Finite Group Databasebeta

← C127×#13799 #44577472

Subgroups — C127×#13799 #44577472

Order 32512.

2398 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C127C211yesmaximal, characteristic
2C2×#381×C127C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C127C212yesmaximal
4C22×#95×C127C211yesmaximal, characteristic
5C127×#1436C214yesmaximal, complemented
6C127×#1434C212yesmaximal, complemented
7C127×C22⋊#95C212yesmaximal
8C4×#95×C127C212yesmaximal, complemented
9C24×C4×C127C2212yes—
10C24×C4×C127C2211yescharacteristic
11C2×#117×C127—28no—
12C2×#117×C127C418yescomplemented
13C22×C4⋊C4×C127C2212yes—
14C22×C22⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2212yes—
16C22×C22⋊C4×C127C2211yescharacteristic
17C22×C42×C127C2214yes—
18C22×C42×C127C2212yes—
19#381×C127C418yescomplemented
20C4×C22⋊C4×C127—28no—
21C2×#95×C127C418yescomplemented
22C2×#95×C127C2214yes—
23C2×#95×C127C2214yes—
24C2×#95×C127C2214yes—
25C2×#95×C127C2211yescharacteristic
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C25×C127C2311yescharacteristic
31C23×C4×C127—24no—
32C23×C4×C127—24no—
33C23×C4×C127—24no—
34C23×C4×C127—24no—
35C23×C4×C127—28no—
36C23×C4×C127—44no—
37C23×C4×C127C2×C418yes—
38C23×C4×C127C2×C414yes—
39C23×C4×C127C2×C414yes—
40C23×C4×C127C2×C414yes—
41C23×C4×C127C2312yes—
42C23×C4×C127C2314yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2311yescharacteristic
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48#117×C127—232no—
49C2×C4⋊C4×C127—28no—
50C2×C4⋊C4×C127C2×C418yescomplemented
51C2×C22⋊C4×C127—24no—
52C2×C22⋊C4×C127—24no—
53C2×C22⋊C4×C127—24no—
54C2×C22⋊C4×C127C2×C414yes—
55C2×C22⋊C4×C127C2×C418yes—
56C2×C22⋊C4×C127C2×C414yes—
57C2×C22⋊C4×C127D418yes—
58C2×C42×C127—28no—
59C2×C42×C127—28no—
60C2×C42×C127—28no—
61C2×C42×C127—44no—
62C2×C42×C127C2×C418yescomplemented
63#95×C127—28no—
64#95×C127—28no—
65#95×C127—44no—
66#95×C127C2×C414yes—
67#95×C127C2×C418yes—
68#95×C127C2×C414yes—
69#95×C127C2×C418yescomplemented
70#95×C127C2×C418yescomplemented
71C24×C127—24no—
72C24×C127—22no—
73C24×C127—22no—
74C24×C127C22×C412yes—
75C24×C127C22×C412yes—
76C24×C127C22×C412yes—
77C24×C127C2×D414yes—
78C24×C127#4114yes—
79C24×C127C2411yescharacteristic
80C22×C4×C127—28no—
81C22×C4×C127—28no—
82C22×C4×C127—216no—
83C22×C4×C127—216no—
84C22×C4×C127—22no—
85C22×C4×C127—22no—
86C22×C4×C127—22no—
87C22×C4×C127—24no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—22no—
91C22×C4×C127—22no—
92C22×C4×C127—24no—
93C22×C4×C127—22no—
94C22×C4×C127—216no—
95C22×C4×C127—22no—
96C22×C4×C127—24no—
97C22×C4×C127—24no—
98C22×C4×C127—24no—
99C22×C4×C127—24no—
100C22×C4×C127—24no—
101C22×C4×C127—24no—
102C22×C4×C127—24no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—22no—
108C22×C4×C127—24no—
109C22×C4×C127—216no—
110C22×C4×C127—48no—
111C22×C4×C127—416no—
112C22×C4×C127—416no—
113C22×C4×C127C42116yescomplemented
114C22×C4×C127C22×C414yes—
