Finite Group Databasebeta

← C127×#15763 #44579436

Subgroups — C127×#15763 #44579436

Order 32512.

2882 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C212yesmaximal, complemented
2C2×#392×C127C214yesmaximal, complemented
3C127×#1446C211yesmaximal, characteristic, complemented
4C127×#1438C214yesmaximal, complemented
5C127×#1437C214yesmaximal, complemented
6C23×Q8×C127C2211yescharacteristic
7C23×D4×C127C2212yes—
8C23×D4×C127C2214yes—
9C2×#124×C127—28no—
10C2×#124×C127—216no—
11C22×C22⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2218yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C42×C127C2212yes—
15#392×C127—216no—
16C2×#95×C127C2214yes—
17C2×#95×C127C2214yes—
18C2×#95×C127C2212yes—
19C25×C127C2314yes—
20C22×Q8×C127—28no—
21C22×Q8×C127—42no—
22C22×Q8×C127D414yescomplemented
23C22×D4×C127—28no—
24C22×D4×C127—216no—
25C22×D4×C127—24no—
26C22×D4×C127—28no—
27C22×D4×C127—28no—
28C22×D4×C127—44no—
29C22×D4×C127—44no—
30C22×D4×C127—44no—
31C22×D4×C127—48no—
32C23×C4×C127C2314yes—
33C23×C4×C127C2311yescharacteristic
34C23×C4×C127C2314yes—
35C23×C4×C127C2312yes—
36#124×C127—264no—
37C2×C22⋊C4×C127—28no—
38C2×C22⋊C4×C127—28no—
39C2×C22⋊C4×C127—28no—
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127—216no—
43C2×C22⋊C4×C127—216no—
44C2×C22⋊C4×C127—48no—
45C2×C22⋊C4×C127D4116yescomplemented
46C2×C42×C127—28no—
47C2×C42×C127—24no—
48#95×C127—28no—
49#95×C127—44no—
50#95×C127—42no—
51C24×C127—24no—
52C24×C127—24no—
53C24×C127—28no—
54C24×C127—28no—
55C24×C127—28no—
56C24×C127—28no—
57C24×C127—28no—
58C24×C127—28no—
59C24×C127C2×D418yes—
60C24×C127C2411yescharacteristic
61C2×Q8×C127—216no—
62C2×Q8×C127—44no—
63C2×Q8×C127—416no—
64C2×D4×C127—216no—
65C2×D4×C127—432no—
66C2×D4×C127—432no—
67C2×D4×C127—48no—
68C2×D4×C127—416no—
69C2×D4×C127—416no—
70C2×D4×C127—432no—
71C2×D4×C127—416no—
72C2×D4×C127—48no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—28no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—28no—
80C22×C4×C127—28no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—22no—
84C22×C4×C127—28no—
85C22×C4×C127C2×D418yes—
86C22×C4×C127C2×D412yes—
87C22×C4×C127C2×D418yes—
88C22×C4×C127C2×D414yes—
89C22×C4×C127#4118yes—
90C22⋊C4×C127—232no—
91C22⋊C4×C127—232no—
92C22⋊C4×C127—432no—
93C42×C127—216no—
94C23×C127—28no—
95C23×C127—28no—
96C23×C127—28no—
97C23×C127—216no—
98C23×C127—216no—
99C23×C127—44no—
100C23×C127—44no—
101C23×C127—48no—
102C23×C127—44no—
103C23×C127—48no—
104C23×C127—44no—
105C23×C127—48no—
106C23×C127—48no—
107C23×C127—48no—
108C23×C127—48no—
109C23×C127—48no—
110C23×C127—48no—
111C23×C127—48no—
112C23×C127—48no—
113C23×C127—48no—
114C23×C127—48no—
115C23×C127C22×D411yescharacteristic
116C23×C127C22×D414yes—
117C23×C127C2×#4114yes—
118C23×C127H(5,𝔽2)12yes—
119C23×C127H(5,𝔽2)14yes—
120Q8×C127—416no—
121D4×C127—432no—
122D4×C127—464no—
123C2×C4×C127—24no—
124C2×C4×C127—24no—
125C2×C4×C127—216no—
126C2×C4×C127—28no—
127C2×C4×C127—24no—
128C2×C4×C127—22no—
129C2×C4×C127—28no—
130C2×C4×C127—216no—
131C2×C4×C127—216no—
132C2×C4×C127—44no—
133C2×C4×C127—44no—
134C2×C4×C127—48no—
135C2×C4×C127—44no—
136C2×C4×C127—44no—
137C2×C4×C127—48no—
138C2×C4×C127—44no—
139C2×C4×C127#12018yes—
140C22×C127—48no—
141C22×C127—416no—
142C22×C127—48no—
143C22×C127—48no—
144C22×C127—416no—
145C22×C127—88no—
146C22×C127—88no—
147C22×C127—88no—
148C22×C127—88no—
149C22×C127C2×#12012yes—
150C22×C127#53214yes—
151C22×C127#53411yescharacteristic
152C22×C127#53514yes—
153C22×C127#53814yes—
154C22×C127D4214yes—
155C22×C127#54618yes—
156C22×C127#55014yes—
157C22×C127#55512yes—
158C22×C127H(3,𝔽4)12yes—
159C4×C127—28no—
160C4×C127—42no—
161C4×C127—48no—
162C4×C127—48no—
163#15763C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—88no—
165C2×C127#240311yescharacteristic
166C2×C127#243114yes—
167C2×C127#255514yes—
168C2×C127#267014yes—
