Finite Group Databasebeta

← C127×#14635 #44578308

Subgroups — C127×#14635 #44578308

Order 32512.

1442 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C211yesmaximal, characteristic
2C127×#1446C212yesmaximal, complemented
3C127×#1442C216yesmaximal, complemented
4C127×#1439C213yesmaximal
5C127×C22⋊#95C213yesmaximal
6C23×Q8×C127C2211yescharacteristic
7C24×C4×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2213yes—
9C22×C22⋊C4×C127C2213yes—
10C22×C22⋊C4×C127C2213yes—
11#393×C127C418yescomplemented
12C2×#95×C127C2216yes—
13C2×#95×C127C2216yes—
14C2×#95×C127C2213yes—
15C2×#95×C127C2216yes—
16C2×#95×C127C2213yes—
17C25×C127C2311yescharacteristic
18C22×Q8×C127—43no—
19C22×Q8×C127—43no—
20C22×Q8×C127C2×C414yescomplemented
21C23×C4×C127—43no—
22C23×C4×C127—43no—
23C23×C4×C127Q814yescomplemented
24C23×C4×C127C2316yes—
25C23×C4×C127C2313yes—
26C23×C4×C127C2313yes—
27C23×C4×C127C2312yes—
28C2×C4⋊C4×C127—46no—
29C2×C4⋊C4×C127—43no—
30C2×C22⋊C4×C127—26no—
31C2×C22⋊C4×C127—43no—
32C2×C22⋊C4×C127—43no—
33C2×C22⋊C4×C127—43no—
34C2×C22⋊C4×C127—43no—
35C2×C22⋊C4×C127C2×C4112yes—
36#95×C127—43no—
37#95×C127—46no—
38#95×C127—46no—
39#95×C127—46no—
40#95×C127C2×C4112yescomplemented
41C24×C127—23no—
42C24×C127—23no—
43C24×C127—23no—
44C24×C127—23no—
45C24×C127C22×C412yes—
46C24×C127C2×Q812yes—
47C24×C127#4112yes—
48C24×C127C2411yescharacteristic
49C2×Q8×C127—412no—
50C2×Q8×C127—412no—
51C2×Q8×C127—44no—
52C22×C4×C127—23no—
53C22×C4×C127—26no—
54C22×C4×C127—26no—
55C22×C4×C127—26no—
56C22×C4×C127—26no—
57C22×C4×C127—26no—
58C22×C4×C127—23no—
59C22×C4×C127—23no—
60C22×C4×C127—23no—
61C22×C4×C127—26no—
62C22×C4×C127—26no—
63C22×C4×C127—26no—
64C22×C4×C127—26no—
65C22×C4×C127—26no—
66C22×C4×C127—26no—
67C22×C4×C127—26no—
68C22×C4×C127—26no—
69C22×C4×C127—412no—
70C22×C4×C127—412no—
71C22×C4×C127—44no—
72C22×C4×C127C22×C416yes—
73C22×C4×C127C22×C416yes—
74C22×C4×C127C2×Q814yes—
75C4⋊C4×C127—412no—
76C22⋊C4×C127—412no—
77C22⋊C4×C127—412no—
78C23×C127—26no—
79C23×C127—26no—
80C23×C127—26no—
81C23×C127—26no—
82C23×C127—26no—
83C23×C127—26no—
84C23×C127—43no—
85C23×C127—43no—
86C23×C127—41no—
87C23×C127—46no—
88C23×C127—43no—
89C23×C127C4×Q814yes—
90C23×C127C23×C411yescharacteristic
91C23×C127C22×Q811yescharacteristic
92C23×C127C2×#4111yescharacteristic
93C23×C127H(5,𝔽2)13yes—
94C23×C127H(5,𝔽2)13yes—
95C23×C127H(5,𝔽2)13yes—
96C23×C1272−1+413yes—
97Q8×C127—416no—
98C2×C4×C127—26no—
99C2×C4×C127—26no—
100C2×C4×C127—212no—
101C2×C4×C127—212no—
102C2×C4×C127—212no—
103C2×C4×C127—416no—
104C2×C4×C127—43no—
105C2×C4×C127—46no—
106C2×C4×C127—43no—
107C2×C4×C127—46no—
108C2×C4×C127—42no—
109C2×C4×C127—43no—
110C2×C4×C127—46no—
111C2×C4×C127—43no—
112C2×C4×C127—46no—
113C2×C4×C127—46no—
114C2×C4×C127—46no—
115C2×C4×C127—46no—
116C2×C4×C127—46no—
117C2×C4×C127—46no—
118C2×C4×C127—46no—
119C22×C127—212no—
120C22×C127—46no—
121C22×C127—42no—
122C22×C127—42no—
123C22×C127—46no—
124C22×C127—42no—
125C22×C127—46no—
126C22×C127C2×C4×Q811yescharacteristic
127C22×C127#51813yes—
128C22×C127#52013yes—
129C22×C127#53813yes—
130C22×C127#53913yes—
131C22×C127#54313yes—
132C22×C127#54413yes—
133C22×C127#56013yes—
134C22×C127H(3,𝔽4)13yes—
135C22×C127H(3,𝔽4)11yescharacteristic
136C22×C127#56216yes—
137C22×C127#56313yes—
138C4×C127—44no—
139C4×C127—46no—
140C4×C127—46no—
141C4×C127—86no—
142#14635C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—44no—
144C2×C127#232913yes—
145C2×C127#237511yescharacteristic
146C2×C127#237913yes—
147C2×C127#282413yes—
148C2×C127#283511yescharacteristic
149C2×C127#284011yescharacteristic
150C2×C127#284113yes—
