Finite Group Databasebeta

← C127×#14026 #44577699

Subgroups — C127×#14026 #44577699

Order 32512.

2358 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C127C211yesmaximal, characteristic
2C22×C4×Q8×C127C211yesmaximal, characteristic, complemented
3C2×#391×C127C211yesmaximal, characteristic, complemented
4C2×#390×C127C211yesmaximal, characteristic
5C2×#390×C127C211yesmaximal, characteristic
6C127×#1439C214yesmaximal, complemented
7C127×#1437C214yesmaximal, complemented
8C127×C4⋊#95C211yesmaximal, characteristic, complemented
9C4×#95×C127C211yesmaximal, characteristic, complemented
10C23×Q8×C127C2211yescharacteristic
11C23×D4×C127C2211yescharacteristic
12C2×#124×C127—24no—
13C2×#124×C127—24no—
14C2×#124×C127C418yescomplemented
15C2×C4×Q8×C127—24no—
16C2×C4×Q8×C127—24no—
17C2×C4×Q8×C127—24no—
18C22×C4⋊C4×C127C2212yes—
19C22×C4⋊C4×C127C2211yescharacteristic
20C22×C4⋊C4×C127C2211yescharacteristic
21C22×C22⋊C4×C127C2212yes—
22C22×C22⋊C4×C127C2214yes—
23C22×C22⋊C4×C127C2214yes—
24C22×C22⋊C4×C127C2212yes—
25C22×C42×C127C2212yes—
26C22×C42×C127C2211yescharacteristic
27C22×C42×C127C2211yescharacteristic
28C22×C42×C127C2211yescharacteristic
29#391×C127—24no—
30#390×C127—24no—
31#390×C127—24no—
32C2×#95×C127C2212yes—
33C2×#95×C127C2212yes—
34C2×#95×C127C2214yes—
35C2×#95×C127C2214yes—
36C25×C127C2312yes—
37C22×Q8×C127—22no—
38C22×Q8×C127—22no—
39C22×Q8×C127—22no—
40C22×Q8×C127—22no—
41C22×Q8×C127C2×C414yes—
42C22×Q8×C127D414yes—
43C22×Q8×C127D414yes—
44C22×D4×C127—22no—
45C22×D4×C127—22no—
46C22×D4×C127—22no—
47C22×D4×C127—22no—
48C22×D4×C127—22no—
49C22×D4×C127—22no—
50C22×D4×C127C2×C414yes—
51C23×C4×C127C2312yes—
52C23×C4×C127C2312yes—
53C23×C4×C127C2311yescharacteristic
54C23×C4×C127C2312yes—
55C23×C4×C127C2312yes—
56C23×C4×C127C2312yes—
57C23×C4×C127C2311yescharacteristic
58C23×C4×C127C2311yescharacteristic
59#124×C127—232no—
60C4×Q8×C127—232no—
61C2×C4⋊C4×C127—24no—
62C2×C4⋊C4×C127—24no—
63C2×C4⋊C4×C127—24no—
64C2×C4⋊C4×C127—22no—
65C2×C4⋊C4×C127—22no—
66C2×C4⋊C4×C127—22no—
67C2×C4⋊C4×C127—22no—
68C2×C4⋊C4×C127—22no—
69C2×C4⋊C4×C127D414yes—
70C2×C22⋊C4×C127—28no—
71C2×C22⋊C4×C127—28no—
72C2×C22⋊C4×C127—28no—
73C2×C22⋊C4×C127—24no—
74C2×C22⋊C4×C127—24no—
75C2×C22⋊C4×C127—28no—
76C2×C22⋊C4×C127—28no—
77C2×C22⋊C4×C127—44no—
78C2×C22⋊C4×C127—44no—
79C2×C22⋊C4×C127C2×C4116yes—
80C2×C42×C127—24no—
81C2×C42×C127—24no—
82C2×C42×C127—24no—
83C2×C42×C127—22no—
84C2×C42×C127—22no—
85C2×C42×C127—22no—
86C2×C42×C127—22no—
87C2×C42×C127—22no—
88C2×C42×C127—22no—
89C2×C42×C127—22no—
90C2×C42×C127C2×C414yes—
91C2×C42×C127D414yes—
92#95×C127—28no—
93#95×C127—24no—
94#95×C127—24no—
95#95×C127—44no—
96C24×C127—22no—
97C24×C127—22no—
98C24×C127—22no—
99C24×C127—22no—
