Finite Group Databasebeta

← C127×#7037 #44570710

Subgroups — C127×#7037 #44570710

Order 32512.

476 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1817C211yesmaximal, characteristic
2C127×#1728C211yesmaximal, characteristic
3C127×#1434C211yesmaximal, characteristic
4C22×M16×C127—21no—
5C22×C42×C127C2211yescharacteristic
6C2×C22⋊C8×C127—21no—
7C2×#95×C127—21no—
8C2×#95×C127—21no—
9C2×#95×C127C412yes—
10#336×C127—21no—
11#336×C127—21no—
12#336×C127C412yescomplemented
13#336×C127C412yescomplemented
14C23×C4×C127—22no—
15C23×C4×C127C2×C411yescharacteristic
16C23×C4×C127D411yescharacteristic
17C23×C4×C127D411yescharacteristic
18C2×M16×C127—24no—
19C2×M16×C127—42no—
20C2×M16×C127—41no—
21C2×M16×C127—41no—
22C22×C8×C127—22no—
23C22×C8×C127—22no—
24C2×C42×C127—42no—
25C2×C42×C127C2×C411yescharacteristic
26C2×C42×C127C2×C411yescharacteristic
27C2×C42×C127D411yescharacteristic
28C2×C42×C127Q811yescharacteristic
29C22⋊C8×C127—42no—
30#95×C127—24no—
31#95×C127—42no—
32#95×C127—41no—
33#95×C127—41no—
34C24×C127C22⋊C411yescharacteristic
35C22×C4×C127—22no—
36C22×C4×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127—22no—
40C22×C4×C127—24no—
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×C127D811yescharacteristic
57C22×C4×C127SD1611yescharacteristic
58C22×C4×C127SD1611yescharacteristic
59C22×C4×C127Q1611yescharacteristic
60M16×C127—44no—
61M16×C127—44no—
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—41no—
69C42×C127—41no—
70C42×C127—41no—
71C42×C127—41no—
72C23×C127—21no—
73C23×C127—21no—
74C23×C127—21no—
75C23×C127—21no—
76C23×C127#9511yescharacteristic
77C23×C127#9912yes—
78C23×C127#10211yescharacteristic
79C23×C127#10311yescharacteristic
80C23×C127#10412yes—
81C2×C4×C127—22no—
82C2×C4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
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—21no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—44no—
101C2×C4×C127—44no—
102C2×C4×C127—44no—
103C2×C4×C127—44no—
104C2×C4×C127—44no—
105C2×C4×C127—82no—
106C2×C4×C127—82no—
107C2×C4×C127—82no—
108C2×C4×C127—82no—
109C2×C4×C127#10211yescharacteristic
110C2×C4×C127#10311yescharacteristic
111C2×C4×C127#10412yes—
112C2×C4×C127#10611yescharacteristic
113C2×C4×C127#10711yescharacteristic
114C8×C127—44no—
115C8×C127—82no—
116C22×C127—22no—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—22no—
120C22×C127—22no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—22no—
124C22×C127#32712yes—
125C22×C127#32812yes—
126C22×C127H(3,ℤ/4)11yescharacteristic
127C22×C127#33911yescharacteristic
128C22×C127#33911yescharacteristic
129C22×C127#34011yescharacteristic
130C22×C127#34211yescharacteristic
131C22×C127#34411yescharacteristic
132C22×C127#34411yescharacteristic
133C4×C127—22no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—41no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—84no—
142#7037C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—22no—
144C2×C127—22no—
145C2×C127#128411yescharacteristic
146C2×C127#128611yescharacteristic
147C2×C127#128811yescharacteristic
148C2×C127#129411yescharacteristic
149C2×C127#130011yescharacteristic
150C2×C127#130311yescharacteristic
151C2×C127#130611yescharacteristic
152#1817C2×C12711yescharacteristic
153#1728C2×C12711yescharacteristic
154#1434C2×C12711yescharacteristic
155C127#703711yescharacteristic, direct product factor, Sylow
156C22×M16—21no—
157C22×C42C22×C12711yescharacteristic
158C2×C22⋊C8—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95C4×C12712yes—
162#336—21no—
163#336—21no—
164#336C4×C12712yescomplemented
165#336C4×C12712yescomplemented
166C23×C4—22no—
167C23×C4C2×C4×C12711yescharacteristic
168C23×C4D4×C12711yescharacteristic
169C23×C4D4×C12711yescharacteristic
170C2×M16—24no—
171C2×M16—42no—
172C2×M16—41no—
173C2×M16—41no—
174C22×C8—22no—
175C22×C8—22no—
176C2×C42—42no—
177C2×C42C2×C4×C12711yescharacteristic
178C2×C42C2×C4×C12711yescharacteristic
179C2×C42D4×C12711yescharacteristic
180C2×C42Q8×C12711yescharacteristic
181C22⋊C8—42no—
182#95—24no—
183#95—42no—
184#95—41no—
185#95—41no—
186C24C22⋊C4×C12711yescharacteristic
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—24no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4—42no—
198C22×C4—42no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4C42×C12711yescharacteristic
203C22×C4C22⋊C4×C12711yescharacteristic
204C22×C4C22⋊C4×C12711yescharacteristic
205C22×C4C4⋊C4×C12711yescharacteristic
206C22×C4C4⋊C4×C12711yescharacteristic
207C22×C4C4⋊C4×C12711yescharacteristic
208C22×C4D8×C12711yescharacteristic
209C22×C4SD16×C12711yescharacteristic
210C22×C4SD16×C12711yescharacteristic
211C22×C4Q16×C12711yescharacteristic
212M16—44no—
213M16—44no—
214C2×C8—24no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C2×C8—42no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—21no—
228C23#95×C12711yescharacteristic
229C23#99×C12712yes—
230C23#102×C12711yescharacteristic
231C23#103×C12711yescharacteristic
232C23#104×C12712yes—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
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—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4#102×C12711yescharacteristic
262C2×C4#103×C12711yescharacteristic
263C2×C4#104×C12712yes—
264C2×C4#106×C12711yescharacteristic
265C2×C4#107×C12711yescharacteristic
266C8—44no—
267C8—82no—
268C22—22no—
269C22—22no—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22#327×C12712yes—
277C22#328×C12712yes—
278C22H(3,ℤ/4)×C12711yescharacteristic
279C22#339×C12711yescharacteristic
280C22#339×C12711yescharacteristic
281C22#340×C12711yescharacteristic
282C22#342×C12711yescharacteristic
283C22#344×C12711yescharacteristic
284C22#344×C12711yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—84no—
294C2—22no—
295C2—22no—
296C2C127×#128411yescharacteristic
297C2C127×#128611yescharacteristic
298C2C127×#128811yescharacteristic
299C2C127×#129411yescharacteristic
300C2C127×#130011yescharacteristic
301C2C127×#130311yescharacteristic
302C2C127×#130611yescharacteristic
subgroupG/H
center, socleC23×C127#95
commutatorC22×C4C42×C127
Frattini, cosocleC22×C42C22×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
12. #336×C127C4semidirect
13. #336×C127C4semidirect
142. #7037C127direct (N × H)
155. C127#7037direct (N × H)
164. #336C4×C127semidirect
165. #336C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#18172
C127×#17282
C127×#14342
#7037127