Finite Group Databasebeta

← C127×#15241 #44578914

Subgroups — C127×#15241 #44578914

Order 32512.

1286 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×#391×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C2×#382×C127C211yesmaximal, characteristic
4C127×#1443C218yesmaximal
5C127×C4⋊#95C212yesmaximal
6C4×#95×C127C211yesmaximal, characteristic
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2211yescharacteristic
9C22×C4⋊C4×C127C2212yes—
10C22×C42×C127C2212yes—
11C22×C42×C127C2211yescharacteristic
12#391×C127—28no—
13#391×C127—24no—
14#382×C127—24no—
15C2×#95×C127C2214yes—
16C2×#95×C127C2218yes—
17C2×#95×C127C2214yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2218yes—
20C22×Q8×C127—22no—
21C22×Q8×C127—22no—
22C22×Q8×C127—24no—
23C22×Q8×C127—24no—
24C22×Q8×C127D414yes—
25C23×C4×C127C2314yes—
26C23×C4×C127C2312yes—
27C23×C4×C127C2312yes—
28C23×C4×C127C2312yes—
29C23×C4×C127C2314yes—
30C23×C4×C127C2311yescharacteristic
31C2×C4⋊C4×C127—24no—
32C2×C4⋊C4×C127—24no—
33C2×C4⋊C4×C127—22no—
34C2×C4⋊C4×C127—24no—
35C2×C4⋊C4×C127—24no—
36C2×C42×C127—24no—
37C2×C42×C127—24no—
38C2×C42×C127—24no—
39C2×C42×C127—24no—
40C2×C42×C127D414yes—
41#95×C127—28no—
42#95×C127—216no—
43#95×C127—28no—
44#95×C127—28no—
45#95×C127—216no—
46C24×C127C2411yescharacteristic
47C2×Q8×C127—28no—
48C2×Q8×C127—216no—
49C2×Q8×C127—44no—
50C2×Q8×C127—44no—
51C2×Q8×C127—48no—
52C22×C4×C127—24no—
53C22×C4×C127—22no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—22no—
57C22×C4×C127—22no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—22no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—24no—
68C22×C4×C127—22no—
69C22×C4×C127—28no—
70C22×C4×C127—28no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—28no—
74C22×C4×C127C2×D414yes—
75C22×C4×C127C2×D414yes—
76C22×C4×C127C2×D412yes—
77C22×C4×C127C2×D412yes—
78C22×C4×C127#4118yes—
79C22×C4×C127#4112yes—
80C22×C4×C127#4114yes—
81C22×C4×C127#4114yes—
82C4⋊C4×C127—48no—
83C4⋊C4×C127—44no—
84C42×C127—28no—
85C42×C127—48no—
86C23×C127C22×D411yescharacteristic
87C23×C127C22×D411yescharacteristic
88C23×C127C2×#4111yescharacteristic
89C23×C127C2×#4112yes—
90C23×C127C2×#4112yes—
91C23×C127C2×#4114yes—
92C23×C1272−1+414yes—
93Q8×C127—416no—
94C2×C4×C127—24no—
95C2×C4×C127—24no—
96C2×C4×C127—28no—
97C2×C4×C127—28no—
98C2×C4×C127—24no—
99C2×C4×C127—24no—
100C2×C4×C127—28no—
101C2×C4×C127—28no—
102C2×C4×C127—44no—
103C2×C4×C127—42no—
104C2×C4×C127—42no—
105C2×C4×C127—44no—
106C2×C4×C127—44no—
107C2×C4×C127—44no—
108C2×C4×C127—44no—
109C2×C4×C127—44no—
110C2×C4×C127—44no—
111C2×C4×C127—44no—
112C2×C4×C127—42no—
113C2×C4×C127—48no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—44no—
117C2×C4×C127—48no—
118C2×C4×C127—48no—
119C2×C4×C127#12114yes—
120C2×C4×C127#12314yes—
121C2×C4×C127#12318yes—
122C2×C4×C127#12414yes—
123C2×C4×C127#12618yes—
124C22×C127C2×#12111yescharacteristic
125C22×C127C2×#12312yes—
126C22×C127C2×#12311yescharacteristic
127C22×C127C2×#12411yescharacteristic
128C22×C127C2×#12612yes—
129C22×C127#52914yes—
130C22×C127#53212yes—
131C22×C127#53612yes—
132C22×C127#54114yes—
133C22×C127#54814yes—
134C22×C127#55214yes—
135C22×C127#55614yes—
136C22×C127#55614yes—
137C4×C127—44no—
138C4×C127—48no—
139C4×C127—44no—
140C4×C127—82no—
141C4×C127—84no—
