Finite Group Databasebeta

← C127×#14157 #44577830

Subgroups — C127×#14157 #44577830

Order 32512.

1822 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C127C211yesmaximal, characteristic
2C2×#388×C127C214yesmaximal, complemented
3C127×#1441C212yesmaximal, complemented
4C127×#1438C212yesmaximal
5C127×#1437C214yesmaximal, complemented
6C4×#95×C127C212yesmaximal, complemented
7C23×D4×C127C2211yescharacteristic
8C22×C4⋊C4×C127C2212yes—
9C22×C4⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2212yes—
11C22×C22⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C42×C127C2214yes—
15C22×C42×C127C2211yescharacteristic
16#390×C127C418yescomplemented
17#388×C127—216no—
18C2×#95×C127C2212yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2214yes—
21C2×#95×C127C2212yes—
22C2×#95×C127C2212yes—
23C25×C127C2312yes—
24C22×D4×C127—24no—
25C22×D4×C127—42no—
26C22×D4×C127—41no—
27C22×D4×C127—41no—
28C22×D4×C127C2×C414yes—
29C23×C4×C127C2312yes—
30C23×C4×C127C2314yes—
31C23×C4×C127C2314yes—
32C23×C4×C127C2312yes—
33C23×C4×C127C2311yescharacteristic
34C2×C4⋊C4×C127—28no—
35C2×C4⋊C4×C127—41no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—42no—
38C2×C4⋊C4×C127C2×C414yes—
39C2×C22⋊C4×C127—28no—
40C2×C22⋊C4×C127—28no—
41C2×C22⋊C4×C127—28no—
42C2×C22⋊C4×C127—28no—
43C2×C22⋊C4×C127—28no—
44C2×C22⋊C4×C127—28no—
45C2×C22⋊C4×C127—42no—
46C2×C22⋊C4×C127—44no—
47C2×C22⋊C4×C127—42no—
48C2×C22⋊C4×C127C2×C4116yes—
49C2×C42×C127—28no—
50C2×C42×C127—28no—
51C2×C42×C127—42no—
52C2×C42×C127—44no—
53C2×C42×C127C2×C414yes—
54#95×C127—28no—
55#95×C127—28no—
56#95×C127—24no—
57#95×C127—42no—
58#95×C127D418yescomplemented
59C24×C127—24no—
60C24×C127—24no—
61C24×C127—24no—
62C24×C127—24no—
63C24×C127—24no—
64C24×C127—22no—
65C24×C127—24no—
66C24×C127—22no—
67C24×C127C22×C414yes—
68C24×C127C2411yescharacteristic
69C2×D4×C127—28no—
70C2×D4×C127—44no—
71C2×D4×C127—44no—
72C2×D4×C127—48no—
73C2×D4×C127—48no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—22no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—24no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—24no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—24no—
89C22×C4×C127—24no—
90C22×C4×C127—22no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—22no—
95C22×C4×C127C22×C414yes—
96C22×C4×C127C22×C412yes—
97C22×C4×C127C22×C414yes—
98C22×C4×C127C2×D418yes—
99C22×C4×C127C2×D414yes—
100C22×C4×C127#4118yes—
101C22×C4×C127#4114yes—
102C22×C4×C127#4114yes—
103C4⋊C4×C127—44no—
104C4⋊C4×C127—48no—
105C22⋊C4×C127—232no—
106C22⋊C4×C127—48no—
107C22⋊C4×C127—416no—
108C22⋊C4×C127—48no—
109C42×C127—44no—
110C42×C127—416no—
111C23×C127—24no—
112C23×C127—28no—
113C23×C127—28no—
114C23×C127—24no—
115C23×C127—24no—
116C23×C127—44no—
117C23×C127—44no—
118C23×C127—44no—
119C23×C127—44no—
120C23×C127—44no—
121C23×C127—44no—
122C23×C127—42no—
123C23×C127—44no—
124C23×C127—44no—
125C23×C127—44no—
126C23×C127—42no—
127C23×C127—42no—
128C23×C127—44no—
129C23×C127—44no—
130C23×C127—44no—
131C23×C127—42no—
132C23×C127C23×C411yescharacteristic
