Finite Group Databasebeta

← D47×#2843 #26422868

Subgroups — D47×#2843 #26422868

Order 12032.

1806 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251658C213yesmaximal, complemented
2#20251657C211yesmaximal, characteristic, complemented
3#20251656C216yesmaximal, complemented
4#20251655C212yesmaximal, complemented
5#20251654C213yesmaximal, complemented
6#400×D47C213yesmaximal
7#398×D47C216yesmaximal
8#395×D47C213yesmaximal
9#384×D47C211yesmaximal, characteristic
10#383×D47C212yesmaximal
11C47×#2843C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2213yes—
14C2×C4⋊C4×D47C2213yes—
15C2×C4⋊C4×D47C2216yes—
16C2×C4⋊C4×D47C2213yes—
17C2×C42×D47C2211yescharacteristic
18#15689065C2216yes—
19#15689064C2216yes—
20#15689063C2213yes—
21#15689062C2213yes—
22#15689061C2213yes—
23#15689057C2216yes—
24#15689057C2216yes—
25#15689056C2216yes—
26#15689056C2216yes—
27#15689055C2216yes—
28#15689054C2216yes—
29#15689053C2216yes—
30#15689044C2216yes—
31#15689044C2213yes—
32#15689043C2216yes—
33#15689043C2213yes—
34#15689042C2213yes—
35#15688993C2211yescharacteristic
36#15688992C2213yes—
37#15688992C2213yes—
38#15688991C2212yes—
39#15688990C2216yes—
40#15688990C2216yes—
41#95×D47C2216yes—
42#95×D47C2216yes—
43#95×D47C2213yes—
44#95×D47C2213yes—
45C47×#400C2213yes—
46C47×#398C2216yes—
47C47×#395C2213yes—
48C47×#384C2211yescharacteristic
49C47×#383C2212yes—
50C22×Dic94C2312yes—
51C22×Dic94C2311yescharacteristic
52C2×Q8×D47—46no—
53C22×C4×D47C2316yes—
54C22×C4×D47C2312yes—
55C22×C4×D47C2311yescharacteristic
56C22×C4×D47C2313yes—
57C22×C4×D47C2313yes—
58C2×C4⋊Dic47C2313yes—
59C2×C4⋊Dic47C2313yes—
60C2×C4⋊Dic47C2316yes—
61C2×C4⋊Dic47C2313yes—
62C2×Dic47⋊C4C2313yes—
63C2×Dic47⋊C4C2313yes—
64C2×Dic47⋊C4C2316yes—
65C2×Dic47⋊C4C2316yes—
66C2×Dic47⋊C4C2316yes—
67C2×Dic47⋊C4C2316yes—
68C4⋊C4×D47—46no—
69C4⋊C4×D47—46no—
70C4⋊C4×D47—46no—
71C4⋊C4×D47—412no—
72C2×C4×Dic47C2313yes—
73C42×D47Q818yescomplemented
74C47⋊#95C2316yes—
75C47⋊#95C2316yes—
76C47⋊#95C2316yes—
77C47⋊#95C2316yes—
78C47⋊#95C2316yes—
79C47⋊#95C2316yes—
80C47⋊#95C2313yes—
81C47⋊#95C2316yes—
82C47⋊#95C2316yes—
83C47⋊#95C2313yes—
84C22×Q8×C47C2311yescharacteristic
85C2×C4⋊C4×C47C2313yes—
86C2×C4⋊C4×C47C2313yes—
87C2×C4⋊C4×C47C2316yes—
88C2×C4⋊C4×C47C2313yes—
89C2×C42×C47C2311yescharacteristic
90#95×C47C2316yes—
91#95×C47C2316yes—
92#95×C47C2313yes—
93#95×C47C2313yes—
94C23×D47C2411yescharacteristic
95C2×Q8×C47—43no—
96C22×C4×C47C2413yes—
97C22×C4×C47C2411yescharacteristic
98C22×C4×C47C2412yes—
99C22×C4×C47C2416yes—
100C22×C4×C47C2413yes—
101C22×Dic47C2416yes—
102C22×Dic47C2412yes—
103C22×Dic47C2411yescharacteristic
104C22×Dic47C2413yes—
105C22×Dic47C2413yes—
106Q8×D47—416no—
107C2×C4×D47—26no—
108C2×C4×D47—26no—
109C2×C4×D47—26no—
110C2×C4×D47—212no—
111C2×C4×D47—212no—
112C2×C4×D47—26no—
