Finite Group Databasebeta

← C127×#16112 #44579785

Subgroups — C127×#16112 #44579785

Order 32512.

1154 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#391×C127C212yesmaximal
2C127×#1446C211yesmaximal, characteristic
3C127×#1443C214yesmaximal
4C127×#1442C214yesmaximal
5C127×#1434C214yesmaximal
6C23×Q8×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2212yes—
8C22×C42×C127C2212yes—
9#391×C127—28no—
10C2×#95×C127C2214yes—
11C2×#95×C127C2214yes—
12C2×#95×C127C2214yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2212yes—
18C22×Q8×C127—28no—
19C22×Q8×C127—42no—
20C22×Q8×C127D414yes—
21C23×C4×C127C2314yes—
22C23×C4×C127C2314yes—
23C23×C4×C127C2311yescharacteristic
24C23×C4×C127C2314yes—
25C23×C4×C127C2312yes—
26C2×C4⋊C4×C127—24no—
27C2×C4⋊C4×C127—42no—
28C2×C4⋊C4×C127—42no—
29C2×C42×C127—24no—
30C2×C42×C127—28no—
31#95×C127—28no—
32#95×C127—28no—
33#95×C127—28no—
34#95×C127—28no—
35#95×C127—28no—
36#95×C127—28no—
37#95×C127—42no—
38#95×C127—44no—
39C24×C127C2411yescharacteristic
40C2×Q8×C127—216no—
41C2×Q8×C127—44no—
42C2×Q8×C127—416no—
43C22×C4×C127—24no—
44C22×C4×C127—22no—
45C22×C4×C127—22no—
46C22×C4×C127—24no—
47C22×C4×C127—24no—
48C22×C4×C127—24no—
49C22×C4×C127—24no—
50C22×C4×C127—24no—
51C22×C4×C127—22no—
52C22×C4×C127—24no—
53C22×C4×C127—24no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—24no—
57C22×C4×C127—24no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—24no—
66C22×C4×C127—24no—
67C22×C4×C127—24no—
68C22×C4×C127C2×D412yes—
69C22×C4×C127C2×D414yes—
70C22×C4×C127#4118yes—
71C22×C4×C127#4118yes—
72C4⋊C4×C127—48no—
73C42×C127—48no—
74C23×C127C22×D411yescharacteristic
75C23×C127C2×#4114yes—
76C23×C127C2×#4114yes—
77C23×C127H(5,𝔽2)12yes—
78C23×C1272−1+414yes—
79Q8×C127—416no—
80C2×C4×C127—24no—
81C2×C4×C127—24no—
82C2×C4×C127—28no—
83C2×C4×C127—28no—
84C2×C4×C127—24no—
85C2×C4×C127—28no—
86C2×C4×C127—22no—
87C2×C4×C127—28no—
88C2×C4×C127—28no—
89C2×C4×C127—44no—
90C2×C4×C127—44no—
91C2×C4×C127—44no—
92C2×C4×C127—44no—
93C2×C4×C127—44no—
94C2×C4×C127—44no—
95C2×C4×C127—44no—
96C2×C4×C127—44no—
97C2×C4×C127—44no—
98C2×C4×C127—44no—
99C2×C4×C127—44no—
100C2×C4×C127—44no—
101C2×C4×C127—44no—
102C2×C4×C127—44no—
103C2×C4×C127—44no—
104C2×C4×C127—44no—
105C2×C4×C127—44no—
106C2×C4×C127—44no—
107C2×C4×C127—44no—
108C2×C4×C127#12318yes—
109C22×C127C2×#12312yes—
110C22×C127#52914yes—
111C22×C127#53411yescharacteristic
112C22×C127#54114yes—
113C22×C127#54214yes—
114C22×C127#54814yes—
115C22×C127#55114yes—
116C22×C127#55214yes—
117C22×C127#55512yes—
118C22×C127#55614yes—
119C22×C127#56312yes—
120C4×C127—28no—
121C4×C127—48no—
122C4×C127—42no—
123C4×C127—84no—
124C4×C127—84no—
125#16112C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127#242114yes—
127C2×C127#248311yescharacteristic
128C2×C127#253214yes—
