Finite Group Databasebeta

← C127×#3190 #30636142

Subgroups — C127×#3190 #30636142

Order 16256.

420 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×C127C211yesmaximal, characteristic
2C2×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
3#485×C127C212yesmaximal, complemented
4#483×C127C211yesmaximal, characteristic, complemented
5#480×C127C211yesmaximal, characteristic, complemented
6#467×C127C212yesmaximal, complemented
7#465×C127C212yesmaximal, complemented
8#452×C127C212yesmaximal, complemented
9#451×C127C211yesmaximal, characteristic, complemented
10#448×C127C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
12C2×#41×C127C2211yescharacteristic
13C22×Q8×C127C2211yescharacteristic
14C23×C4×C127C2211yescharacteristic
15C2×Q16×C127C2212yescomplemented
16C2×SD16×C127C2212yescomplemented
17C22×C8×C127C2212yes—
18#123×C127—21no—
19C22⋊Q8×C127—21no—
20C22⋊Q8×C127—21no—
21C22⋊Q8×C127C2212yes—
22C22⋊Q8×C127C2212yes—
23C22⋊Q8×C127C2211yescharacteristic
24C22⋊Q8×C127C2211yescharacteristic
25#121×C127C2211yescharacteristic
26#121×C127C2211yescharacteristic
27#120×C127—21no—
28C4×D4×C127—21no—
29C4×D4×C127—21no—
30#117×C127C2211yescharacteristic
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127C2211yescharacteristic
33C2×C22⋊C4×C127—21no—
34#107×C127C2212yescomplemented
35#106×C127C2212yescomplemented
36#103×C127C2212yescomplemented
37#103×C127C2212yescomplemented
38#103×C127C2212yescomplemented
39#102×C127C2212yescomplemented
40C22⋊C8×C127C2211yescharacteristic
41C22⋊C8×C127C2211yescharacteristic
42C22⋊C8×C127C2212yes—
43C24×C127D411yescharacteristic
44#41×C127—42no—
45C2×Q8×C127—21no—
46C2×Q8×C127—42no—
47C2×Q8×C127C2312yes—
48C2×Q8×C127C2311yescharacteristic
49C2×D4×C127—21no—
50C2×D4×C127—21no—
51C2×D4×C127—21no—
52C2×D4×C127C2311yescharacteristic
53C22×C4×C127—21no—
54C22×C4×C127—21no—
55C22×C4×C127—21no—
56C22×C4×C127—42no—
57C22×C4×C127D411yescharacteristic
58C22×C4×C127D411yescharacteristic
59C22×C4×C127D411yescharacteristic
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2311yescharacteristic
62C22×C4×C127C2311yescharacteristic
63Q16×C127—42no—
64SD16×C127—42no—
65C2×C8×C127—42no—
66C2×C8×C127C2312yes—
67C2×C8×C127C2312yes—
68C4⋊C4×C127—22no—
69C4⋊C4×C127—22no—
70C4⋊C4×C127—21no—
71C4⋊C4×C127—21no—
72C4⋊C4×C127—21no—
73C4⋊C4×C127C2312yes—
74C4⋊C4×C127C2311yescharacteristic
75C4⋊C4×C127C2311yescharacteristic
76C22⋊C4×C127—22no—
77C22⋊C4×C127—22no—
78C22⋊C4×C127—21no—
79C22⋊C4×C127—21no—
80C22⋊C4×C127—21no—
81C22⋊C4×C127—21no—
82C22⋊C4×C127—21no—
83C42×C127—21no—
84C23×C127—22no—
85C23×C127—22no—
86C23×C127—21no—
87C23×C127—41no—
88C23×C127C2×D411yescharacteristic
89C23×C127C2×D411yescharacteristic
90C23×C127C2×D411yescharacteristic
91Q8×C127—22no—
92Q8×C127—22no—
93Q8×C127—22no—
94Q8×C127—42no—
95D4×C127—22no—
96D4×C127—42no—
97D4×C127—42no—
98D4×C127—42no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—22no—
105C2×C4×C127—21no—
106C2×C4×C127—22no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127C2×D411yescharacteristic
114C2×C4×C127C2×D411yescharacteristic
115C2×C4×C127C2×D411yescharacteristic
116C2×C4×C127C2411yescharacteristic
117C8×C127—22no—
118C8×C127—22no—
119C22×C127—21no—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—44no—
127C22×C127—41no—
128C22×C127—41no—
129C22×C127—41no—
130C22×C127#13512yes—
131C22×C127#13712yes—
132C22×C127C22×D411yescharacteristic
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—21no—
136C4×C127—41no—
137C4×C127—42no—
138C4×C127—42no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127H(5,𝔽2)12yes—
142C2×C127—22no—
143C2×C127—22no—
144C2×C127—41no—
145C2×C127—81no—
146C2×C127#53411yescharacteristic
147C2×C127C2×#13511yescharacteristic
148C2×C127C2×#13711yescharacteristic
149#3190C12711yesmaximal, characteristic, direct product factor, Sylow
150C127#319011yescharacteristic, direct product factor, Sylow
151#525C2×C12711yescharacteristic
152C2×C22⋊Q8C2×C12711yescharacteristic, complemented
153#485C2×C12712yescomplemented
154#483C2×C12711yescharacteristic, complemented
155#480C2×C12711yescharacteristic, complemented
156#467C2×C12712yescomplemented
157#465C2×C12712yescomplemented
158#452C2×C12712yescomplemented
159#451C2×C12711yescharacteristic, complemented
