Finite Group Databasebeta

← D47×#2645 #26383395

Subgroups — D47×#2645 #26383395

Order 12032.

1830 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20249356C213yesmaximal, complemented
2#20249355C212yesmaximal, complemented
3#20249354C213yesmaximal, complemented
4#20249353C211yesmaximal, characteristic, complemented
5#20249352C216yesmaximal, complemented
6#401×D47C212yesmaximal
7#400×D47C216yesmaximal
8#391×D47C213yesmaximal
9#389×D47C213yesmaximal
10#376×D47C211yesmaximal, characteristic
11C47×#2645C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2213yes—
14C2×C4⋊C4×D47C2216yes—
15C2×C42×D47C2213yes—
16C47⋊#401C2216yes—
17C47⋊#401C2216yes—
18C47⋊#401C2212yes—
19#15689065C2216yes—
20#15689065C2216yes—
21#15689064C2216yes—
22#15689064C2216yes—
23#15689063C2216yes—
24#15689062C2216yes—
25#15689061C2216yes—
26#15689030C2213yes—
27#15689029C2213yes—
28#15689028C2213yes—
29#15689027C2216yes—
30#15689027C2216yes—
31#15689022C2213yes—
32#15689021C2213yes—
33#15689020C2216yes—
34#15689019C2213yes—
35#15689018C2216yes—
36#15688969C2213yes—
37#15688968C2213yes—
38#15688968C2211yescharacteristic
39#95×D47C2216yes—
40#95×D47C2216yes—
41#95×D47C2216yes—
42#95×D47C2213yes—
43#95×D47C2211yescharacteristic
44C47×#401C2212yes—
45C47×#400C2216yes—
46C47×#391C2213yes—
47C47×#389C2213yes—
48C47×#376C2211yescharacteristic
49C22×Dic94C2312yes—
50C22×Dic94C2311yescharacteristic
51C2×Q8×D47—212no—
52C22×C4×D47C2313yes—
53C22×C4×D47C2312yes—
54C22×C4×D47C2313yes—
55C22×C4×D47C2316yes—
56C22×C4×D47C2311yescharacteristic
57C2×C4⋊Dic47C2313yes—
58C2×C4⋊Dic47C2316yes—
59C2×Dic47⋊C4C2316yes—
60C2×Dic47⋊C4C2316yes—
61C2×Dic47⋊C4C2316yes—
62C4⋊C4×D47—212no—
63C4⋊C4×D47—412no—
64C2×C4×Dic47C2313yes—
65C2×C4×Dic47C2313yes—
66C2×C4×Dic47C2313yes—
67C42×D47—212no—
68C47⋊#95C2313yes—
69C47⋊#95C2313yes—
70C47⋊#95C2313yes—
71C47⋊#95C2313yes—
72C47⋊#95C2316yes—
73C47⋊#95C2316yes—
74C47⋊#95C2316yes—
75C47⋊#95C2316yes—
76C47⋊#95C2316yes—
77C47⋊#95C2316yes—
78C47⋊#95C2316yes—
79C47⋊#95C2316yes—
80C47⋊#95C2316yes—
81C22×Q8×C47C2311yescharacteristic
82C2×C4⋊C4×C47C2313yes—
83C2×C4⋊C4×C47C2316yes—
84C2×C42×C47C2313yes—
85#95×C47C2313yes—
86#95×C47C2311yescharacteristic
87#95×C47C2316yes—
88#95×C47C2316yes—
89#95×C47C2316yes—
90C23×D47C2411yescharacteristic
91C2×Q8×C47—26no—
92C22×C4×C47C2413yes—
93C22×C4×C47C2413yes—
94C22×C4×C47C2416yes—
95C22×C4×C47C2412yes—
96C22×C4×C47C2411yescharacteristic
97C22×Dic47C2413yes—
98C22×Dic47C2412yes—
99C22×Dic47C2413yes—
100C22×Dic47C2416yes—
101C22×Dic47C2411yescharacteristic
102Q8×D47—416no—
103C2×C4×D47—26no—
104C2×C4×D47—26no—
105C2×C4×D47—212no—
106C2×C4×D47—212no—
107C2×C4×D47—212no—
