Finite Group Databasebeta

← C127×#14473 #44578146

Subgroups — C127×#14473 #44578146

Order 32512.

2134 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×#124×C127C211yesmaximal, characteristic
2C2×#386×C127C212yesmaximal
3C127×#1446C212yesmaximal, complemented
4C127×#1440C214yesmaximal, complemented
5C127×#1434C212yesmaximal, complemented
6C127×C22⋊#95C214yesmaximal, complemented
7C23×Q8×C127C2211yescharacteristic
8C23×D4×C127C2211yescharacteristic
9C24×C4×C127C2212yes—
10C2×#124×C127—28no—
11C2×#124×C127C418yescomplemented
12C22×C22⋊C4×C127C2214yes—
13C22×C22⋊C4×C127C2214yes—
14C22×C22⋊C4×C127C2212yes—
15C22×C42×C127C2211yescharacteristic
16#386×C127—28no—
17C2×#95×C127C2214yes—
18C2×#95×C127C2214yes—
19C2×#95×C127C2212yes—
20C2×#95×C127C2212yes—
21C2×#95×C127C2214yes—
22C2×#95×C127C2212yes—
23C2×#95×C127C2212yes—
24C25×C127C2312yes—
25C22×Q8×C127—24no—
26C22×Q8×C127—42no—
27C22×Q8×C127—41no—
28C22×Q8×C127—41no—
29C22×Q8×C127C2×C414yescomplemented
30C22×D4×C127—41no—
31C22×D4×C127—42no—
32C22×D4×C127—41no—
33C22×D4×C127C2×C414yes—
34C22×D4×C127D418yes—
35C23×C4×C127—24no—
36C23×C4×C127—28no—
37C23×C4×C127—42no—
38C23×C4×C127—42no—
39C23×C4×C127—44no—
40C23×C4×C127C2314yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2312yes—
43C23×C4×C127C2314yes—
44C23×C4×C127C2311yescharacteristic
45#124×C127—232no—
46C2×C22⋊C4×C127—28no—
47C2×C22⋊C4×C127—28no—
48C2×C22⋊C4×C127—28no—
49C2×C22⋊C4×C127—24no—
50C2×C22⋊C4×C127—28no—
51C2×C22⋊C4×C127—44no—
52C2×C22⋊C4×C127—42no—
53C2×C22⋊C4×C127—42no—
54C2×C22⋊C4×C127C2×C4116yescomplemented
55C2×C42×C127—24no—
56C2×C42×C127C2×C414yescomplemented
57#95×C127—28no—
58#95×C127—28no—
59#95×C127—42no—
60#95×C127—42no—
61#95×C127—42no—
62#95×C127—44no—
63#95×C127—42no—
64C24×C127—24no—
65C24×C127—24no—
66C24×C127—24no—
67C24×C127—22no—
68C24×C127—22no—
69C24×C127—22no—
70C24×C127—22no—
71C24×C127—24no—
72C24×C127C22×C414yes—
73C24×C127C2×D414yes—
74C24×C127C2×D414yes—
75C24×C127C2411yescharacteristic
76C2×Q8×C127—28no—
77C2×Q8×C127—44no—
78C2×Q8×C127—44no—
79C2×Q8×C127—48no—
80C2×Q8×C127—48no—
81C2×D4×C127—44no—
82C2×D4×C127—44no—
83C2×D4×C127—48no—
84C2×D4×C127—48no—
85C2×D4×C127C22⋊C4116yes—
86C22×C4×C127—22no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—24no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—22no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
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—48no—
111C22×C4×C127—416no—
112C22×C4×C127—416no—
113C22×C4×C127—48no—
114C22×C4×C127—48no—
115C22×C4×C127C22×C414yes—
116C22×C4×C127C22×C414yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C2×D414yes—
119C22×C4×C127#4118yes—
120C22⋊C4×C127—232no—
121C22⋊C4×C127—416no—
122C22⋊C4×C127—48no—
123C42×C127—28no—
124C23×C127—28no—
125C23×C127—24no—
126C23×C127—24no—
127C23×C127—28no—
128C23×C127—24no—
129C23×C127—24no—
130C23×C127—24no—
131C23×C127—24no—
132C23×C127—28no—
133C23×C127—28no—
134C23×C127—28no—
135C23×C127—28no—
136C23×C127—44no—
137C23×C127—44no—
138C23×C127—44no—
139C23×C127—44no—
140C23×C127—42no—
141C23×C127—42no—
142C23×C127—44no—
143C23×C127—42no—
144C23×C127—44no—
145C23×C127—42no—
146C23×C127C2×C22⋊C418yes—
147C23×C127C23×C411yescharacteristic
148C23×C127C22×D412yes—
