Finite Group Databasebeta

← C127×#20479 #44584152

Subgroups — C127×#20479 #44584152

Order 32512.

1034 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
1C2×#432×C127C211yesmaximal, characteristic
2C22×#97×C127C211yesmaximal, characteristic
3C4×#117×C127C211yesmaximal, characteristic
4C127×#1771C214yesmaximal, complemented
5C127×#1752C212yesmaximal
6C8×C22⋊C4×C127C212yesmaximal
7C127×#1745C212yesmaximal, complemented
8C4×#97×C127C212yesmaximal, complemented
9C23×C8×C127C2212yes—
10C2×#117×C127C412yes—
11C22×C42×C127C2211yescharacteristic
12#432×C127C418yescomplemented
13C2×C4⋊C8×C127C2212yes—
14C2×C22⋊C8×C127C2212yes—
15C2×#97×C127C418yescomplemented
16C2×#97×C127C2214yes—
17C2×#97×C127C2211yescharacteristic
18C2×#97×C127C2211yescharacteristic
19C2×#97×C127C2212yes—
20C2×#97×C127C2212yes—
21C2×C4×C8×C127C2214yes—
22C4×C4⋊C4×C127C412yes—
23C4×C4⋊C4×C127C2212yes—
24C4×C22⋊C4×C127C412yes—
25C4×C22⋊C4×C127C2211yescharacteristic
26C4×C22⋊C4×C127C2211yescharacteristic
27#376×C127C412yes—
28C43×C127C2212yes—
29#336×C127C2214yes—
30#336×C127C2214yes—
31C23×C4×C127C2×C411yescharacteristic
32C23×C4×C127C2×C411yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C22×C8×C127—28no—
35C22×C8×C127C2×C418yes—
36C22×C8×C127C2312yes—
37C22×C8×C127C2314yes—
38C22×C8×C127C2312yes—
39#117×C127—28no—
40C2×C4⋊C4×C127C2×C414yes—
41C2×C22⋊C4×C127C2×C412yes—
42C2×C22⋊C4×C127C2×C412yes—
43C2×C42×C127C2×C414yes—
44C2×C42×C127C2×C414yes—
45C2×C42×C127C2×C411yescharacteristic
46C2×C42×C127C2×C411yescharacteristic
47C2×C42×C127C2×C414yes—
48C2×C42×C127C2×C414yes—
49C2×C42×C127C2312yes—
50C2×C42×C127C2312yes—
51C2×C42×C127C2311yescharacteristic
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127C2×C418yes—
54C22⋊C8×C127C2×C418yes—
55#97×C127—28no—
56#97×C127C2×C414yes—
57#97×C127C2×C418yes—
58#97×C127C2×C414yes—
59#97×C127C2×C418yes—
60C4×C8×C127—28no—
61#95×C127C2×C414yes—
62#95×C127C2×C412yes—
63#95×C127C2×C412yes—
64C24×C127C22×C411yescharacteristic
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—42no—
68C22×C4×C127C4214yes—
69C22×C4×C127C4214yes—
70C22×C4×C127C22×C414yes—
71C22×C4×C127C22×C411yescharacteristic
72C22×C4×C127C22×C411yescharacteristic
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C22×C412yes—
77C22×C4×C127C22×C412yes—
78C22×C4×C127C22×C414yes—
79C22×C4×C127C2411yescharacteristic
80C2×C8×C127—24no—
81C2×C8×C127—24no—
82C2×C8×C127—24no—
83C2×C8×C127—216no—
84C2×C8×C127C22×C414yes—
85C2×C8×C127C22×C418yes—
86C2×C8×C127C22×C414yes—
87C2×C8×C127#4118yes—
88C4⋊C4×C127—28no—
89C22⋊C4×C127—24no—
90C22⋊C4×C127M1618yes—
91C42×C127—28no—
92C42×C127—24no—
93C42×C127—24no—
94C42×C127—44no—
95C42×C127C4214yes—
96C42×C127C4214yes—
97C42×C127C22×C412yes—
98C42×C127C22×C412yes—
99C42×C127C22×C412yes—
100C42×C127C22×C412yes—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127C2×C4212yes—
