Finite Group Databasebeta

← C127×#14262 #44577935

Subgroups — C127×#14262 #44577935

Order 32512.

3390 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C127C211yesmaximal, characteristic
2C2×#385×C127C212yesmaximal, complemented
3C2×#379×C127C211yesmaximal, characteristic
4C2×#379×C127C211yesmaximal, characteristic
5C127×#1439C218yesmaximal, complemented
6C127×C22⋊#95C212yesmaximal, complemented
7C26×C127C2211yescharacteristic
8C24×C4×C127C2212yes—
9C22×C4⋊C4×C127C2214yescomplemented
10C22×C22⋊C4×C127—24no—
11C22×C22⋊C4×C127—28no—
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2211yescharacteristic
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2214yes—
17C22×C22⋊C4×C127C2214yes—
18#385×C127—28no—
19#379×C127—24no—
20#379×C127C418yescomplemented
21C2×#95×C127C2214yescomplemented
22C2×#95×C127C2218yescomplemented
23C25×C127—24no—
24C25×C127—24no—
25C25×C127—48no—
26C25×C127C2×C414yes—
27C25×C127D414yes—
28C25×C127Q814yes—
29C25×C127C2312yes—
30C25×C127C2311yescharacteristic
31C23×C4×C127—24no—
32C23×C4×C127—24no—
33C23×C4×C127—48no—
34C23×C4×C127D418yes—
35C23×C4×C127C2312yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2314yes—
38C23×C4×C127C2314yes—
39C2×C4⋊C4×C127—28no—
40C2×C4⋊C4×C127—48no—
41C2×C22⋊C4×C127—232no—
42C2×C22⋊C4×C127—28no—
43C2×C22⋊C4×C127—24no—
44C2×C22⋊C4×C127—24no—
45C2×C22⋊C4×C127—216no—
46C2×C22⋊C4×C127—28no—
47C2×C22⋊C4×C127—22no—
48C2×C22⋊C4×C127—22no—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—48no—
52C2×C22⋊C4×C127—48no—
53C2×C22⋊C4×C127C2×C418yes—
54C2×C22⋊C4×C127C2×C4116yescomplemented
55#95×C127—28no—
56#95×C127—48no—
57C24×C127—28no—
58C24×C127—216no—
59C24×C127—28no—
60C24×C127—216no—
61C24×C127—28no—
62C24×C127—24no—
63C24×C127—24no—
64C24×C127—28no—
65C24×C127—28no—
66C24×C127—416no—
67C24×C127—416no—
68C24×C127—416no—
69C24×C127—416no—
70C24×C127—416no—
71C24×C127—432no—
72C24×C127C4⋊C4116yescomplemented
73C24×C127C22×C414yes—
74C24×C127C22×C412yes—
75C24×C127C2×D414yes—
76C24×C127C2×D412yes—
77C24×C127C2×D414yes—
78C24×C127C2×Q814yes—
79C24×C127C2×Q812yes—
80C24×C127#4114yes—
81C24×C127C2411yescharacteristic
82C22×C4×C127—216no—
83C22×C4×C127—24no—
84C22×C4×C127—24no—
85C22×C4×C127—24no—
86C22×C4×C127—24no—
87C22×C4×C127—28no—
88C22×C4×C127—28no—
89C22×C4×C127—28no—
90C22×C4×C127—28no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—28no—
97C22×C4×C127—28no—
98C22×C4×C127—416no—
99C22×C4×C127—416no—
100C22×C4×C127—416no—
101C22×C4×C127C22×C418yes—
102C22×C4×C127C2×D418yes—
103C4⋊C4×C127—416no—
104C22⋊C4×C127—232no—
105C22⋊C4×C127—216no—
106C22⋊C4×C127—416no—
107C22⋊C4×C127—416no—
108C22⋊C4×C127—44no—
109C22⋊C4×C127—44no—
110C23×C127—28no—
111C23×C127—28no—
112C23×C127—28no—
113C23×C127—28no—
114C23×C127—216no—
115C23×C127—28no—
116C23×C127—28no—
117C23×C127—28no—
118C23×C127—28no—
119C23×C127—24no—
120C23×C127—28no—
121C23×C127—24no—
122C23×C127—28no—
123C23×C127—28no—
124C23×C127—28no—
125C23×C127—28no—
126C23×C127—232no—
127C23×C127—432no—
128C23×C127—464no—
129C23×C127—432no—
130C23×C127—432no—
131C23×C127—464no—
132C23×C127—48no—
133C23×C127—48no—
134C23×C127—416no—
135C23×C127C2×C4⋊C418yes—
