Finite Group Databasebeta

← C127×#15966 #44579639

Subgroups — C127×#15966 #44579639

Order 32512.

1962 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#386×C127C212yesmaximal
2C2×#385×C127C214yesmaximal, complemented
3C127×#1445C212yesmaximal, complemented
4C127×#1442C212yesmaximal, complemented
5C127×#1440C214yesmaximal, complemented
6C127×#1438C211yesmaximal, characteristic
7C23×D4×C127C2211yescharacteristic
8C24×C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C22⋊C4×C127C2214yes—
12C22×C22⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2214yes—
14#386×C127—28no—
15#385×C127—216no—
16C2×#95×C127C2212yes—
17C2×#95×C127C2214yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2214yes—
20C2×#95×C127C2211yescharacteristic
21C2×#95×C127C2211yescharacteristic
22C2×#95×C127C2212yes—
23C25×C127C2312yes—
24C22×D4×C127—28no—
25C22×D4×C127—41no—
26C22×D4×C127—41no—
27C22×D4×C127D414yes—
28C23×C4×C127—24no—
29C23×C4×C127—28no—
30C23×C4×C127—44no—
31C23×C4×C127—42no—
32C23×C4×C127—42no—
33C23×C4×C127C2314yes—
34C23×C4×C127C2312yes—
35C23×C4×C127C2314yes—
36C23×C4×C127C2311yescharacteristic
37C23×C4×C127C2312yes—
38C2×C4⋊C4×C127—28no—
39C2×C4⋊C4×C127—42no—
40C2×C4⋊C4×C127—42no—
41C2×C4⋊C4×C127—42no—
42C2×C4⋊C4×C127D418yescomplemented
43C2×C22⋊C4×C127—28no—
44C2×C22⋊C4×C127—28no—
45C2×C22⋊C4×C127—28no—
46C2×C22⋊C4×C127—28no—
47C2×C22⋊C4×C127—24no—
48C2×C22⋊C4×C127—28no—
49C2×C22⋊C4×C127—28no—
50C2×C22⋊C4×C127—44no—
51#95×C127—28no—
52#95×C127—28no—
53#95×C127—28no—
54#95×C127—24no—
55#95×C127—41no—
56#95×C127—41no—
57#95×C127—42no—
58C24×C127—24no—
59C24×C127—24no—
60C24×C127—24no—
61C24×C127—24no—
62C24×C127—22no—
63C24×C127—22no—
64C24×C127—24no—
65C24×C127C2×D414yes—
66C24×C127#4118yes—
67C24×C127C2411yescharacteristic
68C2×D4×C127—216no—
69C2×D4×C127—44no—
70C2×D4×C127—48no—
71C2×D4×C127—48no—
72C22×C4×C127—24no—
73C22×C4×C127—24no—
74C22×C4×C127—24no—
75C22×C4×C127—24no—
76C22×C4×C127—24no—
77C22×C4×C127—24no—
78C22×C4×C127—24no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—24no—
88C22×C4×C127—22no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—48no—
97C22×C4×C127—416no—
98C22×C4×C127—416no—
99C22×C4×C127—48no—
100C22×C4×C127—48no—
101C22×C4×C127C2×D412yes—
102C22×C4×C127C2×D414yes—
103C22×C4×C127C2×D418yes—
104C22×C4×C127#4114yes—
105C4⋊C4×C127—48no—
106C4⋊C4×C127—48no—
107C22⋊C4×C127—232no—
108C22⋊C4×C127—416no—
109C22⋊C4×C127—48no—
110C23×C127—24no—
111C23×C127—28no—
112C23×C127—24no—
113C23×C127—28no—
114C23×C127—28no—
115C23×C127—28no—
116C23×C127—28no—
117C23×C127—28no—
118C23×C127—28no—
119C23×C127—28no—
120C23×C127—44no—
121C23×C127—44no—
122C23×C127—44no—
123C23×C127—44no—
124C23×C127—42no—
125C23×C127—44no—
126C23×C127—44no—
127C23×C127—42no—
128C23×C127—42no—
129C23×C127—42no—
130C23×C127#12318yes—
131C23×C127C22×D411yescharacteristic
132C23×C127C22×D412yes—
133C23×C127C2×#4114yes—
