Finite Group Databasebeta

← C127×#13059 #44576732

Subgroups — C127×#13059 #44576732

Order 32512.

578 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C16×C127C211yesmaximal, characteristic, complemented
2C2×#466×C127C211yesmaximal, characteristic
3C2×#357×C127C212yesmaximal, complemented
4C127×#1808C211yesmaximal, characteristic, complemented
5C127×#1380C212yesmaximal, complemented
6C22×D8×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8C2×#121×C127—21no—
9C22×C16×C127—22no—
10C22×C16×C127—24no—
11C22×C16×C127C2212yes—
12#466×C127—22no—
13#466×C127C414yescomplemented
14C2×#107×C127C2212yes—
15C2×#107×C127C2211yescharacteristic
16C2×#102×C127—21no—
17#380×C127—21no—
18#357×C127—24no—
19#340×C127—21no—
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127D411yescharacteristic
23C2×D8×C127—22no—
24C2×D8×C127—21no—
25C2×D8×C127—22no—
26C2×D8×C127C2×C412yes—
27C22×C8×C127—22no—
28C22×C8×C127—22no—
29C22×C8×C127C2×C412yes—
30C22×C8×C127D411yescharacteristic
31C22×C8×C127D412yes—
32C22×C8×C127C2311yescharacteristic
33#121×C127—24no—
34#121×C127—42no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—22no—
37C2×C22⋊C4×C127—41no—
38C2×C22⋊C4×C127—41no—
39C2×C16×C127—28no—
40C2×C16×C127—22no—
41C2×C16×C127—22no—
42C2×C16×C127D414yescomplemented
43#107×C127—21no—
44#107×C127—22no—
45#107×C127—22no—
46#107×C127C2×C412yes—
47#102×C127—24no—
48#95×C127—41no—
49C24×C127—41no—
50C24×C127D811yescharacteristic
51C2×D4×C127—22no—
52C2×D4×C127—44no—
53C2×D4×C127—42no—
54C2×D4×C127—41no—
55C2×D4×C127—42no—
56C2×D4×C127—82no—
57C2×D4×C127—82no—
58C22×C4×C127—22no—
59C22×C4×C127—22no—
60C22×C4×C127—41no—
61C22×C4×C127—42no—
62C22×C4×C127C22⋊C412yes—
63C22×C4×C127D811yescharacteristic
64C22×C4×C127SD1612yes—
65C22×C4×C127C2×D411yescharacteristic
66D8×C127—24no—
67D8×C127—41no—
68D8×C127—41no—
69C2×C8×C127—22no—
70C2×C8×C127—24no—
71C2×C8×C127—22no—
72C2×C8×C127—22no—
73C2×C8×C127C22⋊C412yes—
74C2×C8×C127C22×C411yescharacteristic
75C2×C8×C127C2×D412yes—
76C2×C8×C127C2×D411yescharacteristic
77C2×C8×C127#4112yes—
78C4⋊C4×C127—22no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—42no—
82C22⋊C4×C127—44no—
83C22⋊C4×C127—82no—
84C16×C127—24no—
85C23×C127—22no—
86C23×C127—22no—
87C23×C127—42no—
88C23×C127—82no—
89C23×C127—81no—
90C23×C127—81no—
91C23×C127—82no—
92C23×C127#10212yes—
93C23×C127D1612yes—
94C23×C127SD3212yes—
95C23×C127C2×D811yescharacteristic
96D4×C127—42no—
97D4×C127—42no—
98D4×C127—88no—
99D4×C127—82no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—22no—
103C2×C4×C127—24no—
104C2×C4×C127—42no—
105C2×C4×C127—81no—
106C2×C4×C127—81no—
107C2×C4×C127—82no—
108C2×C4×C127—82no—
109C2×C4×C127—82no—
110C2×C4×C127#10212yes—
111C2×C4×C127C2×C22⋊C411yescharacteristic
112C2×C4×C127#12112yes—
113C2×C4×C127C2×SD1611yescharacteristic
114C2×C4×C127#13512yes—
115C8×C127—22no—
116C8×C127C4×D412yes—
117C8×C127#12011yescharacteristic
118C8×C127#12311yescharacteristic
119C22×C127—22no—
120C22×C127—22no—
121C22×C127—24no—
122C22×C127—24no—
123C22×C127—82no—
124C22×C127—82no—
125C22×C127—82no—
126C22×C127—162no—
127C22×C127—162no—
128C22×C127#35714yescomplemented
129C22×C127C2×#10211yescharacteristic
130C22×C127#46612yes—
131C22×C127C2×D1611yescharacteristic
132C22×C127C2×SD3211yescharacteristic
133C22×C127#50812yes—
134C4×C127—22no—
135C4×C127—82no—
136C4×C127—162no—
137C4×C127#38611yescharacteristic
138C4×C127#41611yescharacteristic
139C4×C127#46512yes—
140#13059C12711yesmaximal, characteristic, direct product factor, Sylow
141C2×C127—24no—
142C2×C127—162no—
143C2×C127#189311yescharacteristic
144C2×C127C2×#35711yescharacteristic
145C2×C127#213811yescharacteristic
146C2×C127#221512yes—
147C2×C127#221712yes—
148C23×C16C2×C12711yescharacteristic, complemented