115C22×C4×C127C22×C418yes—
116C22×C4×C127C22×C414yes—
117C22×C4×C127C22×C412yes—
118C22×C4×C127C22×C412yes—
119C22×C4×C127C22×C412yes—
120C22×C4×C127C22×C412yes—
121C22×C4×C127C22×C412yes—
122C22×C4×C127C22×C412yes—
123C22×C4×C127C22×C414yes—
124C22×C4×C127C22×C414yes—
125C22×C4×C127C2×D418yes—
126C22×C4×C127#4118yes—
127C4⋊C4×C127—216no—
128C22⋊C4×C127—28no—
129C22⋊C4×C127—216no—
130C22⋊C4×C127C22⋊C4116yes—
131C42×C127—216no—
132C42×C127—416no—
133C23×C127—24no—
134C23×C127—24no—
135C23×C127—24no—
136C23×C127—22no—
137C23×C127—22no—
138C23×C127—24no—
139C23×C127—24no—
140C23×C127—28no—
141C23×C127—28no—
142C23×C127—28no—
143C23×C127—28no—
144C23×C127C2×C4214yes—
145C23×C127C2×C22⋊C414yes—
146C23×C127#11714yes—
147C23×C127C4×D418yes—
148C23×C127C4×D418yes—
149C23×C127C23×C411yescharacteristic
150C23×C127C23×C411yescharacteristic
151C23×C127C23×C411yescharacteristic
152C23×C127C22×D412yes—
153C23×C127C2×#4112yes—
154C23×C127C2×#4114yes—
155C23×C127H(5,𝔽2)12yes—
156C23×C1272−1+412yes—
157C2×C4×C127—22no—
158C2×C4×C127—22no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
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—24no—
168C2×C4×C127—24no—
169C2×C4×C127—28no—
170C2×C4×C127—28no—
171C2×C4×C127—28no—
172C2×C4×C127—28no—
173C2×C4×C127—232no—
174C2×C4×C127—24no—
175C2×C4×C127—24no—
176C2×C4×C127—28no—
177C2×C4×C127—24no—
178C2×C4×C127—24no—
179C2×C4×C127—28no—
180C2×C4×C127—24no—
181C2×C4×C127—24no—
182C2×C4×C127—28no—
183C2×C4×C127—432no—
184C2×C4×C127—44no—
185C2×C4×C127—44no—
186C2×C4×C127—44no—
187C2×C4×C127—44no—
188C2×C4×C127—44no—
189C2×C4×C127—44no—
190C2×C4×C127—44no—
191C2×C4×C127—44no—
192C2×C4×C127C2×C4214yes—
193C2×C4×C127C2×C4214yes—
194C2×C4×C127C2×C22⋊C418yes—
195C2×C4×C127#11718yescomplemented
196C22×C127—28no—
197C22×C127—28no—
198C22×C127—28no—
199C22×C127—28no—
200C22×C127—216no—
201C22×C127—24no—
202C22×C127—24no—
203C22×C127C4×C22⋊C418yes—
204C22×C127C22×C4211yescharacteristic
205C22×C127C22×C22⋊C411yescharacteristic
206C22×C127C2×#11712yes—
207C22×C127C2×#11711yescharacteristic
208C22×C127C2×C4×D412yes—
209C22×C127C2×C4×D412yes—
210C22×C127C4×#4112yes—
211C22×C127C4×#4112yes—
212C22×C127#51811yescharacteristic
213C22×C127#51911yescharacteristic
214C22×C127#52012yes—
215C22×C127#52012yes—
216C22×C127#54614yes—
217C22×C127#54714yes—
218C22×C127#55114yes—
219C22×C127#55214yes—
220C4×C127—28no—
221C4×C127—28no—
222C4×C127—24no—
223C4×C127—24no—
224C4×C127—44no—
225C4×C127—44no—
226C4×C127—48no—
227#13799C12711yesmaximal, characteristic, direct product factor, Sylow
228C2×C127—28no—
229C2×C127C2×C4×C22⋊C411yescharacteristic
230C2×C127C4×#11711yescharacteristic
231C2×C127#227411yescharacteristic
232C2×C127#233912yes—
233C2×C127#234212yes—
234C2×C127#234312yes—
235C2×C127#234412yes—
236C2×C127#235914yes—
237C22×#117C2×C12711yescharacteristic
238C2×#381C2×C12711yescharacteristic
239C2×C4×C22⋊C4C2×C12712yes—
240C22×#95C2×C12711yescharacteristic
