Finite Group Databasebeta

← C127×#14651 #44578324

Subgroups — C127×#14651 #44578324

Order 32512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#392×C127C211yesmaximal, characteristic
2C127×#1443C212yesmaximal, complemented
3C127×#1440C213yesmaximal, complemented
4C127×#1438C216yesmaximal, complemented
5C127×#1437C213yesmaximal, complemented
6C23×D4×C127C2213yes—
7C22×C22⋊C4×C127C2216yes—
8C22×C22⋊C4×C127C2213yes—
9C22×C22⋊C4×C127C2213yes—
10C22×C22⋊C4×C127C2213yes—
11C22×C42×C127C2211yescharacteristic
12#392×C127C418yescomplemented
13C2×#95×C127C2216yes—
14C2×#95×C127C2213yes—
15C2×#95×C127C2216yes—
16C2×#95×C127C2211yescharacteristic
17C25×C127C2313yes—
18C22×D4×C127—46no—
19C22×D4×C127—46no—
20C22×D4×C127—43no—
21C22×D4×C127—43no—
22C22×D4×C127C2×C4112yes—
23C23×C4×C127C2316yes—
24C23×C4×C127C2311yescharacteristic
25C23×C4×C127C2313yes—
26C23×C4×C127C2312yes—
27C2×C22⋊C4×C127—212no—
28C2×C22⋊C4×C127—43no—
29C2×C22⋊C4×C127—43no—
30C2×C22⋊C4×C127—46no—
31C2×C22⋊C4×C127—46no—
32C2×C22⋊C4×C127—46no—
33C2×C22⋊C4×C127—46no—
34C2×C22⋊C4×C127—43no—
35C2×C22⋊C4×C127—43no—
36C2×C22⋊C4×C127C2×C4112yes—
37C2×C42×C127—43no—
38#95×C127—46no—
39#95×C127—43no—
40#95×C127—46no—
41#95×C127C2×C414yes—
42C24×C127—26no—
43C24×C127—23no—
44C24×C127—23no—
45C24×C127—26no—
46C24×C127—26no—
47C24×C127—26no—
48C24×C127—26no—
49C24×C127—26no—
50C24×C127C22×C416yes—
51C24×C127C2411yescharacteristic
52C2×D4×C127—412no—
53C2×D4×C127—424no—
54C2×D4×C127—424no—
55C2×D4×C127—412no—
56C2×D4×C127—412no—
57C22×C4×C127—23no—
58C22×C4×C127—26no—
59C22×C4×C127—26no—
60C22×C4×C127—26no—
61C22×C4×C127—23no—
62C22×C4×C127—26no—
63C22×C4×C127—23no—
64C22×C4×C127—23no—
65C22×C4×C127—26no—
66C22×C4×C127—26no—
67C22×C4×C127—26no—
68C22×C4×C127—26no—
69C22×C4×C127—26no—
70C22×C4×C127—26no—
71C22×C4×C127—26no—
72C22×C4×C127C22×C416yes—
73C22×C4×C127C22×C412yes—
74C22×C4×C127#4114yes—
75C22⋊C4×C127—412no—
76C22⋊C4×C127—424no—
77C22⋊C4×C127—412no—
78C22⋊C4×C127—412no—
79C42×C127—44no—
80C23×C127—26no—
81C23×C127—26no—
82C23×C127—26no—
83C23×C127—212no—
84C23×C127—212no—
85C23×C127—46no—
86C23×C127—46no—
87C23×C127—46no—
88C23×C127—46no—
89C23×C127—46no—
90C23×C127—46no—
91C23×C127—43no—
92C23×C127—46no—
93C23×C127—46no—
94C23×C127—46no—
95C23×C127—46no—
96C23×C127—43no—
97C23×C127—43no—
98C23×C127—46no—
99C23×C127—43no—
100C23×C127—46no—
101C23×C127C23×C411yescharacteristic
102C23×C127C2×#4112yes—
103C23×C127H(5,𝔽2)13yes—
104C23×C127H(5,𝔽2)16yes—
105C23×C127H(5,𝔽2)13yes—
106D4×C127—448no—
107C2×C4×C127—26no—
108C2×C4×C127—26no—
109C2×C4×C127—212no—
110C2×C4×C127—212no—
111C2×C4×C127—42no—
112C2×C4×C127—41no—
113C2×C4×C127—46no—
114C2×C4×C127—43no—
115C2×C4×C127—46no—
116C2×C4×C127—43no—
117C2×C4×C127—43no—
118C2×C4×C127—46no—
119C2×C4×C127—46no—
120C2×C4×C127—46no—
121C2×C4×C127—46no—
122C2×C4×C127—46no—
123C2×C4×C127—46no—
124C2×C4×C127—46no—
125C22×C127—46no—
126C22×C127—412no—
127C22×C127—412no—
128C22×C127—46no—
129C22×C127—46no—
130C22×C127—86no—
131C22×C127—86no—
132C22×C127—86no—
133C22×C127—86no—
134C22×C127C4×#4111yescharacteristic
135C22×C127#51813yes—
136C22×C127#51813yes—
137C22×C127#53816yes—
138C22×C127#54016yes—
139C22×C127#56011yescharacteristic
140C22×C127#56016yes—
141C22×C127#56013yes—
142C22×C127#56013yes—
143C22×C127H(3,𝔽4)13yes—
144C4×C127—44no—
145C4×C127—46no—
146C4×C127—42no—
147C4×C127—86no—
148#14651C12711yesmaximal, characteristic, direct product factor, Sylow
149C2×C127—86no—
150C2×C127#233313yes—
151C2×C127#237513yes—
152C2×C127#238011yescharacteristic
