Finite Group Databasebeta

← C127×#12148 #44575821

Subgroups — C127×#12148 #44575821

Order 32512.

622 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2675C211yesmaximal, characteristic, complemented
2C127×#2044C211yesmaximal, characteristic, complemented
3C127×#1595C211yesmaximal, characteristic, complemented
4C127×#1595C211yesmaximal, characteristic, complemented
5C127×#1343C211yesmaximal, characteristic, complemented
6C127×#1343C211yesmaximal, characteristic, complemented
7C127×#1326C211yesmaximal, characteristic, complemented
8#534×C127C2211yescharacteristic
9C2×#121×C127—21no—
10C2×#121×C127—21no—
11C2×#121×C127—21no—
12#447×C127—21no—
13#447×C127—21no—
14C2×#99×C127—21no—
15#396×C127—21no—
16#392×C127—21no—
17#392×C127C2211yescharacteristic
18#392×C127C2211yescharacteristic
19#386×C127—21no—
20#385×C127—21no—
21#385×C127C2211yescharacteristic
22#342×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#323×C127C2211yescharacteristic
26#323×C127C2211yescharacteristic
27C22×D4×C127—21no—
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127—21no—
31C22×D4×C127—21no—
32C22×D4×C127D411yescharacteristic
33C22×D4×C127D411yescharacteristic
34C23×C4×C127—21no—
35C23×C4×C127D411yescharacteristic
36C2×D8×C127—41no—
37C2×D8×C127—41no—
38#123×C127—41no—
39#121×C127—21no—
40#121×C127—21no—
41#121×C127—44no—
42#121×C127—44no—
43#121×C127—42no—
44#121×C127—42no—
45#120×C127—41no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊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—21no—
55C2×C22⋊C4×C127—41no—
56C2×C22⋊C4×C127D411yescharacteristic
57C2×C22⋊C4×C127C2311yescharacteristic
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—41no—
65#95×C127D411yescharacteristic
66#95×C127D411yescharacteristic
67C24×C127—21no—
68C24×C127—21no—
69C24×C127—21no—
70C24×C127C2×D411yescharacteristic
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—42no—
76C2×D4×C127—42no—
77C2×D4×C127—42no—
78C2×D4×C127—42no—
79C2×D4×C127—41no—
80C2×D4×C127—42no—
81C2×D4×C127—42no—
82C2×D4×C127—42no—
83C2×D4×C127—41no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—41no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—81no—
93C2×D4×C127—81no—
94C2×D4×C127—81no—
95C2×D4×C127—81no—
96C2×D4×C127—81no—
97C22×C4×C127—21no—
98C22×C4×C127—21no—
99C22×C4×C127—21no—
100C22×C4×C127—21no—
101C22×C4×C127—21no—
102C22×C4×C127—42no—
103C22×C4×C127—42no—
104C22×C4×C127—42no—
105C22×C4×C127—41no—
106C22×C4×C127—41no—
107C22×C4×C127—81no—
108C22×C4×C127C2×D411yescharacteristic
109C22×C4×C127C2×D411yescharacteristic
110D8×C127—82no—
111D8×C127—82no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—42no—
117C4⋊C4×C127—42no—
118C4⋊C4×C127—42no—
119C22⋊C4×C127—24no—
120C22⋊C4×C127—21no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—42no—
123C22⋊C4×C127—42no—
124C22⋊C4×C127—42no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C22⋊C4×C127—41no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—81no—
130C22⋊C4×C127—82no—
131C22⋊C4×C127D812yescomplemented
132C23×C127—21no—
133C23×C127—21no—
134C23×C127—22no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127—41no—
141C23×C127—41no—
142C23×C127—41no—
143C23×C127—41no—
144C23×C127—41no—
145C23×C127—41no—
146C23×C127—41no—
147C23×C127—41no—
148C23×C127—41no—
149C23×C127—41no—
150C23×C127—41no—
151C23×C127—41no—
152C23×C127—41no—
153C23×C127—81no—
154C23×C127—81no—
155C23×C127#12011yescharacteristic
156C23×C127C2×D811yescharacteristic
157C23×C127AGL(1,ℤ/8)11yescharacteristic
158D4×C127—42no—
159D4×C127—42no—
160D4×C127—81no—
161D4×C127—82no—
162D4×C127—82no—
163D4×C127—84no—
164D4×C127—84no—
165D4×C127—81no—
166D4×C127—81no—
167D4×C127—81no—
168D4×C127—81no—
169D4×C127—81no—
170D4×C127—82no—
171D4×C127—82no—
172D4×C127—81no—
173D4×C127—81no—
174C2×C4×C127—22no—
175C2×C4×C127—22no—
176C2×C4×C127—22no—
177C2×C4×C127—21no—
178C2×C4×C127—21no—
179C2×C4×C127—41no—
180C2×C4×C127—41no—
181C2×C4×C127—41no—
182C2×C4×C127—41no—
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—81no—
195C2×C4×C127—84no—
196C2×C4×C127—81no—
197C2×C4×C127—81no—
198C2×C4×C127—81no—
199C8×C127—81no—
200C8×C127—81no—
201C22×C127—21no—
202C22×C127—21no—
203C22×C127—21no—
204C22×C127—21no—
205C22×C127—41no—
206C22×C127—41no—
207C22×C127—42no—
208C22×C127—42no—
209C22×C127—41no—
210C22×C127—41no—
211C22×C127—42no—
212C22×C127—81no—
213C22×C127—81no—
214C22×C127—81no—
215C22×C127—81no—
216C22×C127—81no—
217C22×C127—81no—
218C22×C127—81no—
219C22×C127—82no—
220C22×C127—81no—
221C22×C127—81no—
222C22×C127—81no—
223C22×C127—81no—
224C22×C127—81no—
