Finite Group Databasebeta

← C127×#12634 #44576307

Subgroups — C127×#12634 #44576307

Order 32512.

452 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2932C211yesmaximal, characteristic
2C127×#2132C211yesmaximal, characteristic
3C127×#2126C211yesmaximal, characteristic
4C127×#1757C212yesmaximal, complemented
5C127×#1395C212yesmaximal, complemented
6C2×#131×C127C411yescharacteristic, complemented
7C2×#131×C127C2211yescharacteristic
8#532×C127C2211yescharacteristic
9#435×C127—22no—
10#435×C127—22no—
11#423×C127C411yescharacteristic, complemented
12#413×C127C2212yes—
13#410×C127C2212yes—
14#408×C127C411yescharacteristic, complemented
15#408×C127C2211yescharacteristic
16#405×C127—22no—
17C2×#97×C127C411yescharacteristic, complemented
18#356×C127C412yescomplemented
19#355×C127C412yescomplemented
20#354×C127C412yes—
21#353×C127C412yes—
22#344×C127—22no—
23C2×#41×C127C2×C411yescharacteristic
24C2×#41×C127C2311yescharacteristic
25#131×C127—42no—
26#131×C127—42no—
27C2×M16×C127—21no—
28C2×M16×C127—22no—
29C2×M16×C127C2×C411yescharacteristic
30C2×M16×C127C2×C411yescharacteristic
31C2×M16×C127D412yes—
32C22×C8×C127—21no—
33C22×C8×C127C2×C411yescharacteristic
34C22×C8×C127C2×C411yescharacteristic
35C22×C8×C127D412yes—
36C4⋊Q8×C127C2×C411yescharacteristic
37#127×C127C2×C411yescharacteristic
38#124×C127C2×C411yescharacteristic
39#124×C127C2×C411yescharacteristic
40#121×C127—22no—
41C4×D4×C127—22no—
42#117×C127—22no—
43C2×C42×C127C2×C411yescharacteristic
44C4⋊C8×C127—22no—
45#101×C127C2×C414yes—
46#100×C127—22no—
47#99×C127—22no—
48#99×C127C2×C414yes—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51#97×C127—21no—
52#97×C127—21no—
53#97×C127—42no—
54C4×C8×C127—42no—
55#41×C127—41no—
56#41×C127—41no—
57#41×C127—41no—
58#41×C127—41no—
59C2×Q8×C127C4211yescharacteristic
60C2×Q8×C127C22×C411yescharacteristic
61C2×D4×C127—21no—
62C2×D4×C127—22no—
63C2×D4×C127C4211yescharacteristic
64C2×D4×C127C22×C411yescharacteristic
65C2×D4×C127#4112yes—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127C22×C411yescharacteristic
69C22×C4×C127C2×D412yes—
70M16×C127—24no—
71M16×C127—41no—
72M16×C127—42no—
73M16×C127—42no—
74M16×C127—42no—
75M16×C127—41no—
76C2×C8×C127—22no—
77C2×C8×C127—22no—
78C2×C8×C127—22no—
79C2×C8×C127—21no—
80C2×C8×C127—21no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—41no—
84C2×C8×C127C22⋊C411yescharacteristic
85C2×C8×C127C22⋊C412yes—
86C2×C8×C127C22⋊C411yescharacteristic
87C4⋊C4×C127—22no—
88C4⋊C4×C127—42no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—24no—
92C42×C127—21no—
93C42×C127—42no—
94C42×C127C4211yescharacteristic
95C42×C127C4211yescharacteristic
96C23×C127—21no—
97C23×C127#11711yescharacteristic
98C23×C127C4×D412yes—
99Q8×C127—41no—
100Q8×C127—41no—
101D4×C127—41no—
102D4×C127—42no—
103D4×C127—41no—
104D4×C127—42no—
105D4×C127—82no—
106C2×C4×C127—22no—
107C2×C4×C127—21no—
108C2×C4×C127—22no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—44no—
116C2×C4×C127—81no—
117C2×C4×C127C2×C4211yescharacteristic
118C2×C4×C127C2×C22⋊C411yescharacteristic
119C2×C4×C127C4×D412yes—
120C8×C127—21no—
121C8×C127—22no—
122C8×C127—44no—
123C8×C127—41no—
124C8×C127—41no—
125C8×C127#9912yes—
126C22×C127—22no—
127C22×C127—21no—
128C22×C127—41no—
129C22×C127—42no—
130C22×C127—42no—
131C22×C127—41no—
132C22×C127C4×C22⋊C411yescharacteristic
133C4×C127—22no—
134C4×C127—21no—
135C4×C127—41no—
136C4×C127—41no—
137C4×C127—41no—
138C4×C127—84no—
139C4×C127C2×#9911yescharacteristic
140C4×C127#41011yescharacteristic
141#12634C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—21no—
143C2×C127—42no—
144C2×C127—41no—
145C2×C127—81no—
146C2×C127C4×#9911yescharacteristic
147#2932C2×C12711yescharacteristic
148#2132C2×C12711yescharacteristic
149#2126C2×C12711yescharacteristic
150#1757C2×C12712yescomplemented