149C23×C127C2×#4114yes—
150C23×C127H(5,𝔽2)12yes—
151C23×C127H(5,𝔽2)11yescharacteristic
152C23×C127H(5,𝔽2)11yescharacteristic
153C23×C127H(5,𝔽2)12yes—
154C23×C1272−1+412yes—
155Q8×C127—416no—
156D4×C127—416no—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—24no—
160C2×C4×C127—24no—
161C2×C4×C127—24no—
162C2×C4×C127—24no—
163C2×C4×C127—24no—
164C2×C4×C127—24no—
165C2×C4×C127—24no—
166C2×C4×C127—24no—
167C2×C4×C127—28no—
168C2×C4×C127—28no—
169C2×C4×C127—28no—
170C2×C4×C127—432no—
171C2×C4×C127—44no—
172C2×C4×C127—44no—
173C2×C4×C127—44no—
174C2×C4×C127—44no—
175C2×C4×C127—44no—
176C2×C4×C127—44no—
177C2×C4×C127—44no—
178C2×C4×C127—44no—
179C2×C4×C127—44no—
180C2×C4×C127—44no—
181C2×C4×C127—44no—
182C2×C4×C127—44no—
183C2×C4×C127—44no—
184C2×C4×C127—44no—
185C2×C4×C127—44no—
186C2×C4×C127C2×C22⋊C414yes—
187C22×C127—28no—
188C22×C127—216no—
189C22×C127—48no—
190C22×C127—44no—
191C22×C127—44no—
192C22×C127—44no—
193C22×C127—44no—
194C22×C127—48no—
195C22×C127—48no—
196C22×C127—44no—
197C22×C127—44no—
198C22×C127C22×C22⋊C411yescharacteristic
199C22×C127C4×#4112yes—
200C22×C127#51811yescharacteristic
201C22×C127#51811yescharacteristic
202C22×C127#52012yes—
203C22×C127#53412yes—
204C22×C127#53412yes—
205C22×C127#53814yes—
206C22×C127#54214yes—
207C22×C127#54614yes—
208C22×C127#54714yes—
209C22×C127#55112yes—
210C22×C127#55512yes—
211C22×C127H(3,𝔽4)11yescharacteristic
212C22×C127#56212yes—
213C22×C127#56311yescharacteristic
214C4×C127—24no—
215C4×C127—44no—
216C4×C127—44no—
217C4×C127—48no—
218C4×C127—84no—
219#14473C12711yesmaximal, characteristic, direct product factor, Sylow
220C2×C127—48no—
221C2×C127#230811yescharacteristic
222C2×C127#233712yes—
223C2×C127#233912yes—
224C2×C127#237211yescharacteristic
225C2×C127#237911yescharacteristic
226C2×C127#268412yes—
227C2×C127#268614yes—
228C2×C127#271712yes—
229C22×#124C2×C12711yescharacteristic
230C2×#386C2×C12712yes—
231#1446C2×C12712yescomplemented
232#1440C2×C12714yescomplemented
233#1434C2×C12712yescomplemented
234C22⋊#95C2×C12714yescomplemented
235C127#1447311yescharacteristic, direct product factor, Sylow
236C23×Q8C22×C12711yescharacteristic
237C23×D4C22×C12711yescharacteristic
238C24×C4C22×C12712yes—
239C2×#124—28no—
240C2×#124C4×C12718yescomplemented
241C22×C22⋊C4C22×C12714yes—
242C22×C22⋊C4C22×C12714yes—
243C22×C22⋊C4C22×C12712yes—
244C22×C42C22×C12711yescharacteristic
245#386—28no—
246C2×#95C22×C12714yes—
247C2×#95C22×C12714yes—
248C2×#95C22×C12712yes—
249C2×#95C22×C12712yes—
250C2×#95C22×C12714yes—
251C2×#95C22×C12712yes—
252C2×#95C22×C12712yes—
253C25C23×C12712yes—
254C22×Q8—24no—
255C22×Q8—42no—
256C22×Q8—41no—
257C22×Q8—41no—
258C22×Q8C2×C4×C12714yescomplemented
259C22×D4—41no—
260C22×D4—42no—
261C22×D4—41no—
262C22×D4C2×C4×C12714yes—
263C22×D4D4×C12718yes—
264C23×C4—24no—
265C23×C4—28no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4C23×C12714yes—
270C23×C4C23×C12712yes—
271C23×C4C23×C12712yes—
272C23×C4C23×C12714yes—
273C23×C4C23×C12711yescharacteristic
274#124—232no—
275C2×C22⋊C4—28no—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—24no—
279C2×C22⋊C4—28no—
280C2×C22⋊C4—44no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4C2×C4×C127116yescomplemented
284C2×C42—24no—