104C23×C127C2×M1614yes—
105C23×C127C23×C411yescharacteristic
106C2×C4×C127—24no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—24no—
112C2×C4×C127—22no—
113C2×C4×C127—28no—
114C2×C4×C127—24no—
115C2×C4×C127—24no—
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—24no—
119C2×C4×C127—44no—
120C2×C4×C127C2×C4212yes—
121C2×C4×C127C2×C4212yes—
122C2×C4×C127C2×C4212yes—
123C2×C4×C127C2×C4212yes—
124C2×C4×C127C2×C4212yes—
125C2×C4×C127C2×M1618yes—
126C2×C4×C127C23×C411yescharacteristic
127C2×C4×C127C23×C411yescharacteristic
128C2×C4×C127C2×#4114yes—
129C8×C127—24no—
130C8×C127—28no—
131C8×C127#11718yescomplemented
132C22×C127—22no—
133C22×C127—28no—
134C22×C127—22no—
135C22×C127C4×M1614yes—
136C22×C127C22×C4211yescharacteristic
137C22×C127C4×#4112yes—
138C22×C127C22×M1612yes—
139C22×C127#56812yes—
140C4×C127—22no—
141C4×C127—22no—
142C4×C127—22no—
143C4×C127—22no—
144C4×C127—28no—
145C4×C127—22no—
146C4×C127—44no—
147C4×C127C2×#11712yes—
148C4×C127C4×#4112yes—
149#20479C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—24no—
151C2×C127C4×#11711yescharacteristic
152C2×C127C2×C4×M1611yescharacteristic
153C2×C127#287311yescharacteristic
154C2×C127#297014yes—
155C2×#432C2×C12711yescharacteristic
156C22×#97C2×C12711yescharacteristic
157C4×#117C2×C12711yescharacteristic
158#1771C2×C12714yescomplemented
159#1752C2×C12712yes—
160C8×C22⋊C4C2×C12712yes—
161#1745C2×C12712yescomplemented
162C4×#97C2×C12712yescomplemented
163C127#2047911yescharacteristic, direct product factor, Sylow
164C23×C8C22×C12712yes—
165C2×#117C4×C12712yes—
166C22×C42C22×C12711yescharacteristic
167#432C4×C12718yescomplemented
168C2×C4⋊C8C22×C12712yes—
169C2×C22⋊C8C22×C12712yes—
170C2×#97C4×C12718yescomplemented
171C2×#97C22×C12714yes—
172C2×#97C22×C12711yescharacteristic
173C2×#97C22×C12711yescharacteristic
174C2×#97C22×C12712yes—
175C2×#97C22×C12712yes—
176C2×C4×C8C22×C12714yes—
177C4×C4⋊C4C4×C12712yes—
178C4×C4⋊C4C22×C12712yes—
179C4×C22⋊C4C4×C12712yes—
180C4×C22⋊C4C22×C12711yescharacteristic
181C4×C22⋊C4C22×C12711yescharacteristic
182#376C4×C12712yes—
183C43C22×C12712yes—
184#336C22×C12714yes—
185#336C22×C12714yes—
186C23×C4C2×C4×C12711yescharacteristic
187C23×C4C2×C4×C12711yescharacteristic
188C23×C4C23×C12711yescharacteristic
189C22×C8—28no—
190C22×C8C2×C4×C12718yes—
191C22×C8C23×C12712yes—
192C22×C8C23×C12714yes—
193C22×C8C23×C12712yes—
194#117—28no—
195C2×C4⋊C4C2×C4×C12714yes—
196C2×C22⋊C4C2×C4×C12712yes—
197C2×C22⋊C4C2×C4×C12712yes—
198C2×C42C2×C4×C12714yes—
199C2×C42C2×C4×C12714yes—
200C2×C42C2×C4×C12711yescharacteristic
201C2×C42C2×C4×C12711yescharacteristic
202C2×C42C2×C4×C12714yes—
203C2×C42C2×C4×C12714yes—
204C2×C42C23×C12712yes—
205C2×C42C23×C12712yes—
206C2×C42C23×C12711yescharacteristic
207C2×C42C23×C12711yescharacteristic
208C4⋊C8C2×C4×C12718yes—
209C22⋊C8C2×C4×C12718yes—
