Finite Group Databasebeta

← C127×#10481 #44574154

Subgroups — C127×#10481 #44574154

Order 32512.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C127C211yesmaximal, characteristic
2C127×#1990C211yesmaximal, characteristic, complemented
3C127×#1954C211yesmaximal, characteristic
4C127×#1802C211yesmaximal, characteristic
5C2×#335×C127C211yesmaximal, characteristic, complemented
6C2×#333×C127C211yesmaximal, characteristic, complemented
7C127×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#476×C127—22no—
11#476×C127—22no—
12C2×#106×C127—21no—
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×#102×C127—21no—
17C2×#102×C127—21no—
18C2×C22⋊C8×C127—21no—
19C2×C22⋊C8×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21#384×C127C2211yescharacteristic
22#340×C127—21no—
23#340×C127—21no—
24#340×C127—21no—
25#335×C127—22no—
26#333×C127—22no—
27C22×Q8×C127—21no—
28C22×D4×C127D411yescharacteristic
29C23×C4×C127—21no—
30C22×C8×C127—21no—
31C22×C8×C127—21no—
32C22×C8×C127—21no—
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127D412yes—
39C4×D4×C127—21no—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#106×C127—24no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D412yes—
58#102×C127—24no—
59#102×C127—42no—
60C22⋊C8×C127—42no—
61C22⋊C8×C127—42no—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64C24×C127—21no—
65C2×Q8×C127—22no—
66C2×Q8×C127—41no—
67C2×Q8×C127—81no—
68C2×Q8×C127—81no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127Q1612yes—
75C22×C4×C127—21no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127#4111yescharacteristic
87C2×C8×C127—21no—
88C2×C8×C127—21no—
89C2×C8×C127—22no—
90C2×C8×C127—21no—
91C2×C8×C127—21no—
92C2×C8×C127—21no—
93C2×C8×C127—41no—
94C2×C8×C127—41no—
95C2×C8×C127—41no—
96C2×C8×C127—41no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—41no—
101C2×C8×C127SD1612yes—
102C4⋊C4×C127—22no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—22no—
105C4⋊C4×C127—21no—
106C4⋊C4×C127—41no—
107C4⋊C4×C127—41no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—81no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C42×C127C2×D411yescharacteristic
116C42×C127C2×D411yescharacteristic
117C42×C127#4111yescharacteristic
118C42×C127#4111yescharacteristic
119C23×C127—22no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127#12111yescharacteristic
127Q8×C127—82no—
128Q8×C127—82no—
129D4×C127—22no—
130D4×C127—22no—
131D4×C127—41no—
132D4×C127—41no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—41no—
136C2×C4×C127—42no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—81no—
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—81no—
147C2×C4×C127—81no—
148C2×C4×C127#12011yescharacteristic
149C2×C4×C127#12111yescharacteristic
150C2×C4×C127#12111yescharacteristic
151C2×C4×C127#12311yescharacteristic
152C2×C4×C127#12311yescharacteristic
153C2×C4×C127#12411yescharacteristic
154C2×C4×C127C2×SD1611yescharacteristic
155C2×C4×C127C2×Q1611yescharacteristic
156C2×C4×C127#13511yescharacteristic
157C2×C4×C127#13511yescharacteristic
158C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C127#13711yescharacteristic
161C2×C4×C127#13711yescharacteristic
162C8×C127—22no—
163C8×C127—42no—
164C8×C127—41no—
165C8×C127—81no—
166C8×C127—81no—
167C22×C127—42no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127#39411yescharacteristic
175C22×C127#46111yescharacteristic
176C22×C127#46311yescharacteristic
177C22×C127#46711yescharacteristic
178C22×C127#46811yescharacteristic
179C22×C127#47111yescharacteristic
180C22×C127#47211yescharacteristic
181C4×C127—21no—
182C4×C127—21no—
183C4×C127—82no—
184C4×C127—81no—
185C4×C127—161no—
186C4×C127#44911yescharacteristic
187C4×C127#45111yescharacteristic
188C4×C127#46011yescharacteristic
189C4×C127#46411yescharacteristic
190C4×C127#46511yescharacteristic
191C4×C127#46811yescharacteristic
192C4×C127#48411yescharacteristic
193C4×C127#48511yescharacteristic
194#10481C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—82no—
196C2×C127#167511yescharacteristic
197C2×C127#168311yescharacteristic
198C2×C127#169111yescharacteristic
199C2×C127#169711yescharacteristic
200C2×C127#203611yescharacteristic
201C2×C127#205111yescharacteristic
202C2×C127#205511yescharacteristic
