Finite Group Databasebeta

← C127×#12586 #44576259

Subgroups — C127×#12586 #44576259

Order 32512.

746 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#101×C127C212yesmaximal
2C127×#2310C211yesmaximal, characteristic
3C127×#1394C214yesmaximal, complemented
4C23×Q8×C127C2211yescharacteristic
5C22×M16×C127—22no—
6C2×#117×C127C411yescharacteristic
7C2×#117×C127C411yescharacteristic
8C2×#101×C127—22no—
9C2×#101×C127—24no—
10C2×#101×C127C418yescomplemented
11C2×#101×C127C2214yes—
12#391×C127—22no—
13#391×C127C412yes—
14#391×C127C2212yes—
15#381×C127—22no—
16C22×Q8×C127—42no—
17C22×Q8×C127—42no—
18C22×Q8×C127C2×C414yes—
19C22×Q8×C127C2×C411yescharacteristic
20C22×Q8×C127D412yes—
21C22×Q8×C127D412yes—
22C22×Q8×C127Q812yes—
23C22×Q8×C127C2311yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D412yes—
26C2×M16×C127—28no—
27C2×M16×C127—24no—
28C2×M16×C127—44no—
29C2×M16×C127—42no—
30C22×C8×C127—42no—
31#117×C127—42no—
32#117×C127—42no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2×C412yes—
35C2×C22⋊C4×C127—21no—
36C2×C22⋊C4×C127—21no—
37C2×C42×C127—21no—
38C2×C42×C127C2×C412yes—
39#101×C127—28no—
40#101×C127—24no—
41#101×C127C2×C418yes—
42#95×C127—24no—
43#95×C127—24no—
44C24×C127C22⋊C411yescharacteristic
45C2×Q8×C127—44no—
46C2×Q8×C127—44no—
47C2×Q8×C127—41no—
48C2×Q8×C127—41no—
49C2×Q8×C127—44no—
50C2×Q8×C127—42no—
51C2×Q8×C127—42no—
52C2×Q8×C127—44no—
53C2×Q8×C127—41no—
54C2×Q8×C127—41no—
55C2×Q8×C127C4212yes—
56C2×Q8×C127C22⋊C414yes—
57C2×Q8×C127C4⋊C414yes—
58C2×Q8×C127C4⋊C412yes—
59C2×Q8×C127C22×C412yes—
60C2×Q8×C127C2×D411yescharacteristic
61C2×Q8×C127C2×Q811yescharacteristic
62C22×C4×C127—22no—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—24no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127C4212yes—
70C22×C4×C127C22⋊C412yes—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C414yes—
73C22×C4×C127C4⋊C412yes—
74C22×C4×C127C4⋊C414yes—
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D412yes—
77M16×C127—28no—
78M16×C127—48no—
79M16×C127—44no—
80C2×C8×C127—48no—
81C2×C8×C127—44no—
82C4⋊C4×C127—42no—
83C4⋊C4×C127—42no—
84C22⋊C4×C127—42no—
85C22⋊C4×C127—42no—
86C42×C127—42no—
87C42×C127—42no—
88C23×C127—42no—
89C23×C127#9512yes—
90C23×C127#9912yes—
91C23×C127#9912yes—
92C23×C127C2×C22⋊C411yescharacteristic
93Q8×C127—42no—
94Q8×C127—44no—
95Q8×C127—42no—
96Q8×C127—44no—
97Q8×C127—42no—
98Q8×C127—41no—
99Q8×C127—41no—
100C2×C4×C127—24no—
101C2×C4×C127—24no—
102C2×C4×C127—24no—
103C2×C4×C127—24no—
104C2×C4×C127—24no—
105C2×C4×C127—24no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127#9512yes—
119C2×C4×C127#9514yes—
120C2×C4×C127C2×C4211yescharacteristic
121C2×C4×C127C2×C22⋊C412yes—
122C2×C4×C127C2×C4⋊C411yescharacteristic
123C2×C4×C127C2×C4⋊C412yes—
124C8×C127—48no—
125C22×C127—22no—
126C22×C127—24no—
127C22×C127—42no—
128C22×C127—42no—
129C22×C127#34214yes—
130C22×C127C2×#9511yescharacteristic
131C22×C127C2×#9911yescharacteristic
132C22×C127C2×#9911yescharacteristic
133C4×C127—22no—
134C4×C127—24no—
135C4×C127—22no—
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—22no—
139C4×C127—82no—
140C4×C127—82no—
141#12586C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—21no—
143C2×C127—24no—
144C2×C127—21no—
145C2×C127C2×#34211yescharacteristic