151#1395C2×C12712yescomplemented
152C127#1263411yescharacteristic, direct product factor, Sylow
153C2×#131C4×C12711yescharacteristic, complemented
154C2×#131C22×C12711yescharacteristic
155#532C22×C12711yescharacteristic
156#435—22no—
157#435—22no—
158#423C4×C12711yescharacteristic, complemented
159#413C22×C12712yes—
160#410C22×C12712yes—
161#408C4×C12711yescharacteristic, complemented
162#408C22×C12711yescharacteristic
163#405—22no—
164C2×#97C4×C12711yescharacteristic, complemented
165#356C4×C12712yescomplemented
166#355C4×C12712yescomplemented
167#354C4×C12712yes—
168#353C4×C12712yes—
169#344—22no—
170C2×#41C2×C4×C12711yescharacteristic
171C2×#41C23×C12711yescharacteristic
172#131—42no—
173#131—42no—
174C2×M16—21no—
175C2×M16—22no—
176C2×M16C2×C4×C12711yescharacteristic
177C2×M16C2×C4×C12711yescharacteristic
178C2×M16D4×C12712yes—
179C22×C8—21no—
180C22×C8C2×C4×C12711yescharacteristic
181C22×C8C2×C4×C12711yescharacteristic
182C22×C8D4×C12712yes—
183C4⋊Q8C2×C4×C12711yescharacteristic
184#127C2×C4×C12711yescharacteristic
185#124C2×C4×C12711yescharacteristic
186#124C2×C4×C12711yescharacteristic
187#121—22no—
188C4×D4—22no—
189#117—22no—
190C2×C42C2×C4×C12711yescharacteristic
191C4⋊C8—22no—
192#101C2×C4×C12714yes—
193#100—22no—
194#99—22no—
195#99C2×C4×C12714yes—
196C22⋊C8—22no—
197C22⋊C8—22no—
198#97—21no—
199#97—21no—
200#97—42no—
201C4×C8—42no—
202#41—41no—
203#41—41no—
204#41—41no—
205#41—41no—
206C2×Q8C42×C12711yescharacteristic
207C2×Q8C22×C4×C12711yescharacteristic
208C2×D4—21no—
209C2×D4—22no—
210C2×D4C42×C12711yescharacteristic
211C2×D4C22×C4×C12711yescharacteristic
212C2×D4#41×C12712yes—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4C22×C4×C12711yescharacteristic
216C22×C4C2×D4×C12712yes—
217M16—24no—
218M16—41no—
219M16—42no—
220M16—42no—
221M16—42no—
222M16—41no—
223C2×C8—22no—
224C2×C8—22no—
225C2×C8—22no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—41no—
231C2×C8C22⋊C4×C12711yescharacteristic
232C2×C8C22⋊C4×C12712yes—
233C2×C8C22⋊C4×C12711yescharacteristic
234C4⋊C4—22no—
235C4⋊C4—42no—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—24no—
239C42—21no—
240C42—42no—
241C42C42×C12711yescharacteristic
242C42C42×C12711yescharacteristic
243C23—21no—
244C23#117×C12711yescharacteristic
245C23C4×D4×C12712yes—
246Q8—41no—
247Q8—41no—
248D4—41no—
249D4—42no—
250D4—41no—
251D4—42no—
252D4—82no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—81no—
264C2×C4C2×C42×C12711yescharacteristic
265C2×C4C2×C22⋊C4×C12711yescharacteristic
266C2×C4C4×D4×C12712yes—
267C8—21no—
268C8—22no—
269C8—44no—
270C8—41no—
271C8—41no—
272C8#99×C12712yes—
273C22—22no—
274C22—21no—
275C22—41no—
276C22—42no—
277C22—42no—
278C22—41no—
279C22C4×C22⋊C4×C12711yescharacteristic
280C4—22no—
281C4—21no—
282C4—41no—
283C4—41no—
284C4—41no—
285C4—84no—
286C4C2×#99×C12711yescharacteristic
287C4#410×C12711yescharacteristic
288C2—21no—
289C2—42no—
290C2—41no—
291C2—81no—
292C2C4×#99×C12711yescharacteristic
subgroupG/H
centerC4×C127C2×#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC2×#41C23×C127
socleC2×C127C4×#99
prime radical#532×C127C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C2×C8×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1757C2semidirect
5. C127×#1395C2semidirect
6. C2×#131×C127C4semidirect
11. #423×C127C4semidirect
14. #408×C127C4semidirect
17. C2×#97×C127C4semidirect
18. #356×C127C4semidirect
19. #355×C127C4semidirect
141. #12634C127direct (N × H)
150. #1757C2×C127semidirect
151. #1395C2×C127semidirect
152. C127#12634direct (N × H)
153. C2×#131C4×C127semidirect
158. #423C4×C127semidirect
161. #408C4×C127semidirect
164. C2×#97C4×C127semidirect
165. #356C4×C127semidirect
166. #355C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29322
C127×#21322
C127×#21262
C127×#17572
C127×#13952
#12634127