Finite Group Databasebeta

← C127×#8451 #44572124

Subgroups — C127×#8451 #44572124

Order 32512.

804 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q82×C127C211yesmaximal, characteristic
2C127×#1956C211yesmaximal, characteristic
3C127×#1803C212yesmaximal
4C2×#333×C127C211yesmaximal, characteristic
5C2×Q8⋊C8×C127C212yesmaximal
6Q82×C127—22no—
7Q82×C127—24no—
8Q82×C127C414yescomplemented
9C2×C4⋊Q8×C127—22no—
10C2×C4⋊Q8×C127—22no—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4×Q8×C127—22no—
13C2×C4×Q8×C127C2212yes—
14C2×C4⋊C8×C127C2212yes—
15C2×#103×C127—22no—
16C2×#103×C127—22no—
17C2×C4×C8×C127C2211yescharacteristic
18#384×C127C2211yescharacteristic
19#340×C127—22no—
20#333×C127—22no—
21Q8⋊C8×C127—24no—
22C22×Q8×C127—22no—
23C22×Q8×C127D412yes—
24C22×Q8×C127D412yes—
25C22×C8×C127—21no—
26C22×C8×C127—22no—
27C4⋊Q8×C127—28no—
28C4⋊Q8×C127—28no—
29C4⋊Q8×C127—28no—
30C4⋊Q8×C127—28no—
31C4⋊Q8×C127—22no—
32C4⋊Q8×C127C2×C412yes—
33C4⋊Q8×C127D412yes—
34C4×Q8×C127—28no—
35C4×Q8×C127—28no—
36C4×Q8×C127—22no—
37C4×Q8×C127—22no—
38C4×Q8×C127C2×C414yes—
39C4×Q8×C127D414yes—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127D412yes—
46C2×C42×C127—22no—
47C2×C42×C127—22no—
48C2×C42×C127C2311yescharacteristic
49C4⋊C8×C127—22no—
50C4⋊C8×C127—22no—
51#103×C127—44no—
52#103×C127—44no—
53C4×C8×C127—22no—
54C2×Q8×C127—28no—
55C2×Q8×C127—22no—
56C2×Q8×C127—22no—
57C2×Q8×C127—22no—
58C2×Q8×C127—22no—
59C2×Q8×C127—42no—
60C2×Q8×C127—42no—
61C2×Q8×C127—82no—
62C2×Q8×C127—82no—
63C2×Q8×C127C22⋊C414yes—
64C2×Q8×C127C22⋊C414yes—
65C2×Q8×C127SD1614yes—
66C2×Q8×C127Q1614yes—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—22no—
70C22×C4×C127—41no—
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127C2×D412yes—
73C2×C8×C127—22no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—42no—
77C2×C8×C127—42no—
78C2×C8×C127—42no—
79C4⋊C4×C127—216no—
80C4⋊C4×C127—24no—
81C4⋊C4×C127—24no—
82C4⋊C4×C127—24no—
83C4⋊C4×C127—24no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127C22⋊C414yes—
89C42×C127—28no—
90C42×C127—24no—
91C42×C127—24no—
92C42×C127C22×C411yescharacteristic
93C42×C127C2×D412yes—
94C42×C127C2×D411yescharacteristic
95C23×C127#12011yescharacteristic
96Q8×C127—24no—
97Q8×C127—24no—
98Q8×C127—24no—
99Q8×C127—44no—
100Q8×C127—82no—
101Q8×C127—88no—
102Q8×C127#10318yescomplemented
103C2×C4×C127—24no—
104C2×C4×C127—24no—
105C2×C4×C127—24no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—24no—
109C2×C4×C127—24no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—42no—
113C2×C4×C127—42no—
114C2×C4×C127—82no—
115C2×C4×C127—81no—
116C2×C4×C127C2×C22⋊C411yescharacteristic
117C2×C4×C127C2×C22⋊C412yes—
118C2×C4×C127#12011yescharacteristic
119C2×C4×C127#12012yes—
120C2×C4×C127C2×SD1612yes—
121C2×C4×C127C2×Q1612yes—
122C2×C4×C127#13712yes—
123C2×C4×C127#13712yes—
124C8×C127—42no—
125C8×C127—82no—
126C22×C127#37911yescharacteristic
127C22×C127#44812yes—
128C22×C127#45112yes—
129C22×C127#45311yescharacteristic
130C22×C127#45511yescharacteristic
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—28no—
134C4×C127—44no—
135C4×C127—44no—
136C4×C127—161no—
137C4×C127C2×#10312yes—
138C4×C127#41912yes—
139C4×C127#44812yes—
140C4×C127#45112yes—
141#8451C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127#162311yescharacteristic
