Finite Group Databasebeta

← C127×#2414 #30635366

Subgroups — C127×#2414 #30635366

Order 16256.

704 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×C127C211yesmaximal, characteristic, complemented
2C2×#121×C127C211yesmaximal, characteristic, complemented
3C2×C4×D4×C127C211yesmaximal, characteristic, complemented
4C2×#117×C127C211yesmaximal, characteristic, complemented
5#394×C127C212yesmaximal, complemented
6#392×C127C212yesmaximal, complemented
7#390×C127C212yesmaximal, complemented
8#390×C127C211yesmaximal, characteristic, complemented
9#389×C127C211yesmaximal, characteristic, complemented
10#388×C127C212yesmaximal, complemented
11#380×C127C211yesmaximal, characteristic, complemented
12C22×D4×C127C2211yescharacteristic
13C22×D4×C127C2211yescharacteristic
14C22×D4×C127C2212yes—
15C22×D4×C127C2212yes—
16C23×C4×C127C2211yescharacteristic
17C23×C4×C127C2211yescharacteristic
18#121×C127—24no—
19#121×C127—24no—
20C4×D4×C127—24no—
21#117×C127—24no—
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24C2×C4⋊C4×C127C2211yescharacteristic
25C2×C4⋊C4×C127C2212yes—
26C2×C4⋊C4×C127C2211yescharacteristic
27C2×C22⋊C4×C127C2212yes—
28C2×C22⋊C4×C127C2211yescharacteristic
29C2×C22⋊C4×C127C2211yescharacteristic
30C2×C22⋊C4×C127C2212yes—
31C2×C22⋊C4×C127C2212yes—
32C2×C22⋊C4×C127C2212yes—
33C2×C22⋊C4×C127C2212yes—
34C2×C22⋊C4×C127C2212yes—
35C2×C42×C127C2212yes—
36C2×C42×C127C2211yescharacteristic
37#95×C127C2212yes—
38#95×C127C2212yes—
39C24×C127C2312yes—
40C24×C127C2311yescharacteristic
41C24×C127C2311yescharacteristic
42C2×D4×C127—22no—
43C2×D4×C127—22no—
44C2×D4×C127—24no—
45C2×D4×C127—24no—
46C2×D4×C127—24no—
47C2×D4×C127—22no—
48C2×D4×C127—22no—
49C2×D4×C127—22no—
50C2×D4×C127—22no—
51C2×D4×C127—42no—
52C2×D4×C127—42no—
53C2×D4×C127—42no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—22no—
58C22×C4×C127—22no—
59C22×C4×C127D414yescomplemented
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2312yes—
62C22×C4×C127C2312yes—
63C22×C4×C127C2311yescharacteristic
64C22×C4×C127C2312yes—
65C22×C4×C127C2311yescharacteristic
66C22×C4×C127C2311yescharacteristic
67C22×C4×C127C2311yescharacteristic
68C4⋊C4×C127—22no—
69C4⋊C4×C127—22no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—42no—
72C4⋊C4×C127D414yescomplemented
73C22⋊C4×C127—22no—
74C22⋊C4×C127—24no—
75C22⋊C4×C127—22no—
76C22⋊C4×C127—24no—
77C22⋊C4×C127—24no—
78C22⋊C4×C127—24no—
79C22⋊C4×C127—42no—
80C22⋊C4×C127—42no—
81C42×C127—24no—
82C42×C127—22no—
83C23×C127—21no—
84C23×C127—21no—
85C23×C127—21no—
86C23×C127—21no—
87C23×C127—21no—
88C23×C127—21no—
89C23×C127—21no—
90C23×C127—21no—
91C23×C127—21no—
92C23×C127—21no—
93C23×C127—21no—
94C23×C127—21no—
95C23×C127—22no—
96C23×C127—22no—
97C23×C127—22no—
98C23×C127—22no—
99C23×C127—22no—
100C23×C127—22no—
101C23×C127—22no—
102C23×C127C2×D412yes—
103C23×C127#4112yes—
104C23×C127C2411yescharacteristic
105D4×C127—28no—
106D4×C127—48no—
107D4×C127—48no—
108D4×C127—44no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—22no—