146C2×C127#213312yes—
147C22×#101C2×C12712yes—
148#2310C2×C12711yescharacteristic
149#1394C2×C12714yescomplemented
150C127#1258611yescharacteristic, direct product factor, Sylow
151C23×Q8C22×C12711yescharacteristic
152C22×M16—22no—
153C2×#117C4×C12711yescharacteristic
154C2×#117C4×C12711yescharacteristic
155C2×#101—22no—
156C2×#101—24no—
157C2×#101C4×C12718yescomplemented
158C2×#101C22×C12714yes—
159#391—22no—
160#391C4×C12712yes—
161#391C22×C12712yes—
162#381—22no—
163C22×Q8—42no—
164C22×Q8—42no—
165C22×Q8C2×C4×C12714yes—
166C22×Q8C2×C4×C12711yescharacteristic
167C22×Q8D4×C12712yes—
168C22×Q8D4×C12712yes—
169C22×Q8Q8×C12712yes—
170C22×Q8C23×C12711yescharacteristic
171C23×C4C2×C4×C12711yescharacteristic
172C23×C4D4×C12712yes—
173C2×M16—28no—
174C2×M16—24no—
175C2×M16—44no—
176C2×M16—42no—
177C22×C8—42no—
178#117—42no—
179#117—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×C4×C12712yes—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C42—21no—
185C2×C42C2×C4×C12712yes—
186#101—28no—
187#101—24no—
188#101C2×C4×C12718yes—
189#95—24no—
190#95—24no—
191C24C22⋊C4×C12711yescharacteristic
192C2×Q8—44no—
193C2×Q8—44no—
194C2×Q8—41no—
195C2×Q8—41no—
196C2×Q8—44no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—44no—
200C2×Q8—41no—
201C2×Q8—41no—
202C2×Q8C42×C12712yes—
203C2×Q8C22⋊C4×C12714yes—
204C2×Q8C4⋊C4×C12714yes—
205C2×Q8C4⋊C4×C12712yes—
206C2×Q8C22×C4×C12712yes—
207C2×Q8C2×D4×C12711yescharacteristic
208C2×Q8C2×Q8×C12711yescharacteristic
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4C42×C12712yes—
217C22×C4C22⋊C4×C12712yes—
218C22×C4C22⋊C4×C12711yescharacteristic
219C22×C4C22⋊C4×C12714yes—
220C22×C4C4⋊C4×C12712yes—
221C22×C4C4⋊C4×C12714yes—
222C22×C4C22×C4×C12711yescharacteristic
223C22×C4C2×D4×C12712yes—
224M16—28no—
225M16—48no—
226M16—44no—
227C2×C8—48no—
228C2×C8—44no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C42—42no—
234C42—42no—
235C23—42no—
236C23#95×C12712yes—
237C23#99×C12712yes—
238C23#99×C12712yes—
239C23C2×C22⋊C4×C12711yescharacteristic
240Q8—42no—
241Q8—44no—
242Q8—42no—
243Q8—44no—
244Q8—42no—
245Q8—41no—
246Q8—41no—
247C2×C4—24no—
248C2×C4—24no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—44no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4#95×C12712yes—
266C2×C4#95×C12714yes—
267C2×C4C2×C42×C12711yescharacteristic
268C2×C4C2×C22⋊C4×C12712yes—
269C2×C4C2×C4⋊C4×C12711yescharacteristic
270C2×C4C2×C4⋊C4×C12712yes—
271C8—48no—
272C22—22no—
273C22—24no—
274C22—42no—
275C22—42no—
276C22#342×C12714yes—
277C22C2×#95×C12711yescharacteristic
278C22C2×#99×C12711yescharacteristic
279C22C2×#99×C12711yescharacteristic
280C4—22no—
281C4—24no—
282C4—22no—
283C4—21no—
284C4—21no—
285C4—22no—
286C4—82no—
287C4—82no—
288C2—21no—
289C2—24no—
290C2—21no—
291C2C2×#342×C12711yescharacteristic
292C2C127×#213312yes—
subgroupG/H
center, socleC22×C127C2×#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×Q8C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C23×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1394C2semidirect
10. C2×#101×C127C4semidirect
141. #12586C127direct (N × H)
149. #1394C2×C127semidirect
150. C127#12586direct (N × H)
157. C2×#101C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#101×C1272
C127×#23102
C127×#13942
#12586127