Finite Group Databasebeta

← C127×#14609 #44578282

Subgroups — C127×#14609 #44578282

Order 32512.

1354 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C211yesmaximal, characteristic
2C127×#1446C212yesmaximal, complemented
3C127×#1440C213yesmaximal
4C127×#1437C213yesmaximal
5C127×#1434C216yesmaximal, complemented
6C23×Q8×C127C2211yescharacteristic
7C22×C22⋊C4×C127C2213yes—
8C22×C22⋊C4×C127C2211yescharacteristic
9C22×C22⋊C4×C127C2213yes—
10C22×C42×C127C2213yes—
11#393×C127C418yescomplemented
12C2×#95×C127C2216yes—
13C2×#95×C127C2213yes—
14C2×#95×C127C2216yes—
15C2×#95×C127C2216yes—
16C2×#95×C127C2213yes—
17C25×C127C2311yescharacteristic
18C22×Q8×C127—43no—
19C22×Q8×C127—43no—
20C22×Q8×C127C2×C414yes—
21C23×C4×C127C2312yes—
22C23×C4×C127C2313yes—
23C23×C4×C127C2313yes—
24C23×C4×C127C2316yes—
25C2×C22⋊C4×C127—212no—
26C2×C22⋊C4×C127—43no—
27C2×C22⋊C4×C127—43no—
28C2×C22⋊C4×C127—43no—
29C2×C22⋊C4×C127—43no—
30C2×C22⋊C4×C127C2×C4112yes—
31C2×C42×C127—212no—
32C2×C42×C127—43no—
33#95×C127—212no—
34#95×C127—43no—
35#95×C127—46no—
36#95×C127—46no—
37#95×C127C2×C4112yes—
38C24×C127—26no—
39C24×C127—23no—
40C24×C127—23no—
41C24×C127—22no—
42C24×C127C22×C412yes—
43C24×C127C2411yescharacteristic
44C2×Q8×C127—412no—
45C2×Q8×C127—412no—
46C2×Q8×C127—44no—
47C22×C4×C127—26no—
48C22×C4×C127—26no—
49C22×C4×C127—26no—
50C22×C4×C127—26no—
51C22×C4×C127—26no—
52C22×C4×C127—26no—
53C22×C4×C127—23no—
54C22×C4×C127—26no—
55C22×C4×C127—26no—
56C22×C4×C127—26no—
57C22×C4×C127—23no—
58C22×C4×C127—23no—
59C22×C4×C127—23no—
60C22×C4×C127—26no—
61C22×C4×C127—26no—
62C22×C4×C127—26no—
63C22×C4×C127—22no—
64C22×C4×C127C22×C416yes—
65C22×C4×C127C22×C416yes—
66C22×C4×C127#41112yes—
67C22⋊C4×C127—412no—
68C22⋊C4×C127—412no—
69C22⋊C4×C127—44no—
70C42×C127—412no—
71C23×C127—26no—
72C23×C127—26no—
73C23×C127—22no—
74C23×C127—46no—
75C23×C127—46no—
76C23×C127—43no—
77C23×C127—43no—
78C23×C127—46no—
79C23×C127—43no—
80C23×C127—41no—
81C23×C127C23×C411yescharacteristic
82C23×C127C2×#4116yes—
83C23×C127H(5,𝔽2)13yes—
84C23×C127H(5,𝔽2)13yes—
85C23×C1272−1+412yes—
86Q8×C127—416no—
87C2×C4×C127—212no—
88C2×C4×C127—26no—
89C2×C4×C127—26no—
90C2×C4×C127—212no—
91C2×C4×C127—212no—
92C2×C4×C127—212no—
93C2×C4×C127—212no—
94C2×C4×C127—46no—
95C2×C4×C127—46no—
96C2×C4×C127—43no—
97C2×C4×C127—43no—
98C2×C4×C127—46no—
99C2×C4×C127—46no—
100C2×C4×C127—46no—
101C2×C4×C127—43no—
102C2×C4×C127—46no—
103C2×C4×C127—43no—
104C2×C4×C127—46no—
105C2×C4×C127—46no—
106C2×C4×C127—42no—
107C22×C127—46no—
108C22×C127—46no—
109C22×C127—42no—
110C22×C127—86no—
111C22×C127—82no—
112C22×C127C4×#4113yes—
113C22×C127#51813yes—
114C22×C127#51911yescharacteristic
115C22×C127#53916yes—
116C22×C127#54216yes—
117C22×C127#55113yes—
118C22×C127#55113yes—
119C22×C127#55516yes—
120C22×C127#56013yes—
121C22×C127H(3,𝔽4)11yescharacteristic
122C4×C127—46no—
123C4×C127—46no—
124C4×C127—412no—
125C4×C127—82no—
126#14609C12711yesmaximal, characteristic, direct product factor, Sylow
127C2×C127—82no—
128C2×C127#233213yes—
129C2×C127#237213yes—