285C2×C42C2×C4×C12714yescomplemented
286#95—28no—
287#95—28no—
288#95—42no—
289#95—42no—
290#95—42no—
291#95—44no—
292#95—42no—
293C24—24no—
294C24—24no—
295C24—24no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24—22no—
300C24—24no—
301C24C22×C4×C12714yes—
302C24C2×D4×C12714yes—
303C24C2×D4×C12714yes—
304C24C24×C12711yescharacteristic
305C2×Q8—28no—
306C2×Q8—44no—
307C2×Q8—44no—
308C2×Q8—48no—
309C2×Q8—48no—
310C2×D4—44no—
311C2×D4—44no—
312C2×D4—48no—
313C2×D4—48no—
314C2×D4C22⋊C4×C127116yes—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—24no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—48no—
340C22×C4—416no—
341C22×C4—416no—
342C22×C4—48no—
343C22×C4—48no—
344C22×C4C22×C4×C12714yes—
345C22×C4C22×C4×C12714yes—
346C22×C4C22×C4×C12712yes—
347C22×C4C2×D4×C12714yes—
348C22×C4#41×C12718yes—
349C22⋊C4—232no—
350C22⋊C4—416no—
351C22⋊C4—48no—
352C42—28no—
353C23—28no—
354C23—24no—
355C23—24no—
356C23—28no—
357C23—24no—
358C23—24no—
359C23—24no—
360C23—24no—
361C23—28no—
362C23—28no—
363C23—28no—
364C23—28no—
365C23—44no—
366C23—44no—
367C23—44no—
368C23—44no—
369C23—42no—
370C23—42no—
371C23—44no—
372C23—42no—
373C23—44no—
374C23—42no—
375C23C2×C22⋊C4×C12718yes—
376C23C23×C4×C12711yescharacteristic
377C23C22×D4×C12712yes—
378C23C2×#41×C12714yes—
379C23H(5,𝔽2)×C12712yes—
380C23H(5,𝔽2)×C12711yescharacteristic
381C23H(5,𝔽2)×C12711yescharacteristic
382C23H(5,𝔽2)×C12712yes—
383C232−1+4×C12712yes—
384Q8—416no—
385D4—416no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—28no—
397C2×C4—28no—
398C2×C4—28no—
399C2×C4—432no—
400C2×C4—44no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4C2×C22⋊C4×C12714yes—
416C22—216no—
417C22—28no—
418C22—48no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22—44no—
423C22—48no—
424C22—48no—
425C22—44no—
426C22—44no—
427C22C22×C22⋊C4×C12711yescharacteristic
428C22C4×#41×C12712yes—
429C22#518×C12711yescharacteristic
430C22#518×C12711yescharacteristic
431C22#520×C12712yes—
432C22#534×C12712yes—
433C22#534×C12712yes—
434C22#538×C12714yes—
435C22#542×C12714yes—
436C22#546×C12714yes—
437C22#547×C12714yes—
438C22#551×C12712yes—
439C22#555×C12712yes—
440C22H(3,𝔽4)×C12711yescharacteristic
441C22#562×C12712yes—
442C22#563×C12711yescharacteristic
443C4—24no—
444C4—44no—
445C4—48no—
446C4—44no—
447C4—84no—
448C2—48no—
449C2C127×#230811yescharacteristic
450C2C127×#233712yes—
451C2C127×#233912yes—
452C2C127×#237211yescharacteristic
453C2C127×#237911yescharacteristic
454C2C127×#268412yes—
455C2C127×#268614yes—
456C2C127×#271712yes—
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. C127×#1446C2semidirect
4. C127×#1440C2semidirect
5. C127×#1434C2semidirect
6. C127×C22⋊#95C2semidirect
11. C2×#124×C127C4semidirect
29. C22×Q8×C127C2×C4semidirect
54. C2×C22⋊C4×C127C2×C4semidirect
56. C2×C42×C127C2×C4semidirect
219. #14473C127direct (N × H)
231. #1446C2×C127semidirect
232. #1440C2×C127semidirect
233. #1434C2×C127semidirect
234. C22⋊#95C2×C127semidirect
235. C127#14473direct (N × H)
240. C2×#124C4×C127semidirect
258. C22×Q8C2×C4×C127semidirect
283. C2×C22⋊C4C2×C4×C127semidirect
285. C2×C42C2×C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C2×#386×C1272
C127×#14462
C127×#14402
C127×#14342
C127×C22⋊#952
#14473127