Finite Group Databasebeta

← C127×#16887 #44580560

Subgroups — C127×#16887 #44580560

Order 32512.

1662 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#393×C127C212yesmaximal, complemented
2C2×#391×C127C211yesmaximal, characteristic, complemented
3C2×#390×C127C211yesmaximal, characteristic
4C127×#1445C212yesmaximal, complemented
5C127×#1440C214yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal
8C127×#1434C211yesmaximal, characteristic, complemented
9C23×Q8×C127C2211yescharacteristic
10C23×D4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2211yescharacteristic
13C22×C22⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2214yes—
15C22×C22⋊C4×C127C2214yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18#393×C127—28no—
19#391×C127—24no—
20#390×C127—24no—
21C2×#95×C127C2212yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2214yes—
28C25×C127C2312yes—
29C22×Q8×C127—22no—
30C22×Q8×C127—22no—
31C22×Q8×C127—42no—
32C22×Q8×C127—42no—
33C22×Q8×C127D414yescomplemented
34C22×D4×C127—24no—
35C22×D4×C127—22no—
36C22×D4×C127—24no—
37C22×D4×C127—42no—
38C23×C4×C127C2312yes—
39C23×C4×C127C2312yes—
40C23×C4×C127C2314yes—
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C23×C4×C127C2311yescharacteristic
44C23×C4×C127C2311yescharacteristic
45C2×C4⋊C4×C127—22no—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—42no—
49C2×C22⋊C4×C127—28no—
50C2×C22⋊C4×C127—24no—
51C2×C22⋊C4×C127—24no—
52C2×C22⋊C4×C127—28no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—24no—
55C2×C22⋊C4×C127—44no—
56C2×C22⋊C4×C127—44no—
57C2×C22⋊C4×C127—44no—
58C2×C22⋊C4×C127—44no—
59C2×C22⋊C4×C127—44no—
60C2×C42×C127—42no—
61C2×C42×C127D414yes—
62#95×C127—24no—
63#95×C127—24no—
64#95×C127—28no—
65#95×C127—24no—
66#95×C127—24no—
67#95×C127—42no—
68#95×C127—44no—
69C24×C127—22no—
70C24×C127—22no—
71C24×C127—22no—
72C24×C127—22no—
73C24×C127—24no—
74C24×C127—24no—
75C24×C127—24no—
76C24×C127—24no—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127#4114yes—
80C24×C127C2411yescharacteristic
81C2×Q8×C127—28no—
82C2×Q8×C127—48no—
83C2×Q8×C127—44no—
84C2×Q8×C127—44no—
85C2×Q8×C127—48no—
86C2×D4×C127—28no—
87C2×D4×C127—416no—
88C2×D4×C127—44no—
89C2×D4×C127—44no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—24no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—24no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—22no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—22no—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127C2×D412yes—
119C22×C4×C127C2×D414yes—
120C22×C4×C127C2×D412yes—
121C22×C4×C127C2×D412yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127#4112yes—
124C22×C4×C127#4114yes—
125C4⋊C4×C127—44no—
126C4⋊C4×C127—44no—
127C22⋊C4×C127—416no—
128C22⋊C4×C127—48no—
129C22⋊C4×C127—416no—
130C22⋊C4×C127—48no—
131C42×C127—44no—
132C23×C127—24no—
133C23×C127—28no—
134C23×C127—24no—
135C23×C127—28no—
136C23×C127—24no—
137C23×C127—42no—
138C23×C127—42no—
139C23×C127—44no—
140C23×C127—42no—
141C23×C127—42no—
142C23×C127—42no—
143C23×C127—42no—
144C23×C127—44no—
145C23×C127—44no—
146C23×C127—44no—
147C23×C127—44no—
148C23×C127—42no—
149C23×C127—44no—
150C23×C127—44no—
151C23×C127—42no—
152C23×C127—44no—
153C23×C127—44no—
154C23×C127—44no—
155C23×C127C22×D411yescharacteristic
156C23×C127C22×D411yescharacteristic
157C23×C127C2×#4111yescharacteristic
158C23×C127C2×#4112yes—
