Finite Group Databasebeta

← C127×#2495 #30635447

Subgroups — C127×#2495 #30635447

Order 16256.

412 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#400×C127C212yesmaximal, complemented
2#397×C127C212yesmaximal
3#389×C127C211yesmaximal, characteristic, complemented
4#389×C127C211yesmaximal, characteristic, complemented
5#388×C127C212yesmaximal
6#383×C127C212yesmaximal, complemented
7#382×C127C211yesmaximal, characteristic, complemented
8#380×C127C211yesmaximal, characteristic
9#380×C127C211yesmaximal, characteristic
10C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
11C4×C22⋊C4×C127C211yesmaximal, characteristic
12C23×C4×C127C2211yescharacteristic
13C2×C4⋊C4×C127C2211yescharacteristic
14C2×C4⋊C4×C127C2211yescharacteristic
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2212yes—
18C2×C4⋊C4×C127C2212yes—
19C2×C22⋊C4×C127C2211yescharacteristic
20C2×C22⋊C4×C127C2211yescharacteristic
21C2×C22⋊C4×C127C2212yes—
22C2×C22⋊C4×C127C2212yes—
23C2×C42×C127C2211yescharacteristic
24C2×C42×C127C2211yescharacteristic
25C2×C42×C127C2212yes—
26#95×C127C2211yescharacteristic
27#95×C127C2211yescharacteristic
28#95×C127C2212yes—
29#95×C127C2212yes—
30#95×C127C2212yes—
31#95×C127C2212yes—
32#95×C127C2212yes—
33#95×C127C2212yes—
34#95×C127C2212yes—
35C24×C127C2311yescharacteristic
36C22×C4×C127—22no—
37C22×C4×C127—22no—
38C22×C4×C127—22no—
39C22×C4×C127C2311yescharacteristic
40C22×C4×C127C2311yescharacteristic
41C22×C4×C127C2312yes—
42C22×C4×C127C2312yes—
43C22×C4×C127C2311yescharacteristic
44C22×C4×C127C2311yescharacteristic
45C22×C4×C127C2312yes—
46C22×C4×C127C2312yes—
47C22×C4×C127C2311yescharacteristic
48C22×C4×C127C2311yescharacteristic
49C4⋊C4×C127—22no—
50C4⋊C4×C127—22no—
51C4⋊C4×C127—22no—
52C4⋊C4×C127—22no—
53C4⋊C4×C127—42no—
54C4⋊C4×C127—42no—
55C22⋊C4×C127—22no—
56C22⋊C4×C127—24no—
57C22⋊C4×C127—22no—
58C22⋊C4×C127—42no—
59C42×C127—22no—
60C42×C127—24no—
61C42×C127—22no—
62C23×C127—21no—
63C23×C127—21no—
64C23×C127—21no—
65C23×C127—21no—
66C23×C127—21no—
67C23×C127—21no—
68C23×C127#4112yes—
69C23×C127C2411yescharacteristic
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—22no—
73C2×C4×C127—21no—
74C2×C4×C127—21no—
75C2×C4×C127—21no—
76C2×C4×C127—22no—
77C2×C4×C127—22no—
78C2×C4×C127—21no—
79C2×C4×C127—21no—
80C2×C4×C127—22no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—22no—
84C2×C4×C127—22no—
85C2×C4×C127—22no—
86C2×C4×C127—21no—
87C2×C4×C127—21no—
88C2×C4×C127—21no—
89C2×C4×C127—22no—
90C2×C4×C127—22no—
91C2×C4×C127—21no—
92C2×C4×C127—22no—
93C2×C4×C127—21no—
94C2×C4×C127—22no—
95C2×C4×C127—21no—
96C2×C4×C127—44no—
97C2×C4×C127#4112yes—
98C2×C4×C127#4112yes—
99C2×C4×C127#4112yes—
100C2×C4×C127#4112yes—
101C22×C127—22no—
102C22×C127—22no—
103C22×C127—22no—
104C22×C127—41no—
105C22×C127—41no—
106C22×C127—41no—
107C22×C127—41no—
108C22×C127C2×#4111yescharacteristic
109C22×C127C2×#4111yescharacteristic
110C22×C127C2×#4111yescharacteristic
111C22×C127C2×#4111yescharacteristic
112C22×C127C2×#4111yescharacteristic
113C22×C127H(5,𝔽2)11yescharacteristic
114C22×C1272−1+411yescharacteristic
115C4×C127—22no—
116C4×C127—41no—
117C4×C127—42no—
118C4×C127—42no—
119C4×C127—41no—
120C4×C127—41no—
121C4×C127—42no—
122C4×C127—41no—
123C4×C127—42no—
124C4×C127#12614yes—
125C2×C127—42no—
126C2×C127C2×#12611yescharacteristic
127C2×C127#52911yescharacteristic
128C2×C127#54211yescharacteristic
129C2×C127#55211yescharacteristic
130C2×C127#55211yescharacteristic
