Finite Group Databasebeta

← C127×#14665 #44578338

Subgroups — C127×#14665 #44578338

Order 32512.

1530 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C127C211yesmaximal, characteristic
2C2×#384×C127C211yesmaximal, characteristic, complemented
3C2×#383×C127C211yesmaximal, characteristic, complemented
4C127×#1441C216yesmaximal, complemented
5C127×#1439C216yesmaximal
6C2×#126×C127—24no—
7C2×#126×C127—24no—
8C2×#126×C127C418yescomplemented
9C22×C4⋊C4×C127C2213yes—
10C22×C4⋊C4×C127C2216yes—
11C22×C22⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2214yes—
13C22×C42×C127C2211yescharacteristic
14#384×C127—24no—
15#383×C127—24no—
16C2×#95×C127C2216yes—
17C2×#95×C127C22112yes—
18C25×C127C2311yescharacteristic
19C23×C4×C127C2314yes—
20C23×C4×C127C2314yes—
21C23×C4×C127C2313yes—
22C23×C4×C127C2313yes—
23#126×C127—232no—
24C2×C4⋊C4×C127—26no—
25C2×C4⋊C4×C127—26no—
26C2×C4⋊C4×C127—212no—
27C2×C4⋊C4×C127—412no—
28C2×C4⋊C4×C127C2×C4112yes—
29C2×C22⋊C4×C127—26no—
30C2×C22⋊C4×C127—26no—
31C2×C22⋊C4×C127—412no—
32C2×C22⋊C4×C127C2×C4112yes—
33C2×C42×C127C2×C414yes—
34C2×C42×C127D414yes—
35C2×C42×C127D414yes—
36#95×C127—212no—
37#95×C127—412no—
38C24×C127—21no—
39C24×C127—21no—
40C24×C127—26no—
41C24×C127—26no—
42C24×C127C22×C412yes—
43C24×C127C2411yescharacteristic
44C22×C4×C127—26no—
45C22×C4×C127—26no—
46C22×C4×C127—23no—
47C22×C4×C127—23no—
48C22×C4×C127—26no—
49C22×C4×C127—26no—
50C22×C4×C127—24no—
51C22×C4×C127—24no—
52C22×C4×C127—212no—
53C22×C4×C127—212no—
54C22×C4×C127—212no—
55C22×C4×C127—212no—
56C22×C4×C127C22×C416yes—
57C22×C4×C127C22×C416yes—
58C22×C4×C127C2×D416yes—
59C22×C4×C127C2×D416yes—
60C4⋊C4×C127—224no—
61C4⋊C4×C127—424no—
62C22⋊C4×C127—224no—
63C22⋊C4×C127—416no—
64C42×C127C22⋊C4116yescomplemented
65C23×C127—22no—
66C23×C127—212no—
67C23×C127—43no—
68C23×C127—43no—
69C23×C127—46no—
70C23×C127—44no—
71C23×C127—412no—
72C23×C127C23×C411yescharacteristic
73C23×C127C22×D411yescharacteristic
74C23×C127C22×D411yescharacteristic
75C23×C127H(5,𝔽2)16yes—
76C23×C1272−1+416yes—
77C2×C4×C127—212no—
78C2×C4×C127—26no—
79C2×C4×C127—26no—
80C2×C4×C127—212no—
81C2×C4×C127—26no—
82C2×C4×C127—212no—
83C2×C4×C127—43no—
84C2×C4×C127—43no—
85C2×C4×C127—46no—
86C2×C4×C127—412no—
87C2×C4×C127—412no—
88C2×C4×C127—44no—
89C2×C4×C127—44no—
90C2×C4×C127—412no—
91C2×C4×C127—412no—
92C2×C4×C127C2×C22⋊C4112yes—
93C22×C127—46no—
94C22×C127—48no—
95C22×C127—81no—
96C22×C127—83no—
97C22×C127—84no—
98C22×C127C22×C22⋊C411yescharacteristic
99C22×C127#52016yes—
100C22×C127#53513yes—
101C22×C127#53613yes—
102C22×C127#53716yes—
103C22×C127#56014yes—
104C22×C127#563112yes—
105C4×C127—212no—
106C4×C127—46no—
107C4×C127—84no—
108C4×C127—84no—
109#14665C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—82no—
111C2×C127#231113yes—
112C2×C127#238314yes—
113C2×C127#281811yescharacteristic
114C2×C127#282113yes—
115C2×C127#282314yes—
116C22×#126C2×C12711yescharacteristic
