Finite Group Databasebeta

← C127×#15730 #44579403

Subgroups — C127×#15730 #44579403

Order 32512.

1474 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C127C211yesmaximal, characteristic
2C2×#385×C127C211yesmaximal, characteristic
3C127×#1441C212yesmaximal, complemented
4C127×#1441C212yesmaximal, complemented
5C127×#1441C212yesmaximal, complemented
6C127×#1439C212yesmaximal
7C127×#1437C211yesmaximal, characteristic
8C127×#1436C212yesmaximal, complemented
9C127×C22⋊#95C212yesmaximal
10C24×C4×C127C2211yescharacteristic
11C22×C4⋊C4×C127C2212yes—
12C22×C4⋊C4×C127C2212yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C22⋊C4×C127C2211yescharacteristic
16C22×C22⋊C4×C127C2212yes—
17C22×C22⋊C4×C127C2211yescharacteristic
18C22×C22⋊C4×C127C2212yes—
19C22×C42×C127C2211yescharacteristic
20#399×C127—24no—
21#385×C127—24no—
22C2×#95×C127C2211yescharacteristic
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2212yes—
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2212yes—
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C25×C127C2311yescharacteristic
34C23×C4×C127—22no—
35C23×C4×C127—24no—
36C23×C4×C127—41no—
37C23×C4×C127—41no—
38C23×C4×C127—42no—
39C23×C4×C127C2312yes—
40C23×C4×C127C2311yescharacteristic
41C23×C4×C127C2311yescharacteristic
42C23×C4×C127C2312yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2312yes—
46C23×C4×C127C2312yes—
47C2×C4⋊C4×C127—24no—
48C2×C4⋊C4×C127—24no—
49C2×C4⋊C4×C127—22no—
50C2×C4⋊C4×C127—24no—
51C2×C4⋊C4×C127—24no—
52C2×C4⋊C4×C127—24no—
53C2×C4⋊C4×C127—24no—
54C2×C4⋊C4×C127—42no—
55C2×C4⋊C4×C127—42no—
56C2×C4⋊C4×C127—42no—
57C2×C4⋊C4×C127—41no—
58C2×C4⋊C4×C127—41no—
59C2×C22⋊C4×C127—22no—
60C2×C22⋊C4×C127—24no—
61C2×C22⋊C4×C127—24no—
62C2×C22⋊C4×C127—24no—
63C2×C22⋊C4×C127—41no—
64C2×C22⋊C4×C127—41no—
65C2×C22⋊C4×C127—42no—
66C2×C22⋊C4×C127—42no—
67C2×C22⋊C4×C127—42no—
68C2×C22⋊C4×C127D414yes—
69C2×C22⋊C4×C127Q818yes—
70C2×C42×C127—41no—
71C2×C42×C127—42no—
72#95×C127—24no—
73#95×C127—22no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—41no—
77#95×C127—42no—
78#95×C127—42no—
79#95×C127—42no—
80#95×C127—42no—
81#95×C127—42no—
82#95×C127—42no—
83C24×C127—22no—
84C24×C127—22no—
85C24×C127—22no—
86C24×C127—22no—
87C24×C127—21no—
88C24×C127—21no—
89C24×C127—22no—
90C24×C127C2×D412yes—
91C24×C127C2×Q814yes—
92C24×C127C2411yescharacteristic
93C22×C4×C127—22no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127—22no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—22no—
102C22×C4×C127—22no—
103C22×C4×C127—22no—
104C22×C4×C127—22no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—22no—
110C22×C4×C127—22no—
111C22×C4×C127—22no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—21no—
115C22×C4×C127—22no—
116C22×C4×C127—22no—
117C22×C4×C127—22no—
118C22×C4×C127—22no—
119C22×C4×C127—22no—
120C22×C4×C127—22no—
121C22×C4×C127—22no—
122C22×C4×C127—21no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—21no—
126C22×C4×C127—21no—
127C22×C4×C127—22no—
128C22×C4×C127—22no—
129C22×C4×C127—22no—
130C22×C4×C127—22no—
131C22×C4×C127—22no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—22no—
135C22×C4×C127—22no—
136C22×C4×C127—22no—
137C22×C4×C127—22no—
138C22×C4×C127—44no—
139C22×C4×C127—48no—
140C22×C4×C127—48no—
141C22×C4×C127—44no—
142C22×C4×C127—44no—
143C22×C4×C127C2×D412yes—
144C22×C4×C127C2×D412yes—
145C22×C4×C127C2×Q814yes—
146C22×C4×C127C2×Q814yes—
147C22×C4×C127#4114yes—
148C22×C4×C127#4114yes—
149C22×C4×C127#4114yes—
150C4⋊C4×C127—48no—
151C4⋊C4×C127—48no—
152C4⋊C4×C127—48no—
153C4⋊C4×C127—44no—
154C22⋊C4×C127—28no—
155C22⋊C4×C127—44no—
