Finite Group Databasebeta

← C127×#12870 #44576543

Subgroups — C127×#12870 #44576543

Order 32512.

420 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×#427×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic
3C127×#1807C211yesmaximal, characteristic
4C127×#1386C214yesmaximal, complemented
5C23×C8×C127C2211yescharacteristic
6C2×#117×C127—21no—
7C2×M32×C127C2212yes—
8#427×C127—21no—
9#427×C127—21no—
10#427×C127C412yescomplemented
11#427×C127C2212yes—
12C2×#107×C127C411yescharacteristic, complemented
13C2×#107×C127C411yescharacteristic, complemented
14C2×#106×C127—21no—
15C2×#106×C127C2212yes—
16#380×C127—21no—
17C22⋊C16×C127—21no—
18C22⋊C16×C127—21no—
19#340×C127—21no—
20C23×C4×C127D411yescharacteristic
21C22×C8×C127—24no—
22C22×C8×C127C2×C411yescharacteristic
23C22×C8×C127C2×C411yescharacteristic
24C22×C8×C127D411yescharacteristic
25C22×C8×C127D411yescharacteristic
26C22×C8×C127D411yescharacteristic
27C22×C8×C127C2311yescharacteristic
28#117×C127—22no—
29#117×C127—22no—
30#117×C127—41no—
31#117×C127—41no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—22no—
35C2×C22⋊C4×C127—41no—
36C2×C22⋊C4×C127—41no—
37C2×C42×C127—41no—
38M32×C127—24no—
39C2×C16×C127—22no—
40#107×C127—21no—
41#107×C127—21no—
42#107×C127C2×C412yes—
43#107×C127C2×C412yes—
44#106×C127—22no—
45#106×C127—22no—
46#106×C127—24no—
47#95×C127—41no—
48C24×C127D811yescharacteristic
49C22×C4×C127—22no—
50C22×C4×C127—22no—
51C22×C4×C127—41no—
52C22×C4×C127—41no—
53C22×C4×C127—42no—
54C22×C4×C127C22⋊C411yescharacteristic
55C22×C4×C127C22⋊C411yescharacteristic
56C22×C4×C127D811yescharacteristic
57C22×C4×C127SD1611yescharacteristic
58C22×C4×C127SD1611yescharacteristic
59C22×C4×C127C2×D411yescharacteristic
60C2×C8×C127—22no—
61C2×C8×C127—22no—
62C2×C8×C127—22no—
63C2×C8×C127—22no—
64C2×C8×C127—22no—
65C2×C8×C127C22⋊C411yescharacteristic
66C2×C8×C127C22⋊C411yescharacteristic
67C2×C8×C127C22×C411yescharacteristic
68C2×C8×C127C2×D411yescharacteristic
69C2×C8×C127#4114yes—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—42no—
75C4⋊C4×C127—42no—
76C22⋊C4×C127—42no—
77C22⋊C4×C127—42no—
78C22⋊C4×C127—82no—
79C42×C127—42no—
80C42×C127—42no—
81C16×C127—42no—
82C23×C127—22no—
83C23×C127—22no—
84C23×C127—41no—
85C23×C127#10211yescharacteristic
86C23×C127#10211yescharacteristic
87C23×C127C2×D811yescharacteristic
88C2×C4×C127—22no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—22no—
94C2×C4×C127—22no—
95C2×C4×C127—42no—
96C2×C4×C127—42no—
97C2×C4×C127—82no—
98C2×C4×C127—82no—
99C2×C4×C127—82no—
100C2×C4×C127—82no—
101C2×C4×C127—82no—
102C2×C4×C127#10211yescharacteristic
103C2×C4×C127#10211yescharacteristic
104C2×C4×C127C2×C22⋊C411yescharacteristic
105C2×C4×C127#12312yes—
106C2×C4×C127C2×SD1611yescharacteristic
107C2×C4×C127#13712yes—
108C8×C127—21no—
109C8×C127—21no—
110C8×C127#11712yes—
111C8×C127#12312yes—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127—21no—
115C22×C127—21no—
116C22×C127—21no—
117C22×C127—21no—
118C22×C127—21no—
119C22×C127—44no—
120C22×C127#36012yes—
121C22×C127C2×#10211yescharacteristic
122C22×C127#48012yes—
123C4×C127—21no—
124C4×C127—21no—
125C4×C127—82no—
126C4×C127—82no—
127C4×C127—162no—
128C4×C127#38111yescharacteristic
129C4×C127#41911yescharacteristic
130C4×C127#48312yes—
131#12870C12711yesmaximal, characteristic, direct product factor, Sylow
132C2×C127—22no—
133C2×C127—22no—
