Finite Group Databasebeta

← C127×#13064 #44576737

Subgroups — C127×#13064 #44576737

Order 32512.

488 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
1C22×M32×C127C211yesmaximal, characteristic, complemented
2C127×#3050C211yesmaximal, characteristic
3C2×#359×C127C212yesmaximal, complemented
4C127×#1810C211yesmaximal, characteristic, complemented
5C127×#1382C212yesmaximal, complemented
6C2×#135×C127C2211yescharacteristic
7C23×C8×C127C2211yescharacteristic
8#525×C127—21no—
9C2×M32×C127—22no—
10C2×M32×C127—24no—
11C22×C16×C127C2212yes—
12#467×C127C412yes—
13#466×C127C412yes—
14#465×C127—22no—
15C2×#108×C127C2212yes—
16#427×C127C2211yescharacteristic
17#416×C127—21no—
18#407×C127—21no—
19#359×C127—24no—
20#341×C127—21no—
21C2×#41×C127—21no—
22C23×C4×C127D411yescharacteristic
23#135×C127—22no—
24#135×C127—22no—
25C2×Q16×C127C2×C411yescharacteristic
26C2×SD16×C127—21no—
27C2×D8×C127C2×C411yescharacteristic
28C2×M16×C127—22no—
29C22×C8×C127—22no—
30C22×C8×C127—22no—
31C22×C8×C127C2×C412yes—
32C22×C8×C127D411yescharacteristic
33C22×C8×C127D412yes—
34C22×C8×C127C2311yescharacteristic
35#123×C127—41no—
36C22⋊Q8×C127—22no—
37#121×C127—22no—
38#120×C127—41no—
39C4×D4×C127—42no—
40#117×C127—21no—
41M32×C127—28no—
42C2×C16×C127—22no—
43C2×C16×C127—22no—
44C2×C16×C127D414yescomplemented
45#108×C127—22no—
46#108×C127—22no—
47#107×C127C2×C412yes—
48#106×C127—21no—
49#103×C127—22no—
50#102×C127—22no—
51C22⋊C8×C127—42no—
52C24×C127SD1611yescharacteristic
53#41×C127—42no—
54#41×C127—42no—
55C2×Q8×C127—21no—
56C2×D4×C127—21no—
57C2×D4×C127—42no—
58C2×D4×C127—41no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—41no—
62C22×C4×C127C22⋊C412yes—
63C22×C4×C127D812yes—
64C22×C4×C127SD1611yescharacteristic
65C22×C4×C127C2×D411yescharacteristic
66Q16×C127—22no—
67SD16×C127—41no—
68SD16×C127—41no—
69D8×C127—22no—
70M16×C127—42no—
71M16×C127—42no—
72C2×C8×C127—22no—
73C2×C8×C127—24no—
74C2×C8×C127—22no—
75C2×C8×C127—22no—
76C2×C8×C127—42no—
77C2×C8×C127C22⋊C412yes—
78C2×C8×C127C22×C411yescharacteristic
79C2×C8×C127C2×D412yes—
80C2×C8×C127C2×D411yescharacteristic
81C2×C8×C127#4112yes—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—42no—
84C22⋊C4×C127—42no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—42no—
87C42×C127—41no—
88C16×C127—24no—
89C23×C127—22no—
90C23×C127—42no—
91C23×C127—41no—
92C23×C127#10212yes—
93C23×C127C2×SD1611yescharacteristic
94Q8×C127—41no—
95Q8×C127—41no—
96D4×C127—41no—
97D4×C127—41no—
98D4×C127—84no—
99D4×C127—82no—
100C2×C4×C127—22no—
101C2×C4×C127—22no—
102C2×C4×C127—22no—
103C2×C4×C127—24no—
104C2×C4×C127—42no—
105C2×C4×C127—41no—
106C2×C4×C127—82no—
107C2×C4×C127#10212yes—
108C2×C4×C127C2×C22⋊C411yescharacteristic
109C2×C4×C127#12112yes—
110C2×C4×C127C2×D811yescharacteristic
111C2×C4×C127#13512yes—
112C8×C127—22no—
113C8×C127—82no—
114C8×C127C4×D412yes—
115C8×C127#12011yescharacteristic
116C8×C127#12311yescharacteristic
117C22×C127—22no—
118C22×C127—22no—
119C22×C127—22no—
120C22×C127—22no—
121C22×C127—44no—
122C22×C127—82no—
123C22×C127—81no—
124C22×C127C2×#10211yescharacteristic
125C22×C127#46512yes—
126C4×C127—22no—
127C4×C127—82no—
128C4×C127—81no—
129C4×C127#38611yescharacteristic
130C4×C127#41611yescharacteristic
131C4×C127#46612yes—
132#13064C12711yesmaximal, characteristic, direct product factor, Sylow
133C2×C127—22no—
134C2×C127—42no—
135C2×C127—161no—
136C2×C127#189311yescharacteristic
137C2×C127#214312yes—
138C22×M32C2×C12711yescharacteristic, complemented
139#3050C2×C12711yescharacteristic
