Finite Group Databasebeta

← C47×#14572 #26054270

Subgroups — C47×#14572 #26054270

Order 12032.

2498 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#392C211yesmaximal, characteristic
2C2×C47×#386C216yesmaximal, complemented
3C47×#1443C212yesmaximal, complemented
4C47×#1439C213yesmaximal, complemented
5C47×C22⋊#95C213yesmaximal, complemented
6C23×D4×C47C2213yes—
7C24×C4×C47C2213yes—
8C22×C4⋊C4×C47C2211yescharacteristic
9C22×C22⋊C4×C47C2216yes—
10C22×C22⋊C4×C47C2213yes—
11C22×C22⋊C4×C47C2213yes—
12C47×#392C418yescomplemented
13C47×#386—224no—
14C2×#95×C47C2216yes—
15C2×#95×C47C2216yes—
16C2×#95×C47C2213yes—
17C2×#95×C47C2211yescharacteristic
18C25×C47C2313yes—
19C22×D4×C47—212no—
20C22×D4×C47—212no—
21C22×D4×C47—43no—
22C22×D4×C47—43no—
23C22×D4×C47C2×C4112yescomplemented
24C23×C4×C47—26no—
25C23×C4×C47—212no—
26C23×C4×C47—43no—
27C23×C4×C47—43no—
28C23×C4×C47—46no—
29C23×C4×C47C2312yes—
30C23×C4×C47C2311yescharacteristic
31C23×C4×C47C2313yes—
32C23×C4×C47C2316yes—
33C2×C4⋊C4×C47—43no—
34C2×C22⋊C4×C47—212no—
35C2×C22⋊C4×C47—212no—
36C2×C22⋊C4×C47—43no—
37C2×C22⋊C4×C47—43no—
38C2×C22⋊C4×C47—43no—
39C2×C22⋊C4×C47—43no—
40C2×C22⋊C4×C47—46no—
41C2×C22⋊C4×C47C2×C4112yescomplemented
42C2×C22⋊C4×C47D4112yescomplemented
43#95×C47—212no—
44#95×C47—212no—
45#95×C47—43no—
46#95×C47C2×C414yescomplemented
47C24×C47—26no—
48C24×C47—26no—
49C24×C47—23no—
50C24×C47—23no—
51C24×C47—23no—
52C24×C47—26no—
53C24×C47—26no—
54C24×C47—23no—
55C24×C47C22×C416yes—
56C24×C47C2×D416yes—
57C24×C47#4116yes—
58C24×C47C2411yescharacteristic
59C2×D4×C47—248no—
60C2×D4×C47—412no—
61C2×D4×C47—412no—
62C2×D4×C47—424no—
63C2×D4×C47—412no—
64C22×C4×C47—26no—
65C22×C4×C47—26no—
66C22×C4×C47—26no—
67C22×C4×C47—26no—
68C22×C4×C47—23no—
69C22×C4×C47—26no—
70C22×C4×C47—26no—
71C22×C4×C47—26no—
72C22×C4×C47—23no—
73C22×C4×C47—23no—
74C22×C4×C47—23no—
75C22×C4×C47—26no—
76C22×C4×C47—26no—
77C22×C4×C47—26no—
78C22×C4×C47—22no—
79C22×C4×C47—412no—
80C22×C4×C47—424no—
81C22×C4×C47—424no—
82C22×C4×C47—412no—
83C22×C4×C47—412no—
84C22×C4×C47C22×C412yes—
85C22×C4×C47C22×C416yes—
86C22×C4×C47C2×D4112yes—
87C4⋊C4×C47—44no—
88C22⋊C4×C47—412no—
89C22⋊C4×C47—412no—
90C22⋊C4×C47—424no—
91C23×C47—212no—
92C23×C47—26no—
93C23×C47—212no—
94C23×C47—26no—
95C23×C47—26no—
96C23×C47—26no—
97C23×C47—26no—
98C23×C47—26no—
99C23×C47—212no—
100C23×C47—212no—
101C23×C47—212no—
102C23×C47—212no—
103C23×C47—46no—
104C23×C47—46no—
105C23×C47—46no—
106C23×C47—46no—
107C23×C47—43no—
108C23×C47—46no—
109C23×C47—43no—
110C23×C47—43no—
111C23×C47—46no—
112C23×C47—43no—
113C23×C47C4×D4112yes—
114C23×C47C23×C411yescharacteristic
115C23×C47C22×D413yes—
116C23×C47C2×#4113yes—
117C23×C47H(5,𝔽2)13yes—
118C23×C47H(5,𝔽2)13yes—
119C23×C47H(5,𝔽2)11yescharacteristic
