Finite Group Databasebeta

← C127×#10340 #44574013

Subgroups — C127×#10340 #44574013

Order 32512.

900 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2659C211yesmaximal, characteristic, complemented
2C127×#1786C212yesmaximal
3C127×#1438C211yesmaximal, characteristic
4C127×#1294C212yesmaximal, complemented
5C127×#1280C211yesmaximal, characteristic, complemented
6C23×D4×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C22×C22⋊C4×C127—21no—
9C22×C22⋊C4×C127—21no—
10C2×#102×C127—22no—
11C2×#102×C127—22no—
12C2×C22⋊C8×C127C2212yes—
13#398×C127—22no—
14#395×C127—22no—
15#380×C127—21no—
16#380×C127C2212yes—
17C2×#95×C127C2211yescharacteristic
18C2×#95×C127C2211yescharacteristic
19C25×C127—21no—
20C22×Q8×C127—21no—
21C22×D4×C127—22no—
22C22×D4×C127—22no—
23C22×D4×C127—21no—
24C22×D4×C127—42no—
25C22×D4×C127—42no—
26C22×D4×C127Q812yescomplemented
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C23×C4×C127C2311yescharacteristic
31C22×C8×C127—22no—
32C22⋊Q8×C127—42no—
33C22⋊Q8×C127—42no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127D412yes—
39C2×C4⋊C4×C127D412yes—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—42no—
42C2×C22⋊C4×C127—42no—
43C2×C22⋊C4×C127—42no—
44C2×C22⋊C4×C127—42no—
45C2×C22⋊C4×C127—42no—
46C2×C22⋊C4×C127—42no—
47#102×C127—44no—
48#102×C127—44no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51#95×C127—22no—
52#95×C127—22no—
53#95×C127—22no—
54#95×C127—22no—
55C24×C127—22no—
56C24×C127—22no—
57C24×C127—22no—
58C24×C127—41no—
59C24×C127—41no—
60C24×C127—41no—
61C24×C127—41no—
62C24×C127—41no—
63C24×C127—41no—
64C24×C127—41no—
65C24×C127—41no—
66C24×C127—41no—
67C24×C127—41no—
68C24×C127—41no—
69C24×C127—41no—
70C24×C127C2×D411yescharacteristic
71C2×Q8×C127—42no—
72C2×Q8×C127—81no—
73C2×Q8×C127—81no—
74C2×D4×C127—24no—
75C2×D4×C127—24no—
76C2×D4×C127—24no—
77C2×D4×C127—42no—
78C2×D4×C127—42no—
79C2×D4×C127—44no—
80C2×D4×C127—48no—
81C2×D4×C127—44no—
82C2×D4×C127—42no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—22no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127—41no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127—41no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127D812yes—
103C22×C4×C127SD1612yes—
104C22×C4×C127C2×D412yes—
105C22×C4×C127C2×Q811yescharacteristic
106C22×C4×C127#4112yes—
107C22×C4×C127#4111yescharacteristic
108C2×C8×C127—42no—
109C2×C8×C127—42no—
110C2×C8×C127—42no—
111C4⋊C4×C127—42no—
112C4⋊C4×C127—42no—
113C4⋊C4×C127—42no—
114C4⋊C4×C127—44no—
115C4⋊C4×C127—81no—
116C4⋊C4×C127—81no—
117C22⋊C4×C127—48no—
118C22⋊C4×C127—48no—
119C22⋊C4×C127—42no—
120C22⋊C4×C127—42no—
121C23×C127—21no—
122C23×C127—21no—
123C23×C127—21no—
124C23×C127—21no—
125C23×C127—24no—
126C23×C127—42no—
127C23×C127—42no—
128C23×C127—42no—
129C23×C127—42no—
130C23×C127—42no—
131C23×C127—42no—
132C23×C127—42no—
133C23×C127—42no—
134C23×C127—42no—
135C23×C127—42no—
136C23×C127—42no—
137C23×C127—42no—
138C23×C127—42no—
139C23×C127—42no—
140C23×C127—42no—
141C23×C127—42no—
142C23×C127—42no—
143C23×C127—42no—
144C23×C127—81no—
145C23×C127—81no—
146C23×C127—81no—
147C23×C127—81no—
148C23×C127—81no—
149C23×C127—81no—
150C23×C127—81no—
151C23×C127—81no—
152C23×C127—81no—
153C23×C127—81no—
154C23×C127—81no—
