Finite Group Databasebeta

← D47×#2859 #26422253

Subgroups — D47×#2859 #26422253

Order 12032.

2558 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D47C212yesmaximal
2#20251751C211yesmaximal, characteristic, complemented
3#20251750C212yesmaximal, complemented
4#20251749C212yesmaximal, complemented
5#20251748C212yesmaximal, complemented
6#20251747C218yesmaximal, complemented
7#389×D47C218yesmaximal
8#384×D47C212yesmaximal
9#382×D47C212yesmaximal
10C43×D47C211yesmaximal, characteristic
11C47×#2859C211yesmaximal, characteristic, complemented
12C2×#13094016C2212yes—
13C2×#13094015C2214yes—
14C2×#13094014C2218yes—
15#125×D47—216no—
16C2×C4⋊C4×D47C2214yes—
17C2×C4⋊C4×D47C2218yes—
18C2×C4⋊C4×D47C2218yes—
19C2×C42×D47C2214yes—
20C2×C42×D47C2211yescharacteristic
21C2×C42×D47C2211yescharacteristic
22C2×C42×D47C2211yescharacteristic
23#15689022C2218yes—
24#15689021C2218yes—
25#15689020C22116yes—
26#15689019C2218yes—
27#15689018C22116yes—
28#15688993C2212yes—
29#15688992C2218yes—
30#15688992C2214yes—
31#15688989C2212yes—
32#15688988C2214yes—
33#15688987C2218yes—
34#95×D47C2218yes—
35C42×Dic47C2214yes—
36C42×Dic47C2211yescharacteristic
37C42×Dic47C2211yescharacteristic
38C42×Dic47C2211yescharacteristic
39C2×#125×C47C2212yes—
40C47×#389C2218yes—
41C47×#384C2212yes—
42C47×#382C2212yes—
43C43×C47C2211yescharacteristic
44C22×C4×D47C2318yes—
45C22×C4×D47C2312yes—
46C22×C4×D47C2312yes—
47C22×C4×D47C2311yescharacteristic
48C22×C4×D47C2312yes—
49#13094016—28no—
50#13094015—216no—
51#13094014—232no—
52C2×C4⋊Dic47C2314yes—
53C2×C4⋊Dic47C2318yes—
54C2×C4⋊Dic47C2318yes—
55C2×Dic47⋊C4C2318yes—
56C2×Dic47⋊C4C23116yes—
57C2×Dic47⋊C4C2318yes—
58C2×Dic47⋊C4C2318yes—
59C4⋊C4×D47—232no—
60C4⋊C4×D47—216no—
61C4⋊C4×D47—232no—
62C2×C4×Dic47C2314yes—
63C2×C4×Dic47C2314yes—
64C2×C4×Dic47C2314yes—
65C2×C4×Dic47C2312yes—
66C2×C4×Dic47C2311yescharacteristic
67C2×C4×Dic47C2312yes—
68C2×C4×Dic47C2311yescharacteristic
69C2×C4×Dic47C2312yes—
70C2×C4×Dic47C2311yescharacteristic
71C42×D47—216no—
72C42×D47D418yes—
73C42×D47Q818yes—
74C42×D47Q818yes—
75C47⋊#95C23116yes—
76C47⋊#95C2318yes—
77#125×C47—28no—
78C2×C4⋊C4×C47C2314yes—
79C2×C4⋊C4×C47C2318yes—
80C2×C4⋊C4×C47C2318yes—
81C2×C42×C47C2314yes—
82C2×C42×C47C2311yescharacteristic
83C2×C42×C47C2311yescharacteristic
84C2×C42×C47C2311yescharacteristic
85#95×C47C2318yes—
86C23×D47C2411yescharacteristic
87C22×C4×C47C2418yes—
88C22×C4×C47C2412yes—
89C22×C4×C47C2412yes—
90C22×C4×C47C2411yescharacteristic
91C22×C4×C47C2412yes—
92C22×Dic47C2418yes—
93C22×Dic47C2412yes—
94C22×Dic47C2412yes—
95C22×Dic47C2411yescharacteristic
96C22×Dic47C2412yes—
97C2×C4×D47—28no—
98C2×C4×D47—28no—
99C2×C4×D47—216no—
100C2×C4×D47—232no—
101C2×C4×D47C2×D418yes—
102C2×C4×D47C2×D414yes—
103C2×C4×D47C2×Q818yes—
104C2×C4×D47C2×Q818yes—
105C2×C4×D47C2×Q814yes—
106C2×C4×D47C2×Q814yes—
107C2×C4×D47#41116yes—
108C4⋊C4×C47—216no—
109C4⋊C4×C47—28no—
110C4⋊C4×C47—216no—
111C42×C47—28no—
112C42×C47C2×D414yes—
113C42×C47C2×Q814yes—