134C23×C127C2×#4112yes—
135C23×C127H(5,𝔽2)11yescharacteristic
136C23×C127H(5,𝔽2)11yescharacteristic
137C23×C127H(5,𝔽2)12yes—
138C23×C1272−1+412yes—
139D4×C127—416no—
140C2×C4×C127—24no—
141C2×C4×C127—28no—
142C2×C4×C127—28no—
143C2×C4×C127—28no—
144C2×C4×C127—24no—
145C2×C4×C127—22no—
146C2×C4×C127—24no—
147C2×C4×C127—28no—
148C2×C4×C127—28no—
149C2×C4×C127—432no—
150C2×C4×C127—44no—
151C2×C4×C127—44no—
152C2×C4×C127—42no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—44no—
160C2×C4×C127—42no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—44no—
165C2×C4×C127—44no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C22×C127—216no—
170C22×C127—28no—
171C22×C127—48no—
172C22×C127—44no—
173C22×C127—48no—
174C22×C127—48no—
175C22×C127—44no—
176C22×C127—48no—
177C22×C127—48no—
178C22×C127C2×#12312yes—
179C22×C127#52514yes—
180C22×C127#53412yes—
181C22×C127#53411yescharacteristic
182C22×C127#53914yes—
183C22×C127#53912yes—
184C22×C127D4212yes—
185C22×C127D4211yescharacteristic
186C22×C127#54712yes—
187C22×C127#54814yes—
188C22×C127#55112yes—
189C22×C127#55112yes—
190C22×C127#55314yes—
191C22×C127#55911yescharacteristic
192C22×C127H(3,𝔽4)11yescharacteristic
193C22×C127#56311yescharacteristic
194C4×C127—44no—
195C4×C127—48no—
196C4×C127—44no—
197C4×C127—42no—
198C4×C127—84no—
199#15966C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127—48no—
201C2×C127#244314yes—
202C2×C127#246312yes—
203C2×C127#248311yescharacteristic
204C2×C127#260012yes—
205C2×C127#267911yescharacteristic
206C2×C127#272411yescharacteristic
207C2×C127#272812yes—
208C2×C127#278212yes—
209C2×#386C2×C12712yes—
210C2×#385C2×C12714yescomplemented
211#1445C2×C12712yescomplemented
212#1442C2×C12712yescomplemented
213#1440C2×C12714yescomplemented
214#1438C2×C12711yescharacteristic
215C127#1596611yescharacteristic, direct product factor, Sylow
216C23×D4C22×C12711yescharacteristic
217C24×C4C22×C12712yes—
218C22×C4⋊C4C22×C12712yes—
219C22×C4⋊C4C22×C12712yes—
220C22×C22⋊C4C22×C12714yes—
221C22×C22⋊C4C22×C12712yes—
222C22×C22⋊C4C22×C12714yes—
223#386—28no—
224#385—216no—
225C2×#95C22×C12712yes—
226C2×#95C22×C12714yes—
227C2×#95C22×C12714yes—
228C2×#95C22×C12714yes—
229C2×#95C22×C12711yescharacteristic
230C2×#95C22×C12711yescharacteristic
231C2×#95C22×C12712yes—
232C25C23×C12712yes—
233C22×D4—28no—
234C22×D4—41no—
235C22×D4—41no—
236C22×D4D4×C12714yes—
237C23×C4—24no—
238C23×C4—28no—
239C23×C4—44no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4C23×C12714yes—
243C23×C4C23×C12712yes—
244C23×C4C23×C12714yes—
245C23×C4C23×C12711yescharacteristic
246C23×C4C23×C12712yes—
247C2×C4⋊C4—28no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4D4×C12718yescomplemented
252C2×C22⋊C4—28no—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—28no—
255C2×C22⋊C4—28no—
256C2×C22⋊C4—24no—
257C2×C22⋊C4—28no—
258C2×C22⋊C4—28no—
259C2×C22⋊C4—44no—
260#95—28no—
261#95—28no—
