Finite Group Databasebeta

← C127×#13940 #44577613

Subgroups — C127×#13940 #44577613

Order 32512.

2230 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C127C211yesmaximal, characteristic
2C2×#381×C127C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
4C127×#1440C212yesmaximal, complemented
5C127×#1438C212yesmaximal
6C127×#1437C212yesmaximal, complemented
7C127×#1436C212yesmaximal, complemented
8C127×#1434C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal, complemented
10C23×D4×C127C2211yescharacteristic
11C24×C4×C127C2211yescharacteristic
12C24×C4×C127C2211yescharacteristic
13C2×C4×D4×C127—24no—
14C2×C4×D4×C127—24no—
15C2×C4×D4×C127C418yescomplemented
16C22×C4⋊C4×C127C2211yescharacteristic
17C22×C22⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2214yes—
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22C22×C42×C127C2211yescharacteristic
23C22×C42×C127C2212yes—
24#381×C127—24no—
25C4×C22⋊C4×C127—24no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2214yes—
29C2×#95×C127C2214yes—
30C2×#95×C127C2212yes—
31C2×#95×C127C2214yes—
32C25×C127C2311yescharacteristic
33C25×C127C2311yescharacteristic
34C22×D4×C127—22no—
35C22×D4×C127—22no—
36C22×D4×C127—24no—
37C22×D4×C127—24no—
38C22×D4×C127C2×C414yes—
39C23×C4×C127—22no—
40C23×C4×C127—22no—
41C23×C4×C127—44no—
42C23×C4×C127—44no—
43C23×C4×C127C2×C414yes—
44C23×C4×C127C2×C414yes—
45C23×C4×C127D414yes—
46C23×C4×C127D414yes—
47C23×C4×C127C2314yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2314yes—
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C4×D4×C127—232no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127C2×C414yes—
58C2×C22⋊C4×C127—22no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—22no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—28no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—28no—
66C2×C22⋊C4×C127—28no—
67C2×C22⋊C4×C127—44no—
68C2×C22⋊C4×C127—44no—
69C2×C22⋊C4×C127C2×C414yes—
70C2×C22⋊C4×C127C2×C414yes—
71C2×C42×C127—22no—
72C2×C42×C127—22no—
73C2×C42×C127—24no—
74C2×C42×C127—44no—
75C2×C42×C127C2×C414yes—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—24no—
79#95×C127—28no—
80#95×C127—28no—
81#95×C127—44no—
82C24×C127—21no—
83C24×C127—21no—
84C24×C127—24no—
85C24×C127—24no—
86C24×C127—22no—
87C24×C127—22no—
88C24×C127—22no—
89C24×C127—24no—
90C24×C127—24no—
91C24×C127C22×C412yes—
92C24×C127C22×C412yes—
93C24×C127C2×D412yes—
94C24×C127C2×D412yes—
95C24×C127#4114yes—
96C24×C127C2411yescharacteristic
97C2×D4×C127—216no—
98C2×D4×C127—216no—
99C2×D4×C127—28no—
100C2×D4×C127—28no—
101C2×D4×C127—28no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—22no—
105C22×C4×C127—24no—
106C22×C4×C127—24no—
107C22×C4×C127—24no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—24no—
113C22×C4×C127—24no—
114C22×C4×C127—24no—
115C22×C4×C127—24no—
116C22×C4×C127—24no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—28no—
120C22×C4×C127—24no—
121C22×C4×C127—24no—
