Finite Group Databasebeta

← C127×#14320 #44577993

Subgroups — C127×#14320 #44577993

Order 32512.

1318 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C127C211yesmaximal, characteristic
2C2×#391×C127C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C127C211yesmaximal, characteristic
4C127×#1446C211yesmaximal, characteristic
5C127×#1445C212yesmaximal
6C127×#1442C212yesmaximal
7C127×#1442C211yesmaximal, characteristic
8C127×#1441C211yesmaximal, characteristic
9C127×#1436C212yesmaximal
10C127×#1434C212yesmaximal
11C127×#1434C211yesmaximal, characteristic
12C23×Q8×C127C2211yescharacteristic
13C22×C4⋊C4×C127C2211yescharacteristic
14C22×C4⋊C4×C127C2211yescharacteristic
15C22×C4⋊C4×C127C2211yescharacteristic
16C22×C4⋊C4×C127C2212yes—
17C22×C42×C127C2211yescharacteristic
18C22×C42×C127C2211yescharacteristic
19C22×C42×C127C2211yescharacteristic
20#395×C127C418yescomplemented
21#391×C127—24no—
22C4×C4⋊C4×C127—24no—
23C2×#95×C127C2212yes—
24C2×#95×C127C2212yes—
25C2×#95×C127C2212yes—
26C2×#95×C127C2211yescharacteristic
27C2×#95×C127C2212yes—
28C2×#95×C127C2212yes—
29C2×#95×C127C2211yescharacteristic
30C2×#95×C127C2211yescharacteristic
31C2×#95×C127C2212yes—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2212yes—
35C2×#95×C127C2212yes—
36C2×#95×C127C2212yes—
37C2×#95×C127C2211yescharacteristic
38C22×Q8×C127—22no—
39C22×Q8×C127—22no—
40C22×Q8×C127—42no—
41C22×Q8×C127—42no—
42C22×Q8×C127C2×C414yes—
43C23×C4×C127C2312yes—
44C23×C4×C127C2312yes—
45C23×C4×C127C2311yescharacteristic
46C23×C4×C127C2312yes—
47C23×C4×C127C2312yes—
48C23×C4×C127C2311yescharacteristic
49C23×C4×C127C2311yescharacteristic
50C23×C4×C127C2311yescharacteristic
51C23×C4×C127C2311yescharacteristic
52C23×C4×C127C2311yescharacteristic
53C23×C4×C127C2311yescharacteristic
54C2×C4⋊C4×C127—22no—
55C2×C4⋊C4×C127—22no—
56C2×C4⋊C4×C127—22no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—42no—
61C2×C4⋊C4×C127—42no—
62C2×C4⋊C4×C127—42no—
63C2×C4⋊C4×C127C2×C414yes—
64C2×C4⋊C4×C127C2×C418yes—
65C2×C42×C127—22no—
66C2×C42×C127—22no—
67C2×C42×C127—22no—
68C2×C42×C127—42no—
69C2×C42×C127—42no—
70C2×C42×C127D414yes—
71C2×C42×C127Q814yescomplemented
72#95×C127—22no—
73#95×C127—22no—
74#95×C127—24no—
75#95×C127—24no—
76#95×C127—24no—
77#95×C127—24no—
78#95×C127—22no—
79#95×C127—24no—
80#95×C127—42no—
81#95×C127—42no—
82#95×C127—42no—
83#95×C127—42no—
84#95×C127—42no—
85#95×C127C2×C414yes—
86#95×C127C2×C418yes—
87C24×C127C2411yescharacteristic
88C2×Q8×C127—28no—
89C2×Q8×C127—48no—
90C2×Q8×C127—44no—
91C2×Q8×C127—44no—
92C2×Q8×C127—48no—
93C22×C4×C127—21no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—22no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—21no—
102C22×C4×C127—22no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—22no—
106C22×C4×C127—22no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—21no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—22no—
113C22×C4×C127—22no—
114C22×C4×C127—22no—
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—22no—
123C22×C4×C127—22no—
124C22×C4×C127—22no—
125C22×C4×C127—22no—
126C22×C4×C127—22no—
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—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—22no—
143C22×C4×C127C22×C414yes—
144C22×C4×C127C22×C414yes—
145C22×C4×C127C22×C412yes—
146C22×C4×C127C22×C412yes—
147C22×C4×C127C22×C412yes—
148C22×C4×C127C2×D412yes—
149C22×C4×C127C2×D412yes—
150C22×C4×C127C2×D412yes—
151C22×C4×C127C2×Q812yes—
152C22×C4×C127C2×Q812yes—
153C22×C4×C127C2×Q812yes—
154C22×C4×C127#4112yes—
155C22×C4×C127#4112yes—
156C22×C4×C127#4112yes—
157C22×C4×C127#4112yes—
158C4⋊C4×C127—28no—
159C4⋊C4×C127—28no—
160C4⋊C4×C127—48no—
161C4⋊C4×C127—44no—
162C42×C127—28no—
163C42×C127—44no—
164C42×C127—44no—
165C23×C127C23×C411yescharacteristic
166C23×C127C22×D411yescharacteristic