131C2×C127#55311yescharacteristic
132C2×C127#55511yescharacteristic
133#2495C12711yesmaximal, characteristic, direct product factor, Sylow
134C127#249511yescharacteristic, direct product factor, Sylow
135#400C2×C12712yescomplemented
136#397C2×C12712yes—
137#389C2×C12711yescharacteristic, complemented
138#389C2×C12711yescharacteristic, complemented
139#388C2×C12712yes—
140#383C2×C12712yescomplemented
141#382C2×C12711yescharacteristic, complemented
142#380C2×C12711yescharacteristic
143#380C2×C12711yescharacteristic
144C4×C4⋊C4C2×C12711yescharacteristic, complemented
145C4×C22⋊C4C2×C12711yescharacteristic
146C23×C4C22×C12711yescharacteristic
147C2×C4⋊C4C22×C12711yescharacteristic
148C2×C4⋊C4C22×C12711yescharacteristic
149C2×C4⋊C4C22×C12711yescharacteristic
150C2×C4⋊C4C22×C12711yescharacteristic
151C2×C4⋊C4C22×C12712yes—
152C2×C4⋊C4C22×C12712yes—
153C2×C22⋊C4C22×C12711yescharacteristic
154C2×C22⋊C4C22×C12711yescharacteristic
155C2×C22⋊C4C22×C12712yes—
156C2×C22⋊C4C22×C12712yes—
157C2×C42C22×C12711yescharacteristic
158C2×C42C22×C12711yescharacteristic
159C2×C42C22×C12712yes—
160#95C22×C12711yescharacteristic
161#95C22×C12711yescharacteristic
162#95C22×C12712yes—
163#95C22×C12712yes—
164#95C22×C12712yes—
165#95C22×C12712yes—
166#95C22×C12712yes—
167#95C22×C12712yes—
168#95C22×C12712yes—
169C24C23×C12711yescharacteristic
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4C23×C12711yescharacteristic
174C22×C4C23×C12711yescharacteristic
175C22×C4C23×C12712yes—
176C22×C4C23×C12712yes—
177C22×C4C23×C12711yescharacteristic
178C22×C4C23×C12711yescharacteristic
179C22×C4C23×C12712yes—
180C22×C4C23×C12712yes—
181C22×C4C23×C12711yescharacteristic
182C22×C4C23×C12711yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C22⋊C4—22no—
190C22⋊C4—24no—
191C22⋊C4—22no—
192C22⋊C4—42no—
193C42—22no—
194C42—24no—
195C42—22no—
196C23—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—21no—
202C23#41×C12712yes—
203C23C24×C12711yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—44no—
231C2×C4#41×C12712yes—
232C2×C4#41×C12712yes—
233C2×C4#41×C12712yes—
234C2×C4#41×C12712yes—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22C2×#41×C12711yescharacteristic
243C22C2×#41×C12711yescharacteristic
244C22C2×#41×C12711yescharacteristic
245C22C2×#41×C12711yescharacteristic
246C22C2×#41×C12711yescharacteristic
247C22H(5,𝔽2)×C12711yescharacteristic
248C222−1+4×C12711yescharacteristic
249C4—22no—
250C4—41no—
251C4—42no—
252C4—42no—
253C4—41no—
254C4—41no—
255C4—42no—
256C4—41no—
257C4—42no—
258C4#126×C12714yes—
259C2—42no—
260C2C2×#126×C12711yescharacteristic
261C2#529×C12711yescharacteristic
262C2#542×C12711yescharacteristic
263C2#552×C12711yescharacteristic
264C2#552×C12711yescharacteristic
265C2#553×C12711yescharacteristic
266C2#555×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC24×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #400×C127C2semidirect
3. #389×C127C2semidirect
4. #389×C127C2semidirect
6. #383×C127C2semidirect
7. #382×C127C2semidirect
10. C4×C4⋊C4×C127C2semidirect
133. #2495C127direct (N × H)
134. C127#2495direct (N × H)
135. #400C2×C127semidirect
137. #389C2×C127semidirect
138. #389C2×C127semidirect
140. #383C2×C127semidirect
141. #382C2×C127semidirect
144. C4×C4⋊C4C2×C127semidirect

Maximal subgroups

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

subgroupindex
#400×C1272
#397×C1272
#389×C1272
#388×C1272
#383×C1272
#382×C1272
#380×C1272
C4×C4⋊C4×C1272
C4×C22⋊C4×C1272
#2495127