Finite Group Databasebeta

← D47×#2863 #26422292

Subgroups — D47×#2863 #26422292

Order 12032.

2142 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251771C213yesmaximal, complemented
2#20251770C211yesmaximal, characteristic, complemented
3#20251769C216yesmaximal, complemented
4#20251768C212yesmaximal, complemented
5#20251767C213yesmaximal, complemented
6#391×D47C213yesmaximal
7#389×D47C213yesmaximal
8#387×D47C216yesmaximal
9#383×D47C212yesmaximal
10C43×D47C211yesmaximal, characteristic
11C47×#2863C211yesmaximal, characteristic, complemented
12C22×Q8×D47C2211yescharacteristic
13C2×C4⋊C4×D47C2216yes—
14C2×C4⋊C4×D47C2213yes—
15C2×C42×D47C2213yes—
16C2×C42×D47C2213yes—
17C2×C42×D47C2211yescharacteristic
18#15689030C2213yes—
19#15689029C2213yes—
20#15689028C2213yes—
21#15689027C2216yes—
22#15689027C2216yes—
23#15689022C2213yes—
24#15689021C2213yes—
25#15689020C2216yes—
26#15689019C2213yes—
27#15689018C2216yes—
28#15689010C2216yes—
29#15689009C2216yes—
30#15689008C2216yes—
31#15689007C2216yes—
32#15689006C2216yes—
33#15689005C2216yes—
34#15689004C2216yes—
35#15688991C2212yes—
36#15688990C2216yes—
37#15688990C2216yes—
38#95×D47C2216yes—
39#95×D47C2216yes—
40#95×D47C2216yes—
41C42×Dic47C2213yes—
42C42×Dic47C2211yescharacteristic
43C42×Dic47C2213yes—
44C47×#391C2213yes—
45C47×#389C2213yes—
46C47×#387C2216yes—
47C47×#383C2212yes—
48C43×C47C2211yescharacteristic
49C22×Dic94C2312yes—
50C22×Dic94C2311yescharacteristic
51C2×Q8×D47—212no—
52C22×C4×D47C2312yes—
53C22×C4×D47C2316yes—
54C22×C4×D47C2313yes—
55C22×C4×D47C2313yes—
56C22×C4×D47C2311yescharacteristic
57C2×C4⋊Dic47C2316yes—
58C2×C4⋊Dic47C2313yes—
59C2×Dic47⋊C4C2316yes—
60C2×Dic47⋊C4C2316yes—
61C2×Dic47⋊C4C2316yes—
62C4⋊C4×D47—224no—
63C4⋊C4×D47—212no—
64C2×C4×Dic47C2313yes—
65C2×C4×Dic47C2313yes—
66C2×C4×Dic47C2313yes—
67C2×C4×Dic47C2313yes—
68C2×C4×Dic47C2313yes—
69C2×C4×Dic47C2313yes—
70C2×C4×Dic47C2313yes—
71C42×D47—212no—
72C42×D47—212no—
73C42×D47Q818yescomplemented
74C47⋊#95C2316yes—
75C47⋊#95C2316yes—
76C47⋊#95C2316yes—
77C47⋊#95C2316yes—
78C47⋊#95C2316yes—
79C47⋊#95C2316yes—
80C47⋊#95C2316yes—
81C47⋊#95C2316yes—
82C47⋊#95C2316yes—
83C22×Q8×C47C2311yescharacteristic
84C2×C4⋊C4×C47C2316yes—
85C2×C4⋊C4×C47C2313yes—
86C2×C42×C47C2313yes—
87C2×C42×C47C2313yes—
88C2×C42×C47C2311yescharacteristic
89#95×C47C2316yes—
90#95×C47C2316yes—
91#95×C47C2316yes—
92C23×D47C2411yescharacteristic
93C2×Q8×C47—26no—
94C22×C4×C47C2416yes—
95C22×C4×C47C2412yes—
96C22×C4×C47C2413yes—
97C22×C4×C47C2413yes—
98C22×C4×C47C2411yescharacteristic
99C22×Dic47C2412yes—
100C22×Dic47C2416yes—
101C22×Dic47C2413yes—
102C22×Dic47C2413yes—
103C22×Dic47C2411yescharacteristic
104Q8×D47—416no—
105C2×C4×D47—26no—
106C2×C4×D47—26no—
107C2×C4×D47—26no—
108C2×C4×D47—26no—
109C2×C4×D47—212no—
110C2×C4×D47—212no—
111C2×C4×D47—212no—
112C2×C4×D47—212no—
113C2×C4×D47C2×Q8112yes—
