Finite Group Databasebeta

← C127×#10484 #44574157

Subgroups — C127×#10484 #44574157

Order 32512.

490 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C127C211yesmaximal, characteristic
2C127×#1956C211yesmaximal, characteristic, complemented
3C127×#1954C211yesmaximal, characteristic
4C127×#1802C211yesmaximal, characteristic
5C2×#334×C127C211yesmaximal, characteristic, complemented
6C2×#332×C127C211yesmaximal, characteristic, complemented
7C127×#1296C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#474×C127—22no—
11#474×C127—22no—
12C2×#107×C127—21no—
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×C4⋊C8×C127C2211yescharacteristic
15C2×C4⋊C8×C127C2211yescharacteristic
16C2×#103×C127—21no—
17C2×#103×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#334×C127—22no—
26#332×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#107×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#103×C127—42no—
59#103×C127—42no—
60#102×C127—24no—
61#102×C127—42no—
62C22⋊C8×C127—42no—
63C22⋊C8×C127—42no—
64C4×C8×C127—21no—
65C4×C8×C127—21no—
66C24×C127—21no—
67C2×Q8×C127—22no—
68C2×Q8×C127—41no—
69C2×Q8×C127—41no—
70C2×Q8×C127—41no—
71C2×Q8×C127—41no—
72C2×Q8×C127—41no—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127SD1612yes—
79C22×C4×C127—21no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127—41no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127—41no—
88C22×C4×C127C2×D411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127#4111yescharacteristic
91C2×C8×C127—21no—
92C2×C8×C127—21no—
93C2×C8×C127—22no—
94C2×C8×C127—21no—
95C2×C8×C127—21no—
96C2×C8×C127—21no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—41no—
101C2×C8×C127—41no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127D812yes—
106C4⋊C4×C127—22no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—22no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—81no—
117C22⋊C4×C127—41no—
118C22⋊C4×C127—41no—
119C42×C127C2×D411yescharacteristic
120C42×C127C2×D411yescharacteristic
121C42×C127#4111yescharacteristic
122C42×C127#4111yescharacteristic
123C23×C127—22no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127—41no—
127C23×C127—41no—
128C23×C127—41no—
129C23×C127—41no—
130C23×C127#12111yescharacteristic
131Q8×C127—42no—
132Q8×C127—42no—
133Q8×C127—81no—
134Q8×C127—81no—
135D4×C127—22no—
136D4×C127—22no—
137D4×C127—41no—
138D4×C127—41no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—41no—
142C2×C4×C127—42no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—81no—
146C2×C4×C127—81no—
147C2×C4×C127—81no—
148C2×C4×C127—81no—
149C2×C4×C127—81no—
150C2×C4×C127—81no—
151C2×C4×C127—81no—
152C2×C4×C127—81no—
153C2×C4×C127—81no—
154C2×C4×C127#12011yescharacteristic
155C2×C4×C127#12111yescharacteristic
156C2×C4×C127#12111yescharacteristic
157C2×C4×C127#12311yescharacteristic
158C2×C4×C127#12311yescharacteristic
159C2×C4×C127#12411yescharacteristic
160C2×C4×C127C2×D811yescharacteristic
161C2×C4×C127C2×SD1611yescharacteristic
162C2×C4×C127#13511yescharacteristic
163C2×C4×C127#13511yescharacteristic
164C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C127#13711yescharacteristic
167C2×C4×C127#13711yescharacteristic
168C8×C127—22no—
169C8×C127—42no—
170C8×C127—41no—
171C8×C127—81no—
172C8×C127—81no—
173C22×C127—42no—
174C22×C127—42no—
175C22×C127—42no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127#39411yescharacteristic
181C22×C127#45911yescharacteristic
182C22×C127#46311yescharacteristic
183C22×C127#46511yescharacteristic
184C22×C127#47011yescharacteristic
185C22×C127#47111yescharacteristic
186C22×C127#47311yescharacteristic
187C4×C127—21no—
188C4×C127—21no—
189C4×C127—81no—
190C4×C127—82no—
191C4×C127—161no—
192C4×C127#44811yescharacteristic
193C4×C127#45211yescharacteristic
194C4×C127#45911yescharacteristic
195C4×C127#46311yescharacteristic
196C4×C127#46611yescharacteristic
197C4×C127#46911yescharacteristic
198C4×C127#48311yescharacteristic
199C4×C127#48511yescharacteristic
200#10484C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—82no—
202C2×C127#166511yescharacteristic
203C2×C127#167911yescharacteristic
204C2×C127#168911yescharacteristic
205C2×C127#170311yescharacteristic
206C2×C127#203511yescharacteristic
207C2×C127#205211yescharacteristic
208C2×C127#205411yescharacteristic