136C23×C127C2×C4⋊C414yes—
137C23×C127C4×D418yes—
138C23×C127#12014yes—
139C23×C127C22⋊Q818yes—
140C23×C127#12314yes—
141C23×C127C23×C411yescharacteristic
142C23×C127C22×D411yescharacteristic
143C23×C127C22×D412yes—
144C23×C127C22×Q811yescharacteristic
145C23×C127C2×#4112yes—
146C23×C127H(5,𝔽2)18yes—
147C2×C4×C127—28no—
148C2×C4×C127—216no—
149C2×C4×C127—28no—
150C2×C4×C127—28no—
151C2×C4×C127—28no—
152C2×C4×C127—432no—
153C2×C4×C127—44no—
154C2×C4×C127—48no—
155C2×C4×C127—44no—
156C2×C4×C127—48no—
157C2×C4×C127—48no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—44no—
161C2×C4×C127—44no—
162C2×C4×C127—44no—
163C2×C4×C127—44no—
164C2×C4×C127—48no—
165C22×C127—28no—
166C22×C127—216no—
167C22×C127—28no—
168C22×C127—28no—
169C22×C127—216no—
170C22×C127—28no—
171C22×C127—28no—
172C22×C127—28no—
173C22×C127—464no—
174C22×C127—416no—
175C22×C127—48no—
176C22×C127—48no—
177C22×C127—416no—
178C22×C127#38518yes—
179C22×C127C22×C4⋊C411yescharacteristic
180C22×C127C2×C4×D412yes—
181C22×C127#51814yes—
182C22×C127C2×#12011yescharacteristic
183C22×C127C2×C22⋊Q812yes—
184C22×C127C2×#12311yescharacteristic
185C22×C127#53414yes—
186C22×C127#53414yes—
187C22×C127#53514yes—
188C22×C127#53818yes—
189C22×C127#54314yes—
190C4×C127—48no—
191C4×C127—48no—
192C4×C127—82no—
193C4×C127—82no—
194#14262C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—28no—
196C2×C127—48no—
197C2×C127C2×#38511yescharacteristic
198C2×C127#231512yes—
199C2×C127#232114yes—
200C2×C127#261312yes—
201C2×C127#262212yes—
202C2×C127#262614yes—
203C23×C22⋊C4C2×C12711yescharacteristic
204C2×#385C2×C12712yescomplemented
205C2×#379C2×C12711yescharacteristic
206C2×#379C2×C12711yescharacteristic
207#1439C2×C12718yescomplemented
208C22⋊#95C2×C12712yescomplemented
209C127#1426211yescharacteristic, direct product factor, Sylow
210C26C22×C12711yescharacteristic
211C24×C4C22×C12712yes—
212C22×C4⋊C4C22×C12714yescomplemented
213C22×C22⋊C4—24no—
214C22×C22⋊C4—28no—
215C22×C22⋊C4C22×C12714yes—
216C22×C22⋊C4C22×C12711yescharacteristic
217C22×C22⋊C4C22×C12711yescharacteristic
218C22×C22⋊C4C22×C12712yes—
219C22×C22⋊C4C22×C12714yes—
220C22×C22⋊C4C22×C12714yes—
221#385—28no—
222#379—24no—
223#379C4×C12718yescomplemented
224C2×#95C22×C12714yescomplemented
225C2×#95C22×C12718yescomplemented
226C25—24no—
227C25—24no—
228C25—48no—
229C25C2×C4×C12714yes—
230C25D4×C12714yes—
231C25Q8×C12714yes—
232C25C23×C12712yes—
233C25C23×C12711yescharacteristic
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—48no—
237C23×C4D4×C12718yes—
238C23×C4C23×C12712yes—
239C23×C4C23×C12712yes—
240C23×C4C23×C12714yes—
241C23×C4C23×C12714yes—
242C2×C4⋊C4—28no—
243C2×C4⋊C4—48no—
244C2×C22⋊C4—232no—
245C2×C22⋊C4—28no—
246C2×C22⋊C4—24no—
247C2×C22⋊C4—24no—
248C2×C22⋊C4—216no—
249C2×C22⋊C4—28no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—24no—
254C2×C22⋊C4—48no—
255C2×C22⋊C4—48no—
256C2×C22⋊C4C2×C4×C12718yes—
257C2×C22⋊C4C2×C4×C127116yescomplemented
258#95—28no—
259#95—48no—
260C24—28no—
261C24—216no—
262C24—28no—
263C24—216no—
264C24—28no—
265C24—24no—
266C24—24no—
267C24—28no—
268C24—28no—
269C24—416no—
270C24—416no—
271C24—416no—