149C2×#466C2×C12711yescharacteristic
150C2×#357C2×C12712yescomplemented
151#1808C2×C12711yescharacteristic, complemented
152#1380C2×C12712yescomplemented
153C127#1305911yescharacteristic, direct product factor, Sylow
154C22×D8C22×C12711yescharacteristic
155C23×C8C22×C12711yescharacteristic
156C2×#121—21no—
157C22×C16—22no—
158C22×C16—24no—
159C22×C16C22×C12712yes—
160#466—22no—
161#466C4×C12714yescomplemented
162C2×#107C22×C12712yes—
163C2×#107C22×C12711yescharacteristic
164C2×#102—21no—
165#380—21no—
166#357—24no—
167#340—21no—
168C22×D4—21no—
169C22×D4—41no—
170C23×C4D4×C12711yescharacteristic
171C2×D8—22no—
172C2×D8—21no—
173C2×D8—22no—
174C2×D8C2×C4×C12712yes—
175C22×C8—22no—
176C22×C8—22no—
177C22×C8C2×C4×C12712yes—
178C22×C8D4×C12711yescharacteristic
179C22×C8D4×C12712yes—
180C22×C8C23×C12711yescharacteristic
181#121—24no—
182#121—42no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—22no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C16—28no—
188C2×C16—22no—
189C2×C16—22no—
190C2×C16D4×C12714yescomplemented
191#107—21no—
192#107—22no—
193#107—22no—
194#107C2×C4×C12712yes—
195#102—24no—
196#95—41no—
197C24—41no—
198C24D8×C12711yescharacteristic
199C2×D4—22no—
200C2×D4—44no—
201C2×D4—42no—
202C2×D4—41no—
203C2×D4—42no—
204C2×D4—82no—
205C2×D4—82no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4—42no—
210C22×C4C22⋊C4×C12712yes—
211C22×C4D8×C12711yescharacteristic
212C22×C4SD16×C12712yes—
213C22×C4C2×D4×C12711yescharacteristic
214D8—24no—
215D8—41no—
216D8—41no—
217C2×C8—22no—
218C2×C8—24no—
219C2×C8—22no—
220C2×C8—22no—
221C2×C8C22⋊C4×C12712yes—
222C2×C8C22×C4×C12711yescharacteristic
223C2×C8C2×D4×C12712yes—
224C2×C8C2×D4×C12711yescharacteristic
225C2×C8#41×C12712yes—
226C4⋊C4—22no—
227C4⋊C4—41no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C22⋊C4—44no—
231C22⋊C4—82no—
232C16—24no—
233C23—22no—
234C23—22no—
235C23—42no—
236C23—81no—
237C23—81no—
238C23—82no—
239C23—82no—
240C23#102×C12712yes—
241C23D16×C12712yes—
242C23SD32×C12712yes—
243C23C2×D8×C12711yescharacteristic
244D4—42no—
245D4—42no—
246D4—88no—
247D4—82no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4#102×C12712yes—
259C2×C4C2×C22⋊C4×C12711yescharacteristic
260C2×C4#121×C12712yes—
261C2×C4C2×SD16×C12711yescharacteristic
262C2×C4#135×C12712yes—
263C8—22no—
264C8C4×D4×C12712yes—
265C8#120×C12711yescharacteristic
266C8#123×C12711yescharacteristic
267C22—22no—
268C22—22no—
269C22—24no—
270C22—24no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—162no—
275C22—162no—
276C22#357×C12714yescomplemented
277C22C2×#102×C12711yescharacteristic
278C22#466×C12712yes—
279C22C2×D16×C12711yescharacteristic
280C22C2×SD32×C12711yescharacteristic
281C22#508×C12712yes—
282C4—22no—
283C4—82no—
284C4—162no—
285C4#386×C12711yescharacteristic
286C4#416×C12711yescharacteristic
287C4#465×C12712yes—
288C2—24no—
289C2—162no—
290C2C127×#189311yescharacteristic
291C2C2×#357×C12711yescharacteristic
292C2C127×#213811yescharacteristic
293C2C127×#221512yes—
294C2C127×#221712yes—
subgroupG/H
center, socleC23×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#466×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C16×C127C2semidirect
3. C2×#357×C127C2semidirect
4. C127×#1808C2semidirect
5. C127×#1380C2semidirect
13. #466×C127C4semidirect
42. C2×C16×C127D4semidirect
128. C22×C127#357semidirect
140. #13059C127direct (N × H)
148. C23×C16C2×C127semidirect
150. C2×#357C2×C127semidirect
151. #1808C2×C127semidirect
152. #1380C2×C127semidirect
153. C127#13059direct (N × H)
161. #466C4×C127semidirect
190. C2×C16D4×C127semidirect
276. C22#357×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C16×C1272
C2×#466×C1272
C2×#357×C1272
C127×#18082
C127×#13802
#13059127