Finite Group Databasebeta

← C127×#12935 #44576608

Subgroups — C127×#12935 #44576608

Order 32512.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D8×C127C211yesmaximal, characteristic
2C2×#366×C127C211yesmaximal, characteristic, complemented
3C2×#357×C127C211yesmaximal, characteristic
4C2×#357×C127C211yesmaximal, characteristic
5C127×#1942C211yesmaximal, characteristic, complemented
6C127×#1380C211yesmaximal, characteristic, complemented
7C127×#1374C211yesmaximal, characteristic, complemented
8C22×D8×C127C2211yescharacteristic
9C2×C4×D4×C127—21no—
10C22×C16×C127C2211yescharacteristic
11C22×C16×C127C2211yescharacteristic
12C4×D8×C127—22no—
13C4×D8×C127—22no—
14C2×#107×C127C2211yescharacteristic
15C2×#107×C127C2211yescharacteristic
16C2×#107×C127C2211yescharacteristic
17C2×#102×C127—21no—
18C2×C4×C8×C127C2211yescharacteristic
19#389×C127—21no—
20#366×C127—22no—
21#357×C127—22no—
22#357×C127C414yescomplemented
23#340×C127—21no—
24C22×D4×C127—21no—
25C23×C4×C127—41no—
26C2×D8×C127—21no—
27C2×D8×C127—21no—
28C2×D8×C127—21no—
29C2×D8×C127C2×C412yes—
30C2×D8×C127D412yes—
31C2×D8×C127Q812yes—
32C22×C8×C127D411yescharacteristic
33C22×C8×C127C2311yescharacteristic
34C4×D4×C127—24no—
35C4×D4×C127—42no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—41no—
40C2×C22⋊C4×C127—41no—
41C2×C42×C127D411yescharacteristic
42C2×C16×C127—21no—
43C2×C16×C127—21no—
44C2×C16×C127—21no—
45C2×C16×C127—21no—
46C2×C16×C127—21no—
47C2×C16×C127C2×C412yescomplemented
48#107×C127—21no—
49#107×C127—21no—
50#107×C127—21no—
51#107×C127—21no—
52#107×C127C2×C412yescomplemented
53#107×C127D412yes—
54#102×C127—24no—
55C4×C8×C127—21no—
56C4×C8×C127—21no—
57#95×C127—41no—
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—
65C22×C4×C127—44no—
66C22×C4×C127—41no—
67C22×C4×C127—41no—
68C22×C4×C127—41no—
69C22×C4×C127—82no—
70C22×C4×C127—82no—
71C22×C4×C127D811yescharacteristic
72C22×C4×C127D811yescharacteristic
73C22×C4×C127C2×D411yescharacteristic
74D8×C127—22no—
75D8×C127—22no—
76D8×C127—22no—
77D8×C127C4⋊C414yescomplemented
78C2×C8×C127—21no—
79C2×C8×C127—21no—
80C2×C8×C127—21no—
81C2×C8×C127C22×C411yescharacteristic
82C2×C8×C127C2×D411yescharacteristic
83C2×C8×C127C2×D411yescharacteristic
84C2×C8×C127C2×Q811yescharacteristic
85C2×C8×C127#4111yescharacteristic
86C2×C8×C127#4111yescharacteristic
87C4⋊C4×C127—22no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—82no—
94C22⋊C4×C127—44no—
95C42×C127—21no—
96C42×C127—21no—
97C16×C127—22no—
98C16×C127—41no—
99C23×C127—42no—
100C23×C127—42no—
101C23×C127—42no—
102C23×C127—81no—
103C23×C127—81no—
104C23×C127—81no—
105C23×C127—81no—
106C23×C127C2×D811yescharacteristic
107D4×C127—24no—
108D4×C127—42no—
109D4×C127—42no—
110D4×C127—42no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—88no—
119C2×C4×C127—81no—
120C2×C4×C127—81no—
121C2×C4×C127—81no—
122C2×C4×C127—81no—
123C2×C4×C127—81no—
124C2×C4×C127—81no—
125C2×C4×C127—81no—
126C2×C4×C127D1612yes—
127C2×C4×C127C4×D411yescharacteristic
128C2×C4×C127#12011yescharacteristic
129C2×C4×C127C22⋊Q811yescharacteristic
130C2×C4×C127#13511yescharacteristic
131C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C127#13711yescharacteristic
133C8×C127—41no—
134C8×C127C2×C4⋊C411yescharacteristic
135C8×C127C4×D411yescharacteristic
136C8×C127C22⋊Q811yescharacteristic
137C8×C127#12311yescharacteristic
138C22×C127—44no—
139C22×C127—82no—
140C22×C127—82no—
141C22×C127—82no—
142C22×C127—82no—
143C22×C127—82no—
144C22×C127—82no—
145C22×C127C4×D811yescharacteristic
146C22×C127#44711yescharacteristic
147C22×C127#47411yescharacteristic
148C22×C127C2×D1611yescharacteristic
149C22×C127#50811yescharacteristic
150C22×C127#50911yescharacteristic
151C22×C127#51011yescharacteristic
152C4×C127—22no—
153C4×C127—41no—
154C4×C127—82no—
155C4×C127—82no—
156C4×C127—161no—
157C4×C127#38511yescharacteristic
158C4×C127#44011yescharacteristic
159C4×C127#45211yescharacteristic
160C4×C127#47811yescharacteristic
161#12935C12711yesmaximal, characteristic, direct product factor, Sylow
162C2×C127—84no—
163C2×C127#186211yescharacteristic
164C2×C127C4×D1611yescharacteristic
165C2×C127#217511yescharacteristic
166C2×C127#218411yescharacteristic
