Finite Group Databasebeta

← C127×#14748 #44578421

Subgroups — C127×#14748 #44578421

Order 32512.

2254 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C127C211yesmaximal, characteristic, complemented
2C2×#386×C127C213yesmaximal
3C2×#385×C127C213yesmaximal, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1443C211yesmaximal, characteristic, complemented
6C127×#1441C213yesmaximal, complemented
7C127×#1439C213yesmaximal, complemented
8C23×D4×C127C2211yescharacteristic
9C24×C4×C127C2213yes—
10C22×C4⋊C4×C127C2213yes—
11C22×C4⋊C4×C127C2213yes—
12C22×C22⋊C4×C127C2213yes—
13C22×C22⋊C4×C127C2213yes—
14C22×C22⋊C4×C127C2213yes—
15#396×C127—24no—
16#386×C127—212no—
17#385×C127—212no—
18C2×#95×C127—24no—
19C2×#95×C127C2213yes—
20C2×#95×C127C2213yes—
21C2×#95×C127C2213yes—
22C2×#95×C127C2213yes—
23C2×#95×C127C2213yes—
24C2×#95×C127C2211yescharacteristic
25C25×C127C2311yescharacteristic
26C25×C127C2311yescharacteristic
27C22×D4×C127—26no—
28C22×D4×C127—26no—
29C22×D4×C127Q814yes—
30C23×C4×C127—26no—
31C23×C4×C127—26no—
32C23×C4×C127—26no—
33C23×C4×C127—26no—
34C23×C4×C127—26no—
35C23×C4×C127—43no—
36C23×C4×C127—43no—
37C23×C4×C127C2313yes—
38C23×C4×C127C2313yes—
39C23×C4×C127C2313yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2313yes—
42C2×C4⋊C4×C127—26no—
43C2×C4⋊C4×C127—26no—
44C2×C4⋊C4×C127—26no—
45C2×C4⋊C4×C127—26no—
46C2×C4⋊C4×C127—43no—
47C2×C4⋊C4×C127—43no—
48C2×C22⋊C4×C127—26no—
49C2×C22⋊C4×C127—26no—
50C2×C22⋊C4×C127—26no—
51C2×C22⋊C4×C127—26no—
52C2×C22⋊C4×C127—26no—
53C2×C22⋊C4×C127—26no—
54C2×C22⋊C4×C127—43no—
55C2×C22⋊C4×C127—43no—
56C2×C22⋊C4×C127D4112yes—
57#95×C127—26no—
58#95×C127—26no—
59#95×C127—26no—
60#95×C127—26no—
61#95×C127—26no—
62#95×C127D414yescomplemented
63C24×C127—21no—
64C24×C127—23no—
65C24×C127—23no—
66C24×C127—21no—
67C24×C127—21no—
68C24×C127—23no—
69C24×C127—23no—
70C24×C127—23no—
71C24×C127—23no—
72C24×C127—21no—
73C24×C127C2×D416yes—
74C24×C127C2×Q812yes—
75C24×C127C2×Q812yes—
76C24×C127#4116yes—
77C24×C127C2411yescharacteristic
78C2×D4×C127—224no—
79C2×D4×C127—412no—
80C2×D4×C127—44no—
81C22×C4×C127—224no—
82C22×C4×C127—23no—
83C22×C4×C127—23no—
84C22×C4×C127—23no—
85C22×C4×C127—23no—
86C22×C4×C127—23no—
87C22×C4×C127—23no—
88C22×C4×C127—23no—
89C22×C4×C127—23no—
90C22×C4×C127—23no—
91C22×C4×C127—23no—
92C22×C4×C127—23no—
93C22×C4×C127—23no—
94C22×C4×C127—23no—
95C22×C4×C127—23no—
96C22×C4×C127—23no—
97C22×C4×C127—23no—
98C22×C4×C127—23no—
99C22×C4×C127—23no—
100C22×C4×C127—23no—
101C22×C4×C127—23no—
102C22×C4×C127—23no—
103C22×C4×C127—23no—
104C22×C4×C127—23no—
105C22×C4×C127—23no—
106C22×C4×C127—23no—
107C22×C4×C127—23no—