120C23×C472−1+411yescharacteristic
121D4×C47—448no—
122C2×C4×C47—212no—
123C2×C4×C47—26no—
124C2×C4×C47—26no—
125C2×C4×C47—212no—
126C2×C4×C47—212no—
127C2×C4×C47—212no—
128C2×C4×C47—448no—
129C2×C4×C47—46no—
130C2×C4×C47—46no—
131C2×C4×C47—43no—
132C2×C4×C47—46no—
133C2×C4×C47—46no—
134C2×C4×C47—43no—
135C2×C4×C47—41no—
136C2×C4×C47—43no—
137C2×C4×C47—46no—
138C2×C4×C47—46no—
139C2×C4×C47—46no—
140C2×C4×C47—42no—
141#14572C4711yesmaximal, characteristic, direct product factor, Sylow
142C22×C47—212no—
143C22×C47—224no—
144C22×C47—412no—
145C22×C47—46no—
146C22×C47—46no—
147C22×C47—46no—
148C22×C47—412no—
149C22×C47—46no—
150C22×C47—46no—
151C22×C47—412no—
152C22×C47—46no—
153C22×C47C2×C4×D413yes—
154C22×C47#51813yes—
155C22×C47#52011yescharacteristic
156C22×C47#53413yes—
157C22×C47#53713yes—
158C22×C47#53813yes—
159C22×C47#53913yes—
160C22×C47D4213yes—
161C22×C47#54616yes—
162C22×C47#55113yes—
163C22×C47#56013yes—
164C22×C47#56011yescharacteristic
165C4×C47—46no—
166C4×C47—42no—
167C4×C47—412no—
168C4×C47—82no—
169C2×#392C2×C4711yescharacteristic
170C2×#386C2×C4716yescomplemented
171#1443C2×C4712yescomplemented
172#1439C2×C4713yescomplemented
173C22⋊#95C2×C4713yescomplemented
174C2×C47—412no—
175C2×C47#232513yes—
176C2×C47#235813yes—
177C2×C47#238011yescharacteristic
178C2×C47#266813yes—
179C2×C47#267511yescharacteristic
180C2×C47#269313yes—
181C2×C47#276011yescharacteristic
182C23×D4C22×C4713yes—
183C24×C4C22×C4713yes—
184C22×C4⋊C4C22×C4711yescharacteristic
185C22×C22⋊C4C22×C4716yes—
186C22×C22⋊C4C22×C4713yes—
187C22×C22⋊C4C22×C4713yes—
188#392C4×C4718yescomplemented
189#386—224no—
190C2×#95C22×C4716yes—
191C2×#95C22×C4716yes—
192C2×#95C22×C4713yes—
193C2×#95C22×C4711yescharacteristic
194C47#1457211yescharacteristic, direct product factor, Sylow
195C25C23×C4713yes—
196C22×D4—212no—
197C22×D4—212no—
198C22×D4—43no—
199C22×D4—43no—
200C22×D4C2×C4×C47112yescomplemented
201C23×C4—26no—
202C23×C4—212no—
203C23×C4—46no—
204C23×C4—43no—
205C23×C4—43no—
206C23×C4C23×C4712yes—
207C23×C4C23×C4711yescharacteristic
208C23×C4C23×C4713yes—
209C23×C4C23×C4716yes—
210C2×C4⋊C4—43no—
211C2×C22⋊C4—212no—
212C2×C22⋊C4—212no—
213C2×C22⋊C4—43no—
214C2×C22⋊C4—43no—
215C2×C22⋊C4—43no—
216C2×C22⋊C4—43no—
217C2×C22⋊C4—46no—
218C2×C22⋊C4C2×C4×C47112yescomplemented
219C2×C22⋊C4D4×C47112yescomplemented
220#95—212no—
221#95—212no—
222#95—43no—
223#95C2×C4×C4714yescomplemented
224C24—26no—
225C24—26no—
226C24—23no—
227C24—23no—
228C24—23no—
229C24—26no—
230C24—26no—
231C24—23no—
232C24C22×C4×C4716yes—
233C24C2×D4×C4716yes—
234C24#41×C4716yes—
235C24C24×C4711yescharacteristic
236C2×D4—248no—
237C2×D4—412no—
238C2×D4—412no—
239C2×D4—424no—
240C2×D4—412no—
241C22×C4—26no—
242C22×C4—26no—