108C2×C4×D47—26no—
109C2×C4×D47—212no—
110C2×C4×D47—26no—
111C2×C4×D47—212no—
112C2×C4×D47#41112yes—
113C2×Dic94—26no—
114C2×Dic94—212no—
115C4⋊C4×C47—26no—
116C4⋊C4×C47—46no—
117C42×C47—26no—
118C4⋊Dic47—26no—
119C4⋊Dic47—46no—
120Dic47⋊C4—212no—
121Dic47⋊C4—46no—
122Dic47⋊C4—46no—
123C4×Dic47—26no—
124C4×Dic47—26no—
125C4×Dic47—26no—
126C23×C47C2511yescharacteristic
127C22×D47C2×#4116yes—
128C22×D47H(5,𝔽2)12yes—
129C22×D472−1+416yes—
130Q8×C47—44no—
131C2×C4×C47—23no—
132C2×C4×C47—23no—
133C2×C4×C47—26no—
134C2×C4×C47—26no—
135C2×C4×C47—23no—
136C2×C4×C47—26no—
137C2×C4×C47—26no—
138C2×C4×C47—23no—
139C2×C4×C47—26no—
140C2×C4×C47C2×#4116yes—
141C2×Dic47—23no—
142C2×Dic47—23no—
143C2×Dic47—26no—
144C2×Dic47—26no—
145C2×Dic47—26no—
146C2×Dic47—23no—
147C2×Dic47—26no—
148C2×Dic47—23no—
149C2×Dic47—26no—
150C2×Dic47C2×#4116yes—
151C4×D47—48no—
152C4×D47—412no—
153C4×D47—412no—
154C4×D47—424no—
155C4×D47#126116yes—
156Dic94—44no—
157Dic94—48no—
158C2×#2645—471nomaximal, Sylow
159C22×C47C22×#4113yes—
160C22×C47C2×H(5,𝔽2)11yescharacteristic
161C22×C47C2×2−1+413yes—
162C2×D47C2×#12614yes—
163C2×D47#541112yes—
164C2×D47#542112yes—
165C4×C47—42no—
166C4×C47—43no—
167C4×C47—43no—
168C4×C47—46no—
169C4×C47C2×#12614yes—
170Dic47—42no—
171Dic47—43no—
172Dic47—43no—
173Dic47—46no—
174Dic47C2×#12614yes—
175#2645—472no—
176#2645—476no—
177#2645—473no—
178#2645—473no—
179#2645—471no—
180#2645D4711yescharacteristic, direct product factor
181C2×#401—472no—
182C2×#400—476no—
183C2×#391—473no—
184C2×#389—473no—
185C2×#376—471no—
186C2×C47C22×#12611yescharacteristic
187C2×C47C2×#54113yes—
188C2×C47C2×#54213yes—
189D47#264518yesdirect product factor
190C23×Q8—471no—
191C22×C4⋊C4—473no—
192C22×C4⋊C4—476no—
193C22×C42—473no—
194#401—476no—
195#401—476no—
196#401—472no—
197#401C2×D4712yes—
198#400—476no—
199#400—476no—
200#400—476no—
201#400—476no—
202#400—476no—
203#400—476no—
204#400—476no—
205#400C2×D4716yes—
206#391—473no—
207#391—473no—
208#391—473no—
209#391—476no—
210#391—476no—
211#391C2×D4713yes—
212#389—476no—
213#389—473no—
214#389—473no—
215#389—473no—
216#389—476no—
217#389C2×D4713yes—
218#376—473no—
219#376—471no—
220#376—473no—
221#376C2×D4711yescharacteristic
222C2×#95—473no—
223C2×#95—476no—
224C2×#95—476no—
225C2×#95—476no—
226C2×#95—471no—
227C47C2×#264511yescharacteristic, complemented, Sylow
228C22×Q8—472no—
229C22×Q8—471no—
230C22×Q8—9412no—
231C22×Q8C22×D4711yescharacteristic
232C23×C4—471no—
233C23×C4—476no—
234C23×C4—473no—
235C23×C4—472no—
236C23×C4—473no—
237C2×C4⋊C4—476no—
238C2×C4⋊C4—473no—
239C2×C4⋊C4—476no—
240C2×C4⋊C4—476no—
241C2×C4⋊C4—476no—
242C2×C4⋊C4—9412no—
243C2×C4⋊C4—18812no—
