Finite Group Databasebeta

← C127×#11711 #44575384

Subgroups — C127×#11711 #44575384

Order 32512.

492 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C2×#341×C127C211yesmaximal, characteristic, complemented
4C127×#1349C214yesmaximal, complemented
5C22×D8×C127C411yescharacteristic
6C22×M16×C127—21no—
7C23×C8×C127C2211yescharacteristic
8C2×#121×C127—21no—
9C2×M32×C127—21no—
10#466×C127—21no—
11#466×C127—21no—
12#466×C127C412yes—
13#466×C127C2212yes—
14C2×#107×C127C411yescharacteristic
15C2×#102×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127C2212yescomplemented
18#341×C127—21no—
19#341×C127C2212yescomplemented
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127D411yescharacteristic
23C2×D8×C127—21no—
24C2×D8×C127—42no—
25C2×D8×C127C2×C412yes—
26C2×M16×C127—24no—
27C2×M16×C127—22no—
28C2×M16×C127—42no—
29C2×M16×C127—41no—
30C22×C8×C127—42no—
31C22×C8×C127—41no—
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C22×C8×C127D411yescharacteristic
36C22×C8×C127D411yescharacteristic
37C22×C8×C127C2311yescharacteristic
38#121×C127—22no—
39#121×C127—22no—
40#121×C127—41no—
41#121×C127—41no—
42C2×C4⋊C4×C127—21no—
43C2×C22⋊C4×C127—41no—
44M32×C127—42no—
45C2×C16×C127—22no—
46#107×C127—21no—
47#107×C127C2×C412yes—
48#102×C127—22no—
49#102×C127—22no—
50C24×C127—41no—
51C24×C127SD1611yescharacteristic
52C2×D4×C127—22no—
53C2×D4×C127—42no—
54C2×D4×C127—42no—
55C2×D4×C127—42no—
56C2×D4×C127—41no—
57C2×D4×C127—42no—
58C2×D4×C127—84no—
59C22×C4×C127—22no—
60C22×C4×C127—22no—
61C22×C4×C127—41no—
62C22×C4×C127C22⋊C411yescharacteristic
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127D811yescharacteristic
65C22×C4×C127D811yescharacteristic
66C22×C4×C127SD1611yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68D8×C127—42no—
69D8×C127—42no—
70M16×C127—24no—
71M16×C127—44no—
72M16×C127—42no—
73C2×C8×C127—22no—
74C2×C8×C127—22no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127—41no—
78C2×C8×C127—41no—
79C2×C8×C127—44no—
80C2×C8×C127—42no—
81C2×C8×C127C22⋊C411yescharacteristic
82C2×C8×C127C22⋊C411yescharacteristic
83C2×C8×C127C22×C411yescharacteristic
84C2×C8×C127C2×D411yescharacteristic
85C4⋊C4×C127—22no—
86C4⋊C4×C127—41no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—42no—
89C16×C127—42no—
90C23×C127—22no—
91C23×C127—22no—
92C23×C127—41no—
93C23×C127—42no—
94C23×C127—82no—
95C23×C127—82no—
96C23×C127—82no—
97C23×C127#10211yescharacteristic
98C23×C127#10211yescharacteristic
99C23×C127C2×SD1611yescharacteristic
100D4×C127—42no—
101D4×C127—42no—
102D4×C127—84no—
103D4×C127—84no—
104D4×C127—82no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—22no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—42no—
113C2×C4×C127—82no—
114C2×C4×C127#9912yes—
115C2×C4×C127#10211yescharacteristic
116C2×C4×C127#10211yescharacteristic
117C2×C4×C127#10412yes—
118C2×C4×C127C2×C22⋊C411yescharacteristic
119C2×C4×C127C2×D811yescharacteristic
120C8×C127—21no—
121C8×C127—21no—
122C8×C127—21no—
123C8×C127—21no—
124C8×C127—44no—
125C22×C127—21no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127—44no—
133C22×C127—82no—
134C22×C127—82no—
135C22×C127—82no—
136C22×C127—164no—
137C22×C127#32712yes—
138C22×C127#36112yes—
139C22×C127C2×#10211yescharacteristic
140C4×C127—21no—
141C4×C127—21no—
142C4×C127—82no—
143C4×C127#32712yes—
144C4×C127C2×#9911yescharacteristic
145C4×C127C2×#10411yescharacteristic
146#11711C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—22no—
148C2×C127—22no—
149C2×C127—41no—
150C2×C127—162no—
151C2×C127C2×#32711yescharacteristic
152C2×C127#214311yescharacteristic
153C2×C127C2×#36111yescharacteristic
154C2×#466C2×C12711yescharacteristic
