Finite Group Databasebeta

← C127×#11750 #44575423

Subgroups — C127×#11750 #44575423

Order 32512.

326 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3168C211yesmaximal, characteristic
2C127×#2163C211yesmaximal, characteristic, complemented
3C4×#108×C127C211yesmaximal, characteristic, complemented
4C127×#1350C212yesmaximal, complemented
5C127×#1349C212yesmaximal
6#529×C127—21no—
7#499×C127C411yescharacteristic
8#495×C127C411yescharacteristic
9#488×C127—21no—
10#467×C127C2211yescharacteristic
11#466×C127C2211yescharacteristic
12#465×C127—21no—
13C4×Q16×C127C411yescharacteristic
14C4×SD16×C127—21no—
15C4×D8×C127C411yescharacteristic
16C2×#108×C127—21no—
17C4×M16×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19C4⋊C16×C127—21no—
20C22⋊C16×C127C2212yes—
21#346×C127—21no—
22#341×C127C2212yes—
23C2×Q16×C127C2×C411yescharacteristic
24C2×SD16×C127—21no—
25C2×D8×C127C2×C411yescharacteristic
26C2×M16×C127—22no—
27C22×C8×C127D411yescharacteristic
28C22×C8×C127C2311yescharacteristic
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#108×C127—24no—
42#107×C127C2×C411yescharacteristic
43#107×C127C2×C411yescharacteristic
44#106×C127—21no—
45#103×C127—21no—
46#103×C127—21no—
47#102×C127—21no—
48#102×C127—21no—
49#97×C127—41no—
50C4×C8×C127—41no—
51C4×C8×C127C2×C411yescharacteristic
52C4×C8×C127C2×C411yescharacteristic
53C4×C8×C127D411yescharacteristic
54C4×C8×C127D411yescharacteristic
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—41no—
58C22×C4×C127—41no—
59C22×C4×C127SD1611yescharacteristic
60C22×C4×C127SD1611yescharacteristic
61C22×C4×C127C2×D411yescharacteristic
62Q16×C127—41no—
63SD16×C127—42no—
64D8×C127—41no—
65M16×C127—24no—
66M16×C127—42no—
67C2×C8×C127—22no—
68C2×C8×C127—41no—
69C2×C8×C127—42no—
70C2×C8×C127C22⋊C411yescharacteristic
71C2×C8×C127C22⋊C411yescharacteristic
72C2×C8×C127C22×C411yescharacteristic
73C2×C8×C127C2×D411yescharacteristic
74C4⋊C4×C127—21no—
75C4⋊C4×C127—21no—
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×C127C22⋊C411yescharacteristic
87C42×C127C22⋊C411yescharacteristic
88C42×C127D811yescharacteristic
89C42×C127D811yescharacteristic
90C16×C127—42no—
91C23×C127—41no—
92C23×C127C2×SD1611yescharacteristic
93Q8×C127—41no—
94Q8×C127—41no—
95D4×C127—41no—
96D4×C127—41no—
97D4×C127—82no—
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—41no—
105C2×C4×C127—82no—
106C2×C4×C127#10211yescharacteristic
107C2×C4×C127#10211yescharacteristic
108C2×C4×C127#10211yescharacteristic
109C2×C4×C127#10211yescharacteristic
110C2×C4×C127C2×C22⋊C411yescharacteristic
111C2×C4×C127C2×D811yescharacteristic
112C8×C127—21no—
113C8×C127—21no—
114C8×C127—21no—
115C8×C127—44no—
116C8×C127#10412yes—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—21no—
120C22×C127—81no—
121C22×C127—81no—
122C22×C127—81no—
123C22×C127C2×#10211yescharacteristic
124C4×C127—21no—
125C4×C127—21no—
126C4×C127—21no—
127C4×C127—21no—
128C4×C127—21no—
129C4×C127—81no—
130C4×C127—81no—
131C4×C127—81no—
132C4×C127#41011yescharacteristic
133C4×C127C2×#10411yescharacteristic
134#11750C12711yesmaximal, characteristic, direct product factor, Sylow
135C2×C127—41no—
136C2×C127—161no—
137C2×C127#150211yescharacteristic
138C2×C127#214311yescharacteristic
