Finite Group Databasebeta

← C127×#11705 #44575378

Subgroups — C127×#11705 #44575378

Order 32512.

508 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C127C211yesmaximal, characteristic
2C127×#2112C211yesmaximal, characteristic, complemented
3C127×#1735C211yesmaximal, characteristic, complemented
4C127×#1347C214yesmaximal, complemented
5C22×D8×C127C411yescharacteristic, complemented
6C23×C8×C127C2211yescharacteristic
7C2×#121×C127—21no—
8C2×#117×C127—21no—
9C2×M32×C127—21no—
10#466×C127—21no—
11#466×C127—21no—
12#466×C127C412yescomplemented
13#466×C127C2212yes—
14C2×#107×C127C411yescharacteristic, complemented
15C2×#102×C127—21no—
16C22⋊C16×C127—21no—
17C22⋊C16×C127C2212yescomplemented
18#340×C127—21no—
19#340×C127C2212yescomplemented
20C22×D4×C127—21no—
21C22×D4×C127—41no—
22C23×C4×C127D411yescharacteristic
23C2×D8×C127—21no—
24C2×D8×C127—42no—
25C2×D8×C127C2×C412yes—
26C22×C8×C127—42no—
27C22×C8×C127C2×C411yescharacteristic
28C22×C8×C127C2×C411yescharacteristic
29C22×C8×C127D411yescharacteristic
30C22×C8×C127D411yescharacteristic
31C22×C8×C127D411yescharacteristic
32C22×C8×C127C2311yescharacteristic
33#121×C127—22no—
34#121×C127—22no—
35#121×C127—41no—
36#121×C127—41no—
37#117×C127—24no—
38#117×C127—42no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—22no—
41C2×C22⋊C4×C127—41no—
42C2×C22⋊C4×C127—41no—
43C2×C42×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×C127D811yescharacteristic
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×C127—42no—
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127C22⋊C411yescharacteristic
65C22×C4×C127D811yescharacteristic
66C22×C4×C127SD1611yescharacteristic
67C22×C4×C127SD1611yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69D8×C127—42no—
70D8×C127—42no—
71C2×C8×C127—22no—
72C2×C8×C127—22no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127C22⋊C411yescharacteristic
78C2×C8×C127C22⋊C411yescharacteristic
79C2×C8×C127C22×C411yescharacteristic
80C2×C8×C127C2×D411yescharacteristic
81C4⋊C4×C127—24no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—42no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—44no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C42×C127—44no—
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×D811yescharacteristic
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—44no—
113C2×C4×C127—42no—
114C2×C4×C127—82no—
115C2×C4×C127—82no—
116C2×C4×C127—82no—
117C2×C4×C127#9912yes—
118C2×C4×C127#10211yescharacteristic
119C2×C4×C127#10211yescharacteristic
120C2×C4×C127#10412yes—
121C2×C4×C127C2×C22⋊C411yescharacteristic
122C2×C4×C127C2×SD1611yescharacteristic
123C8×C127—21no—
124C8×C127—21no—
125C8×C127—21no—
126C8×C127—21no—
127C22×C127—21no—
128C22×C127—21no—
129C22×C127—21no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—44no—
135C22×C127—82no—
136C22×C127—82no—
137C22×C127—82no—
138C22×C127—164no—
139C22×C127#32712yes—
140C22×C127C2×#10211yescharacteristic
141C22×C127#50912yes—
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—84no—
145C4×C127—82no—
146C4×C127#32712yes—
147C4×C127C2×#9911yescharacteristic
148C4×C127C2×#10411yescharacteristic
149#11705C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—22no—
151C2×C127—22no—
152C2×C127—41no—
153C2×C127—162no—
154C2×C127C2×#32711yescharacteristic
155C2×C127#214011yescharacteristic
156C2×C127#214511yescharacteristic
157C2×#466C2×C12711yescharacteristic
158#2112C2×C12711yescharacteristic, complemented
159#1735C2×C12711yescharacteristic, complemented
