Finite Group Databasebeta

← C127×#13956 #44577629

Subgroups — C127×#13956 #44577629

Order 32512.

4686 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#41×C127C211yesmaximal, characteristic
2C2×#386×C127C214yesmaximal, complemented
3C2×#381×C127C211yesmaximal, characteristic, complemented
4C22×#95×C127C211yesmaximal, characteristic, complemented
5C127×#1446C212yesmaximal, complemented
6C127×#1438C212yesmaximal, complemented
7C127×C22⋊#95C214yesmaximal, complemented
8C22×#41×C127—216no—
9C22×#41×C127—24no—
10C22×#41×C127—24no—
11C22×#41×C127C418yescomplemented
12C23×Q8×C127C2211yescharacteristic
13C23×D4×C127C2211yescharacteristic
14C23×D4×C127C2212yes—
15C24×C4×C127C2212yes—
16C24×C4×C127C2212yes—
17C24×C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C22⋊C4×C127C2218yes—
20#386×C127—216no—
21#381×C127—24no—
22C2×#95×C127—24no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2218yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C25×C127C2312yes—
29C25×C127C2311yescharacteristic
30C2×#41×C127—264no—
31C2×#41×C127—264no—
32C2×#41×C127—264no—
33C2×#41×C127—232no—
34C22×Q8×C127—28no—
35C22×Q8×C127—22no—
36C22×Q8×C127—22no—
37C22×Q8×C127C2×C414yescomplemented
38C22×D4×C127—28no—
39C22×D4×C127—24no—
40C22×D4×C127—28no—
41C22×D4×C127—24no—
42C22×D4×C127—22no—
43C22×D4×C127—22no—
44C22×D4×C127C2×C418yes—
45C22×D4×C127C2×C414yescomplemented
46C22×D4×C127D4116yes—
47C23×C4×C127—28no—
48C23×C4×C127—28no—
49C23×C4×C127—28no—
50C23×C4×C127—24no—
51C23×C4×C127—24no—
52C23×C4×C127—24no—
53C23×C4×C127—28no—
54C23×C4×C127—28no—
55C23×C4×C127—44no—
56C23×C4×C127C2×C414yes—
57C23×C4×C127C2×C418yescomplemented
58C23×C4×C127D414yes—
59C23×C4×C127D414yes—
60C23×C4×C127C2314yes—
61C23×C4×C127C2314yes—
62C23×C4×C127C2311yescharacteristic
63C23×C4×C127C2311yescharacteristic
64C23×C4×C127C2312yes—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—216no—
67C2×C22⋊C4×C127—28no—
68C2×C22⋊C4×C127—216no—
69C2×C22⋊C4×C127—48no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127—24no—
74#95×C127—216no—
75C24×C127—24no—
76C24×C127—22no—
77C24×C127—22no—
78C24×C127—22no—
79C24×C127—22no—
80C24×C127—24no—
81C24×C127—28no—
82C24×C127—24no—
83C24×C127—24no—
84C24×C127C22×C414yes—
85C24×C127C22×C412yes—
86C24×C127C2×D418yes—
87C24×C127C2×D412yes—
88C24×C127C2×D418yes—
89C24×C127C2×D412yes—
90C24×C127C2411yescharacteristic
91#41×C127—2256no—
92C2×Q8×C127—216no—
93C2×Q8×C127—216no—
94C2×Q8×C127—216no—
95C2×Q8×C127—28no—
96C2×D4×C127—216no—
97C2×D4×C127—216no—
98C2×D4×C127—216no—
99C2×D4×C127—216no—
100C2×D4×C127—216no—
101C2×D4×C127—232no—
102C2×D4×C127—232no—
103C2×D4×C127—28no—
104C2×D4×C127C22⋊C4132yescomplemented
105C22×C4×C127—232no—
106C22×C4×C127—232no—
107C22×C4×C127—216no—
108C22×C4×C127—216no—
109C22×C4×C127—216no—
110C22×C4×C127—216no—
111C22×C4×C127—24no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—216no—
117C22×C4×C127—216no—
118C22×C4×C127—216no—
119C22×C4×C127—24no—
120C22×C4×C127—28no—
121C22×C4×C127—24no—
122C22×C4×C127—28no—
123C22×C4×C127—24no—