203C2×#476C2×C12711yescharacteristic
204#1990C2×C12711yescharacteristic, complemented
205#1954C2×C12711yescharacteristic
206#1802C2×C12711yescharacteristic
207C2×#335C2×C12711yescharacteristic, complemented
208C2×#333C2×C12711yescharacteristic, complemented
209#1296C2×C12711yescharacteristic, complemented
210C127#1048111yescharacteristic, direct product factor, Sylow
211C2×C4⋊Q8C22×C12711yescharacteristic
212C2×C4×D4C22×C12711yescharacteristic
213#476—22no—
214#476—22no—
215C2×#106—21no—
216C2×C4⋊C8C22×C12711yescharacteristic
217C2×C4⋊C8C22×C12711yescharacteristic
218C2×C4⋊C8C22×C12711yescharacteristic
219C2×#102—21no—
220C2×#102—21no—
221C2×C22⋊C8—21no—
222C2×C22⋊C8—21no—
223C2×C4×C8C22×C12711yescharacteristic
224#384C22×C12711yescharacteristic
225#340—21no—
226#340—21no—
227#340—21no—
228#335—22no—
229#333—22no—
230C22×Q8—21no—
231C22×D4D4×C12711yescharacteristic
232C23×C4—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8D4×C12711yescharacteristic
237C22×C8D4×C12711yescharacteristic
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8D4×C12712yes—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D4×C12711yescharacteristic
252C2×C22⋊C4—21no—
253C2×C42C23×C12711yescharacteristic
254#106—24no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8D4×C12712yes—
261#102—24no—
262#102—42no—
263C22⋊C8—42no—
264C22⋊C8—42no—
265C4×C8—21no—
266C4×C8—21no—
267C24—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—81no—
271C2×Q8—81no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4Q16×C12712yes—
278C22×C4—21no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4C2×D4×C12711yescharacteristic
289C22×C4#41×C12711yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C2×C8SD16×C12712yes—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—81no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C42C2×D4×C12711yescharacteristic
319C42C2×D4×C12711yescharacteristic
320C42#41×C12711yescharacteristic
321C42#41×C12711yescharacteristic
322C23—22no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23#121×C12711yescharacteristic
330Q8—82no—
331Q8—82no—
332D4—22no—
333D4—22no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4#120×C12711yescharacteristic
352C2×C4#121×C12711yescharacteristic
353C2×C4#121×C12711yescharacteristic
354C2×C4#123×C12711yescharacteristic
355C2×C4#123×C12711yescharacteristic
356C2×C4#124×C12711yescharacteristic
357C2×C4C2×SD16×C12711yescharacteristic
358C2×C4C2×Q16×C12711yescharacteristic
359C2×C4#135×C12711yescharacteristic
360C2×C4#135×C12711yescharacteristic
361C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
362C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
363C2×C4#137×C12711yescharacteristic
364C2×C4#137×C12711yescharacteristic
365C8—22no—
366C8—42no—
367C8—41no—
368C8—81no—
369C8—81no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#394×C12711yescharacteristic
378C22#461×C12711yescharacteristic
379C22#463×C12711yescharacteristic
380C22#467×C12711yescharacteristic
381C22#468×C12711yescharacteristic
382C22#471×C12711yescharacteristic
383C22#472×C12711yescharacteristic
384C4—21no—
385C4—21no—
386C4—82no—
387C4—81no—
388C4—161no—
389C4#449×C12711yescharacteristic
390C4#451×C12711yescharacteristic
391C4#460×C12711yescharacteristic
392C4#464×C12711yescharacteristic
393C4#465×C12711yescharacteristic
394C4#468×C12711yescharacteristic
395C4#484×C12711yescharacteristic
396C4#485×C12711yescharacteristic
397C2—82no—
398C2C127×#167511yescharacteristic
399C2C127×#168311yescharacteristic
400C2C127×#169111yescharacteristic
401C2C127×#169711yescharacteristic
402C2C127×#203611yescharacteristic
403C2C127×#205111yescharacteristic
404C2C127×#205511yescharacteristic
subgroupG/H
center, socleC23×C127#121
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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×#1990C2semidirect
5. C2×#335×C127C2semidirect
6. C2×#333×C127C2semidirect
7. C127×#1296C2semidirect
194. #10481C127direct (N × H)
204. #1990C2×C127semidirect
207. C2×#335C2×C127semidirect
208. C2×#333C2×C127semidirect
209. #1296C2×C127semidirect
210. C127#10481direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#476×C1272
C127×#19902
C127×#19542
C127×#18022
C2×#335×C1272
C2×#333×C1272
C127×#12962
#10481127