159C23×C127C2×#4112yes—
160C23×C127H(5,𝔽2)12yes—
161C23×C127H(5,𝔽2)12yes—
162C23×C127H(5,𝔽2)12yes—
163C23×C1272−1+412yes—
164Q8×C127—416no—
165D4×C127—416no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—24no—
170C2×C4×C127—22no—
171C2×C4×C127—24no—
172C2×C4×C127—28no—
173C2×C4×C127—24no—
174C2×C4×C127—22no—
175C2×C4×C127—28no—
176C2×C4×C127—22no—
177C2×C4×C127—22no—
178C2×C4×C127—42no—
179C2×C4×C127—42no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—42no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—44no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—44no—
190C2×C4×C127—44no—
191C2×C4×C127—44no—
192C2×C4×C127—44no—
193C2×C4×C127—44no—
194C2×C4×C127—44no—
195C2×C4×C127—44no—
196C2×C4×C127—44no—
197C2×C4×C127—44no—
198C2×C4×C127—44no—
199C2×C4×C127#12114yes—
200C2×C4×C127#12414yes—
201C22×C127—44no—
202C22×C127—44no—
203C22×C127—48no—
204C22×C127—48no—
205C22×C127—44no—
206C22×C127—82no—
207C22×C127—82no—
208C22×C127—82no—
209C22×C127—84no—
210C22×C127—84no—
211C22×C127—82no—
212C22×C127C2×#12111yescharacteristic
213C22×C127#52511yescharacteristic
214C22×C127C2×#12411yescharacteristic
215C22×C127#53411yescharacteristic
216C22×C127#53412yes—
217C22×C127#53511yescharacteristic
218C22×C127#53511yescharacteristic
219C22×C127#53611yescharacteristic
220C22×C127#53812yes—
221C22×C127#53814yes—
222C22×C127#54214yes—
223C22×C127#54812yes—
224C22×C127#55012yes—
225C22×C127#55114yes—
226C22×C127#55212yes—
227C22×C127#55912yes—
228C22×C127#56214yes—
229C4×C127—24no—
230C4×C127—24no—
231C4×C127—42no—
232C4×C127—44no—
233C4×C127—82no—
234C4×C127—84no—
235C4×C127—82no—
236#16887C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127—84no—
238C2×C127#253611yescharacteristic
239C2×C127#254811yescharacteristic
240C2×C127#256111yescharacteristic
241C2×C127#261711yescharacteristic
242C2×C127#263111yescharacteristic
243C2×C127#264011yescharacteristic
244C2×C127#273014yes—
245C2×C127#275114yes—
246C2×C127#281611yescharacteristic
247C2×#393C2×C12712yescomplemented
248C2×#391C2×C12711yescharacteristic, complemented
249C2×#390C2×C12711yescharacteristic
250#1445C2×C12712yescomplemented
251#1440C2×C12714yescomplemented
252#1439C2×C12712yescomplemented
253#1438C2×C12712yes—
254#1434C2×C12711yescharacteristic, complemented
255C127#1688711yescharacteristic, direct product factor, Sylow
256C23×Q8C22×C12711yescharacteristic
257C23×D4C22×C12711yescharacteristic
258C22×C4⋊C4C22×C12711yescharacteristic
259C22×C4⋊C4C22×C12711yescharacteristic
260C22×C22⋊C4C22×C12712yes—
261C22×C22⋊C4C22×C12714yes—
262C22×C22⋊C4C22×C12714yes—
263C22×C22⋊C4C22×C12712yes—
264C22×C42C22×C12711yescharacteristic
265#393—28no—
266#391—24no—
267#390—24no—
268C2×#95C22×C12712yes—
269C2×#95C22×C12714yes—
270C2×#95C22×C12712yes—
271C2×#95C22×C12712yes—
272C2×#95C22×C12712yes—
273C2×#95C22×C12712yes—
274C2×#95C22×C12714yes—
275C25C23×C12712yes—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—42no—
279C22×Q8—42no—
280C22×Q8D4×C12714yescomplemented
281C22×D4—24no—
282C22×D4—22no—
283C22×D4—24no—
284C22×D4—42no—
285C23×C4C23×C12712yes—
286C23×C4C23×C12712yes—
287C23×C4C23×C12714yes—
288C23×C4C23×C12712yes—
289C23×C4C23×C12711yescharacteristic
290C23×C4C23×C12711yescharacteristic
291C23×C4C23×C12711yescharacteristic
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—42no—