241#1436C2×C12714yescomplemented
242#1434C2×C12712yescomplemented
243C22⋊#95C2×C12712yes—
244C4×#95C2×C12712yescomplemented
245C127#1379911yescharacteristic, direct product factor, Sylow
246C24×C4C22×C12712yes—
247C24×C4C22×C12711yescharacteristic
248C2×#117—28no—
249C2×#117C4×C12718yescomplemented
250C22×C4⋊C4C22×C12712yes—
251C22×C22⋊C4C22×C12711yescharacteristic
252C22×C22⋊C4C22×C12712yes—
253C22×C22⋊C4C22×C12711yescharacteristic
254C22×C42C22×C12714yes—
255C22×C42C22×C12712yes—
256#381C4×C12718yescomplemented
257C4×C22⋊C4—28no—
258C2×#95C4×C12718yescomplemented
259C2×#95C22×C12714yes—
260C2×#95C22×C12714yes—
261C2×#95C22×C12714yes—
262C2×#95C22×C12711yescharacteristic
263C2×#95C22×C12711yescharacteristic
264C2×#95C22×C12712yes—
265C2×#95C22×C12712yes—
266C2×#95C22×C12712yes—
267C25C23×C12711yescharacteristic
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—28no—
273C23×C4—44no—
274C23×C4C2×C4×C12718yes—
275C23×C4C2×C4×C12714yes—
276C23×C4C2×C4×C12714yes—
277C23×C4C2×C4×C12714yes—
278C23×C4C23×C12712yes—
279C23×C4C23×C12714yes—
280C23×C4C23×C12712yes—
281C23×C4C23×C12711yescharacteristic
282C23×C4C23×C12711yescharacteristic
283C23×C4C23×C12712yes—
284C23×C4C23×C12712yes—
285#117—232no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4C2×C4×C12718yescomplemented
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4C2×C4×C12714yes—
292C2×C22⋊C4C2×C4×C12718yes—
293C2×C22⋊C4C2×C4×C12714yes—
294C2×C22⋊C4D4×C12718yes—
295C2×C42—28no—
296C2×C42—28no—
297C2×C42—28no—
298C2×C42—44no—
299C2×C42C2×C4×C12718yescomplemented
300#95—28no—
301#95—28no—
302#95—44no—
303#95C2×C4×C12714yes—
304#95C2×C4×C12718yes—
305#95C2×C4×C12714yes—
306#95C2×C4×C12718yescomplemented
307#95C2×C4×C12718yescomplemented
308C24—24no—
309C24—22no—
310C24—22no—
311C24C22×C4×C12712yes—
312C24C22×C4×C12712yes—
313C24C22×C4×C12712yes—
314C24C2×D4×C12714yes—
315C24#41×C12714yes—
316C24C24×C12711yescharacteristic
317C22×C4—28no—
318C22×C4—28no—
319C22×C4—216no—
320C22×C4—216no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—24no—
330C22×C4—22no—
331C22×C4—216no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—24no—
336C22×C4—24no—
337C22×C4—24no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—24no—
346C22×C4—216no—
347C22×C4—48no—
348C22×C4—416no—
349C22×C4—416no—
350C22×C4C42×C127116yescomplemented
351C22×C4C22×C4×C12714yes—
352C22×C4C22×C4×C12718yes—
353C22×C4C22×C4×C12714yes—
354C22×C4C22×C4×C12712yes—
355C22×C4C22×C4×C12712yes—
356C22×C4C22×C4×C12712yes—
357C22×C4C22×C4×C12712yes—
358C22×C4C22×C4×C12712yes—
359C22×C4C22×C4×C12712yes—
360C22×C4C22×C4×C12714yes—
361C22×C4C22×C4×C12714yes—
362C22×C4C2×D4×C12718yes—
363C22×C4#41×C12718yes—
364C4⋊C4—216no—
365C22⋊C4—28no—
366C22⋊C4—216no—
367C22⋊C4C22⋊C4×C127116yes—
368C42—216no—
369C42—416no—
370C23—24no—
371C23—24no—
372C23—24no—
373C23—22no—
374C23—22no—
375C23—24no—
376C23—24no—
377C23—28no—
