Finite Group Databasebeta

← C127×#12186 #44575859

Subgroups — C127×#12186 #44575859

Order 32512.

682 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2668C211yesmaximal, characteristic, complemented
2C127×#2021C211yesmaximal, characteristic, complemented
3C127×#1613C211yesmaximal, characteristic, complemented
4C127×#1595C211yesmaximal, characteristic, complemented
5C127×#1352C211yesmaximal, characteristic, complemented
6C127×#1343C211yesmaximal, characteristic, complemented
7C127×#1316C211yesmaximal, characteristic, complemented
8#534×C127C2211yescharacteristic
9C2×#121×C127—21no—
10C2×#120×C127—21no—
11C2×#120×C127—21no—
12#481×C127—21no—
13#447×C127—21no—
14C2×#99×C127—21no—
15#399×C127C2211yescharacteristic
16#397×C127—21no—
17#394×C127—21no—
18#392×C127C2211yescharacteristic
19#386×C127—21no—
20#386×C127—21no—
21#379×C127C2211yescharacteristic
22#342×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#323×C127C2211yescharacteristic
26#323×C127C2211yescharacteristic
27C25×C127D411yescharacteristic
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127—41no—
33C22×D4×C127D411yescharacteristic, complemented
34C23×C4×C127—21no—
35C2×D8×C127—41no—
36#123×C127—41no—
37#121×C127—21no—
38#121×C127—21no—
39#121×C127—44no—
40#120×C127—42no—
41#120×C127—41no—
42#120×C127—44no—
43#120×C127—42no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127D411yescharacteristic, complemented
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—21no—
48C2×C22⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C22⋊C4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—41no—
55C2×C22⋊C4×C127D411yescharacteristic
56C2×C22⋊C4×C127C2311yescharacteristic
57#106×C127—41no—
58#102×C127—41no—
59#102×C127—41no—
60#99×C127—42no—
61C22⋊C8×C127—21no—
62C22⋊C8×C127—21no—
63#95×C127—21no—
64#95×C127—21no—
65#95×C127D411yescharacteristic, complemented
66#95×C127D411yescharacteristic, complemented
67C24×C127—21no—
68C24×C127—21no—
69C24×C127—21no—
70C24×C127—21no—
71C24×C127—21no—
72C24×C127—41no—
73C24×C127—41no—
74C24×C127—42no—
75C24×C127—81no—
76C24×C127C2×D411yescharacteristic
77C2×D4×C127—24no—
78C2×D4×C127—21no—
79C2×D4×C127—21no—
80C2×D4×C127—41no—
81C2×D4×C127—42no—
82C2×D4×C127—41no—
83C2×D4×C127—41no—
84C2×D4×C127—42no—
85C2×D4×C127—42no—
86C2×D4×C127—41no—
87C2×D4×C127—42no—
88C2×D4×C127—44no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—81no—
95C2×D4×C127—81no—
96C2×D4×C127—81no—
97C2×D4×C127—81no—
98C2×D4×C127—82no—
99C2×D4×C127—82no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—21no—
103C22×C4×C127—21no—
104C22×C4×C127—21no—
105C22×C4×C127—42no—
106C22×C4×C127—41no—
107C22×C4×C127—81no—
108C22×C4×C127—81no—
109C22×C4×C127C2×D411yescharacteristic
110C22×C4×C127C2×D411yescharacteristic
111D8×C127—82no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127—42no—
118C22⋊C4×C127—22no—
119C22⋊C4×C127—41no—
120C22⋊C4×C127—42no—
121C22⋊C4×C127—42no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—42no—
125C22⋊C4×C127—42no—
126C22⋊C4×C127—42no—
127C22⋊C4×C127—44no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—81no—
131C22⋊C4×C127—81no—
132C23×C127—21no—
133C23×C127—21no—
134C23×C127—22no—
135C23×C127—22no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—42no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127—41no—
146C23×C127—41no—
147C23×C127—42no—