151C2×#393C2×C12711yescharacteristic
152#1446C2×C12712yescomplemented
153#1442C2×C12716yescomplemented
154#1439C2×C12713yes—
155C22⋊#95C2×C12713yes—
156C127#1463511yescharacteristic, direct product factor, Sylow
157C23×Q8C22×C12711yescharacteristic
158C24×C4C22×C12711yescharacteristic
159C22×C4⋊C4C22×C12713yes—
160C22×C22⋊C4C22×C12713yes—
161C22×C22⋊C4C22×C12713yes—
162#393C4×C12718yescomplemented
163C2×#95C22×C12716yes—
164C2×#95C22×C12716yes—
165C2×#95C22×C12713yes—
166C2×#95C22×C12716yes—
167C2×#95C22×C12713yes—
168C25C23×C12711yescharacteristic
169C22×Q8—43no—
170C22×Q8—43no—
171C22×Q8C2×C4×C12714yescomplemented
172C23×C4—43no—
173C23×C4—43no—
174C23×C4Q8×C12714yescomplemented
175C23×C4C23×C12716yes—
176C23×C4C23×C12713yes—
177C23×C4C23×C12713yes—
178C23×C4C23×C12712yes—
179C2×C4⋊C4—46no—
180C2×C4⋊C4—43no—
181C2×C22⋊C4—26no—
182C2×C22⋊C4—43no—
183C2×C22⋊C4—43no—
184C2×C22⋊C4—43no—
185C2×C22⋊C4—43no—
186C2×C22⋊C4C2×C4×C127112yes—
187#95—43no—
188#95—46no—
189#95—46no—
190#95—46no—
191#95C2×C4×C127112yescomplemented
192C24—23no—
193C24—23no—
194C24—23no—
195C24—23no—
196C24C22×C4×C12712yes—
197C24C2×Q8×C12712yes—
198C24#41×C12712yes—
199C24C24×C12711yescharacteristic
200C2×Q8—412no—
201C2×Q8—412no—
202C2×Q8—44no—
203C22×C4—23no—
204C22×C4—26no—
205C22×C4—26no—
206C22×C4—26no—
207C22×C4—26no—
208C22×C4—26no—
209C22×C4—23no—
210C22×C4—23no—
211C22×C4—23no—
212C22×C4—26no—
213C22×C4—26no—
214C22×C4—26no—
215C22×C4—26no—
216C22×C4—26no—
217C22×C4—26no—
218C22×C4—26no—
219C22×C4—26no—
220C22×C4—412no—
221C22×C4—412no—
222C22×C4—44no—
223C22×C4C22×C4×C12716yes—
224C22×C4C22×C4×C12716yes—
225C22×C4C2×Q8×C12714yes—
226C4⋊C4—412no—
227C22⋊C4—412no—
228C22⋊C4—412no—
229C23—26no—
230C23—26no—
231C23—26no—
232C23—26no—
233C23—26no—
234C23—26no—
235C23—43no—
236C23—43no—
237C23—41no—
238C23—46no—
239C23—43no—
240C23C4×Q8×C12714yes—
241C23C23×C4×C12711yescharacteristic
242C23C22×Q8×C12711yescharacteristic
243C23C2×#41×C12711yescharacteristic
244C23H(5,𝔽2)×C12713yes—
245C23H(5,𝔽2)×C12713yes—
246C23H(5,𝔽2)×C12713yes—
247C232−1+4×C12713yes—
248Q8—416no—
249C2×C4—26no—
250C2×C4—26no—
251C2×C4—212no—
252C2×C4—212no—
253C2×C4—212no—
254C2×C4—416no—
255C2×C4—43no—
256C2×C4—46no—
257C2×C4—43no—
258C2×C4—46no—
259C2×C4—42no—
260C2×C4—43no—
261C2×C4—46no—
262C2×C4—43no—
263C2×C4—46no—
264C2×C4—46no—
265C2×C4—46no—
266C2×C4—46no—
267C2×C4—46no—
268C2×C4—46no—
269C2×C4—46no—
270C22—212no—
271C22—46no—
272C22—42no—
273C22—42no—
274C22—46no—
275C22—42no—
276C22—46no—
277C22C2×C4×Q8×C12711yescharacteristic
278C22#518×C12713yes—
279C22#520×C12713yes—
280C22#538×C12713yes—
281C22#539×C12713yes—
282C22#543×C12713yes—
283C22#544×C12713yes—
284C22#560×C12713yes—
285C22H(3,𝔽4)×C12713yes—
286C22H(3,𝔽4)×C12711yescharacteristic
287C22#562×C12716yes—
288C22#563×C12713yes—
289C4—44no—
290C4—46no—
291C4—46no—
292C4—86no—
293C2—44no—
294C2C127×#232913yes—
295C2C127×#237511yescharacteristic
296C2C127×#237913yes—
297C2C127×#282413yes—
298C2C127×#283511yescharacteristic
299C2C127×#284011yescharacteristic
300C2C127×#284113yes—
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
3. C127×#1442C2semidirect
11. #393×C127C4semidirect
20. C22×Q8×C127C2×C4semidirect
23. C23×C4×C127Q8semidirect
40. #95×C127C2×C4semidirect
142. #14635C127direct (N × H)
152. #1446C2×C127semidirect
153. #1442C2×C127semidirect
156. C127#14635direct (N × H)
162. #393C4×C127semidirect
171. C22×Q8C2×C4×C127semidirect
174. C23×C4Q8×C127semidirect
191. #95C2×C4×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×#14422
C127×#14392
C127×C22⋊#952
#14635127