124C22×C4×C127—28no—
125C22×C4×C127—28no—
126C22×C4×C127—24no—
127C22×C4×C127—24no—
128C22×C4×C127—432no—
129C22×C4×C127—48no—
130C22×C4×C127—48no—
131C22×C4×C127C22⋊C4116yescomplemented
132C22×C4×C127C22×C412yes—
133C22×C4×C127C22×C412yes—
134C22×C4×C127C22×C414yes—
135C22×C4×C127C2×D412yes—
136C22×C4×C127C2×D412yes—
137C22×C4×C127C2×D418yes—
138C22×C4×C127C2×D412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127#4118yescomplemented
141C22⋊C4×C127—432no—
142C22⋊C4×C127—48no—
143C23×C127—24no—
144C23×C127—24no—
145C23×C127—24no—
146C23×C127—24no—
147C23×C127—22no—
148C23×C127—22no—
149C23×C127—24no—
150C23×C127—216no—
151C23×C127—216no—
152C23×C127—24no—
153C23×C127—24no—
154C23×C127—28no—
155C23×C127—28no—
156C23×C127—28no—
157C23×C127—28no—
158C23×C127—216no—
159C23×C127—216no—
160C23×C127—44no—
161C23×C127—44no—
162C23×C127—42no—
163C23×C127—42no—
164C23×C127—44no—
165C23×C127—48no—
166C23×C127—48no—
167C23×C127C2×C22⋊C418yes—
168C23×C127C2×C22⋊C418yes—
169C23×C127C2×C22⋊C414yes—
170C23×C127#12018yes—
171C23×C127#12018yes—
172C23×C127C23×C411yescharacteristic
173C23×C127C22×D411yescharacteristic
174C23×C127C22×D411yescharacteristic
175C23×C127C22×D414yes—
176C23×C127C2×#4114yes—
177C23×C127H(5,𝔽2)12yes—
178C23×C1272−1+412yes—
179Q8×C127—232no—
180D4×C127—232no—
181D4×C127—264no—
182C2×C4×C127—264no—
183C2×C4×C127—24no—
184C2×C4×C127—24no—
185C2×C4×C127—24no—
186C2×C4×C127—24no—
187C2×C4×C127—24no—
188C2×C4×C127—24no—
189C2×C4×C127—28no—
190C2×C4×C127—24no—
191C2×C4×C127—28no—
192C2×C4×C127—24no—
193C2×C4×C127—232no—
194C2×C4×C127—28no—
195C2×C4×C127—216no—
196C2×C4×C127—432no—
197C2×C4×C127—44no—
198C2×C4×C127—44no—
199C2×C4×C127—48no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—44no—
203C2×C4×C127—48no—
204C2×C4×C127—48no—
205C2×C4×C127C2×C22⋊C414yes—
206C2×C4×C127C2×C22⋊C418yes—
207C2×C4×C127C2×C22⋊C414yes—
208C22×C127—24no—
209C22×C127—216no—
210C22×C127—28no—
211C22×C127—28no—
212C22×C127—216no—
213C22×C127—24no—
214C22×C127—216no—
215C22×C127—28no—
216C22×C127—44no—
217C22×C127—48no—
218C22×C127—48no—
219C22×C127—48no—
220C22×C127—416no—
221C22×C127—44no—
222C22×C127#37918yes—
223C22×C127C22×C22⋊C411yescharacteristic
224C22×C127C22×C22⋊C412yes—
225C22×C127C4×#4112yes—
226C22×C127#52012yes—
227C22×C127C2×#12012yes—
228C22×C127C2×#12012yes—
229C22×C127#52512yes—
230C22×C127#53212yes—
231C22×C127#53511yescharacteristic
232C22×C127#53611yescharacteristic
233C22×C127#53712yes—
234C22×C127#54618yes—
235C22×C127#54718yes—
236C4×C127—24no—
237C4×C127—28no—
238C4×C127—24no—
239C4×C127—48no—
240C4×C127—84no—
241#13956C12711yesmaximal, characteristic, direct product factor, Sylow
242C2×C127—28no—
243C2×C127—48no—
244C2×C127C2×#37911yescharacteristic
245C2×C127#229711yescharacteristic
246C2×C127#231111yescharacteristic
247C2×C127#233914yes—
248C2×C127#240412yes—
249C2×C127#240612yes—
250C2×C127#243014yes—
251C23×#41C2×C12711yescharacteristic
252C2×#386C2×C12714yescomplemented
253C2×#381C2×C12711yescharacteristic, complemented
254C22×#95C2×C12711yescharacteristic, complemented