108C22×C4×C127—412no—
109C22×C4×C127—412no—
110C22×C4×C127—412no—
111C22×C4×C127—412no—
112C22×C4×C127—412no—
113C22×C4×C127—412no—
114C22×C4×C127C2×D416yes—
115C22×C4×C127C2×D416yes—
116C22×C4×C127C2×D416yes—
117C22×C4×C127C2×Q812yes—
118C22×C4×C127#4116yes—
119C4⋊C4×C127—412no—
120C4⋊C4×C127—412no—
121C22⋊C4×C127—224no—
122C22⋊C4×C127—412no—
123C22⋊C4×C127—412no—
124C23×C127—26no—
125C23×C127—26no—
126C23×C127—26no—
127C23×C127—26no—
128C23×C127—26no—
129C23×C127—26no—
130C23×C127—26no—
131C23×C127—26no—
132C23×C127—22no—
133C23×C127—26no—
134C23×C127—26no—
135C23×C127—22no—
136C23×C127—26no—
137C23×C127—43no—
138C23×C127—43no—
139C23×C127—41no—
140C23×C127—43no—
141C23×C127—43no—
142C23×C127—43no—
143C23×C127—43no—
144C23×C127—43no—
145C23×C127—43no—
146C23×C127—43no—
147C23×C127#121112yes—
148C23×C127C22⋊Q8112yes—
149C23×C127#12614yes—
150C23×C127C22×D413yes—
151C23×C127C22×D411yescharacteristic
152C23×C127C22×Q811yescharacteristic
153C23×C127C2×#4113yes—
154C23×C127C2×#4113yes—
155C23×C127H(5,𝔽2)13yes—
156C23×C1272−1+411yescharacteristic
157D4×C127—416no—
158C2×C4×C127—26no—
159C2×C4×C127—26no—
160C2×C4×C127—26no—
161C2×C4×C127—26no—
162C2×C4×C127—26no—
163C2×C4×C127—26no—
164C2×C4×C127—26no—
165C2×C4×C127—26no—
166C2×C4×C127—26no—
167C2×C4×C127—26no—
168C2×C4×C127—26no—
169C2×C4×C127—26no—
170C2×C4×C127—26no—
171C2×C4×C127—448no—
172C2×C4×C127—43no—
173C2×C4×C127—43no—
174C2×C4×C127—43no—
175C2×C4×C127—43no—
176C2×C4×C127—41no—
177C2×C4×C127—43no—
178C2×C4×C127—43no—
179C2×C4×C127—43no—
180C2×C4×C127—43no—
181C2×C4×C127—43no—
182C2×C4×C127—43no—
183C2×C4×C127—43no—
184C2×C4×C127—43no—
185C2×C4×C127—43no—
186C2×C4×C127—43no—
187C2×C4×C127—43no—
188C2×C4×C127—43no—
189C2×C4×C127—43no—
190C22×C127—24no—
191C22×C127—24no—
192C22×C127—212no—
193C22×C127—212no—
194C22×C127—212no—
195C22×C127—212no—
196C22×C127—42no—
197C22×C127—46no—
198C22×C127—46no—
199C22×C127—81no—
200C22×C127—81no—
201C22×C127—83no—
202C22×C127—83no—
203C22×C127#39618yescomplemented
204C22×C127C2×#12113yes—
205C22×C127C2×C22⋊Q813yes—
206C22×C127#52513yes—
207C22×C127C2×#12611yescharacteristic
208C22×C127#52913yes—
209C22×C127#53813yes—
210C22×C127#53913yes—
211C22×C127D4213yes—
212C22×C127#54613yes—
213C22×C127#54613yes—
214C22×C127#54713yes—
215C22×C127D4×Q811yescharacteristic
216C22×C127#55413yes—
217C4×C127—42no—
218C4×C127—46no—
219C4×C127—46no—
220C4×C127—46no—
221C4×C127—46no—
222#14748C12711yesmaximal, characteristic, direct product factor, Sylow
223C2×C127—28no—
224C2×C127—82no—
225C2×C127C2×#39611yescharacteristic
226C2×C127#242413yes—
227C2×C127#242513yes—
228C2×C127#244913yes—