114C2×C4×D47#41112yes—
115C2×C4×D47#41112yes—
116C2×Dic94—26no—
117C2×Dic94—212no—
118C4⋊C4×C47—26no—
119C4⋊C4×C47—212no—
120C42×C47—26no—
121C42×C47—26no—
122C42×C47C2×Q814yescomplemented
123C4⋊Dic47—26no—
124C4⋊Dic47—212no—
125Dic47⋊C4—212no—
126Dic47⋊C4—212no—
127Dic47⋊C4—212no—
128C4×Dic47—26no—
129C4×Dic47—26no—
130C4×Dic47—26no—
131C4×Dic47—26no—
132C4×Dic47—26no—
133C4×Dic47—26no—
134C4×Dic47C2×Q8112yescomplemented
135C23×C47C2511yescharacteristic
136C22×D47C22×Q812yes—
137C22×D47C2×#4116yes—
138C22×D47C2×#4116yes—
139Q8×C47—44no—
140C2×C4×C47—23no—
141C2×C4×C47—23no—
142C2×C4×C47—23no—
143C2×C4×C47—23no—
144C2×C4×C47—26no—
145C2×C4×C47—26no—
146C2×C4×C47—26no—
147C2×C4×C47—26no—
148C2×C4×C47C22×Q816yes—
149C2×C4×C47C2×#4116yes—
150C2×C4×C47C2×#4116yes—
151C2×Dic47—23no—
152C2×Dic47—23no—
153C2×Dic47—23no—
154C2×Dic47—23no—
155C2×Dic47—26no—
156C2×Dic47—26no—
157C2×Dic47—26no—
158C2×Dic47—26no—
159C2×Dic47C22×Q816yes—
160C2×Dic47C2×#4116yes—
161C2×Dic47C2×#4116yes—
162C4×D47—224no—
163C4×D47—224no—
164C4×D47—48no—
165C4×D47—424no—
166C4×D47#126116yes—
167Dic94—44no—
168Dic94—48no—
169C2×#2863—471nomaximal, Sylow
170C22×C47C23×Q811yescharacteristic
171C22×C47C22×#4113yes—
172C22×C47C22×#4113yes—
173C2×D47C2×#12614yes—
174C2×D47#529112yes—
175C2×D47#533112yes—
176C4×C47—26no—
177C4×C47—26no—
178C4×C47—42no—
179C4×C47—46no—
180C4×C47C2×#12614yes—
181Dic47—26no—
182Dic47—26no—
183Dic47—42no—
184Dic47—46no—
185Dic47C2×#12614yes—
186#2863—473no—
187#2863—473no—
188#2863—476no—
189#2863—472no—
190#2863—471no—
191#2863D4711yescharacteristic, direct product factor
192C2×#391—473no—
193C2×#389—473no—
194C2×#387—476no—
195C2×#383—472no—
196C2×C43—471no—
197C2×C47C22×#12611yescharacteristic
198C2×C47C2×#52913yes—
199C2×C47C2×#53313yes—
200D47#286318yesdirect product factor
201C23×Q8—471no—
202C22×C4⋊C4—476no—
203C22×C4⋊C4—473no—
204C22×C42—471no—
205C22×C42—473no—
206C22×C42—473no—
207#391—473no—
208#391—473no—
209#391—473no—
210#391—476no—
211#391—476no—
212#391C2×D4713yes—
213#389—476no—
214#389—473no—
215#389—473no—
216#389—473no—
217#389—476no—
218#389C2×D4713yes—
219#387—476no—
220#387—476no—
221#387—476no—
222#387—476no—
223#387—476no—
224#387—476no—
225#387—476no—
226#387C2×D4716yes—
227#383—472no—
228#383—476no—
229#383—476no—
230#383C2×D4712yes—
231C2×#95—476no—
232C2×#95—476no—
233C2×#95—476no—
234C43—473no—
235C43—473no—
236C43—471no—
237C43C2×D4711yescharacteristic
238C47C2×#286311yescharacteristic, complemented, Sylow
239C22×Q8—472no—
240C22×Q8—471no—
241C22×Q8—9412no—
242C22×Q8C22×D4711yescharacteristic
243C23×C4—471no—
244C23×C4—473no—
245C23×C4—473no—
246C23×C4—476no—
247C23×C4—472no—
248C2×C4⋊C4—476no—
249C2×C4⋊C4—476no—
250C2×C4⋊C4—476no—
251C2×C4⋊C4—476no—
252C2×C4⋊C4—473no—
253C2×C4⋊C4—9412no—
254C2×C4⋊C4—9424no—
255C2×C4⋊C4C22×D4716yes—
256C2×C4⋊C4C22×D4713yes—
257C2×C42—473no—
