Finite Group Databasebeta

← C127×#11746 #44575419

Subgroups — C127×#11746 #44575419

Order 32512.

352 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
1C127×#3168C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C4×#107×C127C211yesmaximal, 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×#107×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4×C4⋊C4×C127—21no—
19C4⋊C16×C127—21no—
20C22⋊C16×C127C2212yes—
21#346×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×C127—41no—
40C2×C42×C127D411yescharacteristic
41C2×C16×C127—22no—
42#107×C127—24no—
43#107×C127C2×C411yescharacteristic
44#107×C127C2×C411yescharacteristic
45#106×C127—21no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#102×C127—21no—
50C4×C8×C127C2×C411yescharacteristic
51C4×C8×C127C2×C411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127D411yescharacteristic
54#95×C127—41no—
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—41no—
58C22×C4×C127—42no—
59C22×C4×C127—41no—
60C22×C4×C127D811yescharacteristic
61C22×C4×C127D811yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63Q16×C127—41no—
64SD16×C127—42no—
65D8×C127—41no—
66C2×C8×C127—22no—
67C2×C8×C127—41no—
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22×C411yescharacteristic
71C2×C8×C127C2×D411yescharacteristic
72C4⋊C4×C127—24no—
73C4⋊C4×C127—21no—
74C4⋊C4×C127—21no—
75C4⋊C4×C127—42no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—41no—
85C42×C127—41no—
86C42×C127—82no—
87C42×C127C22⋊C411yescharacteristic
88C42×C127C22⋊C411yescharacteristic
89C42×C127SD1611yescharacteristic
90C42×C127SD1611yescharacteristic
91C16×C127—42no—
92C23×C127—41no—
93C23×C127C2×D811yescharacteristic
94Q8×C127—41no—
95Q8×C127—41no—
96D4×C127—41no—
97D4×C127—41no—
98D4×C127—81no—
99D4×C127—81no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—41no—
105C2×C4×C127—44no—
106C2×C4×C127—41no—
107C2×C4×C127—41no—
108C2×C4×C127—41no—
109C2×C4×C127—82no—
110C2×C4×C127—82no—
111C2×C4×C127—82no—
112C2×C4×C127#10211yescharacteristic
113C2×C4×C127#10211yescharacteristic
114C2×C4×C127#10211yescharacteristic
115C2×C4×C127#10211yescharacteristic
116C2×C4×C127C2×C22⋊C411yescharacteristic
117C2×C4×C127C2×SD1611yescharacteristic
118C8×C127—21no—
119C8×C127—21no—
120C8×C127—21no—
121C8×C127#10412yes—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—81no—
125C22×C127—81no—
126C22×C127—81no—
127C22×C127C2×#10211yescharacteristic
128C22×C127#50911yescharacteristic
129C22×C127#51011yescharacteristic
130C4×C127—21no—
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—21no—
134C4×C127—21no—
135C4×C127—84no—
136C4×C127—81no—
137C4×C127—81no—
138C4×C127—81no—
139C4×C127#41011yescharacteristic
140C4×C127C2×#10411yescharacteristic
141#11746C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—21no—
143C2×C127—21no—
144C2×C127—161no—
145C2×C127#150211yescharacteristic
146C2×C127#213911yescharacteristic
147C2×C127#214511yescharacteristic
148#3168C2×C12711yescharacteristic
149#2163C2×C12711yescharacteristic, complemented
150C4×#107C2×C12711yescharacteristic, complemented
151#1348C2×C12712yescomplemented
152#1347C2×C12712yes—
153C127#1174611yescharacteristic, direct product factor, Sylow
154#529—21no—
155#499C4×C12711yescharacteristic, complemented
156#495C4×C12711yescharacteristic, complemented
157#488—21no—
