Finite Group Databasebeta

← C127×#20634 #44584307

Subgroups — C127×#20634 #44584307

Order 32512.

1462 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C127C211yesmaximal, characteristic
2C2×#410×C127C212yesmaximal
3C127×#2316C212yesmaximal, complemented
4C127×#1799C218yesmaximal, complemented
5C127×#1740C212yesmaximal, complemented
6C22×#41×C127C2211yescharacteristic
7#520×C127—28no—
8C2×C4×Q8×C127C412yescomplemented
9C2×C4×D4×C127C412yescomplemented
10C2×C4×D4×C127C2214yes—
11C2×#117×C127C412yescomplemented
12C2×#117×C127C2214yes—
13C2×#117×C127C2211yescharacteristic
14C22×C4⋊C4×C127C412yescomplemented
15C22×C4⋊C4×C127C2211yescharacteristic
16#410×C127—28no—
17C2×#99×C127C2218yes—
18#389×C127—28no—
19#380×C127C2218yes—
20#342×C127C2218yes—
21C2×#41×C127—24no—
22C2×#41×C127—24no—
23C2×#41×C127D414yes—
24C2×#41×C127Q814yes—
25C22×Q8×C127C2×C411yescharacteristic
26C22×D4×C127C2×C411yescharacteristic
27C22×D4×C127C2312yes—
28C23×C4×C127C2×C412yes—
29C23×C4×C127C2×C414yes—
30C23×C4×C127C2312yes—
31C23×C4×C127C2311yescharacteristic
32C4×Q8×C127—28no—
33C4×D4×C127—216no—
34C4×D4×C127—28no—
35#117×C127—24no—
36#117×C127—28no—
37#117×C127—28no—
38#117×C127—28no—
39C2×C4⋊C4×C127—28no—
40C2×C4⋊C4×C127—24no—
41C2×C4⋊C4×C127—28no—
42C2×C4⋊C4×C127C2×C411yescharacteristic
43C2×C4⋊C4×C127C2×C414yes—
44C2×C4⋊C4×C127C2×C411yescharacteristic
45C2×C4⋊C4×C127C2×C412yes—
46C2×C4⋊C4×C127C2×C412yes—
47C2×C4⋊C4×C127D418yes—
48C2×C22⋊C4×C127C2×C414yes—
49C2×C22⋊C4×C127C2318yes—
50C2×C22⋊C4×C127C2312yes—
51C2×C42×C127—24no—
52C2×C42×C127C2×C414yes—
53C2×C42×C127C2×C412yes—
54#99×C127—216no—
55#95×C127—28no—
56C24×C127C22×C412yes—
57C24×C127C2411yescharacteristic
58#41×C127—216no—
59#41×C127—216no—
60C2×Q8×C127—22no—
61C2×Q8×C127—22no—
62C2×Q8×C127C4⋊C414yescomplemented
63C2×D4×C127—24no—
64C2×D4×C127—24no—
65C2×D4×C127—22no—
66C2×D4×C127—22no—
67C2×D4×C127C4⋊C414yescomplemented
68C2×D4×C127C2×D414yes—
69C2×D4×C127C2×Q814yes—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—28no—
73C22×C4×C127—28no—
74C22×C4×C127—82no—
75C22×C4×C127—84no—
76C22×C4×C127C4⋊C418yescomplemented
77C22×C4×C127C22×C412yes—
78C22×C4×C127C22×C412yes—
79C22×C4×C127C22×C412yes—
80C22×C4×C127C22×C414yes—
81C22×C4×C127C22×C411yescharacteristic
82C22×C4×C127C22×C411yescharacteristic
83C22×C4×C127C2×D418yes—
84C22×C4×C127C2×D414yes—
85C22×C4×C127C2×D412yes—
86C22×C4×C127C2×Q812yes—
87C22×C4×C127#4114yes—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—28no—
90C4⋊C4×C127—22no—
91C4⋊C4×C127—48no—
92C4⋊C4×C127—88no—
93C4⋊C4×C127C22⋊C418yes—
94C4⋊C4×C127C22⋊C418yes—
95C22⋊C4×C127—24no—
96C22⋊C4×C127—28no—
97C22⋊C4×C127—28no—
98C22⋊C4×C127—28no—
99C42×C127—28no—
100C42×C127—24no—
101C42×C127—48no—
102C23×C127—22no—
103C23×C127—22no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—42no—
107C23×C127—42no—
108C23×C127C2×C4⋊C414yes—
109C23×C127C23×C411yescharacteristic
110C23×C127C22×D412yes—
111C23×C127C22×D411yescharacteristic
112C23×C127C22×Q811yescharacteristic
113C23×C127C2×#4112yes—
114Q8×C127—28no—
115D4×C127—28no—
