Finite Group Databasebeta

← C127×#15949 #44579622

Subgroups — C127×#15949 #44579622

Order 32512.

2354 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C212yesmaximal
2C2×#385×C127C214yesmaximal, complemented
3C127×#1444C214yesmaximal, complemented
4C127×#1440C214yesmaximal, complemented
5C127×#1438C211yesmaximal, characteristic
6C23×D4×C127C2211yescharacteristic
7C24×C4×C127C2212yes—
8C2×#123×C127—28no—
9C2×#123×C127—216no—
10C22×C4⋊C4×C127C2214yes—
11C22×C4⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C22⋊C4×C127C2214yes—
15#385×C127—216no—
16C2×#95×C127C2214yes—
17C2×#95×C127C2218yes—
18C2×#95×C127C2212yes—
19C25×C127C2312yes—
20C22×D4×C127—28no—
21C22×D4×C127—42no—
22C22×D4×C127D414yes—
23C23×C4×C127—24no—
24C23×C4×C127—28no—
25C23×C4×C127—28no—
26C23×C4×C127—44no—
27C23×C4×C127C2314yes—
28C23×C4×C127C2314yes—
29C23×C4×C127C2311yescharacteristic
30C23×C4×C127C2314yes—
31#123×C127—264no—
32C2×C4⋊C4×C127—28no—
33C2×C4⋊C4×C127—28no—
34C2×C4⋊C4×C127—28no—
35C2×C4⋊C4×C127—216no—
36C2×C4⋊C4×C127—44no—
37C2×C22⋊C4×C127—24no—
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×C127D4116yes—
44#95×C127—216no—
45#95×C127—28no—
46#95×C127—42no—
47C24×C127—24no—
48C24×C127—28no—
49C24×C127—24no—
50C24×C127—28no—
51C24×C127C2×D414yes—
52C24×C127C2×D418yes—
53C24×C127C2411yescharacteristic
54C2×D4×C127—216no—
55C2×D4×C127—44no—
56C2×D4×C127—416no—
57C22×C4×C127—216no—
58C22×C4×C127—28no—
59C22×C4×C127—28no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—28no—
66C22×C4×C127—28no—
67C22×C4×C127—24no—
68C22×C4×C127—22no—
69C22×C4×C127—28no—
70C22×C4×C127—24no—
71C22×C4×C127—28no—
72C22×C4×C127—432no—
73C22×C4×C127—48no—
74C22×C4×C127—48no—
75C22×C4×C127C2×D418yes—
76C22×C4×C127C2×D418yes—
77C22×C4×C127C2×D412yes—
78C22×C4×C127#4118yes—
79C4⋊C4×C127—232no—
80C4⋊C4×C127—416no—
81C22⋊C4×C127—232no—
82C22⋊C4×C127—216no—
83C22⋊C4×C127—232no—
84C23×C127—24no—
85C23×C127—28no—
86C23×C127—24no—
87C23×C127—28no—
88C23×C127—216no—
89C23×C127—216no—
90C23×C127—216no—
91C23×C127—44no—
92C23×C127—44no—
93C23×C127—48no—
94C23×C127—48no—
95C23×C127—44no—
96C23×C127—44no—
97C23×C127#12018yes—
98C23×C127C22×D411yescharacteristic
99C23×C127C22×D414yes—
100C23×C127C2×#4114yes—
101C23×C127H(5,𝔽2)12yes—
102C23×C1272−1+414yes—
103D4×C127—416no—
104C2×C4×C127—28no—
105C2×C4×C127—28no—
106C2×C4×C127—24no—
107C2×C4×C127—216no—
108C2×C4×C127—22no—
109C2×C4×C127—28no—
110C2×C4×C127—216no—
111C2×C4×C127—216no—
112C2×C4×C127—432no—
113C2×C4×C127—44no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—44no—
117C2×C4×C127—44no—
118C2×C4×C127—48no—
119C2×C4×C127—44no—
120C2×C4×C127—48no—
121C2×C4×C127—48no—
122C2×C4×C127—44no—
123C22×C127—28no—
124C22×C127—216no—
125C22×C127—48no—
126C22×C127—416no—
127C22×C127—416no—
128C22×C127—48no—
129C22×C127C2×#12012yes—
130C22×C127#52514yes—
131C22×C127#53411yescharacteristic
132C22×C127#53614yes—
133C22×C127#53914yes—
134C22×C127D4214yes—
135C22×C127#54714yes—
136C22×C127#54718yes—
137C22×C127#55912yes—
138C22×C127#56312yes—
139C4×C127—48no—
140C4×C127—42no—
141C4×C127—48no—
142C4×C127—48no—
143#15949C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—48no—
145C2×C127#240311yescharacteristic
146C2×C127#240614yes—
147C2×C127#245514yes—
148C2×C127#268014yes—