155C23×C127—81no—
156C23×C127—81no—
157C23×C127—81no—
158C23×C127—81no—
159C23×C127—81no—
160C23×C127#12011yescharacteristic
161C23×C127C22⋊Q811yescharacteristic
162C23×C127#12411yescharacteristic
163C23×C127C2×D811yescharacteristic
164C23×C127C2×SD1611yescharacteristic
165C23×C127AGL(1,ℤ/8)11yescharacteristic
166C23×C127#13711yescharacteristic
167Q8×C127—84no—
168D4×C127—28no—
169D4×C127—44no—
170D4×C127—44no—
171D4×C127—44no—
172C2×C4×C127—22no—
173C2×C4×C127—22no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—41no—
177C2×C4×C127—41no—
178C2×C4×C127—42no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
183C2×C4×C127—42no—
184C2×C4×C127—42no—
185C2×C4×C127—42no—
186C2×C4×C127—42no—
187C2×C4×C127—42no—
188C2×C4×C127—42no—
189C2×C4×C127—42no—
190C2×C4×C127—42no—
191C2×C4×C127—42no—
192C2×C4×C127—42no—
193C2×C4×C127—42no—
194C2×C4×C127—81no—
195C2×C4×C127—81no—
196C2×C4×C127—81no—
197C2×C4×C127—81no—
198C2×C4×C127—81no—
199C2×C4×C127—81no—
200C2×C4×C127C22⋊Q812yes—
201C2×C4×C127#12412yes—
202C8×C127—82no—
203C22×C127—21no—
204C22×C127—21no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—21no—
210C22×C127—21no—
211C22×C127—21no—
212C22×C127—21no—
213C22×C127—21no—
214C22×C127—21no—
215C22×C127—44no—
216C22×C127—44no—
217C22×C127—44no—
218C22×C127—82no—
219C22×C127—82no—
220C22×C127—82no—
221C22×C127—82no—
222C22×C127—82no—
223C22×C127—82no—
224C22×C127—82no—
225C22×C127—82no—
226C22×C127—82no—
227C22×C127—82no—
228C22×C127—82no—
229C22×C127—82no—
230C22×C127#39311yescharacteristic
231C22×C127#44711yescharacteristic
232C22×C127#44811yescharacteristic
233C22×C127#45311yescharacteristic
234C22×C127#45411yescharacteristic
235C22×C127B(4,𝔽2)11yescharacteristic
236C22×C127B(4,𝔽2)11yescharacteristic
237C22×C127#47411yescharacteristic
238C22×C127#47611yescharacteristic
239C22×C127#48611yescharacteristic
240C22×C127#48911yescharacteristic
241C4×C127—22no—
242C4×C127—22no—
243C4×C127—42no—
244C4×C127—42no—
245C4×C127—82no—
246C4×C127—82no—
247C4×C127—82no—
248#10340C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—21no—
250C2×C127—21no—
251C2×C127—21no—
252C2×C127—21no—
253C2×C127—84no—
254C2×C127#159511yescharacteristic
255C2×C127#159611yescharacteristic
256C2×C127#159811yescharacteristic
257C2×C127#159911yescharacteristic
258C2×C127#202311yescharacteristic
259C2×C127#202711yescharacteristic
260C2×C127#202911yescharacteristic
261#2659C2×C12711yescharacteristic, complemented
262#1786C2×C12712yes—
263#1438C2×C12711yescharacteristic
264#1294C2×C12712yescomplemented
265#1280C2×C12711yescharacteristic, complemented
266C127#1034011yescharacteristic, direct product factor, Sylow
267C23×D4C22×C12711yescharacteristic
268C2×C22⋊Q8—21no—
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271C2×#102—22no—
272C2×#102—22no—
273C2×C22⋊C8C22×C12712yes—
274#398—22no—
275#395—22no—
276#380—21no—
277#380C22×C12712yes—
278C2×#95C22×C12711yescharacteristic
279C2×#95C22×C12711yescharacteristic
280C25—21no—
281C22×Q8—21no—
282C22×D4—22no—
283C22×D4—22no—
284C22×D4—21no—
285C22×D4—42no—
286C22×D4—42no—
287C22×D4Q8×C12712yescomplemented
288C23×C4—21no—
289C23×C4D4×C12711yescharacteristic
290C23×C4D4×C12711yescharacteristic
291C23×C4C23×C12711yescharacteristic
292C22×C8—22no—
