Finite Group Databasebeta

← C127×#14256 #44577929

Subgroups — C127×#14256 #44577929

Order 32512.

2554 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C127C211yesmaximal, characteristic
2C23×C4⋊C4×C127C211yesmaximal, characteristic, complemented
3C2×#386×C127C212yesmaximal
4C2×#381×C127C211yesmaximal, characteristic, complemented
5C127×#1441C214yesmaximal, complemented
6C127×#1439C214yesmaximal, complemented
7C127×C22⋊#95C212yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C24×C4×C127C2211yescharacteristic
10C24×C4×C127C2212yes—
11C2×#123×C127—24no—
12C2×#123×C127—24no—
13C2×#123×C127C418yescomplemented
14C22×C4⋊C4×C127—28no—
15C22×C4⋊C4×C127—24no—
16C22×C4⋊C4×C127C2214yes—
17C22×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2212yes—
21C22×C22⋊C4×C127C2214yes—
22#386×C127—28no—
23#381×C127—24no—
24C2×#95×C127C2214yes—
25C2×#95×C127C2214yes—
26C2×#95×C127C2218yes—
27C25×C127C2311yescharacteristic
28C25×C127C2311yescharacteristic
29C22×D4×C127—22no—
30C22×D4×C127—22no—
31C22×D4×C127—24no—
32C22×D4×C127—24no—
33C22×D4×C127C2×C414yes—
34C23×C4×C127—24no—
35C23×C4×C127—24no—
36C23×C4×C127—24no—
37C23×C4×C127—24no—
38C23×C4×C127—48no—
39C23×C4×C127C2×C414yes—
40C23×C4×C127D414yes—
41C23×C4×C127D414yes—
42C23×C4×C127D418yes—
43C23×C4×C127C2314yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2314yes—
47C23×C4×C127C2312yes—
48#123×C127—232no—
49C2×C4⋊C4×C127—232no—
50C2×C4⋊C4×C127—216no—
51C2×C4⋊C4×C127—28no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127C2×C418yescomplemented
55C2×C22⋊C4×C127—22no—
56C2×C22⋊C4×C127—22no—
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—24no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—28no—
63C2×C22⋊C4×C127—48no—
64C2×C22⋊C4×C127C2×C414yes—
65C2×C22⋊C4×C127C2×C418yescomplemented
66#95×C127—28no—
67#95×C127—28no—
68#95×C127—48no—
69C24×C127—24no—
70C24×C127—24no—
71C24×C127—21no—
72C24×C127—21no—
73C24×C127—22no—
74C24×C127—22no—
75C24×C127—24no—
76C24×C127—24no—
77C24×C127C22×C412yes—
78C24×C127C22×C412yes—
79C24×C127C2×D412yes—
80C24×C127C2×D412yes—
81C24×C127C2×D414yes—
82C24×C127#4114yes—
83C24×C127C2411yescharacteristic
84C2×D4×C127—28no—
85C2×D4×C127—216no—
86C2×D4×C127—44no—
87C2×D4×C127—48no—
88C2×D4×C127—44no—
89C22×C4×C127—216no—
90C22×C4×C127—28no—
91C22×C4×C127—216no—
92C22×C4×C127—28no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—216no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—22no—
104C22×C4×C127—24no—
105C22×C4×C127—28no—
106C22×C4×C127—28no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—24no—
111C22×C4×C127—28no—
112C22×C4×C127—28no—
113C22×C4×C127—416no—
114C22×C4×C127—416no—
115C22×C4×C127—416no—
116C22×C4×C127C22⋊C4116yescomplemented
117C22×C4×C127C22×C414yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C414yes—
120C22×C4×C127C2×D418yes—
121C22×C4×C127C2×D414yes—
122C22×C4×C127C2×D414yes—
123C4⋊C4×C127—232no—
124C4⋊C4×C127—216no—
125C22⋊C4×C127—28no—
126C22⋊C4×C127—216no—
127C22⋊C4×C127—416no—
128C22⋊C4×C127—48no—
129C23×C127—28no—
130C23×C127—28no—
131C23×C127—24no—
132C23×C127—24no—
133C23×C127—28no—
134C23×C127—28no—
135C23×C127—216no—
136C23×C127—22no—
137C23×C127—24no—
138C23×C127—28no—
139C23×C127—41no—
140C23×C127—42no—
141C23×C127—41no—
142C23×C127—44no—
143C23×C127—42no—
144C23×C127—42no—
145C23×C127—44no—
146C23×C127—44no—
147C23×C127—48no—
148C23×C127C2×C22⋊C414yes—
149C23×C127C4×D418yes—
150C23×C127#12014yes—
151C23×C127#12118yes—