229C2×C127#245013yes—
230C2×C127#264311yescharacteristic
231C2×C127#285211yescharacteristic
232C2×#396C2×C12711yescharacteristic, complemented
233C2×#386C2×C12713yes—
234C2×#385C2×C12713yescomplemented
235C22×#95C2×C12711yescharacteristic, complemented
236#1443C2×C12711yescharacteristic, complemented
237#1441C2×C12713yescomplemented
238#1439C2×C12713yescomplemented
239C127#1474811yescharacteristic, direct product factor, Sylow
240C23×D4C22×C12711yescharacteristic
241C24×C4C22×C12713yes—
242C22×C4⋊C4C22×C12713yes—
243C22×C4⋊C4C22×C12713yes—
244C22×C22⋊C4C22×C12713yes—
245C22×C22⋊C4C22×C12713yes—
246C22×C22⋊C4C22×C12713yes—
247#396—24no—
248#386—212no—
249#385—212no—
250C2×#95—24no—
251C2×#95C22×C12713yes—
252C2×#95C22×C12713yes—
253C2×#95C22×C12713yes—
254C2×#95C22×C12713yes—
255C2×#95C22×C12713yes—
256C2×#95C22×C12711yescharacteristic
257C25C23×C12711yescharacteristic
258C25C23×C12711yescharacteristic
259C22×D4—26no—
260C22×D4—26no—
261C22×D4Q8×C12714yes—
262C23×C4—26no—
263C23×C4—26no—
264C23×C4—26no—
265C23×C4—26no—
266C23×C4—26no—
267C23×C4—43no—
268C23×C4—43no—
269C23×C4C23×C12713yes—
270C23×C4C23×C12713yes—
271C23×C4C23×C12713yes—
272C23×C4C23×C12711yescharacteristic
273C23×C4C23×C12713yes—
274C2×C4⋊C4—26no—
275C2×C4⋊C4—26no—
276C2×C4⋊C4—26no—
277C2×C4⋊C4—26no—
278C2×C4⋊C4—43no—
279C2×C4⋊C4—43no—
280C2×C22⋊C4—26no—
281C2×C22⋊C4—26no—
282C2×C22⋊C4—26no—
283C2×C22⋊C4—26no—
284C2×C22⋊C4—26no—
285C2×C22⋊C4—26no—
286C2×C22⋊C4—43no—
287C2×C22⋊C4—43no—
288C2×C22⋊C4D4×C127112yes—
289#95—26no—
290#95—26no—
291#95—26no—
292#95—26no—
293#95—26no—
294#95D4×C12714yescomplemented
295C24—21no—
296C24—23no—
297C24—23no—
298C24—21no—
299C24—21no—
300C24—23no—
301C24—23no—
302C24—23no—
303C24—23no—
304C24—21no—
305C24C2×D4×C12716yes—
306C24C2×Q8×C12712yes—
307C24C2×Q8×C12712yes—
308C24#41×C12716yes—
309C24C24×C12711yescharacteristic
310C2×D4—224no—
311C2×D4—412no—
312C2×D4—44no—
313C22×C4—224no—
314C22×C4—23no—
315C22×C4—23no—
316C22×C4—23no—
317C22×C4—23no—
318C22×C4—23no—
319C22×C4—23no—
320C22×C4—23no—
321C22×C4—23no—
322C22×C4—23no—
323C22×C4—23no—
324C22×C4—23no—
325C22×C4—23no—
326C22×C4—23no—
327C22×C4—23no—
328C22×C4—23no—
329C22×C4—23no—
330C22×C4—23no—
331C22×C4—23no—
332C22×C4—23no—
333C22×C4—23no—
334C22×C4—23no—
335C22×C4—23no—
336C22×C4—23no—
337C22×C4—23no—
338C22×C4—23no—
339C22×C4—23no—
340C22×C4—412no—
341C22×C4—412no—
342C22×C4—412no—
343C22×C4—412no—
344C22×C4—412no—
345C22×C4—412no—
346C22×C4C2×D4×C12716yes—
347C22×C4C2×D4×C12716yes—
348C22×C4C2×D4×C12716yes—
349C22×C4C2×Q8×C12712yes—
350C22×C4#41×C12716yes—
351C4⋊C4—412no—
352C4⋊C4—412no—
