Finite Group Databasebeta

← C127×#14165 #44577838

Subgroups — C127×#14165 #44577838

Order 32512.

1646 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#381×C127C211yesmaximal, characteristic
2C2×C4×C22⋊C4×C127C212yesmaximal
3C127×#1439C214yesmaximal
4C127×#1436C218yesmaximal, complemented
5C24×C4×C127C2211yescharacteristic
6C22×C4⋊C4×C127C2214yes—
7C22×C22⋊C4×C127C2214yes—
8C22×C22⋊C4×C127C2212yes—
9C22×C42×C127C2214yes—
10#381×C127C418yescomplemented
11C4×C22⋊C4×C127—28no—
12C2×#95×C127C2218yes—
13C2×#95×C127C2214yes—
14C2×#95×C127C2214yes—
15C2×#95×C127C2214yes—
16C25×C127C2311yescharacteristic
17C23×C4×C127—42no—
18C23×C4×C127—42no—
19C23×C4×C127C2×C414yes—
20C23×C4×C127D414yes—
21C23×C4×C127Q814yes—
22C23×C4×C127C2314yes—
23C23×C4×C127C2318yes—
24C23×C4×C127C2312yes—
25C2×C4⋊C4×C127—216no—
26C2×C4⋊C4×C127—44no—
27C2×C22⋊C4×C127—28no—
28C2×C22⋊C4×C127—216no—
29C2×C22⋊C4×C127—42no—
30C2×C22⋊C4×C127—42no—
31C2×C22⋊C4×C127C2×C418yes—
32C2×C42×C127—28no—
33C2×C42×C127—44no—
34C2×C42×C127—44no—
35#95×C127—28no—
36#95×C127—216no—
37#95×C127—44no—
38#95×C127C2×C4116yes—
39C24×C127—28no—
40C24×C127—22no—
41C24×C127—22no—
42C24×C127C22×C412yes—
43C24×C127C2×D412yes—
44C24×C127C2×Q812yes—
45C24×C127C2411yescharacteristic
46C22×C4×C127—24no—
47C22×C4×C127—24no—
48C22×C4×C127—28no—
49C22×C4×C127—28no—
50C22×C4×C127—28no—
51C22×C4×C127—28no—
52C22×C4×C127—28no—
53C22×C4×C127—28no—
54C22×C4×C127—28no—
55C22×C4×C127—24no—
56C22×C4×C127—28no—
57C22×C4×C127—24no—
58C22×C4×C127—48no—
59C22×C4×C127—48no—
60C22×C4×C127—44no—
61C22×C4×C127—44no—
62C22×C4×C127C4⋊C4116yescomplemented
63C22×C4×C127C22×C418yes—
64C22×C4×C127C22×C414yes—
65C22×C4×C127C2×D414yes—
66C22×C4×C127C2×Q814yes—
67C22×C4×C127#41116yes—
68C4⋊C4×C127—416no—
69C22⋊C4×C127—232no—
70C22⋊C4×C127—48no—
71C42×C127—416no—
72C23×C127—28no—
73C23×C127—24no—
74C23×C127—28no—
75C23×C127—28no—
76C23×C127—24no—
77C23×C127—22no—
78C23×C127—22no—
79C23×C127—44no—
80C23×C127—48no—
81C23×C127—44no—
82C23×C127C2×C4⋊C414yes—
83C23×C127C23×C411yescharacteristic
84C23×C127C22×D411yescharacteristic
85C23×C127C22×Q811yescharacteristic
86C23×C127C2×#4118yes—
87C23×C127H(5,𝔽2)12yes—
88C23×C127H(5,𝔽2)12yes—
89C2×C4×C127—28no—
90C2×C4×C127—28no—
91C2×C4×C127—24no—
92C2×C4×C127—24no—
93C2×C4×C127—216no—
94C2×C4×C127—28no—
95C2×C4×C127—216no—
96C2×C4×C127—216no—
97C2×C4×C127—216no—
98C2×C4×C127—416no—
99C2×C4×C127—48no—
100C2×C4×C127—48no—
101C2×C4×C127—44no—
102C2×C4×C127—48no—
103C2×C4×C127—48no—
104C2×C4×C127—48no—
105C2×C4×C127—44no—
106C2×C4×C127C2×C4⋊C418yes—
107C22×C127—24no—
108C22×C127—28no—
109C22×C127—48no—
110C22×C127—44no—
111C22×C127—44no—
112C22×C127—48no—
113C22×C127C22×C4⋊C411yescharacteristic
114C22×C127C4×#4114yes—
115C22×C127#51812yes—
116C22×C127#52514yes—
117C22×C127#53314yes—
118C22×C127#53412yes—
119C22×C127#54311yescharacteristic
120C22×C127#54311yescharacteristic
121C22×C127#55114yes—
122C22×C127#55318yes—
123C22×C127#55914yes—
124C4×C127—28no—
125C4×C127—416no—
126C4×C127—48no—
127#14165C12711yesmaximal, characteristic, direct product factor, Sylow
128C2×C127—44no—
129C2×C127#229612yes—
130C2×C127#231511yescharacteristic
131C2×C127#237414yes—
132C2×C127#260014yes—
