Finite Group Databasebeta

← C47×#14301 #26053999

Subgroups — C47×#14301 #26053999

Order 12032.

1830 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
2C2×C47×#393C211yesmaximal, characteristic
3C2×C47×#388C213yesmaximal
4C47×#1446C211yesmaximal, characteristic, complemented
5C47×#1444C213yesmaximal, complemented
6C47×#1439C213yesmaximal
7C47×#1434C213yesmaximal, complemented
8C23×Q8×C47C2211yescharacteristic
9C2×C4×Q8×C47—212no—
10C22×C4⋊C4×C47C2213yes—
11C22×C4⋊C4×C47C2213yes—
12C22×C22⋊C4×C47C2211yescharacteristic
13C22×C22⋊C4×C47C2213yes—
14C22×C22⋊C4×C47C2213yes—
15C22×C42×C47C2213yes—
16C47×#393C418yescomplemented
17C47×#388—212no—
18C2×#95×C47C2213yes—
19C2×#95×C47C2213yes—
20C2×#95×C47C2213yes—
21C2×#95×C47C2216yes—
22C2×#95×C47C2213yes—
23C25×C47C2311yescharacteristic
24C22×Q8×C47—26no—
25C22×Q8×C47—26no—
26C22×Q8×C47C2×C414yes—
27C23×C4×C47C2311yescharacteristic
28C23×C4×C47C2313yes—
29C23×C4×C47C2313yes—
30C23×C4×C47C2313yes—
31C23×C4×C47C2313yes—
32C23×C4×C47C2311yescharacteristic
33C4×Q8×C47—232no—
34C2×C4⋊C4×C47—212no—
35C2×C4⋊C4×C47—26no—
36C2×C4⋊C4×C47—26no—
37C2×C4⋊C4×C47—46no—
38C2×C22⋊C4×C47—26no—
39C2×C22⋊C4×C47—26no—
40C2×C22⋊C4×C47—26no—
41C2×C22⋊C4×C47—26no—
42C2×C22⋊C4×C47—46no—
43C2×C22⋊C4×C47C2×C4112yes—
44C2×C42×C47—212no—
45C2×C42×C47D4112yes—
46#95×C47—26no—
47#95×C47—26no—
48#95×C47—26no—
49#95×C47—46no—
50#95×C47C2×C4112yes—
51C24×C47—23no—
52C24×C47—23no—
53C24×C47—23no—
54C24×C47—21no—
55C24×C47—21no—
56C24×C47—23no—
57C24×C47C22×C412yes—
58C24×C47C2411yescharacteristic
59C2×Q8×C47—28no—
60C2×Q8×C47—224no—
61C2×Q8×C47—224no—
62C22×C4×C47—26no—
63C22×C4×C47—26no—
64C22×C4×C47—21no—
65C22×C4×C47—23no—
66C22×C4×C47—26no—
67C22×C4×C47—23no—
68C22×C4×C47—23no—
69C22×C4×C47—26no—
70C22×C4×C47—26no—
71C22×C4×C47—23no—
72C22×C4×C47—26no—
73C22×C4×C47—23no—
74C22×C4×C47—23no—
75C22×C4×C47—23no—
76C22×C4×C47—26no—
77C22×C4×C47—26no—
78C22×C4×C47—23no—
79C22×C4×C47—23no—
80C22×C4×C47—23no—
81C22×C4×C47—21no—
82C22×C4×C47C22×C416yes—
83C22×C4×C47C22×C416yes—
84C22×C4×C47C2×D416yes—
85C22×C4×C47C2×D416yes—
86C22×C4×C47C2×D416yes—
87C22×C4×C47#4116yes—
88C4⋊C4×C47—224no—
89C4⋊C4×C47—412no—
90C22⋊C4×C47—224no—
91C22⋊C4×C47—412no—
92C22⋊C4×C47—44no—
93C42×C47—224no—
94C23×C47—26no—
95C23×C47—22no—
96C23×C47—26no—
97C23×C47—41no—
98C23×C47—43no—
99C23×C47—43no—
100C23×C47—43no—
101C23×C47—43no—
102C23×C47—43no—
103C23×C47—43no—
104C23×C47—43no—
105C23×C47—46no—
106C23×C47C23×C411yescharacteristic
107C23×C47C22×D413yes—
108C23×C47C2×#4113yes—
109C23×C47H(5,𝔽2)13yes—
110C23×C472−1+411yescharacteristic
111C23×C472−1+411yescharacteristic
112C23×C472−1+413yes—
113Q8×C47—232no—
114C2×C4×C47—212no—