113C2×C4×D47—212no—
114C2×C4×D47—224no—
115C2×C4×D47C2×Q8112yes—
116C2×Dic94—46no—
117C2×Dic94—43no—
118C4⋊C4×C47—43no—
119C4⋊C4×C47—43no—
120C4⋊C4×C47—46no—
121C4⋊C4×C47—43no—
122C42×C47C2×Q814yescomplemented
123C4⋊Dic47—43no—
124C4⋊Dic47—43no—
125C4⋊Dic47—43no—
126C4⋊Dic47—46no—
127Dic47⋊C4—43no—
128Dic47⋊C4—46no—
129Dic47⋊C4—43no—
130Dic47⋊C4—46no—
131Dic47⋊C4—46no—
132Dic47⋊C4—46no—
133C4×Dic47C2×Q8112yescomplemented
134C23×C47C2511yescharacteristic
135C22×D47C22×Q812yes—
136C22×D47H(5,𝔽2)16yes—
137C22×D472−1+416yes—
138Q8×C47—44no—
139C2×C4×C47—23no—
140C2×C4×C47—23no—
141C2×C4×C47—26no—
142C2×C4×C47—23no—
143C2×C4×C47—26no—
144C2×C4×C47—23no—
145C2×C4×C47—26no—
146C2×C4×C47—212no—
147C2×C4×C47C22×Q816yes—
148C2×Dic47—23no—
149C2×Dic47—23no—
150C2×Dic47—23no—
151C2×Dic47—26no—
152C2×Dic47—26no—
153C2×Dic47—23no—
154C2×Dic47—26no—
155C2×Dic47—212no—
156C2×Dic47C22×Q816yes—
157C4×D47—224no—
158C4×D47—412no—
159C4×D47—44no—
160C4×D47—48no—
161C4×D47—424no—
162Dic94—48no—
163Dic94—44no—
164C2×#2843—471nomaximal, Sylow
165C22×C47C23×Q811yescharacteristic
166C22×C47C2×H(5,𝔽2)13yes—
167C22×C47C2×2−1+413yes—
168C2×D47#544112yes—
169C2×D47#56014yes—
170C2×D47#563112yes—
171C4×C47—26no—
172C4×C47—41no—
173C4×C47—42no—
174C4×C47—43no—
175C4×C47—46no—
176Dic47—26no—
177Dic47—41no—
178Dic47—42no—
179Dic47—43no—
180Dic47—46no—
181#2843—473no—
182#2843—476no—
183#2843—473no—
184#2843—471no—
185#2843—472no—
186#2843D4711yescharacteristic, direct product factor
187C2×#400—473no—
188C2×#398—476no—
189C2×#395—473no—
190C2×#384—471no—
191C2×#383—472no—
192C2×C47C2×#54413yes—
193C2×C47C2×#56011yescharacteristic
194C2×C47C2×#56313yes—
195D47#284318yesdirect product factor
196C23×Q8—471no—
197C22×C4⋊C4—476no—
198C22×C4⋊C4—473no—
199C22×C4⋊C4—473no—
200C22×C4⋊C4—473no—
201C22×C42—471no—
202#400—473no—
203#400—473no—
204#400—473no—
205#400—476no—
206#400—476no—
207#400C2×D4713yes—
208#398—476no—
209#398—476no—
210#398—476no—
211#398—476no—
212#398—476no—
213#398—476no—
214#398—476no—
215#398C2×D4716yes—
216#395—473no—
217#395—476no—
218#395—473no—
219#395—473no—
220#395—476no—
221#395C2×D4713yes—
222#384—473no—
223#384—473no—
224#384—471no—
225#384C2×D4711yescharacteristic
226#383—472no—
227#383—476no—
228#383—476no—
229#383C2×D4712yes—
230C2×#95—476no—
231C2×#95—473no—
232C2×#95—473no—
233C2×#95—476no—
234C47C2×#284311yescharacteristic, complemented, Sylow
235C22×Q8—471no—
236C22×Q8—472no—
237C22×Q8—1886no—
238C22×Q8C22×D4711yescharacteristic
239C23×C4—473no—
240C23×C4—473no—
241C23×C4—472no—
242C23×C4—471no—
243C23×C4—476no—
244C2×C4⋊C4—473no—
245C2×C4⋊C4—473no—
246C2×C4⋊C4—476no—
247C2×C4⋊C4—476no—
248C2×C4⋊C4—476no—
249C2×C4⋊C4—476no—
250C2×C4⋊C4—473no—
251C2×C4⋊C4—473no—
252C2×C4⋊C4—476no—
253C2×C4⋊C4—473no—
254C2×C4⋊C4—1886no—
