Finite Group Databasebeta

← C127×#11647 #44575320

Subgroups — C127×#11647 #44575320

Order 32512.

310 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C127×#2162C211yesmaximal, characteristic, complemented
3C127×#1564C211yesmaximal, 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
16#431×C127—21no—
17C2×C4×C8×C127C2211yescharacteristic
18C4⋊C16×C127—21no—
19C22⋊C16×C127—21no—
20C4×C16×C127C2212yes—
21#335×C127C2212yes—
22#334×C127—21no—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C22×C8×C127C2×C411yescharacteristic
27C22×C8×C127D411yescharacteristic
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×C42×C127D411yescharacteristic
39C2×C16×C127—22no—
40#107×C127C2×C411yescharacteristic
41#107×C127C2×C411yescharacteristic
42#106×C127—21no—
43C4⋊C8×C127—22no—
44#103×C127—21no—
45#103×C127—21no—
46#102×C127—21no—
47#102×C127—21no—
48C22⋊C8×C127—41no—
49C4×C8×C127—41no—
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×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—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C22⋊C4×C127—41no—
78C22⋊C4×C127—41no—
79C22⋊C4×C127—41no—
80C22⋊C4×C127—41no—
81C22⋊C4×C127—41no—
82C42×C127—41no—
83C42×C127C22⋊C411yescharacteristic
84C42×C127D811yescharacteristic
85C42×C127SD1611yescharacteristic
86C42×C127C2×D411yescharacteristic
87C16×C127—42no—
88C23×C127—41no—
89C23×C127#10211yescharacteristic
90Q8×C127—41no—
91Q8×C127—41no—
92D4×C127—41no—
93D4×C127—41no—
94D4×C127—82no—
95C2×C4×C127—21no—
96C2×C4×C127—21no—
97C2×C4×C127—22no—
98C2×C4×C127—41no—
99C2×C4×C127—41no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—82no—
103C2×C4×C127#10211yescharacteristic
104C2×C4×C127#10211yescharacteristic
105C2×C4×C127#10211yescharacteristic
106C2×C4×C127C2×C22⋊C411yescharacteristic
107C2×C4×C127C2×D811yescharacteristic
108C2×C4×C127C2×SD1611yescharacteristic
109C8×C127—21no—
110C8×C127—21no—
111C8×C127—21no—
112C8×C127—82no—
113C8×C127#13112yes—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—81no—
118C22×C127—81no—
119C22×C127—81no—
120C22×C127C2×#10211yescharacteristic
121C4×C127—21no—
122C4×C127—21no—
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—81no—
126C4×C127—81no—
127C4×C127—81no—
128C4×C127#40811yescharacteristic
129C4×C127#42111yescharacteristic
130C4×C127#50812yes—
131#11647C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—41no—
133C2×C127—161no—
134C2×C127#148011yescharacteristic
135C2×C127#213811yescharacteristic
136C2×C127#214311yescharacteristic
137#3168C2×C12711yescharacteristic
138#2162C2×C12711yescharacteristic, complemented
139#1564C2×C12711yescharacteristic, complemented
140#1332C2×C12712yescomplemented
141#1331C2×C12712yescomplemented
142C127#1164711yescharacteristic, direct product factor, Sylow
143#529—21no—
144#499C4×C12711yescharacteristic
145#495C4×C12711yescharacteristic
146#488—21no—
147#467C4×C12711yescharacteristic
148#466C4×C12711yescharacteristic
149#465—21no—
150C4×Q16C22×C12711yescharacteristic
151C4×SD16—21no—
152C4×D8C22×C12711yescharacteristic
153#431—21no—
154C2×C4×C8C22×C12711yescharacteristic
155C4⋊C16—21no—
156C22⋊C16—21no—
157C4×C16C22×C12712yes—
158#335C22×C12712yes—
159#334—21no—
160C2×Q16C2×C4×C12711yescharacteristic
161C2×SD16—21no—
162C2×D8C2×C4×C12711yescharacteristic
163C22×C8C2×C4×C12711yescharacteristic
164C22×C8D4×C12711yescharacteristic
165#126—41no—
166#125—21no—
167#124—21no—
168#123—41no—
169C22⋊Q8—21no—
170#121—21no—
171C4×Q8—21no—
172C4×D4—21no—
173C4×D4—41no—
174#117—41no—
175C2×C42D4×C12711yescharacteristic
176C2×C16—22no—
177#107C2×C4×C12711yescharacteristic
178#107C2×C4×C12711yescharacteristic
179#106—21no—
180C4⋊C8—22no—
181#103—21no—
182#103—21no—
183#102—21no—
184#102—21no—
185C22⋊C8—41no—
186C4×C8—41no—
187C4×C8C2×C4×C12711yescharacteristic
188C4×C8D4×C12711yescharacteristic
189C4×C8D4×C12711yescharacteristic
190C4×C8C23×C12711yescharacteristic
191C2×Q8—21no—
192C2×D4—21no—
193C2×D4—41no—
194C22×C4—41no—
195C22×C4C22⋊C4×C12711yescharacteristic
196C22×C4D8×C12711yescharacteristic
197C22×C4SD16×C12711yescharacteristic
198Q16—22no—
199SD16—42no—
200D8—22no—
201C2×C8—22no—
202C2×C8—41no—
203C2×C8—42no—
204C2×C8C22⋊C4×C12711yescharacteristic
205C2×C8C22⋊C4×C12711yescharacteristic
206C2×C8C22×C4×C12711yescharacteristic
207C2×C8C2×D4×C12711yescharacteristic
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C42—41no—
220C42C22⋊C4×C12711yescharacteristic
221C42D8×C12711yescharacteristic
222C42SD16×C12711yescharacteristic
223C42C2×D4×C12711yescharacteristic
224C16—42no—
225C23—41no—
226C23#102×C12711yescharacteristic
227Q8—41no—
228Q8—41no—
229D4—41no—
230D4—41no—
231D4—82no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—82no—
240C2×C4#102×C12711yescharacteristic
241C2×C4#102×C12711yescharacteristic
242C2×C4#102×C12711yescharacteristic
243C2×C4C2×C22⋊C4×C12711yescharacteristic
244C2×C4C2×D8×C12711yescharacteristic
245C2×C4C2×SD16×C12711yescharacteristic
246C8—21no—
247C8—21no—
248C8—21no—
249C8—82no—
250C8#131×C12712yes—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—81no—
255C22—81no—
256C22—81no—
257C22C2×#102×C12711yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—81no—
263C4—81no—
264C4—81no—
265C4#408×C12711yescharacteristic
266C4#421×C12711yescharacteristic
267C4#508×C12712yes—
268C2—41no—
269C2—161no—
270C2C127×#148011yescharacteristic
271C2C127×#213811yescharacteristic
272C2C127×#214311yescharacteristic
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. C127×#1564C2semidirect
4. C127×#1332C2semidirect
5. C127×#1331C2semidirect
131. #11647C127direct (N × H)
138. #2162C2×C127semidirect
139. #1564C2×C127semidirect
140. #1332C2×C127semidirect
141. #1331C2×C127semidirect
142. C127#11647direct (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
C127×#15642
C127×#13322
C127×#13312
#11647127