158#467C22×C12711yescharacteristic
159#466C22×C12711yescharacteristic
160#465—21no—
161C4×Q16C4×C12711yescharacteristic, complemented
162C4×SD16—21no—
163C4×D8C4×C12711yescharacteristic, complemented
164C2×#107—21no—
165C2×C4×C8C22×C12711yescharacteristic
166C4×C4⋊C4—21no—
167C4⋊C16—21no—
168C22⋊C16C22×C12712yes—
169#346—21no—
170#340C22×C12712yes—
171C2×Q16C2×C4×C12711yescharacteristic
172C2×SD16—21no—
173C2×D8C2×C4×C12711yescharacteristic
174C22×C8D4×C12711yescharacteristic
175C22×C8C23×C12711yescharacteristic
176#126—41no—
177#125—21no—
178#124—21no—
179#123—41no—
180C22⋊Q8—21no—
181#121—21no—
182C4×Q8—21no—
183C4×D4—21no—
184C4×D4—41no—
185#117—41no—
186C2×C4⋊C4—22no—
187C2×C42—41no—
188C2×C42D4×C12711yescharacteristic
189C2×C16—22no—
190#107—24no—
191#107C2×C4×C12711yescharacteristic
192#107C2×C4×C12711yescharacteristic
193#106—21no—
194#103—21no—
195#103—21no—
196#102—21no—
197#102—21no—
198C4×C8C2×C4×C12711yescharacteristic
199C4×C8C2×C4×C12711yescharacteristic
200C4×C8D4×C12711yescharacteristic
201C4×C8D4×C12711yescharacteristic
202#95—41no—
203C2×Q8—21no—
204C2×D4—21no—
205C2×D4—41no—
206C22×C4—42no—
207C22×C4—41no—
208C22×C4D8×C12711yescharacteristic
209C22×C4D8×C12711yescharacteristic
210C22×C4C2×D4×C12711yescharacteristic
211Q16—41no—
212SD16—42no—
213D8—41no—
214C2×C8—22no—
215C2×C8—41no—
216C2×C8C22⋊C4×C12711yescharacteristic
217C2×C8C22⋊C4×C12711yescharacteristic
218C2×C8C22×C4×C12711yescharacteristic
219C2×C8C2×D4×C12711yescharacteristic
220C4⋊C4—24no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—42no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C42—41no—
234C42—82no—
235C42C22⋊C4×C12711yescharacteristic
236C42C22⋊C4×C12711yescharacteristic
237C42SD16×C12711yescharacteristic
238C42SD16×C12711yescharacteristic
239C16—42no—
240C23—41no—
241C23C2×D8×C12711yescharacteristic
242Q8—41no—
243Q8—41no—
244D4—41no—
245D4—41no—
246D4—81no—
247D4—81no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4#102×C12711yescharacteristic
261C2×C4#102×C12711yescharacteristic
262C2×C4#102×C12711yescharacteristic
263C2×C4#102×C12711yescharacteristic
264C2×C4C2×C22⋊C4×C12711yescharacteristic
265C2×C4C2×SD16×C12711yescharacteristic
266C8—21no—
267C8—21no—
268C8—21no—
269C8#104×C12712yes—
270C22—21no—
271C22—21no—
272C22—81no—
273C22—81no—
274C22—81no—
275C22C2×#102×C12711yescharacteristic
276C22#509×C12711yescharacteristic
277C22#510×C12711yescharacteristic
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—84no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4#410×C12711yescharacteristic
288C4C2×#104×C12711yescharacteristic
289C2—21no—
290C2—21no—
291C2—161no—
292C2C127×#150211yescharacteristic
293C2C127×#213911yescharacteristic
294C2C127×#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×#2163C2semidirect
3. C4×#107×C127C2semidirect
4. C127×#1348C2semidirect
7. #499×C127C4semidirect
8. #495×C127C4semidirect
13. C4×Q16×C127C4semidirect
15. C4×D8×C127C4semidirect
141. #11746C127direct (N × H)
149. #2163C2×C127semidirect
150. C4×#107C2×C127semidirect
151. #1348C2×C127semidirect
153. C127#11746direct (N × H)
155. #499C4×C127semidirect
156. #495C4×C127semidirect
161. C4×Q16C4×C127semidirect
163. 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×#21632
C4×#107×C1272
C127×#13482
C127×#13472
#11746127