139C2×C127#214811yescharacteristic
140#3168C2×C12711yescharacteristic
141#2163C2×C12711yescharacteristic, complemented
142C4×#108C2×C12711yescharacteristic, complemented
143#1350C2×C12712yescomplemented
144#1349C2×C12712yes—
145C127#1175011yescharacteristic, direct product factor, Sylow
146#529—21no—
147#499C4×C12711yescharacteristic
148#495C4×C12711yescharacteristic
149#488—21no—
150#467C22×C12711yescharacteristic
151#466C22×C12711yescharacteristic
152#465—21no—
153C4×Q16C4×C12711yescharacteristic
154C4×SD16—21no—
155C4×D8C4×C12711yescharacteristic
156C2×#108—21no—
157C4×M16—21no—
158C2×C4×C8C22×C12711yescharacteristic
159C4⋊C16—21no—
160C22⋊C16C22×C12712yes—
161#346—21no—
162#341C22×C12712yes—
163C2×Q16C2×C4×C12711yescharacteristic
164C2×SD16—21no—
165C2×D8C2×C4×C12711yescharacteristic
166C2×M16—22no—
167C22×C8D4×C12711yescharacteristic
168C22×C8C23×C12711yescharacteristic
169#126—41no—
170#125—21no—
171#124—21no—
172#123—41no—
173C22⋊Q8—21no—
174#121—21no—
175C4×Q8—21no—
176C4×D4—21no—
177C4×D4—41no—
178#117—41no—
179C2×C42D4×C12711yescharacteristic
180C2×C16—22no—
181#108—24no—
182#107C2×C4×C12711yescharacteristic
183#107C2×C4×C12711yescharacteristic
184#106—21no—
185#103—21no—
186#103—21no—
187#102—21no—
188#102—21no—
189#97—41no—
190C4×C8—41no—
191C4×C8C2×C4×C12711yescharacteristic
192C4×C8C2×C4×C12711yescharacteristic
193C4×C8D4×C12711yescharacteristic
194C4×C8D4×C12711yescharacteristic
195C2×Q8—21no—
196C2×D4—21no—
197C2×D4—41no—
198C22×C4—41no—
199C22×C4SD16×C12711yescharacteristic
200C22×C4SD16×C12711yescharacteristic
201C22×C4C2×D4×C12711yescharacteristic
202Q16—41no—
203SD16—42no—
204D8—41no—
205M16—24no—
206M16—42no—
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—42no—
210C2×C8C22⋊C4×C12711yescharacteristic
211C2×C8C22⋊C4×C12711yescharacteristic
212C2×C8C22×C4×C12711yescharacteristic
213C2×C8C2×D4×C12711yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C42—41no—
226C42C22⋊C4×C12711yescharacteristic
227C42C22⋊C4×C12711yescharacteristic
228C42D8×C12711yescharacteristic
229C42D8×C12711yescharacteristic
230C16—42no—
231C23—41no—
232C23C2×SD16×C12711yescharacteristic
233Q8—41no—
234Q8—41no—
235D4—41no—
236D4—41no—
237D4—82no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—82no—
246C2×C4#102×C12711yescharacteristic
247C2×C4#102×C12711yescharacteristic
248C2×C4#102×C12711yescharacteristic
249C2×C4#102×C12711yescharacteristic
250C2×C4C2×C22⋊C4×C12711yescharacteristic
251C2×C4C2×D8×C12711yescharacteristic
252C8—21no—
253C8—21no—
254C8—21no—
255C8—44no—
256C8#104×C12712yes—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22C2×#102×C12711yescharacteristic
264C4—21no—
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4#410×C12711yescharacteristic
273C4C2×#104×C12711yescharacteristic
274C2—41no—
275C2—161no—
276C2C127×#150211yescharacteristic
277C2C127×#214311yescharacteristic
278C2C127×#214811yescharacteristic
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×#108×C127C2semidirect
4. C127×#1350C2semidirect
134. #11750C127direct (N × H)
141. #2163C2×C127semidirect
142. C4×#108C2×C127semidirect
143. #1350C2×C127semidirect
145. C127#11750direct (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
C4×#108×C1272
C127×#13502
C127×#13492
#11750127