378C23—28no—
379C23—28no—
380C23—28no—
381C23C2×C42×C12714yes—
382C23C2×C22⋊C4×C12714yes—
383C23#117×C12714yes—
384C23C4×D4×C12718yes—
385C23C4×D4×C12718yes—
386C23C23×C4×C12711yescharacteristic
387C23C23×C4×C12711yescharacteristic
388C23C23×C4×C12711yescharacteristic
389C23C22×D4×C12712yes—
390C23C2×#41×C12712yes—
391C23C2×#41×C12714yes—
392C23H(5,𝔽2)×C12712yes—
393C232−1+4×C12712yes—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—24no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—28no—
407C2×C4—28no—
408C2×C4—28no—
409C2×C4—28no—
410C2×C4—232no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—28no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—28no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—28no—
420C2×C4—432no—
421C2×C4—44no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—44no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4C2×C42×C12714yes—
430C2×C4C2×C42×C12714yes—
431C2×C4C2×C22⋊C4×C12718yes—
432C2×C4#117×C12718yescomplemented
433C22—28no—
434C22—28no—
435C22—28no—
436C22—28no—
437C22—216no—
438C22—24no—
439C22—24no—
440C22C4×C22⋊C4×C12718yes—
441C22C22×C42×C12711yescharacteristic
442C22C22×C22⋊C4×C12711yescharacteristic
443C22C2×#117×C12712yes—
444C22C2×#117×C12711yescharacteristic
445C22C2×C4×D4×C12712yes—
446C22C2×C4×D4×C12712yes—
447C22C4×#41×C12712yes—
448C22C4×#41×C12712yes—
449C22#518×C12711yescharacteristic
450C22#519×C12711yescharacteristic
451C22#520×C12712yes—
452C22#520×C12712yes—
453C22#546×C12714yes—
454C22#547×C12714yes—
455C22#551×C12714yes—
456C22#552×C12714yes—
457C4—28no—
458C4—28no—
459C4—24no—
460C4—24no—
461C4—44no—
462C4—44no—
463C4—48no—
464C2—28no—
465C2C2×C4×C22⋊C4×C12711yescharacteristic
466C2C4×#117×C12711yescharacteristic
467C2C127×#227411yescharacteristic
468C2C127×#233912yes—
469C2C127×#234212yes—
470C2C127×#234312yes—
471C2C127×#234412yes—
472C2C127×#235914yes—
subgroupG/H
center, socleC24×C127C24
commutatorC22C22×C42×C127
Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
5. C127×#1436C2semidirect
6. C127×#1434C2semidirect
8. C4×#95×C127C2semidirect
12. C2×#117×C127C4semidirect
19. #381×C127C4semidirect
21. C2×#95×C127C4semidirect
50. C2×C4⋊C4×C127C2×C4semidirect
62. C2×C42×C127C2×C4semidirect
69. #95×C127C2×C4semidirect
70. #95×C127C2×C4semidirect
113. C22×C4×C127C42semidirect
195. C2×C4×C127#117semidirect
227. #13799C127direct (N × H)
241. #1436C2×C127semidirect
242. #1434C2×C127semidirect
244. C4×#95C2×C127semidirect
245. C127#13799direct (N × H)
249. C2×#117C4×C127semidirect
256. #381C4×C127semidirect
258. C2×#95C4×C127semidirect
287. C2×C4⋊C4C2×C4×C127semidirect
299. C2×C42C2×C4×C127semidirect
306. #95C2×C4×C127semidirect
307. #95C2×C4×C127semidirect
350. C22×C4C42×C127semidirect
432. C2×C4#117×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×#381×C1272
C2×C4×C22⋊C4×C1272
C22×#95×C1272
C127×#14362
C127×#14342
C127×C22⋊#952
C4×#95×C1272
#13799127