167C23×C127C22×Q811yescharacteristic
168C23×C127C2×#4111yescharacteristic
169C23×C127C2×#4111yescharacteristic
170C23×C127C2×#4111yescharacteristic
171C23×C127C2×#4111yescharacteristic
172C23×C127H(5,𝔽2)12yes—
173C23×C127H(5,𝔽2)12yes—
174C23×C1272−1+412yes—
175C23×C1272−1+412yes—
176Q8×C127—416no—
177C2×C4×C127—22no—
178C2×C4×C127—22no—
179C2×C4×C127—24no—
180C2×C4×C127—22no—
181C2×C4×C127—22no—
182C2×C4×C127—22no—
183C2×C4×C127—22no—
184C2×C4×C127—22no—
185C2×C4×C127—22no—
186C2×C4×C127—22no—
187C2×C4×C127—22no—
188C2×C4×C127—24no—
189C2×C4×C127—24no—
190C2×C4×C127—24no—
191C2×C4×C127—22no—
192C2×C4×C127—24no—
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—22no—
200C2×C4×C127—22no—
201C2×C4×C127—22no—
202C2×C4×C127—22no—
203C2×C4×C127—22no—
204C2×C4×C127—24no—
205C2×C4×C127—24no—
206C2×C4×C127—41no—
207C2×C4×C127—41no—
208C2×C4×C127—42no—
209C2×C4×C127—41no—
210C2×C4×C127—41no—
211C2×C4×C127—42no—
212C2×C4×C127—41no—
213C2×C4×C127—41no—
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—42no—
227C2×C4×C127—42no—
228C2×C4×C127—42no—
229C2×C4×C127—42no—
230C2×C4×C127—42no—
231C2×C4×C127—42no—
232C2×C4×C127—42no—
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×C127C4×D414yes—
240C2×C4×C127C4×Q814yes—
241C2×C4×C127C22⋊Q814yes—
242C22×C127C2×C4×D411yescharacteristic
243C22×C127C2×C4×Q811yescharacteristic
244C22×C127C4×#4111yescharacteristic
245C22×C127#51812yes—
246C22×C127#51912yes—
247C22×C127C2×C22⋊Q811yescharacteristic
248C22×C127#52511yescharacteristic
249C22×C127#52911yescharacteristic
250C22×C127#53311yescharacteristic
251C22×C127#53411yescharacteristic
252C22×C127#53511yescharacteristic
253C22×C127#53611yescharacteristic
254C22×C127#53611yescharacteristic
255C22×C127#53812yes—
256C22×C127#53912yes—
257C22×C127#53912yes—
258C22×C127#54112yes—
259C22×C127#54212yes—
260C22×C127#54212yes—
261C22×C127#54212yes—
262C22×C127#54212yes—
263C22×C127#54412yes—
264C22×C127#54412yes—
265C4×C127—24no—
266C4×C127—24no—
267C4×C127—24no—
268C4×C127—42no—
269C4×C127—44no—
270C4×C127—44no—
271C4×C127—42no—
272C4×C127—42no—
273C4×C127—42no—
274C4×C127—82no—
275C4×C127—82no—
276#14320C12711yesmaximal, characteristic, direct product factor, Sylow
277C2×C127C4×C22⋊Q811yescharacteristic
278C2×C127#232111yescharacteristic
279C2×C127#232711yescharacteristic
280C2×C127#233112yes—
281C2×C127#233212yes—
282C2×C127#262711yescharacteristic
283C2×C127#262811yescharacteristic
284C2×C127#263211yescharacteristic
285C2×C127#263811yescharacteristic
286C2×C127#265012yes—
287C2×C127#266612yes—
288C2×#395C2×C12711yescharacteristic
289C2×#391C2×C12711yescharacteristic
290C2×C4×C4⋊C4C2×C12711yescharacteristic
291#1446C2×C12711yescharacteristic
292#1445C2×C12712yes—
293#1442C2×C12712yes—
294#1442C2×C12711yescharacteristic
295#1441C2×C12711yescharacteristic
296#1436C2×C12712yes—
297#1434C2×C12711yescharacteristic
298#1434C2×C12712yes—
299C127#1432011yescharacteristic, direct product factor, Sylow
300C23×Q8C22×C12711yescharacteristic
301C22×C4⋊C4C22×C12711yescharacteristic
302C22×C4⋊C4C22×C12711yescharacteristic
303C22×C4⋊C4C22×C12711yescharacteristic
304C22×C4⋊C4C22×C12712yes—
305C22×C42C22×C12711yescharacteristic
306C22×C42C22×C12711yescharacteristic
307C22×C42C22×C12711yescharacteristic
308#395C4×C12718yescomplemented
309#391—24no—
310C4×C4⋊C4—24no—
311C2×#95C22×C12712yes—
312C2×#95C22×C12712yes—
313C2×#95C22×C12712yes—
314C2×#95C22×C12711yescharacteristic
315C2×#95C22×C12712yes—
316C2×#95C22×C12712yes—
317C2×#95C22×C12711yescharacteristic
318C2×#95C22×C12711yescharacteristic
319C2×#95C22×C12712yes—
320C2×#95C22×C12712yes—
321C2×#95C22×C12712yes—
322C2×#95C22×C12712yes—
323C2×#95C22×C12712yes—
324C2×#95C22×C12712yes—
325C2×#95C22×C12711yescharacteristic
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—42no—
329C22×Q8—42no—
330C22×Q8C2×C4×C12714yes—