210#97—28no—
211#97C2×C4×C12714yes—
212#97C2×C4×C12718yes—
213#97C2×C4×C12714yes—
214#97C2×C4×C12718yes—
215C4×C8—28no—
216#95C2×C4×C12714yes—
217#95C2×C4×C12712yes—
218#95C2×C4×C12712yes—
219C24C22×C4×C12711yescharacteristic
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—42no—
223C22×C4C42×C12714yes—
224C22×C4C42×C12714yes—
225C22×C4C22×C4×C12714yes—
226C22×C4C22×C4×C12711yescharacteristic
227C22×C4C22×C4×C12711yescharacteristic
228C22×C4C22×C4×C12711yescharacteristic
229C22×C4C22×C4×C12711yescharacteristic
230C22×C4C22×C4×C12711yescharacteristic
231C22×C4C22×C4×C12712yes—
232C22×C4C22×C4×C12712yes—
233C22×C4C22×C4×C12714yes—
234C22×C4C24×C12711yescharacteristic
235C2×C8—24no—
236C2×C8—24no—
237C2×C8—24no—
238C2×C8—216no—
239C2×C8C22×C4×C12714yes—
240C2×C8C22×C4×C12718yes—
241C2×C8C22×C4×C12714yes—
242C2×C8#41×C12718yes—
243C4⋊C4—28no—
244C22⋊C4—24no—
245C22⋊C4M16×C12718yes—
246C42—28no—
247C42—24no—
248C42—24no—
249C42—44no—
250C42C42×C12714yes—
251C42C42×C12714yes—
252C42C22×C4×C12712yes—
253C42C22×C4×C12712yes—
254C42C22×C4×C12712yes—
255C42C22×C4×C12712yes—
256C23—22no—
257C23—22no—
258C23C2×C42×C12712yes—
259C23C2×M16×C12714yes—
260C23C23×C4×C12711yescharacteristic
261C2×C4—24no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—28no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—44no—
275C2×C4C2×C42×C12712yes—
276C2×C4C2×C42×C12712yes—
277C2×C4C2×C42×C12712yes—
278C2×C4C2×C42×C12712yes—
279C2×C4C2×C42×C12712yes—
280C2×C4C2×M16×C12718yes—
281C2×C4C23×C4×C12711yescharacteristic
282C2×C4C23×C4×C12711yescharacteristic
283C2×C4C2×#41×C12714yes—
284C8—24no—
285C8—28no—
286C8#117×C12718yescomplemented
287C22—22no—
288C22—28no—
289C22—22no—
290C22C4×M16×C12714yes—
291C22C22×C42×C12711yescharacteristic
292C22C4×#41×C12712yes—
293C22C22×M16×C12712yes—
294C22#568×C12712yes—
295C4—22no—
296C4—22no—
297C4—22no—
298C4—22no—
299C4—28no—
300C4—22no—
301C4—44no—
302C4C2×#117×C12712yes—
303C4C4×#41×C12712yes—
304C2—24no—
305C2C4×#117×C12711yescharacteristic
306C2C2×C4×M16×C12711yescharacteristic
307C2C127×#287311yescharacteristic
308C2C127×#297014yes—
subgroupG/H
centerC22×C4×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC22×C4C24×C127
socleC23×C127C23×C4
prime radicalC24×C127C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1771C2semidirect
7. C127×#1745C2semidirect
8. C4×#97×C127C2semidirect
12. #432×C127C4semidirect
15. C2×#97×C127C4semidirect
131. C8×C127#117semidirect
149. #20479C127direct (N × H)
158. #1771C2×C127semidirect
161. #1745C2×C127semidirect
162. C4×#97C2×C127semidirect
163. C127#20479direct (N × H)
167. #432C4×C127semidirect
170. C2×#97C4×C127semidirect
286. C8#117×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#432×C1272
C22×#97×C1272
C4×#117×C1272
C127×#17712
C127×#17522
C8×C22⋊C4×C1272
C127×#17452
C4×#97×C1272
#20479127