122C22×C4×C127—24no—
123C22×C4×C127—24no—
124C22×C4×C127—24no—
125C22×C4×C127—24no—
126C22×C4×C127—24no—
127C22×C4×C127—48no—
128C22×C4×C127—48no—
129C22×C4×C127—48no—
130C22×C4×C127—48no—
131C22×C4×C127—48no—
132C22×C4×C127—48no—
133C22×C4×C127C22⋊C4116yescomplemented
134C22×C4×C127C22×C412yes—
135C22×C4×C127C22×C412yes—
136C22×C4×C127C22×C412yes—
137C22×C4×C127C22×C412yes—
138C22×C4×C127C22×C412yes—
139C22×C4×C127C2×D412yes—
140C22×C4×C127C2×D412yes—
141C22×C4×C127C2×D412yes—
142C22×C4×C127C2×D412yes—
143C22×C4×C127#4118yes—
144C22×C4×C127#4114yes—
145C4⋊C4×C127—28no—
146C22⋊C4×C127—216no—
147C22⋊C4×C127—28no—
148C22⋊C4×C127—28no—
149C22⋊C4×C127—416no—
150C22⋊C4×C127—48no—
151C42×C127—28no—
152C42×C127—48no—
153C23×C127—22no—
154C23×C127—22no—
155C23×C127—22no—
156C23×C127—22no—
157C23×C127—24no—
158C23×C127—24no—
159C23×C127—24no—
160C23×C127—24no—
161C23×C127—24no—
162C23×C127—24no—
163C23×C127—24no—
164C23×C127—24no—
165C23×C127—24no—
166C23×C127—24no—
167C23×C127—24no—
168C23×C127—24no—
169C23×C127—28no—
170C23×C127—28no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—42no—
174C23×C127—42no—
175C23×C127—44no—
176C23×C127—44no—
177C23×C127—44no—
178C23×C127—44no—
179C23×C127—44no—
180C23×C127—44no—
181C23×C127C2×C22⋊C414yes—
182C23×C127#11714yes—
183C23×C127C23×C411yescharacteristic
184C23×C127C22×D411yescharacteristic
185C23×C127C22×D411yescharacteristic
186C23×C127C2×#4112yes—
187C23×C127C2×#4112yes—
188C23×C127C2×#4114yes—
189C23×C127H(5,𝔽2)14yes—
190D4×C127—232no—
191C2×C4×C127—22no—
192C2×C4×C127—22no—
193C2×C4×C127—24no—
194C2×C4×C127—24no—
195C2×C4×C127—24no—
196C2×C4×C127—24no—
197C2×C4×C127—24no—
198C2×C4×C127—24no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—28no—
206C2×C4×C127—28no—
207C2×C4×C127—28no—
208C2×C4×C127—416no—
209C2×C4×C127—416no—
210C2×C4×C127—44no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—44no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—44no—
217C2×C4×C127—44no—
218C2×C4×C127—44no—
219C2×C4×C127—44no—
220C2×C4×C127—44no—
221C2×C4×C127—44no—
222C2×C4×C127—44no—
223C2×C4×C127—44no—
224C2×C4×C127—44no—
225C2×C4×C127C2×C22⋊C414yes—
226C2×C4×C127C2×C22⋊C414yes—
227C2×C4×C127#11714yes—
228C22×C127—24no—
229C22×C127—28no—
230C22×C127—24no—
231C22×C127—24no—
232C22×C127—24no—
233C22×C127—42no—
234C22×C127—48no—
235C22×C127—48no—
236C22×C127—48no—
237C22×C127—48no—
238C22×C127—44no—
239C22×C127—44no—
240C22×C127—44no—
241C22×C127—42no—
242C22×C127C22×C22⋊C411yescharacteristic
243C22×C127C2×#11711yescharacteristic
244C22×C127C2×#11711yescharacteristic
245C22×C127C4×#4112yes—
246C22×C127#51812yes—
247C22×C127#52512yes—
248C22×C127#52512yes—
249C22×C127#52512yes—
250C22×C127#53212yes—
251C22×C127#53412yes—
252C22×C127#53412yes—
253C22×C127#55114yes—
254C22×C127#55314yes—
255C22×C127#55314yes—
256C22×C127#55914yes—
257C4×C127—24no—
258C4×C127—24no—
259C4×C127—24no—
260C4×C127—42no—
261C4×C127—48no—
262C4×C127—42no—
263C4×C127—84no—
