Finite Group Databasebeta

← C127×#10472 #44574145

Subgroups — C127×#10472 #44574145

Order 32512.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C127C211yesmaximal, characteristic
2C127×#1957C211yesmaximal, characteristic, complemented
3C127×#1954C211yesmaximal, characteristic, complemented
4C127×#1802C211yesmaximal, characteristic, complemented
5C2×#335×C127C211yesmaximal, characteristic, complemented
6C2×#331×C127C211yesmaximal, characteristic, complemented
7C127×#1296C211yesmaximal, characteristic, complemented
8C22×D8×C127—21no—
9C2×#127×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11#459×C127—22no—
12#459×C127—22no—
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×#102×C127—21no—
17C2×#102×C127—21no—
18C2×#102×C127—21no—
19C2×#102×C127—21no—
20C2×C22⋊C8×C127—21no—
21C2×C22⋊C8×C127—21no—
22C2×C4×C8×C127C2211yescharacteristic
23#384×C127C2211yescharacteristic
24#340×C127—21no—
25#335×C127—22no—
26#331×C127—22no—
27C22×D4×C127—21no—
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127D411yescharacteristic
31C23×C4×C127—21no—
32C2×D8×C127—24no—
33C2×D8×C127—42no—
34C2×D8×C127—42no—
35C22×C8×C127—21no—
36C22×C8×C127—21no—
37C22×C8×C127—21no—
38C22×C8×C127D411yescharacteristic
39C22×C8×C127D411yescharacteristic
40#127×C127—21no—
41#127×C127—21no—
42#127×C127—21no—
43#127×C127D412yes—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—21no—
53C2×C42×C127C2311yescharacteristic
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127D412yes—
60#102×C127—24no—
61#102×C127—42no—
62#102×C127—42no—
63#102×C127—42no—
64C22⋊C8×C127—42no—
65C22⋊C8×C127—42no—
66C4×C8×C127—21no—
67C4×C8×C127—21no—
68C24×C127—21no—
69C24×C127—41no—
70C2×D4×C127—21no—
71C2×D4×C127—22no—
72C2×D4×C127—22no—
73C2×D4×C127—21no—
74C2×D4×C127—22no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C2×D4×C127—41no—
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—81no—
90C2×D4×C127—81no—
91C2×D4×C127D812yes—
92C22×C4×C127—21no—
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×C127C2×D411yescharacteristic
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127#4111yescharacteristic
103D8×C127—48no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—22no—
107C2×C8×C127—21no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C2×C8×C127—41no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127D812yescomplemented
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—41no—
122C4⋊C4×C127—41no—
123C4⋊C4×C127—41no—
124C4⋊C4×C127—41no—
125C4⋊C4×C127—81no—
126C22⋊C4×C127—41no—
127C22⋊C4×C127—41no—
128C42×C127C2×D411yescharacteristic
129C42×C127C2×D411yescharacteristic
130C42×C127#4111yescharacteristic
131C42×C127#4111yescharacteristic
132C23×C127—22no—
133C23×C127—41no—
134C23×C127—41no—
135C23×C127—41no—
136C23×C127—41no—
137C23×C127—41no—
138C23×C127—41no—
139C23×C127—42no—
140C23×C127—81no—
141C23×C127—81no—
142C23×C127—81no—
143C23×C127—81no—
144C23×C127—81no—
145C23×C127—81no—
146C23×C127#12111yescharacteristic
147D4×C127—22no—
148D4×C127—22no—
149D4×C127—42no—
150D4×C127—41no—
151D4×C127—42no—
152D4×C127—42no—
153D4×C127—42no—
154D4×C127—41no—
155D4×C127—82no—
156D4×C127—82no—
157D4×C127—81no—
158D4×C127—81no—
159D4×C127—81no—
160D4×C127—81no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—81no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127—81no—
171C2×C4×C127—81no—
172C2×C4×C127—81no—
173C2×C4×C127#12011yescharacteristic
174C2×C4×C127#12111yescharacteristic
175C2×C4×C127#12111yescharacteristic
176C2×C4×C127#12311yescharacteristic
177C2×C4×C127#12311yescharacteristic
178C2×C4×C127#12411yescharacteristic
179C2×C4×C127C2×D811yescharacteristic
180C2×C4×C127C2×D811yescharacteristic
181C2×C4×C127#13511yescharacteristic
182C2×C4×C127#13511yescharacteristic
183C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
184C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C127#13711yescharacteristic
187C8×C127—22no—
188C8×C127—42no—
189C8×C127—41no—
190C8×C127—81no—
191C8×C127—81no—
192C22×C127—42no—
193C22×C127—42no—
194C22×C127—42no—
195C22×C127—81no—
196C22×C127—81no—
197C22×C127—81no—
198C22×C127—81no—
199C22×C127—82no—
200C22×C127—82no—
201C22×C127—82no—
202C22×C127—161no—
203C22×C127—161no—
204C22×C127—161no—
205C22×C127—161no—
206C22×C127#39411yescharacteristic
207C22×C127#45911yescharacteristic
208C22×C127#46311yescharacteristic
209C22×C127#46611yescharacteristic
210C22×C127#46811yescharacteristic
211C22×C127#47111yescharacteristic
212C22×C127#47211yescharacteristic
213C4×C127—21no—
214C4×C127—21no—
215C4×C127—81no—
216C4×C127—161no—
217C4×C127#44711yescharacteristic
218C4×C127#45211yescharacteristic
219C4×C127#45911yescharacteristic
220C4×C127#46311yescharacteristic
221C4×C127#46611yescharacteristic
222C4×C127#46911yescharacteristic
223C4×C127#48011yescharacteristic
224C4×C127#48211yescharacteristic
225#10472C12711yesmaximal, characteristic, direct product factor, Sylow