153C2×C127#282512yes—
154C2×C127#282816yes—
155C2×#392C2×C12711yescharacteristic
156#1443C2×C12712yescomplemented
157#1440C2×C12713yescomplemented
158#1438C2×C12716yescomplemented
159#1437C2×C12713yescomplemented
160C127#1465111yescharacteristic, direct product factor, Sylow
161C23×D4C22×C12713yes—
162C22×C22⋊C4C22×C12716yes—
163C22×C22⋊C4C22×C12713yes—
164C22×C22⋊C4C22×C12713yes—
165C22×C22⋊C4C22×C12713yes—
166C22×C42C22×C12711yescharacteristic
167#392C4×C12718yescomplemented
168C2×#95C22×C12716yes—
169C2×#95C22×C12713yes—
170C2×#95C22×C12716yes—
171C2×#95C22×C12711yescharacteristic
172C25C23×C12713yes—
173C22×D4—46no—
174C22×D4—46no—
175C22×D4—43no—
176C22×D4—43no—
177C22×D4C2×C4×C127112yes—
178C23×C4C23×C12716yes—
179C23×C4C23×C12711yescharacteristic
180C23×C4C23×C12713yes—
181C23×C4C23×C12712yes—
182C2×C22⋊C4—212no—
183C2×C22⋊C4—43no—
184C2×C22⋊C4—43no—
185C2×C22⋊C4—46no—
186C2×C22⋊C4—46no—
187C2×C22⋊C4—46no—
188C2×C22⋊C4—46no—
189C2×C22⋊C4—43no—
190C2×C22⋊C4—43no—
191C2×C22⋊C4C2×C4×C127112yes—
192C2×C42—43no—
193#95—46no—
194#95—43no—
195#95—46no—
196#95C2×C4×C12714yes—
197C24—26no—
198C24—23no—
199C24—23no—
200C24—26no—
201C24—26no—
202C24—26no—
203C24—26no—
204C24—26no—
205C24C22×C4×C12716yes—
206C24C24×C12711yescharacteristic
207C2×D4—412no—
208C2×D4—424no—
209C2×D4—424no—
210C2×D4—412no—
211C2×D4—412no—
212C22×C4—23no—
213C22×C4—26no—
214C22×C4—26no—
215C22×C4—26no—
216C22×C4—23no—
217C22×C4—26no—
218C22×C4—23no—
219C22×C4—23no—
220C22×C4—26no—
221C22×C4—26no—
222C22×C4—26no—
223C22×C4—26no—
224C22×C4—26no—
225C22×C4—26no—
226C22×C4—26no—
227C22×C4C22×C4×C12716yes—
228C22×C4C22×C4×C12712yes—
229C22×C4#41×C12714yes—
230C22⋊C4—412no—
231C22⋊C4—424no—
232C22⋊C4—412no—
233C22⋊C4—412no—
234C42—44no—
235C23—26no—
236C23—26no—
237C23—26no—
238C23—212no—
239C23—212no—
240C23—46no—
241C23—46no—
242C23—46no—
243C23—46no—
244C23—46no—
245C23—46no—
246C23—43no—
247C23—46no—
248C23—46no—
249C23—46no—
250C23—46no—
251C23—43no—
252C23—43no—
253C23—46no—
254C23—43no—
255C23—46no—
256C23C23×C4×C12711yescharacteristic
257C23C2×#41×C12712yes—
258C23H(5,𝔽2)×C12713yes—
259C23H(5,𝔽2)×C12716yes—
260C23H(5,𝔽2)×C12713yes—
261D4—448no—
262C2×C4—26no—
263C2×C4—26no—
264C2×C4—212no—
265C2×C4—212no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—46no—
269C2×C4—43no—
270C2×C4—46no—
271C2×C4—43no—
272C2×C4—43no—
273C2×C4—46no—
274C2×C4—46no—
275C2×C4—46no—
276C2×C4—46no—
277C2×C4—46no—
278C2×C4—46no—
279C2×C4—46no—
280C22—46no—
281C22—412no—
282C22—412no—
283C22—46no—
284C22—46no—
285C22—86no—
286C22—86no—
287C22—86no—
288C22—86no—
289C22C4×#41×C12711yescharacteristic
290C22#518×C12713yes—
291C22#518×C12713yes—
292C22#538×C12716yes—
293C22#540×C12716yes—
294C22#560×C12711yescharacteristic
295C22#560×C12716yes—
296C22#560×C12713yes—
297C22#560×C12713yes—
298C22H(3,𝔽4)×C12713yes—
299C4—44no—
300C4—46no—
301C4—42no—
302C4—86no—
303C2—86no—
304C2C127×#233313yes—
305C2C127×#237513yes—
306C2C127×#238011yescharacteristic
307C2C127×#282512yes—
308C2C127×#282816yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC2×#392×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1443C2semidirect
3. C127×#1440C2semidirect
4. C127×#1438C2semidirect
5. C127×#1437C2semidirect
12. #392×C127C4semidirect
148. #14651C127direct (N × H)
156. #1443C2×C127semidirect
157. #1440C2×C127semidirect
158. #1438C2×C127semidirect
159. #1437C2×C127semidirect
160. C127#14651direct (N × H)
167. #392C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#392×C1272
C127×#14432
C127×#14402
C127×#14382
C127×#14372
#14651127