Finite Group Databasebeta

← C127×#11567 #44575240

Subgroups — C127×#11567 #44575240

Order 32512.

462 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2548C211yesmaximal, characteristic
2C127×#1467C211yesmaximal, characteristic, complemented
3C127×#1461C211yesmaximal, characteristic, complemented
4C127×#1318C214yesmaximal, complemented
5C2×#127×C127C411yescharacteristic
6C2×#124×C127C412yes—
7C2×C4×Q8×C127C2211yescharacteristic
8#432×C127—21no—
9#431×C127—21no—
10#394×C127—21no—
11#394×C127—21no—
12#390×C127—21no—
13#390×C127—21no—
14#390×C127C2212yes—
15C4×C4⋊C4×C127C411yescharacteristic
16#324×C127—21no—
17#324×C127—21no—
18#324×C127C2212yes—
19#324×C127C2212yes—
20C22×Q8×C127C2×C411yescharacteristic
21C22×D4×C127—21no—
22C22×D4×C127—21no—
23C22×D4×C127C2×C412yes—
24#127×C127—41no—
25#127×C127—41no—
26#124×C127—44no—
27C4×Q8×C127—41no—
28C4×Q8×C127—41no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127D411yescharacteristic
31C2×C4⋊C4×C127D411yescharacteristic
32C2×C4⋊C4×C127C2311yescharacteristic
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127—22no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C42×C127C2×C411yescharacteristic
38C2×C42×C127C2×C412yes—
39C2×C42×C127D411yescharacteristic
40C2×C42×C127D411yescharacteristic
41C4⋊C8×C127—41no—
42C4⋊C8×C127—41no—
43C22⋊C8×C127—22no—
44C22⋊C8×C127—22no—
45#97×C127—41no—
46C4×C8×C127—41no—
47#95×C127—21no—
48C24×C127—22no—
49C2×Q8×C127—22no—
50C2×Q8×C127—22no—
51C2×Q8×C127—41no—
52C2×D4×C127—24no—
53C2×D4×C127—42no—
54C2×D4×C127—42no—
55C2×D4×C127—42no—
56C2×D4×C127—42no—
57C2×D4×C127—42no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C2×D4×C127—82no—
61C22×C4×C127—22no—
62C22×C4×C127C22⋊C411yescharacteristic
63C22×C4×C127C22⋊C411yescharacteristic
64C22×C4×C127C22⋊C411yescharacteristic
65C22×C4×C127C22⋊C411yescharacteristic
66C22×C4×C127C22×C411yescharacteristic
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69C2×C8×C127—42no—
70C2×C8×C127—42no—
71C4⋊C4×C127—41no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—42no—
75C22⋊C4×C127—44no—
76C22⋊C4×C127—44no—
77C22⋊C4×C127—82no—
78C22⋊C4×C127—82no—
79C42×C127—21no—
80C42×C127—21no—
81C42×C127—21no—
82C42×C127—21no—
83C42×C127—21no—
84C42×C127—21no—
85C42×C127—42no—
86C23×C127—42no—
87C23×C127—42no—
88C23×C127—42no—
89C23×C127—42no—
90C23×C127—42no—
91C23×C127—42no—
92C23×C127—42no—
93C23×C127C2×C22⋊C411yescharacteristic
94Q8×C127—44no—
95D4×C127—84no—
96D4×C127—82no—
97D4×C127—84no—
98D4×C127—82no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—22no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127#9911yescharacteristic
117C2×C4×C127#9911yescharacteristic
118C2×C4×C127#10012yes—
119C2×C4×C127#13112yes—
120C8×C127—82no—
121C8×C127—82no—
122C22×C127—21no—
123C22×C127—21no—
124C22×C127—82no—
125C22×C127—82no—
126C22×C127—82no—
127C22×C127—82no—
128C22×C127—82no—
129C22×C127—82no—
130C22×C127—82no—
131C22×C127#40811yescharacteristic
132C22×C127C2×#9911yescharacteristic
133C22×C127C2×#10011yescharacteristic
134C4×C127—21no—
135C4×C127—22no—
136C4×C127—22no—
137C4×C127—41no—
138C4×C127—41no—
139C4×C127—41no—
140C4×C127—41no—
141C4×C127—82no—
142C4×C127#35512yes—