264#13940C12711yesmaximal, characteristic, direct product factor, Sylow
265C2×C127—44no—
266C2×C127—44no—
267C2×C127#228011yescharacteristic
268C2×C127#229711yescharacteristic
269C2×C127#230811yescharacteristic
270C2×C127#235312yes—
271C2×C127#235712yes—
272C2×C127#260014yes—
273C2×C127#260214yes—
274C22×C4×D4C2×C12711yescharacteristic
275C2×#381C2×C12711yescharacteristic, complemented
276C2×C4×C22⋊C4C2×C12711yescharacteristic, complemented
277#1440C2×C12712yescomplemented
278#1438C2×C12712yes—
279#1437C2×C12712yescomplemented
280#1436C2×C12712yescomplemented
281#1434C2×C12712yescomplemented
282C22⋊#95C2×C12712yescomplemented
283C127#1394011yescharacteristic, direct product factor, Sylow
284C23×D4C22×C12711yescharacteristic
285C24×C4C22×C12711yescharacteristic
286C24×C4C22×C12711yescharacteristic
287C2×C4×D4—24no—
288C2×C4×D4—24no—
289C2×C4×D4C4×C12718yescomplemented
290C22×C4⋊C4C22×C12711yescharacteristic
291C22×C22⋊C4C22×C12712yes—
292C22×C22⋊C4C22×C12714yes—
293C22×C22⋊C4C22×C12711yescharacteristic
294C22×C22⋊C4C22×C12711yescharacteristic
295C22×C22⋊C4C22×C12712yes—
296C22×C42C22×C12711yescharacteristic
297C22×C42C22×C12712yes—
298#381—24no—
299C4×C22⋊C4—24no—
300C2×#95C22×C12712yes—
301C2×#95C22×C12712yes—
302C2×#95C22×C12714yes—
303C2×#95C22×C12714yes—
304C2×#95C22×C12712yes—
305C2×#95C22×C12714yes—
306C25C23×C12711yescharacteristic
307C25C23×C12711yescharacteristic
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4C2×C4×C12714yes—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—44no—
316C23×C4—44no—
317C23×C4C2×C4×C12714yes—
318C23×C4C2×C4×C12714yes—
319C23×C4D4×C12714yes—
320C23×C4D4×C12714yes—
321C23×C4C23×C12714yes—
322C23×C4C23×C12711yescharacteristic
323C23×C4C23×C12711yescharacteristic
324C23×C4C23×C12714yes—
325C23×C4C23×C12711yescharacteristic
326C23×C4C23×C12711yescharacteristic
327C23×C4C23×C12711yescharacteristic
328C4×D4—232no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4C2×C4×C12714yes—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4C2×C4×C12714yes—
344C2×C22⋊C4C2×C4×C12714yes—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—24no—
348C2×C42—44no—
349C2×C42C2×C4×C12714yes—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—28no—
354#95—28no—
355#95—44no—
356C24—21no—
357C24—21no—
358C24—24no—
359C24—24no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—24no—
364C24—24no—
365C24C22×C4×C12712yes—
366C24C22×C4×C12712yes—
367C24C2×D4×C12712yes—
368C24C2×D4×C12712yes—
369C24#41×C12714yes—
370C24C24×C12711yescharacteristic
371C2×D4—216no—
372C2×D4—216no—
373C2×D4—28no—
374C2×D4—28no—
375C2×D4—28no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—28no—
394C22×C4—24no—
395C22×C4—24no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—48no—
402C22×C4—48no—
403C22×C4—48no—
404C22×C4—48no—
405C22×C4—48no—
406C22×C4—48no—
407C22×C4C22⋊C4×C127116yescomplemented
408C22×C4C22×C4×C12712yes—
409C22×C4C22×C4×C12712yes—
410C22×C4C22×C4×C12712yes—
