Finite Group Databasebeta

← C127×#14440 #44578113

Subgroups — C127×#14440 #44578113

Order 32512.

2118 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#390×C127C211yesmaximal, characteristic
2C2×#386×C127C212yesmaximal
3C2×#385×C127C214yesmaximal, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1439C214yesmaximal, complemented
6C127×C4⋊#95C212yesmaximal, complemented
7C23×D4×C127C2211yescharacteristic
8C24×C4×C127C2212yes—
9C22×C4⋊C4×C127C2212yes—
10C22×C4⋊C4×C127C2212yes—
11C22×C4⋊C4×C127C2211yescharacteristic
12C22×C4⋊C4×C127C2212yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C22⋊C4×C127C2214yes—
15C22×C22⋊C4×C127C2212yes—
16C22×C42×C127C2211yescharacteristic
17#390×C127C418yescomplemented
18#386×C127—28no—
19#385×C127—216no—
20C2×#95×C127C2214yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2214yes—
23C2×#95×C127C2212yes—
24C25×C127C2312yes—
25C22×D4×C127—41no—
26C22×D4×C127—41no—
27C22×D4×C127—41no—
28C22×D4×C127—41no—
29C22×D4×C127C2×C414yes—
30C22×D4×C127D414yes—
31C22×D4×C127Q814yes—
32C23×C4×C127—24no—
33C23×C4×C127—28no—
34C23×C4×C127—44no—
35C23×C4×C127—42no—
36C23×C4×C127—42no—
37C23×C4×C127C2314yes—
38C23×C4×C127C2312yes—
39C23×C4×C127C2314yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2312yes—
42C2×C4⋊C4×C127—28no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—41no—
45C2×C4⋊C4×C127—41no—
46C2×C4⋊C4×C127—42no—
47C2×C4⋊C4×C127—42no—
48C2×C4⋊C4×C127—42no—
49C2×C4⋊C4×C127—42no—
50C2×C4⋊C4×C127—42no—
51C2×C4⋊C4×C127C2×C414yescomplemented
52C2×C4⋊C4×C127D418yescomplemented
53C2×C22⋊C4×C127—28no—
54C2×C22⋊C4×C127—28no—
55C2×C22⋊C4×C127—28no—
56C2×C22⋊C4×C127—24no—
57C2×C22⋊C4×C127—28no—
58C2×C22⋊C4×C127—44no—
59C2×C22⋊C4×C127—42no—
60C2×C22⋊C4×C127—42no—
61C2×C22⋊C4×C127C2×C4116yescomplemented
62C2×C42×C127—41no—
63C2×C42×C127—41no—
64C2×C42×C127C2×C414yescomplemented
65#95×C127—28no—
66#95×C127—28no—
67#95×C127—28no—
68#95×C127—42no—
69C24×C127—24no—
70C24×C127—24no—
71C24×C127—24no—
72C24×C127—22no—
73C24×C127—22no—
74C24×C127—22no—
75C24×C127—22no—
76C24×C127—24no—
77C24×C127C22×C414yes—
78C24×C127C2×D414yes—
79C24×C127C2×Q814yes—
80C24×C127C2411yescharacteristic
81C2×D4×C127—44no—
82C2×D4×C127—44no—
83C2×D4×C127—44no—
84C2×D4×C127—44no—
85C2×D4×C127—44no—
86C2×D4×C127—44no—
87C2×D4×C127C4⋊C4116yescomplemented
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—22no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—22no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—22no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127—24no—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—24no—
110C22×C4×C127—24no—
111C22×C4×C127—24no—
112C22×C4×C127—24no—
113C22×C4×C127—48no—
114C22×C4×C127—416no—
115C22×C4×C127—416no—
116C22×C4×C127—48no—
117C22×C4×C127—48no—
118C22×C4×C127C22×C414yes—
