Finite Group Databasebeta

← C127×#2415 #30635367

Subgroups — C127×#2415 #30635367

Order 16256.

604 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×C127C211yesmaximal, characteristic, complemented
3C2×C4×D4×C127C211yesmaximal, characteristic
4C2×#117×C127C211yesmaximal, characteristic, complemented
5#397×C127C212yesmaximal, complemented
6#394×C127C212yesmaximal
7#391×C127C211yesmaximal, characteristic, complemented
8#389×C127C212yesmaximal, complemented
9#389×C127C211yesmaximal, characteristic, complemented
10#388×C127C212yesmaximal, complemented
11#380×C127C211yesmaximal, characteristic, complemented
12C22×Q8×C127C2211yescharacteristic
13C22×D4×C127C2211yescharacteristic
14C23×C4×C127C2211yescharacteristic
15C23×C4×C127C2211yescharacteristic
16C22⋊Q8×C127—24no—
17C22⋊Q8×C127—24no—
18C4×D4×C127—24no—
19#117×C127—24no—
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2211yescharacteristic
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2212yes—
24C2×C4⋊C4×C127C2212yes—
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×C42×C127C2212yes—
34C2×C42×C127C2211yescharacteristic
35#95×C127C2212yes—
36#95×C127C2212yes—
37#95×C127C2212yes—
38#95×C127C2212yes—
39C24×C127C2311yescharacteristic
40C24×C127C2311yescharacteristic
41C2×Q8×C127—22no—
42C2×Q8×C127—22no—
43C2×Q8×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—22no—
47C22×C4×C127—22no—
48C22×C4×C127—22no—
49C22×C4×C127—22no—
50C22×C4×C127—22no—
51C22×C4×C127—22no—
52C22×C4×C127D414yes—
53C22×C4×C127C2311yescharacteristic
54C22×C4×C127C2312yes—
55C22×C4×C127C2312yes—
56C22×C4×C127C2312yes—
57C22×C4×C127C2311yescharacteristic
58C22×C4×C127C2312yes—
59C22×C4×C127C2311yescharacteristic
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2311yescharacteristic
62C4⋊C4×C127—22no—
63C4⋊C4×C127—22no—
64C4⋊C4×C127—22no—
65C4⋊C4×C127—24no—
66C4⋊C4×C127—24no—
67C4⋊C4×C127—24no—
68C4⋊C4×C127D414yescomplemented
69C22⋊C4×C127—22no—
70C22⋊C4×C127—24no—
71C22⋊C4×C127—24no—
72C22⋊C4×C127—24no—
73C22⋊C4×C127—22no—
74C22⋊C4×C127—24no—
75C42×C127—24no—
76C42×C127—22no—
77C23×C127—21no—
78C23×C127—21no—
79C23×C127—21no—
80C23×C127—21no—
81C23×C127—21no—
82C23×C127—21no—
83C23×C127—21no—
84C23×C127—21no—
85C23×C127—21no—
86C23×C127—21no—
87C23×C127—21no—
88C23×C127—21no—
89C23×C127C2×D412yes—
90C23×C127#4112yes—
91C23×C127C2411yescharacteristic
92Q8×C127—44no—
93D4×C127—28no—
94C2×C4×C127—21no—
95C2×C4×C127—21no—
96C2×C4×C127—22no—
97C2×C4×C127—21no—
98C2×C4×C127—21no—
99C2×C4×C127—22no—
100C2×C4×C127—28no—
101C2×C4×C127—21no—
102C2×C4×C127—22no—
103C2×C4×C127—22no—
104C2×C4×C127—21no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—21no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—22no—
116C2×C4×C127—44no—
117C2×C4×C127C2×D414yes—
118C2×C4×C127C2×D412yes—
119C2×C4×C127C2×D412yes—
120C2×C4×C127C2×D412yes—
121C2×C4×C127#4112yes—
122C2×C4×C127#4112yes—
123C22×C127—22no—
124C22×C127—22no—
125C22×C127—22no—
126C22×C127—22no—
127C22×C127—22no—
128C22×C127—22no—
129C22×C127—41no—
130C22×C127—41no—
131C22×C127—41no—
132C22×C127—41no—
133C22×C127—41no—
134C22×C127—41no—
135C22×C127—41no—
136C22×C127—41no—
137C22×C127C22×D411yescharacteristic
138C22×C127C22×D411yescharacteristic
139C22×C127C2×#4111yescharacteristic
140C22×C127C2×#4111yescharacteristic
141C22×C127C2×#4111yescharacteristic
142C22×C1272−1+411yescharacteristic
143C22×C1272−1+411yescharacteristic
144C4×C127—22no—
145C4×C127—22no—
146C4×C127—24no—
147C4×C127—41no—
148C4×C127—42no—
149C4×C127—42no—
150C4×C127—41no—
151C4×C127—42no—
152C4×C127#12114yes—
153C2×C127—42no—
154C2×C127—42no—
155C2×C127C2×#12111yescharacteristic
156C2×C127#52511yescharacteristic
157C2×C127#53611yescharacteristic
158C2×C127#54711yescharacteristic
159C2×C127#54811yescharacteristic
160C2×C127#55211yescharacteristic
161C2×C127#55611yescharacteristic
162#2415C12711yesmaximal, characteristic, direct product factor, Sylow