114C42×C47C2×Q814yes—
115C4⋊Dic47—28no—
116C4⋊Dic47—216no—
117C4⋊Dic47—216no—
118Dic47⋊C4—216no—
119Dic47⋊C4—216no—
120Dic47⋊C4—216no—
121Dic47⋊C4—232no—
122C4×Dic47—28no—
123C4×Dic47—28no—
124C4×Dic47—28no—
125C4×Dic47C2×D418yes—
126C4×Dic47C2×D414yes—
127C4×Dic47C2×Q814yes—
128C4×Dic47C2×Q818yes—
129C4×Dic47C2×Q814yes—
130C4×Dic47C2×Q818yes—
131C23×C47C2511yescharacteristic
132C22×D47C22×D412yes—
133C22×D47C22×Q812yes—
134C22×D47C22×Q812yes—
135C22×D47C2×#4118yes—
136C2×C4×C47—24no—
137C2×C4×C47—24no—
138C2×C4×C47—28no—
139C2×C4×C47—216no—
140C2×C4×C47C22×D414yes—
141C2×C4×C47C22×D412yes—
142C2×C4×C47C22×Q814yes—
143C2×C4×C47C22×Q814yes—
144C2×C4×C47C22×Q812yes—
145C2×C4×C47C22×Q812yes—
146C2×C4×C47C2×#4118yes—
147C2×Dic47—24no—
148C2×Dic47—24no—
149C2×Dic47—28no—
150C2×Dic47—216no—
151C2×Dic47C22×D414yes—
152C2×Dic47C22×D412yes—
153C2×Dic47C22×Q814yes—
154C2×Dic47C22×Q814yes—
155C2×Dic47C22×Q812yes—
156C2×Dic47C22×Q812yes—
157C2×Dic47C2×#4118yes—
158C4×D47—216no—
159C4×D47—216no—
160C4×D47—432no—
161C4×D47#125132yescomplemented
162C4×D47C4⋊Q8116yes—
163C2×#2859—471nomaximal, Sylow
164C22×C47C23×D411yescharacteristic
165C22×C47C23×Q811yescharacteristic
166C22×C47C23×Q811yescharacteristic
167C22×C47C22×#4114yes—
168C2×D47C2×#12518yes—
169C2×D47C2×C4⋊Q814yes—
170C2×D47#53218yes—
171C2×D47#53318yes—
172C4×C47—24no—
173C4×C47—24no—
174C4×C47—48no—
175C4×C47C2×#12518yescomplemented
176C4×C47C2×C4⋊Q814yes—
177Dic47—24no—
178Dic47—24no—
179Dic47—48no—
180Dic47C2×#12518yescomplemented
181Dic47C2×C4⋊Q814yes—
182C22×#125—472no—
183#2859—478no—
184#2859—472no—
185#2859—472no—
186#2859—471no—
187#2859—472no—
188#2859D4711yescharacteristic, direct product factor
189C2×#389—478no—
190C2×#384—472no—
191C2×#382—472no—
192C2×C43—471no—
193C2×C47C22×#12512yes—
194C2×C47C22×C4⋊Q811yescharacteristic
195C2×C47C2×#53212yes—
196C2×C47C2×#53312yes—
197D47#285918yesdirect product factor
198C2×#125—478no—
199C2×#125—474no—
200C2×#125—472no—
201C2×#125—9416no—
202C2×#125C2×D4712yes—
203C22×C4⋊C4—474no—
204C22×C4⋊C4—478no—
205C22×C4⋊C4—478no—
206C22×C42—471no—
207C22×C42—471no—
208C22×C42—471no—
209C22×C42—474no—
210#389—4716no—
211#389—478no—
212#389—478no—
213#389—478no—
214#389—4716no—
215#389C2×D4718yes—
216#384—478no—
217#384—474no—
218#384—472no—
219#384C2×D4712yes—
220#382—474no—
221#382—472no—
222#382—478no—
223#382C2×D4712yes—
224C2×#95—478no—
225C43—474no—
226C43—471no—
227C43—471no—
228C43—471no—
229C43C2×D4711yescharacteristic
230C47C2×#285911yescharacteristic, complemented, Sylow
231C23×C4—471no—
232C23×C4—472no—
233C23×C4—472no—
234C23×C4—472no—
235C23×C4—478no—
236#125—28no—
237#125—9432no—
238#125—9416no—
239#125—948no—
240C2×C4⋊C4—478no—
241C2×C4⋊C4—478no—
242C2×C4⋊C4—478no—
243C2×C4⋊C4—474no—
244C2×C4⋊C4—478no—
245C2×C4⋊C4—4716no—
246C2×C4⋊C4—478no—
247C2×C4⋊C4—9416no—
248C2×C4⋊C4—9432no—
249C2×C4⋊C4—9432no—
250C2×C4⋊C4C22×D4714yes—
251C2×C4⋊C4C22×D4718yes—
252C2×C4⋊C4C22×D4718yes—
253C2×C42—472no—
254C2×C42—471no—
