Finite Group Databasebeta

← C127×#11648 #44575321

Subgroups — C127×#11648 #44575321

Order 32512.

320 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
1C127×#3168C211yesmaximal, characteristic
2C127×#2162C211yesmaximal, characteristic, complemented
3C2×#335×C127C211yesmaximal, characteristic, complemented
4C127×#1332C212yesmaximal, complemented
5C127×#1331C212yesmaximal, complemented
6#529×C127—21no—
7#499×C127C411yescharacteristic
8#495×C127C411yescharacteristic
9#488×C127—21no—
10#467×C127C411yescharacteristic
11#466×C127C411yescharacteristic
12#465×C127—21no—
13C4×Q16×C127C2211yescharacteristic
14C4×SD16×C127—21no—
15C4×D8×C127C2211yescharacteristic
16C2×C4⋊C8×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4⋊C16×C127—21no—
19C22⋊C16×C127—21no—
20C4×C16×C127C2212yes—
21#335×C127—21no—
22#335×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C22×C8×C127—41no—
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127D411yescharacteristic
29#126×C127—41no—
30#125×C127—21no—
31#124×C127—21no—
32#123×C127—41no—
33C22⋊Q8×C127—21no—
34#121×C127—21no—
35C4×Q8×C127—21no—
36C4×D4×C127—21no—
37C4×D4×C127—41no—
38#117×C127—41no—
39C2×C42×C127D411yescharacteristic
40C2×C16×C127—22no—
41#107×C127C2×C411yescharacteristic
42#107×C127C2×C411yescharacteristic
43#106×C127—21no—
44C4⋊C8×C127—22no—
45C4⋊C8×C127—41no—
46#103×C127—21no—
47#103×C127—21no—
48#102×C127—21no—
49#102×C127—21no—
50C4×C8×C127C2×C411yescharacteristic
51C4×C8×C127D411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127C2311yescharacteristic
54C2×Q8×C127—21no—
55C2×D4×C127—21no—
56C2×D4×C127—41no—
57C22×C4×C127—41no—
58C22×C4×C127C22⋊C411yescharacteristic
59C22×C4×C127D811yescharacteristic
60C22×C4×C127SD1611yescharacteristic
61Q16×C127—22no—
62SD16×C127—42no—
63D8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127—41no—
66C2×C8×C127—42no—
67C2×C8×C127—82no—
68C2×C8×C127C22⋊C411yescharacteristic
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22×C411yescharacteristic
71C2×C8×C127C2×D411yescharacteristic
72C4⋊C4×C127—21no—
73C4⋊C4×C127—21no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C22⋊C4×C127—41no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C42×C127—41no—
84C42×C127C22⋊C411yescharacteristic
85C42×C127D811yescharacteristic
86C42×C127SD1611yescharacteristic
87C42×C127C2×D411yescharacteristic
88C16×C127—42no—
89C23×C127—41no—
90C23×C127#10211yescharacteristic
91Q8×C127—41no—
92Q8×C127—41no—
93D4×C127—41no—
94D4×C127—41no—
95D4×C127—82no—
96C2×C4×C127—22no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—41no—
104C2×C4×C127—81no—
105C2×C4×C127—81no—
106C2×C4×C127#10211yescharacteristic
107C2×C4×C127#10211yescharacteristic
108C2×C4×C127#10211yescharacteristic
109C2×C4×C127C2×C22⋊C411yescharacteristic
110C2×C4×C127C2×D811yescharacteristic
111C2×C4×C127C2×SD1611yescharacteristic
112C8×C127—21no—
113C8×C127—21no—
114C8×C127—21no—
115C8×C127—82no—
116C8×C127#13112yes—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—81no—
120C22×C127—81no—
121C22×C127—81no—
122C22×C127#35912yes—
123C22×C127C2×#10211yescharacteristic
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—81no—
129C4×C127—81no—
130C4×C127—81no—
131C4×C127#40811yescharacteristic
132C4×C127#42111yescharacteristic
133C4×C127#50911yescharacteristic
134C4×C127#51011yescharacteristic
135#11648C12711yesmaximal, characteristic, direct product factor, Sylow
136C2×C127—22no—
137C2×C127—161no—