243C22×C4—26no—
244C22×C4—26no—
245C22×C4—23no—
246C22×C4—26no—
247C22×C4—23no—
248C22×C4—26no—
249C22×C4—26no—
250C22×C4—26no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—26no—
254C22×C4—26no—
255C22×C4—22no—
256C22×C4—412no—
257C22×C4—424no—
258C22×C4—424no—
259C22×C4—412no—
260C22×C4—412no—
261C22×C4C22×C4×C4716yes—
262C22×C4C22×C4×C4712yes—
263C22×C4C2×D4×C47112yes—
264C4⋊C4—44no—
265C22⋊C4—412no—
266C22⋊C4—412no—
267C22⋊C4—424no—
268C23—212no—
269C23—26no—
270C23—212no—
271C23—26no—
272C23—26no—
273C23—26no—
274C23—26no—
275C23—26no—
276C23—212no—
277C23—212no—
278C23—212no—
279C23—212no—
280C23—46no—
281C23—46no—
282C23—46no—
283C23—46no—
284C23—43no—
285C23—46no—
286C23—43no—
287C23—43no—
288C23—46no—
289C23—43no—
290C23C4×D4×C47112yes—
291C23C23×C4×C4711yescharacteristic
292C23C22×D4×C4713yes—
293C23C2×#41×C4713yes—
294C23H(5,𝔽2)×C4713yes—
295C23H(5,𝔽2)×C4713yes—
296C23H(5,𝔽2)×C4711yescharacteristic
297C232−1+4×C4711yescharacteristic
298D4—448no—
299C2×C4—212no—
300C2×C4—26no—
301C2×C4—26no—
302C2×C4—212no—
303C2×C4—212no—
304C2×C4—212no—
305C2×C4—448no—
306C2×C4—46no—
307C2×C4—46no—
308C2×C4—43no—
309C2×C4—46no—
310C2×C4—46no—
311C2×C4—43no—
312C2×C4—41no—
313C2×C4—43no—
314C2×C4—46no—
315C2×C4—46no—
316C2×C4—46no—
317C2×C4—42no—
318C22—212no—
319C22—224no—
320C22—412no—
321C22—46no—
322C22—46no—
323C22—46no—
324C22—412no—
325C22—46no—
326C22—46no—
327C22—412no—
328C22—46no—
329C22C2×C4×D4×C4713yes—
330C22C47×#51813yes—
331C22C47×#52011yescharacteristic
332C22C47×#53413yes—
333C22C47×#53713yes—
334C22C47×#53813yes—
335C22C47×#53913yes—
336C22D42×C4713yes—
337C22C47×#54616yes—
338C22C47×#55113yes—
339C22C47×#56013yes—
340C22C47×#56011yescharacteristic
341C4—46no—
342C4—42no—
343C4—412no—
344C4—82no—
345C2—412no—
346C2C47×#232513yes—
347C2C47×#235813yes—
348C2C47×#238011yescharacteristic
349C2C47×#266813yes—
350C2C47×#267511yescharacteristic
351C2C47×#269313yes—
352C2C47×#276011yescharacteristic
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC2×C47×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#386C2semidirect
3. C47×#1443C2semidirect
4. C47×#1439C2semidirect
5. C47×C22⋊#95C2semidirect
12. C47×#392C4semidirect
23. C22×D4×C47C2×C4semidirect
41. C2×C22⋊C4×C47C2×C4semidirect
42. C2×C22⋊C4×C47D4semidirect
46. #95×C47C2×C4semidirect
141. #14572C47direct (N × H)
170. C2×#386C2×C47semidirect
171. #1443C2×C47semidirect
172. #1439C2×C47semidirect
173. C22⋊#95C2×C47semidirect
188. #392C4×C47semidirect
194. C47#14572direct (N × H)
200. C22×D4C2×C4×C47semidirect
218. C2×C22⋊C4C2×C4×C47semidirect
219. C2×C22⋊C4D4×C47semidirect
223. #95C2×C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#3922
C2×C47×#3862
C47×#14432
C47×#14392
C47×C22⋊#952
#1457247