148C23×C127—42no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127—41no—
154C23×C127—41no—
155C23×C127—41no—
156C23×C127—81no—
157C23×C127—82no—
158C23×C127—81no—
159C23×C127—82no—
160C23×C127—84no—
161C23×C127—81no—
162C23×C127—81no—
163C23×C127—81no—
164C23×C127#12011yescharacteristic
165C23×C127#13511yescharacteristic
166C23×C127AGL(1,ℤ/8)11yescharacteristic
167D4×C127—42no—
168D4×C127—84no—
169D4×C127—81no—
170D4×C127—81no—
171D4×C127—81no—
172D4×C127—81no—
173D4×C127—81no—
174D4×C127—82no—
175D4×C127—82no—
176D4×C127—84no—
177D4×C127—88no—
178D4×C127—81no—
179D4×C127—81no—
180C2×C4×C127—22no—
181C2×C4×C127—21no—
182C2×C4×C127—21no—
183C2×C4×C127—41no—
184C2×C4×C127—41no—
185C2×C4×C127—41no—
186C2×C4×C127—41no—
187C2×C4×C127—42no—
188C2×C4×C127—41no—
189C2×C4×C127—41no—
190C2×C4×C127—41no—
191C2×C4×C127—41no—
192C2×C4×C127—41no—
193C2×C4×C127—41no—
194C2×C4×C127—41no—
195C2×C4×C127—41no—
196C2×C4×C127—41no—
197C2×C4×C127—41no—
198C2×C4×C127—41no—
199C2×C4×C127—41no—
200C2×C4×C127—84no—
201C2×C4×C127—81no—
202C2×C4×C127—81no—
203C8×C127—81no—
204C8×C127—81no—
205C22×C127—21no—
206C22×C127—21no—
207C22×C127—21no—
208C22×C127—21no—
209C22×C127—41no—
210C22×C127—41no—
211C22×C127—42no—
212C22×C127—42no—
213C22×C127—42no—
214C22×C127—42no—
215C22×C127—41no—
216C22×C127—41no—
217C22×C127—44no—
218C22×C127—42no—
219C22×C127—42no—
220C22×C127—81no—
221C22×C127—81no—
222C22×C127—81no—
223C22×C127—81no—
224C22×C127—81no—
225C22×C127—82no—
226C22×C127—82no—
227C22×C127—82no—
228C22×C127—82no—
229C22×C127—81no—
230C22×C127—81no—
231C22×C127—81no—
232C22×C127—81no—
233C22×C127—81no—
234C22×C127—81no—
235C22×C127—81no—
236C22×C127—161no—
237C22×C127#44911yescharacteristic
238C22×C127#45311yescharacteristic
239C22×C127B(4,𝔽2)11yescharacteristic
240C4×C127—42no—
241C4×C127—41no—
242C4×C127—41no—
243C4×C127—81no—
244C4×C127—81no—
245C4×C127—82no—
246C4×C127—81no—
247C4×C127—81no—
248#12186C12711yesmaximal, characteristic, direct product factor, Sylow
249C2×C127—21no—
250C2×C127—21no—
251C2×C127—41no—
252C2×C127—41no—
253C2×C127—82no—
254C2×C127—82no—
255C2×C127—161no—
256C2×C127#160011yescharacteristic
257C2×C127#219611yescharacteristic
258C2×C127#220011yescharacteristic
259#2668C2×C12711yescharacteristic, complemented
260#2021C2×C12711yescharacteristic, complemented
261#1613C2×C12711yescharacteristic, complemented
262#1595C2×C12711yescharacteristic, complemented
263#1352C2×C12711yescharacteristic, complemented
264#1343C2×C12711yescharacteristic, complemented
265#1316C2×C12711yescharacteristic, complemented
266C127#1218611yescharacteristic, direct product factor, Sylow
267#534C22×C12711yescharacteristic
268C2×#121—21no—
269C2×#120—21no—
270C2×#120—21no—
271#481—21no—
272#447—21no—
273C2×#99—21no—
274#399C22×C12711yescharacteristic
275#397—21no—
276#394—21no—
277#392C22×C12711yescharacteristic
278#386—21no—
279#386—21no—
280#379C22×C12711yescharacteristic
281#342C22×C12711yescharacteristic
282#327—21no—
283#327—21no—
284#323C22×C12711yescharacteristic
285#323C22×C12711yescharacteristic
286C25D4×C12711yescharacteristic
287C22×D4—21no—
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—41no—
292C22×D4D4×C12711yescharacteristic, complemented
293C23×C4—21no—
294C2×D8—41no—
295#123—41no—
296#121—21no—
297#121—21no—
298#121—44no—
299#120—42no—
300#120—41no—
301#120—44no—