100C24×C127—24no—
101C24×C127—24no—
102C24×C127—22no—
103C24×C127—22no—
104C24×C127—24no—
105C24×C127—24no—
106C24×C127C22×C414yes—
107C24×C127C2411yescharacteristic
108C2×Q8×C127—28no—
109C2×Q8×C127—28no—
110C2×Q8×C127—28no—
111C2×Q8×C127—28no—
112C2×Q8×C127—28no—
113C2×Q8×C127—28no—
114C2×Q8×C127C22⋊C4116yescomplemented
115C2×D4×C127—28no—
116C2×D4×C127—28no—
117C2×D4×C127—28no—
118C2×D4×C127—44no—
119C2×D4×C127—44no—
120C2×D4×C127—44no—
121C2×D4×C127—44no—
122C22×C4×C127—21no—
123C22×C4×C127—21no—
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—21no—
135C22×C4×C127—22no—
136C22×C4×C127—21no—
137C22×C4×C127—22no—
138C22×C4×C127—22no—
139C22×C4×C127—22no—
140C22×C4×C127—22no—
141C22×C4×C127—22no—
142C22×C4×C127—24no—
143C22×C4×C127—22no—
144C22×C4×C127—24no—
145C22×C4×C127—22no—
146C22×C4×C127—22no—
147C22×C4×C127—22no—
148C22×C4×C127—22no—
149C22×C4×C127—22no—
150C22×C4×C127—22no—
151C22×C4×C127—24no—
152C22×C4×C127—22no—
153C22×C4×C127—24no—
154C22×C4×C127C22×C414yes—
155C22×C4×C127C22×C414yes—
156C22×C4×C127C22×C412yes—
157C22×C4×C127C2×D414yes—
158C22×C4×C127C2×D412yes—
159C22×C4×C127C2×D414yes—
160C22×C4×C127C2×D414yes—
161C22×C4×C127C2×D412yes—
162C22×C4×C127C2×D412yes—
163C22×C4×C127C2×D412yes—
164C22×C4×C127C2×D412yes—
165C22×C4×C127C2×D412yes—
166C22×C4×C127#4114yes—
167C22×C4×C127#4114yes—
168C22×C4×C127#4112yes—
169C22×C4×C127#4112yes—
170C4⋊C4×C127—216no—
171C4⋊C4×C127—28no—
172C4⋊C4×C127—44no—
173C22⋊C4×C127—232no—
174C22⋊C4×C127—416no—
175C22⋊C4×C127—48no—
176C22⋊C4×C127—48no—
177C42×C127—216no—
178C42×C127—28no—
179C42×C127—28no—
180C42×C127—44no—
181C23×C127—24no—
182C23×C127—24no—
183C23×C127—24no—
184C23×C127—28no—
185C23×C127—28no—
186C23×C127—42no—
187C23×C127—42no—
188C23×C127—42no—
189C23×C127—42no—
190C23×C127—42no—
191C23×C127—44no—
192C23×C127—42no—
193C23×C127—42no—
194C23×C127—42no—
195C23×C127—44no—
196C23×C127—44no—
197C23×C127—44no—
198C23×C127—44no—
199C23×C127—44no—
200C23×C127—44no—
201C23×C127—44no—
202C23×C127—44no—
203C23×C127—44no—
204C23×C127C23×C411yescharacteristic
205C23×C127C22×D411yescharacteristic
206C23×C127C22×D411yescharacteristic
207C23×C127C22×D411yescharacteristic
208C23×C127C22×D411yescharacteristic
209C23×C127C2×#4111yescharacteristic
210C23×C127C2×#4111yescharacteristic
211C23×C127C2×#4112yes—
212C23×C127C2×#4112yes—
213C23×C127H(5,𝔽2)12yes—
214C23×C1272−1+412yes—
215Q8×C127—232no—
216D4×C127—416no—
217C2×C4×C127—24no—
218C2×C4×C127—24no—
219C2×C4×C127—22no—
220C2×C4×C127—24no—
221C2×C4×C127—24no—
222C2×C4×C127—24no—
223C2×C4×C127—24no—
224C2×C4×C127—22no—
225C2×C4×C127—24no—
226C2×C4×C127—24no—
227C2×C4×C127—24no—
228C2×C4×C127—24no—
229C2×C4×C127—24no—
230C2×C4×C127—24no—
231C2×C4×C127—22no—
