Finite Group Databasebeta

← C127×#14167 #44577840

Subgroups — C127×#14167 #44577840

Order 32512.

2058 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C2×C4×C22⋊C4×C127C212yesmaximal, complemented
3C127×#1440C212yesmaximal, complemented
4C127×#1438C212yesmaximal
5C127×#1437C214yesmaximal, complemented
6C127×#1436C214yesmaximal, complemented
7C23×D4×C127C2211yescharacteristic
8C24×C4×C127C2211yescharacteristic
9C2×#123×C127—28no—
10C2×#123×C127C418yescomplemented
11C22×C4⋊C4×C127C2212yes—
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C42×C127C2214yes—
17C4×C22⋊C4×C127—28no—
18C2×#95×C127C2218yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2214yes—
21C25×C127C2311yescharacteristic
22C25×C127C2311yescharacteristic
23C22×D4×C127—24no—
24C22×D4×C127—44no—
25C22×D4×C127C2×C414yes—
26C23×C4×C127—44no—
27C23×C4×C127C2×C414yes—
28C23×C4×C127D418yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2311yescharacteristic
31C23×C4×C127C2318yes—
32C23×C4×C127C2312yes—
33#123×C127—232no—
34C2×C4⋊C4×C127—24no—
35C2×C4⋊C4×C127—24no—
36C2×C4⋊C4×C127C2×C418yes—
37C2×C22⋊C4×C127—24no—
38C2×C22⋊C4×C127—28no—
39C2×C22⋊C4×C127—24no—
40C2×C22⋊C4×C127—24no—
41C2×C22⋊C4×C127—216no—
42C2×C22⋊C4×C127—216no—
43C2×C22⋊C4×C127—44no—
44C2×C22⋊C4×C127C2×C414yes—
45C2×C22⋊C4×C127C2×C418yes—
46C2×C42×C127—28no—
47C2×C42×C127—48no—
48#95×C127—28no—
49#95×C127—216no—
50#95×C127—44no—
51C24×C127—28no—
52C24×C127—24no—
53C24×C127—22no—
54C24×C127—28no—
55C24×C127—24no—
56C24×C127C22×C412yes—
57C24×C127C22×C412yes—
58C24×C127C2×D414yes—
59C24×C127C2411yescharacteristic
60C2×D4×C127—28no—
61C2×D4×C127—48no—
62C2×D4×C127—416no—
63C22×C4×C127—28no—
64C22×C4×C127—28no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—28no—
69C22×C4×C127—28no—
70C22×C4×C127—28no—
71C22×C4×C127—28no—
72C22×C4×C127—28no—
73C22×C4×C127—24no—
74C22×C4×C127—28no—
75C22×C4×C127—48no—
76C22×C4×C127—416no—
77C22×C4×C127C22⋊C4116yescomplemented
78C22×C4×C127C22×C414yes—
79C22×C4×C127C22×C412yes—
80C22×C4×C127C22×C414yes—
81C22×C4×C127C2×D414yes—
82C22×C4×C127C2×D414yes—
83C22×C4×C127#41116yes—
84C4⋊C4×C127—216no—
85C22⋊C4×C127—232no—
86C22⋊C4×C127—28no—
87C22⋊C4×C127—216no—
88C22⋊C4×C127—416no—
89C42×C127—416no—
90C23×C127—28no—
91C23×C127—24no—
92C23×C127—28no—
93C23×C127—28no—
94C23×C127—28no—
95C23×C127—22no—
96C23×C127—28no—
97C23×C127—24no—
98C23×C127—44no—
99C23×C127—48no—
100C23×C127—44no—
101C23×C127—44no—
102C23×C127—44no—
103C23×C127—44no—
104C23×C127—44no—
105C23×C127—48no—
106C23×C127—44no—
107C23×C127C2×C22⋊C414yes—
108C23×C127C23×C411yescharacteristic
109C23×C127C22×D412yes—
110C23×C127C2×#4118yes—
111C23×C127H(5,𝔽2)14yes—
112D4×C127—416no—
113C2×C4×C127—28no—
114C2×C4×C127—28no—
115C2×C4×C127—28no—
116C2×C4×C127—24no—
117C2×C4×C127—22no—
118C2×C4×C127—28no—
119C2×C4×C127—24no—
120C2×C4×C127—216no—
121C2×C4×C127—216no—
122C2×C4×C127—216no—
123C2×C4×C127—416no—
124C2×C4×C127—44no—
125C2×C4×C127—48no—
126C2×C4×C127—44no—
127C2×C4×C127—48no—
128C2×C4×C127—44no—
129C2×C4×C127—48no—
130C2×C4×C127—48no—
131C2×C4×C127C2×C22⋊C418yes—
132C22×C127—24no—
133C22×C127—28no—
134C22×C127—416no—
135C22×C127—48no—
136C22×C127—42no—
137C22×C127—48no—
138C22×C127—44no—
139C22×C127—88no—
140C22×C127C22×C22⋊C411yescharacteristic
141C22×C127C4×#4114yes—
142C22×C127#51812yes—
143C22×C127#52514yes—
144C22×C127#53214yes—
145C22×C127#53414yes—
146C22×C127#55114yes—
147C22×C127#55318yes—
148C22×C127#55914yes—
149C4×C127—28no—
150C4×C127—42no—
151C4×C127—416no—
152C4×C127—44no—
153#14167C12711yesmaximal, characteristic, direct product factor, Sylow
154C2×C127—44no—
155C2×C127—82no—
156C2×C127#229712yes—
157C2×C127#230811yescharacteristic
158C2×C127#237414yes—
159C2×C127#260218yes—
160C22×#123C2×C12711yescharacteristic