155#2112C2×C12711yescharacteristic, complemented
156C2×#341C2×C12711yescharacteristic, complemented
157#1349C2×C12714yescomplemented
158C127#1171111yescharacteristic, direct product factor, Sylow
159C22×D8C4×C12711yescharacteristic
160C22×M16—21no—
161C23×C8C22×C12711yescharacteristic
162C2×#121—21no—
163C2×M32—21no—
164#466—21no—
165#466—21no—
166#466C4×C12712yes—
167#466C22×C12712yes—
168C2×#107C4×C12711yescharacteristic
169C2×#102—21no—
170C22⋊C16—21no—
171C22⋊C16C22×C12712yescomplemented
172#341—21no—
173#341C22×C12712yescomplemented
174C22×D4—21no—
175C22×D4—41no—
176C23×C4D4×C12711yescharacteristic
177C2×D8—21no—
178C2×D8—42no—
179C2×D8C2×C4×C12712yes—
180C2×M16—24no—
181C2×M16—22no—
182C2×M16—42no—
183C2×M16—41no—
184C22×C8—42no—
185C22×C8—41no—
186C22×C8C2×C4×C12711yescharacteristic
187C22×C8C2×C4×C12711yescharacteristic
188C22×C8D4×C12711yescharacteristic
189C22×C8D4×C12711yescharacteristic
190C22×C8D4×C12711yescharacteristic
191C22×C8C23×C12711yescharacteristic
192#121—22no—
193#121—22no—
194#121—41no—
195#121—41no—
196C2×C4⋊C4—21no—
197C2×C22⋊C4—41no—
198M32—42no—
199C2×C16—22no—
200#107—21no—
201#107C2×C4×C12712yes—
202#102—22no—
203#102—22no—
204C24—41no—
205C24SD16×C12711yescharacteristic
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—41no—
211C2×D4—42no—
212C2×D4—84no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4C22⋊C4×C12711yescharacteristic
217C22×C4C22⋊C4×C12711yescharacteristic
218C22×C4D8×C12711yescharacteristic
219C22×C4D8×C12711yescharacteristic
220C22×C4SD16×C12711yescharacteristic
221C22×C4C2×D4×C12711yescharacteristic
222D8—42no—
223D8—42no—
224M16—24no—
225M16—44no—
226M16—42no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—44no—
234C2×C8—42no—
235C2×C8C22⋊C4×C12711yescharacteristic
236C2×C8C22⋊C4×C12711yescharacteristic
237C2×C8C22×C4×C12711yescharacteristic
238C2×C8C2×D4×C12711yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—41no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C16—42no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—42no—
248C23—82no—
249C23—82no—
250C23—82no—
251C23#102×C12711yescharacteristic
252C23#102×C12711yescharacteristic
253C23C2×SD16×C12711yescharacteristic
254D4—42no—
255D4—42no—
256D4—84no—
257D4—84no—
258D4—82no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—82no—
268C2×C4#99×C12712yes—
269C2×C4#102×C12711yescharacteristic
270C2×C4#102×C12711yescharacteristic
271C2×C4#104×C12712yes—
272C2×C4C2×C22⋊C4×C12711yescharacteristic
273C2×C4C2×D8×C12711yescharacteristic
274C8—21no—
275C8—21no—
276C8—21no—
277C8—21no—
278C8—44no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—82no—
288C22—82no—
289C22—82no—
290C22—164no—
291C22#327×C12712yes—
292C22#361×C12712yes—
293C22C2×#102×C12711yescharacteristic
294C4—21no—
295C4—21no—
296C4—82no—
297C4#327×C12712yes—
298C4C2×#99×C12711yescharacteristic
299C4C2×#104×C12711yescharacteristic
300C2—22no—
301C2—22no—
302C2—41no—
303C2—162no—
304C2C2×#327×C12711yescharacteristic
305C2C127×#214311yescharacteristic
306C2C2×#361×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#102
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#466×C127C2
LCSG ▷ C2×C8 ▷ C2×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
2. C127×#2112C2semidirect
3. C2×#341×C127C2semidirect
4. C127×#1349C2semidirect
17. C22⋊C16×C127C22semidirect
19. #341×C127C22semidirect
146. #11711C127direct (N × H)
155. #2112C2×C127semidirect
156. C2×#341C2×C127semidirect
157. #1349C2×C127semidirect
158. C127#11711direct (N × H)
171. C22⋊C16C22×C127semidirect
173. #341C22×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1272
C127×#21122
C2×#341×C1272
C127×#13492
#11711127