262#95—28no—
263#95—24no—
264#95—41no—
265#95—41no—
266#95—42no—
267C24—24no—
268C24—24no—
269C24—24no—
270C24—24no—
271C24—22no—
272C24—22no—
273C24—24no—
274C24C2×D4×C12714yes—
275C24#41×C12718yes—
276C24C24×C12711yescharacteristic
277C2×D4—216no—
278C2×D4—44no—
279C2×D4—48no—
280C2×D4—48no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—24no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—48no—
306C22×C4—416no—
307C22×C4—416no—
308C22×C4—48no—
309C22×C4—48no—
310C22×C4C2×D4×C12712yes—
311C22×C4C2×D4×C12714yes—
312C22×C4C2×D4×C12718yes—
313C22×C4#41×C12714yes—
314C4⋊C4—48no—
315C4⋊C4—48no—
316C22⋊C4—232no—
317C22⋊C4—416no—
318C22⋊C4—48no—
319C23—24no—
320C23—28no—
321C23—24no—
322C23—28no—
323C23—28no—
324C23—28no—
325C23—28no—
326C23—28no—
327C23—28no—
328C23—28no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—44no—
333C23—42no—
334C23—44no—
335C23—44no—
336C23—42no—
337C23—42no—
338C23—42no—
339C23#123×C12718yes—
340C23C22×D4×C12711yescharacteristic
341C23C22×D4×C12712yes—
342C23C2×#41×C12714yes—
343C23C2×#41×C12712yes—
344C23H(5,𝔽2)×C12711yescharacteristic
345C23H(5,𝔽2)×C12711yescharacteristic
346C23H(5,𝔽2)×C12712yes—
347C232−1+4×C12712yes—
348D4—416no—
349C2×C4—24no—
350C2×C4—28no—
351C2×C4—28no—
352C2×C4—28no—
353C2×C4—24no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—28no—
357C2×C4—28no—
358C2×C4—432no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—42no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—44no—
377C2×C4—44no—
378C22—216no—
379C22—28no—
380C22—48no—
381C22—44no—
382C22—48no—
383C22—48no—
384C22—44no—
385C22—48no—
386C22—48no—
387C22C2×#123×C12712yes—
388C22#525×C12714yes—
389C22#534×C12712yes—
390C22#534×C12711yescharacteristic
391C22#539×C12714yes—
392C22#539×C12712yes—
393C22D42×C12712yes—
394C22D42×C12711yescharacteristic
395C22#547×C12712yes—
396C22#548×C12714yes—
397C22#551×C12712yes—
398C22#551×C12712yes—
399C22#553×C12714yes—
400C22#559×C12711yescharacteristic
401C22H(3,𝔽4)×C12711yescharacteristic
402C22#563×C12711yescharacteristic
403C4—44no—
404C4—48no—
405C4—44no—
406C4—42no—
407C4—84no—
408C2—48no—
409C2C127×#244314yes—
410C2C127×#246312yes—
411C2C127×#248311yescharacteristic
412C2C127×#260012yes—
413C2C127×#267911yescharacteristic
414C2C127×#272411yescharacteristic
415C2C127×#272812yes—
416C2C127×#278212yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC23×D4×C127C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#385×C127C2semidirect
3. C127×#1445C2semidirect
4. C127×#1442C2semidirect
5. C127×#1440C2semidirect
42. C2×C4⋊C4×C127D4semidirect
199. #15966C127direct (N × H)
210. C2×#385C2×C127semidirect
211. #1445C2×C127semidirect
212. #1442C2×C127semidirect
213. #1440C2×C127semidirect
215. C127#15966direct (N × H)
251. C2×C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#386×C1272
C2×#385×C1272
C127×#14452
C127×#14422
C127×#14402
C127×#14382
#15966127