133C2×C127#260712yes—
134C2×C127#260812yes—
135C2×#381C2×C12711yescharacteristic
136C2×C4×C22⋊C4C2×C12712yes—
137#1439C2×C12714yes—
138#1436C2×C12718yescomplemented
139C127#1416511yescharacteristic, direct product factor, Sylow
140C24×C4C22×C12711yescharacteristic
141C22×C4⋊C4C22×C12714yes—
142C22×C22⋊C4C22×C12714yes—
143C22×C22⋊C4C22×C12712yes—
144C22×C42C22×C12714yes—
145#381C4×C12718yescomplemented
146C4×C22⋊C4—28no—
147C2×#95C22×C12718yes—
148C2×#95C22×C12714yes—
149C2×#95C22×C12714yes—
150C2×#95C22×C12714yes—
151C25C23×C12711yescharacteristic
152C23×C4—42no—
153C23×C4—42no—
154C23×C4C2×C4×C12714yes—
155C23×C4D4×C12714yes—
156C23×C4Q8×C12714yes—
157C23×C4C23×C12714yes—
158C23×C4C23×C12718yes—
159C23×C4C23×C12712yes—
160C2×C4⋊C4—216no—
161C2×C4⋊C4—44no—
162C2×C22⋊C4—28no—
163C2×C22⋊C4—216no—
164C2×C22⋊C4—42no—
165C2×C22⋊C4—42no—
166C2×C22⋊C4C2×C4×C12718yes—
167C2×C42—28no—
168C2×C42—44no—
169C2×C42—44no—
170#95—28no—
171#95—216no—
172#95—44no—
173#95C2×C4×C127116yes—
174C24—28no—
175C24—22no—
176C24—22no—
177C24C22×C4×C12712yes—
178C24C2×D4×C12712yes—
179C24C2×Q8×C12712yes—
180C24C24×C12711yescharacteristic
181C22×C4—24no—
182C22×C4—24no—
183C22×C4—28no—
184C22×C4—28no—
185C22×C4—28no—
186C22×C4—28no—
187C22×C4—28no—
188C22×C4—28no—
189C22×C4—28no—
190C22×C4—24no—
191C22×C4—28no—
192C22×C4—24no—
193C22×C4—48no—
194C22×C4—48no—
195C22×C4—44no—
196C22×C4—44no—
197C22×C4C4⋊C4×C127116yescomplemented
198C22×C4C22×C4×C12718yes—
199C22×C4C22×C4×C12714yes—
200C22×C4C2×D4×C12714yes—
201C22×C4C2×Q8×C12714yes—
202C22×C4#41×C127116yes—
203C4⋊C4—416no—
204C22⋊C4—232no—
205C22⋊C4—48no—
206C42—416no—
207C23—28no—
208C23—24no—
209C23—28no—
210C23—28no—
211C23—24no—
212C23—22no—
213C23—22no—
214C23—44no—
215C23—48no—
216C23—44no—
217C23C2×C4⋊C4×C12714yes—
218C23C23×C4×C12711yescharacteristic
219C23C22×D4×C12711yescharacteristic
220C23C22×Q8×C12711yescharacteristic
221C23C2×#41×C12718yes—
222C23H(5,𝔽2)×C12712yes—
223C23H(5,𝔽2)×C12712yes—
224C2×C4—28no—
225C2×C4—28no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—216no—
229C2×C4—28no—
230C2×C4—216no—
231C2×C4—216no—
232C2×C4—216no—
233C2×C4—416no—
234C2×C4—48no—
235C2×C4—48no—
236C2×C4—44no—
237C2×C4—48no—
238C2×C4—48no—
239C2×C4—48no—
240C2×C4—44no—
241C2×C4C2×C4⋊C4×C12718yes—
242C22—24no—
243C22—28no—
244C22—48no—
245C22—44no—
246C22—44no—
247C22—48no—
248C22C22×C4⋊C4×C12711yescharacteristic
249C22C4×#41×C12714yes—
250C22#518×C12712yes—
251C22#525×C12714yes—
252C22#533×C12714yes—
253C22#534×C12712yes—
254C22#543×C12711yescharacteristic
255C22#543×C12711yescharacteristic
256C22#551×C12714yes—
257C22#553×C12718yes—
258C22#559×C12714yes—
259C4—28no—
260C4—416no—
261C4—48no—
262C2—44no—
263C2C127×#229612yes—
264C2C127×#231511yescharacteristic
265C2C127×#237414yes—
266C2C127×#260014yes—
267C2C127×#260712yes—
268C2C127×#260812yes—
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
4. C127×#1436C2semidirect
10. #381×C127C4semidirect
62. C22×C4×C127C4⋊C4semidirect
127. #14165C127direct (N × H)
138. #1436C2×C127semidirect
139. C127#14165direct (N × H)
145. #381C4×C127semidirect
197. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#381×C1272
C2×C4×C22⋊C4×C1272
C127×#14392
C127×#14362
#14165127