226C2×C127—82no—
227C2×C127—162no—
228C2×C127#166711yescharacteristic
229C2×C127#168111yescharacteristic
230C2×C127#168511yescharacteristic
231C2×C127#169711yescharacteristic
232C2×C127#203311yescharacteristic
233C2×C127#205111yescharacteristic
234C2×C127#205411yescharacteristic
235C2×#459C2×C12711yescharacteristic
236#1957C2×C12711yescharacteristic, complemented
237#1954C2×C12711yescharacteristic, complemented
238#1802C2×C12711yescharacteristic, complemented
239C2×#335C2×C12711yescharacteristic, complemented
240C2×#331C2×C12711yescharacteristic, complemented
241#1296C2×C12711yescharacteristic, complemented
242C127#1047211yescharacteristic, direct product factor, Sylow
243C22×D8—21no—
244C2×#127C22×C12711yescharacteristic
245C2×C4×D4C22×C12711yescharacteristic
246#459—22no—
247#459—22no—
248C2×C4⋊C8C22×C12711yescharacteristic
249C2×C4⋊C8C22×C12711yescharacteristic
250C2×C4⋊C8C22×C12711yescharacteristic
251C2×#102—21no—
252C2×#102—21no—
253C2×#102—21no—
254C2×#102—21no—
255C2×C22⋊C8—21no—
256C2×C22⋊C8—21no—
257C2×C4×C8C22×C12711yescharacteristic
258#384C22×C12711yescharacteristic
259#340—21no—
260#335—22no—
261#331—22no—
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4D4×C12711yescharacteristic
266C23×C4—21no—
267C2×D8—24no—
268C2×D8—42no—
269C2×D8—42no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8D4×C12711yescharacteristic
274C22×C8D4×C12711yescharacteristic
275#127—21no—
276#127—21no—
277#127—21no—
278#127D4×C12712yes—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4D4×C12711yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C23×C12711yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8D4×C12712yes—
295#102—24no—
296#102—42no—
297#102—42no—
298#102—42no—
299C22⋊C8—42no—
300C22⋊C8—42no—
301C4×C8—21no—
302C4×C8—21no—
303C24—21no—
304C24—41no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4D8×C12712yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C2×D4×C12711yescharacteristic
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4#41×C12711yescharacteristic
338D8—48no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—22no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—41no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8D8×C12712yescomplemented
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—81no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42C2×D4×C12711yescharacteristic
364C42C2×D4×C12711yescharacteristic
365C42#41×C12711yescharacteristic
366C42#41×C12711yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23#121×C12711yescharacteristic
382D4—22no—
383D4—22no—
384D4—42no—
385D4—41no—
386D4—42no—
387D4—42no—
388D4—42no—
389D4—41no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4#120×C12711yescharacteristic
409C2×C4#121×C12711yescharacteristic
410C2×C4#121×C12711yescharacteristic
411C2×C4#123×C12711yescharacteristic
412C2×C4#123×C12711yescharacteristic
413C2×C4#124×C12711yescharacteristic
414C2×C4C2×D8×C12711yescharacteristic
415C2×C4C2×D8×C12711yescharacteristic
416C2×C4#135×C12711yescharacteristic
417C2×C4#135×C12711yescharacteristic
418C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
419C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
420C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
421C2×C4#137×C12711yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—81no—
426C8—81no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22#394×C12711yescharacteristic
442C22#459×C12711yescharacteristic
443C22#463×C12711yescharacteristic
444C22#466×C12711yescharacteristic
445C22#468×C12711yescharacteristic
446C22#471×C12711yescharacteristic
447C22#472×C12711yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—161no—
452C4#447×C12711yescharacteristic
453C4#452×C12711yescharacteristic
454C4#459×C12711yescharacteristic
455C4#463×C12711yescharacteristic
456C4#466×C12711yescharacteristic
457C4#469×C12711yescharacteristic
458C4#480×C12711yescharacteristic
459C4#482×C12711yescharacteristic
460C2—82no—
461C2—162no—
462C2C127×#166711yescharacteristic
463C2C127×#168111yescharacteristic
464C2C127×#168511yescharacteristic
465C2C127×#169711yescharacteristic
466C2C127×#203311yescharacteristic
467C2C127×#205111yescharacteristic
468C2C127×#205411yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#459×C127C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1957C2semidirect
3. C127×#1954C2semidirect
4. C127×#1802C2semidirect
5. C2×#335×C127C2semidirect
6. C2×#331×C127C2semidirect
7. C127×#1296C2semidirect
118. C2×C8×C127D8semidirect
225. #10472C127direct (N × H)
236. #1957C2×C127semidirect
237. #1954C2×C127semidirect
238. #1802C2×C127semidirect
239. C2×#335C2×C127semidirect
240. C2×#331C2×C127semidirect
241. #1296C2×C127semidirect
242. C127#10472direct (N × H)
353. C2×C8D8×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1272
C127×#19572
C127×#19542
C127×#18022
C2×#335×C1272
C2×#331×C1272
C127×#12962
#10472127