Finite Group Databasebeta

← C127×#11651 #44575324

Subgroups — C127×#11651 #44575324

Order 32512.

316 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C2×#334×C127C211yesmaximal, characteristic, complemented
4C127×#1334C212yesmaximal, complemented
5C127×#1333C212yesmaximal, 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—
20#346×C127C2212yes—
21#334×C127—21no—
22#334×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—41no—
100C2×C4×C127—41no—
101C2×C4×C127—41no—
102C2×C4×C127—41no—
103C2×C4×C127—82no—
104C2×C4×C127#10211yescharacteristic
105C2×C4×C127#10211yescharacteristic
106C2×C4×C127#10211yescharacteristic
107C2×C4×C127C2×C22⋊C411yescharacteristic
108C2×C4×C127C2×D811yescharacteristic
109C2×C4×C127C2×SD1611yescharacteristic
110C8×C127—21no—
111C8×C127—21no—
112C8×C127—21no—
113C8×C127—82no—
114C8×C127#13112yes—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—81no—
118C22×C127—81no—
119C22×C127—81no—
120C22×C127#36012yes—
121C22×C127C2×#10211yescharacteristic
122C4×C127—21no—
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—81no—
128C4×C127—81no—
129C4×C127—81no—
130C4×C127#40811yescharacteristic
131C4×C127#42111yescharacteristic
132#11651C12711yesmaximal, characteristic, direct product factor, Sylow
133C2×C127—22no—
134C2×C127—161no—
135C2×C127#148011yescharacteristic
136C2×C127C2×#36011yescharacteristic
137C2×C127#214811yescharacteristic
138#3168C2×C12711yescharacteristic
139#2163C2×C12711yescharacteristic, complemented
140C2×#334C2×C12711yescharacteristic, complemented
141#1334C2×C12712yescomplemented
142#1333C2×C12712yescomplemented
143C127#1165111yescharacteristic, direct product factor, Sylow
144#529—21no—
145#499C4×C12711yescharacteristic
146#495C4×C12711yescharacteristic
147#488—21no—
148#467C4×C12711yescharacteristic
149#466C4×C12711yescharacteristic
150#465—21no—
151C4×Q16C22×C12711yescharacteristic
152C4×SD16—21no—
153C4×D8C22×C12711yescharacteristic
154C2×C4⋊C8—21no—
155C2×C4×C8C22×C12711yescharacteristic
156C4⋊C16—21no—
157C22⋊C16—21no—
158#346C22×C12712yes—
159#334—21no—
160#334C22×C12712yes—
161C2×Q16C2×C4×C12711yescharacteristic
162C2×SD16—21no—
163C2×D8C2×C4×C12711yescharacteristic
164C22×C8—41no—
165C22×C8C2×C4×C12711yescharacteristic
166C22×C8D4×C12711yescharacteristic
167#126—41no—
168#125—21no—
169#124—21no—
170#123—41no—
171C22⋊Q8—21no—
172#121—21no—
173C4×Q8—21no—
174C4×D4—21no—
175C4×D4—41no—
176#117—41no—
177C2×C42D4×C12711yescharacteristic
178C2×C16—22no—
179#107C2×C4×C12711yescharacteristic
180#107C2×C4×C12711yescharacteristic
181#106—21no—
182C4⋊C8—22no—
183C4⋊C8—41no—
184#103—21no—
185#103—21no—
186#102—21no—
187#102—21no—
188C4×C8C2×C4×C12711yescharacteristic
189C4×C8D4×C12711yescharacteristic
190C4×C8D4×C12711yescharacteristic
191C4×C8C23×C12711yescharacteristic
192C2×Q8—21no—
193C2×D4—21no—
194C2×D4—41no—
195C22×C4—41no—
196C22×C4C22⋊C4×C12711yescharacteristic
197C22×C4D8×C12711yescharacteristic
198C22×C4SD16×C12711yescharacteristic
199Q16—22no—
200SD16—42no—
201D8—22no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—42no—
205C2×C8—82no—
206C2×C8C22⋊C4×C12711yescharacteristic
207C2×C8C22⋊C4×C12711yescharacteristic
208C2×C8C22×C4×C12711yescharacteristic
209C2×C8C2×D4×C12711yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C42—41no—
222C42C22⋊C4×C12711yescharacteristic
223C42D8×C12711yescharacteristic
224C42SD16×C12711yescharacteristic
225C42C2×D4×C12711yescharacteristic
226C16—42no—
227C23—41no—
228C23#102×C12711yescharacteristic
229Q8—41no—
230Q8—41no—
231D4—41no—
232D4—41no—
233D4—82no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—82no—
242C2×C4#102×C12711yescharacteristic
243C2×C4#102×C12711yescharacteristic
244C2×C4#102×C12711yescharacteristic
245C2×C4C2×C22⋊C4×C12711yescharacteristic
246C2×C4C2×D8×C12711yescharacteristic
247C2×C4C2×SD16×C12711yescharacteristic
248C8—21no—
249C8—21no—
250C8—21no—
251C8—82no—
252C8#131×C12712yes—
253C22—21no—
254C22—21no—
255C22—81no—
256C22—81no—
257C22—81no—
258C22#360×C12712yes—
259C22C2×#102×C12711yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—81no—
268C4#408×C12711yescharacteristic
269C4#421×C12711yescharacteristic
270C2—22no—
271C2—161no—
272C2C127×#148011yescharacteristic
273C2C2×#360×C12711yescharacteristic
274C2C127×#214811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC4×C8C23×C127
prime radical#466×C127C4
LCSG ▷ C2×C8 ▷ 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. C2×#334×C127C2semidirect
4. C127×#1334C2semidirect
5. C127×#1333C2semidirect
132. #11651C127direct (N × H)
139. #2163C2×C127semidirect
140. C2×#334C2×C127semidirect
141. #1334C2×C127semidirect
142. #1333C2×C127semidirect
143. C127#11651direct (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×#21632
C2×#334×C1272
C127×#13342
C127×#13332
#11651127