Finite Group Databasebeta

← C127×#12585 #44576258

Subgroups — C127×#12585 #44576258

Order 32512.

822 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#413×C127C212yesmaximal
2C127×#2297C211yesmaximal, characteristic
3C127×#1394C214yesmaximal, complemented
4C22×#41×C127C2211yescharacteristic
5C22×M16×C127—22no—
6C2×#117×C127C411yescharacteristic
7C22×C42×C127C411yescharacteristic
8#413×C127—24no—
9#413×C127C418yescomplemented
10C2×#101×C127C2214yes—
11C2×#100×C127—22no—
12#391×C127C2212yes—
13#390×C127C412yes—
14#386×C127—22no—
15C4×C22⋊C4×C127—22no—
16C2×#41×C127—42no—
17C2×#41×C127—41no—
18C2×#41×C127—41no—
19C2×#41×C127C2×C414yes—
20C2×#41×C127D412yes—
21C2×#41×C127Q812yes—
22C22×Q8×C127C2311yescharacteristic
23C22×D4×C127C2×C411yescharacteristic
24C22×D4×C127D412yes—
25C23×C4×C127—21no—
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127D412yes—
28C2×M16×C127—28no—
29C2×M16×C127—24no—
30C2×M16×C127—42no—
31C2×M16×C127—44no—
32C22×C8×C127—42no—
33#117×C127—41no—
34#117×C127—41no—
35C2×C4⋊C4×C127C2×C412yes—
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—24no—
38C2×C42×C127—21no—
39C2×C42×C127—21no—
40C2×C42×C127—42no—
41C2×C42×C127C2×C412yes—
42#101×C127—24no—
43#101×C127C2×C418yescomplemented
44#100×C127—28no—
45#95×C127—24no—
46C24×C127C22⋊C412yes—
47C24×C127C22⋊C411yescharacteristic
48#41×C127—44no—
49#41×C127—44no—
50#41×C127—42no—
51#41×C127—42no—
52#41×C127—42no—
53#41×C127—42no—
54C2×Q8×C127—41no—
55C2×Q8×C127—41no—
56C2×Q8×C127C22×C412yes—
57C2×Q8×C127C2×D411yescharacteristic
58C2×Q8×C127C2×Q811yescharacteristic
59C2×D4×C127—41no—
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127C4212yes—
64C2×D4×C127C22⋊C414yes—
65C2×D4×C127C4⋊C412yes—
66C2×D4×C127C4⋊C414yes—
67C22×C4×C127—22no—
68C22×C4×C127—21no—
69C22×C4×C127—22no—
70C22×C4×C127—24no—
71C22×C4×C127—21no—
72C22×C4×C127—22no—
73C22×C4×C127—22no—
74C22×C4×C127—22no—
75C22×C4×C127—44no—
76C22×C4×C127—42no—
77C22×C4×C127C4212yes—
78C22×C4×C127C22⋊C414yes—
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C4⋊C412yes—
81C22×C4×C127C4⋊C414yes—
82C22×C4×C127C22×C411yescharacteristic
83C22×C4×C127C2×D412yes—
84M16×C127—28no—
85M16×C127—44no—
86M16×C127—48no—
87C2×C8×C127—44no—
88C2×C8×C127—48no—
89C4⋊C4×C127—42no—
90C22⋊C4×C127—48no—
91C22⋊C4×C127—42no—
92C42×C127—42no—
93C42×C127—42no—
94C42×C127—41no—
95C42×C127—41no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—22no—
99C23×C127—22no—
100C23×C127—42no—
101C23×C127—44no—
102C23×C127#9512yes—
103C23×C127#9514yes—
104C23×C127C2×C22⋊C411yescharacteristic
105Q8×C127—42no—
106Q8×C127—41no—
107Q8×C127—41no—
108D4×C127—42no—
109D4×C127—44no—
110D4×C127—42no—
111D4×C127—44no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—22no—
119C2×C4×C127—22no—
120C2×C4×C127—22no—
121C2×C4×C127—24no—
122C2×C4×C127—22no—
123C2×C4×C127—24no—
124C2×C4×C127—24no—
125C2×C4×C127—42no—
126C2×C4×C127—48no—
127C2×C4×C127—42no—
128C2×C4×C127—44no—
129C2×C4×C127—42no—
130C2×C4×C127#9512yes—
131C2×C4×C127#9911yescharacteristic
132C2×C4×C127#9912yes—
133C2×C4×C127#9911yescharacteristic
134C2×C4×C127C2×C4211yescharacteristic
135C2×C4×C127C2×C22⋊C412yes—
136C2×C4×C127C2×C4⋊C411yescharacteristic
137C2×C4×C127C2×C4⋊C412yes—
138C8×C127—48no—
139C22×C127—22no—
140C22×C127—22no—
141C22×C127—24no—
142C22×C127—42no—
143C22×C127—44no—
144C22×C127—42no—
145C22×C127—42no—
146C22×C127—44no—
147C22×C127—82no—
148C22×C127C2×#9511yescharacteristic
149C22×C127C2×#9911yescharacteristic
150C22×C127C2×#9911yescharacteristic
151C4×C127—22no—
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—22no—
155C4×C127—44no—
156C4×C127—82no—
157C4×C127#34212yes—
158C4×C127#34212yes—
159#12585C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—21no—