114C2×C4×C127—22no—
115C2×C4×C127—28no—
116C2×C4×C127—21no—
117C2×C4×C127—22no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—22no—
121C2×C4×C127—22no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—21no—
127C2×C4×C127—22no—
128C2×C4×C127—44no—
129C2×C4×C127C2×D414yes—
130C2×C4×C127C2×D412yes—
131C2×C4×C127C2×D412yes—
132C2×C4×C127C2×D412yes—
133C2×C4×C127#4112yes—
134C2×C4×C127#4112yes—
135C22×C127—22no—
136C22×C127—22no—
137C22×C127—22no—
138C22×C127—22no—
139C22×C127—22no—
140C22×C127—22no—
141C22×C127—41no—
142C22×C127—41no—
143C22×C127—41no—
144C22×C127—41no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—42no—
150C22×C127—42no—
151C22×C127—42no—
152C22×C127—42no—
153C22×C127—42no—
154C22×C127—42no—
155C22×C127—42no—
156C22×C127C22×D411yescharacteristic
157C22×C127C22×D411yescharacteristic
158C22×C127C2×#4111yescharacteristic
159C22×C127C2×#4111yescharacteristic
160C22×C127C2×#4111yescharacteristic
161C22×C127H(5,𝔽2)11yescharacteristic
162C22×C127H(5,𝔽2)11yescharacteristic
163C4×C127—22no—
164C4×C127—22no—
165C4×C127—24no—
166C4×C127—41no—
167C4×C127—41no—
168C4×C127—42no—
169C4×C127—42no—
170C4×C127#12114yes—
171C2×C127—42no—
172C2×C127—42no—
173C2×C127—82no—
174C2×C127C2×#12111yescharacteristic
175C2×C127#52511yescharacteristic
176C2×C127#53511yescharacteristic
177C2×C127#54611yescharacteristic
178C2×C127#55011yescharacteristic
179C2×C127#55311yescharacteristic
180C2×C127#55511yescharacteristic
181#2414C12711yesmaximal, characteristic, direct product factor, Sylow
182C127#241411yescharacteristic, direct product factor, Sylow
183C2×#121C2×C12711yescharacteristic, complemented
184C2×#121C2×C12711yescharacteristic, complemented
185C2×C4×D4C2×C12711yescharacteristic, complemented
186C2×#117C2×C12711yescharacteristic, complemented
187#394C2×C12712yescomplemented
188#392C2×C12712yescomplemented
189#390C2×C12712yescomplemented
190#390C2×C12711yescharacteristic, complemented
191#389C2×C12711yescharacteristic, complemented
192#388C2×C12712yescomplemented
193#380C2×C12711yescharacteristic, complemented
194C22×D4C22×C12711yescharacteristic
195C22×D4C22×C12711yescharacteristic
196C22×D4C22×C12712yes—
197C22×D4C22×C12712yes—
198C23×C4C22×C12711yescharacteristic
199C23×C4C22×C12711yescharacteristic
200#121—24no—
201#121—24no—
202C4×D4—24no—
203#117—24no—
204C2×C4⋊C4C22×C12711yescharacteristic
205C2×C4⋊C4C22×C12711yescharacteristic
206C2×C4⋊C4C22×C12711yescharacteristic
207C2×C4⋊C4C22×C12712yes—
208C2×C4⋊C4C22×C12711yescharacteristic
209C2×C22⋊C4C22×C12712yes—
210C2×C22⋊C4C22×C12711yescharacteristic
211C2×C22⋊C4C22×C12711yescharacteristic
212C2×C22⋊C4C22×C12712yes—
213C2×C22⋊C4C22×C12712yes—
214C2×C22⋊C4C22×C12712yes—
215C2×C22⋊C4C22×C12712yes—
216C2×C22⋊C4C22×C12712yes—
217C2×C42C22×C12712yes—
218C2×C42C22×C12711yescharacteristic
219#95C22×C12712yes—
220#95C22×C12712yes—
221C24C23×C12712yes—
222C24C23×C12711yescharacteristic
223C24C23×C12711yescharacteristic