143#11567C12711yesmaximal, characteristic, direct product factor, Sylow
144C2×C127—21no—
145C2×C127—21no—
146C2×C127—162no—
147C2×C127#147111yescharacteristic
148C2×C127#212811yescharacteristic
149C2×C127C2×#35511yescharacteristic
150#2548C2×C12711yescharacteristic
151#1467C2×C12711yescharacteristic, complemented
152#1461C2×C12711yescharacteristic, complemented
153#1318C2×C12714yescomplemented
154C127#1156711yescharacteristic, direct product factor, Sylow
155C2×#127C4×C12711yescharacteristic
156C2×#124C4×C12712yes—
157C2×C4×Q8C22×C12711yescharacteristic
158#432—21no—
159#431—21no—
160#394—21no—
161#394—21no—
162#390—21no—
163#390—21no—
164#390C22×C12712yes—
165C4×C4⋊C4C4×C12711yescharacteristic
166#324—21no—
167#324—21no—
168#324C22×C12712yes—
169#324C22×C12712yes—
170C22×Q8C2×C4×C12711yescharacteristic
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C2×C4×C12712yes—
174#127—41no—
175#127—41no—
176#124—44no—
177C4×Q8—41no—
178C4×Q8—41no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4D4×C12711yescharacteristic
181C2×C4⋊C4D4×C12711yescharacteristic
182C2×C4⋊C4C23×C12711yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C42C2×C4×C12711yescharacteristic
188C2×C42C2×C4×C12712yes—
189C2×C42D4×C12711yescharacteristic
190C2×C42D4×C12711yescharacteristic
191C4⋊C8—41no—
192C4⋊C8—41no—
193C22⋊C8—22no—
194C22⋊C8—22no—
195#97—41no—
196C4×C8—41no—
197#95—21no—
198C24—22no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—41no—
202C2×D4—24no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C2×D4—82no—
211C22×C4—22no—
212C22×C4C22⋊C4×C12711yescharacteristic
213C22×C4C22⋊C4×C12711yescharacteristic
214C22×C4C22⋊C4×C12711yescharacteristic
215C22×C4C22⋊C4×C12711yescharacteristic
216C22×C4C22×C4×C12711yescharacteristic
217C22×C4C2×D4×C12711yescharacteristic
218C22×C4C2×D4×C12711yescharacteristic
219C2×C8—42no—
220C2×C8—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C22⋊C4—44no—
226C22⋊C4—44no—
227C22⋊C4—82no—
228C22⋊C4—82no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23—42no—
240C23—42no—
241C23—42no—
242C23—42no—
243C23C2×C22⋊C4×C12711yescharacteristic
244Q8—44no—
245D4—84no—
246D4—82no—
247D4—84no—
248D4—82no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#99×C12711yescharacteristic
267C2×C4#99×C12711yescharacteristic
268C2×C4#100×C12712yes—
269C2×C4#131×C12712yes—
270C8—82no—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22—82no—
281C22#408×C12711yescharacteristic
282C22C2×#99×C12711yescharacteristic
283C22C2×#100×C12711yescharacteristic
284C4—21no—
285C4—22no—
286C4—22no—
287C4—41no—
288C4—41no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4#355×C12712yes—
293C2—21no—
294C2—21no—
295C2—162no—
296C2C127×#147111yescharacteristic
297C2C127×#212811yescharacteristic
298C2C2×#355×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC2×#127×C127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1467C2semidirect
3. C127×#1461C2semidirect
4. C127×#1318C2semidirect
143. #11567C127direct (N × H)
151. #1467C2×C127semidirect
152. #1461C2×C127semidirect
153. #1318C2×C127semidirect
154. C127#11567direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25482
C127×#14672
C127×#14612
C127×#13182
#11567127