Finite Group Databasebeta

← C127×#14340 #44578013

Subgroups — C127×#14340 #44578013

Order 32512.

1926 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×#117×C127C211yesmaximal, characteristic
2C2×#384×C127C211yesmaximal, characteristic, complemented
3C2×#382×C127C211yesmaximal, characteristic, complemented
4C2×#380×C127C212yesmaximal
5C127×#1441C214yesmaximal, complemented
6C127×#1439C214yesmaximal
7C127×C4⋊#95C212yesmaximal, complemented
8C24×C4×C127C2211yescharacteristic
9C2×#117×C127—24no—
10C2×#117×C127—24no—
11C2×#117×C127C418yescomplemented
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2212yes—
15C22×C4⋊C4×C127C2214yes—
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2214yes—
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20#384×C127—24no—
21#382×C127—24no—
22#380×C127—28no—
23C2×#95×C127C2214yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2218yes—
26C25×C127C2311yescharacteristic
27C23×C4×C127—22no—
28C23×C4×C127—22no—
29C23×C4×C127—22no—
30C23×C4×C127—22no—
31C23×C4×C127C2×C414yes—
32C23×C4×C127D414yes—
33C23×C4×C127Q814yes—
34C23×C4×C127C2314yes—
35C23×C4×C127C2314yes—
36C23×C4×C127C2312yes—
37C23×C4×C127C2312yes—
38C23×C4×C127C2311yescharacteristic
39C23×C4×C127C2311yescharacteristic
40#117×C127—232no—
41C2×C4⋊C4×C127—24no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—24no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127—28no—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—24no—
50C2×C4⋊C4×C127—48no—
51C2×C4⋊C4×C127C2×C418yes—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127—28no—
55C2×C22⋊C4×C127—48no—
56C2×C22⋊C4×C127C2×C418yes—
57C2×C42×C127—22no—
58C2×C42×C127—22no—
59C2×C42×C127C2×C414yes—
60C2×C42×C127C2×C414yes—
61C2×C42×C127D414yes—
62C2×C42×C127D414yes—
63#95×C127—28no—
64#95×C127—28no—
65#95×C127—48no—
66C24×C127—21no—
67C24×C127—21no—
68C24×C127—21no—
69C24×C127—21no—
70C24×C127—24no—
71C24×C127—24no—
72C24×C127C22×C412yes—
73C24×C127C2×D412yes—
74C24×C127C2×Q812yes—
75C24×C127C2411yescharacteristic
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—24no—
81C22×C4×C127—24no—
82C22×C4×C127—28no—
83C22×C4×C127—28no—
84C22×C4×C127—28no—
85C22×C4×C127—28no—
86C22×C4×C127—28no—
87C22×C4×C127—28no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—24no—
91C22×C4×C127—24no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—24no—
95C22×C4×C127—24no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—28no—
99C22×C4×C127—28no—
100C22×C4×C127—28no—
101C22×C4×C127—28no—
102C22×C4×C127C4⋊C4116yescomplemented
103C22×C4×C127C22×C414yes—
104C22×C4×C127C22×C414yes—
105C22×C4×C127C22×C412yes—
106C22×C4×C127C22×C412yes—
107C22×C4×C127C2×D414yes—
108C22×C4×C127C2×D414yes—
109C22×C4×C127C2×D412yes—
110C22×C4×C127C2×D412yes—
111C22×C4×C127C2×D412yes—
112C22×C4×C127C2×D412yes—
113C22×C4×C127C2×Q812yes—
114C22×C4×C127C2×Q812yes—
115C22×C4×C127#4112yes—
116C22×C4×C127#4112yes—
117C4⋊C4×C127—216no—
118C4⋊C4×C127—416no—
119C4⋊C4×C127—48no—
120C4⋊C4×C127—48no—
121C22⋊C4×C127—216no—
122C22⋊C4×C127—416no—
123C42×C127—28no—
124C42×C127C22⋊C4116yescomplemented
125C23×C127—22no—
126C23×C127—22no—
127C23×C127—28no—
128C23×C127—22no—
129C23×C127—22no—
130C23×C127—22no—
131C23×C127—22no—
132C23×C127—24no—
133C23×C127—24no—
134C23×C127—28no—
135C23×C127—42no—
136C23×C127—42no—
137C23×C127—44no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127—44no—
141C23×C127C2×C4⋊C414yes—
142C23×C127C23×C411yescharacteristic
143C23×C127C22×D411yescharacteristic
144C23×C127C22×D411yescharacteristic
145C23×C127C22×D411yescharacteristic
146C23×C127C22×Q811yescharacteristic
