Finite Group Databasebeta

← C127×#7024 #44570697

Subgroups — C127×#7024 #44570697

Order 32512.

468 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1797C211yesmaximal, characteristic
2C4×C22⋊C8×C127C211yesmaximal, characteristic
3C127×#1434C211yesmaximal, characteristic
4C22×C42×C127C2211yescharacteristic
5C2×C4⋊C8×C127—21no—
6C2×C22⋊C8×C127—21no—
7C2×C22⋊C8×C127—21no—
8C2×C4×C8×C127C412yescomplemented
9C2×#95×C127—21no—
10C2×#95×C127—21no—
11C2×#95×C127C412yes—
12#336×C127—21no—
13#336×C127C412yescomplemented
14C23×C4×C127—22no—
15C23×C4×C127C2×C411yescharacteristic
16C23×C4×C127D411yescharacteristic
17C23×C4×C127D411yescharacteristic
18C22×C8×C127—22no—
19C22×C8×C127—22no—
20C2×C42×C127—42no—
21C2×C42×C127C2×C411yescharacteristic
22C2×C42×C127C2×C411yescharacteristic
23C2×C42×C127D411yescharacteristic
24C2×C42×C127Q811yescharacteristic
25C4⋊C8×C127—42no—
26C22⋊C8×C127—24no—
27C22⋊C8×C127—41no—
28C22⋊C8×C127—41no—
29C4×C8×C127—42no—
30#95×C127—22no—
31#95×C127—42no—
32#95×C127—41no—
33#95×C127—41no—
34#95×C127C814yescomplemented
35C24×C127C22⋊C411yescharacteristic
36C22×C4×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—24no—
39C22×C4×C127—41no—
40C22×C4×C127—41no—
41C22×C4×C127—41no—
42C22×C4×C127—41no—
43C22×C4×C127—41no—
44C22×C4×C127—42no—
45C22×C4×C127—42no—
46C22×C4×C127—42no—
47C22×C4×C127—42no—
48C22×C4×C127—42no—
49C22×C4×C127—42no—
50C22×C4×C127C4211yescharacteristic
51C22×C4×C127C22⋊C411yescharacteristic
52C22×C4×C127C22⋊C411yescharacteristic
53C22×C4×C127C4⋊C411yescharacteristic
54C22×C4×C127C4⋊C411yescharacteristic
55C22×C4×C127C4⋊C411yescharacteristic
56C22×C4×C127C2×C812yes—
57C22×C4×C127M1612yes—
58C22×C4×C127D811yescharacteristic
59C22×C4×C127SD1611yescharacteristic
60C22×C4×C127SD1611yescharacteristic
61C22×C4×C127Q1611yescharacteristic
62C2×C8×C127—24no—
63C2×C8×C127—42no—
64C2×C8×C127—42no—
65C2×C8×C127—42no—
66C2×C8×C127—42no—
67C2×C8×C127—42no—
68C42×C127—22no—
69C42×C127—22no—
70C42×C127—41no—
71C42×C127—41no—
72C23×C127—21no—
73C23×C127—21no—
74C23×C127—21no—
75C23×C127—21no—
76C23×C127#9511yescharacteristic
77C23×C127C22⋊C812yes—
78C23×C127#10211yescharacteristic
79C23×C127#10311yescharacteristic
80C23×C127#10412yes—
81C2×C4×C127—21no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
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×C127—44no—
101C2×C4×C127—44no—
102C2×C4×C127—44no—
103C2×C4×C127—44no—
104C2×C4×C127—82no—
105C2×C4×C127—82no—
106C2×C4×C127—82no—
107C2×C4×C127—82no—
108C2×C4×C127C4×C811yescharacteristic
109C2×C4×C127#9711yescharacteristic
110C2×C4×C127#9912yes—
111C2×C4×C127#10211yescharacteristic
112C2×C4×C127#10311yescharacteristic
113C2×C4×C127C4⋊C812yes—
114C2×C4×C127#10611yescharacteristic
115C2×C4×C127#10711yescharacteristic
116C8×C127—44no—
117C8×C127—82no—
118C22×C127—22no—
119C22×C127—22no—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—22no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—22no—
126C22×C127D4⋊C812yes—
127C22×C127Q8⋊C812yes—
128C22×C127#33611yescharacteristic
129C22×C127H(3,ℤ/4)11yescharacteristic
130C22×C127H(3,ℤ/4)11yescharacteristic
131C22×C127#33911yescharacteristic
132C22×C127#34011yescharacteristic
133C22×C127#34211yescharacteristic
134C22×C127#34411yescharacteristic
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—22no—
138C4×C127—22no—
139C4×C127—21no—
140C4×C127—21no—
141C4×C127—21no—
142C4×C127—21no—
143C4×C127—41no—
144C4×C127—84no—
145#7024C12711yesmaximal, characteristic, direct product factor, Sylow
146C2×C127—22no—
147C2×C127—22no—
