Finite Group Databasebeta

← C127×#2635 #30635587

Subgroups — C127×#2635 #30635587

Order 16256.

620 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×C127C211yesmaximal, characteristic, complemented
2C2×C4×D4×C127C211yesmaximal, characteristic, complemented
3#400×C127C211yesmaximal, characteristic, complemented
4#399×C127C211yesmaximal, characteristic, complemented
5#394×C127C211yesmaximal, characteristic, complemented
6#394×C127C212yesmaximal, complemented
7#392×C127C211yesmaximal, characteristic, complemented
8#392×C127C212yesmaximal, complemented
9#388×C127C212yesmaximal, complemented
10#386×C127C212yesmaximal, complemented
11#381×C127C211yesmaximal, characteristic, complemented
12C22×D4×C127C2211yescharacteristic
13C22×D4×C127C2212yes—
14C22×D4×C127C2211yescharacteristic
15C22×D4×C127C2212yes—
16C23×C4×C127C2211yescharacteristic
17C23×C4×C127C2211yescharacteristic
18#121×C127—24no—
19C4×D4×C127—24no—
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2211yescharacteristic
22C2×C4⋊C4×C127C2212yes—
23C2×C22⋊C4×C127C2211yescharacteristic
24C2×C22⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2212yes—
26C2×C22⋊C4×C127C2212yes—
27C2×C22⋊C4×C127C2212yes—
28C2×C22⋊C4×C127C2212yes—
29C2×C22⋊C4×C127C2212yes—
30C2×C22⋊C4×C127C2212yes—
31C2×C42×C127C2211yescharacteristic
32#95×C127C2212yes—
33#95×C127C2211yescharacteristic
34#95×C127C2211yescharacteristic
35#95×C127C2212yes—
36#95×C127C2212yes—
37C24×C127C2312yes—
38C24×C127C2311yescharacteristic
39C24×C127C2311yescharacteristic
40C2×D4×C127—22no—
41C2×D4×C127—22no—
42C2×D4×C127—24no—
43C2×D4×C127—24no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—42no—
47C2×D4×C127—42no—
48C2×D4×C127—42no—
49C2×D4×C127—42no—
50C2×D4×C127—42no—
51C22×C4×C127—22no—
52C22×C4×C127—42no—
53C22×C4×C127—42no—
54C22×C4×C127D414yescomplemented
55C22×C4×C127C2312yes—
56C22×C4×C127C2312yes—
57C22×C4×C127C2311yescharacteristic
58C22×C4×C127C2312yes—
59C22×C4×C127C2311yescharacteristic
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2311yescharacteristic
62C22×C4×C127C2311yescharacteristic
63C4⋊C4×C127—22no—
64C4⋊C4×C127—22no—
65C4⋊C4×C127—42no—
66C22⋊C4×C127—22no—
67C22⋊C4×C127—22no—
68C22⋊C4×C127—24no—
69C22⋊C4×C127—24no—
70C22⋊C4×C127—42no—
71C22⋊C4×C127—42no—
72C22⋊C4×C127—42no—
73C22⋊C4×C127—42no—
74C42×C127—22no—
75C23×C127—21no—
76C23×C127—21no—
77C23×C127—21no—
78C23×C127—21no—
79C23×C127—22no—
80C23×C127—22no—
81C23×C127—22no—
82C23×C127—22no—
83C23×C127—22no—
84C23×C127—22no—
85C23×C127—22no—
86C23×C127—22no—
87C23×C127—22no—
88C23×C127—22no—
89C23×C127—22no—
90C23×C127C2×D412yes—
91C23×C127#4112yes—
92C23×C127C2411yescharacteristic
93D4×C127—28no—
94D4×C127—44no—
95D4×C127—48no—
96D4×C127—48no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—22no—
100C2×C4×C127—22no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—22no—
104C2×C4×C127—22no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—44no—
115C2×C4×C127—44no—
116C2×C4×C127C2×D412yes—
117C2×C4×C127C2×D412yes—
118C2×C4×C127#4112yes—
119C22×C127—22no—
120C22×C127—22no—
121C22×C127—22no—
122C22×C127—22no—
123C22×C127—24no—
124C22×C127—41no—
125C22×C127—41no—
126C22×C127—42no—
127C22×C127—42no—
128C22×C127—42no—
129C22×C127—42no—
130C22×C127—42no—
131C22×C127—42no—
132C22×C127—42no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127C22×D411yescharacteristic
137C22×C127C2×#4111yescharacteristic
138C22×C127C2×#4111yescharacteristic
139C22×C127H(5,𝔽2)12yes—
140C22×C127H(5,𝔽2)12yes—
141C4×C127—22no—
142C4×C127—22no—
143C4×C127—22no—
144C4×C127—41no—
145C4×C127—41no—
146C4×C127—42no—
147C4×C127—42no—
148C4×C127—42no—
149C2×C127—42no—
150C2×C127—42no—
151C2×C127—82no—
152C2×C127#52511yescharacteristic
153C2×C127#53411yescharacteristic
154C2×C127#53511yescharacteristic