296C2×C22⋊C4—28no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—44no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C42—42no—
308C2×C42D4×C12714yes—
309#95—24no—
310#95—24no—
311#95—28no—
312#95—24no—
313#95—24no—
314#95—42no—
315#95—44no—
316C24—22no—
317C24—22no—
318C24—22no—
319C24—22no—
320C24—24no—
321C24—24no—
322C24—24no—
323C24—24no—
324C24—22no—
325C24—22no—
326C24#41×C12714yes—
327C24C24×C12711yescharacteristic
328C2×Q8—28no—
329C2×Q8—48no—
330C2×Q8—44no—
331C2×Q8—44no—
332C2×Q8—48no—
333C2×D4—28no—
334C2×D4—416no—
335C2×D4—44no—
336C2×D4—44no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—24no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4C2×D4×C12712yes—
366C22×C4C2×D4×C12714yes—
367C22×C4C2×D4×C12712yes—
368C22×C4C2×D4×C12712yes—
369C22×C4C2×D4×C12712yes—
370C22×C4#41×C12712yes—
371C22×C4#41×C12714yes—
372C4⋊C4—44no—
373C4⋊C4—44no—
374C22⋊C4—416no—
375C22⋊C4—48no—
376C22⋊C4—416no—
377C22⋊C4—48no—
378C42—44no—
379C23—24no—
380C23—28no—
381C23—24no—
382C23—28no—
383C23—24no—
384C23—42no—
385C23—42no—
386C23—44no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—42no—
396C23—44no—
397C23—44no—
398C23—42no—
399C23—44no—
400C23—44no—
401C23—44no—
402C23C22×D4×C12711yescharacteristic
403C23C22×D4×C12711yescharacteristic
404C23C2×#41×C12711yescharacteristic
405C23C2×#41×C12712yes—
406C23C2×#41×C12712yes—
407C23H(5,𝔽2)×C12712yes—
408C23H(5,𝔽2)×C12712yes—
409C23H(5,𝔽2)×C12712yes—
410C232−1+4×C12712yes—
411Q8—416no—
412D4—416no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—28no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—28no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—44no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4#121×C12714yes—
447C2×C4#124×C12714yes—
448C22—44no—
449C22—48no—
450C22—48no—
451C22—44no—
452C22—44no—
453C22—82no—
454C22—82no—
455C22—84no—
456C22—84no—
457C22—82no—
458C22—82no—
459C22C2×#121×C12711yescharacteristic
460C22#525×C12711yescharacteristic
461C22C2×#124×C12711yescharacteristic
462C22#534×C12712yes—
463C22#534×C12711yescharacteristic
464C22#535×C12711yescharacteristic
465C22#535×C12711yescharacteristic
466C22#536×C12711yescharacteristic
467C22#538×C12712yes—
468C22#538×C12714yes—
469C22#542×C12714yes—
470C22#548×C12712yes—
471C22#550×C12712yes—
472C22#551×C12714yes—
473C22#552×C12712yes—
474C22#559×C12712yes—
475C22#562×C12714yes—
476C4—24no—
477C4—24no—
478C4—44no—
479C4—42no—
480C4—82no—
481C4—84no—
482C4—82no—
483C2—84no—
484C2C127×#253611yescharacteristic
485C2C127×#254811yescharacteristic
486C2C127×#256111yescharacteristic
487C2C127×#261711yescharacteristic
488C2C127×#263111yescharacteristic
489C2C127×#264011yescharacteristic
490C2C127×#273014yes—
491C2C127×#275114yes—
492C2C127×#281611yescharacteristic
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
1. C2×#393×C127C2semidirect
2. C2×#391×C127C2semidirect
4. C127×#1445C2semidirect
5. C127×#1440C2semidirect
6. C127×#1439C2semidirect
8. C127×#1434C2semidirect
33. C22×Q8×C127D4semidirect
236. #16887C127direct (N × H)
247. C2×#393C2×C127semidirect
248. C2×#391C2×C127semidirect
250. #1445C2×C127semidirect
251. #1440C2×C127semidirect
252. #1439C2×C127semidirect
254. #1434C2×C127semidirect
255. C127#16887direct (N × H)
280. C22×Q8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#393×C1272
C2×#391×C1272
C2×#390×C1272
C127×#14452
C127×#14402
C127×#14392
C127×#14382
C127×#14342
#16887127