129C2×C127#273112yes—
130C2×C127#276214yes—
131C2×#391C2×C12712yes—
132#1446C2×C12711yescharacteristic
133#1443C2×C12714yes—
134#1442C2×C12714yes—
135#1434C2×C12714yes—
136C127#1611211yescharacteristic, direct product factor, Sylow
137C23×Q8C22×C12711yescharacteristic
138C22×C4⋊C4C22×C12712yes—
139C22×C42C22×C12712yes—
140#391—28no—
141C2×#95C22×C12714yes—
142C2×#95C22×C12714yes—
143C2×#95C22×C12714yes—
144C2×#95C22×C12714yes—
145C2×#95C22×C12714yes—
146C2×#95C22×C12714yes—
147C2×#95C22×C12714yes—
148C2×#95C22×C12712yes—
149C22×Q8—28no—
150C22×Q8—42no—
151C22×Q8D4×C12714yes—
152C23×C4C23×C12714yes—
153C23×C4C23×C12714yes—
154C23×C4C23×C12711yescharacteristic
155C23×C4C23×C12714yes—
156C23×C4C23×C12712yes—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4—42no—
160C2×C42—24no—
161C2×C42—28no—
162#95—28no—
163#95—28no—
164#95—28no—
165#95—28no—
166#95—28no—
167#95—28no—
168#95—42no—
169#95—44no—
170C24C24×C12711yescharacteristic
171C2×Q8—216no—
172C2×Q8—44no—
173C2×Q8—416no—
174C22×C4—24no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—24no—
178C22×C4—24no—
179C22×C4—24no—
180C22×C4—24no—
181C22×C4—24no—
182C22×C4—22no—
183C22×C4—24no—
184C22×C4—24no—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—24no—
189C22×C4—24no—
190C22×C4—24no—
191C22×C4—24no—
192C22×C4—24no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—24no—
196C22×C4—24no—
197C22×C4—24no—
198C22×C4—24no—
199C22×C4C2×D4×C12712yes—
200C22×C4C2×D4×C12714yes—
201C22×C4#41×C12718yes—
202C22×C4#41×C12718yes—
203C4⋊C4—48no—
204C42—48no—
205C23C22×D4×C12711yescharacteristic
206C23C2×#41×C12714yes—
207C23C2×#41×C12714yes—
208C23H(5,𝔽2)×C12712yes—
209C232−1+4×C12714yes—
210Q8—416no—
211C2×C4—24no—
212C2×C4—24no—
213C2×C4—28no—
214C2×C4—28no—
215C2×C4—24no—
216C2×C4—28no—
217C2×C4—22no—
218C2×C4—28no—
219C2×C4—28no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—44no—
225C2×C4—44no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—44no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4—44no—
238C2×C4—44no—
239C2×C4#123×C12718yes—
240C22C2×#123×C12712yes—
241C22#529×C12714yes—
242C22#534×C12711yescharacteristic
243C22#541×C12714yes—
244C22#542×C12714yes—
245C22#548×C12714yes—
246C22#551×C12714yes—
247C22#552×C12714yes—
248C22#555×C12712yes—
249C22#556×C12714yes—
250C22#563×C12712yes—
251C4—28no—
252C4—48no—
253C4—42no—
254C4—84no—
255C4—84no—
256C2C127×#242114yes—
257C2C127×#248311yescharacteristic
258C2C127×#253214yes—
259C2C127×#273112yes—
260C2C127×#276214yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutator, Frattini, cosocleC24C24×C127
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
125. #16112C127direct (N × H)
136. C127#16112direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#391×C1272
C127×#14462
C127×#14432
C127×#14422
C127×#14342
#16112127