155C2×C127#53812yes—
156C2×C127#54012yes—
157#2635C12711yesmaximal, characteristic, direct product factor, Sylow
158C127#263511yescharacteristic, direct product factor, Sylow
159C2×#121C2×C12711yescharacteristic, complemented
160C2×C4×D4C2×C12711yescharacteristic, complemented
161#400C2×C12711yescharacteristic, complemented
162#399C2×C12711yescharacteristic, complemented
163#394C2×C12711yescharacteristic, complemented
164#394C2×C12712yescomplemented
165#392C2×C12711yescharacteristic, complemented
166#392C2×C12712yescomplemented
167#388C2×C12712yescomplemented
168#386C2×C12712yescomplemented
169#381C2×C12711yescharacteristic, complemented
170C22×D4C22×C12711yescharacteristic
171C22×D4C22×C12712yes—
172C22×D4C22×C12711yescharacteristic
173C22×D4C22×C12712yes—
174C23×C4C22×C12711yescharacteristic
175C23×C4C22×C12711yescharacteristic
176#121—24no—
177C4×D4—24no—
178C2×C4⋊C4C22×C12711yescharacteristic
179C2×C4⋊C4C22×C12711yescharacteristic
180C2×C4⋊C4C22×C12712yes—
181C2×C22⋊C4C22×C12711yescharacteristic
182C2×C22⋊C4C22×C12711yescharacteristic
183C2×C22⋊C4C22×C12712yes—
184C2×C22⋊C4C22×C12712yes—
185C2×C22⋊C4C22×C12712yes—
186C2×C22⋊C4C22×C12712yes—
187C2×C22⋊C4C22×C12712yes—
188C2×C22⋊C4C22×C12712yes—
189C2×C42C22×C12711yescharacteristic
190#95C22×C12712yes—
191#95C22×C12711yescharacteristic
192#95C22×C12711yescharacteristic
193#95C22×C12712yes—
194#95C22×C12712yes—
195C24C23×C12712yes—
196C24C23×C12711yescharacteristic
197C24C23×C12711yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—24no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—42no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4D4×C12714yescomplemented
213C22×C4C23×C12712yes—
214C22×C4C23×C12712yes—
215C22×C4C23×C12711yescharacteristic
216C22×C4C23×C12712yes—
217C22×C4C23×C12711yescharacteristic
218C22×C4C23×C12711yescharacteristic
219C22×C4C23×C12711yescharacteristic
220C22×C4C23×C12711yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—22no—
223C4⋊C4—42no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C22⋊C4—24no—
227C22⋊C4—24no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—42no—
232C42—22no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23C2×D4×C12712yes—
249C23#41×C12712yes—
250C23C24×C12711yescharacteristic
251D4—28no—
252D4—44no—
253D4—48no—
254D4—48no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4C2×D4×C12712yes—
275C2×C4C2×D4×C12712yes—
276C2×C4#41×C12712yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22C22×D4×C12711yescharacteristic
295C22C2×#41×C12711yescharacteristic
296C22C2×#41×C12711yescharacteristic
297C22H(5,𝔽2)×C12712yes—
298C22H(5,𝔽2)×C12712yes—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—41no—
305C4—42no—
306C4—42no—
307C2—42no—
308C2—42no—
309C2—82no—
310C2#525×C12711yescharacteristic
311C2#534×C12711yescharacteristic
312C2#535×C12711yescharacteristic
313C2#538×C12712yes—
314C2#540×C12712yes—
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#121×C127C2semidirect
2. C2×C4×D4×C127C2semidirect
3. #400×C127C2semidirect
4. #399×C127C2semidirect
5. #394×C127C2semidirect
6. #394×C127C2semidirect
7. #392×C127C2semidirect
8. #392×C127C2semidirect
9. #388×C127C2semidirect
10. #386×C127C2semidirect
11. #381×C127C2semidirect
54. C22×C4×C127D4semidirect
157. #2635C127direct (N × H)
158. C127#2635direct (N × H)
159. C2×#121C2×C127semidirect
160. C2×C4×D4C2×C127semidirect
161. #400C2×C127semidirect
162. #399C2×C127semidirect
163. #394C2×C127semidirect
164. #394C2×C127semidirect
165. #392C2×C127semidirect
166. #392C2×C127semidirect
167. #388C2×C127semidirect
168. #386C2×C127semidirect
169. #381C2×C127semidirect
212. C22×C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C1272
C2×C4×D4×C1272
#400×C1272
#399×C1272
#394×C1272
#392×C1272
#388×C1272
#386×C1272
#381×C1272
#2635127