169C2×C127#273312yes—
170C22×#124C2×C12712yescomplemented
171C2×#392C2×C12714yescomplemented
172#1446C2×C12711yescharacteristic, complemented
173#1438C2×C12714yescomplemented
174#1437C2×C12714yescomplemented
175C127#1576311yescharacteristic, direct product factor, Sylow
176C23×Q8C22×C12711yescharacteristic
177C23×D4C22×C12712yes—
178C23×D4C22×C12714yes—
179C2×#124—28no—
180C2×#124—216no—
181C22×C22⋊C4C22×C12714yes—
182C22×C22⋊C4C22×C12718yes—
183C22×C22⋊C4C22×C12714yes—
184C22×C42C22×C12712yes—
185#392—216no—
186C2×#95C22×C12714yes—
187C2×#95C22×C12714yes—
188C2×#95C22×C12712yes—
189C25C23×C12714yes—
190C22×Q8—28no—
191C22×Q8—42no—
192C22×Q8D4×C12714yescomplemented
193C22×D4—28no—
194C22×D4—216no—
195C22×D4—24no—
196C22×D4—28no—
197C22×D4—28no—
198C22×D4—44no—
199C22×D4—44no—
200C22×D4—44no—
201C22×D4—48no—
202C23×C4C23×C12711yescharacteristic
203C23×C4C23×C12714yes—
204C23×C4C23×C12714yes—
205C23×C4C23×C12712yes—
206#124—264no—
207C2×C22⋊C4—28no—
208C2×C22⋊C4—28no—
209C2×C22⋊C4—28no—
210C2×C22⋊C4—28no—
211C2×C22⋊C4—28no—
212C2×C22⋊C4—216no—
213C2×C22⋊C4—216no—
214C2×C22⋊C4—48no—
215C2×C22⋊C4D4×C127116yescomplemented
216C2×C42—28no—
217C2×C42—24no—
218#95—28no—
219#95—44no—
220#95—42no—
221C24—24no—
222C24—24no—
223C24—28no—
224C24—28no—
225C24—28no—
226C24—28no—
227C24—28no—
228C24—28no—
229C24C2×D4×C12718yes—
230C24C24×C12711yescharacteristic
231C2×Q8—216no—
232C2×Q8—44no—
233C2×Q8—416no—
234C2×D4—216no—
235C2×D4—432no—
236C2×D4—432no—
237C2×D4—48no—
238C2×D4—416no—
239C2×D4—416no—
240C2×D4—432no—
241C2×D4—416no—
242C2×D4—48no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—28no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—28no—
250C22×C4—28no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—28no—
255C22×C4C2×D4×C12718yes—
256C22×C4C2×D4×C12712yes—
257C22×C4C2×D4×C12718yes—
258C22×C4C2×D4×C12714yes—
259C22×C4#41×C12718yes—
260C22⋊C4—232no—
261C22⋊C4—232no—
262C22⋊C4—432no—
263C42—216no—
264C23—28no—
265C23—28no—
266C23—28no—
267C23—216no—
268C23—216no—
269C23—44no—
270C23—44no—
271C23—48no—
272C23—44no—
273C23—48no—
274C23—44no—
275C23—48no—
276C23—48no—
277C23—48no—
278C23—48no—
279C23—48no—
280C23—48no—
281C23—48no—
282C23—48no—
283C23—48no—
284C23—48no—
285C23C22×D4×C12711yescharacteristic
286C23C22×D4×C12714yes—
287C23C2×#41×C12714yes—
288C23H(5,𝔽2)×C12712yes—
289C23H(5,𝔽2)×C12714yes—
290Q8—416no—
291D4—432no—
292D4—464no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—216no—
296C2×C4—28no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—28no—
300C2×C4—216no—
301C2×C4—216no—
302C2×C4—44no—
303C2×C4—48no—
304C2×C4—44no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—48no—
308C2×C4—44no—
309C2×C4#120×C12718yes—
310C22—48no—
311C22—416no—
312C22—48no—
313C22—48no—
314C22—416no—
315C22—88no—
316C22—88no—
317C22—88no—
318C22—88no—
319C22C2×#120×C12712yes—
320C22#532×C12714yes—
321C22#534×C12711yescharacteristic
322C22#535×C12714yes—
323C22#538×C12714yes—
324C22D42×C12714yes—
325C22#546×C12718yes—
326C22#550×C12714yes—
327C22#555×C12712yes—
328C22H(3,𝔽4)×C12712yes—
329C4—28no—
330C4—42no—
331C4—48no—
332C4—48no—
333C2—88no—
334C2C127×#240311yescharacteristic
335C2C127×#243114yes—
336C2C127×#255514yes—
337C2C127×#267014yes—
338C2C127×#273312yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#124×C127C2semidirect
2. C2×#392×C127C2semidirect
3. C127×#1446C2semidirect
4. C127×#1438C2semidirect
5. C127×#1437C2semidirect
22. C22×Q8×C127D4semidirect
45. C2×C22⋊C4×C127D4semidirect
163. #15763C127direct (N × H)
170. C22×#124C2×C127semidirect
171. C2×#392C2×C127semidirect
172. #1446C2×C127semidirect
173. #1438C2×C127semidirect
174. #1437C2×C127semidirect
175. C127#15763direct (N × H)
192. C22×Q8D4×C127semidirect
215. C2×C22⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C2×#392×C1272
C127×#14462
C127×#14382
C127×#14372
#15763127