138C2×C127#148011yescharacteristic
139C2×C127#213911yescharacteristic
140C2×C127C2×#35911yescharacteristic
141#3168C2×C12711yescharacteristic
142#2162C2×C12711yescharacteristic, complemented
143C2×#335C2×C12711yescharacteristic, complemented
144#1332C2×C12712yescomplemented
145#1331C2×C12712yescomplemented
146C127#1164811yescharacteristic, direct product factor, Sylow
147#529—21no—
148#499C4×C12711yescharacteristic
149#495C4×C12711yescharacteristic
150#488—21no—
151#467C4×C12711yescharacteristic
152#466C4×C12711yescharacteristic
153#465—21no—
154C4×Q16C22×C12711yescharacteristic
155C4×SD16—21no—
156C4×D8C22×C12711yescharacteristic
157C2×C4⋊C8—21no—
158C2×C4×C8C22×C12711yescharacteristic
159C4⋊C16—21no—
160C22⋊C16—21no—
161C4×C16C22×C12712yes—
162#335—21no—
163#335C22×C12712yes—
164C2×Q16C2×C4×C12711yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C12711yescharacteristic
167C22×C8—41no—
168C22×C8C2×C4×C12711yescharacteristic
169C22×C8D4×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×C42D4×C12711yescharacteristic
181C2×C16—22no—
182#107C2×C4×C12711yescharacteristic
183#107C2×C4×C12711yescharacteristic
184#106—21no—
185C4⋊C8—22no—
186C4⋊C8—41no—
187#103—21no—
188#103—21no—
189#102—21no—
190#102—21no—
191C4×C8C2×C4×C12711yescharacteristic
192C4×C8D4×C12711yescharacteristic
193C4×C8D4×C12711yescharacteristic
194C4×C8C23×C12711yescharacteristic
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4C22⋊C4×C12711yescharacteristic
200C22×C4D8×C12711yescharacteristic
201C22×C4SD16×C12711yescharacteristic
202Q16—22no—
203SD16—42no—
204D8—22no—
205C2×C8—22no—
206C2×C8—41no—
207C2×C8—42no—
208C2×C8—82no—
209C2×C8C22⋊C4×C12711yescharacteristic
210C2×C8C22⋊C4×C12711yescharacteristic
211C2×C8C22×C4×C12711yescharacteristic
212C2×C8C2×D4×C12711yescharacteristic
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C42—41no—
225C42C22⋊C4×C12711yescharacteristic
226C42D8×C12711yescharacteristic
227C42SD16×C12711yescharacteristic
228C42C2×D4×C12711yescharacteristic
229C16—42no—
230C23—41no—
231C23#102×C12711yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—82no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4#102×C12711yescharacteristic
248C2×C4#102×C12711yescharacteristic
249C2×C4#102×C12711yescharacteristic
250C2×C4C2×C22⋊C4×C12711yescharacteristic
251C2×C4C2×D8×C12711yescharacteristic
252C2×C4C2×SD16×C12711yescharacteristic
253C8—21no—
254C8—21no—
255C8—21no—
256C8—82no—
257C8#131×C12712yes—
258C22—21no—
259C22—21no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22#359×C12712yes—
264C22C2×#102×C12711yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4#408×C12711yescharacteristic
273C4#421×C12711yescharacteristic
274C4#509×C12711yescharacteristic
275C4#510×C12711yescharacteristic
276C2—22no—
277C2—161no—
278C2C127×#148011yescharacteristic
279C2C127×#213911yescharacteristic
280C2C2×#359×C12711yescharacteristic
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
socleC22×C127C2×#102
prime radical#466×C127C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×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. C2×#335×C127C2semidirect
4. C127×#1332C2semidirect
5. C127×#1331C2semidirect
135. #11648C127direct (N × H)
142. #2162C2×C127semidirect
143. C2×#335C2×C127semidirect
144. #1332C2×C127semidirect
145. #1331C2×C127semidirect
146. C127#11648direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31682
C127×#21622
C2×#335×C1272
C127×#13322
C127×#13312
#11648127