119C22×C4×C127C22×C412yes—
120C22×C4×C127C22×C414yes—
121C22×C4×C127C2×D418yes—
122C22×C4×C127C2×D412yes—
123C22×C4×C127C2×D414yes—
124C22×C4×C127C2×Q812yes—
125C22×C4×C127#4114yes—
126C4⋊C4×C127—44no—
127C4⋊C4×C127—48no—
128C4⋊C4×C127—48no—
129C4⋊C4×C127—48no—
130C22⋊C4×C127—232no—
131C22⋊C4×C127—416no—
132C22⋊C4×C127—48no—
133C42×C127—44no—
134C23×C127—28no—
135C23×C127—24no—
136C23×C127—24no—
137C23×C127—28no—
138C23×C127—24no—
139C23×C127—24no—
140C23×C127—24no—
141C23×C127—24no—
142C23×C127—28no—
143C23×C127—28no—
144C23×C127—28no—
145C23×C127—28no—
146C23×C127—44no—
147C23×C127—44no—
148C23×C127—44no—
149C23×C127—44no—
150C23×C127—42no—
151C23×C127—44no—
152C23×C127—42no—
153C23×C127—42no—
154C23×C127—44no—
155C23×C127—42no—
156C23×C127C2×C4⋊C418yes—
157C23×C127C23×C411yescharacteristic
158C23×C127C22×D411yescharacteristic
159C23×C127C22×D412yes—
160C23×C127C22×Q811yescharacteristic
161C23×C127C2×#4112yes—
162C23×C127H(5,𝔽2)11yescharacteristic
163C23×C127H(5,𝔽2)11yescharacteristic
164C23×C127H(5,𝔽2)11yescharacteristic
165C23×C127H(5,𝔽2)11yescharacteristic
166C23×C127H(5,𝔽2)12yes—
167C23×C1272−1+412yes—
168D4×C127—416no—
169C2×C4×C127—24no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—24no—
173C2×C4×C127—24no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—24no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—22no—
180C2×C4×C127—22no—
181C2×C4×C127—28no—
182C2×C4×C127—24no—
183C2×C4×C127—28no—
184C2×C4×C127—28no—
185C2×C4×C127—28no—
186C2×C4×C127—432no—
187C2×C4×C127—44no—
188C2×C4×C127—44no—
189C2×C4×C127—42no—
190C2×C4×C127—44no—
191C2×C4×C127—44no—
192C2×C4×C127—42no—
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—44no—
200C2×C4×C127—44no—
201C2×C4×C127C2×C4⋊C414yes—
202C2×C4×C127C4×D418yes—
203C22×C127—28no—
204C22×C127—216no—
205C22×C127—48no—
206C22×C127—44no—
207C22×C127—44no—
208C22×C127—44no—
209C22×C127—48no—
210C22×C127—44no—
211C22×C127—44no—
212C22×C127—48no—
213C22×C127—44no—
214C22×C127C22×C4⋊C411yescharacteristic
215C22×C127C2×C4×D412yes—
216C22×C127#51811yescharacteristic
217C22×C127#51811yescharacteristic
218C22×C127#52012yes—
219C22×C127#53411yescharacteristic
220C22×C127#53411yescharacteristic
221C22×C127#53412yes—
222C22×C127#53712yes—
223C22×C127#53812yes—
224C22×C127#53912yes—
225C22×C127#54311yescharacteristic
226C22×C127#54311yescharacteristic
227C22×C127D4212yes—
228C22×C127D4211yescharacteristic
229C22×C127#54712yes—
230C22×C127D4×Q812yes—
231C22×C127#55012yes—
232C22×C127#55412yes—
233C22×C127#55911yescharacteristic
234C22×C127H(3,𝔽4)11yescharacteristic
235C22×C127#56212yes—
236C22×C127#56311yescharacteristic
237C4×C127—24no—
238C4×C127—28no—
239C4×C127—44no—
240C4×C127—48no—
241C4×C127—84no—
242#14440C12711yesmaximal, characteristic, direct product factor, Sylow
243C2×C127—48no—