232C2×C4×C127—24no—
233C2×C4×C127—22no—
234C2×C4×C127—22no—
235C2×C4×C127—24no—
236C2×C4×C127—28no—
237C2×C4×C127—24no—
238C2×C4×C127—42no—
239C2×C4×C127—42no—
240C2×C4×C127—42no—
241C2×C4×C127—42no—
242C2×C4×C127—42no—
243C2×C4×C127—42no—
244C2×C4×C127—42no—
245C2×C4×C127—42no—
246C2×C4×C127—42no—
247C2×C4×C127—42no—
248C2×C4×C127—42no—
249C2×C4×C127—42no—
250C2×C4×C127—44no—
251C2×C4×C127—42no—
252C2×C4×C127—42no—
253C2×C4×C127—42no—
254C2×C4×C127—44no—
255C2×C4×C127—44no—
256C2×C4×C127C2×C22⋊C418yes—
257C2×C4×C127C2×C22⋊C414yes—
258C2×C4×C127C4×D414yes—
259C2×C4×C127C4×D414yes—
260C2×C4×C127#12014yes—
261C2×C4×C127#12114yes—
262C2×C4×C127#12114yes—
263C2×C4×C127#12314yes—
264C2×C4×C127#12414yescomplemented
265C22×C127—44no—
266C22×C127—48no—
267C22×C127—48no—
268C22×C127—44no—
269C22×C127—44no—
270C22×C127—84no—
271C22×C127—82no—
272C22×C127—82no—
273C22×C127—84no—
274C22×C127—82no—
275C22×C127—82no—
276C22×C127C22×C22⋊C411yescharacteristic
277C22×C127C2×C4×D411yescharacteristic
278C22×C127C2×C4×D411yescharacteristic
279C22×C127C4×#4112yes—
280C22×C127#52012yes—
281C22×C127C2×#12011yescharacteristic
282C22×C127C2×#12111yescharacteristic
283C22×C127C2×#12111yescharacteristic
284C22×C127C2×#12311yescharacteristic
285C22×C127C2×#12411yescharacteristic
286C22×C127#52912yes—
287C22×C127#53211yescharacteristic
288C22×C127#53511yescharacteristic
289C22×C127#53611yescharacteristic
290C22×C127#54212yes—
291C22×C127#54612yes—
292C22×C127#54812yes—
293C22×C127#54812yes—
294C22×C127#54812yes—
295C22×C127#55012yes—
296C22×C127#55012yes—
297C22×C127#55612yes—
298C22×C127#55912yes—
299C4×C127—24no—
300C4×C127—28no—
301C4×C127—44no—
302C4×C127—44no—
303C4×C127—42no—
304C4×C127—44no—
305C4×C127—82no—
306C4×C127#38618yes—
307#14026C12711yesmaximal, characteristic, direct product factor, Sylow
308C2×C127—84no—
309C2×C127C2×#38611yescharacteristic
310C2×C127C4×#12411yescharacteristic
311C2×C127#232611yescharacteristic
312C2×C127#234112yes—
313C2×C127#236712yes—
314C2×C127#242612yes—
315C2×C127#243111yescharacteristic
316C2×C127#243611yescharacteristic
317C2×C127#244812yes—
318C2×C127#254511yescharacteristic
319C2×C127#254811yescharacteristic
320C22×#124C2×C12711yescharacteristic
321C22×C4×Q8C2×C12711yescharacteristic, complemented
322C2×#391C2×C12711yescharacteristic, complemented
323C2×#390C2×C12711yescharacteristic
324C2×#390C2×C12711yescharacteristic
325#1439C2×C12714yescomplemented
326#1437C2×C12714yescomplemented
327C4⋊#95C2×C12711yescharacteristic, complemented
328C4×#95C2×C12711yescharacteristic, complemented
329C127#1402611yescharacteristic, direct product factor, Sylow
330C23×Q8C22×C12711yescharacteristic
331C23×D4C22×C12711yescharacteristic
332C2×#124—24no—