134C2×C127—41no—
135C2×C127#182311yescharacteristic
136C2×C127C2×#36011yescharacteristic
137C2×C127#214511yescharacteristic
138C2×#427C2×C12711yescharacteristic
139#2112C2×C12711yescharacteristic
140#1807C2×C12711yescharacteristic
141#1386C2×C12714yescomplemented
142C127#1287011yescharacteristic, direct product factor, Sylow
143C23×C8C22×C12711yescharacteristic
144C2×#117—21no—
145C2×M32C22×C12712yes—
146#427—21no—
147#427—21no—
148#427C4×C12712yescomplemented
149#427C22×C12712yes—
150C2×#107C4×C12711yescharacteristic, complemented
151C2×#107C4×C12711yescharacteristic, complemented
152C2×#106—21no—
153C2×#106C22×C12712yes—
154#380—21no—
155C22⋊C16—21no—
156C22⋊C16—21no—
157#340—21no—
158C23×C4D4×C12711yescharacteristic
159C22×C8—24no—
160C22×C8C2×C4×C12711yescharacteristic
161C22×C8C2×C4×C12711yescharacteristic
162C22×C8D4×C12711yescharacteristic
163C22×C8D4×C12711yescharacteristic
164C22×C8D4×C12711yescharacteristic
165C22×C8C23×C12711yescharacteristic
166#117—22no—
167#117—22no—
168#117—41no—
169#117—41no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C22⋊C4—41no—
174C2×C22⋊C4—41no—
175C2×C42—41no—
176M32—24no—
177C2×C16—22no—
178#107—21no—
179#107—21no—
180#107C2×C4×C12712yes—
181#107C2×C4×C12712yes—
182#106—22no—
183#106—22no—
184#106—24no—
185#95—41no—
186C24D8×C12711yescharacteristic
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—42no—
192C22×C4C22⋊C4×C12711yescharacteristic
193C22×C4C22⋊C4×C12711yescharacteristic
194C22×C4D8×C12711yescharacteristic
195C22×C4SD16×C12711yescharacteristic
196C22×C4SD16×C12711yescharacteristic
197C22×C4C2×D4×C12711yescharacteristic
198C2×C8—22no—
199C2×C8—22no—
200C2×C8—22no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8C22⋊C4×C12711yescharacteristic
204C2×C8C22⋊C4×C12711yescharacteristic
205C2×C8C22×C4×C12711yescharacteristic
206C2×C8C2×D4×C12711yescharacteristic
207C2×C8#41×C12714yes—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—82no—
217C42—42no—
218C42—42no—
219C16—42no—
220C23—22no—
221C23—22no—
222C23—41no—
223C23#102×C12711yescharacteristic
224C23#102×C12711yescharacteristic
225C23C2×D8×C12711yescharacteristic
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4#102×C12711yescharacteristic
241C2×C4#102×C12711yescharacteristic
242C2×C4C2×C22⋊C4×C12711yescharacteristic
243C2×C4#123×C12712yes—
244C2×C4C2×SD16×C12711yescharacteristic
245C2×C4#137×C12712yes—
246C8—21no—
247C8—21no—
248C8#117×C12712yes—
249C8#123×C12712yes—
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—44no—
258C22#360×C12712yes—
259C22C2×#102×C12711yescharacteristic
260C22#480×C12712yes—
261C4—21no—
262C4—21no—
263C4—82no—
264C4—82no—
265C4—162no—
266C4#381×C12711yescharacteristic
267C4#419×C12711yescharacteristic
268C4#483×C12712yes—
269C2—22no—
270C2—22no—
271C2—41no—
272C2C127×#182311yescharacteristic
273C2C2×#360×C12711yescharacteristic
274C2C127×#214511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC24×C127D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1386C2semidirect
10. #427×C127C4semidirect
12. C2×#107×C127C4semidirect
13. C2×#107×C127C4semidirect
131. #12870C127direct (N × H)
141. #1386C2×C127semidirect
142. C127#12870direct (N × H)
148. #427C4×C127semidirect
150. C2×#107C4×C127semidirect
151. C2×#107C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#427×C1272
C127×#21122
C127×#18072
C127×#13862
#12870127