140C2×#359C2×C12712yescomplemented
141#1810C2×C12711yescharacteristic, complemented
142#1382C2×C12712yescomplemented
143C127#1306411yescharacteristic, direct product factor, Sylow
144C2×#135C22×C12711yescharacteristic
145C23×C8C22×C12711yescharacteristic
146#525—21no—
147C2×M32—22no—
148C2×M32—24no—
149C22×C16C22×C12712yes—
150#467C4×C12712yes—
151#466C4×C12712yes—
152#465—22no—
153C2×#108C22×C12712yes—
154#427C22×C12711yescharacteristic
155#416—21no—
156#407—21no—
157#359—24no—
158#341—21no—
159C2×#41—21no—
160C23×C4D4×C12711yescharacteristic
161#135—22no—
162#135—22no—
163C2×Q16C2×C4×C12711yescharacteristic
164C2×SD16—21no—
165C2×D8C2×C4×C12711yescharacteristic
166C2×M16—22no—
167C22×C8—22no—
168C22×C8—22no—
169C22×C8C2×C4×C12712yes—
170C22×C8D4×C12711yescharacteristic
171C22×C8D4×C12712yes—
172C22×C8C23×C12711yescharacteristic
173#123—41no—
174C22⋊Q8—22no—
175#121—22no—
176#120—41no—
177C4×D4—42no—
178#117—21no—
179M32—28no—
180C2×C16—22no—
181C2×C16—22no—
182C2×C16D4×C12714yescomplemented
183#108—22no—
184#108—22no—
185#107C2×C4×C12712yes—
186#106—21no—
187#103—22no—
188#102—22no—
189C22⋊C8—42no—
190C24SD16×C12711yescharacteristic
191#41—42no—
192#41—42no—
193C2×Q8—21no—
194C2×D4—21no—
195C2×D4—42no—
196C2×D4—41no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4C22⋊C4×C12712yes—
201C22×C4D8×C12712yes—
202C22×C4SD16×C12711yescharacteristic
203C22×C4C2×D4×C12711yescharacteristic
204Q16—22no—
205SD16—41no—
206SD16—41no—
207D8—22no—
208M16—42no—
209M16—42no—
210C2×C8—22no—
211C2×C8—24no—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—42no—
215C2×C8C22⋊C4×C12712yes—
216C2×C8C22×C4×C12711yescharacteristic
217C2×C8C2×D4×C12712yes—
218C2×C8C2×D4×C12711yescharacteristic
219C2×C8#41×C12712yes—
220C4⋊C4—22no—
221C4⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—41no—
224C22⋊C4—42no—
225C42—41no—
226C16—24no—
227C23—22no—
228C23—42no—
229C23—41no—
230C23#102×C12712yes—
231C23C2×SD16×C12711yescharacteristic
232Q8—41no—
233Q8—41no—
234D4—41no—
235D4—41no—
236D4—84no—
237D4—82no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—24no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—82no—
245C2×C4#102×C12712yes—
246C2×C4C2×C22⋊C4×C12711yescharacteristic
247C2×C4#121×C12712yes—
248C2×C4C2×D8×C12711yescharacteristic
249C2×C4#135×C12712yes—
250C8—22no—
251C8—82no—
252C8C4×D4×C12712yes—
253C8#120×C12711yescharacteristic
254C8#123×C12711yescharacteristic
255C22—22no—
256C22—22no—
257C22—22no—
258C22—22no—
259C22—44no—
260C22—82no—
261C22—81no—
262C22C2×#102×C12711yescharacteristic
263C22#465×C12712yes—
264C4—22no—
265C4—82no—
266C4—81no—
267C4#386×C12711yescharacteristic
268C4#416×C12711yescharacteristic
269C4#466×C12712yes—
270C2—22no—
271C2—42no—
272C2—161no—
273C2C127×#189311yescharacteristic
274C2C127×#214312yes—
subgroupG/H
centerC2×C4×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
socleC22×C127C2×#102
prime radicalC127×#3050C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C23×C4×C127 ◁ C23×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×M32×C127C2semidirect
3. C2×#359×C127C2semidirect
4. C127×#1810C2semidirect
5. C127×#1382C2semidirect
44. C2×C16×C127D4semidirect
132. #13064C127direct (N × H)
138. C22×M32C2×C127semidirect
140. C2×#359C2×C127semidirect
141. #1810C2×C127semidirect
142. #1382C2×C127semidirect
143. C127#13064direct (N × H)
182. C2×C16D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×M32×C1272
C127×#30502
C2×#359×C1272
C127×#18102
C127×#13822
#13064127