Finite Group Databasebeta

← D47×#2255 #26371771

Subgroups — D47×#2255 #26371771

Order 12032.

518 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#500×D47C211yesmaximal, characteristic
2#499×D47C211yesmaximal, characteristic
3#20245675C211yesmaximal, characteristic, complemented
4#20245674C211yesmaximal, characteristic, complemented
5#20245673C212yesmaximal, complemented
6#20245672C212yesmaximal, complemented
7#20245671C211yesmaximal, characteristic, complemented
8#367×D47C212yesmaximal
9#366×D47C212yesmaximal
10#346×D47C211yesmaximal, characteristic
11C47×#2255C211yesmaximal, characteristic, complemented
12C4⋊Q8×D47—21no—
13#125×D47—21no—
14C2×C16×D47C2212yes—
15#15689528C2211yescharacteristic
16#15689527—21no—
17#15689527C2212yes—
18#15689526—21no—
19#15689525C2211yescharacteristic
20#15689524C2211yescharacteristic
21#15689524C2211yescharacteristic
22#15689523—21no—
23#15689522—21no—
24#107×D47—21no—
25#107×D47C2211yescharacteristic
26#107×D47C2212yes—
27#107×D47C2211yescharacteristic
28#106×D47—21no—
29C4×C8×D47C2211yescharacteristic
30#15688951C2212yes—
31#15688950C2212yes—
32#15688950C2212yes—
33#15688949C2212yes—
34#15688948C2212yes—
35#15688948C2212yes—
36#15688899C2211yescharacteristic
37#15688898C2212yes—
38C47×#500C2211yescharacteristic
39C47×#499C2211yescharacteristic
40C47×#367C2212yes—
41C47×#366C2212yes—
42C47×#346C2211yescharacteristic
43C2×Q8×D47—41no—
44C2×C8×D47D411yescharacteristic
45C2×C8×D47C2311yescharacteristic
46#13094024—21no—
47#13094023—22no—
48#13094023—41no—
49#13094022—41no—
50#13094016—21no—
51#13094015—21no—
52#13094015—21no—
53#13094014—41no—
54#13094014—41no—
55C4⋊C4×D47—21no—
56C4⋊C4×D47—21no—
57C4⋊C4×D47—22no—
58C4⋊C4×D47—41no—
59C4⋊C4×D47—41no—
60C4⋊C4×D47—41no—
61C42×D47D411yescharacteristic
62C2×C47⋊C16C2312yes—
63C16×D47Q818yescomplemented
64#13093958—21no—
65#13093958C2311yescharacteristic
66#13093958C2311yescharacteristic
67#13093958C2312yes—
68#13093957—21no—
69#13093957—21no—
70#13093957—22no—
71#13093957—22no—
72#13093956—21no—
73#13093955—21no—
74#13093955—21no—
75C4×C47⋊C8D411yescharacteristic
76C8×Dic47D411yescharacteristic
77C8×Dic47C2311yescharacteristic
78C4⋊Q8×C47—21no—
79#125×C47—21no—
80C2×C16×C47C2312yes—
81#107×C47—21no—
82#107×C47C2311yescharacteristic
83#107×C47C2311yescharacteristic
84#107×C47C2312yes—
85#106×C47—21no—
86C4×C8×C47C2311yescharacteristic
87C2×Q8×C47—41no—
88Q8×D47—84no—
89C2×C4×D47—41no—
90C2×C4×D47—41no—
91C2×C4×D47—42no—
92C2×C4×D47D811yescharacteristic
93C2×C4×D47D811yescharacteristic
94C2×C4×D47C2×D411yescharacteristic
95C2×Dic94—41no—
96C2×Dic94—42no—
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2411yescharacteristic
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C42×C47C2×D411yescharacteristic
106C4⋊Dic47—21no—
107C4⋊Dic47—21no—
108C4⋊Dic47—22no—
109C4⋊Dic47—41no—
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112Dic47⋊C4—41no—
113Dic47⋊C4—41no—
114Dic47⋊C4—41no—
115Dic47⋊C4—41no—
116Dic47⋊C4—42no—
117Dic47⋊C4—41no—
118Dic47⋊C4—41no—
119Dic47⋊C4—42no—
120C4×Dic47D811yescharacteristic
121C4×Dic47D811yescharacteristic
122C4×Dic47C2×D411yescharacteristic
123C2×C47⋊C8C2×D411yescharacteristic
124C2×C47⋊C8C2×D411yescharacteristic
125C8×D47Q1614yes—
126C8×D47C2×Q814yes—
127C16×C47C2×Q814yescomplemented
128C47⋊C16C2×Q814yescomplemented
129C22×D47C2×D811yescharacteristic
130Q8×C47—82no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47C2×D811yescharacteristic
135C2×C4×C47C2×D811yescharacteristic
136C2×C4×C47C22×D411yescharacteristic
137C2×Dic47—41no—
138C2×Dic47—41no—
139C2×Dic47—42no—
140C2×Dic47C2×D811yescharacteristic
141C2×Dic47C2×D811yescharacteristic
142C2×Dic47C2×D811yescharacteristic
143C4×D47—22no—
144C4×D47—22no—
145C4×D47—82no—
146C4×D47—84no—
147C4×D47—82no—
148C4×D47C4⋊Q812yes—
149C4×D47C2×Q1612yes—
150Dic94—84no—
151Dic94—82no—