142C4×C127#39718yes—
143#15241C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127C2×#39711yescharacteristic
145C2×C127#242114yes—
146C2×C127#249912yes—
147C2×C127#251414yes—
148C2×C127#254512yes—
149C2×C127#264211yescharacteristic
150C2×C127#286111yescharacteristic
151C2×#391C2×C12711yescharacteristic
152C2×#391C2×C12712yes—
153C2×#382C2×C12711yescharacteristic
154#1443C2×C12718yes—
155C4⋊#95C2×C12712yes—
156C4×#95C2×C12711yescharacteristic
157C127#1524111yescharacteristic, direct product factor, Sylow
158C23×Q8C22×C12711yescharacteristic
159C22×C4⋊C4C22×C12711yescharacteristic
160C22×C4⋊C4C22×C12712yes—
161C22×C42C22×C12712yes—
162C22×C42C22×C12711yescharacteristic
163#391—28no—
164#391—24no—
165#382—24no—
166C2×#95C22×C12714yes—
167C2×#95C22×C12718yes—
168C2×#95C22×C12714yes—
169C2×#95C22×C12714yes—
170C2×#95C22×C12718yes—
171C22×Q8—22no—
172C22×Q8—22no—
173C22×Q8—24no—
174C22×Q8—24no—
175C22×Q8D4×C12714yes—
176C23×C4C23×C12714yes—
177C23×C4C23×C12712yes—
178C23×C4C23×C12712yes—
179C23×C4C23×C12712yes—
180C23×C4C23×C12714yes—
181C23×C4C23×C12711yescharacteristic
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C42—24no—
188C2×C42—24no—
189C2×C42—24no—
190C2×C42—24no—
191C2×C42D4×C12714yes—
192#95—28no—
193#95—216no—
194#95—28no—
195#95—28no—
196#95—216no—
197C24C24×C12711yescharacteristic
198C2×Q8—28no—
199C2×Q8—216no—
200C2×Q8—44no—
201C2×Q8—44no—
202C2×Q8—48no—
203C22×C4—24no—
204C22×C4—22no—
205C22×C4—24no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—28no—
221C22×C4—28no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—28no—
225C22×C4C2×D4×C12714yes—
226C22×C4C2×D4×C12714yes—
227C22×C4C2×D4×C12712yes—
228C22×C4C2×D4×C12712yes—
229C22×C4#41×C12718yes—
230C22×C4#41×C12712yes—
231C22×C4#41×C12714yes—
232C22×C4#41×C12714yes—
233C4⋊C4—48no—
234C4⋊C4—44no—
235C42—28no—
236C42—48no—
237C23C22×D4×C12711yescharacteristic
238C23C22×D4×C12711yescharacteristic
239C23C2×#41×C12711yescharacteristic
240C23C2×#41×C12712yes—
241C23C2×#41×C12712yes—
242C23C2×#41×C12714yes—
243C232−1+4×C12714yes—
244Q8—416no—
245C2×C4—24no—
246C2×C4—24no—
247C2×C4—28no—
248C2×C4—28no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—28no—
252C2×C4—28no—
253C2×C4—44no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—48no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—48no—
269C2×C4—48no—
270C2×C4#121×C12714yes—
271C2×C4#123×C12714yes—
272C2×C4#123×C12718yes—
273C2×C4#124×C12714yes—
274C2×C4#126×C12718yes—
275C22C2×#121×C12711yescharacteristic
276C22C2×#123×C12712yes—
277C22C2×#123×C12711yescharacteristic
278C22C2×#124×C12711yescharacteristic
279C22C2×#126×C12712yes—
280C22#529×C12714yes—
281C22#532×C12712yes—
282C22#536×C12712yes—
283C22#541×C12714yes—
284C22#548×C12714yes—
285C22#552×C12714yes—
286C22#556×C12714yes—
287C22#556×C12714yes—
288C4—44no—
289C4—48no—
290C4—44no—
291C4—82no—
292C4—84no—
293C4#397×C12718yes—
294C2C2×#397×C12711yescharacteristic
295C2C127×#242114yes—
296C2C127×#249912yes—
297C2C127×#251414yes—
298C2C127×#254512yes—
299C2C127×#264211yescharacteristic
300C2C127×#286111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
143. #15241C127direct (N × H)
157. C127#15241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C2×#382×C1272
C127×#14432
C127×C4⋊#952
C4×#95×C1272
#15241127