Finite Group Databasebeta

← C127×#14152 #44577825

Subgroups — C127×#14152 #44577825

Order 32512.

2798 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C127C211yesmaximal, characteristic
2C2×#386×C127C214yesmaximal, complemented
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1445C212yesmaximal, complemented
6C127×#1438C212yesmaximal, complemented
7C127×#1437C214yesmaximal, complemented
8C23×D4×C127C2212yes—
9C23×D4×C127C2211yescharacteristic
10C24×C4×C127C2212yes—
11C24×C4×C127C2211yescharacteristic
12C2×#121×C127—24no—
13C2×#121×C127—24no—
14C2×#121×C127C418yescomplemented
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2218yes—
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2212yes—
19C22×C42×C127C2212yes—
20#386×C127—216no—
21C4×C22⋊C4×C127—24no—
22C2×#95×C127—24no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2218yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C25×C127C2312yes—
28C25×C127C2311yescharacteristic
29C22×D4×C127—24no—
30C22×D4×C127—24no—
31C22×D4×C127—28no—
32C22×D4×C127—28no—
33C22×D4×C127—22no—
34C22×D4×C127—22no—
35C22×D4×C127—44no—
36C22×D4×C127C2×C418yes—
37C22×D4×C127C2×C414yescomplemented
38C23×C4×C127—24no—
39C23×C4×C127—28no—
40C23×C4×C127—28no—
41C23×C4×C127—44no—
42C23×C4×C127—44no—
43C23×C4×C127C2×C414yes—
44C23×C4×C127D414yes—
45C23×C4×C127D414yes—
46C23×C4×C127C2312yes—
47C23×C4×C127C2314yes—
48C23×C4×C127C2314yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51#121×C127—232no—
52C2×C4⋊C4×C127—22no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127C2×C414yescomplemented
55C2×C22⋊C4×C127—24no—
56C2×C22⋊C4×C127—24no—
57C2×C22⋊C4×C127—24no—
58C2×C22⋊C4×C127—24no—
59C2×C22⋊C4×C127—216no—
60C2×C22⋊C4×C127—216no—
61C2×C22⋊C4×C127—48no—
62C2×C22⋊C4×C127C2×C418yescomplemented
63C2×C22⋊C4×C127D418yescomplemented
64C2×C42×C127—24no—
65C2×C42×C127—44no—
66#95×C127—24no—
67#95×C127—24no—
68#95×C127—24no—
69#95×C127—216no—
70C24×C127—24no—
71C24×C127—24no—
72C24×C127—24no—
73C24×C127—22no—
74C24×C127—22no—
75C24×C127—28no—
76C24×C127—24no—
77C24×C127—28no—
78C24×C127C22×C414yes—
79C24×C127C22×C412yes—
80C24×C127C2×D412yes—
81C24×C127C2×D412yes—
82C24×C127C2×D414yes—
83C24×C127#4114yes—
84C24×C127C2411yescharacteristic
85C2×D4×C127—216no—
86C2×D4×C127—232no—
87C2×D4×C127—28no—
88C2×D4×C127—48no—
89C2×D4×C127—48no—
90C2×D4×C127—48no—
91C2×D4×C127—416no—
92C2×D4×C127—48no—
93C2×D4×C127—48no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—216no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—28no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127—28no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—28no—
108C22×C4×C127—28no—
109C22×C4×C127—48no—
110C22×C4×C127—48no—
111C22×C4×C127—48no—
112C22×C4×C127—432no—
113C22×C4×C127—48no—
114C22×C4×C127—48no—
115C22×C4×C127C22⋊C4116yescomplemented
116C22×C4×C127C22×C414yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C2×D418yes—
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D412yes—
124C22×C4×C127#4118yes—
125C4⋊C4×C127—28no—
126C22⋊C4×C127—216no—
127C22⋊C4×C127—216no—
128C22⋊C4×C127—432no—
129C42×C127—48no—
130C23×C127—24no—
131C23×C127—24no—
132C23×C127—24no—
133C23×C127—24no—
134C23×C127—24no—
135C23×C127—24no—
136C23×C127—216no—
137C23×C127—216no—
138C23×C127—24no—
139C23×C127—28no—
140C23×C127—28no—
141C23×C127—28no—
142C23×C127—44no—
143C23×C127—44no—
144C23×C127—42no—
145C23×C127—42no—
146C23×C127—44no—
147C23×C127—44no—
148C23×C127—44no—
149C23×C127—48no—
150C23×C127—48no—
151C23×C127—416no—
152C23×C127C2×C22⋊C414yes—
153C23×C127C4×D418yes—
154C23×C127#12118yes—
155C23×C127#12414yes—
156C23×C127#12714yes—
157C23×C127C23×C411yescharacteristic
158C23×C127C22×D411yescharacteristic