411C22×C4C22×C4×C12712yes—
412C22×C4C22×C4×C12712yes—
413C22×C4C2×D4×C12712yes—
414C22×C4C2×D4×C12712yes—
415C22×C4C2×D4×C12712yes—
416C22×C4C2×D4×C12712yes—
417C22×C4#41×C12718yes—
418C22×C4#41×C12714yes—
419C4⋊C4—28no—
420C22⋊C4—216no—
421C22⋊C4—28no—
422C22⋊C4—28no—
423C22⋊C4—416no—
424C22⋊C4—48no—
425C42—28no—
426C42—48no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—24no—
432C23—24no—
433C23—24no—
434C23—24no—
435C23—24no—
436C23—24no—
437C23—24no—
438C23—24no—
439C23—24no—
440C23—24no—
441C23—24no—
442C23—24no—
443C23—28no—
444C23—28no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—44no—
453C23—44no—
454C23—44no—
455C23C2×C22⋊C4×C12714yes—
456C23#117×C12714yes—
457C23C23×C4×C12711yescharacteristic
458C23C22×D4×C12711yescharacteristic
459C23C22×D4×C12711yescharacteristic
460C23C2×#41×C12712yes—
461C23C2×#41×C12712yes—
462C23C2×#41×C12714yes—
463C23H(5,𝔽2)×C12714yes—
464D4—232no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—28no—
480C2×C4—28no—
481C2×C4—28no—
482C2×C4—416no—
483C2×C4—416no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—44no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—44no—
495C2×C4—44no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4C2×C22⋊C4×C12714yes—
500C2×C4C2×C22⋊C4×C12714yes—
501C2×C4#117×C12714yes—
502C22—28no—
503C22—24no—
504C22—24no—
505C22—24no—
506C22—24no—
507C22—48no—
508C22—48no—
509C22—48no—
510C22—48no—
511C22—44no—
512C22—44no—
513C22—44no—
514C22—42no—
515C22—42no—
516C22C22×C22⋊C4×C12711yescharacteristic
517C22C2×#117×C12711yescharacteristic
518C22C2×#117×C12711yescharacteristic
519C22C4×#41×C12712yes—
520C22#518×C12712yes—
521C22#525×C12712yes—
522C22#525×C12712yes—
523C22#525×C12712yes—
524C22#532×C12712yes—
525C22#534×C12712yes—
526C22#534×C12712yes—
527C22#551×C12714yes—
528C22#553×C12714yes—
529C22#553×C12714yes—
530C22#559×C12714yes—
531C4—24no—
532C4—24no—
533C4—24no—
534C4—48no—
535C4—42no—
536C4—42no—
537C4—84no—
538C2—44no—
539C2—44no—
540C2C127×#228011yescharacteristic
541C2C127×#229711yescharacteristic
542C2C127×#230811yescharacteristic
543C2C127×#235312yes—
544C2C127×#235712yes—
545C2C127×#260014yes—
546C2C127×#260214yes—
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
2. C2×#381×C127C2semidirect
3. C2×C4×C22⋊C4×C127C2semidirect
4. C127×#1440C2semidirect
6. C127×#1437C2semidirect
7. C127×#1436C2semidirect
8. C127×#1434C2semidirect
9. C127×C22⋊#95C2semidirect
15. C2×C4×D4×C127C4semidirect
133. C22×C4×C127C22⋊C4semidirect
264. #13940C127direct (N × H)
275. C2×#381C2×C127semidirect
276. C2×C4×C22⋊C4C2×C127semidirect
277. #1440C2×C127semidirect
279. #1437C2×C127semidirect
280. #1436C2×C127semidirect
281. #1434C2×C127semidirect
282. C22⋊#95C2×C127semidirect
283. C127#13940direct (N × H)
289. C2×C4×D4C4×C127semidirect
407. C22×C4C22⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1272
C2×#381×C1272
C2×C4×C22⋊C4×C1272
C127×#14402
C127×#14382
C127×#14372
C127×#14362
C127×#14342
C127×C22⋊#952
#13940127