Finite Group Databasebeta

← C127×#15240 #44578913

Subgroups — C127×#15240 #44578913

Order 32512.

1430 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C2×#391×C127C211yesmaximal, characteristic
3C2×#384×C127C211yesmaximal, characteristic
4C2×#382×C127C212yesmaximal
5C127×#1445C218yesmaximal
6C4×#95×C127C211yesmaximal, characteristic
7C23×Q8×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2214yes—
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2212yes—
11C22×C42×C127C2212yes—
12C22×C42×C127C2211yescharacteristic
13#391×C127—28no—
14#391×C127—24no—
15#384×C127—24no—
16#382×C127—28no—
17C2×#95×C127C2214yes—
18C2×#95×C127C2218yes—
19C2×#95×C127C2218yes—
20C2×#95×C127C2214yes—
21C22×Q8×C127—22no—
22C22×Q8×C127—24no—
23C22×Q8×C127—24no—
24C22×Q8×C127—22no—
25C22×Q8×C127Q814yes—
26C23×C4×C127C2314yes—
27C23×C4×C127C2312yes—
28C23×C4×C127C2314yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2311yescharacteristic
32C2×C4⋊C4×C127—24no—
33C2×C4⋊C4×C127—24no—
34C2×C4⋊C4×C127—28no—
35C2×C4⋊C4×C127—24no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—24no—
38C2×C4⋊C4×C127—216no—
39C2×C42×C127—24no—
40C2×C42×C127—24no—
41C2×C42×C127—24no—
42C2×C42×C127D418yes—
43C2×C42×C127D414yes—
44#95×C127—216no—
45#95×C127—216no—
46#95×C127—28no—
47#95×C127—28no—
48C24×C127C2411yescharacteristic
49C2×Q8×C127—216no—
50C2×Q8×C127—28no—
51C2×Q8×C127—48no—
52C2×Q8×C127—44no—
53C2×Q8×C127—44no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—22no—
57C22×C4×C127—24no—
58C22×C4×C127—28no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—22no—
63C22×C4×C127—28no—
64C22×C4×C127—24no—
65C22×C4×C127—24no—
66C22×C4×C127—22no—
67C22×C4×C127—24no—
68C22×C4×C127—24no—
69C22×C4×C127—216no—
70C22×C4×C127—28no—
71C22×C4×C127C2×D418yes—
72C22×C4×C127C2×D414yes—
73C22×C4×C127C2×D412yes—
74C22×C4×C127C2×D414yes—
75C22×C4×C127C2×Q814yes—
76C22×C4×C127C2×Q812yes—
77C22×C4×C127#4118yes—
78C22×C4×C127#4114yes—
79C22×C4×C127#4112yes—
80C4⋊C4×C127—416no—
81C4⋊C4×C127—44no—
82C4⋊C4×C127—48no—
83C42×C127—28no—
84C42×C127—216no—
85C23×C127C22×D411yescharacteristic
86C23×C127C22×D412yes—
87C23×C127C22×Q811yescharacteristic
88C23×C127C2×#4112yes—
89C23×C127C2×#4111yescharacteristic
90C23×C127C2×#4114yes—
91C23×C1272−1+414yes—
92Q8×C127—416no—
93C2×C4×C127—24no—
94C2×C4×C127—24no—
95C2×C4×C127—216no—
96C2×C4×C127—28no—
97C2×C4×C127—24no—
98C2×C4×C127—28no—
99C2×C4×C127—28no—
100C2×C4×C127—28no—
101C2×C4×C127—44no—
102C2×C4×C127—42no—
103C2×C4×C127—42no—
104C2×C4×C127—48no—
105C2×C4×C127—48no—
106C2×C4×C127—48no—
107C2×C4×C127—44no—
108C2×C4×C127—42no—
109C2×C4×C127—48no—
110C2×C4×C127—48no—
111C2×C4×C127—48no—
112C2×C4×C127—44no—
113C2×C4×C127C22⋊Q818yes—
114C2×C4×C127C22⋊Q814yes—
115C2×C4×C127#12318yes—
116C2×C4×C127#12314yes—
117C2×C4×C127#12418yes—
118C2×C4×C127#12714yes—
119C22×C127C2×C22⋊Q812yes—
120C22×C127C2×C22⋊Q811yescharacteristic
121C22×C127C2×#12312yes—
122C22×C127C2×#12311yescharacteristic
123C22×C127C2×#12412yes—
124C22×C127C2×#12711yescharacteristic
125C22×C127#53214yes—
126C22×C127#53614yes—
127C22×C127#53612yes—
128C22×C127#55218yes—
129C22×C127#55614yes—
130C22×C127#55714yes—
131C4×C127—28no—
132C4×C127—44no—
133C4×C127—48no—
134C4×C127—84no—
135C4×C127—82no—
136C4×C127#39918yes—
137#15240C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127C2×#39911yescharacteristic
139C2×C127#249914yes—
140C2×C127#250312yes—