133C23×C127C22×D412yes—
134C23×C127C2×#4112yes—
135C23×C127C2×#4112yes—
136C23×C127C2×#4114yes—
137C23×C127H(5,𝔽2)11yescharacteristic
138C23×C127H(5,𝔽2)12yes—
139C23×C127H(5,𝔽2)11yescharacteristic
140D4×C127—416no—
141C2×C4×C127—24no—
142C2×C4×C127—24no—
143C2×C4×C127—22no—
144C2×C4×C127—22no—
145C2×C4×C127—24no—
146C2×C4×C127—24no—
147C2×C4×C127—28no—
148C2×C4×C127—28no—
149C2×C4×C127—28no—
150C2×C4×C127—24no—
151C2×C4×C127—28no—
152C2×C4×C127—28no—
153C2×C4×C127—28no—
154C2×C4×C127—28no—
155C2×C4×C127—28no—
156C2×C4×C127—28no—
157C2×C4×C127—44no—
158C2×C4×C127—44no—
159C2×C4×C127—44no—
160C2×C4×C127—44no—
161C2×C4×C127—42no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—44no—
167C2×C4×C127—42no—
168C2×C4×C127#11714yes—
169C2×C4×C127C4×D418yes—
170C22×C127—44no—
171C22×C127—48no—
172C22×C127—44no—
173C22×C127—44no—
174C22×C127—48no—
175C22×C127—84no—
176C22×C127—84no—
177C22×C127—84no—
178C22×C127—84no—
179C22×C127C2×#11711yescharacteristic
180C22×C127C2×C4×D412yes—
181C22×C127C4×#4112yes—
182C22×C127#51811yescharacteristic
183C22×C127#51811yescharacteristic
184C22×C127#52914yes—
185C22×C127#53214yes—
186C22×C127#53812yes—
187C22×C127#53812yes—
188C22×C127D4211yescharacteristic
189C22×C127#54614yes—
190C22×C127#55012yes—
191C22×C127#55112yes—
192C22×C127#55314yes—
193C22×C127#55512yes—
194C22×C127#55911yescharacteristic
195C4×C127—24no—
196C4×C127—28no—
197C4×C127—44no—
198C4×C127—48no—
199C4×C127—48no—
200#14157C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—84no—
202C2×C127#229312yes—
203C2×C127#231211yescharacteristic
204C2×C127#236412yes—
205C2×C127#236611yescharacteristic
206C2×C127#237211yescharacteristic
207C2×C127#255414yes—
208C2×C127#255512yes—
209C2×C127#259312yes—
210C2×#390C2×C12711yescharacteristic
211C2×#388C2×C12714yescomplemented
212#1441C2×C12712yescomplemented
213#1438C2×C12712yes—
214#1437C2×C12714yescomplemented
215C4×#95C2×C12712yescomplemented
216C127#1415711yescharacteristic, direct product factor, Sylow
217C23×D4C22×C12711yescharacteristic
218C22×C4⋊C4C22×C12712yes—
219C22×C4⋊C4C22×C12711yescharacteristic
220C22×C22⋊C4C22×C12712yes—
221C22×C22⋊C4C22×C12714yes—
222C22×C22⋊C4C22×C12712yes—
223C22×C22⋊C4C22×C12714yes—
224C22×C42C22×C12714yes—
225C22×C42C22×C12711yescharacteristic
226#390C4×C12718yescomplemented
227#388—216no—
228C2×#95C22×C12712yes—
229C2×#95C22×C12714yes—
230C2×#95C22×C12714yes—
231C2×#95C22×C12712yes—
232C2×#95C22×C12712yes—
233C25C23×C12712yes—
234C22×D4—24no—
235C22×D4—42no—
236C22×D4—41no—
237C22×D4—41no—
238C22×D4C2×C4×C12714yes—
239C23×C4C23×C12712yes—
240C23×C4C23×C12714yes—
241C23×C4C23×C12714yes—
242C23×C4C23×C12712yes—
243C23×C4C23×C12711yescharacteristic
244C2×C4⋊C4—28no—
245C2×C4⋊C4—41no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4C2×C4×C12714yes—
249C2×C22⋊C4—28no—
250C2×C22⋊C4—28no—
251C2×C22⋊C4—28no—
252C2×C22⋊C4—28no—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—28no—
255C2×C22⋊C4—42no—
256C2×C22⋊C4—44no—
257C2×C22⋊C4—42no—
258C2×C22⋊C4C2×C4×C127116yes—
259C2×C42—28no—