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—24no—
227C2×D4—24no—
228C2×D4—24no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—42no—
234C2×D4—42no—
235C2×D4—42no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4D4×C12714yescomplemented
242C22×C4C23×C12711yescharacteristic
243C22×C4C23×C12712yes—
244C22×C4C23×C12712yes—
245C22×C4C23×C12711yescharacteristic
246C22×C4C23×C12712yes—
247C22×C4C23×C12711yescharacteristic
248C22×C4C23×C12711yescharacteristic
249C22×C4C23×C12711yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—42no—
254C4⋊C4D4×C12714yescomplemented
255C22⋊C4—22no—
256C22⋊C4—24no—
257C22⋊C4—22no—
258C22⋊C4—24no—
259C22⋊C4—24no—
260C22⋊C4—24no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C42—24no—
264C42—22no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—22no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23C2×D4×C12712yes—
285C23#41×C12712yes—
286C23C24×C12711yescharacteristic
287D4—28no—
288D4—48no—
289D4—48no—
290D4—44no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—28no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—44no—
311C2×C4C2×D4×C12714yes—
312C2×C4C2×D4×C12712yes—
313C2×C4C2×D4×C12712yes—
314C2×C4C2×D4×C12712yes—
315C2×C4#41×C12712yes—
316C2×C4#41×C12712yes—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—42no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22C22×D4×C12711yescharacteristic
339C22C22×D4×C12711yescharacteristic
340C22C2×#41×C12711yescharacteristic
341C22C2×#41×C12711yescharacteristic
342C22C2×#41×C12711yescharacteristic
343C22H(5,𝔽2)×C12711yescharacteristic
344C22H(5,𝔽2)×C12711yescharacteristic
345C4—22no—
346C4—22no—
347C4—24no—
348C4—41no—
349C4—42no—
350C4—41no—
351C4—42no—
352C4#121×C12714yes—
353C2—42no—
354C2—42no—
355C2—82no—
356C2C2×#121×C12711yescharacteristic
357C2#525×C12711yescharacteristic
358C2#535×C12711yescharacteristic
359C2#546×C12711yescharacteristic
360C2#550×C12711yescharacteristic
361C2#553×C12711yescharacteristic
362C2#555×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#121×C127C2semidirect
2. C2×#121×C127C2semidirect
3. C2×C4×D4×C127C2semidirect
4. C2×#117×C127C2semidirect
5. #394×C127C2semidirect
6. #392×C127C2semidirect
7. #390×C127C2semidirect
8. #390×C127C2semidirect
9. #389×C127C2semidirect
10. #388×C127C2semidirect
11. #380×C127C2semidirect
59. C22×C4×C127D4semidirect
72. C4⋊C4×C127D4semidirect
181. #2414C127direct (N × H)
182. C127#2414direct (N × H)
183. C2×#121C2×C127semidirect
184. C2×#121C2×C127semidirect
185. C2×C4×D4C2×C127semidirect
186. C2×#117C2×C127semidirect
187. #394C2×C127semidirect
188. #392C2×C127semidirect
189. #390C2×C127semidirect
190. #390C2×C127semidirect
191. #389C2×C127semidirect
192. #388C2×C127semidirect
193. #380C2×C127semidirect
241. C22×C4D4×C127semidirect
254. C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C1272
C2×C4×D4×C1272
C2×#117×C1272
#394×C1272
#392×C1272
#390×C1272
#389×C1272
#388×C1272
#380×C1272
#2414127