147C23×C127C2×#4111yescharacteristic
148C23×C127C2×#4111yescharacteristic
149C23×C127H(5,𝔽2)14yes—
150C23×C1272−1+414yes—
151C2×C4×C127—22no—
152C2×C4×C127—22no—
153C2×C4×C127—28no—
154C2×C4×C127—22no—
155C2×C4×C127—22no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—24no—
159C2×C4×C127—24no—
160C2×C4×C127—28no—
161C2×C4×C127—232no—
162C2×C4×C127—24no—
163C2×C4×C127—28no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—44no—
167C2×C4×C127—44no—
168C2×C4×C127—44no—
169C2×C4×C127—44no—
170C2×C4×C127—44no—
171C2×C4×C127—48no—
172C2×C4×C127—44no—
173C2×C4×C127—44no—
174C2×C4×C127—48no—
175C2×C4×C127—48no—
176C2×C4×C127—48no—
177C2×C4×C127C2×C22⋊C418yes—
178C2×C4×C127C2×C22⋊C414yes—
179C2×C4×C127C2×C4⋊C414yes—
180C2×C4×C127C2×C4⋊C414yes—
181C2×C4×C127#11714yes—
182C2×C4×C127#12114yes—
183C2×C4×C127#12114yes—
184C2×C4×C127C22⋊Q814yes—
185C2×C4×C127C22⋊Q814yes—
186C22×C127—28no—
187C22×C127—24no—
188C22×C127—44no—
189C22×C127—44no—
190C22×C127—42no—
191C22×C127—44no—
192C22×C127—42no—
193C22×C127—44no—
194C22×C127—44no—
195C22×C127C22×C22⋊C411yescharacteristic
196C22×C127C22×C4⋊C411yescharacteristic
197C22×C127C2×#11711yescharacteristic
198C22×C127#52014yes—
199C22×C127C2×#12111yescharacteristic
200C22×C127C2×#12111yescharacteristic
201C22×C127C2×C22⋊Q811yescharacteristic
202C22×C127C2×C22⋊Q811yescharacteristic
203C22×C127#53512yes—
204C22×C127#53512yes—
205C22×C127#53612yes—
206C22×C127#53612yes—
207C22×C127#53714yes—
208C22×C127#54012yes—
209C22×C127#54112yes—
210C22×C127#54214yes—
211C22×C127#54414yes—
212C4×C127—28no—
213C4×C127—24no—
214C4×C127—44no—
215C4×C127—84no—
216C4×C127—84no—
217C4×C127#38018yes—
218#14340C12711yesmaximal, characteristic, direct product factor, Sylow
219C2×C127—44no—
220C2×C127C2×#38011yescharacteristic
221C2×C127#231112yes—
222C2×C127#231412yes—
223C2×C127#231712yes—
224C2×C127#261911yescharacteristic
225C2×C127#262012yes—
226C2×C127#262111yescharacteristic
227C2×C127#262812yes—
228C2×C127#262912yes—
229C22×#117C2×C12711yescharacteristic
230C2×#384C2×C12711yescharacteristic, complemented
231C2×#382C2×C12711yescharacteristic, complemented
232C2×#380C2×C12712yes—
233#1441C2×C12714yescomplemented
234#1439C2×C12714yes—
235C4⋊#95C2×C12712yescomplemented
236C127#1434011yescharacteristic, direct product factor, Sylow
237C24×C4C22×C12711yescharacteristic
238C2×#117—24no—
239C2×#117—24no—
240C2×#117C4×C12718yescomplemented
241C22×C4⋊C4C22×C12712yes—
242C22×C4⋊C4C22×C12712yes—
243C22×C4⋊C4C22×C12712yes—
244C22×C4⋊C4C22×C12714yes—
245C22×C22⋊C4C22×C12712yes—
246C22×C22⋊C4C22×C12714yes—
247C22×C42C22×C12711yescharacteristic
248C22×C42C22×C12711yescharacteristic
249#384—24no—
250#382—24no—
251#380—28no—
252C2×#95C22×C12714yes—
253C2×#95C22×C12714yes—
254C2×#95C22×C12718yes—
255C25C23×C12711yescharacteristic
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4C2×C4×C12714yes—
261C23×C4D4×C12714yes—
262C23×C4Q8×C12714yes—
263C23×C4C23×C12714yes—
264C23×C4C23×C12714yes—
265C23×C4C23×C12712yes—
266C23×C4C23×C12712yes—
267C23×C4C23×C12711yescharacteristic
268C23×C4C23×C12711yescharacteristic
269#117—232no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—48no—
280C2×C4⋊C4C2×C4×C12718yes—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—24no—
283C2×C22⋊C4—28no—
284C2×C22⋊C4—48no—
285C2×C22⋊C4C2×C4×C12718yes—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42C2×C4×C12714yes—
289C2×C42C2×C4×C12714yes—
290C2×C42D4×C12714yes—
291C2×C42D4×C12714yes—
292#95—28no—
293#95—28no—
294#95—48no—
295C24—21no—
296C24—21no—
297C24—21no—
298C24—21no—
299C24—24no—
300C24—24no—
301C24C22×C4×C12712yes—
