Finite Group Databasebeta

← C127×#14344 #44578017

Subgroups — C127×#14344 #44578017

Order 32512.

2150 conjugacy classes of subgroups.

The subgroup lattice has 570 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×#380×C127C211yesmaximal, characteristic, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1440C212yesmaximal, complemented
6C127×#1439C212yesmaximal, complemented
7C127×#1438C212yesmaximal
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×C4⋊C4×C127C2212yes—
18C22×C22⋊C4×C127C2211yescharacteristic
19C22×C22⋊C4×C127C2211yescharacteristic
20C22×C22⋊C4×C127C2214yes—
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2212yes—
23C22×C42×C127C2211yescharacteristic
24#381×C127—24no—
25#380×C127—24no—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2214yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2214yes—
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×C127C2314yes—
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
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×C127—24no—
58C2×C4⋊C4×C127—44no—
59C2×C4⋊C4×C127C2×C414yes—
60C2×C22⋊C4×C127—22no—
61C2×C22⋊C4×C127—22no—
62C2×C22⋊C4×C127—22no—
63C2×C22⋊C4×C127—22no—
64C2×C22⋊C4×C127—24no—
65C2×C22⋊C4×C127—24no—
66C2×C22⋊C4×C127—28no—
67C2×C22⋊C4×C127—44no—
68C2×C22⋊C4×C127—44no—
69C2×C22⋊C4×C127—44no—
70C2×C22⋊C4×C127—44no—
71C2×C22⋊C4×C127C2×C414yes—
72C2×C22⋊C4×C127C2×C414yes—
73C2×C42×C127—22no—
74C2×C42×C127—22no—
75C2×C42×C127C2×C414yes—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—24no—
79#95×C127—28no—
80#95×C127—44no—
81#95×C127—44no—
82C24×C127—21no—
83C24×C127—21no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—22no—
87C24×C127—22no—
88C24×C127—22no—
89C24×C127—24no—
90C24×C127—24no—
91C24×C127—22no—
92C24×C127—22no—
93C24×C127C22×C412yes—
94C24×C127C22×C412yes—
95C24×C127C2×D412yes—
96C24×C127C2×D412yes—
97C24×C127#4114yes—
98C24×C127C2411yescharacteristic
99C2×D4×C127—216no—
100C2×D4×C127—216no—
101C2×D4×C127—28no—
102C2×D4×C127—28no—
103C2×D4×C127—28no—
104C22×C4×C127—21no—
105C22×C4×C127—21no—
106C22×C4×C127—22no—
107C22×C4×C127—24no—
108C22×C4×C127—24no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—21no—
113C22×C4×C127—22no—
114C22×C4×C127—24no—
115C22×C4×C127—22no—
116C22×C4×C127—28no—
117C22×C4×C127—24no—
118C22×C4×C127—24no—
119C22×C4×C127—24no—
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—24no—
128C22×C4×C127—24no—
129C22×C4×C127—24no—
130C22×C4×C127—24no—
131C22×C4×C127—48no—
132C22×C4×C127—48no—
133C22×C4×C127—48no—
134C22×C4×C127—48no—
135C22×C4×C127—48no—
136C22×C4×C127—48no—
137C22×C4×C127C22⋊C4116yescomplemented
138C22×C4×C127C22×C412yes—
139C22×C4×C127C22×C412yes—
140C22×C4×C127C22×C412yes—
141C22×C4×C127C22×C412yes—
142C22×C4×C127C22×C412yes—
143C22×C4×C127C2×D412yes—
144C22×C4×C127C2×D412yes—
145C22×C4×C127C2×D412yes—
146C22×C4×C127C2×D412yes—
147C22×C4×C127#4114yes—
148C4⋊C4×C127—28no—
149C4⋊C4×C127—48no—
150C22⋊C4×C127—28no—
151C22⋊C4×C127—28no—
152C22⋊C4×C127—48no—
153C22⋊C4×C127—48no—
154C22⋊C4×C127—416no—
155C42×C127—28no—
156C23×C127—22no—
157C23×C127—22no—
158C23×C127—22no—
159C23×C127—22no—
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—24no—
170C23×C127—22no—
171C23×C127—22no—
172C23×C127—24no—
173C23×C127—28no—
174C23×C127—28no—
175C23×C127—42no—
176C23×C127—42no—
177C23×C127—41no—
178C23×C127—41no—
179C23×C127—42no—
180C23×C127—44no—
181C23×C127—44no—
182C23×C127—44no—
183C23×C127—44no—
184C23×C127—44no—
185C23×C127—44no—
186C23×C127C2×C22⋊C414yes—
187C23×C127#11714yes—
188C23×C127C23×C411yescharacteristic
189C23×C127C22×D411yescharacteristic
190C23×C127C22×D411yescharacteristic
191C23×C127C2×#4112yes—
192C23×C127C2×#4112yes—