255#1446C2×C12712yescomplemented
256#1438C2×C12712yescomplemented
257C22⋊#95C2×C12714yescomplemented
258C127#1395611yescharacteristic, direct product factor, Sylow
259C22×#41—216no—
260C22×#41—24no—
261C22×#41—24no—
262C22×#41C4×C12718yescomplemented
263C23×Q8C22×C12711yescharacteristic
264C23×D4C22×C12711yescharacteristic
265C23×D4C22×C12712yes—
266C24×C4C22×C12712yes—
267C24×C4C22×C12712yes—
268C24×C4C22×C12711yescharacteristic
269C22×C22⋊C4C22×C12712yes—
270C22×C22⋊C4C22×C12718yes—
271#386—216no—
272#381—24no—
273C2×#95—24no—
274C2×#95C22×C12712yes—
275C2×#95C22×C12712yes—
276C2×#95C22×C12718yes—
277C2×#95C22×C12712yes—
278C2×#95C22×C12712yes—
279C25C23×C12712yes—
280C25C23×C12711yescharacteristic
281C2×#41—264no—
282C2×#41—264no—
283C2×#41—264no—
284C2×#41—232no—
285C22×Q8—28no—
286C22×Q8—22no—
287C22×Q8—22no—
288C22×Q8C2×C4×C12714yescomplemented
289C22×D4—28no—
290C22×D4—24no—
291C22×D4—28no—
292C22×D4—24no—
293C22×D4—22no—
294C22×D4—22no—
295C22×D4C2×C4×C12718yes—
296C22×D4C2×C4×C12714yescomplemented
297C22×D4D4×C127116yes—
298C23×C4—28no—
299C23×C4—28no—
300C23×C4—28no—
301C23×C4—24no—
302C23×C4—24no—
303C23×C4—24no—
304C23×C4—28no—
305C23×C4—28no—
306C23×C4—44no—
307C23×C4C2×C4×C12714yes—
308C23×C4C2×C4×C12718yescomplemented
309C23×C4D4×C12714yes—
310C23×C4D4×C12714yes—
311C23×C4C23×C12714yes—
312C23×C4C23×C12714yes—
313C23×C4C23×C12711yescharacteristic
314C23×C4C23×C12711yescharacteristic
315C23×C4C23×C12712yes—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—216no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—216no—
320C2×C22⋊C4—48no—
321#95—24no—
322#95—24no—
323#95—24no—
324#95—24no—
325#95—216no—
326C24—24no—
327C24—22no—
328C24—22no—
329C24—22no—
330C24—22no—
331C24—24no—
332C24—28no—
333C24—24no—
334C24—24no—
335C24C22×C4×C12714yes—
336C24C22×C4×C12712yes—
337C24C2×D4×C12718yes—
338C24C2×D4×C12712yes—
339C24C2×D4×C12718yes—
340C24C2×D4×C12712yes—
341C24C24×C12711yescharacteristic
342#41—2256no—
343C2×Q8—216no—
344C2×Q8—216no—
345C2×Q8—216no—
346C2×Q8—28no—
347C2×D4—216no—
348C2×D4—216no—
349C2×D4—216no—
350C2×D4—216no—
351C2×D4—216no—
352C2×D4—232no—
353C2×D4—232no—
354C2×D4—28no—
355C2×D4C22⋊C4×C127132yescomplemented
356C22×C4—232no—
357C22×C4—232no—
358C22×C4—216no—
359C22×C4—216no—
360C22×C4—216no—
361C22×C4—216no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—24no—
367C22×C4—216no—
368C22×C4—216no—
369C22×C4—216no—
370C22×C4—24no—
371C22×C4—28no—
372C22×C4—24no—
373C22×C4—28no—
374C22×C4—24no—
375C22×C4—28no—
376C22×C4—28no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—432no—
380C22×C4—48no—
381C22×C4—48no—
382C22×C4C22⋊C4×C127116yescomplemented
383C22×C4C22×C4×C12712yes—
384C22×C4C22×C4×C12712yes—
385C22×C4C22×C4×C12714yes—
386C22×C4C2×D4×C12712yes—
387C22×C4C2×D4×C12712yes—
388C22×C4C2×D4×C12718yes—
389C22×C4C2×D4×C12712yes—
390C22×C4C2×D4×C12712yes—
391C22×C4#41×C12718yescomplemented
392C22⋊C4—432no—
393C22⋊C4—48no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23—24no—
398C23—22no—
399C23—22no—