225C22×C127—81no—
226C22×C127—81no—
227C22×C127—81no—
228C22×C127—161no—
229C22×C127#44711yescharacteristic
230C22×C127#45411yescharacteristic
231C22×C127B(4,𝔽2)11yescharacteristic
232C4×C127—42no—
233C4×C127—42no—
234C4×C127—41no—
235C4×C127—42no—
236C4×C127—41no—
237C4×C127—81no—
238C4×C127—81no—
239C4×C127—161no—
240#12148C12711yesmaximal, characteristic, direct product factor, Sylow
241C2×C127—21no—
242C2×C127—21no—
243C2×C127—41no—
244C2×C127—41no—
245C2×C127—82no—
246C2×C127—161no—
247C2×C127—161no—
248C2×C127#159811yescharacteristic
249C2×C127#219611yescharacteristic
250C2×C127#220011yescharacteristic
251#2675C2×C12711yescharacteristic, complemented
252#2044C2×C12711yescharacteristic, complemented
253#1595C2×C12711yescharacteristic, complemented
254#1595C2×C12711yescharacteristic, complemented
255#1343C2×C12711yescharacteristic, complemented
256#1343C2×C12711yescharacteristic, complemented
257#1326C2×C12711yescharacteristic, complemented
258C127#1214811yescharacteristic, direct product factor, Sylow
259#534C22×C12711yescharacteristic
260C2×#121—21no—
261C2×#121—21no—
262C2×#121—21no—
263#447—21no—
264#447—21no—
265C2×#99—21no—
266#396—21no—
267#392—21no—
268#392C22×C12711yescharacteristic
269#392C22×C12711yescharacteristic
270#386—21no—
271#385—21no—
272#385C22×C12711yescharacteristic
273#342C22×C12711yescharacteristic
274#327—21no—
275#327—21no—
276#323C22×C12711yescharacteristic
277#323C22×C12711yescharacteristic
278C22×D4—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4D4×C12711yescharacteristic
284C22×D4D4×C12711yescharacteristic
285C23×C4—21no—
286C23×C4D4×C12711yescharacteristic
287C2×D8—41no—
288C2×D8—41no—
289#123—41no—
290#121—21no—
291#121—21no—
292#121—44no—
293#121—44no—
294#121—42no—
295#121—42no—
296#120—41no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4D4×C12711yescharacteristic
308C2×C22⋊C4C23×C12711yescharacteristic
309#102—41no—
310#102—41no—
311#99—42no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314#95—21no—
315#95—41no—
316#95D4×C12711yescharacteristic
317#95D4×C12711yescharacteristic
318C24—21no—
319C24—21no—
320C24—21no—
321C24C2×D4×C12711yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—42no—
329C2×D4—42no—
330C2×D4—41no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—81no—
344C2×D4—81no—
345C2×D4—81no—
346C2×D4—81no—
347C2×D4—81no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—81no—
359C22×C4C2×D4×C12711yescharacteristic
360C22×C4C2×D4×C12711yescharacteristic
361D8—82no—
362D8—82no—
363C2×C8—41no—
364C2×C8—41no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—42no—
368C4⋊C4—42no—
369C4⋊C4—42no—
370C22⋊C4—24no—
371C22⋊C4—21no—
372C22⋊C4—41no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—81no—
381C22⋊C4—82no—
382C22⋊C4D8×C12712yescomplemented
383C23—21no—
384C23—21no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—81no—
405C23—81no—
406C23#120×C12711yescharacteristic
407C23C2×D8×C12711yescharacteristic
408C23AGL(1,ℤ/8)×C12711yescharacteristic
409D4—42no—
410D4—42no—
411D4—81no—
412D4—82no—
413D4—82no—
414D4—84no—
415D4—84no—
416D4—81no—
417D4—81no—
418D4—81no—
419D4—81no—
420D4—81no—
421D4—82no—
422D4—82no—
423D4—81no—
424D4—81no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—84no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C8—81no—
451C8—81no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—42no—
459C22—42no—
460C22—41no—
461C22—41no—
462C22—42no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—82no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—161no—
480C22#447×C12711yescharacteristic
481C22#454×C12711yescharacteristic
482C22B(4,𝔽2)×C12711yescharacteristic
483C4—42no—
484C4—42no—
485C4—41no—
486C4—42no—
487C4—41no—
488C4—81no—
489C4—81no—
490C4—161no—
491C2—21no—
492C2—21no—
493C2—41no—
494C2—41no—
495C2—82no—
496C2—161no—
497C2—161no—
498C2C127×#159811yescharacteristic
499C2C127×#219611yescharacteristic
500C2C127×#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×#2675C2semidirect
2. C127×#2044C2semidirect
3. C127×#1595C2semidirect
4. C127×#1595C2semidirect
5. C127×#1343C2semidirect
6. C127×#1343C2semidirect
7. C127×#1326C2semidirect
131. C22⋊C4×C127D8semidirect
240. #12148C127direct (N × H)
251. #2675C2×C127semidirect
252. #2044C2×C127semidirect
253. #1595C2×C127semidirect
254. #1595C2×C127semidirect
255. #1343C2×C127semidirect
256. #1343C2×C127semidirect
257. #1326C2×C127semidirect
258. C127#12148direct (N × H)
382. C22⋊C4D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26752
C127×#20442
C127×#15952
C127×#13432
C127×#13262
#12148127