Finite Group Databasebeta

← C127×#11677 #44575350

Subgroups — C127×#11677 #44575350

Order 32512.

332 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C2×#346×C127C211yesmaximal, characteristic, complemented
3C127×#1566C211yesmaximal, characteristic, complemented
4C127×#1334C212yesmaximal, complemented
5C127×#1333C212yesmaximal, complemented
6#529×C127—21no—
7C22×C16×C127—21no—
8#499×C127C411yescharacteristic
9#495×C127C411yescharacteristic
10#488×C127—21no—
11#467×C127C411yescharacteristic
12#466×C127C411yescharacteristic
13#465×C127—21no—
14C4×Q16×C127C2211yescharacteristic
15C4×SD16×C127—21no—
16C4×D8×C127C2211yescharacteristic
17#423×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19#346×C127—21no—
20#346×C127C2212yes—
21#334×C127—21no—
22#334×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C2×M16×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—24no—
41C2×C16×C127—22no—
42#107×C127C2×C411yescharacteristic
43#107×C127C2×C411yescharacteristic
44#106×C127—21no—
45C4⋊C8×C127—22no—
46C4⋊C8×C127—41no—
47#103×C127—21no—
48#103×C127—21no—
49#102×C127—21no—
50#102×C127—21no—
51C4×C8×C127C2×C411yescharacteristic
52C4×C8×C127D411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C4×C8×C127C2311yescharacteristic
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127C22⋊C411yescharacteristic
60C22×C4×C127D811yescharacteristic
61C22×C4×C127SD1611yescharacteristic
62Q16×C127—22no—
63SD16×C127—42no—
64D8×C127—22no—
65M16×C127—82no—
66C2×C8×C127—22no—
67C2×C8×C127—22no—
68C2×C8×C127—42no—
69C2×C8×C127C22⋊C411yescharacteristic
70C2×C8×C127C22⋊C411yescharacteristic
71C2×C8×C127C22×C411yescharacteristic
72C2×C8×C127C2×D411yescharacteristic
73C4⋊C4×C127—21no—
74C4⋊C4×C127—21no—
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×C127D811yescharacteristic
87C42×C127SD1611yescharacteristic
88C42×C127C2×D411yescharacteristic
89C16×C127—24no—
90C23×C127—41no—
91C23×C127#10211yescharacteristic
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#10211yescharacteristic
106C2×C4×C127#10211yescharacteristic
107C2×C4×C127#10211yescharacteristic
108C2×C4×C127C2×C22⋊C411yescharacteristic
109C2×C4×C127C2×D811yescharacteristic
110C2×C4×C127C2×SD1611yescharacteristic
111C8×C127—21no—
112C8×C127—21no—
113C8×C127—82no—
114C8×C127#10412yes—
115C8×C127#13112yes—
116C22×C127—21no—
117C22×C127—21no—
118C22×C127—81no—
119C22×C127—81no—
120C22×C127—81no—
121C22×C127#36012yes—
122C22×C127C2×#10211yescharacteristic
123C4×C127—21no—
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×C127C2×#10411yescharacteristic
133#11677C12711yesmaximal, characteristic, direct product factor, Sylow
134C2×C127—22no—
135C2×C127—161no—
136C2×C127#149211yescharacteristic
137C2×C127C2×#36011yescharacteristic
138C2×C127#214811yescharacteristic
139#3168C2×C12711yescharacteristic
140C2×#346C2×C12711yescharacteristic, complemented
141#1566C2×C12711yescharacteristic, complemented
142#1334C2×C12712yescomplemented
143#1333C2×C12712yescomplemented
144C127#1167711yescharacteristic, direct product factor, Sylow
145#529—21no—