353C22⋊C4—224no—
354C22⋊C4—412no—
355C22⋊C4—412no—
356C23—26no—
357C23—26no—
358C23—26no—
359C23—26no—
360C23—26no—
361C23—26no—
362C23—26no—
363C23—26no—
364C23—22no—
365C23—26no—
366C23—26no—
367C23—22no—
368C23—26no—
369C23—43no—
370C23—43no—
371C23—41no—
372C23—43no—
373C23—43no—
374C23—43no—
375C23—43no—
376C23—43no—
377C23—43no—
378C23—43no—
379C23#121×C127112yes—
380C23C22⋊Q8×C127112yes—
381C23#126×C12714yes—
382C23C22×D4×C12713yes—
383C23C22×D4×C12711yescharacteristic
384C23C22×Q8×C12711yescharacteristic
385C23C2×#41×C12713yes—
386C23C2×#41×C12713yes—
387C23H(5,𝔽2)×C12713yes—
388C232−1+4×C12711yescharacteristic
389D4—416no—
390C2×C4—26no—
391C2×C4—26no—
392C2×C4—26no—
393C2×C4—26no—
394C2×C4—26no—
395C2×C4—26no—
396C2×C4—26no—
397C2×C4—26no—
398C2×C4—26no—
399C2×C4—26no—
400C2×C4—26no—
401C2×C4—26no—
402C2×C4—26no—
403C2×C4—448no—
404C2×C4—43no—
405C2×C4—43no—
406C2×C4—43no—
407C2×C4—43no—
408C2×C4—41no—
409C2×C4—43no—
410C2×C4—43no—
411C2×C4—43no—
412C2×C4—43no—
413C2×C4—43no—
414C2×C4—43no—
415C2×C4—43no—
416C2×C4—43no—
417C2×C4—43no—
418C2×C4—43no—
419C2×C4—43no—
420C2×C4—43no—
421C2×C4—43no—
422C22—24no—
423C22—24no—
424C22—212no—
425C22—212no—
426C22—212no—
427C22—212no—
428C22—42no—
429C22—46no—
430C22—46no—
431C22—81no—
432C22—81no—
433C22—83no—
434C22—83no—
435C22#396×C12718yescomplemented
436C22C2×#121×C12713yes—
437C22C2×C22⋊Q8×C12713yes—
438C22#525×C12713yes—
439C22C2×#126×C12711yescharacteristic
440C22#529×C12713yes—
441C22#538×C12713yes—
442C22#539×C12713yes—
443C22D42×C12713yes—
444C22#546×C12713yes—
445C22#546×C12713yes—
446C22#547×C12713yes—
447C22D4×Q8×C12711yescharacteristic
448C22#554×C12713yes—
449C4—42no—
450C4—46no—
451C4—46no—
452C4—46no—
453C4—46no—
454C2—28no—
455C2—82no—
456C2C2×#396×C12711yescharacteristic
457C2C127×#242413yes—
458C2C127×#242513yes—
459C2C127×#244913yes—
460C2C127×#245013yes—
461C2C127×#264311yescharacteristic
462C2C127×#285211yescharacteristic
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×#396×C127C2semidirect
3. C2×#385×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1443C2semidirect
6. C127×#1441C2semidirect
7. C127×#1439C2semidirect
62. #95×C127D4semidirect
203. C22×C127#396semidirect
222. #14748C127direct (N × H)
232. C2×#396C2×C127semidirect
234. C2×#385C2×C127semidirect
235. C22×#95C2×C127semidirect
236. #1443C2×C127semidirect
237. #1441C2×C127semidirect
238. #1439C2×C127semidirect
239. C127#14748direct (N × H)
294. #95D4×C127semidirect
435. C22#396×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C1272
C2×#386×C1272
C2×#385×C1272
C22×#95×C1272
C127×#14432
C127×#14412
C127×#14392
#14748127