Finite Group Databasebeta

← C127×#9563 #44573236

Subgroups — C127×#9563 #44573236

Order 32512.

466 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#1982C211yesmaximal, characteristic
2C127×#1957C211yesmaximal, characteristic
3C127×#1947C211yesmaximal, characteristic, complemented
4C8×C4⋊C4×C127C211yesmaximal, characteristic, complemented
5C2×#331×C127C211yesmaximal, characteristic
6C127×#1296C211yesmaximal, characteristic, complemented
7C127×#1277C211yesmaximal, characteristic, complemented
8C2×#127×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×C4⋊C8×C127C2211yescharacteristic
11C2×C4⋊C8×C127C2211yescharacteristic
12C2×C4⋊C8×C127C2211yescharacteristic
13C2×#102×C127—21no—
14C2×#102×C127—21no—
15C2×#102×C127—21no—
16C2×#102×C127—21no—
17C2×C4×C8×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19#384×C127C2211yescharacteristic
20C4×C4⋊C4×C127C2211yescharacteristic
21#340×C127—21no—
22#336×C127—21no—
23#331×C127C414yescomplemented
24C22×D4×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127—21no—
27C22×C8×C127—21no—
28C22×C8×C127—21no—
29C22×C8×C127—21no—
30C22×C8×C127D411yescharacteristic
31C22×C8×C127D411yescharacteristic
32#127×C127—21no—
33#127×C127—21no—
34#127×C127—21no—
35#127×C127C2×C412yes—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C42×C127—21no—
42C2×C42×C127C2311yescharacteristic
43#107×C127—42no—
44C4⋊C8×C127—21no—
45C4⋊C8×C127—21no—
46C4⋊C8×C127—21no—
47C4⋊C8×C127—21no—
48C4⋊C8×C127C2×C412yes—
49C4⋊C8×C127C2×C412yes—
50#102×C127—42no—
51#102×C127—42no—
52#102×C127—42no—
53#102×C127—42no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C4×C8×C127—42no—
57#95×C127—21no—
58C24×C127—41no—
59C2×D4×C127—22no—
60C2×D4×C127—22no—
61C2×D4×C127—22no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—41no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—81no—
74C2×D4×C127—81no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—41no—
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127#4111yescharacteristic
81C2×C8×C127—21no—
82C2×C8×C127—21no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—21no—
86C2×C8×C127—21no—
87C2×C8×C127—21no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C2×C8×C127—41no—
94C2×C8×C127—41no—
95C2×C8×C127D812yes—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—81no—
103C4⋊C4×C127D812yes—
104C4⋊C4×C127SD1612yes—
105C42×C127—41no—
106C42×C127—41no—
107C42×C127C22×C411yescharacteristic
108C42×C127#4111yescharacteristic
109C42×C127#4111yescharacteristic
110C42×C127#4111yescharacteristic
111C23×C127—42no—
112C23×C127—81no—
113C23×C127—81no—
114C23×C127—81no—
115C23×C127—81no—
116C23×C127—81no—
117C23×C127—81no—
118C23×C127#12111yescharacteristic
119D4×C127—42no—
120D4×C127—42no—
121D4×C127—42no—
122D4×C127—42no—
123D4×C127—82no—
124D4×C127—82no—
125D4×C127—81no—
126D4×C127—81no—
127D4×C127—81no—
128D4×C127—81no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—22no—
132C2×C4×C127—22no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127#11711yescharacteristic
141C2×C4×C127C4×D411yescharacteristic
142C2×C4×C127C4×D411yescharacteristic
143C2×C4×C127#12311yescharacteristic
144C2×C4×C127#12411yescharacteristic
145C2×C4×C127#12611yescharacteristic
146C2×C4×C127C2×D811yescharacteristic
147C2×C4×C127C2×D811yescharacteristic
148C2×C4×C127C2×SD1611yescharacteristic
149C2×C4×C127#13511yescharacteristic
150C2×C4×C127#13511yescharacteristic
151C2×C4×C127#13511yescharacteristic
152C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C127#13711yescharacteristic
154C8×C127—22no—
155C8×C127—42no—
156C8×C127—42no—
157C8×C127—41no—
158C8×C127—81no—
159C22×C127—82no—
160C22×C127—82no—
161C22×C127—82no—
162C22×C127—161no—
163C22×C127—161no—
164C22×C127—161no—
165C22×C127—161no—
166C22×C127#38811yescharacteristic
167C22×C127#45911yescharacteristic
168C22×C127#46411yescharacteristic
169C22×C127#46511yescharacteristic
170C22×C127#46611yescharacteristic
171C22×C127#47111yescharacteristic
172C22×C127#47211yescharacteristic
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—42no—
176C4×C127—42no—
177C4×C127—161no—
178C4×C127C4×D811yescharacteristic
179C4×C127C4×D811yescharacteristic
180C4×C127C4×SD1611yescharacteristic
181C4×C127#44011yescharacteristic
182C4×C127#48011yescharacteristic
183C4×C127#48211yescharacteristic
184C4×C127#48611yescharacteristic
185C4×C127#48811yescharacteristic
186#9563C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127—162no—
188C2×C127#166511yescharacteristic
189C2×C127#166711yescharacteristic