244C2×C4⋊C4C22×D4713yes—
245C2×C4⋊C4C22×D4716yes—
246C2×C42—473no—
247C2×C42—473no—
248C2×C42—473no—
249C2×C42—9412no—
250C2×C42C22×D4713yes—
251#95—473no—
252#95—473no—
253#95—473no—
254#95—473no—
255#95—476no—
256#95—476no—
257#95—476no—
258#95—476no—
259#95—476no—
260#95—476no—
261#95—476no—
262#95—476no—
263#95—476no—
264#95C22×D4713yes—
265#95C22×D4711yescharacteristic
266#95C22×D4716yes—
267#95C22×D4716yes—
268#95C22×D4716yes—
269C24—471no—
270C2×Q8—26no—
271C2×Q8—9412no—
272C2×Q8—946no—
273C2×Q8—18816no—
274C22×C4—471no—
275C22×C4—4712no—
276C22×C4—473no—
277C22×C4—472no—
278C22×C4—473no—
279C22×C4—476no—
280C22×C4—946no—
281C22×C4—946no—
282C22×C4—9412no—
283C22×C4—9412no—
284C22×C4—946no—
285C22×C4—9412no—
286C22×C4—946no—
287C22×C4—9412no—
288C22×C4—9412no—
289C22×C4C23×D4713yes—
290C22×C4C23×D4712yes—
291C22×C4C23×D4713yes—
292C22×C4C23×D4716yes—
293C22×C4C23×D4711yescharacteristic
294C4⋊C4—26no—
295C4⋊C4—46no—
296C4⋊C4—9412no—
297C4⋊C4—946no—
298C4⋊C4—1886no—
299C4⋊C4—1886no—
300C4⋊C4—1886no—
301C42—26no—
302C42—946no—
303C42—946no—
304C42—946no—
305C23—476no—
306C23—472no—
307C23—476no—
308C23C24×D4711yescharacteristic
309Q8—44no—
310Q8—1888no—
311Q8—1884no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—23no—
317C2×C4—26no—
318C2×C4—26no—
319C2×C4—23no—
320C2×C4—26no—
321C2×C4—476no—
322C2×C4—4716no—
323C2×C4—943no—
324C2×C4—943no—
325C2×C4—946no—
326C2×C4—946no—
327C2×C4—946no—
328C2×C4—943no—
329C2×C4—946no—
330C2×C4—943no—
331C2×C4—946no—
332C2×C4—18812no—
333C2×C4—18812no—
334C2×C4—18824no—
335C2×C4—1888no—
336C2×C4#41×D4716yes—
337C22—474no—
338C22—4712no—
339C22—4712no—
340C22C2×#41×D4713yes—
341C22H(5,𝔽2)×D4711yescharacteristic
342C222−1+4×D4713yes—
343C4—42no—
344C4—43no—
345C4—43no—
346C4—46no—
347C4—474no—
348C4—1882no—
349C4—1883no—
350C4—1883no—
351C4—1886no—
352C4#126×D4714yes—
353C2—478no—
354C2C2×#126×D4711yescharacteristic
355C2#541×D4713yes—
356C2#542×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2645C2
prime radicalC23×D47C24
hypercenter#2645D47
hypocenterC47C2×#2645
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2645

Complements

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

NH ≅ G/Ntype
1. #20249356C2semidirect
2. #20249355C2semidirect
3. #20249354C2semidirect
4. #20249353C2semidirect
5. #20249352C2semidirect
11. C47×#2645C2semidirect
180. #2645D47direct (N × H)
189. D47#2645direct (N × H)
227. C47C2×#2645semidirect

Maximal subgroups

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

subgroupindex
#202493562
#202493552
#202493542
#202493532
#202493522
#401×D472
#400×D472
#391×D472
#389×D472
#376×D472
C47×#26452
C2×#264547