Finite Group Databasebeta

← C127×#3330 #30636282

Subgroups — C127×#3330 #30636282

Order 16256.

420 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#547×C127C211yesmaximal, characteristic, complemented
2#547×C127C211yesmaximal, characteristic, complemented
3#487×C127C211yesmaximal, characteristic, complemented
4#484×C127C212yesmaximal, complemented
5#474×C127C211yesmaximal, characteristic, complemented
6#468×C127C212yesmaximal, complemented
7#461×C127C211yesmaximal, characteristic, complemented
8#449×C127C212yesmaximal, complemented
9C4×D8×C127C211yesmaximal, characteristic, complemented
10#436×C127C211yesmaximal, characteristic, complemented
11#417×C127C212yesmaximal, complemented
12C2×#41×C127—21no—
13C2×#41×C127C2212yes—
14C2×SD16×C127C2212yes—
15C2×D8×C127C2211yescharacteristic
16C2×M16×C127C2212yes—
17C4⋊Q8×C127C2211yescharacteristic
18C4⋊Q8×C127C2211yescharacteristic
19#123×C127—22no—
20#123×C127—22no—
21C22⋊Q8×C127—21no—
22C22⋊Q8×C127C2212yes—
23#121×C127—21no—
24#121×C127C2212yes—
25C4×D4×C127C2211yescharacteristic
26C4×D4×C127C2211yescharacteristic
27C4×D4×C127C2211yescharacteristic
28C2×C4⋊C4×C127—21no—
29C2×C4⋊C4×C127C2212yes—
30#107×C127C2211yescharacteristic
31#107×C127C2212yes—
32C4⋊C8×C127C2211yescharacteristic
33#103×C127C2212yes—
34#103×C127C2212yes—
35#103×C127C2212yes—
36#102×C127C2211yescharacteristic
37#102×C127C2212yes—
38#102×C127C2211yescharacteristic
39C22⋊C8×C127C2212yes—
40C4×C8×C127C2211yescharacteristic
41#41×C127—24no—
42#41×C127—42no—
43#41×C127—44no—
44C2×Q8×C127—21no—
45C2×Q8×C127C2312yes—
46C2×D4×C127—22no—
47C2×D4×C127—22no—
48C2×D4×C127D411yescharacteristic
49C2×D4×C127C2311yescharacteristic
50C2×D4×C127C2311yescharacteristic
51C22×C4×C127—22no—
52C22×C4×C127—21no—
53C22×C4×C127—22no—
54C22×C4×C127—21no—
55C22×C4×C127C2312yes—
56SD16×C127—42no—
57D8×C127—22no—
58M16×C127—42no—
59C2×C8×C127C2311yescharacteristic
60C2×C8×C127C2311yescharacteristic
61C2×C8×C127C2312yes—
62C4⋊C4×C127—21no—
63C4⋊C4×C127—22no—
64C4⋊C4×C127—22no—
65C4⋊C4×C127—21no—
66C4⋊C4×C127—21no—
67C4⋊C4×C127D411yescharacteristic
68C4⋊C4×C127C2311yescharacteristic
69C4⋊C4×C127C2312yes—
70C4⋊C4×C127C2311yescharacteristic
71C22⋊C4×C127—22no—
72C22⋊C4×C127—21no—
73C22⋊C4×C127—21no—
74C22⋊C4×C127—22no—
75C22⋊C4×C127D412yes—
76C42×C127C2311yescharacteristic
77C23×C127—21no—
78C23×C127—21no—
79C23×C127C2×D412yes—
80Q8×C127—22no—
81Q8×C127—22no—
82Q8×C127—42no—
83D4×C127—22no—
84D4×C127—21no—
85D4×C127—21no—
86D4×C127—21no—
87D4×C127—44no—
88D4×C127—44no—
89D4×C127#4112yescomplemented
90C2×C4×C127—22no—
91C2×C4×C127—22no—
92C2×C4×C127—21no—
93C2×C4×C127—22no—
94C2×C4×C127—21no—
95C2×C4×C127—22no—
96C2×C4×C127—44no—
97C2×C4×C127—44no—
98C2×C4×C127—42no—
99C2×C4×C127—42no—
100C2×C4×C127C2×D411yescharacteristic
101C2×C4×C127C2×D412yes—
102C2×C4×C127C2×D411yescharacteristic
103C2×C4×C127C2411yescharacteristic
104C8×C127—21no—
105C8×C127—21no—
106C8×C127—22no—
107C22×C127—22no—
108C22×C127—22no—
109C22×C127—22no—
110C22×C127—22no—
111C22×C127—41no—
112C22×C127—41no—
113C22×C127—41no—
114C22×C127—41no—
115C22×C127—41no—
116C22×C127C22×D411yescharacteristic
117C4×C127—22no—
118C4×C127—21no—
119C4×C127—42no—
120C4×C127—41no—
121C4×C127—41no—
122C4×C127—42no—
123C4×C127AGL(1,ℤ/8)12yes—
124C4×C127C2×#4111yescharacteristic
125C4×C127H(5,𝔽2)11yescharacteristic
126C2×C127—42no—
127C2×C127—42no—
128C2×C127—81no—
129C2×C127#54611yescharacteristic
130C2×C127C2×AGL(1,ℤ/8)11yescharacteristic
131C2×C127#57811yescharacteristic
132#3330C12711yesmaximal, characteristic, direct product factor, Sylow
133C127#333011yescharacteristic, direct product factor, Sylow
134#547C2×C12711yescharacteristic, complemented
135#547C2×C12711yescharacteristic, complemented