159C23×C127C22×D411yescharacteristic
160C23×C127C22×D412yes—
161C23×C127C2×#4112yes—
162C23×C127C2×#4114yes—
163C23×C127H(5,𝔽2)14yes—
164D4×C127—416no—
165D4×C127—432no—
166C2×C4×C127—24no—
167C2×C4×C127—24no—
168C2×C4×C127—24no—
169C2×C4×C127—24no—
170C2×C4×C127—24no—
171C2×C4×C127—24no—
172C2×C4×C127—24no—
173C2×C4×C127—28no—
174C2×C4×C127—28no—
175C2×C4×C127—28no—
176C2×C4×C127—216no—
177C2×C4×C127—216no—
178C2×C4×C127—416no—
179C2×C4×C127—432no—
180C2×C4×C127—44no—
181C2×C4×C127—42no—
182C2×C4×C127—44no—
183C2×C4×C127—42no—
184C2×C4×C127—44no—
185C2×C4×C127—44no—
186C2×C4×C127—44no—
187C2×C4×C127—48no—
188C2×C4×C127—48no—
189C2×C4×C127C2×C22⋊C414yes—
190C2×C4×C127C2×C22⋊C414yes—
191C22×C127—24no—
192C22×C127—28no—
193C22×C127—216no—
194C22×C127—28no—
195C22×C127—216no—
196C22×C127—24no—
197C22×C127—44no—
198C22×C127—416no—
199C22×C127—44no—
200C22×C127—44no—
201C22×C127—84no—
202C22×C127—84no—
203C22×C127—88no—
204C22×C127#39018yes—
205C22×C127C22×C22⋊C411yescharacteristic
206C22×C127C2×C4×D412yes—
207C22×C127C4×#4112yes—
208C22×C127#51812yes—
209C22×C127C2×#12112yes—
210C22×C127#52512yes—
211C22×C127C2×#12411yescharacteristic
212C22×C127C2×#12711yescharacteristic
213C22×C127#53212yes—
214C22×C127#53412yes—
215C22×C127#53412yes—
216C22×C127#54618yes—
217C22×C127#55318yes—
218C4×C127—24no—
219C4×C127—24no—
220C4×C127—48no—
221C4×C127—48no—
222C4×C127—44no—
223#14152C12711yesmaximal, characteristic, direct product factor, Sylow
224C2×C127—28no—
225C2×C127—84no—
226C2×C127C2×#39011yescharacteristic
227C2×C127#229711yescharacteristic
228C2×C127#230811yescharacteristic
229C2×C127#236414yes—
230C2×C127#253912yes—
231C2×C127#254314yes—
232C2×C127#259112yes—
233C22×#121C2×C12711yescharacteristic
234C2×#386C2×C12714yescomplemented
235C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
236C22×#95C2×C12711yescharacteristic, complemented
237#1445C2×C12712yescomplemented
238#1438C2×C12712yescomplemented
239#1437C2×C12714yescomplemented
240C127#1415211yescharacteristic, direct product factor, Sylow
241C23×D4C22×C12712yes—
242C23×D4C22×C12711yescharacteristic
243C24×C4C22×C12712yes—
244C24×C4C22×C12711yescharacteristic
245C2×#121—24no—
246C2×#121—24no—
247C2×#121C4×C12718yescomplemented
248C22×C4⋊C4C22×C12711yescharacteristic
249C22×C22⋊C4C22×C12718yes—
250C22×C22⋊C4C22×C12712yes—
251C22×C22⋊C4C22×C12712yes—
252C22×C42C22×C12712yes—
253#386—216no—
254C4×C22⋊C4—24no—
255C2×#95—24no—
256C2×#95C22×C12712yes—
257C2×#95C22×C12718yes—
258C2×#95C22×C12712yes—
259C2×#95C22×C12712yes—
260C25C23×C12712yes—
261C25C23×C12711yescharacteristic
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—28no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—44no—
269C22×D4C2×C4×C12718yes—
270C22×D4C2×C4×C12714yescomplemented
271C23×C4—24no—
272C23×C4—28no—
273C23×C4—28no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×C4×C12714yes—
277C23×C4D4×C12714yes—
278C23×C4D4×C12714yes—
279C23×C4C23×C12712yes—
280C23×C4C23×C12714yes—
281C23×C4C23×C12714yes—
282C23×C4C23×C12711yescharacteristic
283C23×C4C23×C12711yescharacteristic
284#121—232no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4C2×C4×C12714yescomplemented
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—216no—
293C2×C22⋊C4—216no—
294C2×C22⋊C4—48no—
295C2×C22⋊C4C2×C4×C12718yescomplemented
296C2×C22⋊C4D4×C12718yescomplemented
297C2×C42—24no—
298C2×C42—44no—
299#95—24no—
300#95—24no—
301#95—24no—
302#95—216no—
303C24—24no—
304C24—24no—
305C24—24no—
306C24—22no—
307C24—22no—
308C24—28no—
309C24—24no—
310C24—28no—
311C24C22×C4×C12714yes—
312C24C22×C4×C12712yes—
313C24C2×D4×C12712yes—
314C24C2×D4×C12712yes—
315C24C2×D4×C12714yes—
316C24#41×C12714yes—
317C24C24×C12711yescharacteristic
