D4×C127C4semidirect
24. C23×C4×C127C2×C4semidirect
28. C2×C4⋊C4×C127C2×C4semidirect
35. C2×C22⋊C4×C127C2×C4semidirect
38. C2×C42×C127C2×C4semidirect
118. #20689C127direct (N × H)
127. #1820C2×C127semidirect
128. #1819C2×C127semidirect
129. C2×#342C2×C127semidirect
130. C127#20689direct (N × H)
133. C2×C4×D4C4×C127semidirect
149. C23×C4C2×C4×C127semidirect
153. C2×C4⋊C4C2×C4×C127semidirect
160. C2×C22⋊C4C2×C4×C127semidirect
163. C2×C42C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1272
C127×#23082
C127×#18202
C127×#18192
C2×#342×C1272
#20689127