130C2×C127#237511yescharacteristic
131C2×C127#273716yes—
132C2×C127#278512yes—
133C2×#393C2×C12711yescharacteristic
134#1446C2×C12712yescomplemented
135#1440C2×C12713yes—
136#1437C2×C12713yes—
137#1434C2×C12716yescomplemented
138C127#1460911yescharacteristic, direct product factor, Sylow
139C23×Q8C22×C12711yescharacteristic
140C22×C22⋊C4C22×C12713yes—
141C22×C22⋊C4C22×C12711yescharacteristic
142C22×C22⋊C4C22×C12713yes—
143C22×C42C22×C12713yes—
144#393C4×C12718yescomplemented
145C2×#95C22×C12716yes—
146C2×#95C22×C12713yes—
147C2×#95C22×C12716yes—
148C2×#95C22×C12716yes—
149C2×#95C22×C12713yes—
150C25C23×C12711yescharacteristic
151C22×Q8—43no—
152C22×Q8—43no—
153C22×Q8C2×C4×C12714yes—
154C23×C4C23×C12712yes—
155C23×C4C23×C12713yes—
156C23×C4C23×C12713yes—
157C23×C4C23×C12716yes—
158C2×C22⋊C4—212no—
159C2×C22⋊C4—43no—
160C2×C22⋊C4—43no—
161C2×C22⋊C4—43no—
162C2×C22⋊C4—43no—
163C2×C22⋊C4C2×C4×C127112yes—
164C2×C42—212no—
165C2×C42—43no—
166#95—212no—
167#95—43no—
168#95—46no—
169#95—46no—
170#95C2×C4×C127112yes—
171C24—26no—
172C24—23no—
173C24—23no—
174C24—22no—
175C24C22×C4×C12712yes—
176C24C24×C12711yescharacteristic
177C2×Q8—412no—
178C2×Q8—412no—
179C2×Q8—44no—
180C22×C4—26no—
181C22×C4—26no—
182C22×C4—26no—
183C22×C4—26no—
184C22×C4—26no—
185C22×C4—26no—
186C22×C4—23no—
187C22×C4—26no—
188C22×C4—26no—
189C22×C4—26no—
190C22×C4—23no—
191C22×C4—23no—
192C22×C4—23no—
193C22×C4—26no—
194C22×C4—26no—
195C22×C4—26no—
196C22×C4—22no—
197C22×C4C22×C4×C12716yes—
198C22×C4C22×C4×C12716yes—
199C22×C4#41×C127112yes—
200C22⋊C4—412no—
201C22⋊C4—412no—
202C22⋊C4—44no—
203C42—412no—
204C23—26no—
205C23—26no—
206C23—22no—
207C23—46no—
208C23—46no—
209C23—43no—
210C23—43no—
211C23—46no—
212C23—43no—
213C23—41no—
214C23C23×C4×C12711yescharacteristic
215C23C2×#41×C12716yes—
216C23H(5,𝔽2)×C12713yes—
217C23H(5,𝔽2)×C12713yes—
218C232−1+4×C12712yes—
219Q8—416no—
220C2×C4—212no—
221C2×C4—26no—
222C2×C4—26no—
223C2×C4—212no—
224C2×C4—212no—
225C2×C4—212no—
226C2×C4—212no—
227C2×C4—46no—
228C2×C4—46no—
229C2×C4—43no—
230C2×C4—43no—
231C2×C4—46no—
232C2×C4—46no—
233C2×C4—43no—
234C2×C4—46no—
235C2×C4—46no—
236C2×C4—43no—
237C2×C4—46no—
238C2×C4—46no—
239C2×C4—42no—
240C22—46no—
241C22—46no—
242C22—42no—
243C22—86no—
244C22—82no—
245C22C4×#41×C12713yes—
246C22#518×C12713yes—
247C22#519×C12711yescharacteristic
248C22#539×C12716yes—
249C22#542×C12716yes—
250C22#551×C12713yes—
251C22#551×C12713yes—
252C22#555×C12716yes—
253C22#560×C12713yes—
254C22H(3,𝔽4)×C12711yescharacteristic
255C4—46no—
256C4—46no—
257C4—412no—
258C4—82no—
259C2—82no—
260C2C127×#233213yes—
261C2C127×#237213yes—
262C2C127×#237511yescharacteristic
263C2C127×#273716yes—
264C2C127×#278512yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1446C2semidirect
5. C127×#1434C2semidirect
11. #393×C127C4semidirect
126. #14609C127direct (N × H)
134. #1446C2×C127semidirect
137. #1434C2×C127semidirect
138. C127#14609direct (N × H)
144. #393C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C127×#14462
C127×#14402
C127×#14372
C127×#14342
#14609127