148C2×C127#127411yescharacteristic
149C2×C127#127911yescharacteristic
150C2×C127#128211yescharacteristic
151C2×C127#128411yescharacteristic
152C2×C127#128611yescharacteristic
153C2×C127#128811yescharacteristic
154C2×C127#128911yescharacteristic
155#1797C2×C12711yescharacteristic
156C4×C22⋊C8C2×C12711yescharacteristic
157#1434C2×C12711yescharacteristic
158C127#702411yescharacteristic, direct product factor, Sylow
159C22×C42C22×C12711yescharacteristic
160C2×C4⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C4×C8C4×C12712yescomplemented
164C2×#95—21no—
165C2×#95—21no—
166C2×#95C4×C12712yes—
167#336—21no—
168#336C4×C12712yescomplemented
169C23×C4—22no—
170C23×C4C2×C4×C12711yescharacteristic
171C23×C4D4×C12711yescharacteristic
172C23×C4D4×C12711yescharacteristic
173C22×C8—22no—
174C22×C8—22no—
175C2×C42—42no—
176C2×C42C2×C4×C12711yescharacteristic
177C2×C42C2×C4×C12711yescharacteristic
178C2×C42D4×C12711yescharacteristic
179C2×C42Q8×C12711yescharacteristic
180C4⋊C8—42no—
181C22⋊C8—24no—
182C22⋊C8—41no—
183C22⋊C8—41no—
184C4×C8—42no—
185#95—22no—
186#95—42no—
187#95—41no—
188#95—41no—
189#95C8×C12714yescomplemented
190C24C22⋊C4×C12711yescharacteristic
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—24no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4C42×C12711yescharacteristic
206C22×C4C22⋊C4×C12711yescharacteristic
207C22×C4C22⋊C4×C12711yescharacteristic
208C22×C4C4⋊C4×C12711yescharacteristic
209C22×C4C4⋊C4×C12711yescharacteristic
210C22×C4C4⋊C4×C12711yescharacteristic
211C22×C4C2×C8×C12712yes—
212C22×C4M16×C12712yes—
213C22×C4D8×C12711yescharacteristic
214C22×C4SD16×C12711yescharacteristic
215C22×C4SD16×C12711yescharacteristic
216C22×C4Q16×C12711yescharacteristic
217C2×C8—24no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C42—22no—
224C42—22no—
225C42—41no—
226C42—41no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23#95×C12711yescharacteristic
232C23C22⋊C8×C12712yes—
233C23#102×C12711yescharacteristic
234C23#103×C12711yescharacteristic
235C23#104×C12712yes—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4C4×C8×C12711yescharacteristic
264C2×C4#97×C12711yescharacteristic
265C2×C4#99×C12712yes—
266C2×C4#102×C12711yescharacteristic
267C2×C4#103×C12711yescharacteristic
268C2×C4C4⋊C8×C12712yes—
269C2×C4#106×C12711yescharacteristic
270C2×C4#107×C12711yescharacteristic
271C8—44no—
272C8—82no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—21no—
280C22—21no—
281C22D4⋊C8×C12712yes—
282C22Q8⋊C8×C12712yes—
283C22#336×C12711yescharacteristic
284C22H(3,ℤ/4)×C12711yescharacteristic
285C22H(3,ℤ/4)×C12711yescharacteristic
286C22#339×C12711yescharacteristic
287C22#340×C12711yescharacteristic
288C22#342×C12711yescharacteristic
289C22#344×C12711yescharacteristic
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—22no—
297C4—22no—
298C4—41no—
299C4—84no—
300C2—22no—
301C2—22no—
302C2C127×#127411yescharacteristic
303C2C127×#127911yescharacteristic
304C2C127×#128211yescharacteristic
305C2C127×#128411yescharacteristic
306C2C127×#128611yescharacteristic
307C2C127×#128811yescharacteristic
308C2C127×#128911yescharacteristic
subgroupG/H
center, socleC23×C127#95
commutatorC2×C4C4×C8×C127
Frattini, cosocleC22×C42C22×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. C2×C4×C8×C127C4semidirect
13. #336×C127C4semidirect
34. #95×C127C8semidirect
145. #7024C127direct (N × H)
158. C127#7024direct (N × H)
163. C2×C4×C8C4×C127semidirect
168. #336C4×C127semidirect
189. #95C8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#17972
C4×C22⋊C8×C1272
C127×#14342
#7024127