152C23×C127#12314yes—
153C23×C127C23×C411yescharacteristic
154C23×C127C22×D411yescharacteristic
155C23×C127C22×D411yescharacteristic
156C23×C127C22×D412yes—
157C23×C127C2×#4112yes—
158C23×C127H(5,𝔽2)14yes—
159C23×C1272−1+414yes—
160D4×C127—416no—
161C2×C4×C127—28no—
162C2×C4×C127—24no—
163C2×C4×C127—28no—
164C2×C4×C127—24no—
165C2×C4×C127—232no—
166C2×C4×C127—24no—
167C2×C4×C127—22no—
168C2×C4×C127—24no—
169C2×C4×C127—28no—
170C2×C4×C127—28no—
171C2×C4×C127—28no—
172C2×C4×C127—28no—
173C2×C4×C127—432no—
174C2×C4×C127—41no—
175C2×C4×C127—42no—
176C2×C4×C127—41no—
177C2×C4×C127—48no—
178C2×C4×C127—42no—
179C2×C4×C127—48no—
180C2×C4×C127—42no—
181C2×C4×C127—44no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—44no—
185C2×C4×C127—48no—
186C2×C4×C127—48no—
187C2×C4×C127C2×C22⋊C418yes—
188C22×C127—28no—
189C22×C127—216no—
190C22×C127—24no—
191C22×C127—24no—
192C22×C127—216no—
193C22×C127—28no—
194C22×C127—44no—
195C22×C127—48no—
196C22×C127—42no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—84no—
200C22×C127—82no—
201C22×C127#38618yes—
202C22×C127C22×C22⋊C411yescharacteristic
203C22×C127C2×C4×D412yes—
204C22×C127#52014yes—
205C22×C127C2×#12011yescharacteristic
206C22×C127C2×#12112yes—
207C22×C127C2×#12311yescharacteristic
208C22×C127#53414yes—
209C22×C127#53512yes—
210C22×C127#53612yes—
211C22×C127#53614yes—
212C22×C127#53714yes—
213C22×C127#53918yes—
214C4×C127—28no—
215C4×C127—44no—
216C4×C127—48no—
217C4×C127—42no—
218C4×C127—84no—
219#14256C12711yesmaximal, characteristic, direct product factor, Sylow
220C2×C127—28no—
221C2×C127—82no—
222C2×C127C2×#38611yescharacteristic
223C2×C127#231112yes—
224C2×C127#232214yes—
225C2×C127#261311yescharacteristic
226C2×C127#261411yescharacteristic
227C2×C127#261814yes—
228C2×C127#262312yes—
229C22×#123C2×C12711yescharacteristic
230C23×C4⋊C4C2×C12711yescharacteristic, complemented
231C2×#386C2×C12712yes—
232C2×#381C2×C12711yescharacteristic, complemented
233#1441C2×C12714yescomplemented
234#1439C2×C12714yescomplemented
235C22⋊#95C2×C12712yescomplemented
236C127#1425611yescharacteristic, direct product factor, Sylow
237C23×D4C22×C12711yescharacteristic
238C24×C4C22×C12711yescharacteristic
239C24×C4C22×C12712yes—
240C2×#123—24no—
241C2×#123—24no—
242C2×#123C4×C12718yescomplemented
243C22×C4⋊C4—28no—
244C22×C4⋊C4—24no—
245C22×C4⋊C4C22×C12714yes—
246C22×C4⋊C4C22×C12712yes—
247C22×C22⋊C4C22×C12712yes—
248C22×C22⋊C4C22×C12711yescharacteristic
249C22×C22⋊C4C22×C12712yes—
250C22×C22⋊C4C22×C12714yes—
251#386—28no—
252#381—24no—
253C2×#95C22×C12714yes—
254C2×#95C22×C12714yes—
255C2×#95C22×C12718yes—
256C25C23×C12711yescharacteristic
257C25C23×C12711yescharacteristic
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4C2×C4×C12714yes—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—48no—
268C23×C4C2×C4×C12714yes—
269C23×C4D4×C12714yes—
270C23×C4D4×C12714yes—
271C23×C4D4×C12718yes—
272C23×C4C23×C12714yes—
273C23×C4C23×C12712yes—
274C23×C4C23×C12711yescharacteristic
275C23×C4C23×C12714yes—
276C23×C4C23×C12712yes—
277#123—232no—
278C2×C4⋊C4—232no—
279C2×C4⋊C4—216no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4C2×C4×C12718yescomplemented
284C2×C22⋊C4—22no—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—28no—
292C2×C22⋊C4—48no—
293C2×C22⋊C4C2×C4×C12714yes—
294C2×C22⋊C4C2×C4×C12718yescomplemented
295#95—28no—
296#95—28no—
297#95—48no—
298C24—24no—
299C24—24no—
300C24—21no—
301C24—21no—
302C24—22no—
303C24—22no—
304C24—24no—