156C22⋊C4×C127—48no—
157C22⋊C4×C127—48no—
158C42×C127—44no—
159C23×C127—22no—
160C23×C127—24no—
161C23×C127—22no—
162C23×C127—24no—
163C23×C127—24no—
164C23×C127—24no—
165C23×C127—24no—
166C23×C127—24no—
167C23×C127—24no—
168C23×C127—24no—
169C23×C127—42no—
170C23×C127—42no—
171C23×C127—42no—
172C23×C127—42no—
173C23×C127—41no—
174C23×C127—42no—
175C23×C127—42no—
176C23×C127—41no—
177C23×C127—41no—
178C23×C127—41no—
179C23×C127C4⋊Q814yes—
180C23×C127C22×D411yescharacteristic
181C23×C127C22×Q812yes—
182C23×C127C2×#4112yes—
183C23×C127C2×#4112yes—
184C23×C127C2×#4112yes—
185C23×C127H(5,𝔽2)11yescharacteristic
186C23×C127H(5,𝔽2)11yescharacteristic
187C23×C127H(5,𝔽2)12yes—
188C23×C127H(5,𝔽2)12yes—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
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—24no—
202C2×C4×C127—24no—
203C2×C4×C127—24no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—24no—
207C2×C4×C127—24no—
208C2×C4×C127—416no—
209C2×C4×C127—42no—
210C2×C4×C127—42no—
211C2×C4×C127—42no—
212C2×C4×C127—42no—
213C2×C4×C127—42no—
214C2×C4×C127—42no—
215C2×C4×C127—42no—
216C2×C4×C127—42no—
217C2×C4×C127—42no—
218C2×C4×C127—42no—
219C2×C4×C127—42no—
220C2×C4×C127—42no—
221C2×C4×C127—42no—
222C2×C4×C127—42no—
223C2×C4×C127—42no—
224C2×C4×C127—42no—
225C2×C4×C127—42no—
226C2×C4×C127—41no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—41no—
230C2×C4×C127—41no—
231C2×C4×C127—42no—
232C2×C4×C127—41no—
233C2×C4×C127—42no—
234C2×C4×C127—42no—
235C2×C4×C127—42no—
236C2×C4×C127—42no—
237C2×C4×C127—42no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C22×C127—24no—
243C22×C127—28no—
244C22×C127—44no—
245C22×C127—42no—
246C22×C127—42no—
247C22×C127—44no—
248C22×C127—44no—
249C22×C127—44no—
250C22×C127—44no—
251C22×C127#52511yescharacteristic
252C22×C127#52912yes—
253C22×C127C2×C4⋊Q811yescharacteristic
254C22×C127#53312yes—
255C22×C127#53411yescharacteristic
256C22×C127#53812yes—
257C22×C127#54012yes—
258C22×C127#54012yes—
259C22×C127#54312yes—
260C22×C127#54612yes—
261C22×C127#54612yes—
262C22×C127#55112yes—
263C22×C127#55111yescharacteristic
264C22×C127#55312yes—
265C22×C127#55412yes—
266C22×C127#55412yes—
267C22×C127#55412yes—
268C22×C127#55412yes—
269C22×C127#55911yescharacteristic
270C22×C127#56011yescharacteristic
271C22×C127#56011yescharacteristic
272C4×C127—42no—
273C4×C127—44no—
274C4×C127—42no—
275C4×C127—44no—
276C4×C127—44no—
277C4×C127—44no—
278C4×C127—44no—
279C4×C127—82no—
280#15730C12711yesmaximal, characteristic, direct product factor, Sylow
281C2×C127—44no—
282C2×C127#245712yes—
283C2×C127#252212yes—
284C2×C127#254912yes—
285C2×C127#258311yescharacteristic
286C2×C127#258912yes—
287C2×C127#269711yescharacteristic
288C2×C127#270911yescharacteristic
289C2×C127#274812yes—
290C2×C127#278012yes—
291C2×#399C2×C12711yescharacteristic
292C2×#385C2×C12711yescharacteristic
293#1441C2×C12712yescomplemented
294#1441C2×C12712yescomplemented
295#1441C2×C12712yescomplemented
296#1439C2×C12712yes—
297#1437C2×C12711yescharacteristic
298#1436C2×C12712yescomplemented
299C22⋊#95C2×C12712yes—
300C127#1573011yescharacteristic, direct product factor, Sylow
301C24×C4C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12712yes—
303C22×C4⋊C4C22×C12712yes—
304C22×C4⋊C4C22×C12712yes—
305C22×C4⋊C4C22×C12711yescharacteristic
306C22×C22⋊C4C22×C12711yescharacteristic
307C22×C22⋊C4C22×C12712yes—
308C22×C22⋊C4C22×C12711yescharacteristic
309C22×C22⋊C4C22×C12712yes—
310C22×C42C22×C12711yescharacteristic
311#399—24no—
312#385—24no—
313C2×#95C22×C12711yescharacteristic
314C2×#95C22×C12712yes—