167C2×C127#218911yescharacteristic
168C2×C127#222411yescharacteristic
169C2×C127#222811yescharacteristic
170C2×C4×D8C2×C12711yescharacteristic
171C2×#366C2×C12711yescharacteristic, complemented
172C2×#357C2×C12711yescharacteristic
173C2×#357C2×C12711yescharacteristic
174#1942C2×C12711yescharacteristic, complemented
175#1380C2×C12711yescharacteristic, complemented
176#1374C2×C12711yescharacteristic, complemented
177C127#1293511yescharacteristic, direct product factor, Sylow
178C22×D8C22×C12711yescharacteristic
179C2×C4×D4—21no—
180C22×C16C22×C12711yescharacteristic
181C22×C16C22×C12711yescharacteristic
182C4×D8—22no—
183C4×D8—22no—
184C2×#107C22×C12711yescharacteristic
185C2×#107C22×C12711yescharacteristic
186C2×#107C22×C12711yescharacteristic
187C2×#102—21no—
188C2×C4×C8C22×C12711yescharacteristic
189#389—21no—
190#366—22no—
191#357—22no—
192#357C4×C12714yescomplemented
193#340—21no—
194C22×D4—21no—
195C23×C4—41no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8C2×C4×C12712yes—
200C2×D8D4×C12712yes—
201C2×D8Q8×C12712yes—
202C22×C8D4×C12711yescharacteristic
203C22×C8C23×C12711yescharacteristic
204C4×D4—24no—
205C4×D4—42no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—41no—
210C2×C22⋊C4—41no—
211C2×C42D4×C12711yescharacteristic
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16C2×C4×C12712yescomplemented
218#107—21no—
219#107—21no—
220#107—21no—
221#107—21no—
222#107C2×C4×C12712yescomplemented
223#107D4×C12712yes—
224#102—24no—
225C4×C8—21no—
226C4×C8—21no—
227#95—41no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—44no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—82no—
240C22×C4—82no—
241C22×C4D8×C12711yescharacteristic
242C22×C4D8×C12711yescharacteristic
243C22×C4C2×D4×C12711yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8C4⋊C4×C12714yescomplemented
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C22×C4×C12711yescharacteristic
252C2×C8C2×D4×C12711yescharacteristic
253C2×C8C2×D4×C12711yescharacteristic
254C2×C8C2×Q8×C12711yescharacteristic
255C2×C8#41×C12711yescharacteristic
256C2×C8#41×C12711yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—82no—
264C22⋊C4—44no—
265C42—21no—
266C42—21no—
267C16—22no—
268C16—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23C2×D8×C12711yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—88no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4D16×C12712yes—
297C2×C4C4×D4×C12711yescharacteristic
298C2×C4#120×C12711yescharacteristic
299C2×C4C22⋊Q8×C12711yescharacteristic
300C2×C4#135×C12711yescharacteristic
301C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
302C2×C4#137×C12711yescharacteristic
303C8—41no—
304C8C2×C4⋊C4×C12711yescharacteristic
305C8C4×D4×C12711yescharacteristic
306C8C22⋊Q8×C12711yescharacteristic
307C8#123×C12711yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22C4×D8×C12711yescharacteristic
316C22#447×C12711yescharacteristic
317C22#474×C12711yescharacteristic
318C22C2×D16×C12711yescharacteristic
319C22#508×C12711yescharacteristic
320C22#509×C12711yescharacteristic
321C22#510×C12711yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—82no—
326C4—161no—
327C4#385×C12711yescharacteristic
328C4#440×C12711yescharacteristic
329C4#452×C12711yescharacteristic
330C4#478×C12711yescharacteristic
331C2—84no—
332C2C127×#186211yescharacteristic
333C2C4×D16×C12711yescharacteristic
334C2C127×#217511yescharacteristic
335C2C127×#218411yescharacteristic
336C2C127×#218911yescharacteristic
337C2C127×#222411yescharacteristic
338C2C127×#222811yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#366×C127C2semidirect
5. C127×#1942C2semidirect
6. C127×#1380C2semidirect
7. C127×#1374C2semidirect
22. #357×C127C4semidirect
47. C2×C16×C127C2×C4semidirect
52. #107×C127C2×C4semidirect
77. D8×C127C4⋊C4semidirect
161. #12935C127direct (N × H)
171. C2×#366C2×C127semidirect
174. #1942C2×C127semidirect
175. #1380C2×C127semidirect
176. #1374C2×C127semidirect
177. C127#12935direct (N × H)
192. #357C4×C127semidirect
217. C2×C16C2×C4×C127semidirect
222. #107C2×C4×C127semidirect
247. D8C4⋊C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D8×C1272
C2×#366×C1272
C2×#357×C1272
C127×#19422
C127×#13802
C127×#13742
#12935127