Finite Group Databasebeta

← C127×#10465 #44574138

Subgroups — C127×#10465 #44574138

Order 32512.

452 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3036C211yesmaximal, characteristic
2C127×#1804C211yesmaximal, characteristic, complemented
3C127×#1570C211yesmaximal, characteristic, complemented
4C127×#1540C211yesmaximal, characteristic, complemented
5C127×#1517C211yesmaximal, characteristic, complemented
6C127×#1460C211yesmaximal, characteristic, complemented
7C127×#1286C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C127—21no—
9#532×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11#463×C127—22no—
12#461×C127—21no—
13#459×C127—21no—
14#431×C127C2211yescharacteristic
15#431×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#417×C127—21no—
19C2×#102×C127—21no—
20#382×C127C2211yescharacteristic
21#340×C127—21no—
22#334×C127—22no—
23#332×C127—21no—
24#331×C127—21no—
25#327×C127—22no—
26#323×C127—22no—
27C2×#41×C127—21no—
28C22×D4×C127D411yescharacteristic
29C23×C4×C127—21no—
30AGL(1,ℤ/8)×C127—42no—
31AGL(1,ℤ/8)×C127—42no—
32C2×SD16×C127—22no—
33C2×D8×C127—22no—
34C2×M16×C127—21no—
35C22×C8×C127—21no—
36C4⋊Q8×C127D411yescharacteristic
37#127×C127D411yescharacteristic
38#124×C127—21no—
39#121×C127—21no—
40#121×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C4×D4×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C4×D4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127—21no—
50C2×C42×C127C2311yescharacteristic
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127D412yes—
57#103×C127—22no—
58#102×C127—22no—
59#102×C127—42no—
60C22⋊C8×C127—21no—
61C22⋊C8×C127D412yes—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64#95×C127—21no—
65#95×C127—21no—
66C24×C127—21no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70#41×C127—41no—
71C2×Q8×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—21no—
79C2×D4×C127—21no—
80C2×D4×C127—41no—
81C2×D4×C127SD1612yes—
82C22×C4×C127—21no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127—82no—
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127#4111yescharacteristic
91SD16×C127—44no—
92D8×C127—44no—
93M16×C127—41no—
94M16×C127—41no—
95C2×C8×C127—22no—
96C2×C8×C127—22no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—41no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127—41no—
106C4⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C42×C127C2×D411yescharacteristic
112C42×C127C2×D411yescharacteristic
113C42×C127#4111yescharacteristic
114C42×C127#4111yescharacteristic
115C23×C127—22no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—81no—
120C23×C127—81no—
121C23×C127#12111yescharacteristic
122Q8×C127—41no—
123Q8×C127—41no—
124D4×C127—22no—
125D4×C127—22no—
126D4×C127—41no—
127D4×C127—41no—
128D4×C127—41no—
129D4×C127—41no—
130D4×C127—81no—
131D4×C127—81no—
132D4×C127—81no—
133D4×C127—81no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—82no—
139C2×C4×C127—82no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127—81no—
144C2×C4×C127—81no—
145C2×C4×C127—81no—
146C2×C4×C127#12011yescharacteristic
147C2×C4×C127#12111yescharacteristic
148C2×C4×C127#12111yescharacteristic
149C2×C4×C127#12311yescharacteristic
150C2×C4×C127#12311yescharacteristic
151C2×C4×C127#12411yescharacteristic
152C2×C4×C127C2×SD1611yescharacteristic
153C2×C4×C127#13511yescharacteristic
154C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
156C8×C127—42no—
157C8×C127—42no—
158C8×C127—81no—
159C8×C127—81no—
160C22×C127—21no—
161C22×C127—21no—
162C22×C127—42no—
163C22×C127—82no—
164C22×C127—82no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127#39411yescharacteristic
171C22×C127#46511yescharacteristic
172C22×C127#46911yescharacteristic
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—81no—
178C4×C127—81no—
179C4×C127—161no—
180C4×C127#44911yescharacteristic
181C4×C127#45011yescharacteristic
182C4×C127#48111yescharacteristic
183C4×C127#48211yescharacteristic
