Finite Group Databasebeta

← C127×#11459 #44575132

Subgroups — C127×#11459 #44575132

Order 32512.

386 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#431×C127C211yesmaximal, characteristic
2C127×#2162C212yesmaximal, complemented
3C127×#1322C212yesmaximal, complemented
4C127×#1314C212yesmaximal
5C22×C42×C127C411yescharacteristic
6#431×C127—22no—
7#431×C127—22no—
8C2×C4⋊C8×C127C411yescharacteristic
9C2×C4⋊C8×C127C2211yescharacteristic
10C2×C22⋊C8×C127C411yescharacteristic
11C2×C22⋊C8×C127C2211yescharacteristic
12C2×C4×C8×C127C411yescharacteristic
13C2×C4×C8×C127C2211yescharacteristic
14C4⋊C16×C127—22no—
15C22⋊C16×C127C2214yes—
16C4×C16×C127—22no—
17C23×C4×C127C811yescharacteristic
18C23×C4×C127C811yescharacteristic
19C23×C4×C127C2×C411yescharacteristic
20C22×C8×C127C2×C411yescharacteristic
21C22×C8×C127C2×C411yescharacteristic
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127C2311yescharacteristic
24C2×C42×C127—21no—
25C2×C42×C127—21no—
26C2×C42×C127—21no—
27C2×C42×C127—21no—
28C2×C42×C127C811yescharacteristic
29C2×C42×C127C811yescharacteristic
30C2×C42×C127C2×C411yescharacteristic
31C2×C42×C127C2×C411yescharacteristic
32C2×C16×C127—24no—
33C4⋊C8×C127—22no—
34C4⋊C8×C127—22no—
35C22⋊C8×C127—22no—
36C22⋊C8×C127—22no—
37C4×C8×C127—21no—
38C4×C8×C127—21no—
39C4×C8×C127D412yes—
40C4×C8×C127D412yes—
41C24×C127C2×C811yescharacteristic
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—22no—
45C22×C4×C127—21no—
46C22×C4×C127—21no—
47C22×C4×C127—21no—
48C22×C4×C127—21no—
49C22×C4×C127—42no—
50C22×C4×C127—41no—
51C22×C4×C127—41no—
52C22×C4×C127C1614yescomplemented
53C22×C4×C127C2×C811yescharacteristic
54C22×C4×C127C2×C811yescharacteristic
55C22×C4×C127C2×C811yescharacteristic
56C22×C4×C127C2×C811yescharacteristic
57C22×C4×C127C2×C811yescharacteristic
58C22×C4×C127C22×C411yescharacteristic
59C2×C8×C127—21no—
60C2×C8×C127—21no—
61C2×C8×C127—41no—
62C2×C8×C127—41no—
63C2×C8×C127—41no—
64C2×C8×C127—41no—
65C2×C8×C127C22⋊C412yes—
66C2×C8×C127C2×D412yes—
67C42×C127—21no—
68C42×C127—21no—
69C42×C127—21no—
70C42×C127—21no—
71C42×C127—21no—
72C42×C127—21no—
73C42×C127C22⋊C411yescharacteristic
74C42×C127C22⋊C411yescharacteristic
75C42×C127M1611yescharacteristic
76C42×C127M1611yescharacteristic
77C16×C127—44no—
78C23×C127—21no—
79C23×C127—21no—
80C23×C127—41no—
81C23×C127—41no—
82C23×C127C2×C1612yes—
83C23×C127C22×C811yescharacteristic
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—24no—
87C2×C4×C127—24no—
88C2×C4×C127—22no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—42no—
94C2×C4×C127—42no—
95C2×C4×C127—42no—
96C2×C4×C127—41no—
97C2×C4×C127—41no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127C22⋊C811yescharacteristic
101C2×C4×C127C22⋊C811yescharacteristic
102C2×C4×C127C22⋊C811yescharacteristic
103C2×C4×C127C22⋊C811yescharacteristic
104C2×C4×C127C2×C1612yes—
105C2×C4×C127C2×C1612yes—
106C2×C4×C127M3212yes—
107C2×C4×C127C2×C22⋊C411yescharacteristic
108C2×C4×C127C2×M1611yescharacteristic
109C8×C127—22no—
110C8×C127—22no—
111C8×C127—41no—
112C8×C127—41no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127—22no—
116C22×C127—42no—
117C22×C127—42no—
118C22×C127—41no—
119C22×C127—41no—
120C22×C127C2×C22⋊C811yescharacteristic
121C22×C127C22×C1611yescharacteristic
122C22×C127C2×M3211yescharacteristic
123C4×C127—22no—
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—41no—
127C4×C127—41no—
128C4×C127C22⋊C1612yes—
129C4×C127C22⋊C1612yes—
130C4×C127#34912yes—
131C4×C127#41011yescharacteristic
132C4×C127#41311yescharacteristic
133#11459C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—21no—