255C2×C42—472no—
256C2×C42—471no—
257C2×C42—471no—
258C2×C42—472no—
259C2×C42—478no—
260C2×C42—478no—
261C2×C42—478no—
262C2×C42—474no—
263C2×C42—474no—
264C2×C42—474no—
265C2×C42—9416no—
266C2×C42C22×D4714yes—
267C2×C42C22×D4711yescharacteristic
268C2×C42C22×D4711yescharacteristic
269C2×C42C22×D4711yescharacteristic
270#95—4716no—
271#95—478no—
272#95C22×D4718yes—
273C24—471no—
274C22×C4—471no—
275C22×C4—472no—
276C22×C4—474no—
277C22×C4—478no—
278C22×C4—474no—
279C22×C4—474no—
280C22×C4—4716no—
281C22×C4—472no—
282C22×C4—472no—
283C22×C4—478no—
284C22×C4—478no—
285C22×C4—478no—
286C22×C4—948no—
287C22×C4—948no—
288C22×C4—9416no—
289C22×C4—9432no—
290C22×C4C23×D4718yes—
291C22×C4C23×D4712yes—
292C22×C4C23×D4712yes—
293C22×C4C23×D4711yescharacteristic
294C22×C4C23×D4712yes—
295C4⋊C4—216no—
296C4⋊C4—28no—
297C4⋊C4—216no—
298C4⋊C4—9432no—
299C4⋊C4—9416no—
300C4⋊C4—9416no—
301C4⋊C4—9416no—
302C4⋊C4—9416no—
303C4⋊C4—948no—
304C4⋊C4—9416no—
305C42—28no—
306C42—478no—
307C42—474no—
308C42—478no—
309C42—474no—
310C42—478no—
311C42—474no—
312C42—948no—
313C42—948no—
314C42—948no—
315C42D4×D4714yes—
316C42Q8×D4714yes—
317C42Q8×D4714yes—
318C23—472no—
319C23—472no—
320C23—472no—
321C23—478no—
322C23C24×D4711yescharacteristic
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—28no—
326C2×C4—216no—
327C2×C4—472no—
328C2×C4—474no—
329C2×C4—472no—
330C2×C4—472no—
331C2×C4—478no—
332C2×C4—4732no—
333C2×C4—4716no—
334C2×C4—474no—
335C2×C4—474no—
336C2×C4—9416no—
337C2×C4—9416no—
338C2×C4—944no—
339C2×C4—944no—
340C2×C4—948no—
341C2×C4—9416no—
342C2×C4—18832no—
343C2×C4C2×D4×D4714yes—
344C2×C4C2×D4×D4712yes—
345C2×C4C2×Q8×D4714yes—
346C2×C4C2×Q8×D4714yes—
347C2×C4C2×Q8×D4712yes—
348C2×C4C2×Q8×D4712yes—
349C2×C4#41×D4718yes—
350C22—478no—
351C22—474no—
352C22—478no—
353C22—478no—
354C22C22×D4×D4711yescharacteristic
355C22C22×Q8×D4711yescharacteristic
356C22C22×Q8×D4711yescharacteristic
357C22C2×#41×D4714yes—
358C4—24no—
359C4—24no—
360C4—48no—
361C4—478no—
362C4—474no—
363C4—944no—
364C4—944no—
365C4—1888no—
366C4#125×D4718yescomplemented
367C4C4⋊Q8×D4714yes—
368C2—478no—
369C2C2×#125×D4712yes—
370C2C2×C4⋊Q8×D4711yescharacteristic
371C2#532×D4712yes—
372C2#533×D4712yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2859C2
prime radicalC23×D47C24
hypercenter#2859D47
hypocenterC47C2×#2859
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2859

Complements

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

NH ≅ G/Ntype
2. #20251751C2semidirect
3. #20251750C2semidirect
4. #20251749C2semidirect
5. #20251748C2semidirect
6. #20251747C2semidirect
11. C47×#2859C2semidirect
161. C4×D47#125semidirect
175. C4×C47C2×#125semidirect
180. Dic47C2×#125semidirect
188. #2859D47direct (N × H)
197. D47#2859direct (N × H)
230. C47C2×#2859semidirect
366. C4#125×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D472
#202517512
#202517502
#202517492
#202517482
#202517472
#389×D472
#384×D472
#382×D472
C43×D472
C47×#28592
C2×#285947