161C2×C127—21no—
162C2×C127—42no—
163C2×C127—44no—
164C2×C127C2×#34211yescharacteristic
165C2×C127#213212yes—
166C2×#413C2×C12712yes—
167#2297C2×C12711yescharacteristic
168#1394C2×C12714yescomplemented
169C127#1258511yescharacteristic, direct product factor, Sylow
170C22×#41C22×C12711yescharacteristic
171C22×M16—22no—
172C2×#117C4×C12711yescharacteristic
173C22×C42C4×C12711yescharacteristic
174#413—24no—
175#413C4×C12718yescomplemented
176C2×#101C22×C12714yes—
177C2×#100—22no—
178#391C22×C12712yes—
179#390C4×C12712yes—
180#386—22no—
181C4×C22⋊C4—22no—
182C2×#41—42no—
183C2×#41—41no—
184C2×#41—41no—
185C2×#41C2×C4×C12714yes—
186C2×#41D4×C12712yes—
187C2×#41Q8×C12712yes—
188C22×Q8C23×C12711yescharacteristic
189C22×D4C2×C4×C12711yescharacteristic
190C22×D4D4×C12712yes—
191C23×C4—21no—
192C23×C4C2×C4×C12711yescharacteristic
193C23×C4D4×C12712yes—
194C2×M16—28no—
195C2×M16—24no—
196C2×M16—42no—
197C2×M16—44no—
198C22×C8—42no—
199#117—41no—
200#117—41no—
201C2×C4⋊C4C2×C4×C12712yes—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—24no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—42no—
207C2×C42C2×C4×C12712yes—
208#101—24no—
209#101C2×C4×C12718yescomplemented
210#100—28no—
211#95—24no—
212C24C22⋊C4×C12712yes—
213C24C22⋊C4×C12711yescharacteristic
214#41—44no—
215#41—44no—
216#41—42no—
217#41—42no—
218#41—42no—
219#41—42no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8C22×C4×C12712yes—
223C2×Q8C2×D4×C12711yescharacteristic
224C2×Q8C2×Q8×C12711yescharacteristic
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4C42×C12712yes—
230C2×D4C22⋊C4×C12714yes—
231C2×D4C4⋊C4×C12712yes—
232C2×D4C4⋊C4×C12714yes—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—44no—
242C22×C4—42no—
243C22×C4C42×C12712yes—
244C22×C4C22⋊C4×C12714yes—
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C4⋊C4×C12712yes—
247C22×C4C4⋊C4×C12714yes—
248C22×C4C22×C4×C12711yescharacteristic
249C22×C4C2×D4×C12712yes—
250M16—28no—
251M16—44no—
252M16—48no—
253C2×C8—44no—
254C2×C8—48no—
255C4⋊C4—42no—
256C22⋊C4—48no—
257C22⋊C4—42no—
258C42—42no—
259C42—42no—
260C42—41no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—22no—
265C23—22no—
266C23—42no—
267C23—44no—
268C23#95×C12712yes—
269C23#95×C12714yes—
270C23C2×C22⋊C4×C12711yescharacteristic
271Q8—42no—
272Q8—41no—
273Q8—41no—
274D4—42no—
275D4—44no—
276D4—42no—
277D4—44no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—24no—
290C2×C4—24no—
291C2×C4—42no—
292C2×C4—48no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4#95×C12712yes—
297C2×C4#99×C12712yes—
298C2×C4#99×C12711yescharacteristic
299C2×C4#99×C12711yescharacteristic
300C2×C4C2×C42×C12711yescharacteristic
301C2×C4C2×C22⋊C4×C12712yes—
302C2×C4C2×C4⋊C4×C12711yescharacteristic
303C2×C4C2×C4⋊C4×C12712yes—
304C8—48no—
305C22—22no—
306C22—22no—
307C22—24no—
308C22—42no—
309C22—44no—
310C22—42no—
311C22—42no—
312C22—44no—
313C22—82no—
314C22C2×#95×C12711yescharacteristic
315C22C2×#99×C12711yescharacteristic
316C22C2×#99×C12711yescharacteristic
317C4—22no—
318C4—21no—
319C4—21no—
320C4—22no—
321C4—44no—
322C4—82no—
323C4#342×C12712yes—
324C4#342×C12712yes—
325C2—21no—
326C2—21no—
327C2—42no—
328C2—44no—
329C2C2×#342×C12711yescharacteristic
330C2C127×#213212yes—
subgroupG/H
centerC2×C4×C127#99
commutatorC2×C4C2×C42×C127
Frattini, cosocleC22×Q8C23×C127
socleC22×C127C2×#99
prime radicalC22×#41×C127C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1394C2semidirect
9. #413×C127C4semidirect
43. #101×C127C2×C4semidirect
159. #12585C127direct (N × H)
168. #1394C2×C127semidirect
169. C127#12585direct (N × H)
175. #413C4×C127semidirect
209. #101C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#413×C1272
C127×#22972
C127×#13942
#12585127