Finite Group Databasebeta

← C127×#17070 #44580743

Subgroups — C127×#17070 #44580743

Order 32512.

1314 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#398×C127C214yesmaximal
2C2×#389×C127C212yesmaximal
3C127×#1441C214yesmaximal
4C127×#1441C214yesmaximal
5C127×C4⋊#95C211yesmaximal, characteristic
6C22×C4⋊C4×C127C2214yes—
7C22×C4⋊C4×C127C2214yes—
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C42×C127C2211yescharacteristic
12#398×C127—216no—
13#389×C127—28no—
14C2×#95×C127C2214yes—
15C2×#95×C127C2218yes—
16C2×#95×C127C2214yes—
17C2×#95×C127C2214yes—
18C23×C4×C127C2314yes—
19C23×C4×C127C2314yes—
20C23×C4×C127C2314yes—
21C23×C4×C127C2312yes—
22C23×C4×C127C2311yescharacteristic
23C2×C4⋊C4×C127—24no—
24C2×C4⋊C4×C127—24no—
25C2×C4⋊C4×C127—24no—
26C2×C4⋊C4×C127—28no—
27C2×C4⋊C4×C127—216no—
28C2×C4⋊C4×C127—28no—
29C2×C4⋊C4×C127—28no—
30C2×C4⋊C4×C127—42no—
31C2×C4⋊C4×C127—42no—
32C2×C4⋊C4×C127—44no—
33C2×C4⋊C4×C127—44no—
34C2×C4⋊C4×C127D418yes—
35C2×C4⋊C4×C127Q818yes—
36C2×C42×C127—42no—
37C2×C42×C127D414yes—
38#95×C127—28no—
39#95×C127—28no—
40#95×C127—216no—
41#95×C127—44no—
42C24×C127C2411yescharacteristic
43C22×C4×C127—24no—
44C22×C4×C127—22no—
45C22×C4×C127—21no—
46C22×C4×C127—24no—
47C22×C4×C127—21no—
48C22×C4×C127—28no—
49C22×C4×C127—24no—
50C22×C4×C127—24no—
51C22×C4×C127—24no—
52C22×C4×C127—24no—
53C22×C4×C127—24no—
54C22×C4×C127—24no—
55C22×C4×C127—24no—
56C22×C4×C127—24no—
57C22×C4×C127—28no—
58C22×C4×C127—24no—
59C22×C4×C127—24no—
60C22×C4×C127—24no—
61C22×C4×C127—28no—
62C22×C4×C127—28no—
63C22×C4×C127C2×D418yes—
64C22×C4×C127C2×D414yes—
65C22×C4×C127C2×D414yes—
66C22×C4×C127C2×D412yes—
67C22×C4×C127C2×Q818yes—
68C22×C4×C127C2×Q814yes—
69C22×C4×C127#4114yes—
70C4⋊C4×C127—216no—
71C4⋊C4×C127—48no—
72C4⋊C4×C127—416no—
73C4⋊C4×C127—48no—
74C4⋊C4×C127—416no—
75C42×C127—44no—
76C23×C127C22×D411yescharacteristic
77C23×C127C22×D412yes—
78C23×C127C22×Q812yes—
79C23×C127C2×#4112yes—
80C23×C127H(5,𝔽2)12yes—
81C23×C127H(5,𝔽2)11yescharacteristic
82C23×C1272−1+414yes—
83C23×C1272−1+411yescharacteristic
84C2×C4×C127—24no—
85C2×C4×C127—22no—
86C2×C4×C127—24no—
87C2×C4×C127—28no—
88C2×C4×C127—22no—
89C2×C4×C127—28no—
90C2×C4×C127—24no—
91C2×C4×C127—24no—
92C2×C4×C127—28no—
93C2×C4×C127—28no—
94C2×C4×C127—28no—
95C2×C4×C127—28no—
96C2×C4×C127—216no—
97C2×C4×C127—44no—
98C2×C4×C127—48no—
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—48no—
108C2×C4×C127—48no—
109C2×C4×C127#12118yes—
110C2×C4×C127C4⋊Q814yes—
111C22×C127C2×#12112yes—
112C22×C127C2×C4⋊Q811yescharacteristic
113C22×C127#53411yescharacteristic
114C22×C127#53612yes—
115C22×C127#53711yescharacteristic
116C22×C127#53714yes—
117C22×C127#53914yes—
118C22×C127#54312yes—
119C22×C127#54412yes—
120C22×C127D4211yescharacteristic
121C22×C127#54712yes—
122C22×C127D4×Q814yes—
123C22×C127#55511yescharacteristic
124C22×C127#55714yes—
125C22×C127#56312yes—
126C22×C127#56412yes—
127C4×C127—28no—
128C4×C127—24no—
129C4×C127—48no—
130C4×C127—48no—
131C4×C127—84no—
132#17070C12711yesmaximal, characteristic, direct product factor, Sylow
133C2×C127#253711yescharacteristic
134C2×C127#254612yes—
135C2×C127#261812yes—