135C2×C127—21no—
136C2×C127—42no—
137C2×C127#145811yescharacteristic
138C2×C127C2×C22⋊C1611yescharacteristic
139C2×C127C2×#34911yescharacteristic
140C2×#431C2×C12711yescharacteristic
141#2162C2×C12712yescomplemented
142#1322C2×C12712yescomplemented
143#1314C2×C12712yes—
144C127#1145911yescharacteristic, direct product factor, Sylow
145C22×C42C4×C12711yescharacteristic
146#431—22no—
147#431—22no—
148C2×C4⋊C8C4×C12711yescharacteristic
149C2×C4⋊C8C22×C12711yescharacteristic
150C2×C22⋊C8C4×C12711yescharacteristic
151C2×C22⋊C8C22×C12711yescharacteristic
152C2×C4×C8C4×C12711yescharacteristic
153C2×C4×C8C22×C12711yescharacteristic
154C4⋊C16—22no—
155C22⋊C16C22×C12714yes—
156C4×C16—22no—
157C23×C4C8×C12711yescharacteristic
158C23×C4C8×C12711yescharacteristic
159C23×C4C2×C4×C12711yescharacteristic
160C22×C8C2×C4×C12711yescharacteristic
161C22×C8C2×C4×C12711yescharacteristic
162C22×C8C2×C4×C12711yescharacteristic
163C22×C8C23×C12711yescharacteristic
164C2×C42—21no—
165C2×C42—21no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42C8×C12711yescharacteristic
169C2×C42C8×C12711yescharacteristic
170C2×C42C2×C4×C12711yescharacteristic
171C2×C42C2×C4×C12711yescharacteristic
172C2×C16—24no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175C22⋊C8—22no—
176C22⋊C8—22no—
177C4×C8—21no—
178C4×C8—21no—
179C4×C8D4×C12712yes—
180C4×C8D4×C12712yes—
181C24C2×C8×C12711yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—42no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4C16×C12714yescomplemented
193C22×C4C2×C8×C12711yescharacteristic
194C22×C4C2×C8×C12711yescharacteristic
195C22×C4C2×C8×C12711yescharacteristic
196C22×C4C2×C8×C12711yescharacteristic
197C22×C4C2×C8×C12711yescharacteristic
198C22×C4C22×C4×C12711yescharacteristic
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8C22⋊C4×C12712yes—
206C2×C8C2×D4×C12712yes—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42C22⋊C4×C12711yescharacteristic
214C42C22⋊C4×C12711yescharacteristic
215C42M16×C12711yescharacteristic
216C42M16×C12711yescharacteristic
217C16—44no—
218C23—21no—
219C23—21no—
220C23—41no—
221C23—41no—
222C23C2×C16×C12712yes—
223C23C22×C8×C12711yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4C22⋊C8×C12711yescharacteristic
241C2×C4C22⋊C8×C12711yescharacteristic
242C2×C4C22⋊C8×C12711yescharacteristic
243C2×C4C22⋊C8×C12711yescharacteristic
244C2×C4C2×C16×C12712yes—
245C2×C4C2×C16×C12712yes—
246C2×C4M32×C12712yes—
247C2×C4C2×C22⋊C4×C12711yescharacteristic
248C2×C4C2×M16×C12711yescharacteristic
249C8—22no—
250C8—22no—
251C8—41no—
252C8—41no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22—41no—
260C22C2×C22⋊C8×C12711yescharacteristic
261C22C22×C16×C12711yescharacteristic
262C22C2×M32×C12711yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—41no—
267C4—41no—
268C4C22⋊C16×C12712yes—
269C4C22⋊C16×C12712yes—
270C4#349×C12712yes—
271C4#410×C12711yescharacteristic
272C4#413×C12711yescharacteristic
273C2—21no—
274C2—21no—
275C2—42no—
276C2C127×#145811yescharacteristic
277C2C2×C22⋊C16×C12711yescharacteristic
278C2C2×#349×C12711yescharacteristic
subgroupG/H
centerC42×C127C22⋊C4
commutatorC22C22×C16×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×C22⋊C8
prime radicalC24×C127C2×C8
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2162C2semidirect
3. C127×#1322C2semidirect
52. C22×C4×C127C16semidirect
133. #11459C127direct (N × H)
141. #2162C2×C127semidirect
142. #1322C2×C127semidirect
144. C127#11459direct (N × H)
192. C22×C4C16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#431×C1272
C127×#21622
C127×#13222
C127×#13142
#11459127