244C2×C127#231511yescharacteristic
245C2×C127#232512yes—
246C2×C127D4×C4⋊C412yes—
247C2×C127#236611yescharacteristic
248C2×C127#237911yescharacteristic
249C2×C127#267911yescharacteristic
250C2×C127#268212yes—
251C2×C127#268311yescharacteristic
252C2×C127#272411yescharacteristic
253C2×C127#273212yes—
254C2×C127#280411yescharacteristic
255C2×#390C2×C12711yescharacteristic
256C2×#386C2×C12712yes—
257C2×#385C2×C12714yescomplemented
258#1441C2×C12712yescomplemented
259#1439C2×C12714yescomplemented
260C4⋊#95C2×C12712yescomplemented
261C127#1444011yescharacteristic, direct product factor, Sylow
262C23×D4C22×C12711yescharacteristic
263C24×C4C22×C12712yes—
264C22×C4⋊C4C22×C12712yes—
265C22×C4⋊C4C22×C12712yes—
266C22×C4⋊C4C22×C12711yescharacteristic
267C22×C4⋊C4C22×C12712yes—
268C22×C22⋊C4C22×C12714yes—
269C22×C22⋊C4C22×C12714yes—
270C22×C22⋊C4C22×C12712yes—
271C22×C42C22×C12711yescharacteristic
272#390C4×C12718yescomplemented
273#386—28no—
274#385—216no—
275C2×#95C22×C12714yes—
276C2×#95C22×C12714yes—
277C2×#95C22×C12714yes—
278C2×#95C22×C12712yes—
279C25C23×C12712yes—
280C22×D4—41no—
281C22×D4—41no—
282C22×D4—41no—
283C22×D4—41no—
284C22×D4C2×C4×C12714yes—
285C22×D4D4×C12714yes—
286C22×D4Q8×C12714yes—
287C23×C4—24no—
288C23×C4—28no—
289C23×C4—44no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C23×C12714yes—
293C23×C4C23×C12712yes—
294C23×C4C23×C12714yes—
295C23×C4C23×C12711yescharacteristic
296C23×C4C23×C12712yes—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4C2×C4×C12714yescomplemented
307C2×C4⋊C4D4×C12718yescomplemented
308C2×C22⋊C4—28no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4C2×C4×C127116yescomplemented
317C2×C42—41no—
318C2×C42—41no—
319C2×C42C2×C4×C12714yescomplemented
320#95—28no—
321#95—28no—
322#95—28no—
323#95—42no—
324C24—24no—
325C24—24no—
326C24—24no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—24no—
332C24C22×C4×C12714yes—
333C24C2×D4×C12714yes—
334C24C2×Q8×C12714yes—
335C24C24×C12711yescharacteristic
336C2×D4—44no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4C4⋊C4×C127116yescomplemented
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—24no—
360C22×C4—24no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—24no—
368C22×C4—48no—
369C22×C4—416no—
370C22×C4—416no—
371C22×C4—48no—
372C22×C4—48no—
373C22×C4C22×C4×C12714yes—
374C22×C4C22×C4×C12712yes—
375C22×C4C22×C4×C12714yes—
376C22×C4C2×D4×C12718yes—
377C22×C4C2×D4×C12712yes—
378C22×C4C2×D4×C12714yes—
379C22×C4C2×Q8×C12712yes—
380C22×C4#41×C12714yes—
381C4⋊C4—44no—
382C4⋊C4—48no—
383C4⋊C4—48no—
384C4⋊C4—48no—
385C22⋊C4—232no—
386C22⋊C4—416no—
387C22⋊C4—48no—
388C42—44no—
389C23—28no—
390C23—24no—
391C23—24no—
392C23—28no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23—28no—
398C23—28no—
399C23—28no—
400C23—28no—
401C23—44no—
402C23—44no—