115C2×C4×C47—26no—
116C2×C4×C47—26no—
117C2×C4×C47—212no—
118C2×C4×C47—26no—
119C2×C4×C47—26no—
120C2×C4×C47—26no—
121C2×C4×C47—212no—
122C2×C4×C47—26no—
123C2×C4×C47—26no—
124C2×C4×C47—26no—
125C2×C4×C47—43no—
126C2×C4×C47—46no—
127C2×C4×C47—43no—
128C2×C4×C47—46no—
129C2×C4×C47—46no—
130C2×C4×C47—41no—
131C2×C4×C47—43no—
132C2×C4×C47—43no—
133C2×C4×C47—43no—
134C2×C4×C47—43no—
135C2×C4×C47—43no—
136C2×C4×C47—46no—
137C2×C4×C47—46no—
138C2×C4×C47C4×D4112yes—
139C2×C4×C47#12014yes—
140#14301C4711yesmaximal, characteristic, direct product factor, Sylow
141C22×C47—46no—
142C22×C47—46no—
143C22×C47—42no—
144C22×C47—81no—
145C22×C47—81no—
146C22×C47—83no—
147C22×C47—83no—
148C22×C47C2×C4×D413yes—
149C22×C47#51911yescharacteristic
150C22×C47#52013yes—
151C22×C47C2×#12011yescharacteristic
152C22×C47#52513yes—
153C22×C47#53513yes—
154C22×C47#53613yes—
155C22×C47#53613yes—
156C22×C47#53713yes—
157C22×C47#54113yes—
158C22×C47#54213yes—
159C22×C47#54216yes—
160C4×C47—24no—
161C4×C47—212no—
162C4×C47—46no—
163C4×C47—46no—
164C4×C47—81no—
165C4×C47—83no—
166C22×C4×Q8C2×C4711yescharacteristic, complemented
167C2×#393C2×C4711yescharacteristic
168C2×#388C2×C4713yes—
169#1446C2×C4711yescharacteristic, complemented
170#1444C2×C4713yescomplemented
171#1439C2×C4713yes—
172#1434C2×C4713yescomplemented
173C2×C47—82no—
174C2×C47C4×#12011yescharacteristic
175C2×C47#232313yes—
176C2×C47#232613yes—
177C2×C47#261411yescharacteristic
178C2×C47#261511yescharacteristic
179C2×C47#263213yes—
180C2×C47#263713yes—
181C23×Q8C22×C4711yescharacteristic
182C2×C4×Q8—212no—
183C22×C4⋊C4C22×C4713yes—
184C22×C4⋊C4C22×C4713yes—
185C22×C22⋊C4C22×C4711yescharacteristic
186C22×C22⋊C4C22×C4713yes—
187C22×C22⋊C4C22×C4713yes—
188C22×C42C22×C4713yes—
189#393C4×C4718yescomplemented
190#388—212no—
191C2×#95C22×C4713yes—
192C2×#95C22×C4713yes—
193C2×#95C22×C4713yes—
194C2×#95C22×C4716yes—
195C2×#95C22×C4713yes—
196C47#1430111yescharacteristic, direct product factor, Sylow
197C25C23×C4711yescharacteristic
198C22×Q8—26no—
199C22×Q8—26no—
200C22×Q8C2×C4×C4714yes—
201C23×C4C23×C4711yescharacteristic
202C23×C4C23×C4713yes—
203C23×C4C23×C4713yes—
204C23×C4C23×C4713yes—
205C23×C4C23×C4713yes—
206C23×C4C23×C4711yescharacteristic
207C4×Q8—232no—
208C2×C4⋊C4—212no—
209C2×C4⋊C4—26no—
210C2×C4⋊C4—26no—
211C2×C4⋊C4—46no—
212C2×C22⋊C4—26no—
213C2×C22⋊C4—26no—
214C2×C22⋊C4—26no—
215C2×C22⋊C4—26no—
216C2×C22⋊C4—46no—
217C2×C22⋊C4C2×C4×C47112yes—
218C2×C42—212no—
219C2×C42D4×C47112yes—
220#95—26no—
221#95—26no—
222#95—26no—
223#95—46no—
224#95C2×C4×C47112yes—
225C24—23no—
226C24—23no—
227C24—23no—
228C24—21no—
229C24—21no—
230C24—23no—
231C24C22×C4×C4712yes—
232C24C24×C4711yescharacteristic