318C2×D4—216no—
319C2×D4—232no—
320C2×D4—28no—
321C2×D4—48no—
322C2×D4—48no—
323C2×D4—48no—
324C2×D4—416no—
325C2×D4—48no—
326C2×D4—48no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—216no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
333C22×C4—28no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—28no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—28no—
341C22×C4—28no—
342C22×C4—48no—
343C22×C4—48no—
344C22×C4—48no—
345C22×C4—432no—
346C22×C4—48no—
347C22×C4—48no—
348C22×C4C22⋊C4×C127116yescomplemented
349C22×C4C22×C4×C12714yes—
350C22×C4C22×C4×C12712yes—
351C22×C4C22×C4×C12712yes—
352C22×C4C2×D4×C12718yes—
353C22×C4C2×D4×C12712yes—
354C22×C4C2×D4×C12712yes—
355C22×C4C2×D4×C12712yes—
356C22×C4C2×D4×C12712yes—
357C22×C4#41×C12718yes—
358C4⋊C4—28no—
359C22⋊C4—216no—
360C22⋊C4—216no—
361C22⋊C4—432no—
362C42—48no—
363C23—24no—
364C23—24no—
365C23—24no—
366C23—24no—
367C23—24no—
368C23—24no—
369C23—216no—
370C23—216no—
371C23—24no—
372C23—28no—
373C23—28no—
374C23—28no—
375C23—44no—
376C23—44no—
377C23—42no—
378C23—42no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—48no—
383C23—48no—
384C23—416no—
385C23C2×C22⋊C4×C12714yes—
386C23C4×D4×C12718yes—
387C23#121×C12718yes—
388C23#124×C12714yes—
389C23#127×C12714yes—
390C23C23×C4×C12711yescharacteristic
391C23C22×D4×C12711yescharacteristic
392C23C22×D4×C12711yescharacteristic
393C23C22×D4×C12712yes—
394C23C2×#41×C12712yes—
395C23C2×#41×C12714yes—
396C23H(5,𝔽2)×C12714yes—
397D4—416no—
398D4—432no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—28no—
409C2×C4—216no—
410C2×C4—216no—
411C2×C4—416no—
412C2×C4—432no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—44no—
416C2×C4—42no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—48no—
421C2×C4—48no—
422C2×C4C2×C22⋊C4×C12714yes—
423C2×C4C2×C22⋊C4×C12714yes—
424C22—28no—
425C22—216no—
426C22—28no—
427C22—216no—
428C22—24no—
429C22—24no—
430C22—416no—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—84no—
435C22—84no—
436C22—88no—
437C22#390×C12718yes—
438C22C22×C22⋊C4×C12711yescharacteristic
439C22C2×C4×D4×C12712yes—
440C22C4×#41×C12712yes—
441C22#518×C12712yes—
442C22C2×#121×C12712yes—
443C22#525×C12712yes—
444C22C2×#124×C12711yescharacteristic
445C22C2×#127×C12711yescharacteristic
446C22#532×C12712yes—
447C22#534×C12712yes—
448C22#534×C12712yes—
449C22#546×C12718yes—
450C22#553×C12718yes—
451C4—24no—
452C4—24no—
453C4—48no—
454C4—48no—
455C4—44no—
456C2—28no—
457C2—84no—
458C2C2×#390×C12711yescharacteristic
459C2C127×#229711yescharacteristic
460C2C127×#230811yescharacteristic
461C2C127×#236414yes—
462C2C127×#253912yes—
463C2C127×#254314yes—
464C2C127×#259112yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC22×#121×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#386×C127C2semidirect
3. C2×C4×C22⋊C4×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1445C2semidirect
6. C127×#1438C2semidirect
7. C127×#1437C2semidirect
14. C2×#121×C127C4semidirect
37. C22×D4×C127C2×C4semidirect
54. C2×C4⋊C4×C127C2×C4semidirect
62. C2×C22⋊C4×C127C2×C4semidirect
63. C2×C22⋊C4×C127D4semidirect
115. C22×C4×C127C22⋊C4semidirect
223. #14152C127direct (N × H)
234. C2×#386C2×C127semidirect
235. C2×C4×C22⋊C4C2×C127semidirect
236. C22×#95C2×C127semidirect
237. #1445C2×C127semidirect
238. #1438C2×C127semidirect
239. #1437C2×C127semidirect
240. C127#14152direct (N × H)
247. C2×#121C4×C127semidirect
270. C22×D4C2×C4×C127semidirect
287. C2×C4⋊C4C2×C4×C127semidirect
295. C2×C22⋊C4C2×C4×C127semidirect
296. C2×C22⋊C4D4×C127semidirect
348. 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×#121×C1272
C2×#386×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14452
C127×#14382
C127×#14372
#14152127