193C23×C127H(5,𝔽2)14yes—
194C23×C127H(5,𝔽2)12yes—
195C23×C1272−1+412yes—
196D4×C127—232no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—24no—
200C2×C4×C127—24no—
201C2×C4×C127—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—22no—
208C2×C4×C127—22no—
209C2×C4×C127—24no—
210C2×C4×C127—24no—
211C2×C4×C127—416no—
212C2×C4×C127—416no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—41no—
216C2×C4×C127—41no—
217C2×C4×C127—42no—
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×C127—44no—
226C2×C4×C127—44no—
227C2×C4×C127—44no—
228C2×C4×C127—44no—
229C2×C4×C127—44no—
230C2×C4×C127—44no—
231C2×C4×C127—44no—
232C2×C4×C127C2×C22⋊C414yes—
233C2×C4×C127C2×C22⋊C414yes—
234C2×C4×C127#11714yes—
235C22×C127—24no—
236C22×C127—24no—
237C22×C127—28no—
238C22×C127—24no—
239C22×C127—24no—
240C22×C127—42no—
241C22×C127—42no—
242C22×C127—44no—
243C22×C127—44no—
244C22×C127—44no—
245C22×C127—48no—
246C22×C127—48no—
247C22×C127—44no—
248C22×C127—44no—
249C22×C127—44no—
250C22×C127—44no—
251C22×C127C22×C22⋊C411yescharacteristic
252C22×C127C2×#11711yescharacteristic
253C22×C127C2×#11711yescharacteristic
254C22×C127#51812yes—
255C22×C127#52012yes—
256C22×C127#52512yes—
257C22×C127#52512yes—
258C22×C127#53412yes—
259C22×C127#53412yes—
260C22×C127#53511yescharacteristic
261C22×C127#53611yescharacteristic
262C22×C127#53712yes—
263C22×C127#53814yes—
264C22×C127#53914yes—
265C22×C127#54014yes—
266C22×C127#54214yes—
267C4×C127—24no—
268C4×C127—24no—
269C4×C127—24no—
270C4×C127—42no—
271C4×C127—42no—
272C4×C127—84no—
273C4×C127—84no—
274#14344C12711yesmaximal, characteristic, direct product factor, Sylow
275C2×C127—44no—
276C2×C127—44no—
277C2×C127#228011yescharacteristic
278C2×C127#230811yescharacteristic
279C2×C127#231111yescharacteristic
280C2×C127#231812yes—
281C2×C127#231912yes—
282C2×C127#263014yes—
283C2×C127#263512yes—
284C2×C127#263812yes—
285C22×C4×D4C2×C12711yescharacteristic
286C2×#381C2×C12711yescharacteristic, complemented
287C2×#380C2×C12711yescharacteristic, complemented
288#1441C2×C12712yescomplemented
289#1440C2×C12712yescomplemented
290#1439C2×C12712yescomplemented
291#1438C2×C12712yes—
292#1434C2×C12712yescomplemented
293C22⋊#95C2×C12712yescomplemented
294C127#1434411yescharacteristic, direct product factor, Sylow
295C23×D4C22×C12711yescharacteristic
296C24×C4C22×C12711yescharacteristic
297C24×C4C22×C12711yescharacteristic
298C2×C4×D4—24no—
299C2×C4×D4—24no—
300C2×C4×D4C4×C12718yescomplemented
301C22×C4⋊C4C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12712yes—
303C22×C22⋊C4C22×C12711yescharacteristic
304C22×C22⋊C4C22×C12711yescharacteristic
305C22×C22⋊C4C22×C12714yes—
306C22×C22⋊C4C22×C12712yes—
307C22×C22⋊C4C22×C12712yes—
308C22×C42C22×C12711yescharacteristic
309#381—24no—
310#380—24no—
311C2×#95C22×C12712yes—
312C2×#95C22×C12712yes—
313C2×#95C22×C12714yes—
314C2×#95C22×C12712yes—
315C2×#95C22×C12714yes—
316C2×#95C22×C12714yes—
317C25C23×C12711yescharacteristic
318C25C23×C12711yescharacteristic
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—24no—
322C22×D4—24no—
323C22×D4C2×C4×C12714yes—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—44no—
327C23×C4—44no—
328C23×C4C2×C4×C12714yes—
329C23×C4C2×C4×C12714yes—
330C23×C4D4×C12714yes—
331C23×C4D4×C12714yes—
332C23×C4C23×C12714yes—
333C23×C4C23×C12714yes—
334C23×C4C23×C12711yescharacteristic
335C23×C4C23×C12711yescharacteristic
336C23×C4C23×C12711yescharacteristic
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C4×D4—232no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×C4×C12714yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×C4×C12714yes—