146C22×C16—21no—
147#499C4×C12711yescharacteristic
148#495C4×C12711yescharacteristic
149#488—21no—
150#467C4×C12711yescharacteristic
151#466C4×C12711yescharacteristic
152#465—21no—
153C4×Q16C22×C12711yescharacteristic
154C4×SD16—21no—
155C4×D8C22×C12711yescharacteristic
156#423—21no—
157C2×C4×C8C22×C12711yescharacteristic
158#346—21no—
159#346C22×C12712yes—
160#334—21no—
161#334C22×C12712yes—
162C2×Q16C2×C4×C12711yescharacteristic
163C2×SD16—21no—
164C2×D8C2×C4×C12711yescharacteristic
165C2×M16—41no—
166C22×C8C2×C4×C12711yescharacteristic
167C22×C8D4×C12711yescharacteristic
168#126—41no—
169#125—21no—
170#124—21no—
171#123—41no—
172C22⋊Q8—21no—
173#121—21no—
174C4×Q8—21no—
175C4×D4—21no—
176C4×D4—41no—
177#117—41no—
178C2×C42D4×C12711yescharacteristic
179C2×C16—24no—
180C2×C16—22no—
181#107C2×C4×C12711yescharacteristic
182#107C2×C4×C12711yescharacteristic
183#106—21no—
184C4⋊C8—22no—
185C4⋊C8—41no—
186#103—21no—
187#103—21no—
188#102—21no—
189#102—21no—
190C4×C8C2×C4×C12711yescharacteristic
191C4×C8D4×C12711yescharacteristic
192C4×C8D4×C12711yescharacteristic
193C4×C8C23×C12711yescharacteristic
194C2×Q8—21no—
195C2×D4—21no—
196C2×D4—41no—
197C22×C4—41no—
198C22×C4C22⋊C4×C12711yescharacteristic
199C22×C4D8×C12711yescharacteristic
200C22×C4SD16×C12711yescharacteristic
201Q16—22no—
202SD16—42no—
203D8—22no—
204M16—82no—
205C2×C8—22no—
206C2×C8—22no—
207C2×C8—42no—
208C2×C8C22⋊C4×C12711yescharacteristic
209C2×C8C22⋊C4×C12711yescharacteristic
210C2×C8C22×C4×C12711yescharacteristic
211C2×C8C2×D4×C12711yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C42—41no—
224C42C22⋊C4×C12711yescharacteristic
225C42D8×C12711yescharacteristic
226C42SD16×C12711yescharacteristic
227C42C2×D4×C12711yescharacteristic
228C16—24no—
229C23—41no—
230C23#102×C12711yescharacteristic
231Q8—41no—
232Q8—41no—
233D4—41no—
234D4—41no—
235D4—82no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—82no—
244C2×C4#102×C12711yescharacteristic
245C2×C4#102×C12711yescharacteristic
246C2×C4#102×C12711yescharacteristic
247C2×C4C2×C22⋊C4×C12711yescharacteristic
248C2×C4C2×D8×C12711yescharacteristic
249C2×C4C2×SD16×C12711yescharacteristic
250C8—21no—
251C8—21no—
252C8—82no—
253C8#104×C12712yes—
254C8#131×C12712yes—
255C22—21no—
256C22—21no—
257C22—81no—
258C22—81no—
259C22—81no—
260C22#360×C12712yes—
261C22C2×#102×C12711yescharacteristic
262C4—21no—
263C4—21no—
264C4—21no—
265C4—21no—
266C4—21no—
267C4—81no—
268C4—81no—
269C4—81no—
270C4#408×C12711yescharacteristic
271C4C2×#104×C12711yescharacteristic
272C2—22no—
273C2—161no—
274C2C127×#149211yescharacteristic
275C2C2×#360×C12711yescharacteristic
276C2C127×#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. C2×#346×C127C2semidirect
3. C127×#1566C2semidirect
4. C127×#1334C2semidirect
5. C127×#1333C2semidirect
133. #11677C127direct (N × H)
140. C2×#346C2×C127semidirect
141. #1566C2×C127semidirect
142. #1334C2×C127semidirect
143. #1333C2×C127semidirect
144. C127#11677direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31682
C2×#346×C1272
C127×#15662
C127×#13342
C127×#13332
#11677127