Finite Group Databasebeta

← C127×#14674 #44578347

Subgroups — C127×#14674 #44578347

Order 32512.

1486 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×#381×C127C211yesmaximal, characteristic
2C2×#380×C127C212yesmaximal
3C127×#1444C214yesmaximal, complemented
4C127×#1442C214yesmaximal, complemented
5C127×#1439C214yesmaximal
6C24×C4×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2212yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2214yes—
10C22×C22⋊C4×C127C2214yes—
11C22×C22⋊C4×C127C2212yes—
12#381×C127C418yescomplemented
13#380×C127—28no—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2218yes—
17C2×#95×C127C2214yes—
18C25×C127C2311yescharacteristic
19C23×C4×C127—42no—
20C23×C4×C127—42no—
21C23×C4×C127C2×C414yes—
22C23×C4×C127D414yes—
23C23×C4×C127Q814yes—
24C23×C4×C127C2314yes—
25C23×C4×C127C2314yes—
26C23×C4×C127C2314yes—
27C23×C4×C127C2312yes—
28C2×C4⋊C4×C127—24no—
29C2×C4⋊C4×C127—24no—
30C2×C4⋊C4×C127—44no—
31C2×C4⋊C4×C127—44no—
32C2×C4⋊C4×C127—48no—
33C2×C4⋊C4×C127—44no—
34C2×C22⋊C4×C127—28no—
35C2×C22⋊C4×C127—42no—
36C2×C22⋊C4×C127—42no—
37C2×C22⋊C4×C127—48no—
38C2×C22⋊C4×C127C2×C418yes—
39#95×C127—28no—
40#95×C127—44no—
41#95×C127—48no—
42#95×C127C2×C4116yes—
43C24×C127—24no—
44C24×C127—22no—
45C24×C127—22no—
46C24×C127—24no—
47C24×C127C22×C412yes—
48C24×C127C2×D412yes—
49C24×C127C2×Q812yes—
50C24×C127C2411yescharacteristic
51C22×C4×C127—24no—
52C22×C4×C127—24no—
53C22×C4×C127—24no—
54C22×C4×C127—28no—
55C22×C4×C127—24no—
56C22×C4×C127—28no—
57C22×C4×C127—24no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—28no—
61C22×C4×C127—28no—
62C22×C4×C127—28no—
63C22×C4×C127—28no—
64C22×C4×C127—24no—
65C22×C4×C127—28no—
66C22×C4×C127—48no—
67C22×C4×C127—44no—
68C22×C4×C127—44no—
69C22×C4×C127—48no—
70C22×C4×C127C4⋊C4116yescomplemented
71C22×C4×C127C22×C418yes—
72C22×C4×C127C22×C414yes—
73C22×C4×C127C2×D414yes—
74C22×C4×C127C2×Q814yes—
75C4⋊C4×C127—48no—
76C4⋊C4×C127—48no—
77C4⋊C4×C127—416no—
78C22⋊C4×C127—48no—
79C22⋊C4×C127—416no—
80C23×C127—24no—
81C23×C127—28no—
82C23×C127—22no—
83C23×C127—22no—
84C23×C127—24no—
85C23×C127—24no—
86C23×C127—24no—
87C23×C127—28no—
88C23×C127—44no—
89C23×C127—48no—
90C23×C127—44no—
91C23×C127C2×C4⋊C414yes—
92C23×C127C23×C411yescharacteristic
93C23×C127C22×D411yescharacteristic
94C23×C127C22×Q811yescharacteristic
95C23×C127H(5,𝔽2)12yes—
96C23×C127H(5,𝔽2)12yes—
97C23×C127H(5,𝔽2)14yes—
98C23×C1272−1+414yes—
99C2×C4×C127—28no—
100C2×C4×C127—24no—
101C2×C4×C127—24no—
102C2×C4×C127—28no—
103C2×C4×C127—28no—
104C2×C4×C127—216no—
105C2×C4×C127—416no—
106C2×C4×C127—44no—
107C2×C4×C127—48no—
108C2×C4×C127—44no—
109C2×C4×C127—44no—
110C2×C4×C127—44no—
111C2×C4×C127—44no—
112C2×C4×C127—44no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—48no—
116C2×C4×C127—48no—
117C2×C4×C127—416no—
118C2×C4×C127C2×C4⋊C418yes—
119C22×C127—24no—
120C22×C127—28no—
121C22×C127—44no—
122C22×C127—42no—
123C22×C127—48no—
124C22×C127—48no—
125C22×C127—42no—
126C22×C127C22×C4⋊C411yescharacteristic
127C22×C127#51812yes—
128C22×C127#52014yes—
129C22×C127#53411yescharacteristic
130C22×C127#53411yescharacteristic
131C22×C127#53512yes—
132C22×C127#53612yes—
133C22×C127#54312yes—
134C22×C127#54414yes—
135C22×C127#56014yes—
136C22×C127#56218yes—
137C22×C127#56314yes—
138C4×C127—28no—
139C4×C127—48no—
140C4×C127—84no—
141C4×C127—84no—
142#14674C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—44no—
144C2×C127#231511yescharacteristic
145C2×C127#231712yes—
146C2×C127#237614yes—
147C2×C127#281511yescharacteristic
148C2×C127#281612yes—
149C2×C127#281711yescharacteristic