136C2×C127#265911yescharacteristic
137C2×C127#268312yes—
138C2×C127#272614yes—
139C2×C127#280912yes—
140C2×C127#282211yescharacteristic
141C2×#398C2×C12714yes—
142C2×#389C2×C12712yes—
143#1441C2×C12714yes—
144#1441C2×C12714yes—
145C4⋊#95C2×C12711yescharacteristic
146C127#1707011yescharacteristic, direct product factor, Sylow
147C22×C4⋊C4C22×C12714yes—
148C22×C4⋊C4C22×C12714yes—
149C22×C4⋊C4C22×C12712yes—
150C22×C4⋊C4C22×C12712yes—
151C22×C4⋊C4C22×C12712yes—
152C22×C42C22×C12711yescharacteristic
153#398—216no—
154#389—28no—
155C2×#95C22×C12714yes—
156C2×#95C22×C12718yes—
157C2×#95C22×C12714yes—
158C2×#95C22×C12714yes—
159C23×C4C23×C12714yes—
160C23×C4C23×C12714yes—
161C23×C4C23×C12714yes—
162C23×C4C23×C12712yes—
163C23×C4C23×C12711yescharacteristic
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—28no—
168C2×C4⋊C4—216no—
169C2×C4⋊C4—28no—
170C2×C4⋊C4—28no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—44no—
175C2×C4⋊C4D4×C12718yes—
176C2×C4⋊C4Q8×C12718yes—
177C2×C42—42no—
178C2×C42D4×C12714yes—
179#95—28no—
180#95—28no—
181#95—216no—
182#95—44no—
183C24C24×C12711yescharacteristic
184C22×C4—24no—
185C22×C4—22no—
186C22×C4—21no—
187C22×C4—24no—
188C22×C4—21no—
189C22×C4—28no—
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—28no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—24no—
202C22×C4—28no—
203C22×C4—28no—
204C22×C4C2×D4×C12718yes—
205C22×C4C2×D4×C12714yes—
206C22×C4C2×D4×C12714yes—
207C22×C4C2×D4×C12712yes—
208C22×C4C2×Q8×C12718yes—
209C22×C4C2×Q8×C12714yes—
210C22×C4#41×C12714yes—
211C4⋊C4—216no—
212C4⋊C4—48no—
213C4⋊C4—416no—
214C4⋊C4—48no—
215C4⋊C4—416no—
216C42—44no—
217C23C22×D4×C12711yescharacteristic
218C23C22×D4×C12712yes—
219C23C22×Q8×C12712yes—
220C23C2×#41×C12712yes—
221C23H(5,𝔽2)×C12712yes—
222C23H(5,𝔽2)×C12711yescharacteristic
223C232−1+4×C12714yes—
224C232−1+4×C12711yescharacteristic
225C2×C4—24no—
226C2×C4—22no—
227C2×C4—24no—
228C2×C4—28no—
229C2×C4—22no—
230C2×C4—28no—
231C2×C4—24no—
232C2×C4—24no—
233C2×C4—28no—
234C2×C4—28no—
235C2×C4—28no—
236C2×C4—28no—
237C2×C4—216no—
238C2×C4—44no—
239C2×C4—48no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—44no—
248C2×C4—48no—
249C2×C4—48no—
250C2×C4#121×C12718yes—
251C2×C4C4⋊Q8×C12714yes—
252C22C2×#121×C12712yes—
253C22C2×C4⋊Q8×C12711yescharacteristic
254C22#534×C12711yescharacteristic
255C22#536×C12712yes—
256C22#537×C12714yes—
257C22#537×C12711yescharacteristic
258C22#539×C12714yes—
259C22#543×C12712yes—
260C22#544×C12712yes—
261C22D42×C12711yescharacteristic
262C22#547×C12712yes—
263C22D4×Q8×C12714yes—
264C22#555×C12711yescharacteristic
265C22#557×C12714yes—
266C22#563×C12712yes—
267C22#564×C12712yes—
268C4—28no—
269C4—24no—
270C4—48no—
271C4—48no—
272C4—84no—
273C2C127×#253711yescharacteristic
274C2C127×#254612yes—
275C2C127×#261812yes—
276C2C127×#265911yescharacteristic
277C2C127×#268312yes—
278C2C127×#272614yes—
279C2C127×#280912yes—
280C2C127×#282211yescharacteristic
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
132. #17070C127direct (N × H)
146. C127#17070direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#398×C1272
C2×#389×C1272
C127×#14412
C127×C4⋊#952
#17070127