260C2×C42—28no—
261C2×C42—42no—
262C2×C42—44no—
263C2×C42C2×C4×C12714yes—
264#95—28no—
265#95—28no—
266#95—24no—
267#95—42no—
268#95D4×C12718yescomplemented
269C24—24no—
270C24—24no—
271C24—24no—
272C24—24no—
273C24—24no—
274C24—22no—
275C24—24no—
276C24—22no—
277C24C22×C4×C12714yes—
278C24C24×C12711yescharacteristic
279C2×D4—28no—
280C2×D4—44no—
281C2×D4—44no—
282C2×D4—48no—
283C2×D4—48no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—24no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4C22×C4×C12714yes—
306C22×C4C22×C4×C12712yes—
307C22×C4C22×C4×C12714yes—
308C22×C4C2×D4×C12718yes—
309C22×C4C2×D4×C12714yes—
310C22×C4#41×C12718yes—
311C22×C4#41×C12714yes—
312C22×C4#41×C12714yes—
313C4⋊C4—44no—
314C4⋊C4—48no—
315C22⋊C4—232no—
316C22⋊C4—48no—
317C22⋊C4—416no—
318C22⋊C4—48no—
319C42—44no—
320C42—416no—
321C23—24no—
322C23—28no—
323C23—28no—
324C23—24no—
325C23—24no—
326C23—44no—
327C23—44no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—42no—
333C23—44no—
334C23—44no—
335C23—44no—
336C23—42no—
337C23—42no—
338C23—44no—
339C23—44no—
340C23—44no—
341C23—42no—
342C23C23×C4×C12711yescharacteristic
343C23C22×D4×C12712yes—
344C23C2×#41×C12712yes—
345C23C2×#41×C12712yes—
346C23C2×#41×C12714yes—
347C23H(5,𝔽2)×C12711yescharacteristic
348C23H(5,𝔽2)×C12712yes—
349C23H(5,𝔽2)×C12711yescharacteristic
350D4—416no—
351C2×C4—24no—
352C2×C4—22no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—28no—
358C2×C4—28no—
359C2×C4—28no—
360C2×C4—24no—
361C2×C4—28no—
362C2×C4—28no—
363C2×C4—28no—
364C2×C4—28no—
365C2×C4—28no—
366C2×C4—28no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—42no—
378C2×C4#117×C12714yes—
379C2×C4C4×D4×C12718yes—
380C22—44no—
381C22—48no—
382C22—44no—
383C22—44no—
384C22—48no—
385C22—84no—
386C22—84no—
387C22—84no—
388C22—84no—
389C22C2×#117×C12711yescharacteristic
390C22C2×C4×D4×C12712yes—
391C22C4×#41×C12712yes—
392C22#518×C12711yescharacteristic
393C22#518×C12711yescharacteristic
394C22#529×C12714yes—
395C22#532×C12714yes—
396C22#538×C12712yes—
397C22#538×C12712yes—
398C22D42×C12711yescharacteristic
399C22#546×C12714yes—
400C22#550×C12712yes—
401C22#551×C12712yes—
402C22#553×C12714yes—
403C22#555×C12712yes—
404C22#559×C12711yescharacteristic
405C4—24no—
406C4—28no—
407C4—44no—
408C4—48no—
409C4—48no—
410C2—84no—
411C2C127×#229312yes—
412C2C127×#231211yescharacteristic
413C2C127×#236412yes—
414C2C127×#236611yescharacteristic
415C2C127×#237211yescharacteristic
416C2C127×#255414yes—
417C2C127×#255512yes—
418C2C127×#259312yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C127C2semidirect
3. C127×#1441C2semidirect
5. C127×#1437C2semidirect
6. C4×#95×C127C2semidirect
16. #390×C127C4semidirect
58. #95×C127D4semidirect
200. #14157C127direct (N × H)
211. C2×#388C2×C127semidirect
212. #1441C2×C127semidirect
214. #1437C2×C127semidirect
215. C4×#95C2×C127semidirect
216. C127#14157direct (N × H)
226. #390C4×C127semidirect
268. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C1272
C2×#388×C1272
C127×#14412
C127×#14382
C127×#14372
C4×#95×C1272
#14157127