209C2×#474C2×C12711yescharacteristic
210#1956C2×C12711yescharacteristic, complemented
211#1954C2×C12711yescharacteristic
212#1802C2×C12711yescharacteristic
213C2×#334C2×C12711yescharacteristic, complemented
214C2×#332C2×C12711yescharacteristic, complemented
215#1296C2×C12711yescharacteristic, complemented
216C127#1048411yescharacteristic, direct product factor, Sylow
217C2×C4⋊Q8C22×C12711yescharacteristic
218C2×C4×D4C22×C12711yescharacteristic
219#474—22no—
220#474—22no—
221C2×#107—21no—
222C2×C4⋊C8C22×C12711yescharacteristic
223C2×C4⋊C8C22×C12711yescharacteristic
224C2×C4⋊C8C22×C12711yescharacteristic
225C2×#103—21no—
226C2×#103—21no—
227C2×#102—21no—
228C2×#102—21no—
229C2×C22⋊C8—21no—
230C2×C22⋊C8—21no—
231C2×C4×C8C22×C12711yescharacteristic
232#384C22×C12711yescharacteristic
233#340—21no—
234#334—22no—
235#332—22no—
236C22×Q8—21no—
237C22×D4D4×C12711yescharacteristic
238C23×C4—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8D4×C12711yescharacteristic
243C22×C8D4×C12711yescharacteristic
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8D4×C12712yes—
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4D4×C12711yescharacteristic
258C2×C22⋊C4—21no—
259C2×C42C23×C12711yescharacteristic
260#107—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8D4×C12712yes—
267#103—42no—
268#103—42no—
269#102—24no—
270#102—42no—
271C22⋊C8—42no—
272C22⋊C8—42no—
273C4×C8—21no—
274C4×C8—21no—
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4SD16×C12712yes—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4C2×D4×C12711yescharacteristic
298C22×C4C2×D4×C12711yescharacteristic
299C22×C4#41×C12711yescharacteristic
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—22no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8D8×C12712yes—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—22no—
318C4⋊C4—21no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C42C2×D4×C12711yescharacteristic
329C42C2×D4×C12711yescharacteristic
330C42#41×C12711yescharacteristic
331C42#41×C12711yescharacteristic
332C23—22no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23#121×C12711yescharacteristic
340Q8—42no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344D4—22no—
345D4—22no—
346D4—41no—
347D4—41no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4#120×C12711yescharacteristic
364C2×C4#121×C12711yescharacteristic
365C2×C4#121×C12711yescharacteristic
366C2×C4#123×C12711yescharacteristic
367C2×C4#123×C12711yescharacteristic
368C2×C4#124×C12711yescharacteristic
369C2×C4C2×D8×C12711yescharacteristic
370C2×C4C2×SD16×C12711yescharacteristic
371C2×C4#135×C12711yescharacteristic
372C2×C4#135×C12711yescharacteristic
373C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
374C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
375C2×C4#137×C12711yescharacteristic
376C2×C4#137×C12711yescharacteristic
377C8—22no—
378C8—42no—
379C8—41no—
380C8—81no—
381C8—81no—
382C22—42no—
383C22—42no—
384C22—42no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#394×C12711yescharacteristic
390C22#459×C12711yescharacteristic
391C22#463×C12711yescharacteristic
392C22#465×C12711yescharacteristic
393C22#470×C12711yescharacteristic
394C22#471×C12711yescharacteristic
395C22#473×C12711yescharacteristic
396C4—21no—
397C4—21no—
398C4—81no—
399C4—82no—
400C4—161no—
401C4#448×C12711yescharacteristic
402C4#452×C12711yescharacteristic
403C4#459×C12711yescharacteristic
404C4#463×C12711yescharacteristic
405C4#466×C12711yescharacteristic
406C4#469×C12711yescharacteristic
407C4#483×C12711yescharacteristic
408C4#485×C12711yescharacteristic
409C2—82no—
410C2C127×#166511yescharacteristic
411C2C127×#167911yescharacteristic
412C2C127×#168911yescharacteristic
413C2C127×#170311yescharacteristic
414C2C127×#203511yescharacteristic
415C2C127×#205211yescharacteristic
416C2C127×#205411yescharacteristic
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×#1956C2semidirect
5. C2×#334×C127C2semidirect
6. C2×#332×C127C2semidirect
7. C127×#1296C2semidirect
200. #10484C127direct (N × H)
210. #1956C2×C127semidirect
213. C2×#334C2×C127semidirect
214. C2×#332C2×C127semidirect
215. #1296C2×C127semidirect
216. C127#10484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#474×C1272
C127×#19562
C127×#19542
C127×#18022
C2×#334×C1272
C2×#332×C1272
C127×#12962
#10484127