357C2×C22⋊C4C2×C4×C12714yes—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42C2×C4×C12714yes—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—44no—
366#95—44no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—24no—
375C24—24no—
376C24—22no—
377C24—22no—
378C24C22×C4×C12712yes—
379C24C22×C4×C12712yes—
380C24C2×D4×C12712yes—
381C24C2×D4×C12712yes—
382C24#41×C12714yes—
383C24C24×C12711yescharacteristic
384C2×D4—216no—
385C2×D4—216no—
386C2×D4—28no—
387C2×D4—28no—
388C2×D4—28no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—28no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—48no—
419C22×C4—48no—
420C22×C4—48no—
421C22×C4—48no—
422C22×C4C22⋊C4×C127116yescomplemented
423C22×C4C22×C4×C12712yes—
424C22×C4C22×C4×C12712yes—
425C22×C4C22×C4×C12712yes—
426C22×C4C22×C4×C12712yes—
427C22×C4C22×C4×C12712yes—
428C22×C4C2×D4×C12712yes—
429C22×C4C2×D4×C12712yes—
430C22×C4C2×D4×C12712yes—
431C22×C4C2×D4×C12712yes—
432C22×C4#41×C12714yes—
433C4⋊C4—28no—
434C4⋊C4—48no—
435C22⋊C4—28no—
436C22⋊C4—28no—
437C22⋊C4—48no—
438C22⋊C4—48no—
439C22⋊C4—416no—
440C42—28no—
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—24no—
446C23—24no—
447C23—24no—
448C23—24no—
449C23—24no—
450C23—24no—
451C23—24no—
452C23—24no—
453C23—24no—
454C23—24no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—28no—
459C23—28no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—44no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23C2×C22⋊C4×C12714yes—
472C23#117×C12714yes—
473C23C23×C4×C12711yescharacteristic
474C23C22×D4×C12711yescharacteristic
475C23C22×D4×C12711yescharacteristic
476C23C2×#41×C12712yes—
477C23C2×#41×C12712yes—
478C23H(5,𝔽2)×C12714yes—
479C23H(5,𝔽2)×C12712yes—
480C232−1+4×C12712yes—
481D4—232no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—416no—
497C2×C4—416no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—44no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—44no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4C2×C22⋊C4×C12714yes—
518C2×C4C2×C22⋊C4×C12714yes—
519C2×C4#117×C12714yes—
520C22—28no—
521C22—24no—
522C22—24no—
523C22—24no—
524C22—24no—
525C22—44no—
526C22—44no—
527C22—44no—
528C22—48no—
529C22—48no—
530C22—44no—
531C22—44no—
532C22—44no—
533C22—44no—
534C22—42no—
535C22—42no—
536C22C22×C22⋊C4×C12711yescharacteristic
537C22C2×#117×C12711yescharacteristic
538C22C2×#117×C12711yescharacteristic
539C22#518×C12712yes—
540C22#520×C12712yes—
541C22#525×C12712yes—
542C22#525×C12712yes—
543C22#534×C12712yes—
544C22#534×C12712yes—
545C22#535×C12711yescharacteristic
546C22#536×C12711yescharacteristic
547C22#537×C12712yes—
548C22#538×C12714yes—
549C22#539×C12714yes—
550C22#540×C12714yes—
551C22#542×C12714yes—
552C4—24no—
553C4—24no—
554C4—24no—
555C4—42no—
556C4—42no—
557C4—84no—
558C4—84no—
559C2—44no—
560C2—44no—
561C2C127×#228011yescharacteristic
562C2C127×#230811yescharacteristic
563C2C127×#231111yescharacteristic
564C2C127×#231812yes—
565C2C127×#231912yes—
566C2C127×#263014yes—
567C2C127×#263512yes—
568C2C127×#263812yes—
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×#380×C127C2semidirect
4. C127×#1441C2semidirect
5. C127×#1440C2semidirect
6. C127×#1439C2semidirect
8. C127×#1434C2semidirect
9. C127×C22⋊#95C2semidirect
15. C2×C4×D4×C127C4semidirect
137. C22×C4×C127C22⋊C4semidirect
274. #14344C127direct (N × H)
286. C2×#381C2×C127semidirect
287. C2×#380C2×C127semidirect
288. #1441C2×C127semidirect
289. #1440C2×C127semidirect
290. #1439C2×C127semidirect
292. #1434C2×C127semidirect
293. C22⋊#95C2×C127semidirect
294. C127#14344direct (N × H)
300. C2×C4×D4C4×C127semidirect
422. 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×#380×C1272
C127×#14412
C127×#14402
C127×#14392
C127×#14382
C127×#14342
C127×C22⋊#952
#14344127