333C2×#124—24no—
334C2×#124C4×C12718yescomplemented
335C2×C4×Q8—24no—
336C2×C4×Q8—24no—
337C2×C4×Q8—24no—
338C22×C4⋊C4C22×C12712yes—
339C22×C4⋊C4C22×C12711yescharacteristic
340C22×C4⋊C4C22×C12711yescharacteristic
341C22×C22⋊C4C22×C12712yes—
342C22×C22⋊C4C22×C12714yes—
343C22×C22⋊C4C22×C12714yes—
344C22×C22⋊C4C22×C12712yes—
345C22×C42C22×C12712yes—
346C22×C42C22×C12711yescharacteristic
347C22×C42C22×C12711yescharacteristic
348C22×C42C22×C12711yescharacteristic
349#391—24no—
350#390—24no—
351#390—24no—
352C2×#95C22×C12712yes—
353C2×#95C22×C12712yes—
354C2×#95C22×C12714yes—
355C2×#95C22×C12714yes—
356C25C23×C12712yes—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8C2×C4×C12714yes—
362C22×Q8D4×C12714yes—
363C22×Q8D4×C12714yes—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4C2×C4×C12714yes—
371C23×C4C23×C12712yes—
372C23×C4C23×C12712yes—
373C23×C4C23×C12711yescharacteristic
374C23×C4C23×C12712yes—
375C23×C4C23×C12712yes—
376C23×C4C23×C12712yes—
377C23×C4C23×C12711yescharacteristic
378C23×C4C23×C12711yescharacteristic
379#124—232no—
380C4×Q8—232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4D4×C12714yes—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4C2×C4×C127116yes—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42C2×C4×C12714yes—
411C2×C42D4×C12714yes—
412#95—28no—
413#95—24no—
414#95—24no—
415#95—44no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—24no—
426C24C22×C4×C12714yes—
427C24C24×C12711yescharacteristic
428C2×Q8—28no—
429C2×Q8—28no—
430C2×Q8—28no—
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8C22⋊C4×C127116yescomplemented
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—28no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4C22×C4×C12714yes—
475C22×C4C22×C4×C12714yes—
476C22×C4C22×C4×C12712yes—
477C22×C4C2×D4×C12714yes—
478C22×C4C2×D4×C12712yes—
479C22×C4C2×D4×C12714yes—
480C22×C4C2×D4×C12714yes—
481C22×C4C2×D4×C12712yes—
482C22×C4C2×D4×C12712yes—
483C22×C4C2×D4×C12712yes—
484C22×C4C2×D4×C12712yes—
485C22×C4C2×D4×C12712yes—
486C22×C4#41×C12714yes—
487C22×C4#41×C12714yes—
488C22×C4#41×C12712yes—
489C22×C4#41×C12712yes—
490C4⋊C4—216no—
491C4⋊C4—28no—
492C4⋊C4—44no—
493C22⋊C4—232no—
494C22⋊C4—416no—
495C22⋊C4—48no—
496C22⋊C4—48no—
497C42—216no—
498C42—28no—
499C42—28no—
500C42—44no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—28no—
505C23—28no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—44no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—44no—
516C23—44no—
517C23—44no—
518C23—44no—
519C23—44no—
520C23—44no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23C23×C4×C12711yescharacteristic
525C23C22×D4×C12711yescharacteristic
526C23C22×D4×C12711yescharacteristic
