Finite Group Databasebeta

← C127×#13142 #44576815

Subgroups — C127×#13142 #44576815

Order 32512.

356 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
1C2×#365×C127C211yesmaximal, characteristic, complemented
2C2×#361×C127C211yesmaximal, characteristic
3C127×#2140C211yesmaximal, characteristic
4C127×#1972C211yesmaximal, characteristic
5C127×#1773C211yesmaximal, characteristic, complemented
6C127×#1386C211yesmaximal, characteristic, complemented
7C127×#1375C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×M32×C127C2211yescharacteristic
10C2×M32×C127C2211yescharacteristic
11C2×#108×C127C2211yescharacteristic
12#427×C127C2211yescharacteristic
13C2×#106×C127C2211yescharacteristic
14C2×#102×C127—21no—
15#405×C127—21no—
16C2×#97×C127C2211yescharacteristic
17#390×C127—21no—
18#365×C127—22no—
19#361×C127—22no—
20#357×C127C414yescomplemented
21#339×C127—21no—
22C22×D4×C127—21no—
23C2×D8×C127—21no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127C2×C412yes—
29C2×M16×C127—21no—
30C22×C8×C127D411yescharacteristic
31C22×C8×C127C2311yescharacteristic
32#117×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C22⋊C4×C127—42no—
35C2×C42×C127D411yescharacteristic
36M32×C127—21no—
37M32×C127—21no—
38M32×C127—21no—
39M32×C127—21no—
40C2×C16×C127—21no—
41C2×C16×C127C2×C412yes—
42#108×C127—21no—
43#108×C127D412yes—
44#107×C127C2×C412yes—
45#106×C127—21no—
46#106×C127—21no—
47#106×C127—21no—
48#102×C127—42no—
49#97×C127—21no—
50#97×C127—21no—
51#97×C127—41no—
52C4×C8×C127—41no—
53C24×C127—41no—
54C2×D4×C127—22no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C22×C4×C127—21no—
61C22×C4×C127—41no—
62C22×C4×C127C2×D411yescharacteristic
63D8×C127—22no—
64D8×C127—22no—
65D8×C127—41no—
66D8×C127—41no—
67M16×C127—22no—
68M16×C127—41no—
69C2×C8×C127—21no—
70C2×C8×C127—21no—
71C2×C8×C127—41no—
72C2×C8×C127SD1612yes—
73C2×C8×C127C22×C411yescharacteristic
74C2×C8×C127C2×D411yescharacteristic
75C2×C8×C127#4111yescharacteristic
76C2×C8×C127#4111yescharacteristic
77C2×C8×C127#4111yescharacteristic
78C2×C8×C127#4111yescharacteristic
79C4⋊C4×C127—22no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—84no—
84C42×C127—21no—
85C42×C127—21no—
86C42×C127—41no—
87C16×C127—22no—
88C16×C127—41no—
89C23×C127—42no—
90C23×C127—82no—
91C23×C127—82no—
92C23×C127—81no—
93C23×C127—81no—
94C23×C127AGL(1,ℤ/8)11yescharacteristic
95D4×C127—42no—
96D4×C127—42no—
97D4×C127—81no—
98D4×C127—81no—
99C2×C4×C127—42no—
100C2×C4×C127—42no—
101C2×C4×C127—41no—
102C2×C4×C127—82no—
103C2×C4×C127—81no—
104C2×C4×C127C4×D411yescharacteristic
105C2×C4×C127#12111yescharacteristic
106C2×C4×C127#12311yescharacteristic
107C2×C4×C127C2×SD1611yescharacteristic
108C2×C4×C127#13511yescharacteristic
109C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
110C8×C127—22no—
111C8×C127—42no—
112C8×C127#11711yescharacteristic
113C8×C127C4×D411yescharacteristic
114C8×C127#12411yescharacteristic
115C8×C127#12611yescharacteristic
116C22×C127—22no—
117C22×C127—84no—
118C22×C127—82no—
119C22×C127—162no—
120C22×C127—161no—
121C22×C127—161no—
122C22×C127#44211yescharacteristic
123C22×C127#46011yescharacteristic
124C22×C127#48211yescharacteristic
125C4×C127—81no—
126C4×C127—82no—
127C4×C127—161no—
128C4×C127#38811yescharacteristic
129C4×C127C4×SD1611yescharacteristic
130C4×C127#46311yescharacteristic
131C4×C127#48111yescharacteristic
132#13142C12711yesmaximal, characteristic, direct product factor, Sylow
133C2×C127—21no—
134C2×C127—21no—
135C2×C127—162no—
136C2×C127#192611yescharacteristic
137C2×C127AGL(1,ℤ/16)12yes—
138C2×#365C2×C12711yescharacteristic, complemented
139C2×#361C2×C12711yescharacteristic
