Finite Group Databasebeta

← C47×#29110 #26068808

Subgroups — C47×#29110 #26068808

Order 12032.

1078 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2851C211yesmaximal, characteristic, complemented
2C2×C47×#390C211yesmaximal, characteristic
3C47×#2073C212yesmaximal, complemented
4C47×#2025C212yesmaximal, complemented
5C47×#1936C214yesmaximal, complemented
6C47×#1823C212yesmaximal, complemented
7C47×#1786C212yesmaximal
8C47×#1749C211yesmaximal, characteristic, complemented
9C23×D4×C47C2211yescharacteristic
10C2×#125×C47C2211yescharacteristic, complemented
11C22×C4⋊C4×C47C2211yescharacteristic
12C22×C22⋊C4×C47—22no—
13C22×C42×C47C2211yescharacteristic
14C2×#102×C47C2214yes—
15C2×#102×C47C2214yes—
16C2×C22⋊C8×C47C2212yes—
17C2×#97×C47C2212yescomplemented
18C47×#390—22no—
19C47×#390C2212yes—
20C47×#390C2212yes—
21C47×#389C2212yescomplemented
22C47×#387—22no—
23C47×#385—22no—
24C47×#382C2211yescharacteristic, complemented
25C47×#380C2212yes—
26C47×#340C2214yescomplemented
27C47×#340C2214yescomplemented
28C47×#336C2212yescomplemented
29C25×C47—21no—
30C22×D4×C47—24no—
31C22×D4×C47—21no—
32C22×D4×C47—24no—
33C22×D4×C47—42no—
34C22×D4×C47C2312yes—
35C23×C4×C47—21no—
36C23×C4×C47D412yes—
37C23×C4×C47C2311yescharacteristic
38C22×C8×C47C2314yes—
39#125×C47—42no—
40C2×C4⋊C4×C47—24no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—22no—
43C2×C4⋊C4×C47—22no—
44C2×C4⋊C4×C47C2312yes—
45C2×C4⋊C4×C47C2312yes—
46C2×C4⋊C4×C47C2312yes—
47C2×C22⋊C4×C47—22no—
48C2×C22⋊C4×C47—24no—
49C2×C22⋊C4×C47—24no—
50C2×C22⋊C4×C47—48no—
51C2×C42×C47—42no—
52C2×C42×C47D412yes—
53C2×C42×C47C2311yescharacteristic
54C2×C42×C47C2311yescharacteristic
55#102×C47—28no—
56#102×C47—44no—
57C22⋊C8×C47—24no—
58#97×C47—42no—
59#95×C47—22no—
60#95×C47—22no—
61#95×C47—22no—
62C24×C47—24no—
63C24×C47—22no—
64C24×C47—42no—
65C24×C47—44no—
66C24×C47—42no—
67C24×C47—44no—
68C24×C47C2×D411yescharacteristic
69C2×D4×C47—24no—
70C2×D4×C47—24no—
71C2×D4×C47—22no—
72C2×D4×C47—24no—
73C2×D4×C47—416no—
74C2×D4×C47—42no—
75C2×D4×C47—42no—
76C2×D4×C47#4114yes—
77C22×C4×C47—22no—
78C22×C4×C47—22no—
79C22×C4×C47—24no—
80C22×C4×C47—22no—
81C22×C4×C47—22no—
82C22×C4×C47—22no—
83C22×C4×C47—42no—
84C22×C4×C47—42no—
85C22×C4×C47—42no—
86C22×C4×C47—44no—
87C22×C4×C47C2×D412yes—
88C22×C4×C47C2×D412yes—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47#4114yes—
91C22×C4×C47C2411yescharacteristic
92C2×C8×C47—24no—
93C2×C8×C47—24no—
94C2×C8×C47—24no—
95C4⋊C4×C47—24no—
96C4⋊C4×C47—24no—
97C4⋊C4×C47—24no—
98C4⋊C4×C47—44no—
99C4⋊C4×C47—44no—
100C4⋊C4×C47—42no—
101C22⋊C4×C47—48no—
102C22⋊C4×C47—48no—
103C22⋊C4×C47—44no—
104C42×C47—22no—
105C42×C47—22no—
106C42×C47—42no—
107C23×C47—21no—
108C23×C47—21no—
109C23×C47—22no—
110C23×C47—24no—
111C23×C47—48no—
112C23×C47—416no—
113C23×C47—42no—
114C23×C47—42no—
115C23×C47—44no—
116C23×C47—44no—
117C23×C47—84no—