233C2×Q8—28no—
234C2×Q8—224no—
235C2×Q8—224no—
236C22×C4—26no—
237C22×C4—26no—
238C22×C4—21no—
239C22×C4—23no—
240C22×C4—23no—
241C22×C4—26no—
242C22×C4—23no—
243C22×C4—23no—
244C22×C4—26no—
245C22×C4—26no—
246C22×C4—26no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—26no—
251C22×C4—26no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—21no—
256C22×C4C22×C4×C4716yes—
257C22×C4C22×C4×C4716yes—
258C22×C4C2×D4×C4716yes—
259C22×C4C2×D4×C4716yes—
260C22×C4C2×D4×C4716yes—
261C22×C4#41×C4716yes—
262C4⋊C4—224no—
263C4⋊C4—412no—
264C22⋊C4—224no—
265C22⋊C4—412no—
266C22⋊C4—44no—
267C42—224no—
268C23—26no—
269C23—22no—
270C23—26no—
271C23—41no—
272C23—43no—
273C23—43no—
274C23—43no—
275C23—43no—
276C23—43no—
277C23—43no—
278C23—43no—
279C23—46no—
280C23C23×C4×C4711yescharacteristic
281C23C22×D4×C4713yes—
282C23C2×#41×C4713yes—
283C23H(5,𝔽2)×C4713yes—
284C232−1+4×C4711yescharacteristic
285C232−1+4×C4711yescharacteristic
286C232−1+4×C4713yes—
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—26no—
291C2×C4—212no—
292C2×C4—26no—
293C2×C4—26no—
294C2×C4—26no—
295C2×C4—212no—
296C2×C4—26no—
297C2×C4—26no—
298C2×C4—26no—
299C2×C4—43no—
300C2×C4—46no—
301C2×C4—43no—
302C2×C4—46no—
303C2×C4—46no—
304C2×C4—41no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—43no—
308C2×C4—43no—
309C2×C4—43no—
310C2×C4—46no—
311C2×C4—46no—
312C2×C4C4×D4×C47112yes—
313C2×C4#120×C4714yes—
314C22—42no—
315C22—46no—
316C22—46no—
317C22—81no—
318C22—81no—
319C22—83no—
320C22—83no—
321C22C2×C4×D4×C4713yes—
322C22C47×#51911yescharacteristic
323C22C47×#52013yes—
324C22C2×#120×C4711yescharacteristic
325C22C47×#52513yes—
326C22C47×#53513yes—
327C22C47×#53613yes—
328C22C47×#53613yes—
329C22C47×#53713yes—
330C22C47×#54113yes—
331C22C47×#54213yes—
332C22C47×#54216yes—
333C4—212no—
334C4—24no—
335C4—46no—
336C4—46no—
337C4—81no—
338C4—83no—
339C2—82no—
340C2C4×#120×C4711yescharacteristic
341C2C47×#232313yes—
342C2C47×#232613yes—
343C2C47×#261411yescharacteristic
344C2C47×#261511yescharacteristic
345C2C47×#263213yes—
346C2C47×#263713yes—
subgroupG/H
center, socleC24×C47C24
commutatorC23C23×C4×C47
Frattini, cosocleC24C24×C47
prime radicalC25×C47C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×Q8×C47C2semidirect
4. C47×#1446C2semidirect
5. C47×#1444C2semidirect
7. C47×#1434C2semidirect
16. C47×#393C4semidirect
140. #14301C47direct (N × H)
166. C22×C4×Q8C2×C47semidirect
169. #1446C2×C47semidirect
170. #1444C2×C47semidirect
172. #1434C2×C47semidirect
189. #393C4×C47semidirect
196. C47#14301direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C472
C2×C47×#3932
C2×C47×#3882
C47×#14462
C47×#14442
C47×#14392
C47×#14342
#1430147