116D4×C127—28no—
117D4×C127—28no—
118C2×C4×C127—22no—
119C2×C4×C127—22no—
120C2×C4×C127—216no—
121C2×C4×C127—22no—
122C2×C4×C127—22no—
123C2×C4×C127—48no—
124C2×C4×C127—44no—
125C2×C4×C127—42no—
126C2×C4×C127—42no—
127C2×C4×C127—48no—
128C2×C4×C127—48no—
129C2×C4×C127—48no—
130C2×C4×C127—88no—
131C2×C4×C127C2×C22⋊C418yes—
132C2×C4×C127C2×C22⋊C412yes—
133C2×C4×C127C2×C22⋊C412yes—
134C2×C4×C127C2×C4⋊C414yes—
135C2×C4×C127C2×C4⋊C412yes—
136C2×C4×C127C2×C4⋊C412yes—
137C2×C4×C127#11712yes—
138C2×C4×C127#11712yes—
139C2×C4×C127#12118yes—
140C2×C4×C127C22⋊Q818yes—
141C22×C127—22no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—21no—
145C22×C127—24no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—42no—
149C22×C127—44no—
150C22×C127—44no—
151C22×C127—42no—
152C22×C127—42no—
153C22×C127C22×C22⋊C411yescharacteristic
154C22×C127C22×C4⋊C411yescharacteristic
155C22×C127C2×#11711yescharacteristic
156C22×C127C2×#12112yes—
157C22×C127C2×C22⋊Q812yes—
158C4×C127—28no—
159C4×C127—24no—
160C4×C127—42no—
161C4×C127—42no—
162C4×C127—88no—
163C4×C127#38014yes—
164C4×C127#38014yes—
165#20634C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—22no—
167C2×C127—21no—
168C2×C127—21no—
169C2×C127—22no—
170C2×C127—44no—
171C2×C127C2×#38011yescharacteristic
172C2×C127#288311yescharacteristic
173C2×C127#288411yescharacteristic
174C2×#520C2×C12711yescharacteristic
175C2×#410C2×C12712yes—
176#2316C2×C12712yescomplemented
177#1799C2×C12718yescomplemented
178#1740C2×C12712yescomplemented
179C127#2063411yescharacteristic, direct product factor, Sylow
180C22×#41C22×C12711yescharacteristic
181#520—28no—
182C2×C4×Q8C4×C12712yescomplemented
183C2×C4×D4C4×C12712yescomplemented
184C2×C4×D4C22×C12714yes—
185C2×#117C4×C12712yescomplemented
186C2×#117C22×C12714yes—
187C2×#117C22×C12711yescharacteristic
188C22×C4⋊C4C4×C12712yescomplemented
189C22×C4⋊C4C22×C12711yescharacteristic
190#410—28no—
191C2×#99C22×C12718yes—
192#389—28no—
193#380C22×C12718yes—
194#342C22×C12718yes—
195C2×#41—24no—
196C2×#41—24no—
197C2×#41D4×C12714yes—
198C2×#41Q8×C12714yes—
199C22×Q8C2×C4×C12711yescharacteristic
200C22×D4C2×C4×C12711yescharacteristic
201C22×D4C23×C12712yes—
202C23×C4C2×C4×C12712yes—
203C23×C4C2×C4×C12714yes—
204C23×C4C23×C12712yes—
205C23×C4C23×C12711yescharacteristic
206C4×Q8—28no—
207C4×D4—216no—
208C4×D4—28no—
209#117—24no—
210#117—28no—
211#117—28no—
212#117—28no—
213C2×C4⋊C4—28no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4C2×C4×C12711yescharacteristic
217C2×C4⋊C4C2×C4×C12714yes—
218C2×C4⋊C4C2×C4×C12711yescharacteristic
219C2×C4⋊C4C2×C4×C12712yes—
220C2×C4⋊C4C2×C4×C12712yes—
221C2×C4⋊C4D4×C12718yes—
222C2×C22⋊C4C2×C4×C12714yes—
223C2×C22⋊C4C23×C12718yes—
224C2×C22⋊C4C23×C12712yes—
225C2×C42—24no—
226C2×C42C2×C4×C12714yes—
227C2×C42C2×C4×C12712yes—
228#99—216no—
229#95—28no—
230C24C22×C4×C12712yes—
231C24C24×C12711yescharacteristic
232#41—216no—
233#41—216no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8C4⋊C4×C12714yescomplemented
237C2×D4—24no—
238C2×D4—24no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4C4⋊C4×C12714yescomplemented