255C2×C4⋊C4—1886no—
256C2×C4⋊C4—1886no—
257C2×C4⋊C4—18812no—
258C2×C4⋊C4C22×D4713yes—
259C2×C4⋊C4C22×D4713yes—
260C2×C4⋊C4C22×D4716yes—
261C2×C4⋊C4C22×D4713yes—
262C2×C42—473no—
263C2×C42—478no—
264C2×C42C22×D4711yescharacteristic
265#95—476no—
266#95—476no—
267#95—476no—
268#95—476no—
269#95—476no—
270#95—476no—
271#95—473no—
272#95—476no—
273#95—473no—
274#95—476no—
275#95C22×D4716yes—
276#95C22×D4716yes—
277#95C22×D4713yes—
278#95C22×D4713yes—
279C24—471no—
280C2×Q8—43no—
281C2×Q8—1883no—
282C2×Q8—1886no—
283C2×Q8—18816no—
284C22×C4—473no—
285C22×C4—4712no—
286C22×C4—476no—
287C22×C4—472no—
288C22×C4—471no—
289C22×C4—473no—
290C22×C4—946no—
291C22×C4—946no—
292C22×C4—9412no—
293C22×C4—946no—
294C22×C4—9412no—
295C22×C4—946no—
296C22×C4—9412no—
297C22×C4—9424no—
298C22×C4C23×D4716yes—
299C22×C4C23×D4712yes—
300C22×C4C23×D4711yescharacteristic
301C22×C4C23×D4713yes—
302C22×C4C23×D4713yes—
303C4⋊C4—43no—
304C4⋊C4—43no—
305C4⋊C4—43no—
306C4⋊C4—46no—
307C4⋊C4—1886no—
308C4⋊C4—1883no—
309C4⋊C4—1886no—
310C4⋊C4—1886no—
311C4⋊C4—1883no—
312C4⋊C4—1886no—
313C4⋊C4—1883no—
314C4⋊C4—1883no—
315C4⋊C4—1883no—
316C4⋊C4—1886no—
317C42—4712no—
318C42Q8×D4714yescomplemented
319C23—472no—
320C23—476no—
321C23—476no—
322C23C24×D4711yescharacteristic
323Q8—44no—
324Q8—1884no—
325Q8—1888no—
326C2×C4—23no—
327C2×C4—23no—
328C2×C4—26no—
329C2×C4—23no—
330C2×C4—26no—
331C2×C4—23no—
332C2×C4—26no—
333C2×C4—212no—
334C2×C4—476no—
335C2×C4—9424no—
336C2×C4—943no—
337C2×C4—943no—
338C2×C4—943no—
339C2×C4—946no—
340C2×C4—946no—
341C2×C4—943no—
342C2×C4—946no—
343C2×C4—9412no—
344C2×C4—18812no—
345C2×C4—18824no—
346C2×C4—1884no—
347C2×C4—1888no—
348C2×C4C2×Q8×D4716yes—
349C22—4712no—
350C22—474no—
351C22—4712no—
352C22C22×Q8×D4711yescharacteristic
353C22H(5,𝔽2)×D4713yes—
354C222−1+4×D4713yes—
355C4—26no—
356C4—41no—
357C4—42no—
358C4—43no—
359C4—46no—
360C4—946no—
361C4—1881no—
362C4—1882no—
363C4—1883no—
364C4—1886no—
365C2—478no—
366C2#544×D4713yes—
367C2#560×D4711yescharacteristic
368C2#563×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2843C2
prime radicalC23×D47C24
hypercenter#2843D47
hypocenterC47C2×#2843
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2843

Complements

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

NH ≅ G/Ntype
1. #20251658C2semidirect
2. #20251657C2semidirect
3. #20251656C2semidirect
4. #20251655C2semidirect
5. #20251654C2semidirect
11. C47×#2843C2semidirect
73. C42×D47Q8semidirect
122. C42×C47C2×Q8semidirect
133. C4×Dic47C2×Q8semidirect
186. #2843D47direct (N × H)
195. D47#2843direct (N × H)
234. C47C2×#2843semidirect
318. C42Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#202516582
#202516572
#202516562
#202516552
#202516542
#400×D472
#398×D472
#395×D472
#384×D472
#383×D472
C47×#28432
C2×#284347