163C127#241511yescharacteristic, direct product factor, Sylow
164C2×C22⋊Q8C2×C12711yescharacteristic, complemented
165C2×C22⋊Q8C2×C12711yescharacteristic, complemented
166C2×C4×D4C2×C12711yescharacteristic
167C2×#117C2×C12711yescharacteristic, complemented
168#397C2×C12712yescomplemented
169#394C2×C12712yes—
170#391C2×C12711yescharacteristic, complemented
171#389C2×C12712yescomplemented
172#389C2×C12711yescharacteristic, complemented
173#388C2×C12712yescomplemented
174#380C2×C12711yescharacteristic, complemented
175C22×Q8C22×C12711yescharacteristic
176C22×D4C22×C12711yescharacteristic
177C23×C4C22×C12711yescharacteristic
178C23×C4C22×C12711yescharacteristic
179C22⋊Q8—24no—
180C22⋊Q8—24no—
181C4×D4—24no—
182#117—24no—
183C2×C4⋊C4C22×C12711yescharacteristic
184C2×C4⋊C4C22×C12711yescharacteristic
185C2×C4⋊C4C22×C12711yescharacteristic
186C2×C4⋊C4C22×C12712yes—
187C2×C4⋊C4C22×C12712yes—
188C2×C4⋊C4C22×C12712yes—
189C2×C4⋊C4C22×C12711yescharacteristic
190C2×C22⋊C4C22×C12712yes—
191C2×C22⋊C4C22×C12711yescharacteristic
192C2×C22⋊C4C22×C12711yescharacteristic
193C2×C22⋊C4C22×C12712yes—
194C2×C22⋊C4C22×C12712yes—
195C2×C22⋊C4C22×C12712yes—
196C2×C42C22×C12712yes—
197C2×C42C22×C12711yescharacteristic
198#95C22×C12712yes—
199#95C22×C12712yes—
200#95C22×C12712yes—
201#95C22×C12712yes—
202C24C23×C12711yescharacteristic
203C24C23×C12711yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4D4×C12714yes—
216C22×C4C23×C12711yescharacteristic
217C22×C4C23×C12712yes—
218C22×C4C23×C12712yes—
219C22×C4C23×C12712yes—
220C22×C4C23×C12711yescharacteristic
221C22×C4C23×C12712yes—
222C22×C4C23×C12711yescharacteristic
223C22×C4C23×C12711yescharacteristic
224C22×C4C23×C12711yescharacteristic
225C4⋊C4—22no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—24no—
229C4⋊C4—24no—
230C4⋊C4—24no—
231C4⋊C4D4×C12714yescomplemented
232C22⋊C4—22no—
233C22⋊C4—24no—
234C22⋊C4—24no—
235C22⋊C4—24no—
236C22⋊C4—22no—
237C22⋊C4—24no—
238C42—24no—
239C42—22no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23C2×D4×C12712yes—
253C23#41×C12712yes—
254C23C24×C12711yescharacteristic
255Q8—44no—
256D4—28no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—28no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—44no—
280C2×C4C2×D4×C12714yes—
281C2×C4C2×D4×C12712yes—
282C2×C4C2×D4×C12712yes—
283C2×C4C2×D4×C12712yes—
284C2×C4#41×C12712yes—
285C2×C4#41×C12712yes—
286C22—22no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22C22×D4×C12711yescharacteristic
301C22C22×D4×C12711yescharacteristic
302C22C2×#41×C12711yescharacteristic
303C22C2×#41×C12711yescharacteristic
304C22C2×#41×C12711yescharacteristic
305C222−1+4×C12711yescharacteristic
306C222−1+4×C12711yescharacteristic
307C4—22no—
308C4—22no—
309C4—24no—
310C4—41no—
311C4—42no—
312C4—42no—
313C4—41no—
314C4—42no—
315C4#121×C12714yes—
316C2—42no—
317C2—42no—
318C2C2×#121×C12711yescharacteristic
319C2#525×C12711yescharacteristic
320C2#536×C12711yescharacteristic
321C2#547×C12711yescharacteristic
322C2#548×C12711yescharacteristic
323C2#552×C12711yescharacteristic
324C2#556×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC22×D4×C127C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×C127C2semidirect
2. C2×C22⋊Q8×C127C2semidirect
4. C2×#117×C127C2semidirect
5. #397×C127C2semidirect
7. #391×C127C2semidirect
8. #389×C127C2semidirect
9. #389×C127C2semidirect
10. #388×C127C2semidirect
11. #380×C127C2semidirect
68. C4⋊C4×C127D4semidirect
162. #2415C127direct (N × H)
163. C127#2415direct (N × H)
164. C2×C22⋊Q8C2×C127semidirect
165. C2×C22⋊Q8C2×C127semidirect
167. C2×#117C2×C127semidirect
168. #397C2×C127semidirect
170. #391C2×C127semidirect
171. #389C2×C127semidirect
172. #389C2×C127semidirect
173. #388C2×C127semidirect
174. #380C2×C127semidirect
231. C4⋊C4D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C1272
C2×C4×D4×C1272
C2×#117×C1272
#397×C1272
#394×C1272
#391×C1272
#389×C1272
#388×C1272
#380×C1272
#2415127