403C23—44no—
404C23—44no—
405C23—42no—
406C23—44no—
407C23—42no—
408C23—42no—
409C23—44no—
410C23—42no—
411C23C2×C4⋊C4×C12718yes—
412C23C23×C4×C12711yescharacteristic
413C23C22×D4×C12711yescharacteristic
414C23C22×D4×C12712yes—
415C23C22×Q8×C12711yescharacteristic
416C23C2×#41×C12712yes—
417C23H(5,𝔽2)×C12711yescharacteristic
418C23H(5,𝔽2)×C12711yescharacteristic
419C23H(5,𝔽2)×C12711yescharacteristic
420C23H(5,𝔽2)×C12711yescharacteristic
421C23H(5,𝔽2)×C12712yes—
422C232−1+4×C12712yes—
423D4—416no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—28no—
437C2×C4—24no—
438C2×C4—28no—
439C2×C4—28no—
440C2×C4—28no—
441C2×C4—432no—
442C2×C4—44no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4C2×C4⋊C4×C12714yes—
457C2×C4C4×D4×C12718yes—
458C22—28no—
459C22—216no—
460C22—48no—
461C22—44no—
462C22—44no—
463C22—44no—
464C22—48no—
465C22—44no—
466C22—44no—
467C22—48no—
468C22—44no—
469C22C22×C4⋊C4×C12711yescharacteristic
470C22C2×C4×D4×C12712yes—
471C22#518×C12711yescharacteristic
472C22#518×C12711yescharacteristic
473C22#520×C12712yes—
474C22#534×C12711yescharacteristic
475C22#534×C12711yescharacteristic
476C22#534×C12712yes—
477C22#537×C12712yes—
478C22#538×C12712yes—
479C22#539×C12712yes—
480C22#543×C12711yescharacteristic
481C22#543×C12711yescharacteristic
482C22D42×C12712yes—
483C22D42×C12711yescharacteristic
484C22#547×C12712yes—
485C22D4×Q8×C12712yes—
486C22#550×C12712yes—
487C22#554×C12712yes—
488C22#559×C12711yescharacteristic
489C22H(3,𝔽4)×C12711yescharacteristic
490C22#562×C12712yes—
491C22#563×C12711yescharacteristic
492C4—24no—
493C4—28no—
494C4—44no—
495C4—48no—
496C4—84no—
497C2—48no—
498C2C127×#231511yescharacteristic
499C2C127×#232512yes—
500C2D4×C4⋊C4×C12712yes—
501C2C127×#236611yescharacteristic
502C2C127×#237911yescharacteristic
503C2C127×#267911yescharacteristic
504C2C127×#268212yes—
505C2C127×#268311yescharacteristic
506C2C127×#272411yescharacteristic
507C2C127×#273212yes—
508C2C127×#280411yescharacteristic
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
3. C2×#385×C127C2semidirect
4. C127×#1441C2semidirect
5. C127×#1439C2semidirect
6. C127×C4⋊#95C2semidirect
17. #390×C127C4semidirect
51. C2×C4⋊C4×C127C2×C4semidirect
52. C2×C4⋊C4×C127D4semidirect
61. C2×C22⋊C4×C127C2×C4semidirect
64. C2×C42×C127C2×C4semidirect
87. C2×D4×C127C4⋊C4semidirect
242. #14440C127direct (N × H)
257. C2×#385C2×C127semidirect
258. #1441C2×C127semidirect
259. #1439C2×C127semidirect
260. C4⋊#95C2×C127semidirect
261. C127#14440direct (N × H)
272. #390C4×C127semidirect
306. C2×C4⋊C4C2×C4×C127semidirect
307. C2×C4⋊C4D4×C127semidirect
316. C2×C22⋊C4C2×C4×C127semidirect
319. C2×C42C2×C4×C127semidirect
342. C2×D4C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#390×C1272
C2×#386×C1272
C2×#385×C1272
C127×#14412
C127×#14392
C127×C4⋊#952
#14440127