Finite Group Databasebeta

← C2×C127×#1829 #44584384

Subgroups — C2×C127×#1829 #44584384

Order 32512.

1434 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×#518×C127C211yesmaximal, characteristic
2C22×#100×C127C212yesmaximal
3C127×#1829C218yesmaximal, direct product factor
4C2×#344×C127C214yesmaximal, complemented
5C23×D4×C127C2211yescharacteristic
6C22×M16×C127C2214yes—
7#518×C127—24no—
8#518×C127C414yes—
9#518×C127C2214yes—
10C2×C4×D4×C127—24no—
11C2×#117×C127C2212yes—
12C22×C22⋊C4×C127C414yes—
13C2×#100×C127—24no—
14C2×#100×C127—24no—
15C2×#100×C127C2218yes—
16#344×C127C22116yescomplemented
17C25×C127C2×C412yes—
18C22×D4×C127—24no—
19C22×D4×C127—24no—
20C22×D4×C127C2×C412yes—
21C22×D4×C127D414yes—
22C22×D4×C127D414yes—
23C22×D4×C127C2312yes—
24C23×C4×C127—24no—
25C23×C4×C127C2311yescharacteristic
26C2×M16×C127—24no—
27C2×M16×C127—24no—
28C2×M16×C127—24no—
29C2×M16×C127—24no—
30C2×M16×C127—24no—
31C2×M16×C127C2318yes—
32C22×C8×C127—24no—
33C4×D4×C127—216no—
34C4×D4×C127—216no—
35#117×C127—22no—
36#117×C127—22no—
37#117×C127C2×C414yes—
38#117×C127C2314yes—
39C2×C4⋊C4×C127—22no—
40C2×C22⋊C4×C127—24no—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127C2×C414yes—
43C2×C22⋊C4×C127C2×C4116yes—
44C2×C42×C127—22no—
45#100×C127—216no—
46C24×C127—24no—
47C24×C127—24no—
48C24×C127—84no—
49C24×C127C22⋊C414yes—
50C24×C127C22⋊C414yes—
51C24×C127C22×C414yes—
52C24×C127C22×C411yescharacteristic
53C2×D4×C127—28no—
54C2×D4×C127—28no—
55C2×D4×C127—28no—
56C2×D4×C127—28no—
57C2×D4×C127—28no—
58C2×D4×C127—28no—
59C2×D4×C127C22⋊C418yes—
60C2×D4×C127C2×D418yes—
61C22×C4×C127—24no—
62C22×C4×C127—216no—
63C22×C4×C127—88no—
64C22×C4×C127C22×C411yescharacteristic
65C22×C4×C127C2×D412yes—
66C22×C4×C127C2×D412yes—
67C22×C4×C127#4114yes—
68C22×C4×C127#4114yes—
69C22×C4×C127C2411yescharacteristic
70M16×C127—28no—
71M16×C127—28no—
72M16×C127—44no—
73M16×C127—44no—
74C2×C8×C127—28no—
75C2×C8×C127—44no—
76C2×C8×C127—44no—
77C4⋊C4×C127—24no—
78C4⋊C4×C127—24no—
79C22⋊C4×C127—24no—
80C22⋊C4×C127—216no—
81C22⋊C4×C127C22×C418yes—
82C42×C127—24no—
83C42×C127—24no—
84C23×C127—24no—
85C23×C127—24no—
86C23×C127—28no—
87C23×C127—28no—
88C23×C127—42no—
89C23×C127—48no—
90C23×C127—88no—
91C23×C127—84no—
92C23×C127—84no—
93C23×C127—88no—
94C23×C127C2×C22⋊C411yescharacteristic
95C23×C127C2×C22⋊C418yes—
96C23×C127C2×C22⋊C411yescharacteristic
97C23×C127#11712yes—
98C23×C127#11712yes—
99C23×C127C23×C411yescharacteristic
100D4×C127—216no—
101D4×C127—216no—
102C2×C4×C127—28no—
103C2×C4×C127—48no—
104C2×C4×C127—816no—
105C2×C4×C127C2×C22⋊C412yes—
106C2×C4×C127#11714yes—
107C2×C4×C127#12314yes—
108C2×C4×C127#12314yes—
109C2×C4×C127#12314yes—
110C2×C4×C127#12314yes—
111C2×C4×C127C22×D412yes—
112C2×C4×C127C2×#4114yes—
113C8×C127—48no—
114C22×C127—22no—
115C22×C127—24no—
116C22×C127—28no—
117C22×C127—41no—
118C22×C127—42no—
119C22×C127—41no—
120C22×C127—48no—
121C22×C127—48no—
122C22×C127—48no—
123C22×C127—88no—
124C22×C127—88no—
125C22×C127#38111yescharacteristic
126C22×C127#38112yes—
127C22×C127#38111yescharacteristic
128C22×C127C22×C22⋊C411yescharacteristic
129C22×C127C2×#11712yes—
130C4×C127—48no—
131C4×C127#38114yes—
132C4×C127C2×#12314yes—
133C2×#1829C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—21no—
135C2×C127—21no—
136C2×C127—22no—
137C2×C127—22no—
138C2×C127—48no—
139C2×C127#182912yesdirect product factor
140C2×C127C2×#38111yescharacteristic