141C2×C127#256514yes—
142C2×C127#256812yes—
143C2×C127#265811yescharacteristic
144C2×C127#285811yescharacteristic
145C2×#391C2×C12711yescharacteristic
146C2×#391C2×C12712yes—
147C2×#384C2×C12711yescharacteristic
148C2×#382C2×C12712yes—
149#1445C2×C12718yes—
150C4×#95C2×C12711yescharacteristic
151C127#1524011yescharacteristic, direct product factor, Sylow
152C23×Q8C22×C12711yescharacteristic
153C22×C4⋊C4C22×C12714yes—
154C22×C4⋊C4C22×C12711yescharacteristic
155C22×C4⋊C4C22×C12712yes—
156C22×C42C22×C12712yes—
157C22×C42C22×C12711yescharacteristic
158#391—28no—
159#391—24no—
160#384—24no—
161#382—28no—
162C2×#95C22×C12714yes—
163C2×#95C22×C12718yes—
164C2×#95C22×C12718yes—
165C2×#95C22×C12714yes—
166C22×Q8—22no—
167C22×Q8—24no—
168C22×Q8—24no—
169C22×Q8—22no—
170C22×Q8Q8×C12714yes—
171C23×C4C23×C12714yes—
172C23×C4C23×C12712yes—
173C23×C4C23×C12714yes—
174C23×C4C23×C12712yes—
175C23×C4C23×C12712yes—
176C23×C4C23×C12711yescharacteristic
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—216no—
184C2×C42—24no—
185C2×C42—24no—
186C2×C42—24no—
187C2×C42D4×C12718yes—
188C2×C42D4×C12714yes—
189#95—216no—
190#95—216no—
191#95—28no—
192#95—28no—
193C24C24×C12711yescharacteristic
194C2×Q8—28no—
195C2×Q8—216no—
196C2×Q8—48no—
197C2×Q8—44no—
198C2×Q8—44no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—22no—
202C22×C4—24no—
203C22×C4—28no—
204C22×C4—24no—
205C22×C4—24no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—28no—
209C22×C4—24no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—216no—
215C22×C4—28no—
216C22×C4C2×D4×C12718yes—
217C22×C4C2×D4×C12714yes—
218C22×C4C2×D4×C12712yes—
219C22×C4C2×D4×C12714yes—
220C22×C4C2×Q8×C12714yes—
221C22×C4C2×Q8×C12712yes—
222C22×C4#41×C12718yes—
223C22×C4#41×C12714yes—
224C22×C4#41×C12712yes—
225C4⋊C4—416no—
226C4⋊C4—44no—
227C4⋊C4—48no—
228C42—28no—
229C42—216no—
230C23C22×D4×C12711yescharacteristic
231C23C22×D4×C12712yes—
232C23C22×Q8×C12711yescharacteristic
233C23C2×#41×C12712yes—
234C23C2×#41×C12711yescharacteristic
235C23C2×#41×C12714yes—
236C232−1+4×C12714yes—
237Q8—416no—
238C2×C4—24no—
239C2×C4—24no—
240C2×C4—216no—
241C2×C4—24no—
242C2×C4—28no—
243C2×C4—28no—
244C2×C4—28no—
245C2×C4—28no—
246C2×C4—44no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—48no—
250C2×C4—48no—
251C2×C4—48no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—48no—
255C2×C4—48no—
256C2×C4—44no—
257C2×C4—48no—
258C2×C4C22⋊Q8×C12714yes—
259C2×C4C22⋊Q8×C12718yes—
260C2×C4#123×C12718yes—
261C2×C4#123×C12714yes—
262C2×C4#124×C12718yes—
263C2×C4#127×C12714yes—
264C22C2×C22⋊Q8×C12711yescharacteristic
265C22C2×C22⋊Q8×C12712yes—
266C22C2×#123×C12712yes—
267C22C2×#123×C12711yescharacteristic
268C22C2×#124×C12712yes—
269C22C2×#127×C12711yescharacteristic
270C22#532×C12714yes—
271C22#536×C12712yes—
272C22#536×C12714yes—
273C22#552×C12718yes—
274C22#556×C12714yes—
275C22#557×C12714yes—
276C4—28no—
277C4—44no—
278C4—48no—
279C4—84no—
280C4—82no—
281C4#399×C12718yes—
282C2C2×#399×C12711yescharacteristic
283C2C127×#249914yes—
284C2C127×#250312yes—
285C2C127×#256514yes—
286C2C127×#256812yes—
287C2C127×#265811yescharacteristic
288C2C127×#285811yescharacteristic
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
137. #15240C127direct (N × H)
151. C127#15240direct (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×#384×C1272
C2×#382×C1272
C127×#14452
C4×#95×C1272
#15240127