149C2×C127#272412yes—
150C22×#123C2×C12712yes—
151C2×#385C2×C12714yescomplemented
152#1444C2×C12714yescomplemented
153#1440C2×C12714yescomplemented
154#1438C2×C12711yescharacteristic
155C127#1594911yescharacteristic, direct product factor, Sylow
156C23×D4C22×C12711yescharacteristic
157C24×C4C22×C12712yes—
158C2×#123—28no—
159C2×#123—216no—
160C22×C4⋊C4C22×C12714yes—
161C22×C4⋊C4C22×C12714yes—
162C22×C22⋊C4C22×C12712yes—
163C22×C22⋊C4C22×C12714yes—
164C22×C22⋊C4C22×C12714yes—
165#385—216no—
166C2×#95C22×C12714yes—
167C2×#95C22×C12718yes—
168C2×#95C22×C12712yes—
169C25C23×C12712yes—
170C22×D4—28no—
171C22×D4—42no—
172C22×D4D4×C12714yes—
173C23×C4—24no—
174C23×C4—28no—
175C23×C4—28no—
176C23×C4—44no—
177C23×C4C23×C12714yes—
178C23×C4C23×C12714yes—
179C23×C4C23×C12711yescharacteristic
180C23×C4C23×C12714yes—
181#123—264no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—28no—
184C2×C4⋊C4—28no—
185C2×C4⋊C4—216no—
186C2×C4⋊C4—44no—
187C2×C22⋊C4—24no—
188C2×C22⋊C4—28no—
189C2×C22⋊C4—28no—
190C2×C22⋊C4—28no—
191C2×C22⋊C4—28no—
192C2×C22⋊C4—216no—
193C2×C22⋊C4D4×C127116yes—
194#95—216no—
195#95—28no—
196#95—42no—
197C24—24no—
198C24—28no—
199C24—24no—
200C24—28no—
201C24C2×D4×C12714yes—
202C24C2×D4×C12718yes—
203C24C24×C12711yescharacteristic
204C2×D4—216no—
205C2×D4—44no—
206C2×D4—416no—
207C22×C4—216no—
208C22×C4—28no—
209C22×C4—28no—
210C22×C4—24no—
211C22×C4—24no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—28no—
216C22×C4—28no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—28no—
220C22×C4—24no—
221C22×C4—28no—
222C22×C4—432no—
223C22×C4—48no—
224C22×C4—48no—
225C22×C4C2×D4×C12718yes—
226C22×C4C2×D4×C12718yes—
227C22×C4C2×D4×C12712yes—
228C22×C4#41×C12718yes—
229C4⋊C4—232no—
230C4⋊C4—416no—
231C22⋊C4—232no—
232C22⋊C4—216no—
233C22⋊C4—232no—
234C23—24no—
235C23—28no—
236C23—24no—
237C23—28no—
238C23—216no—
239C23—216no—
240C23—216no—
241C23—44no—
242C23—44no—
243C23—48no—
244C23—48no—
245C23—44no—
246C23—44no—
247C23#120×C12718yes—
248C23C22×D4×C12711yescharacteristic
249C23C22×D4×C12714yes—
250C23C2×#41×C12714yes—
251C23H(5,𝔽2)×C12712yes—
252C232−1+4×C12714yes—
253D4—416no—
254C2×C4—28no—
255C2×C4—28no—
256C2×C4—24no—
257C2×C4—216no—
258C2×C4—22no—
259C2×C4—28no—
260C2×C4—216no—
261C2×C4—216no—
262C2×C4—432no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—48no—
269C2×C4—44no—
270C2×C4—48no—
271C2×C4—48no—
272C2×C4—44no—
273C22—28no—
274C22—216no—
275C22—48no—
276C22—416no—
277C22—416no—
278C22—48no—
279C22C2×#120×C12712yes—
280C22#525×C12714yes—
281C22#534×C12711yescharacteristic
282C22#536×C12714yes—
283C22#539×C12714yes—
284C22D42×C12714yes—
285C22#547×C12714yes—
286C22#547×C12718yes—
287C22#559×C12712yes—
288C22#563×C12712yes—
289C4—48no—
290C4—42no—
291C4—48no—
292C4—48no—
293C2—48no—
294C2C127×#240311yescharacteristic
295C2C127×#240614yes—
296C2C127×#245514yes—
297C2C127×#268014yes—
298C2C127×#272412yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#385×C127C2semidirect
3. C127×#1444C2semidirect
4. C127×#1440C2semidirect
143. #15949C127direct (N × H)
151. C2×#385C2×C127semidirect
152. #1444C2×C127semidirect
153. #1440C2×C127semidirect
155. C127#15949direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C2×#385×C1272
C127×#14442
C127×#14402
C127×#14382
#15949127