Finite Group Databasebeta

← C127×#11855 #44575528

Subgroups — C127×#11855 #44575528

Order 32512.

324 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C127×#2162C211yesmaximal, characteristic, complemented
3C127×#1835C211yesmaximal, characteristic, complemented
4C127×#1348C212yesmaximal, complemented
5C127×#1347C212yesmaximal
6#529×C127—21no—
7#499×C127C411yescharacteristic, complemented
8#495×C127C411yescharacteristic, complemented
9#488×C127—21no—
10#467×C127C2211yescharacteristic
11#466×C127C2211yescharacteristic
12#465×C127—21no—
13C4×Q16×C127C411yescharacteristic, complemented
14C4×SD16×C127—21no—
15C4×D8×C127C411yescharacteristic, complemented
16C2×C4×C8×C127C2211yescharacteristic
17#382×C127—21no—
18C4⋊C16×C127—21no—
19C22⋊C16×C127C2212yes—
20C4×C16×C127—21no—
21#340×C127—21no—
22#340×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C22×C8×C127C2311yescharacteristic
28#126×C127—41no—
29#125×C127—21no—
30#124×C127—21no—
31#123×C127—41no—
32C22⋊Q8×C127—21no—
33#121×C127—21no—
34C4×Q8×C127—21no—
35C4×D4×C127—21no—
36C4×D4×C127—41no—
37#117×C127—41no—
38C2×C4⋊C4×C127—22no—
39C2×C42×C127D411yescharacteristic
40C2×C16×C127—22no—
41#107×C127C2×C411yescharacteristic
42#107×C127C2×C411yescharacteristic
43#106×C127—21no—
44#103×C127—21no—
45#103×C127—21no—
46#102×C127—21no—
47#102×C127—21no—
48C4×C8×C127C2×C411yescharacteristic
49C4×C8×C127C2×C411yescharacteristic
50C4×C8×C127D411yescharacteristic
51C4×C8×C127D411yescharacteristic
52#95×C127—41no—
53#95×C127—41no—
54C2×Q8×C127—21no—
55C2×D4×C127—21no—
56C2×D4×C127—41no—
57C22×C4×C127—41no—
58C22×C4×C127—42no—
59C22×C4×C127D811yescharacteristic
60C22×C4×C127D811yescharacteristic
61C22×C4×C127C2×D411yescharacteristic
62Q16×C127—41no—
63SD16×C127—42no—
64D8×C127—41no—
65C2×C8×C127—41no—
66C2×C8×C127—41no—
67C2×C8×C127C22⋊C411yescharacteristic
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22×C411yescharacteristic
70C2×C8×C127C2×D411yescharacteristic
71C4⋊C4×C127—21no—
72C4⋊C4×C127—21no—
73C4⋊C4×C127—42no—
74C4⋊C4×C127—42no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C42×C127—41no—
85C42×C127C22⋊C411yescharacteristic
86C42×C127C22⋊C411yescharacteristic
87C42×C127SD1611yescharacteristic
88C42×C127SD1611yescharacteristic
89C16×C127—42no—
90C23×C127—41no—
91C23×C127C2×D811yescharacteristic
92Q8×C127—41no—
93Q8×C127—41no—
94D4×C127—41no—
95D4×C127—41no—
96D4×C127—82no—
97C2×C4×C127—22no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—82no—
105C2×C4×C127—82no—
106C2×C4×C127—82no—
107C2×C4×C127—82no—
108C2×C4×C127#10211yescharacteristic
109C2×C4×C127#10211yescharacteristic
110C2×C4×C127#10211yescharacteristic
111C2×C4×C127#10211yescharacteristic
112C2×C4×C127C2×C22⋊C411yescharacteristic
113C2×C4×C127C2×SD1611yescharacteristic
114C8×C127—21no—
115C8×C127—21no—
116C8×C127—21no—
117C8×C127—21no—
118C22×C127—21no—
119C22×C127—21no—
120C22×C127—81no—
121C22×C127—81no—
122C22×C127—81no—
123C22×C127C2×#10211yescharacteristic
124C22×C127#50812yes—
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—21no—
129C4×C127—21no—
130C4×C127—81no—
131C4×C127—81no—
132C4×C127—81no—
133C4×C127—162no—
134C4×C127#41011yescharacteristic
135C4×C127#42111yescharacteristic
136#11855C12711yesmaximal, characteristic, direct product factor, Sylow
137C2×C127—22no—
138C2×C127—161no—
139C2×C127#151711yescharacteristic
140C2×C127#213811yescharacteristic
141C2×C127#214511yescharacteristic
142#3168C2×C12711yescharacteristic
143#2162C2×C12711yescharacteristic, complemented
