Finite Group Databasebeta

← C127×#15762 #44579435

Subgroups — C127×#15762 #44579435

Order 32512.

2018 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Q8×C127C212yesmaximal
2C2×#395×C127C214yesmaximal
3C127×#1446C211yesmaximal, characteristic
4C127×#1444C214yesmaximal
5C127×#1436C214yesmaximal
6C23×Q8×C127C2212yes—
7C23×Q8×C127C2211yescharacteristic
8C2×C4⋊Q8×C127—28no—
9C2×C4⋊Q8×C127—216no—
10C22×C4⋊C4×C127C2214yes—
11C22×C4⋊C4×C127C2214yes—
12C22×C4⋊C4×C127C2214yes—
13C22×C42×C127C2212yes—
14#395×C127—216no—
15C2×#95×C127C2218yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2212yes—
18C2×#95×C127C2214yes—
19C22×Q8×C127—28no—
20C22×Q8×C127—28no—
21C22×Q8×C127—24no—
22C22×Q8×C127—28no—
23C22×Q8×C127—42no—
24C22×Q8×C127—44no—
25C22×Q8×C127D414yes—
26C23×C4×C127C2314yes—
27C23×C4×C127C2311yescharacteristic
28C23×C4×C127C2314yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2314yes—
31C4⋊Q8×C127—264no—
32C2×C4⋊C4×C127—28no—
33C2×C4⋊C4×C127—28no—
34C2×C4⋊C4×C127—28no—
35C2×C4⋊C4×C127—28no—
36C2×C4⋊C4×C127—28no—
37C2×C4⋊C4×C127—216no—
38C2×C4⋊C4×C127—44no—
39C2×C4⋊C4×C127D4116yes—
40C2×C42×C127—24no—
41C2×C42×C127—28no—
42#95×C127—28no—
43#95×C127—216no—
44#95×C127—42no—
45#95×C127Q8116yescomplemented
46C24×C127C2411yescharacteristic
47C2×Q8×C127—216no—
48C2×Q8×C127—216no—
49C2×Q8×C127—44no—
50C2×Q8×C127—416no—
51C2×Q8×C127—432no—
52C2×Q8×C127—48no—
53C2×Q8×C127—48no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—24no—
57C22×C4×C127—24no—
58C22×C4×C127—28no—
59C22×C4×C127—28no—
60C22×C4×C127—28no—
61C22×C4×C127—24no—
62C22×C4×C127—24no—
63C22×C4×C127—24no—
64C22×C4×C127—24no—
65C22×C4×C127—22no—
66C22×C4×C127—28no—
67C22×C4×C127—24no—
68C22×C4×C127—28no—
69C22×C4×C127C2×D412yes—
70C22×C4×C127C2×D418yes—
71C22×C4×C127C2×D418yes—
72C22×C4×C127C2×D414yes—
73C22×C4×C127C2×D418yes—
74C22×C4×C127C2×Q818yes—
75C22×C4×C127C2×Q8116yes—
76C4⋊C4×C127—232no—
77C4⋊C4×C127—232no—
78C4⋊C4×C127—416no—
79C42×C127—216no—
80C23×C127C22×D411yescharacteristic
81C23×C127C22×D414yes—
82C23×C127C22×Q814yes—
83C23×C127H(5,𝔽2)12yes—
84C23×C1272−1+414yes—
85Q8×C127—416no—
86Q8×C127—432no—
87C2×C4×C127—28no—
88C2×C4×C127—24no—
89C2×C4×C127—24no—
90C2×C4×C127—28no—
91C2×C4×C127—216no—
92C2×C4×C127—216no—
93C2×C4×C127—216no—
94C2×C4×C127—24no—
95C2×C4×C127—28no—
96C2×C4×C127—22no—
97C2×C4×C127—28no—
98C2×C4×C127—216no—
99C2×C4×C127—216no—
100C2×C4×C127—44no—
101C2×C4×C127—44no—
102C2×C4×C127—48no—
103C2×C4×C127—44no—
104C2×C4×C127—48no—
105C2×C4×C127—44no—
106C2×C4×C127—44no—
107C2×C4×C127#12018yes—
108C2×C4×C127C4⋊Q8116yescomplemented
109C22×C127C2×#12012yes—
110C22×C127C2×C4⋊Q814yes—
111C22×C127#53411yescharacteristic
112C22×C127#53614yes—
113C22×C127#54414yes—
114C22×C127D4214yes—
115C22×C127D4×Q818yes—
116C22×C127D4×Q814yes—
117C22×C127Q8212yes—
118C22×C127#56312yes—
119C4×C127—28no—
120C4×C127—216no—
121C4×C127—42no—
122C4×C127—48no—
123C4×C127—48no—
124#15762C12711yesmaximal, characteristic, direct product factor, Sylow
125C2×C127#240311yescharacteristic
126C2×C127#243414yes—
127C2×C127#255114yes—
