Finite Group Databasebeta

← C127×#2445 #30635397

Subgroups — C127×#2445 #30635397

Order 16256.

696 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#127×C127C211yesmaximal, characteristic
2C2×#123×C127C212yesmaximal, complemented
3C2×C4×D4×C127C211yesmaximal, characteristic, complemented
4#394×C127C212yesmaximal, complemented
5#394×C127C212yesmaximal, complemented
6#390×C127C211yesmaximal, characteristic, complemented
7#390×C127C211yesmaximal, characteristic, complemented
8#390×C127C211yesmaximal, characteristic, complemented
9#389×C127C211yesmaximal, characteristic, complemented
10#386×C127C212yesmaximal, complemented
11C4×C4⋊C4×C127C211yesmaximal, characteristic, complemented
12C22×D4×C127C2211yescharacteristic
13C22×D4×C127C2212yes—
14C22×D4×C127C2212yes—
15C22×D4×C127C2211yescharacteristic
16C23×C4×C127C2212yes—
17#127×C127—24no—
18#123×C127—28no—
19C4×D4×C127—24no—
20C2×C4⋊C4×C127C2211yescharacteristic
21C2×C4⋊C4×C127C2212yes—
22C2×C4⋊C4×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24C2×C4⋊C4×C127C2211yescharacteristic
25C2×C22⋊C4×C127C2212yes—
26C2×C22⋊C4×C127C2212yes—
27C2×C22⋊C4×C127C2212yes—
28C2×C22⋊C4×C127C2212yes—
29C2×C22⋊C4×C127C2212yes—
30C2×C22⋊C4×C127C2212yes—
31C2×C22⋊C4×C127C2212yes—
32C2×C42×C127C2211yescharacteristic
33C2×C42×C127C2211yescharacteristic
34C2×C42×C127C2211yescharacteristic
35#95×C127C2211yescharacteristic
36#95×C127C2211yescharacteristic
37#95×C127C2212yes—
38C24×C127C2312yes—
39C24×C127C2312yes—
40C2×D4×C127—24no—
41C2×D4×C127—24no—
42C2×D4×C127—24no—
43C2×D4×C127—22no—
44C2×D4×C127—22no—
45C2×D4×C127—22no—
46C2×D4×C127—24no—
47C2×D4×C127—22no—
48C2×D4×C127—22no—
49C2×D4×C127—42no—
50C2×D4×C127—42no—
51C2×D4×C127D414yes—
52C22×C4×C127—24no—
53C22×C4×C127—24no—
54C22×C4×C127—42no—
55C22×C4×C127C2311yescharacteristic
56C22×C4×C127C2311yescharacteristic
57C22×C4×C127C2312yes—
58C22×C4×C127C2312yes—
59C22×C4×C127C2311yescharacteristic
60C22×C4×C127C2311yescharacteristic
61C22×C4×C127C2311yescharacteristic
62C22×C4×C127C2311yescharacteristic
63C22×C4×C127C2311yescharacteristic
64C4⋊C4×C127—22no—
65C4⋊C4×C127—24no—
66C4⋊C4×C127—22no—
67C4⋊C4×C127—22no—
68C4⋊C4×C127D414yescomplemented
69C22⋊C4×C127—24no—
70C22⋊C4×C127—24no—
71C22⋊C4×C127—24no—
72C22⋊C4×C127—24no—
73C22⋊C4×C127—42no—
74C22⋊C4×C127—42no—
75C22⋊C4×C127—42no—
76C42×C127—22no—
77C42×C127—22no—
78C42×C127—22no—
79C23×C127—22no—
80C23×C127—22no—
81C23×C127—22no—
82C23×C127—22no—
83C23×C127—22no—
84C23×C127—22no—
85C23×C127—22no—
86C23×C127—22no—
87C23×C127—22no—
88C23×C127—22no—
89C23×C127—22no—
90C23×C127—22no—
91C23×C127—22no—
92C23×C127C2×D414yes—
93C23×C127C2411yescharacteristic
94D4×C127—28no—
95D4×C127—48no—
96D4×C127—48no—
97D4×C127—44no—
98C2×C4×C127—21no—
99C2×C4×C127—21no—
100C2×C4×C127—21no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—22no—
117C2×C4×C127—22no—
118C2×C4×C127—48no—
119C2×C4×C127C2×D412yes—
120C2×C4×C127C2×D412yes—
121C2×C4×C127C2×D412yes—
122C2×C4×C127C2×D412yes—
123C2×C4×C127#4112yes—
124C2×C4×C127#4112yes—
125C2×C4×C127#4112yes—
126C22×C127—24no—
127C22×C127—24no—
128C22×C127—24no—
129C22×C127—42no—
130C22×C127—42no—
131C22×C127—42no—
132C22×C127—42no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127—42no—
137C22×C127—42no—
138C22×C127—42no—
139C22×C127—42no—
140C22×C127C22×D411yescharacteristic
141C22×C127C22×D411yescharacteristic
142C22×C127C2×#4111yescharacteristic
143C22×C127C2×#4111yescharacteristic
144C22×C127C2×#4111yescharacteristic
145C22×C127H(5,𝔽2)11yescharacteristic
146C22×C127H(5,𝔽2)11yescharacteristic
147C4×C127—22no—
148C4×C127—22no—
149C4×C127—22no—
150C4×C127—22no—
151C4×C127—41no—
152C4×C127—42no—
153C4×C127—41no—
154C4×C127—42no—
155C4×C127#12314yescomplemented
156C2×C127—44no—
157C2×C127—82no—
158C2×C127C2×#12311yescharacteristic
159C2×C127#53211yescharacteristic
160C2×C127#54011yescharacteristic
161C2×C127D4211yescharacteristic
162C2×C127#54611yescharacteristic
163C2×C127#55011yescharacteristic
164C2×C127#55911yescharacteristic
165#2445C12711yesmaximal, characteristic, direct product factor, Sylow
166C127#244511yescharacteristic, direct product factor, Sylow