144#1835C2×C12711yescharacteristic, complemented
145#1348C2×C12712yescomplemented
146#1347C2×C12712yes—
147C127#1185511yescharacteristic, direct product factor, Sylow
148#529—21no—
149#499C4×C12711yescharacteristic, complemented
150#495C4×C12711yescharacteristic, complemented
151#488—21no—
152#467C22×C12711yescharacteristic
153#466C22×C12711yescharacteristic
154#465—21no—
155C4×Q16C4×C12711yescharacteristic, complemented
156C4×SD16—21no—
157C4×D8C4×C12711yescharacteristic, complemented
158C2×C4×C8C22×C12711yescharacteristic
159#382—21no—
160C4⋊C16—21no—
161C22⋊C16C22×C12712yes—
162C4×C16—21no—
163#340—21no—
164#340C22×C12712yes—
165C2×Q16C2×C4×C12711yescharacteristic
166C2×SD16—21no—
167C2×D8C2×C4×C12711yescharacteristic
168C22×C8D4×C12711yescharacteristic
169C22×C8C23×C12711yescharacteristic
170#126—41no—
171#125—21no—
172#124—21no—
173#123—41no—
174C22⋊Q8—21no—
175#121—21no—
176C4×Q8—21no—
177C4×D4—21no—
178C4×D4—41no—
179#117—41no—
180C2×C4⋊C4—22no—
181C2×C42D4×C12711yescharacteristic
182C2×C16—22no—
183#107C2×C4×C12711yescharacteristic
184#107C2×C4×C12711yescharacteristic
185#106—21no—
186#103—21no—
187#103—21no—
188#102—21no—
189#102—21no—
190C4×C8C2×C4×C12711yescharacteristic
191C4×C8C2×C4×C12711yescharacteristic
192C4×C8D4×C12711yescharacteristic
193C4×C8D4×C12711yescharacteristic
194#95—41no—
195#95—41no—
196C2×Q8—21no—
197C2×D4—21no—
198C2×D4—41no—
199C22×C4—41no—
200C22×C4—42no—
201C22×C4D8×C12711yescharacteristic
202C22×C4D8×C12711yescharacteristic
203C22×C4C2×D4×C12711yescharacteristic
204Q16—41no—
205SD16—42no—
206D8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8C22⋊C4×C12711yescharacteristic
210C2×C8C22⋊C4×C12711yescharacteristic
211C2×C8C22×C4×C12711yescharacteristic
212C2×C8C2×D4×C12711yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C42—41no—
227C42C22⋊C4×C12711yescharacteristic
228C42C22⋊C4×C12711yescharacteristic
229C42SD16×C12711yescharacteristic
230C42SD16×C12711yescharacteristic
231C16—42no—
232C23—41no—
233C23C2×D8×C12711yescharacteristic
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—41no—
238D4—82no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4#102×C12711yescharacteristic
251C2×C4#102×C12711yescharacteristic
252C2×C4#102×C12711yescharacteristic
253C2×C4#102×C12711yescharacteristic
254C2×C4C2×C22⋊C4×C12711yescharacteristic
255C2×C4C2×SD16×C12711yescharacteristic
256C8—21no—
257C8—21no—
258C8—21no—
259C8—21no—
260C22—21no—
261C22—21no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22C2×#102×C12711yescharacteristic
266C22#508×C12712yes—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—81no—
273C4—81no—
274C4—81no—
275C4—162no—
276C4#410×C12711yescharacteristic
277C4#421×C12711yescharacteristic
278C2—22no—
279C2—161no—
280C2C127×#151711yescharacteristic
281C2C127×#213811yescharacteristic
282C2C127×#214511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radical#466×C127C22
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2162C2semidirect
3. C127×#1835C2semidirect
4. C127×#1348C2semidirect
7. #499×C127C4semidirect
8. #495×C127C4semidirect
13. C4×Q16×C127C4semidirect
15. C4×D8×C127C4semidirect
136. #11855C127direct (N × H)
143. #2162C2×C127semidirect
144. #1835C2×C127semidirect
145. #1348C2×C127semidirect
147. C127#11855direct (N × H)
149. #499C4×C127semidirect
150. #495C4×C127semidirect
155. C4×Q16C4×C127semidirect
157. C4×D8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31682
C127×#21622
C127×#18352
C127×#13482
C127×#13472
#11855127