118C23×C47—88no—
119C23×C47—84no—
120C23×C47#12412yes—
121C23×C47AGL(1,ℤ/8)14yes—
122C23×C47C22×D411yescharacteristic
123D4×C47—28no—
124D4×C47—48no—
125D4×C47—44no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—28no—
129C2×C4×C47—22no—
130C2×C4×C47—22no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—22no—
134C2×C4×C47—22no—
135C2×C4×C47—48no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47—44no—
140C2×C4×C47—42no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—84no—
145C2×C4×C47#12412yes—
146C2×C4×C47C2×#4112yes—
147C2×C4×C47C2×#4112yes—
148C2×C4×C47H(5,𝔽2)12yes—
149C8×C47—44no—
150#29110C4711yesmaximal, characteristic, direct product factor, Sylow
151C22×C47—22no—
152C22×C47—24no—
153C22×C47—22no—
154C22×C47—24no—
155C22×C47—44no—
156C22×C47—48no—
157C22×C47—816no—
158C22×C47—82no—
159C22×C47—82no—
160C22×C47—84no—
161C22×C47#49014yes—
162C22×C47#52511yescharacteristic
163C22×C47C2×#12411yescharacteristic
164C22×C47#53411yescharacteristic
165C22×C47C2×AGL(1,ℤ/8)12yes—
166C22×C47#57512yes—
167C4×C47—22no—
168C4×C47—42no—
169C4×C47—42no—
170C4×C47—82no—
171C4×C47—82no—
172C4×C47—82no—
173C4×C47#55114yes—
174#2851C2×C4711yescharacteristic, complemented
175C2×#390C2×C4711yescharacteristic
176#2073C2×C4712yescomplemented
177#2025C2×C4712yescomplemented
178#1936C2×C4714yescomplemented
179#1823C2×C4712yescomplemented
180#1786C2×C4712yes—
181#1749C2×C4711yescharacteristic, complemented
182C2×C47—24no—
183C2×C47—84no—
184C2×C47#256111yescharacteristic
185C2×C47#311412yes—
186C2×C47C2×#49011yescharacteristic
187C2×C47#314011yescharacteristic
188C2×C47#319412yes—
189C23×D4C22×C4711yescharacteristic
190C2×#125C22×C4711yescharacteristic, complemented
191C22×C4⋊C4C22×C4711yescharacteristic
192C22×C22⋊C4—22no—
193C22×C42C22×C4711yescharacteristic
194C2×#102C22×C4714yes—
195C2×#102C22×C4714yes—
196C2×C22⋊C8C22×C4712yes—
197C2×#97C22×C4712yescomplemented
198#390—22no—
199#390C22×C4712yes—
200#390C22×C4712yes—
201#389C22×C4712yescomplemented
202#387—22no—
203#385—22no—
204#382C22×C4711yescharacteristic, complemented
205#380C22×C4712yes—
206#340C22×C4714yescomplemented
207#340C22×C4714yescomplemented
208#336C22×C4712yescomplemented
209C47#2911011yescharacteristic, direct product factor, Sylow
210C25—21no—
211C22×D4—24no—
212C22×D4—21no—
213C22×D4—24no—
214C22×D4—42no—
215C22×D4C23×C4712yes—
216C23×C4—21no—
217C23×C4D4×C4712yes—
218C23×C4C23×C4711yescharacteristic
219C22×C8C23×C4714yes—
220#125—42no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4C23×C4712yes—
226C2×C4⋊C4C23×C4712yes—
227C2×C4⋊C4C23×C4712yes—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—24no—
230C2×C22⋊C4—24no—
231C2×C22⋊C4—48no—
232C2×C42—42no—
233C2×C42D4×C4712yes—
234C2×C42C23×C4711yescharacteristic
235C2×C42C23×C4711yescharacteristic
236#102—28no—
237#102—44no—
238C22⋊C8—24no—
239#97—42no—