400C23—24no—
401C23—216no—
402C23—216no—
403C23—24no—
404C23—24no—
405C23—28no—
406C23—28no—
407C23—28no—
408C23—28no—
409C23—216no—
410C23—216no—
411C23—44no—
412C23—44no—
413C23—42no—
414C23—42no—
415C23—44no—
416C23—48no—
417C23—48no—
418C23C2×C22⋊C4×C12718yes—
419C23C2×C22⋊C4×C12718yes—
420C23C2×C22⋊C4×C12714yes—
421C23#120×C12718yes—
422C23#120×C12718yes—
423C23C23×C4×C12711yescharacteristic
424C23C22×D4×C12711yescharacteristic
425C23C22×D4×C12711yescharacteristic
426C23C22×D4×C12714yes—
427C23C2×#41×C12714yes—
428C23H(5,𝔽2)×C12712yes—
429C232−1+4×C12712yes—
430Q8—232no—
431D4—232no—
432D4—264no—
433C2×C4—264no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—28no—
441C2×C4—24no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—232no—
445C2×C4—28no—
446C2×C4—216no—
447C2×C4—432no—
448C2×C4—44no—
449C2×C4—44no—
450C2×C4—48no—
451C2×C4—44no—
452C2×C4—44no—
453C2×C4—44no—
454C2×C4—48no—
455C2×C4—48no—
456C2×C4C2×C22⋊C4×C12714yes—
457C2×C4C2×C22⋊C4×C12718yes—
458C2×C4C2×C22⋊C4×C12714yes—
459C22—216no—
460C22—28no—
461C22—28no—
462C22—216no—
463C22—24no—
464C22—24no—
465C22—216no—
466C22—28no—
467C22—48no—
468C22—48no—
469C22—48no—
470C22—416no—
471C22—44no—
472C22—44no—
473C22#379×C12718yes—
474C22C22×C22⋊C4×C12712yes—
475C22C22×C22⋊C4×C12711yescharacteristic
476C22C4×#41×C12712yes—
477C22#520×C12712yes—
478C22C2×#120×C12712yes—
479C22C2×#120×C12712yes—
480C22#525×C12712yes—
481C22#532×C12712yes—
482C22#535×C12711yescharacteristic
483C22#536×C12711yescharacteristic
484C22#537×C12712yes—
485C22#546×C12718yes—
486C22#547×C12718yes—
487C4—24no—
488C4—28no—
489C4—24no—
490C4—48no—
491C4—84no—
492C2—28no—
493C2—48no—
494C2C2×#379×C12711yescharacteristic
495C2C127×#229711yescharacteristic
496C2C127×#231111yescharacteristic
497C2C127×#233914yes—
498C2C127×#240412yes—
499C2C127×#240612yes—
500C2C127×#243014yes—
subgroupG/H
center, socleC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
prime radicalC23×#41×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#386×C127C2semidirect
3. C2×#381×C127C2semidirect
4. C22×#95×C127C2semidirect
5. C127×#1446C2semidirect
6. C127×#1438C2semidirect
7. C127×C22⋊#95C2semidirect
11. C22×#41×C127C4semidirect
37. C22×Q8×C127C2×C4semidirect
45. C22×D4×C127C2×C4semidirect
57. C23×C4×C127C2×C4semidirect
104. C2×D4×C127C22⋊C4semidirect
131. C22×C4×C127C22⋊C4semidirect
140. C22×C4×C127#41semidirect
241. #13956C127direct (N × H)
252. C2×#386C2×C127semidirect
253. C2×#381C2×C127semidirect
254. C22×#95C2×C127semidirect
255. #1446C2×C127semidirect
256. #1438C2×C127semidirect
257. C22⋊#95C2×C127semidirect
258. C127#13956direct (N × H)
262. C22×#41C4×C127semidirect
288. C22×Q8C2×C4×C127semidirect
296. C22×D4C2×C4×C127semidirect
308. C23×C4C2×C4×C127semidirect
355. C2×D4C22⋊C4×C127semidirect
382. C22×C4C22⋊C4×C127semidirect
391. C22×C4#41×C127semidirect

Maximal subgroups

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

subgroupindex
C23×#41×C1272
C2×#386×C1272
C2×#381×C1272
C22×#95×C1272
C127×#14462
C127×#14382
C127×C22⋊#952
#13956127