Finite Group Databasebeta

← C127×#10475 #44574148

Subgroups — C127×#10475 #44574148

Order 32512.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C127C211yesmaximal, characteristic
2C127×#1984C211yesmaximal, characteristic, complemented
3C127×#1957C211yesmaximal, characteristic
4C127×#1803C211yesmaximal, characteristic, complemented
5C2×#334×C127C211yesmaximal, characteristic, complemented
6C2×#331×C127C211yesmaximal, characteristic
7C127×#1296C211yesmaximal, characteristic, complemented
8C22×SD16×C127—21no—
9C2×#127×C127C2211yescharacteristic
10C2×C4×Q8×C127C2211yescharacteristic
11#460×C127—22no—
12#460×C127—22no—
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×#103×C127—21no—
17C2×#102×C127—21no—
18C2×#102×C127—21no—
19C2×#102×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21#384×C127C2211yescharacteristic
22#340×C127—21no—
23#336×C127—21no—
24#336×C127—21no—
25#334×C127—22no—
26#331×C127—22no—
27C22×Q8×C127D411yescharacteristic
28C22×D4×C127—21no—
29C22×D4×C127—21no—
30C22×D4×C127—21no—
31C2×SD16×C127—24no—
32C2×SD16×C127—42no—
33C2×SD16×C127—42no—
34C22×C8×C127—21no—
35C22×C8×C127—21no—
36C22×C8×C127—21no—
37C22×C8×C127D411yescharacteristic
38C22×C8×C127D411yescharacteristic
39#127×C127—21no—
40#127×C127—21no—
41#127×C127—21no—
42#127×C127D412yes—
43C4×Q8×C127—21no—
44C4×Q8×C127—21no—
45C4×Q8×C127—21no—
46C4×Q8×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C42×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#103×C127—42no—
61#102×C127—24no—
62#102×C127—42no—
63#102×C127—42no—
64C4×C8×C127—21no—
65C4×C8×C127—21no—
66C24×C127—41no—
67C2×Q8×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—21no—
70C2×Q8×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127SD1612yes—
73C2×D4×C127—22no—
74C2×D4×C127—22no—
75C2×D4×C127—22no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
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—81no—
88C2×D4×C127—81no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—41no—
92C22×C4×C127C2×D411yescharacteristic
93C22×C4×C127C2×D411yescharacteristic
94C22×C4×C127#4111yescharacteristic
95SD16×C127—48no—
96C2×C8×C127—21no—
97C2×C8×C127—21no—
98C2×C8×C127—22no—
99C2×C8×C127—21no—
100C2×C8×C127—21no—
101C2×C8×C127—21no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127—41no—
106C2×C8×C127—41no—
107C2×C8×C127—41no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C2×C8×C127SD1612yescomplemented
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—41no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—81no—
120C42×C127—41no—
121C42×C127—41no—
122C42×C127C2×D411yescharacteristic
123C42×C127C2×D411yescharacteristic
124C42×C127#4111yescharacteristic
125C42×C127#4111yescharacteristic
126C23×C127—42no—
127C23×C127—81no—
128C23×C127—81no—
129C23×C127—81no—
130C23×C127—81no—
131C23×C127—81no—
132C23×C127—81no—
133C23×C127#12111yescharacteristic
134Q8×C127—22no—
135Q8×C127—22no—
136Q8×C127—41no—
137Q8×C127—41no—
138D4×C127—42no—
139D4×C127—42no—
140D4×C127—42no—
141D4×C127—42no—
142D4×C127—82no—
143D4×C127—82no—
144D4×C127—81no—
145D4×C127—81no—
146D4×C127—81no—
147D4×C127—81no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—22no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—81no—
157C2×C4×C127—81no—
158C2×C4×C127—81no—
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127#12111yescharacteristic
162C2×C4×C127#12311yescharacteristic
163C2×C4×C127#12311yescharacteristic
164C2×C4×C127#12411yescharacteristic
165C2×C4×C127C2×SD1611yescharacteristic
166C2×C4×C127C2×SD1611yescharacteristic
167C2×C4×C127#13511yescharacteristic
168C2×C4×C127#13511yescharacteristic
169C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C127#13711yescharacteristic
173C8×C127—22no—
174C8×C127—42no—
175C8×C127—41no—
176C8×C127—81no—
177C8×C127—81no—
178C22×C127—82no—
179C22×C127—82no—
180C22×C127—82no—
181C22×C127—161no—
182C22×C127—161no—
183C22×C127—161no—
184C22×C127—161no—
185C22×C127#39411yescharacteristic
186C22×C127#46011yescharacteristic
187C22×C127#46411yescharacteristic
188C22×C127#46511yescharacteristic
189C22×C127#46911yescharacteristic
190C22×C127#47111yescharacteristic
191C22×C127#47211yescharacteristic
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—42no—
195C4×C127—81no—
196C4×C127—161no—
197C4×C127#44911yescharacteristic
198C4×C127#45011yescharacteristic
199C4×C127#46111yescharacteristic
200C4×C127#46311yescharacteristic
201C4×C127#46511yescharacteristic
202C4×C127#46811yescharacteristic
203C4×C127#48111yescharacteristic
204C4×C127#48211yescharacteristic
205#10475C12711yesmaximal, characteristic, direct product factor, Sylow