141C2×#518C2×C12711yescharacteristic
142C22×#100C2×C12712yes—
143#1829C2×C12718yesdirect product factor
144C2×#344C2×C12714yescomplemented
145C127C2×#182911yescharacteristic, direct product factor, Sylow
146C23×D4C22×C12711yescharacteristic
147C22×M16C22×C12714yes—
148#518—24no—
149#518C4×C12714yes—
150#518C22×C12714yes—
151C2×C4×D4—24no—
152C2×#117C22×C12712yes—
153C22×C22⋊C4C4×C12714yes—
154C2×#100—24no—
155C2×#100—24no—
156C2×#100C22×C12718yes—
157#344C22×C127116yescomplemented
158C25C2×C4×C12712yes—
159C22×D4—24no—
160C22×D4—24no—
161C22×D4C2×C4×C12712yes—
162C22×D4D4×C12714yes—
163C22×D4D4×C12714yes—
164C22×D4C23×C12712yes—
165C23×C4—24no—
166C23×C4C23×C12711yescharacteristic
167C2×M16—24no—
168C2×M16—24no—
169C2×M16—24no—
170C2×M16—24no—
171C2×M16—24no—
172C2×M16C23×C12718yes—
173C22×C8—24no—
174C4×D4—216no—
175C4×D4—216no—
176#117—22no—
177#117—22no—
178#117C2×C4×C12714yes—
179#117C23×C12714yes—
180C2×C4⋊C4—22no—
181C2×C22⋊C4—24no—
182C2×C22⋊C4—28no—
183C2×C22⋊C4C2×C4×C12714yes—
184C2×C22⋊C4C2×C4×C127116yes—
185C2×C42—22no—
186#100—216no—
187C24—24no—
188C24—24no—
189C24—84no—
190C24C22⋊C4×C12714yes—
191C24C22⋊C4×C12714yes—
192C24C22×C4×C12714yes—
193C24C22×C4×C12711yescharacteristic
194C2×D4—28no—
195C2×D4—28no—
196C2×D4—28no—
197C2×D4—28no—
198C2×D4—28no—
199C2×D4—28no—
200C2×D4C22⋊C4×C12718yes—
201C2×D4C2×D4×C12718yes—
202C22×C4—24no—
203C22×C4—216no—
204C22×C4—88no—
205C22×C4C22×C4×C12711yescharacteristic
206C22×C4C2×D4×C12712yes—
207C22×C4C2×D4×C12712yes—
208C22×C4#41×C12714yes—
209C22×C4#41×C12714yes—
210C22×C4C24×C12711yescharacteristic
211M16—28no—
212M16—28no—
213M16—44no—
214M16—44no—
215C2×C8—28no—
216C2×C8—44no—
217C2×C8—44no—
218C4⋊C4—24no—
219C4⋊C4—24no—
220C22⋊C4—24no—
221C22⋊C4—216no—
222C22⋊C4C22×C4×C12718yes—
223C42—24no—
224C42—24no—
225C23—24no—
226C23—24no—
227C23—28no—
228C23—28no—
229C23—42no—
230C23—48no—
231C23—88no—
232C23—84no—
233C23—84no—
234C23—88no—
235C23C2×C22⋊C4×C12711yescharacteristic
236C23C2×C22⋊C4×C12718yes—
237C23C2×C22⋊C4×C12711yescharacteristic
238C23#117×C12712yes—
239C23#117×C12712yes—
240C23C23×C4×C12711yescharacteristic
241D4—216no—
242D4—216no—
243C2×C4—28no—
244C2×C4—48no—
245C2×C4—816no—
246C2×C4C2×C22⋊C4×C12712yes—
247C2×C4#117×C12714yes—
248C2×C4#123×C12714yes—
249C2×C4#123×C12714yes—
250C2×C4#123×C12714yes—
251C2×C4#123×C12714yes—
252C2×C4C22×D4×C12712yes—
253C2×C4C2×#41×C12714yes—
254C8—48no—
255C22—22no—
256C22—24no—
257C22—28no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—48no—
262C22—48no—
263C22—48no—
264C22—88no—
265C22—88no—
266C22#381×C12711yescharacteristic
267C22#381×C12712yes—
268C22#381×C12711yescharacteristic
269C22C22×C22⋊C4×C12711yescharacteristic
270C22C2×#117×C12712yes—
271C4—48no—
272C4#381×C12714yes—
273C4C2×#123×C12714yes—
274C2—21no—
275C2—21no—
276C2—22no—
277C2—22no—
278C2—48no—
279C2C127×#182912yesdirect product factor
280C2C2×#381×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#381
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1829C2direct (N × H)
4. C2×#344×C127C2semidirect
16. #344×C127C22semidirect
133. C2×#1829C127direct (N × H)
139. C2×C127#1829direct (N × H)
143. #1829C2×C127direct (N × H)
144. C2×#344C2×C127semidirect
145. C127C2×#1829direct (N × H)
157. #344C22×C127semidirect
279. C2C127×#1829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#518×C1272
C22×#100×C1272
C127×#18292
C2×#344×C1272
C2×#1829127