160#448C2×C12711yescharacteristic, complemented
161C2×C22⋊C8C2×C12711yescharacteristic, complemented
162C2×#41C22×C12711yescharacteristic
163C22×Q8C22×C12711yescharacteristic
164C23×C4C22×C12711yescharacteristic
165C2×Q16C22×C12712yescomplemented
166C2×SD16C22×C12712yescomplemented
167C22×C8C22×C12712yes—
168#123—21no—
169C22⋊Q8—21no—
170C22⋊Q8—21no—
171C22⋊Q8C22×C12712yes—
172C22⋊Q8C22×C12712yes—
173C22⋊Q8C22×C12711yescharacteristic
174C22⋊Q8C22×C12711yescharacteristic
175#121C22×C12711yescharacteristic
176#121C22×C12711yescharacteristic
177#120—21no—
178C4×D4—21no—
179C4×D4—21no—
180#117C22×C12711yescharacteristic
181C2×C4⋊C4—21no—
182C2×C4⋊C4C22×C12711yescharacteristic
183C2×C22⋊C4—21no—
184#107C22×C12712yescomplemented
185#106C22×C12712yescomplemented
186#103C22×C12712yescomplemented
187#103C22×C12712yescomplemented
188#103C22×C12712yescomplemented
189#102C22×C12712yescomplemented
190C22⋊C8C22×C12711yescharacteristic
191C22⋊C8C22×C12711yescharacteristic
192C22⋊C8C22×C12712yes—
193C24D4×C12711yescharacteristic
194#41—42no—
195C2×Q8—21no—
196C2×Q8—42no—
197C2×Q8C23×C12712yes—
198C2×Q8C23×C12711yescharacteristic
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—21no—
202C2×D4C23×C12711yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—42no—
207C22×C4D4×C12711yescharacteristic
208C22×C4D4×C12711yescharacteristic
209C22×C4D4×C12711yescharacteristic
210C22×C4C23×C12711yescharacteristic
211C22×C4C23×C12711yescharacteristic
212C22×C4C23×C12711yescharacteristic
213Q16—42no—
214SD16—42no—
215C2×C8—42no—
216C2×C8C23×C12712yes—
217C2×C8C23×C12712yes—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—21no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4C23×C12712yes—
224C4⋊C4C23×C12711yescharacteristic
225C4⋊C4C23×C12711yescharacteristic
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—21no—
229C22⋊C4—21no—
230C22⋊C4—21no—
231C22⋊C4—21no—
232C22⋊C4—21no—
233C42—21no—
234C23—22no—
235C23—22no—
236C23—21no—
237C23—41no—
238C23C2×D4×C12711yescharacteristic
239C23C2×D4×C12711yescharacteristic
240C23C2×D4×C12711yescharacteristic
241Q8—22no—
242Q8—22no—
243Q8—22no—
244Q8—42no—
245D4—22no—
246D4—42no—
247D4—42no—
248D4—42no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4C2×D4×C12711yescharacteristic
264C2×C4C2×D4×C12711yescharacteristic
265C2×C4C2×D4×C12711yescharacteristic
266C2×C4C24×C12711yescharacteristic
267C8—22no—
268C8—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—44no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22#135×C12712yes—
281C22#137×C12712yes—
282C22C22×D4×C12711yescharacteristic
283C4—21no—
284C4—21no—
285C4—21no—
286C4—41no—
287C4—42no—
288C4—42no—
289C4—41no—
290C4—41no—
291C4H(5,𝔽2)×C12712yes—
292C2—22no—
293C2—22no—
294C2—41no—
295C2—81no—
296C2#534×C12711yescharacteristic
297C2C2×#135×C12711yescharacteristic
298C2C2×#137×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
prime radical#525×C127C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×C127C2semidirect
3. #485×C127C2semidirect
4. #483×C127C2semidirect
5. #480×C127C2semidirect
6. #467×C127C2semidirect
7. #465×C127C2semidirect
8. #452×C127C2semidirect
9. #451×C127C2semidirect
10. #448×C127C2semidirect
11. C2×C22⋊C8×C127C2semidirect
15. C2×Q16×C127C22semidirect
16. C2×SD16×C127C22semidirect
34. #107×C127C22semidirect
35. #106×C127C22semidirect
36. #103×C127C22semidirect
37. #103×C127C22semidirect
38. #103×C127C22semidirect
39. #102×C127C22semidirect
149. #3190C127direct (N × H)
150. C127#3190direct (N × H)
152. C2×C22⋊Q8C2×C127semidirect
153. #485C2×C127semidirect
154. #483C2×C127semidirect
155. #480C2×C127semidirect
156. #467C2×C127semidirect
157. #465C2×C127semidirect
158. #452C2×C127semidirect
159. #451C2×C127semidirect
160. #448C2×C127semidirect
161. C2×C22⋊C8C2×C127semidirect
165. C2×Q16C22×C127semidirect
166. C2×SD16C22×C127semidirect
184. #107C22×C127semidirect
185. #106C22×C127semidirect
186. #103C22×C127semidirect
187. #103C22×C127semidirect
188. #103C22×C127semidirect
189. #102C22×C127semidirect

Maximal subgroups

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

subgroupindex
#525×C1272
C2×C22⋊Q8×C1272
#485×C1272
#483×C1272
#480×C1272
#467×C1272
#465×C1272
#452×C1272
#451×C1272
#448×C1272
C2×C22⋊C8×C1272
#3190127