128C2×C127#267714yes—
129C2×C127#273412yes—
130C22×C4⋊Q8C2×C12712yes—
131C2×#395C2×C12714yes—
132#1446C2×C12711yescharacteristic
133#1444C2×C12714yes—
134#1436C2×C12714yes—
135C127#1576211yescharacteristic, direct product factor, Sylow
136C23×Q8C22×C12712yes—
137C23×Q8C22×C12711yescharacteristic
138C2×C4⋊Q8—28no—
139C2×C4⋊Q8—216no—
140C22×C4⋊C4C22×C12714yes—
141C22×C4⋊C4C22×C12714yes—
142C22×C4⋊C4C22×C12714yes—
143C22×C42C22×C12712yes—
144#395—216no—
145C2×#95C22×C12718yes—
146C2×#95C22×C12714yes—
147C2×#95C22×C12712yes—
148C2×#95C22×C12714yes—
149C22×Q8—28no—
150C22×Q8—28no—
151C22×Q8—24no—
152C22×Q8—28no—
153C22×Q8—42no—
154C22×Q8—44no—
155C22×Q8D4×C12714yes—
156C23×C4C23×C12714yes—
157C23×C4C23×C12711yescharacteristic
158C23×C4C23×C12714yes—
159C23×C4C23×C12712yes—
160C23×C4C23×C12714yes—
161C4⋊Q8—264no—
162C2×C4⋊C4—28no—
163C2×C4⋊C4—28no—
164C2×C4⋊C4—28no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—28no—
167C2×C4⋊C4—216no—
168C2×C4⋊C4—44no—
169C2×C4⋊C4D4×C127116yes—
170C2×C42—24no—
171C2×C42—28no—
172#95—28no—
173#95—216no—
174#95—42no—
175#95Q8×C127116yescomplemented
176C24C24×C12711yescharacteristic
177C2×Q8—216no—
178C2×Q8—216no—
179C2×Q8—44no—
180C2×Q8—416no—
181C2×Q8—432no—
182C2×Q8—48no—
183C2×Q8—48no—
184C22×C4—24no—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—28no—
189C22×C4—28no—
190C22×C4—28no—
191C22×C4—24no—
192C22×C4—24no—
193C22×C4—24no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—28no—
197C22×C4—24no—
198C22×C4—28no—
199C22×C4C2×D4×C12712yes—
200C22×C4C2×D4×C12718yes—
201C22×C4C2×D4×C12718yes—
202C22×C4C2×D4×C12714yes—
203C22×C4C2×D4×C12718yes—
204C22×C4C2×Q8×C12718yes—
205C22×C4C2×Q8×C127116yes—
206C4⋊C4—232no—
207C4⋊C4—232no—
208C4⋊C4—416no—
209C42—216no—
210C23C22×D4×C12711yescharacteristic
211C23C22×D4×C12714yes—
212C23C22×Q8×C12714yes—
213C23H(5,𝔽2)×C12712yes—
214C232−1+4×C12714yes—
215Q8—416no—
216Q8—432no—
217C2×C4—28no—
218C2×C4—24no—
219C2×C4—24no—
220C2×C4—28no—
221C2×C4—216no—
222C2×C4—216no—
223C2×C4—216no—
224C2×C4—24no—
225C2×C4—28no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—216no—
229C2×C4—216no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—48no—
233C2×C4—44no—
234C2×C4—48no—
235C2×C4—44no—
236C2×C4—44no—
237C2×C4#120×C12718yes—
238C2×C4C4⋊Q8×C127116yescomplemented
239C22C2×#120×C12712yes—
240C22C2×C4⋊Q8×C12714yes—
241C22#534×C12711yescharacteristic
242C22#536×C12714yes—
243C22#544×C12714yes—
244C22D42×C12714yes—
245C22D4×Q8×C12718yes—
246C22D4×Q8×C12714yes—
247C22Q82×C12712yes—
248C22#563×C12712yes—
249C4—28no—
250C4—216no—
251C4—42no—
252C4—48no—
253C4—48no—
254C2C127×#240311yescharacteristic
255C2C127×#243414yes—
256C2C127×#255114yes—
257C2C127×#267714yes—
258C2C127×#273412yes—
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
45. #95×C127Q8semidirect
108. C2×C4×C127C4⋊Q8semidirect
124. #15762C127direct (N × H)
135. C127#15762direct (N × H)
175. #95Q8×C127semidirect
238. C2×C4C4⋊Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Q8×C1272
C2×#395×C1272
C127×#14462
C127×#14442
C127×#14362
#15762127