167C2×#127C2×C12711yescharacteristic
168C2×#123C2×C12712yescomplemented
169C2×C4×D4C2×C12711yescharacteristic, complemented
170#394C2×C12712yescomplemented
171#394C2×C12712yescomplemented
172#390C2×C12711yescharacteristic, complemented
173#390C2×C12711yescharacteristic, complemented
174#390C2×C12711yescharacteristic, complemented
175#389C2×C12711yescharacteristic, complemented
176#386C2×C12712yescomplemented
177C4×C4⋊C4C2×C12711yescharacteristic, complemented
178C22×D4C22×C12711yescharacteristic
179C22×D4C22×C12712yes—
180C22×D4C22×C12712yes—
181C22×D4C22×C12711yescharacteristic
182C23×C4C22×C12712yes—
183#127—24no—
184#123—28no—
185C4×D4—24no—
186C2×C4⋊C4C22×C12711yescharacteristic
187C2×C4⋊C4C22×C12712yes—
188C2×C4⋊C4C22×C12711yescharacteristic
189C2×C4⋊C4C22×C12711yescharacteristic
190C2×C4⋊C4C22×C12711yescharacteristic
191C2×C22⋊C4C22×C12712yes—
192C2×C22⋊C4C22×C12712yes—
193C2×C22⋊C4C22×C12712yes—
194C2×C22⋊C4C22×C12712yes—
195C2×C22⋊C4C22×C12712yes—
196C2×C22⋊C4C22×C12712yes—
197C2×C22⋊C4C22×C12712yes—
198C2×C42C22×C12711yescharacteristic
199C2×C42C22×C12711yescharacteristic
200C2×C42C22×C12711yescharacteristic
201#95C22×C12711yescharacteristic
202#95C22×C12711yescharacteristic
203#95C22×C12712yes—
204C24C23×C12712yes—
205C24C23×C12712yes—
206C2×D4—24no—
207C2×D4—24no—
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—22no—
212C2×D4—24no—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4D4×C12714yes—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—42no—
221C22×C4C23×C12711yescharacteristic
222C22×C4C23×C12711yescharacteristic
223C22×C4C23×C12712yes—
224C22×C4C23×C12712yes—
225C22×C4C23×C12711yescharacteristic
226C22×C4C23×C12711yescharacteristic
227C22×C4C23×C12711yescharacteristic
228C22×C4C23×C12711yescharacteristic
229C22×C4C23×C12711yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4D4×C12714yescomplemented
235C22⋊C4—24no—
236C22⋊C4—24no—
237C22⋊C4—24no—
238C22⋊C4—24no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C42—22no—
243C42—22no—
244C42—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23C2×D4×C12714yes—
259C23C24×C12711yescharacteristic
260D4—28no—
261D4—48no—
262D4—48no—
263D4—44no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—48no—
285C2×C4C2×D4×C12712yes—
286C2×C4C2×D4×C12712yes—
287C2×C4C2×D4×C12712yes—
288C2×C4C2×D4×C12712yes—
289C2×C4#41×C12712yes—
290C2×C4#41×C12712yes—
291C2×C4#41×C12712yes—
292C22—24no—
293C22—24no—
294C22—24no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22C22×D4×C12711yescharacteristic
307C22C22×D4×C12711yescharacteristic
308C22C2×#41×C12711yescharacteristic
309C22C2×#41×C12711yescharacteristic
310C22C2×#41×C12711yescharacteristic
311C22H(5,𝔽2)×C12711yescharacteristic
312C22H(5,𝔽2)×C12711yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—22no—
317C4—41no—
318C4—42no—
319C4—41no—
320C4—42no—
321C4#123×C12714yescomplemented
322C2—44no—
323C2—82no—
324C2C2×#123×C12711yescharacteristic
325C2#532×C12711yescharacteristic
326C2#540×C12711yescharacteristic
327C2D42×C12711yescharacteristic
328C2#546×C12711yescharacteristic
329C2#550×C12711yescharacteristic
330C2#559×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C24
commutator, Frattini, cosocleC23C24×C127
prime radicalC2×#127×C127C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#123×C127C2semidirect
3. C2×C4×D4×C127C2semidirect
4. #394×C127C2semidirect
5. #394×C127C2semidirect
6. #390×C127C2semidirect
7. #390×C127C2semidirect
8. #390×C127C2semidirect
9. #389×C127C2semidirect
10. #386×C127C2semidirect
11. C4×C4⋊C4×C127C2semidirect
68. C4⋊C4×C127D4semidirect
155. C4×C127#123semidirect
165. #2445C127direct (N × H)
166. C127#2445direct (N × H)
168. C2×#123C2×C127semidirect
169. C2×C4×D4C2×C127semidirect
170. #394C2×C127semidirect
171. #394C2×C127semidirect
172. #390C2×C127semidirect
173. #390C2×C127semidirect
174. #390C2×C127semidirect
175. #389C2×C127semidirect
176. #386C2×C127semidirect
177. C4×C4⋊C4C2×C127semidirect
234. C4⋊C4D4×C127semidirect
321. C4#123×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#127×C1272
C2×#123×C1272
C2×C4×D4×C1272
#394×C1272
#390×C1272
#389×C1272
#386×C1272
C4×C4⋊C4×C1272
#2445127