331C23×C4C23×C12712yes—
332C23×C4C23×C12712yes—
333C23×C4C23×C12711yescharacteristic
334C23×C4C23×C12712yes—
335C23×C4C23×C12712yes—
336C23×C4C23×C12711yescharacteristic
337C23×C4C23×C12711yescharacteristic
338C23×C4C23×C12711yescharacteristic
339C23×C4C23×C12711yescharacteristic
340C23×C4C23×C12711yescharacteristic
341C23×C4C23×C12711yescharacteristic
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4C2×C4×C12714yes—
352C2×C4⋊C4C2×C4×C12718yes—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42D4×C12714yes—
359C2×C42Q8×C12714yescomplemented
360#95—22no—
361#95—22no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—22no—
367#95—24no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—42no—
373#95C2×C4×C12714yes—
374#95C2×C4×C12718yes—
375C24C24×C12711yescharacteristic
376C2×Q8—28no—
377C2×Q8—48no—
378C2×Q8—44no—
379C2×Q8—44no—
380C2×Q8—48no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
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—22no—
430C22×C4—22no—
431C22×C4C22×C4×C12714yes—
432C22×C4C22×C4×C12714yes—
433C22×C4C22×C4×C12712yes—
434C22×C4C22×C4×C12712yes—
435C22×C4C22×C4×C12712yes—
436C22×C4C2×D4×C12712yes—
437C22×C4C2×D4×C12712yes—
438C22×C4C2×D4×C12712yes—
439C22×C4C2×Q8×C12712yes—
440C22×C4C2×Q8×C12712yes—
441C22×C4C2×Q8×C12712yes—
442C22×C4#41×C12712yes—
443C22×C4#41×C12712yes—
444C22×C4#41×C12712yes—
445C22×C4#41×C12712yes—
446C4⋊C4—28no—
447C4⋊C4—28no—
448C4⋊C4—48no—
449C4⋊C4—44no—
450C42—28no—
451C42—44no—
452C42—44no—
453C23C23×C4×C12711yescharacteristic
454C23C22×D4×C12711yescharacteristic
455C23C22×Q8×C12711yescharacteristic
456C23C2×#41×C12711yescharacteristic
457C23C2×#41×C12711yescharacteristic
458C23C2×#41×C12711yescharacteristic
459C23C2×#41×C12711yescharacteristic
460C23H(5,𝔽2)×C12712yes—
461C23H(5,𝔽2)×C12712yes—
462C232−1+4×C12712yes—
463C232−1+4×C12712yes—
464Q8—416no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
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—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4C4×D4×C12714yes—
528C2×C4C4×Q8×C12714yes—
529C2×C4C22⋊Q8×C12714yes—
530C22C2×C4×D4×C12711yescharacteristic
531C22C2×C4×Q8×C12711yescharacteristic
532C22C4×#41×C12711yescharacteristic
533C22#518×C12712yes—
534C22#519×C12712yes—
535C22C2×C22⋊Q8×C12711yescharacteristic
536C22#525×C12711yescharacteristic
537C22#529×C12711yescharacteristic
538C22#533×C12711yescharacteristic
539C22#534×C12711yescharacteristic
540C22#535×C12711yescharacteristic
541C22#536×C12711yescharacteristic
542C22#536×C12711yescharacteristic
543C22#538×C12712yes—
544C22#539×C12712yes—
545C22#539×C12712yes—
546C22#541×C12712yes—
547C22#542×C12712yes—
548C22#542×C12712yes—
549C22#542×C12712yes—
550C22#542×C12712yes—
551C22#544×C12712yes—
552C22#544×C12712yes—
553C4—24no—
554C4—24no—
555C4—24no—
556C4—44no—
557C4—42no—
558C4—44no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—82no—
563C4—82no—
564C2C4×C22⋊Q8×C12711yescharacteristic
565C2C127×#232111yescharacteristic
566C2C127×#232711yescharacteristic
567C2C127×#233112yes—
568C2C127×#233212yes—
569C2C127×#262711yescharacteristic
570C2C127×#262811yescharacteristic
571C2C127×#263211yescharacteristic
572C2C127×#263811yescharacteristic
573C2C127×#265012yes—
574C2C127×#266612yes—
subgroupG/H
center, socle, prime radicalC24×C127C24
commutatorC23C23×C4×C127
Frattini, cosocleC24C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C127 ◁ G

Complements

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

NH ≅ G/Ntype
20. #395×C127C4semidirect
71. C2×C42×C127Q8semidirect
276. #14320C127direct (N × H)
299. C127#14320direct (N × H)
308. #395C4×C127semidirect
359. C2×C42Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1272
C2×#391×C1272
C2×C4×C4⋊C4×C1272
C127×#14462
C127×#14452
C127×#14422
C127×#14412
C127×#14362
C127×#14342
#14320127