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12712yes—
318C2×#95C22×C12712yes—
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12711yescharacteristic
323C2×#95C22×C12712yes—
324C25C23×C12711yescharacteristic
325C23×C4—22no—
326C23×C4—24no—
327C23×C4—41no—
328C23×C4—41no—
329C23×C4—42no—
330C23×C4C23×C12712yes—
331C23×C4C23×C12711yescharacteristic
332C23×C4C23×C12711yescharacteristic
333C23×C4C23×C12712yes—
334C23×C4C23×C12712yes—
335C23×C4C23×C12712yes—
336C23×C4C23×C12712yes—
337C23×C4C23×C12712yes—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4D4×C12714yes—
360C2×C22⋊C4Q8×C12718yes—
361C2×C42—41no—
362C2×C42—42no—
363#95—24no—
364#95—22no—
365#95—24no—
366#95—24no—
367#95—41no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95—42no—
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24C2×D4×C12712yes—
382C24C2×Q8×C12714yes—
383C24C24×C12711yescharacteristic
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—44no—
430C22×C4—48no—
431C22×C4—48no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4C2×D4×C12712yes—
435C22×C4C2×D4×C12712yes—
436C22×C4C2×Q8×C12714yes—
437C22×C4C2×Q8×C12714yes—
438C22×C4#41×C12714yes—
439C22×C4#41×C12714yes—
440C22×C4#41×C12714yes—
441C4⋊C4—48no—
442C4⋊C4—48no—
443C4⋊C4—48no—
444C4⋊C4—44no—
445C22⋊C4—28no—
446C22⋊C4—44no—
447C22⋊C4—48no—
448C22⋊C4—48no—
449C42—44no—
450C23—22no—
451C23—24no—
452C23—22no—
453C23—24no—
454C23—24no—
455C23—24no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—41no—
465C23—42no—
466C23—42no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23C4⋊Q8×C12714yes—
471C23C22×D4×C12711yescharacteristic
472C23C22×Q8×C12712yes—
473C23C2×#41×C12712yes—
474C23C2×#41×C12712yes—
475C23C2×#41×C12712yes—
476C23H(5,𝔽2)×C12711yescharacteristic
477C23H(5,𝔽2)×C12711yescharacteristic
478C23H(5,𝔽2)×C12712yes—
479C23H(5,𝔽2)×C12712yes—
480C2×C4—24no—
481C2×C4—24no—
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—24no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—416no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C22—24no—
534C22—28no—
535C22—44no—
536C22—42no—
537C22—42no—
538C22—44no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22#525×C12711yescharacteristic
543C22#529×C12712yes—
544C22C2×C4⋊Q8×C12711yescharacteristic
545C22#533×C12712yes—
546C22#534×C12711yescharacteristic
547C22#538×C12712yes—
548C22#540×C12712yes—
549C22#540×C12712yes—
550C22#543×C12712yes—
551C22#546×C12712yes—
552C22#546×C12712yes—
553C22#551×C12712yes—
554C22#551×C12711yescharacteristic
555C22#553×C12712yes—
556C22#554×C12712yes—
557C22#554×C12712yes—
558C22#554×C12712yes—
559C22#554×C12712yes—
560C22#559×C12711yescharacteristic
561C22#560×C12711yescharacteristic
562C22#560×C12711yescharacteristic
563C4—44no—
564C4—42no—
565C4—42no—
566C4—44no—
567C4—44no—
568C4—44no—
569C4—44no—
570C4—82no—
571C2—44no—
572C2C127×#245712yes—
573C2C127×#252212yes—
574C2C127×#254912yes—
575C2C127×#258311yescharacteristic
576C2C127×#258912yes—
577C2C127×#269711yescharacteristic
578C2C127×#270911yescharacteristic
579C2C127×#274812yes—
580C2C127×#278012yes—
subgroupG/H
center, socleC24×C127C24
commutator, Frattini, cosocleC24C24×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1441C2semidirect
4. C127×#1441C2semidirect
5. C127×#1441C2semidirect
8. C127×#1436C2semidirect
280. #15730C127direct (N × H)
293. #1441C2×C127semidirect
294. #1441C2×C127semidirect
295. #1441C2×C127semidirect
298. #1436C2×C127semidirect
300. C127#15730direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#399×C1272
C2×#385×C1272
C127×#14412
C127×#14392
C127×#14372
C127×#14362
C127×C22⋊#952
#15730127