206C2×C127—162no—
207C2×C127#166611yescharacteristic
208C2×C127#167811yescharacteristic
209C2×C127#168811yescharacteristic
210C2×C127#170211yescharacteristic
211C2×C127#203411yescharacteristic
212C2×C127#205111yescharacteristic
213C2×C127#205511yescharacteristic
214C2×#460C2×C12711yescharacteristic
215#1984C2×C12711yescharacteristic, complemented
216#1957C2×C12711yescharacteristic
217#1803C2×C12711yescharacteristic, complemented
218C2×#334C2×C12711yescharacteristic, complemented
219C2×#331C2×C12711yescharacteristic
220#1296C2×C12711yescharacteristic, complemented
221C127#1047511yescharacteristic, direct product factor, Sylow
222C22×SD16—21no—
223C2×#127C22×C12711yescharacteristic
224C2×C4×Q8C22×C12711yescharacteristic
225#460—22no—
226#460—22no—
227C2×C4⋊C8C22×C12711yescharacteristic
228C2×C4⋊C8C22×C12711yescharacteristic
229C2×C4⋊C8C22×C12711yescharacteristic
230C2×#103—21no—
231C2×#102—21no—
232C2×#102—21no—
233C2×#102—21no—
234C2×C4×C8C22×C12711yescharacteristic
235#384C22×C12711yescharacteristic
236#340—21no—
237#336—21no—
238#336—21no—
239#334—22no—
240#331—22no—
241C22×Q8D4×C12711yescharacteristic
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C2×SD16—24no—
246C2×SD16—42no—
247C2×SD16—42no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C22×C8D4×C12711yescharacteristic
252C22×C8D4×C12711yescharacteristic
253#127—21no—
254#127—21no—
255#127—21no—
256#127D4×C12712yes—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C12711yescharacteristic
266C2×C42—21no—
267C2×C42C23×C12711yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8D4×C12712yes—
274#103—42no—
275#102—24no—
276#102—42no—
277#102—42no—
278C4×C8—21no—
279C4×C8—21no—
280C24—41no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8SD16×C12712yes—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—81no—
302C2×D4—81no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4#41×C12711yescharacteristic
309SD16—48no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8SD16×C12712yescomplemented
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42C2×D4×C12711yescharacteristic
337C42C2×D4×C12711yescharacteristic
338C42#41×C12711yescharacteristic
339C42#41×C12711yescharacteristic
340C23—42no—
341C23—81no—
342C23—81no—
343C23—81no—
344C23—81no—
345C23—81no—
346C23—81no—
347C23#121×C12711yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—42no—
356D4—82no—
357D4—82no—
358D4—81no—
359D4—81no—
360D4—81no—
361D4—81no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#120×C12711yescharacteristic
374C2×C4#121×C12711yescharacteristic
375C2×C4#121×C12711yescharacteristic
376C2×C4#123×C12711yescharacteristic
377C2×C4#123×C12711yescharacteristic
378C2×C4#124×C12711yescharacteristic
379C2×C4C2×SD16×C12711yescharacteristic
380C2×C4C2×SD16×C12711yescharacteristic
381C2×C4#135×C12711yescharacteristic
382C2×C4#135×C12711yescharacteristic
383C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
384C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
385C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
386C2×C4#137×C12711yescharacteristic
387C8—22no—
388C8—42no—
389C8—41no—
390C8—81no—
391C8—81no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—161no—
396C22—161no—
397C22—161no—
398C22—161no—
399C22#394×C12711yescharacteristic
400C22#460×C12711yescharacteristic
401C22#464×C12711yescharacteristic
402C22#465×C12711yescharacteristic
403C22#469×C12711yescharacteristic
404C22#471×C12711yescharacteristic
405C22#472×C12711yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#449×C12711yescharacteristic
412C4#450×C12711yescharacteristic
413C4#461×C12711yescharacteristic
414C4#463×C12711yescharacteristic
415C4#465×C12711yescharacteristic
416C4#468×C12711yescharacteristic
417C4#481×C12711yescharacteristic
418C4#482×C12711yescharacteristic
419C2—162no—
420C2C127×#166611yescharacteristic
421C2C127×#167811yescharacteristic
422C2C127×#168811yescharacteristic
423C2C127×#170211yescharacteristic
424C2C127×#203411yescharacteristic
425C2C127×#205111yescharacteristic
426C2C127×#205511yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
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×#1984C2semidirect
4. C127×#1803C2semidirect
5. C2×#334×C127C2semidirect
7. C127×#1296C2semidirect
110. C2×C8×C127SD16semidirect
205. #10475C127direct (N × H)
215. #1984C2×C127semidirect
217. #1803C2×C127semidirect
218. C2×#334C2×C127semidirect
220. #1296C2×C127semidirect
221. C127#10475direct (N × H)
324. C2×C8SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1272
C127×#19842
C127×#19572
C127×#18032
C2×#334×C1272
C2×#331×C1272
C127×#12962
#10475127