302#120—42no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C12711yescharacteristic, complemented
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4D4×C12711yescharacteristic
315C2×C22⋊C4C23×C12711yescharacteristic
316#106—41no—
317#102—41no—
318#102—41no—
319#99—42no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322#95—21no—
323#95—21no—
324#95D4×C12711yescharacteristic, complemented
325#95D4×C12711yescharacteristic, complemented
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—41no—
332C24—41no—
333C24—42no—
334C24—81no—
335C24C2×D4×C12711yescharacteristic
336C2×D4—24no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4—41no—
340C2×D4—42no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—42no—
347C2×D4—44no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—81no—
354C2×D4—81no—
355C2×D4—81no—
356C2×D4—81no—
357C2×D4—82no—
358C2×D4—82no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4—81no—
367C22×C4—81no—
368C22×C4C2×D4×C12711yescharacteristic
369C22×C4C2×D4×C12711yescharacteristic
370D8—82no—
371C2×C8—41no—
372C2×C8—41no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—41no—
376C4⋊C4—42no—
377C22⋊C4—22no—
378C22⋊C4—41no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—42no—
386C22⋊C4—44no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—81no—
390C22⋊C4—81no—
391C23—21no—
392C23—21no—
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—81no—
416C23—82no—
417C23—81no—
418C23—82no—
419C23—84no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23#120×C12711yescharacteristic
424C23#135×C12711yescharacteristic
425C23AGL(1,ℤ/8)×C12711yescharacteristic
426D4—42no—
427D4—84no—
428D4—81no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—82no—
434D4—82no—
435D4—84no—
436D4—88no—
437D4—81no—
438D4—81no—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—84no—
460C2×C4—81no—
461C2×C4—81no—
462C8—81no—
463C8—81no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—41no—
469C22—41no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22—82no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—161no—
496C22#449×C12711yescharacteristic
497C22#453×C12711yescharacteristic
498C22B(4,𝔽2)×C12711yescharacteristic
499C4—42no—
500C4—41no—
501C4—41no—
502C4—81no—
503C4—81no—
504C4—82no—
505C4—81no—
506C4—81no—
507C2—21no—
508C2—21no—
509C2—41no—
510C2—41no—
511C2—82no—
512C2—82no—
513C2—161no—
514C2C127×#160011yescharacteristic
515C2C127×#219611yescharacteristic
516C2C127×#220011yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C127
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2668C2semidirect
2. C127×#2021C2semidirect
3. C127×#1613C2semidirect
4. C127×#1595C2semidirect
5. C127×#1352C2semidirect
6. C127×#1343C2semidirect
7. C127×#1316C2semidirect
33. C22×D4×C127D4semidirect
45. C2×C4⋊C4×C127D4semidirect
65. #95×C127D4semidirect
66. #95×C127D4semidirect
248. #12186C127direct (N × H)
259. #2668C2×C127semidirect
260. #2021C2×C127semidirect
261. #1613C2×C127semidirect
262. #1595C2×C127semidirect
263. #1352C2×C127semidirect
264. #1343C2×C127semidirect
265. #1316C2×C127semidirect
266. C127#12186direct (N × H)
292. C22×D4D4×C127semidirect
304. C2×C4⋊C4D4×C127semidirect
324. #95D4×C127semidirect
325. #95D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26682
C127×#20212
C127×#16132
C127×#15952
C127×#13522
C127×#13432
C127×#13162
#12186127