136#487C2×C12711yescharacteristic, complemented
137#484C2×C12712yescomplemented
138#474C2×C12711yescharacteristic, complemented
139#468C2×C12712yescomplemented
140#461C2×C12711yescharacteristic, complemented
141#449C2×C12712yescomplemented
142C4×D8C2×C12711yescharacteristic, complemented
143#436C2×C12711yescharacteristic, complemented
144#417C2×C12712yescomplemented
145C2×#41—21no—
146C2×#41C22×C12712yes—
147C2×SD16C22×C12712yes—
148C2×D8C22×C12711yescharacteristic
149C2×M16C22×C12712yes—
150C4⋊Q8C22×C12711yescharacteristic
151C4⋊Q8C22×C12711yescharacteristic
152#123—22no—
153#123—22no—
154C22⋊Q8—21no—
155C22⋊Q8C22×C12712yes—
156#121—21no—
157#121C22×C12712yes—
158C4×D4C22×C12711yescharacteristic
159C4×D4C22×C12711yescharacteristic
160C4×D4C22×C12711yescharacteristic
161C2×C4⋊C4—21no—
162C2×C4⋊C4C22×C12712yes—
163#107C22×C12711yescharacteristic
164#107C22×C12712yes—
165C4⋊C8C22×C12711yescharacteristic
166#103C22×C12712yes—
167#103C22×C12712yes—
168#103C22×C12712yes—
169#102C22×C12711yescharacteristic
170#102C22×C12712yes—
171#102C22×C12711yescharacteristic
172C22⋊C8C22×C12712yes—
173C4×C8C22×C12711yescharacteristic
174#41—24no—
175#41—42no—
176#41—44no—
177C2×Q8—21no—
178C2×Q8C23×C12712yes—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4D4×C12711yescharacteristic
182C2×D4C23×C12711yescharacteristic
183C2×D4C23×C12711yescharacteristic
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—21no—
188C22×C4C23×C12712yes—
189SD16—42no—
190D8—22no—
191M16—42no—
192C2×C8C23×C12711yescharacteristic
193C2×C8C23×C12711yescharacteristic
194C2×C8C23×C12712yes—
195C4⋊C4—21no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4D4×C12711yescharacteristic
201C4⋊C4C23×C12711yescharacteristic
202C4⋊C4C23×C12712yes—
203C4⋊C4C23×C12711yescharacteristic
204C22⋊C4—22no—
205C22⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—22no—
208C22⋊C4D4×C12712yes—
209C42C23×C12711yescharacteristic
210C23—21no—
211C23—21no—
212C23C2×D4×C12712yes—
213Q8—22no—
214Q8—22no—
215Q8—42no—
216D4—22no—
217D4—21no—
218D4—21no—
219D4—21no—
220D4—44no—
221D4—44no—
222D4#41×C12712yescomplemented
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4C2×D4×C12711yescharacteristic
234C2×C4C2×D4×C12712yes—
235C2×C4C2×D4×C12711yescharacteristic
236C2×C4C24×C12711yescharacteristic
237C8—21no—
238C8—21no—
239C8—22no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22C22×D4×C12711yescharacteristic
250C4—22no—
251C4—21no—
252C4—42no—
253C4—41no—
254C4—42no—
255C4—41no—
256C4AGL(1,ℤ/8)×C12712yes—
257C4C2×#41×C12711yescharacteristic
258C4H(5,𝔽2)×C12711yescharacteristic
259C2—42no—
260C2—42no—
261C2—81no—
262C2#546×C12711yescharacteristic
263C2C2×AGL(1,ℤ/8)×C12711yescharacteristic
264C2#578×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×D4
commutator, Frattini, cosocleC2×C4C24×C127
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. #547×C127C2semidirect
2. #547×C127C2semidirect
3. #487×C127C2semidirect
4. #484×C127C2semidirect
5. #474×C127C2semidirect
6. #468×C127C2semidirect
7. #461×C127C2semidirect
8. #449×C127C2semidirect
9. C4×D8×C127C2semidirect
10. #436×C127C2semidirect
11. #417×C127C2semidirect
89. D4×C127#41semidirect
132. #3330C127direct (N × H)
133. C127#3330direct (N × H)
134. #547C2×C127semidirect
135. #547C2×C127semidirect
136. #487C2×C127semidirect
137. #484C2×C127semidirect
138. #474C2×C127semidirect
139. #468C2×C127semidirect
140. #461C2×C127semidirect
141. #449C2×C127semidirect
142. C4×D8C2×C127semidirect
143. #436C2×C127semidirect
144. #417C2×C127semidirect
222. D4#41×C127semidirect

Maximal subgroups

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

subgroupindex
#547×C1272
#487×C1272
#484×C1272
#474×C1272
#468×C1272
#461×C1272
#449×C1272
C4×D8×C1272
#436×C1272
#417×C1272
#3330127