240#95—22no—
241#95—22no—
242#95—22no—
243C24—24no—
244C24—22no—
245C24—42no—
246C24—44no—
247C24—42no—
248C24—44no—
249C24C2×D4×C4711yescharacteristic
250C2×D4—24no—
251C2×D4—24no—
252C2×D4—22no—
253C2×D4—24no—
254C2×D4—416no—
255C2×D4—42no—
256C2×D4—42no—
257C2×D4#41×C4714yes—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—44no—
268C22×C4C2×D4×C4712yes—
269C22×C4C2×D4×C4712yes—
270C22×C4C2×D4×C4711yescharacteristic
271C22×C4#41×C4714yes—
272C22×C4C24×C4711yescharacteristic
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—24no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C4⋊C4—42no—
282C22⋊C4—48no—
283C22⋊C4—48no—
284C22⋊C4—44no—
285C42—22no—
286C42—22no—
287C42—42no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—24no—
292C23—48no—
293C23—416no—
294C23—42no—
295C23—42no—
296C23—44no—
297C23—44no—
298C23—84no—
299C23—88no—
300C23—84no—
301C23#124×C4712yes—
302C23AGL(1,ℤ/8)×C4714yes—
303C23C22×D4×C4711yescharacteristic
304D4—28no—
305D4—48no—
306D4—44no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—28no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—48no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—84no—
326C2×C4#124×C4712yes—
327C2×C4C2×#41×C4712yes—
328C2×C4C2×#41×C4712yes—
329C2×C4H(5,𝔽2)×C4712yes—
330C8—44no—
331C22—22no—
332C22—24no—
333C22—22no—
334C22—24no—
335C22—44no—
336C22—48no—
337C22—816no—
338C22—82no—
339C22—82no—
340C22—84no—
341C22C47×#49014yes—
342C22C47×#52511yescharacteristic
343C22C2×#124×C4711yescharacteristic
344C22C47×#53411yescharacteristic
345C22C2×AGL(1,ℤ/8)×C4712yes—
346C22C47×#57512yes—
347C4—22no—
348C4—42no—
349C4—42no—
350C4—82no—
351C4—82no—
352C4—82no—
353C4C47×#55114yes—
354C2—24no—
355C2—84no—
356C2C47×#256111yescharacteristic
357C2C47×#311412yes—
358C2C2×C47×#49011yescharacteristic
359C2C47×#314011yescharacteristic
360C2C47×#319412yes—
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC23×D4×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#2851C2semidirect
3. C47×#2073C2semidirect
4. C47×#2025C2semidirect
5. C47×#1936C2semidirect
6. C47×#1823C2semidirect
8. C47×#1749C2semidirect
10. C2×#125×C47C22semidirect
17. C2×#97×C47C22semidirect
21. C47×#389C22semidirect
24. C47×#382C22semidirect
26. C47×#340C22semidirect
27. C47×#340C22semidirect
28. C47×#336C22semidirect
150. #29110C47direct (N × H)
174. #2851C2×C47semidirect
176. #2073C2×C47semidirect
177. #2025C2×C47semidirect
178. #1936C2×C47semidirect
179. #1823C2×C47semidirect
181. #1749C2×C47semidirect
190. C2×#125C22×C47semidirect
197. C2×#97C22×C47semidirect
201. #389C22×C47semidirect
204. #382C22×C47semidirect
206. #340C22×C47semidirect
207. #340C22×C47semidirect
208. #336C22×C47semidirect
209. C47#29110direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#28512
C2×C47×#3902
C47×#20732
C47×#20252
C47×#19362
C47×#18232
C47×#17862
C47×#17492
#2911047