150C2×C127#284114yes—
151C2×#381C2×C12711yescharacteristic
152C2×#380C2×C12712yes—
153#1444C2×C12714yescomplemented
154#1442C2×C12714yescomplemented
155#1439C2×C12714yes—
156C127#1467411yescharacteristic, direct product factor, Sylow
157C24×C4C22×C12711yescharacteristic
158C22×C4⋊C4C22×C12712yes—
159C22×C4⋊C4C22×C12712yes—
160C22×C4⋊C4C22×C12714yes—
161C22×C22⋊C4C22×C12714yes—
162C22×C22⋊C4C22×C12712yes—
163#381C4×C12718yescomplemented
164#380—28no—
165C2×#95C22×C12714yes—
166C2×#95C22×C12714yes—
167C2×#95C22×C12718yes—
168C2×#95C22×C12714yes—
169C25C23×C12711yescharacteristic
170C23×C4—42no—
171C23×C4—42no—
172C23×C4C2×C4×C12714yes—
173C23×C4D4×C12714yes—
174C23×C4Q8×C12714yes—
175C23×C4C23×C12714yes—
176C23×C4C23×C12714yes—
177C23×C4C23×C12714yes—
178C23×C4C23×C12712yes—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—44no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—48no—
184C2×C4⋊C4—44no—
185C2×C22⋊C4—28no—
186C2×C22⋊C4—42no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—48no—
189C2×C22⋊C4C2×C4×C12718yes—
190#95—28no—
191#95—44no—
192#95—48no—
193#95C2×C4×C127116yes—
194C24—24no—
195C24—22no—
196C24—22no—
197C24—24no—
198C24C22×C4×C12712yes—
199C24C2×D4×C12712yes—
200C24C2×Q8×C12712yes—
201C24C24×C12711yescharacteristic
202C22×C4—24no—
203C22×C4—24no—
204C22×C4—24no—
205C22×C4—28no—
206C22×C4—24no—
207C22×C4—28no—
208C22×C4—24no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—28no—
212C22×C4—28no—
213C22×C4—28no—
214C22×C4—28no—
215C22×C4—24no—
216C22×C4—28no—
217C22×C4—48no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—48no—
221C22×C4C4⋊C4×C127116yescomplemented
222C22×C4C22×C4×C12718yes—
223C22×C4C22×C4×C12714yes—
224C22×C4C2×D4×C12714yes—
225C22×C4C2×Q8×C12714yes—
226C4⋊C4—48no—
227C4⋊C4—48no—
228C4⋊C4—416no—
229C22⋊C4—48no—
230C22⋊C4—416no—
231C23—24no—
232C23—28no—
233C23—22no—
234C23—22no—
235C23—24no—
236C23—24no—
237C23—24no—
238C23—28no—
239C23—44no—
240C23—48no—
241C23—44no—
242C23C2×C4⋊C4×C12714yes—
243C23C23×C4×C12711yescharacteristic
244C23C22×D4×C12711yescharacteristic
245C23C22×Q8×C12711yescharacteristic
246C23H(5,𝔽2)×C12712yes—
247C23H(5,𝔽2)×C12712yes—
248C23H(5,𝔽2)×C12714yes—
249C232−1+4×C12714yes—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—28no—
254C2×C4—28no—
255C2×C4—216no—
256C2×C4—416no—
257C2×C4—44no—
258C2×C4—48no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—48no—
267C2×C4—48no—
268C2×C4—416no—
269C2×C4C2×C4⋊C4×C12718yes—
270C22—24no—
271C22—28no—
272C22—48no—
273C22—48no—
274C22—42no—
275C22—44no—
276C22—42no—
277C22C22×C4⋊C4×C12711yescharacteristic
278C22#518×C12712yes—
279C22#520×C12714yes—
280C22#534×C12711yescharacteristic
281C22#534×C12711yescharacteristic
282C22#535×C12712yes—
283C22#536×C12712yes—
284C22#543×C12712yes—
285C22#544×C12714yes—
286C22#560×C12714yes—
287C22#562×C12718yes—
288C22#563×C12714yes—
289C4—28no—
290C4—48no—
291C4—84no—
292C4—84no—
293C2—44no—
294C2C127×#231511yescharacteristic
295C2C127×#231712yes—
296C2C127×#237614yes—
297C2C127×#281511yescharacteristic
298C2C127×#281612yes—
299C2C127×#281711yescharacteristic
300C2C127×#284114yes—
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
3. C127×#1444C2semidirect
4. C127×#1442C2semidirect
12. #381×C127C4semidirect
70. C22×C4×C127C4⋊C4semidirect
142. #14674C127direct (N × H)
153. #1444C2×C127semidirect
154. #1442C2×C127semidirect
156. C127#14674direct (N × H)
163. #381C4×C127semidirect
221. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#381×C1272
C2×#380×C1272
C127×#14442
C127×#14422
C127×#14392
#14674127