302C24C2×D4×C12712yes—
303C24C2×Q8×C12712yes—
304C24C24×C12711yescharacteristic
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—28no—
312C22×C4—28no—
313C22×C4—28no—
314C22×C4—28no—
315C22×C4—28no—
316C22×C4—28no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—24no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—24no—
326C22×C4—24no—
327C22×C4—28no—
328C22×C4—28no—
329C22×C4—28no—
330C22×C4—28no—
331C22×C4C4⋊C4×C127116yescomplemented
332C22×C4C22×C4×C12714yes—
333C22×C4C22×C4×C12714yes—
334C22×C4C22×C4×C12712yes—
335C22×C4C22×C4×C12712yes—
336C22×C4C2×D4×C12714yes—
337C22×C4C2×D4×C12714yes—
338C22×C4C2×D4×C12712yes—
339C22×C4C2×D4×C12712yes—
340C22×C4C2×D4×C12712yes—
341C22×C4C2×D4×C12712yes—
342C22×C4C2×Q8×C12712yes—
343C22×C4C2×Q8×C12712yes—
344C22×C4#41×C12712yes—
345C22×C4#41×C12712yes—
346C4⋊C4—216no—
347C4⋊C4—416no—
348C4⋊C4—48no—
349C4⋊C4—48no—
350C22⋊C4—216no—
351C22⋊C4—416no—
352C42—28no—
353C42C22⋊C4×C127116yescomplemented
354C23—22no—
355C23—22no—
356C23—28no—
357C23—22no—
358C23—22no—
359C23—22no—
360C23—22no—
361C23—24no—
362C23—24no—
363C23—28no—
364C23—42no—
365C23—42no—
366C23—44no—
367C23—42no—
368C23—42no—
369C23—44no—
370C23C2×C4⋊C4×C12714yes—
371C23C23×C4×C12711yescharacteristic
372C23C22×D4×C12711yescharacteristic
373C23C22×D4×C12711yescharacteristic
374C23C22×D4×C12711yescharacteristic
375C23C22×Q8×C12711yescharacteristic
376C23C2×#41×C12711yescharacteristic
377C23C2×#41×C12711yescharacteristic
378C23H(5,𝔽2)×C12714yes—
379C232−1+4×C12714yes—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—28no—
390C2×C4—232no—
391C2×C4—24no—
392C2×C4—28no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—44no—
400C2×C4—48no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—48no—
404C2×C4—48no—
405C2×C4—48no—
406C2×C4C2×C22⋊C4×C12718yes—
407C2×C4C2×C22⋊C4×C12714yes—
408C2×C4C2×C4⋊C4×C12714yes—
409C2×C4C2×C4⋊C4×C12714yes—
410C2×C4#117×C12714yes—
411C2×C4#121×C12714yes—
412C2×C4#121×C12714yes—
413C2×C4C22⋊Q8×C12714yes—
414C2×C4C22⋊Q8×C12714yes—
415C22—28no—
416C22—24no—
417C22—44no—
418C22—42no—
419C22—44no—
420C22—42no—
421C22—44no—
422C22—44no—
423C22—44no—
424C22C22×C22⋊C4×C12711yescharacteristic
425C22C22×C4⋊C4×C12711yescharacteristic
426C22C2×#117×C12711yescharacteristic
427C22#520×C12714yes—
428C22C2×#121×C12711yescharacteristic
429C22C2×#121×C12711yescharacteristic
430C22C2×C22⋊Q8×C12711yescharacteristic
431C22C2×C22⋊Q8×C12711yescharacteristic
432C22#535×C12712yes—
433C22#535×C12712yes—
434C22#536×C12712yes—
435C22#536×C12712yes—
436C22#537×C12714yes—
437C22#540×C12712yes—
438C22#541×C12712yes—
439C22#542×C12714yes—
440C22#544×C12714yes—
441C4—24no—
442C4—28no—
443C4—44no—
444C4—84no—
445C4—84no—
446C4#380×C12718yes—
447C2—44no—
448C2C2×#380×C12711yescharacteristic
449C2C127×#231112yes—
450C2C127×#231412yes—
451C2C127×#231712yes—
452C2C127×#261911yescharacteristic
453C2C127×#262012yes—
454C2C127×#262111yescharacteristic
455C2C127×#262812yes—
456C2C127×#262912yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#384×C127C2semidirect
3. C2×#382×C127C2semidirect
5. C127×#1441C2semidirect
7. C127×C4⋊#95C2semidirect
11. C2×#117×C127C4semidirect
102. C22×C4×C127C4⋊C4semidirect
124. C42×C127C22⋊C4semidirect
218. #14340C127direct (N × H)
230. C2×#384C2×C127semidirect
231. C2×#382C2×C127semidirect
233. #1441C2×C127semidirect
235. C4⋊#95C2×C127semidirect
236. C127#14340direct (N × H)
240. C2×#117C4×C127semidirect
331. C22×C4C4⋊C4×C127semidirect
353. C42C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C1272
C2×#384×C1272
C2×#382×C1272
C2×#380×C1272
C127×#14412
C127×#14392
C127×C4⋊#952
#14340127