527C23C22×D4×C12711yescharacteristic
528C23C22×D4×C12711yescharacteristic
529C23C2×#41×C12711yescharacteristic
530C23C2×#41×C12711yescharacteristic
531C23C2×#41×C12712yes—
532C23C2×#41×C12712yes—
533C23H(5,𝔽2)×C12712yes—
534C232−1+4×C12712yes—
535Q8—232no—
536D4—416no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—28no—
557C2×C4—24no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—44no—
576C2×C4C2×C22⋊C4×C12718yes—
577C2×C4C2×C22⋊C4×C12714yes—
578C2×C4C4×D4×C12714yes—
579C2×C4C4×D4×C12714yes—
580C2×C4#120×C12714yes—
581C2×C4#121×C12714yes—
582C2×C4#121×C12714yes—
583C2×C4#123×C12714yes—
584C2×C4#124×C12714yescomplemented
585C22—44no—
586C22—48no—
587C22—48no—
588C22—44no—
589C22—44no—
590C22—84no—
591C22—82no—
592C22—82no—
593C22—84no—
594C22—82no—
595C22—82no—
596C22C22×C22⋊C4×C12711yescharacteristic
597C22C2×C4×D4×C12711yescharacteristic
598C22C2×C4×D4×C12711yescharacteristic
599C22C4×#41×C12712yes—
600C22#520×C12712yes—
601C22C2×#120×C12711yescharacteristic
602C22C2×#121×C12711yescharacteristic
603C22C2×#121×C12711yescharacteristic
604C22C2×#123×C12711yescharacteristic
605C22C2×#124×C12711yescharacteristic
606C22#529×C12712yes—
607C22#532×C12711yescharacteristic
608C22#535×C12711yescharacteristic
609C22#536×C12711yescharacteristic
610C22#542×C12712yes—
611C22#546×C12712yes—
612C22#548×C12712yes—
613C22#548×C12712yes—
614C22#548×C12712yes—
615C22#550×C12712yes—
616C22#550×C12712yes—
617C22#556×C12712yes—
618C22#559×C12712yes—
619C4—24no—
620C4—28no—
621C4—44no—
622C4—44no—
623C4—42no—
624C4—44no—
625C4—82no—
626C4#386×C12718yes—
627C2—84no—
628C2C2×#386×C12711yescharacteristic
629C2C4×#124×C12711yescharacteristic
630C2C127×#232611yescharacteristic
631C2C127×#234112yes—
632C2C127×#236712yes—
633C2C127×#242612yes—
634C2C127×#243111yescharacteristic
635C2C127×#243611yescharacteristic
636C2C127×#244812yes—
637C2C127×#254511yescharacteristic
638C2C127×#254811yescharacteristic
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. C22×C4×Q8×C127C2semidirect
3. C2×#391×C127C2semidirect
6. C127×#1439C2semidirect
7. C127×#1437C2semidirect
8. C127×C4⋊#95C2semidirect
9. C4×#95×C127C2semidirect
14. C2×#124×C127C4semidirect
114. C2×Q8×C127C22⋊C4semidirect
264. C2×C4×C127#124semidirect
307. #14026C127direct (N × H)
321. C22×C4×Q8C2×C127semidirect
322. C2×#391C2×C127semidirect
325. #1439C2×C127semidirect
326. #1437C2×C127semidirect
327. C4⋊#95C2×C127semidirect
328. C4×#95C2×C127semidirect
329. C127#14026direct (N × H)
334. C2×#124C4×C127semidirect
434. C2×Q8C22⋊C4×C127semidirect
584. C2×C4#124×C127semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C1272
C22×C4×Q8×C1272
C2×#391×C1272
C2×#390×C1272
C127×#14392
C127×#14372
C127×C4⋊#952
C4×#95×C1272
#14026127