140#2140C2×C12711yescharacteristic
141#1972C2×C12711yescharacteristic
142#1773C2×C12711yescharacteristic, complemented
143#1386C2×C12711yescharacteristic, complemented
144#1375C2×C12711yescharacteristic, complemented
145C127#1314211yescharacteristic, direct product factor, Sylow
146C22×D8C22×C12711yescharacteristic
147C2×M32C22×C12711yescharacteristic
148C2×M32C22×C12711yescharacteristic
149C2×#108C22×C12711yescharacteristic
150#427C22×C12711yescharacteristic
151C2×#106C22×C12711yescharacteristic
152C2×#102—21no—
153#405—21no—
154C2×#97C22×C12711yescharacteristic
155#390—21no—
156#365—22no—
157#361—22no—
158#357C4×C12714yescomplemented
159#339—21no—
160C22×D4—21no—
161C2×D8—21no—
162C2×D8—21no—
163C2×D8—21no—
164C2×D8—21no—
165C2×D8—21no—
166C2×D8C2×C4×C12712yes—
167C2×M16—21no—
168C22×C8D4×C12711yescharacteristic
169C22×C8C23×C12711yescharacteristic
170#117—21no—
171C2×C4⋊C4—21no—
172C2×C22⋊C4—42no—
173C2×C42D4×C12711yescharacteristic
174M32—21no—
175M32—21no—
176M32—21no—
177M32—21no—
178C2×C16—21no—
179C2×C16C2×C4×C12712yes—
180#108—21no—
181#108D4×C12712yes—
182#107C2×C4×C12712yes—
183#106—21no—
184#106—21no—
185#106—21no—
186#102—42no—
187#97—21no—
188#97—21no—
189#97—41no—
190C4×C8—41no—
191C24—41no—
192C2×D4—22no—
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—41no—
197C2×D4—41no—
198C22×C4—21no—
199C22×C4—41no—
200C22×C4C2×D4×C12711yescharacteristic
201D8—22no—
202D8—22no—
203D8—41no—
204D8—41no—
205M16—22no—
206M16—41no—
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8SD16×C12712yes—
211C2×C8C22×C4×C12711yescharacteristic
212C2×C8C2×D4×C12711yescharacteristic
213C2×C8#41×C12711yescharacteristic
214C2×C8#41×C12711yescharacteristic
215C2×C8#41×C12711yescharacteristic
216C2×C8#41×C12711yescharacteristic
217C4⋊C4—22no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—84no—
222C42—21no—
223C42—21no—
224C42—41no—
225C16—22no—
226C16—41no—
227C23—42no—
228C23—82no—
229C23—82no—
230C23—81no—
231C23—81no—
232C23AGL(1,ℤ/8)×C12711yescharacteristic
233D4—42no—
234D4—42no—
235D4—81no—
236D4—81no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—41no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4C4×D4×C12711yescharacteristic
243C2×C4#121×C12711yescharacteristic
244C2×C4#123×C12711yescharacteristic
245C2×C4C2×SD16×C12711yescharacteristic
246C2×C4#135×C12711yescharacteristic
247C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
248C8—22no—
249C8—42no—
250C8#117×C12711yescharacteristic
251C8C4×D4×C12711yescharacteristic
252C8#124×C12711yescharacteristic
253C8#126×C12711yescharacteristic
254C22—22no—
255C22—84no—
256C22—82no—
257C22—162no—
258C22—161no—
259C22—161no—
260C22#442×C12711yescharacteristic
261C22#460×C12711yescharacteristic
262C22#482×C12711yescharacteristic
263C4—81no—
264C4—82no—
265C4—161no—
266C4#388×C12711yescharacteristic
267C4C4×SD16×C12711yescharacteristic
268C4#463×C12711yescharacteristic
269C4#481×C12711yescharacteristic
270C2—21no—
271C2—21no—
272C2—162no—
273C2C127×#192611yescharacteristic
274C2C127×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C127#442
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#97×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#365×C127C2semidirect
5. C127×#1773C2semidirect
6. C127×#1386C2semidirect
7. C127×#1375C2semidirect
20. #357×C127C4semidirect
132. #13142C127direct (N × H)
138. C2×#365C2×C127semidirect
142. #1773C2×C127semidirect
143. #1386C2×C127semidirect
144. #1375C2×C127semidirect
145. C127#13142direct (N × H)
158. #357C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#365×C1272
C2×#361×C1272
C127×#21402
C127×#19722
C127×#17732
C127×#13862
C127×#13752
#13142127