161C2×C4×C22⋊C4C2×C12712yescomplemented
162#1440C2×C12712yescomplemented
163#1438C2×C12712yes—
164#1437C2×C12714yescomplemented
165#1436C2×C12714yescomplemented
166C127#1416711yescharacteristic, direct product factor, Sylow
167C23×D4C22×C12711yescharacteristic
168C24×C4C22×C12711yescharacteristic
169C2×#123—28no—
170C2×#123C4×C12718yescomplemented
171C22×C4⋊C4C22×C12712yes—
172C22×C22⋊C4C22×C12714yes—
173C22×C22⋊C4C22×C12714yes—
174C22×C22⋊C4C22×C12712yes—
175C22×C22⋊C4C22×C12711yescharacteristic
176C22×C42C22×C12714yes—
177C4×C22⋊C4—28no—
178C2×#95C22×C12718yes—
179C2×#95C22×C12714yes—
180C2×#95C22×C12714yes—
181C25C23×C12711yescharacteristic
182C25C23×C12711yescharacteristic
183C22×D4—24no—
184C22×D4—44no—
185C22×D4C2×C4×C12714yes—
186C23×C4—44no—
187C23×C4C2×C4×C12714yes—
188C23×C4D4×C12718yes—
189C23×C4C23×C12712yes—
190C23×C4C23×C12711yescharacteristic
191C23×C4C23×C12718yes—
192C23×C4C23×C12712yes—
193#123—232no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4C2×C4×C12718yes—
197C2×C22⋊C4—24no—
198C2×C22⋊C4—28no—
199C2×C22⋊C4—24no—
200C2×C22⋊C4—24no—
201C2×C22⋊C4—216no—
202C2×C22⋊C4—216no—
203C2×C22⋊C4—44no—
204C2×C22⋊C4C2×C4×C12714yes—
205C2×C22⋊C4C2×C4×C12718yes—
206C2×C42—28no—
207C2×C42—48no—
208#95—28no—
209#95—216no—
210#95—44no—
211C24—28no—
212C24—24no—
213C24—22no—
214C24—28no—
215C24—24no—
216C24C22×C4×C12712yes—
217C24C22×C4×C12712yes—
218C24C2×D4×C12714yes—
219C24C24×C12711yescharacteristic
220C2×D4—28no—
221C2×D4—48no—
222C2×D4—416no—
223C22×C4—28no—
224C22×C4—28no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—28no—
229C22×C4—28no—
230C22×C4—28no—
231C22×C4—28no—
232C22×C4—28no—
233C22×C4—24no—
234C22×C4—28no—
235C22×C4—48no—
236C22×C4—416no—
237C22×C4C22⋊C4×C127116yescomplemented
238C22×C4C22×C4×C12714yes—
239C22×C4C22×C4×C12712yes—
240C22×C4C22×C4×C12714yes—
241C22×C4C2×D4×C12714yes—
242C22×C4C2×D4×C12714yes—
243C22×C4#41×C127116yes—
244C4⋊C4—216no—
245C22⋊C4—232no—
246C22⋊C4—28no—
247C22⋊C4—216no—
248C22⋊C4—416no—
249C42—416no—
250C23—28no—
251C23—24no—
252C23—28no—
253C23—28no—
254C23—28no—
255C23—22no—
256C23—28no—
257C23—24no—
258C23—44no—
259C23—48no—
260C23—44no—
261C23—44no—
262C23—44no—
263C23—44no—
264C23—44no—
265C23—48no—
266C23—44no—
267C23C2×C22⋊C4×C12714yes—
268C23C23×C4×C12711yescharacteristic
269C23C22×D4×C12712yes—
270C23C2×#41×C12718yes—
271C23H(5,𝔽2)×C12714yes—
272D4—416no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—28no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—28no—
279C2×C4—24no—
280C2×C4—216no—
281C2×C4—216no—
282C2×C4—216no—
283C2×C4—416no—
284C2×C4—44no—
285C2×C4—48no—
286C2×C4—44no—
287C2×C4—48no—
288C2×C4—44no—
289C2×C4—48no—
290C2×C4—48no—
291C2×C4C2×C22⋊C4×C12718yes—
292C22—28no—
293C22—24no—
294C22—416no—
295C22—48no—
296C22—48no—
297C22—44no—
298C22—42no—
299C22—88no—
300C22C22×C22⋊C4×C12711yescharacteristic
301C22C4×#41×C12714yes—
302C22#518×C12712yes—
303C22#525×C12714yes—
304C22#532×C12714yes—
305C22#534×C12714yes—
306C22#551×C12714yes—
307C22#553×C12718yes—
308C22#559×C12714yes—
309C4—28no—
310C4—416no—
311C4—44no—
312C4—42no—
313C2—44no—
314C2—82no—
315C2C127×#229712yes—
316C2C127×#230811yescharacteristic
317C2C127×#237414yes—
318C2C127×#260218yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊C4×C127C2semidirect
3. C127×#1440C2semidirect
5. C127×#1437C2semidirect
6. C127×#1436C2semidirect
10. C2×#123×C127C4semidirect
77. C22×C4×C127C22⋊C4semidirect
153. #14167C127direct (N × H)
161. C2×C4×C22⋊C4C2×C127semidirect
162. #1440C2×C127semidirect
164. #1437C2×C127semidirect
165. #1436C2×C127semidirect
166. C127#14167direct (N × H)
170. C2×#123C4×C127semidirect
237. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×C4×C22⋊C4×C1272
C127×#14402
C127×#14382
C127×#14372
C127×#14362
#14167127