143C2×C127#163311yescharacteristic
144C2×C127#164512yes—
145C2×C127#178712yes—
146C2×C127#179211yescharacteristic
147C2×Q82C2×C12711yescharacteristic
148#1956C2×C12711yescharacteristic
149#1803C2×C12712yes—
150C2×#333C2×C12711yescharacteristic
151C2×Q8⋊C8C2×C12712yes—
152C127#845111yescharacteristic, direct product factor, Sylow
153Q82—22no—
154Q82—24no—
155Q82C4×C12714yescomplemented
156C2×C4⋊Q8—22no—
157C2×C4⋊Q8—22no—
158C2×C4⋊Q8C22×C12711yescharacteristic
159C2×C4×Q8—22no—
160C2×C4×Q8C22×C12712yes—
161C2×C4⋊C8C22×C12712yes—
162C2×#103—22no—
163C2×#103—22no—
164C2×C4×C8C22×C12711yescharacteristic
165#384C22×C12711yescharacteristic
166#340—22no—
167#333—22no—
168Q8⋊C8—24no—
169C22×Q8—22no—
170C22×Q8D4×C12712yes—
171C22×Q8D4×C12712yes—
172C22×C8—21no—
173C22×C8—22no—
174C4⋊Q8—28no—
175C4⋊Q8—28no—
176C4⋊Q8—28no—
177C4⋊Q8—28no—
178C4⋊Q8—22no—
179C4⋊Q8C2×C4×C12712yes—
180C4⋊Q8D4×C12712yes—
181C4×Q8—28no—
182C4×Q8—28no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8C2×C4×C12714yes—
186C4×Q8D4×C12714yes—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4D4×C12712yes—
193C2×C42—22no—
194C2×C42—22no—
195C2×C42C23×C12711yescharacteristic
196C4⋊C8—22no—
197C4⋊C8—22no—
198#103—44no—
199#103—44no—
200C4×C8—22no—
201C2×Q8—28no—
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—42no—
207C2×Q8—42no—
208C2×Q8—82no—
209C2×Q8—82no—
210C2×Q8C22⋊C4×C12714yes—
211C2×Q8C22⋊C4×C12714yes—
212C2×Q8SD16×C12714yes—
213C2×Q8Q16×C12714yes—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—41no—
218C22×C4C2×D4×C12711yescharacteristic
219C22×C4C2×D4×C12712yes—
220C2×C8—22no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C4⋊C4—216no—
227C4⋊C4—24no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—24no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4C22⋊C4×C12714yes—
236C42—28no—
237C42—24no—
238C42—24no—
239C42C22×C4×C12711yescharacteristic
240C42C2×D4×C12712yes—
241C42C2×D4×C12711yescharacteristic
242C23#120×C12711yescharacteristic
243Q8—24no—
244Q8—24no—
245Q8—24no—
246Q8—44no—
247Q8—82no—
248Q8—88no—
249Q8#103×C12718yescomplemented
250C2×C4—24no—
251C2×C4—24no—
252C2×C4—24no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—81no—
263C2×C4C2×C22⋊C4×C12711yescharacteristic
264C2×C4C2×C22⋊C4×C12712yes—
265C2×C4#120×C12711yescharacteristic
266C2×C4#120×C12712yes—
267C2×C4C2×SD16×C12712yes—
268C2×C4C2×Q16×C12712yes—
269C2×C4#137×C12712yes—
270C2×C4#137×C12712yes—
271C8—42no—
272C8—82no—
273C22#379×C12711yescharacteristic
274C22#448×C12712yes—
275C22#451×C12712yes—
276C22#453×C12711yescharacteristic
277C22#455×C12711yescharacteristic
278C4—28no—
279C4—21no—
280C4—21no—
281C4—44no—
282C4—44no—
283C4—161no—
284C4C2×#103×C12712yes—
285C4#419×C12712yes—
286C4#448×C12712yes—
287C4#451×C12712yes—
288C2C127×#162311yescharacteristic
289C2C127×#163311yescharacteristic
290C2C127×#164512yes—
291C2C127×#178712yes—
292C2C127×#179211yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
8. Q82×C127C4semidirect
102. Q8×C127#103semidirect
141. #8451C127direct (N × H)
152. C127#8451direct (N × H)
155. Q82C4×C127semidirect
249. Q8#103×C127semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1272
C127×#19562
C127×#18032
C2×#333×C1272
C2×Q8⋊C8×C1272
#8451127