305C24—24no—
306C24C22×C4×C12712yes—
307C24C22×C4×C12712yes—
308C24C2×D4×C12712yes—
309C24C2×D4×C12712yes—
310C24C2×D4×C12714yes—
311C24#41×C12714yes—
312C24C24×C12711yescharacteristic
313C2×D4—28no—
314C2×D4—216no—
315C2×D4—44no—
316C2×D4—48no—
317C2×D4—44no—
318C22×C4—216no—
319C22×C4—28no—
320C22×C4—216no—
321C22×C4—28no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—216no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—28no—
335C22×C4—28no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—28no—
341C22×C4—28no—
342C22×C4—416no—
343C22×C4—416no—
344C22×C4—416no—
345C22×C4C22⋊C4×C127116yescomplemented
346C22×C4C22×C4×C12714yes—
347C22×C4C22×C4×C12712yes—
348C22×C4C22×C4×C12714yes—
349C22×C4C2×D4×C12718yes—
350C22×C4C2×D4×C12714yes—
351C22×C4C2×D4×C12714yes—
352C4⋊C4—232no—
353C4⋊C4—216no—
354C22⋊C4—28no—
355C22⋊C4—216no—
356C22⋊C4—416no—
357C22⋊C4—48no—
358C23—28no—
359C23—28no—
360C23—24no—
361C23—28no—
362C23—24no—
363C23—28no—
364C23—216no—
365C23—22no—
366C23—24no—
367C23—28no—
368C23—41no—
369C23—42no—
370C23—41no—
371C23—44no—
372C23—42no—
373C23—44no—
374C23—42no—
375C23—44no—
376C23—48no—
377C23C2×C22⋊C4×C12714yes—
378C23C4×D4×C12718yes—
379C23#120×C12714yes—
380C23#121×C12718yes—
381C23#123×C12714yes—
382C23C23×C4×C12711yescharacteristic
383C23C22×D4×C12711yescharacteristic
384C23C22×D4×C12711yescharacteristic
385C23C22×D4×C12712yes—
386C23C2×#41×C12712yes—
387C23H(5,𝔽2)×C12714yes—
388C232−1+4×C12714yes—
389D4—416no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—28no—
393C2×C4—24no—
394C2×C4—232no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—28no—
399C2×C4—28no—
400C2×C4—28no—
401C2×C4—28no—
402C2×C4—432no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—48no—
407C2×C4—48no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—48no—
415C2×C4—48no—
416C2×C4C2×C22⋊C4×C12718yes—
417C22—216no—
418C22—24no—
419C22—24no—
420C22—216no—
421C22—28no—
422C22—28no—
423C22—48no—
424C22—42no—
425C22—44no—
426C22—81no—
427C22—81no—
428C22—84no—
429C22—82no—
430C22#386×C12718yes—
431C22C22×C22⋊C4×C12711yescharacteristic
432C22C2×C4×D4×C12712yes—
433C22#520×C12714yes—
434C22C2×#120×C12711yescharacteristic
435C22C2×#121×C12712yes—
436C22C2×#123×C12711yescharacteristic
437C22#534×C12714yes—
438C22#535×C12712yes—
439C22#536×C12714yes—
440C22#536×C12712yes—
441C22#537×C12714yes—
442C22#539×C12718yes—
443C4—28no—
444C4—48no—
445C4—42no—
446C4—44no—
447C4—84no—
448C2—28no—
449C2—82no—
450C2C2×#386×C12711yescharacteristic
451C2C127×#231112yes—
452C2C127×#232214yes—
453C2C127×#261311yescharacteristic
454C2C127×#261411yescharacteristic
455C2C127×#261814yes—
456C2C127×#262312yes—
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. C23×C4⋊C4×C127C2semidirect
4. C2×#381×C127C2semidirect
5. C127×#1441C2semidirect
6. C127×#1439C2semidirect
7. C127×C22⋊#95C2semidirect
13. C2×#123×C127C4semidirect
54. C2×C4⋊C4×C127C2×C4semidirect
65. C2×C22⋊C4×C127C2×C4semidirect
116. C22×C4×C127C22⋊C4semidirect
219. #14256C127direct (N × H)
230. C23×C4⋊C4C2×C127semidirect
232. C2×#381C2×C127semidirect
233. #1441C2×C127semidirect
234. #1439C2×C127semidirect
235. C22⋊#95C2×C127semidirect
236. C127#14256direct (N × H)
242. C2×#123C4×C127semidirect
283. C2×C4⋊C4C2×C4×C127semidirect
294. C2×C22⋊C4C2×C4×C127semidirect
345. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1272
C23×C4⋊C4×C1272
C2×#386×C1272
C2×#381×C1272
C127×#14412
C127×#14392
C127×C22⋊#952
#14256127