258C2×C42—478no—
259C2×C42—473no—
260C2×C42—473no—
261C2×C42—473no—
262C2×C42—473no—
263C2×C42—473no—
264C2×C42—473no—
265C2×C42—9412no—
266C2×C42—9412no—
267C2×C42C22×D4713yes—
268C2×C42C22×D4713yes—
269C2×C42C22×D4711yescharacteristic
270#95—476no—
271#95—476no—
272#95—476no—
273#95—476no—
274#95—476no—
275#95—476no—
276#95—476no—
277#95—476no—
278#95—476no—
279#95C22×D4716yes—
280#95C22×D4716yes—
281#95C22×D4716yes—
282C24—471no—
283C2×Q8—26no—
284C2×Q8—9412no—
285C2×Q8—946no—
286C2×Q8—18816no—
287C22×C4—471no—
288C22×C4—4712no—
289C22×C4—473no—
290C22×C4—473no—
291C22×C4—4712no—
292C22×C4—4712no—
293C22×C4—472no—
294C22×C4—476no—
295C22×C4—946no—
296C22×C4—946no—
297C22×C4—946no—
298C22×C4—946no—
299C22×C4—9412no—
300C22×C4—9412no—
301C22×C4—9412no—
302C22×C4—9412no—
303C22×C4C23×D4712yes—
304C22×C4C23×D4716yes—
305C22×C4C23×D4713yes—
306C22×C4C23×D4713yes—
307C22×C4C23×D4711yescharacteristic
308C4⋊C4—212no—
309C4⋊C4—26no—
310C4⋊C4—9412no—
311C4⋊C4—9412no—
312C4⋊C4—9412no—
313C4⋊C4—9412no—
314C4⋊C4—946no—
315C42—26no—
316C42—26no—
317C42—4712no—
318C42—946no—
319C42—946no—
320C42—946no—
321C42—946no—
322C42—946no—
323C42—946no—
324C42Q8×D4714yescomplemented
325C23—472no—
326C23—476no—
327C23—476no—
328C23C24×D4711yescharacteristic
329Q8—44no—
330Q8—1888no—
331Q8—1884no—
332C2×C4—23no—
333C2×C4—23no—
334C2×C4—23no—
335C2×C4—23no—
336C2×C4—26no—
337C2×C4—26no—
338C2×C4—26no—
339C2×C4—26no—
340C2×C4—476no—
341C2×C4—4716no—
342C2×C4—476no—
343C2×C4—476no—
344C2×C4—9424no—
345C2×C4—9424no—
346C2×C4—943no—
347C2×C4—943no—
348C2×C4—943no—
349C2×C4—943no—
350C2×C4—946no—
351C2×C4—946no—
352C2×C4—946no—
353C2×C4—946no—
354C2×C4—18824no—
355C2×C4—1888no—
356C2×C4C2×Q8×D4716yes—
357C2×C4#41×D4716yes—
358C2×C4#41×D4716yes—
359C22—474no—
360C22—4712no—
361C22—4712no—
362C22C22×Q8×D4711yescharacteristic
363C22C2×#41×D4713yes—
364C22C2×#41×D4713yes—
365C4—26no—
366C4—26no—
367C4—42no—
368C4—46no—
369C4—474no—
370C4—946no—
371C4—946no—
372C4—1882no—
373C4—1886no—
374C4#126×D4714yes—
375C2—478no—
376C2C2×#126×D4711yescharacteristic
377C2#529×D4713yes—
378C2#533×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2863C2
prime radicalC23×D47C24
hypercenter#2863D47
hypocenterC47C2×#2863
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2863

Complements

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

NH ≅ G/Ntype
1. #20251771C2semidirect
2. #20251770C2semidirect
3. #20251769C2semidirect
4. #20251768C2semidirect
5. #20251767C2semidirect
11. C47×#2863C2semidirect
73. C42×D47Q8semidirect
122. C42×C47C2×Q8semidirect
134. C4×Dic47C2×Q8semidirect
191. #2863D47direct (N × H)
200. D47#2863direct (N × H)
238. C47C2×#2863semidirect
324. C42Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#202517712
#202517702
#202517692
#202517682
#202517672
#391×D472
#389×D472
#387×D472
#383×D472
C43×D472
C47×#28632
C2×#286347