190C2×C127#167811yescharacteristic
191C2×C127#168211yescharacteristic
192C2×C127#192511yescharacteristic
193C2×C127#193111yescharacteristic
194C2×C127#193411yescharacteristic
195#1982C2×C12711yescharacteristic
196#1957C2×C12711yescharacteristic
197#1947C2×C12711yescharacteristic, complemented
198C8×C4⋊C4C2×C12711yescharacteristic, complemented
199C2×#331C2×C12711yescharacteristic
200#1296C2×C12711yescharacteristic, complemented
201#1277C2×C12711yescharacteristic, complemented
202C127#956311yescharacteristic, direct product factor, Sylow
203C2×#127C22×C12711yescharacteristic
204C2×#107—21no—
205C2×C4⋊C8C22×C12711yescharacteristic
206C2×C4⋊C8C22×C12711yescharacteristic
207C2×C4⋊C8C22×C12711yescharacteristic
208C2×#102—21no—
209C2×#102—21no—
210C2×#102—21no—
211C2×#102—21no—
212C2×C4×C8—21no—
213C2×C4×C8C22×C12711yescharacteristic
214#384C22×C12711yescharacteristic
215C4×C4⋊C4C22×C12711yescharacteristic
216#340—21no—
217#336—21no—
218#331C4×C12714yescomplemented
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8D4×C12711yescharacteristic
226C22×C8D4×C12711yescharacteristic
227#127—21no—
228#127—21no—
229#127—21no—
230#127C2×C4×C12712yes—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4D4×C12711yescharacteristic
235C2×C4⋊C4D4×C12711yescharacteristic
236C2×C42—21no—
237C2×C42C23×C12711yescharacteristic
238#107—42no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8C2×C4×C12712yes—
244C4⋊C8C2×C4×C12712yes—
245#102—42no—
246#102—42no—
247#102—42no—
248#102—42no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8—42no—
252#95—21no—
253C24—41no—
254C2×D4—22no—
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—81no—
269C2×D4—81no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4C2×D4×C12711yescharacteristic
274C22×C4C2×D4×C12711yescharacteristic
275C22×C4#41×C12711yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8D8×C12712yes—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—81no—
298C4⋊C4D8×C12712yes—
299C4⋊C4SD16×C12712yes—
300C42—41no—
301C42—41no—
302C42C22×C4×C12711yescharacteristic
303C42#41×C12711yescharacteristic
304C42#41×C12711yescharacteristic
305C42#41×C12711yescharacteristic
306C23—42no—
307C23—81no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23#121×C12711yescharacteristic
314D4—42no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—82no—
319D4—82no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#117×C12711yescharacteristic
336C2×C4C4×D4×C12711yescharacteristic
337C2×C4C4×D4×C12711yescharacteristic
338C2×C4#123×C12711yescharacteristic
339C2×C4#124×C12711yescharacteristic
340C2×C4#126×C12711yescharacteristic
341C2×C4C2×D8×C12711yescharacteristic
342C2×C4C2×D8×C12711yescharacteristic
343C2×C4C2×SD16×C12711yescharacteristic
344C2×C4#135×C12711yescharacteristic
345C2×C4#135×C12711yescharacteristic
346C2×C4#135×C12711yescharacteristic
347C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
348C2×C4#137×C12711yescharacteristic
349C8—22no—
350C8—42no—
351C8—42no—
352C8—41no—
353C8—81no—
354C22—82no—
355C22—82no—
356C22—82no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—161no—
361C22#388×C12711yescharacteristic
362C22#459×C12711yescharacteristic
363C22#464×C12711yescharacteristic
364C22#465×C12711yescharacteristic
365C22#466×C12711yescharacteristic
366C22#471×C12711yescharacteristic
367C22#472×C12711yescharacteristic
368C4—21no—
369C4—21no—
370C4—42no—
371C4—42no—
372C4—161no—
373C4C4×D8×C12711yescharacteristic
374C4C4×D8×C12711yescharacteristic
375C4C4×SD16×C12711yescharacteristic
376C4#440×C12711yescharacteristic
377C4#480×C12711yescharacteristic
378C4#482×C12711yescharacteristic
379C4#486×C12711yescharacteristic
380C4#488×C12711yescharacteristic
381C2—162no—
382C2C127×#166511yescharacteristic
383C2C127×#166711yescharacteristic
384C2C127×#167811yescharacteristic
385C2C127×#168211yescharacteristic
386C2C127×#192511yescharacteristic
387C2C127×#193111yescharacteristic
388C2C127×#193411yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#127×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1947C2semidirect
4. C8×C4⋊C4×C127C2semidirect
6. C127×#1296C2semidirect
7. C127×#1277C2semidirect
23. #331×C127C4semidirect
186. #9563C127direct (N × H)
197. #1947C2×C127semidirect
198. C8×C4⋊C4C2×C127semidirect
200. #1296C2×C127semidirect
201. #1277C2×C127semidirect
202. C127#9563direct (N × H)
218. #331C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#19822
C127×#19572
C127×#19472
C8×C4⋊C4×C1272
C2×#331×C1272
C127×#12962
C127×#12772
#9563127