272C24—416no—
273C24—416no—
274C24—432no—
275C24C4⋊C4×C127116yescomplemented
276C24C22×C4×C12714yes—
277C24C22×C4×C12712yes—
278C24C2×D4×C12714yes—
279C24C2×D4×C12712yes—
280C24C2×D4×C12714yes—
281C24C2×Q8×C12714yes—
282C24C2×Q8×C12712yes—
283C24#41×C12714yes—
284C24C24×C12711yescharacteristic
285C22×C4—216no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—28no—
291C22×C4—28no—
292C22×C4—28no—
293C22×C4—28no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—28no—
300C22×C4—28no—
301C22×C4—416no—
302C22×C4—416no—
303C22×C4—416no—
304C22×C4C22×C4×C12718yes—
305C22×C4C2×D4×C12718yes—
306C4⋊C4—416no—
307C22⋊C4—232no—
308C22⋊C4—216no—
309C22⋊C4—416no—
310C22⋊C4—416no—
311C22⋊C4—44no—
312C22⋊C4—44no—
313C23—28no—
314C23—28no—
315C23—28no—
316C23—28no—
317C23—216no—
318C23—28no—
319C23—28no—
320C23—28no—
321C23—28no—
322C23—24no—
323C23—28no—
324C23—24no—
325C23—28no—
326C23—28no—
327C23—28no—
328C23—28no—
329C23—232no—
330C23—432no—
331C23—464no—
332C23—432no—
333C23—432no—
334C23—464no—
335C23—48no—
336C23—48no—
337C23—416no—
338C23C2×C4⋊C4×C12718yes—
339C23C2×C4⋊C4×C12714yes—
340C23C4×D4×C12718yes—
341C23#120×C12714yes—
342C23C22⋊Q8×C12718yes—
343C23#123×C12714yes—
344C23C23×C4×C12711yescharacteristic
345C23C22×D4×C12711yescharacteristic
346C23C22×D4×C12712yes—
347C23C22×Q8×C12711yescharacteristic
348C23C2×#41×C12712yes—
349C23H(5,𝔽2)×C12718yes—
350C2×C4—28no—
351C2×C4—216no—
352C2×C4—28no—
353C2×C4—28no—
354C2×C4—28no—
355C2×C4—432no—
356C2×C4—44no—
357C2×C4—48no—
358C2×C4—48no—
359C2×C4—44no—
360C2×C4—48no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—48no—
368C22—28no—
369C22—216no—
370C22—28no—
371C22—28no—
372C22—216no—
373C22—28no—
374C22—28no—
375C22—28no—
376C22—464no—
377C22—416no—
378C22—48no—
379C22—48no—
380C22—416no—
381C22#385×C12718yes—
382C22C22×C4⋊C4×C12711yescharacteristic
383C22C2×C4×D4×C12712yes—
384C22#518×C12714yes—
385C22C2×#120×C12711yescharacteristic
386C22C2×C22⋊Q8×C12712yes—
387C22C2×#123×C12711yescharacteristic
388C22#534×C12714yes—
389C22#534×C12714yes—
390C22#535×C12714yes—
391C22#538×C12718yes—
392C22#543×C12714yes—
393C4—48no—
394C4—48no—
395C4—82no—
396C4—82no—
397C2—28no—
398C2—48no—
399C2C2×#385×C12711yescharacteristic
400C2C127×#231512yes—
401C2C127×#232114yes—
402C2C127×#261312yes—
403C2C127×#262212yes—
404C2C127×#262614yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC26×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#385×C127C2semidirect
5. C127×#1439C2semidirect
6. C127×C22⋊#95C2semidirect
9. C22×C4⋊C4×C127C22semidirect
20. #379×C127C4semidirect
21. C2×#95×C127C22semidirect
22. C2×#95×C127C22semidirect
54. C2×C22⋊C4×C127C2×C4semidirect
72. C24×C127C4⋊C4semidirect
194. #14262C127direct (N × H)
204. C2×#385C2×C127semidirect
207. #1439C2×C127semidirect
208. C22⋊#95C2×C127semidirect
209. C127#14262direct (N × H)
212. C22×C4⋊C4C22×C127semidirect
223. #379C4×C127semidirect
224. C2×#95C22×C127semidirect
225. C2×#95C22×C127semidirect
257. C2×C22⋊C4C2×C4×C127semidirect
275. C24C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1272
C2×#385×C1272
C2×#379×C1272
C127×#14392
C127×C22⋊#952
#14262127