184#10465C12711yesmaximal, characteristic, direct product factor, Sylow
185C2×C127—21no—
186C2×C127—21no—
187C2×C127—82no—
188C2×C127—161no—
189C2×C127#203411yescharacteristic
190C2×C127#204811yescharacteristic
191C2×C127#205311yescharacteristic
192#3036C2×C12711yescharacteristic
193#1804C2×C12711yescharacteristic, complemented
194#1570C2×C12711yescharacteristic, complemented
195#1540C2×C12711yescharacteristic, complemented
196#1517C2×C12711yescharacteristic, complemented
197#1460C2×C12711yescharacteristic, complemented
198#1286C2×C12711yescharacteristic, complemented
199C127#1046511yescharacteristic, direct product factor, Sylow
200C2×AGL(1,ℤ/8)—21no—
201#532C22×C12711yescharacteristic
202C2×C4×D4C22×C12711yescharacteristic
203#463—22no—
204#461—21no—
205#459—21no—
206#431C22×C12711yescharacteristic
207#431C22×C12711yescharacteristic
208#423C22×C12711yescharacteristic
209C2×C4⋊C8C22×C12711yescharacteristic
210#417—21no—
211C2×#102—21no—
212#382C22×C12711yescharacteristic
213#340—21no—
214#334—22no—
215#332—21no—
216#331—21no—
217#327—22no—
218#323—22no—
219C2×#41—21no—
220C22×D4D4×C12711yescharacteristic
221C23×C4—21no—
222AGL(1,ℤ/8)—42no—
223AGL(1,ℤ/8)—42no—
224C2×SD16—22no—
225C2×D8—22no—
226C2×M16—21no—
227C22×C8—21no—
228C4⋊Q8D4×C12711yescharacteristic
229#127D4×C12711yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4D4×C12711yescharacteristic
241C2×C22⋊C4—21no—
242C2×C42C23×C12711yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8D4×C12712yes—
249#103—22no—
250#102—22no—
251#102—42no—
252C22⋊C8—21no—
253C22⋊C8D4×C12712yes—
254C4×C8—21no—
255C4×C8—21no—
256#95—21no—
257#95—21no—
258C24—21no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4SD16×C12712yes—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—82no—
280C22×C4C2×D4×C12711yescharacteristic
281C22×C4C2×D4×C12711yescharacteristic
282C22×C4#41×C12711yescharacteristic
283SD16—44no—
284D8—44no—
285M16—41no—
286M16—41no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—41no—
302C22⋊C4—41no—
303C42C2×D4×C12711yescharacteristic
304C42C2×D4×C12711yescharacteristic
305C42#41×C12711yescharacteristic
306C42#41×C12711yescharacteristic
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—81no—
312C23—81no—
313C23#121×C12711yescharacteristic
314Q8—41no—
315Q8—41no—
316D4—22no—
317D4—22no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4#120×C12711yescharacteristic
339C2×C4#121×C12711yescharacteristic
340C2×C4#121×C12711yescharacteristic
341C2×C4#123×C12711yescharacteristic
342C2×C4#123×C12711yescharacteristic
343C2×C4#124×C12711yescharacteristic
344C2×C4C2×SD16×C12711yescharacteristic
345C2×C4#135×C12711yescharacteristic
346C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
348C8—42no—
349C8—42no—
350C8—81no—
351C8—81no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—82no—
356C22—82no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22#394×C12711yescharacteristic
363C22#465×C12711yescharacteristic
364C22#469×C12711yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—81no—
370C4—81no—
371C4—161no—
372C4#449×C12711yescharacteristic
373C4#450×C12711yescharacteristic
374C4#481×C12711yescharacteristic
375C4#482×C12711yescharacteristic
376C2—21no—
377C2—21no—
378C2—82no—
379C2—161no—
380C2C127×#203411yescharacteristic
381C2C127×#204811yescharacteristic
382C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3036C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1804C2semidirect
3. C127×#1570C2semidirect
4. C127×#1540C2semidirect
5. C127×#1517C2semidirect
6. C127×#1460C2semidirect
7. C127×#1286C2semidirect
184. #10465C127direct (N × H)
193. #1804C2×C127semidirect
194. #1570C2×C127semidirect
195. #1540C2×C127semidirect
196. #1517C2×C127semidirect
197. #1460C2×C127semidirect
198. #1286C2×C127semidirect
199. C127#10465direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30362
C127×#18042
C127×#15702
C127×#15402
C127×#15172
C127×#14602
C127×#12862
#10465127