160#1347C2×C12714yescomplemented
161C127#1170511yescharacteristic, direct product factor, Sylow
162C22×D8C4×C12711yescharacteristic, complemented
163C23×C8C22×C12711yescharacteristic
164C2×#121—21no—
165C2×#117—21no—
166C2×M32—21no—
167#466—21no—
168#466—21no—
169#466C4×C12712yescomplemented
170#466C22×C12712yes—
171C2×#107C4×C12711yescharacteristic, complemented
172C2×#102—21no—
173C22⋊C16—21no—
174C22⋊C16C22×C12712yescomplemented
175#340—21no—
176#340C22×C12712yescomplemented
177C22×D4—21no—
178C22×D4—41no—
179C23×C4D4×C12711yescharacteristic
180C2×D8—21no—
181C2×D8—42no—
182C2×D8C2×C4×C12712yes—
183C22×C8—42no—
184C22×C8C2×C4×C12711yescharacteristic
185C22×C8C2×C4×C12711yescharacteristic
186C22×C8D4×C12711yescharacteristic
187C22×C8D4×C12711yescharacteristic
188C22×C8D4×C12711yescharacteristic
189C22×C8C23×C12711yescharacteristic
190#121—22no—
191#121—22no—
192#121—41no—
193#121—41no—
194#117—24no—
195#117—42no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C22⋊C4—41no—
199C2×C22⋊C4—41no—
200C2×C42—41no—
201M32—42no—
202C2×C16—22no—
203#107—21no—
204#107C2×C4×C12712yes—
205#102—22no—
206#102—22no—
207C24—41no—
208C24D8×C12711yescharacteristic
209C2×D4—22no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—41no—
214C2×D4—42no—
215C2×D4—84no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—42no—
220C22×C4C22⋊C4×C12711yescharacteristic
221C22×C4C22⋊C4×C12711yescharacteristic
222C22×C4D8×C12711yescharacteristic
223C22×C4SD16×C12711yescharacteristic
224C22×C4SD16×C12711yescharacteristic
225C22×C4C2×D4×C12711yescharacteristic
226D8—42no—
227D8—42no—
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8C22⋊C4×C12711yescharacteristic
235C2×C8C22⋊C4×C12711yescharacteristic
236C2×C8C22×C4×C12711yescharacteristic
237C2×C8C2×D4×C12711yescharacteristic
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C22⋊C4—44no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C42—44no—
246C16—42no—
247C23—22no—
248C23—22no—
249C23—41no—
250C23—42no—
251C23—82no—
252C23—82no—
253C23—82no—
254C23#102×C12711yescharacteristic
255C23#102×C12711yescharacteristic
256C23C2×D8×C12711yescharacteristic
257D4—42no—
258D4—42no—
259D4—84no—
260D4—84no—
261D4—82no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—82no—
274C2×C4#99×C12712yes—
275C2×C4#102×C12711yescharacteristic
276C2×C4#102×C12711yescharacteristic
277C2×C4#104×C12712yes—
278C2×C4C2×C22⋊C4×C12711yescharacteristic
279C2×C4C2×SD16×C12711yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—164no—
296C22#327×C12712yes—
297C22C2×#102×C12711yescharacteristic
298C22#509×C12712yes—
299C4—21no—
300C4—21no—
301C4—84no—
302C4—82no—
303C4#327×C12712yes—
304C4C2×#99×C12711yescharacteristic
305C4C2×#104×C12711yescharacteristic
306C2—22no—
307C2—22no—
308C2—41no—
309C2—162no—
310C2C2×#327×C12711yescharacteristic
311C2C127×#214011yescharacteristic
312C2C127×#214511yescharacteristic
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. C127×#1735C2semidirect
4. C127×#1347C2semidirect
5. C22×D8×C127C4semidirect
12. #466×C127C4semidirect
14. C2×#107×C127C4semidirect
17. C22⋊C16×C127C22semidirect
19. #340×C127C22semidirect
149. #11705C127direct (N × H)
158. #2112C2×C127semidirect
159. #1735C2×C127semidirect
160. #1347C2×C127semidirect
161. C127#11705direct (N × H)
162. C22×D8C4×C127semidirect
169. #466C4×C127semidirect
171. C2×#107C4×C127semidirect
174. C22⋊C16C22×C127semidirect
176. #340C22×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
C127×#17352
C127×#13472
#11705127