242C2×D4C2×D4×C12714yes—
243C2×D4C2×Q8×C12714yes—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—28no—
247C22×C4—28no—
248C22×C4—82no—
249C22×C4—84no—
250C22×C4C4⋊C4×C12718yescomplemented
251C22×C4C22×C4×C12712yes—
252C22×C4C22×C4×C12712yes—
253C22×C4C22×C4×C12712yes—
254C22×C4C22×C4×C12714yes—
255C22×C4C22×C4×C12711yescharacteristic
256C22×C4C22×C4×C12711yescharacteristic
257C22×C4C2×D4×C12718yes—
258C22×C4C2×D4×C12714yes—
259C22×C4C2×D4×C12712yes—
260C22×C4C2×Q8×C12712yes—
261C22×C4#41×C12714yes—
262C4⋊C4—22no—
263C4⋊C4—28no—
264C4⋊C4—22no—
265C4⋊C4—48no—
266C4⋊C4—88no—
267C4⋊C4C22⋊C4×C12718yes—
268C4⋊C4C22⋊C4×C12718yes—
269C22⋊C4—24no—
270C22⋊C4—28no—
271C22⋊C4—28no—
272C22⋊C4—28no—
273C42—28no—
274C42—24no—
275C42—48no—
276C23—22no—
277C23—22no—
278C23—41no—
279C23—41no—
280C23—42no—
281C23—42no—
282C23C2×C4⋊C4×C12714yes—
283C23C23×C4×C12711yescharacteristic
284C23C22×D4×C12712yes—
285C23C22×D4×C12711yescharacteristic
286C23C22×Q8×C12711yescharacteristic
287C23C2×#41×C12712yes—
288Q8—28no—
289D4—28no—
290D4—28no—
291D4—28no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—216no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—48no—
298C2×C4—44no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—48no—
302C2×C4—48no—
303C2×C4—48no—
304C2×C4—88no—
305C2×C4C2×C22⋊C4×C12718yes—
306C2×C4C2×C22⋊C4×C12712yes—
307C2×C4C2×C22⋊C4×C12712yes—
308C2×C4C2×C4⋊C4×C12714yes—
309C2×C4C2×C4⋊C4×C12712yes—
310C2×C4C2×C4⋊C4×C12712yes—
311C2×C4#117×C12712yes—
312C2×C4#117×C12712yes—
313C2×C4#121×C12718yes—
314C2×C4C22⋊Q8×C12718yes—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—21no—
319C22—24no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—44no—
324C22—44no—
325C22—42no—
326C22—42no—
327C22C22×C22⋊C4×C12711yescharacteristic
328C22C22×C4⋊C4×C12711yescharacteristic
329C22C2×#117×C12711yescharacteristic
330C22C2×#121×C12712yes—
331C22C2×C22⋊Q8×C12712yes—
332C4—28no—
333C4—24no—
334C4—42no—
335C4—42no—
336C4—88no—
337C4#380×C12714yes—
338C4#380×C12714yes—
339C2—22no—
340C2—21no—
341C2—21no—
342C2—22no—
343C2—44no—
344C2C2×#380×C12711yescharacteristic
345C2C127×#288311yescharacteristic
346C2C127×#288411yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#41×C127C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#2316C2semidirect
4. C127×#1799C2semidirect
5. C127×#1740C2semidirect
8. C2×C4×Q8×C127C4semidirect
9. C2×C4×D4×C127C4semidirect
11. C2×#117×C127C4semidirect
14. C22×C4⋊C4×C127C4semidirect
62. C2×Q8×C127C4⋊C4semidirect
67. C2×D4×C127C4⋊C4semidirect
76. C22×C4×C127C4⋊C4semidirect
165. #20634C127direct (N × H)
176. #2316C2×C127semidirect
177. #1799C2×C127semidirect
178. #1740C2×C127semidirect
179. C127#20634direct (N × H)
182. C2×C4×Q8C4×C127semidirect
183. C2×C4×D4C4×C127semidirect
185. C2×#117C4×C127semidirect
188. C22×C4⋊C4C4×C127semidirect
236. C2×Q8C4⋊C4×C127semidirect
241. C2×D4C4⋊C4×C127semidirect
250. C22×C4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1272
C2×#410×C1272
C127×#23162
C127×#17992
C127×#17402
#20634127