117C2×#384C2×C12711yescharacteristic, complemented
118C2×#383C2×C12711yescharacteristic, complemented
119#1441C2×C12716yescomplemented
120#1439C2×C12716yes—
121C127#1466511yescharacteristic, direct product factor, Sylow
122C2×#126—24no—
123C2×#126—24no—
124C2×#126C4×C12718yescomplemented
125C22×C4⋊C4C22×C12713yes—
126C22×C4⋊C4C22×C12716yes—
127C22×C22⋊C4C22×C12713yes—
128C22×C22⋊C4C22×C12714yes—
129C22×C42C22×C12711yescharacteristic
130#384—24no—
131#383—24no—
132C2×#95C22×C12716yes—
133C2×#95C22×C127112yes—
134C25C23×C12711yescharacteristic
135C23×C4C23×C12714yes—
136C23×C4C23×C12714yes—
137C23×C4C23×C12713yes—
138C23×C4C23×C12713yes—
139#126—232no—
140C2×C4⋊C4—26no—
141C2×C4⋊C4—26no—
142C2×C4⋊C4—212no—
143C2×C4⋊C4—412no—
144C2×C4⋊C4C2×C4×C127112yes—
145C2×C22⋊C4—26no—
146C2×C22⋊C4—26no—
147C2×C22⋊C4—412no—
148C2×C22⋊C4C2×C4×C127112yes—
149C2×C42C2×C4×C12714yes—
150C2×C42D4×C12714yes—
151C2×C42D4×C12714yes—
152#95—212no—
153#95—412no—
154C24—21no—
155C24—21no—
156C24—26no—
157C24—26no—
158C24C22×C4×C12712yes—
159C24C24×C12711yescharacteristic
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—23no—
163C22×C4—23no—
164C22×C4—26no—
165C22×C4—26no—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—212no—
169C22×C4—212no—
170C22×C4—212no—
171C22×C4—212no—
172C22×C4C22×C4×C12716yes—
173C22×C4C22×C4×C12716yes—
174C22×C4C2×D4×C12716yes—
175C22×C4C2×D4×C12716yes—
176C4⋊C4—224no—
177C4⋊C4—424no—
178C22⋊C4—224no—
179C22⋊C4—416no—
180C42C22⋊C4×C127116yescomplemented
181C23—22no—
182C23—212no—
183C23—43no—
184C23—43no—
185C23—46no—
186C23—44no—
187C23—412no—
188C23C23×C4×C12711yescharacteristic
189C23C22×D4×C12711yescharacteristic
190C23C22×D4×C12711yescharacteristic
191C23H(5,𝔽2)×C12716yes—
192C232−1+4×C12716yes—
193C2×C4—212no—
194C2×C4—26no—
195C2×C4—26no—
196C2×C4—212no—
197C2×C4—26no—
198C2×C4—212no—
199C2×C4—43no—
200C2×C4—43no—
201C2×C4—46no—
202C2×C4—412no—
203C2×C4—412no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—412no—
207C2×C4—412no—
208C2×C4C2×C22⋊C4×C127112yes—
209C22—48no—
210C22—46no—
211C22—81no—
212C22—83no—
213C22—84no—
214C22C22×C22⋊C4×C12711yescharacteristic
215C22#520×C12716yes—
216C22#535×C12713yes—
217C22#536×C12713yes—
218C22#537×C12716yes—
219C22#560×C12714yes—
220C22#563×C127112yes—
221C4—212no—
222C4—46no—
223C4—84no—
224C4—84no—
225C2—82no—
226C2C127×#231113yes—
227C2C127×#238314yes—
228C2C127×#281811yescharacteristic
229C2C127×#282113yes—
230C2C127×#282314yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#384×C127C2semidirect
3. C2×#383×C127C2semidirect
4. C127×#1441C2semidirect
8. C2×#126×C127C4semidirect
64. C42×C127C22⋊C4semidirect
109. #14665C127direct (N × H)
117. C2×#384C2×C127semidirect
118. C2×#383C2×C127semidirect
119. #1441C2×C127semidirect
121. C127#14665direct (N × H)
124. C2×#126C4×C127semidirect
180. C42C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1272
C2×#384×C1272
C2×#383×C1272
C127×#14412
C127×#14392
#14665127