293C22⋊Q8—42no—
294C22⋊Q8—42no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4D4×C12712yes—
300C2×C4⋊C4D4×C12712yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308#102—44no—
309#102—44no—
310C22⋊C8—22no—
311C22⋊C8—22no—
312#95—22no—
313#95—22no—
314#95—22no—
315#95—22no—
316C24—22no—
317C24—22no—
318C24—22no—
319C24—41no—
320C24—41no—
321C24—41no—
322C24—41no—
323C24—41no—
324C24—41no—
325C24—41no—
326C24—41no—
327C24—41no—
328C24—41no—
329C24—41no—
330C24—41no—
331C24C2×D4×C12711yescharacteristic
332C2×Q8—42no—
333C2×Q8—81no—
334C2×Q8—81no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—24no—
338C2×D4—42no—
339C2×D4—42no—
340C2×D4—44no—
341C2×D4—48no—
342C2×D4—44no—
343C2×D4—42no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4D8×C12712yes—
364C22×C4SD16×C12712yes—
365C22×C4C2×D4×C12712yes—
366C22×C4C2×Q8×C12711yescharacteristic
367C22×C4#41×C12712yes—
368C22×C4#41×C12711yescharacteristic
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C4⋊C4—42no—
373C4⋊C4—42no—
374C4⋊C4—42no—
375C4⋊C4—44no—
376C4⋊C4—81no—
377C4⋊C4—81no—
378C22⋊C4—48no—
379C22⋊C4—48no—
380C22⋊C4—42no—
381C22⋊C4—42no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—24no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—42no—
391C23—42no—
392C23—42no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23—42no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—42no—
404C23—42no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—81no—
416C23—81no—
417C23—81no—
418C23—81no—
419C23—81no—
420C23—81no—
421C23#120×C12711yescharacteristic
422C23C22⋊Q8×C12711yescharacteristic
423C23#124×C12711yescharacteristic
424C23C2×D8×C12711yescharacteristic
425C23C2×SD16×C12711yescharacteristic
426C23AGL(1,ℤ/8)×C12711yescharacteristic
427C23#137×C12711yescharacteristic
428Q8—84no—
429D4—28no—
430D4—44no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4C22⋊Q8×C12712yes—
462C2×C4#124×C12712yes—
463C8—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—82no—
491C22#393×C12711yescharacteristic
492C22#447×C12711yescharacteristic
493C22#448×C12711yescharacteristic
494C22#453×C12711yescharacteristic
495C22#454×C12711yescharacteristic
496C22B(4,𝔽2)×C12711yescharacteristic
497C22B(4,𝔽2)×C12711yescharacteristic
498C22#474×C12711yescharacteristic
499C22#476×C12711yescharacteristic
500C22#486×C12711yescharacteristic
501C22#489×C12711yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—82no—
507C4—82no—
508C4—82no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—84no—
514C2C127×#159511yescharacteristic
515C2C127×#159611yescharacteristic
516C2C127×#159811yescharacteristic
517C2C127×#159911yescharacteristic
518C2C127×#202311yescharacteristic
519C2C127×#202711yescharacteristic
520C2C127×#202911yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC23×D4×C127C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2659C2semidirect
4. C127×#1294C2semidirect
5. C127×#1280C2semidirect
26. C22×D4×C127Q8semidirect
248. #10340C127direct (N × H)
261. #2659C2×C127semidirect
264. #1294C2×C127semidirect
265. #1280C2×C127semidirect
266. C127#10340direct (N × H)
287. C22×D4Q8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26592
C127×#17862
C127×#14382
C127×#12942
C127×#12802
#10340127