152C8×C47C2×Q1612yes—
153C8×C47C22×Q812yes—
154C47⋊C8C4⋊Q812yes—
155C47⋊C8C2×Q1612yes—
156C2×#2255—471nomaximal, Sylow
157C22×C47C22×D811yescharacteristic
158C2×D47#50012yes—
159C2×D47#50912yes—
160C2×D47#51012yes—
161C4×C47—21no—
162C4×C47—21no—
163C4×C47—82no—
164C4×C47—81no—
165C4×C47—81no—
166C4×C47C2×C4⋊Q811yescharacteristic
167C4×C47C22×Q1611yescharacteristic
168Dic47—21no—
169Dic47—21no—
170Dic47—82no—
171Dic47—81no—
172Dic47—81no—
173Dic47#50012yes—
174C2×#500—471no—
175C2×#499—471no—
176#2255—471no—
177#2255—471no—
178#2255—472no—
179#2255—472no—
180#2255—471no—
181#2255D4711yescharacteristic, direct product factor
182C2×#367—472no—
183C2×#366—472no—
184C2×#346—471no—
185C2×C47C2×#50011yescharacteristic
186C2×C47C2×#50911yescharacteristic
187C2×C47C2×#51011yescharacteristic
188D47#225514yesdirect product factor
189C2×C4⋊Q8—941no—
190C2×#125—941no—
191C22×C16—472no—
192#500—472no—
193#500—471no—
194#500—941no—
195#500—941no—
196#500C2×D4711yescharacteristic
197#499—471no—
198#499—471no—
199#499—471no—
200#499—941no—
201#499—941no—
202#499C2×D4711yescharacteristic
203C2×#107—471no—
204C2×#107—471no—
205C2×#107—472no—
206C2×#107—941no—
207C2×#106—941no—
208C2×C4×C8—471no—
209#367—472no—
210#367—472no—
211#367—472no—
212#367C2×D4712yes—
213#366—472no—
214#366—472no—
215#366—472no—
216#366C2×D4712yes—
217#346—472no—
218#346—471no—
219#346C2×D4711yescharacteristic
220C47C2×#225511yescharacteristic, complemented, Sylow
221C22×Q8—1881no—
222C22×C8—471no—
223C22×C8—471no—
224C4⋊Q8—21no—
225C4⋊Q8—942no—
226C4⋊Q8—941no—
227C4⋊Q8—1881no—
228C4⋊Q8—1881no—
229#125—21no—
230#125—941no—
231#125—941no—
232#125—941no—
233#125—1881no—
234#125—1881no—
235C2×C4⋊C4—941no—
236C2×C4⋊C4—941no—
237C2×C4⋊C4—942no—
238C2×C4⋊C4—1881no—
239C2×C4⋊C4—1881no—
240C2×C4⋊C4—1881no—
241C2×C42—471no—
242C2×C16—472no—
243C2×C16—478no—
244C2×C16C22×D4712yes—
245#107—21no—
246#107—471no—
247#107—472no—
248#107—471no—
249#107—941no—
250#107—941no—
251#107—942no—
252#107—942no—
253#107—941no—
254#107C22×D4711yescharacteristic
255#107C22×D4712yes—
256#107C22×D4711yescharacteristic
257#106—21no—
258#106—941no—
259#106—941no—
260#106—941no—
261C4×C8—471no—
262C4×C8—471no—
263C4×C8—471no—
264C4×C8C22×D4711yescharacteristic
265C2×Q8—41no—
266C2×Q8—3764no—
267C2×Q8—1882no—
268C2×Q8—1881no—
269C22×C4—471no—
270C22×C4—471no—
271C22×C4—471no—
272C22×C4—1881no—
273C22×C4—1881no—
274C22×C4—1882no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—474no—
278C2×C8—474no—
279C2×C8D4×D4711yescharacteristic
280C2×C8C23×D4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—22no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—942no—
290C4⋊C4—1881no—
291C4⋊C4—1881no—
292C4⋊C4—1882no—
293C4⋊C4—1881no—
294C4⋊C4—1881no—
295C4⋊C4—1882no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C4⋊C4—1881no—
299C4⋊C4—1881no—
300C4⋊C4—1881no—
301C42—471no—
302C42—471no—
303C42—471no—
304C42D4×D4711yescharacteristic
305C16—474no—
306C16Q8×D4714yescomplemented
307C23—471no—
308Q8—82no—
309Q8—3762no—
310Q8—3764no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—471no—
315C2×C4—472no—
316C2×C4—472no—
317C2×C4—471no—
318C2×C4—471no—
319C2×C4—942no—
320C2×C4—942no—
321C2×C4—3762no—
322C2×C4—3762no—
323C2×C4—3764no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1882no—
327C2×C4D8×D4711yescharacteristic
328C2×C4D8×D4711yescharacteristic
329C2×C4C2×D4×D4711yescharacteristic
330C8—472no—
331C8—472no—
332C8Q16×D4712yes—
333C8C2×Q8×D4712yes—
334C22—472no—
335C22—472no—
336C22—472no—
337C22C2×D8×D4711yescharacteristic
338C4—21no—
339C4—21no—
340C4—81no—
341C4—82no—
342C4—81no—
343C4—472no—
344C4—941no—
345C4—941no—
346C4—3761no—
347C4—3762no—
348C4—3761no—
349C4C4⋊Q8×D4711yescharacteristic
350C4C2×Q16×D4711yescharacteristic
351C2—474no—
352C2#500×D4711yescharacteristic
353C2#509×D4711yescharacteristic
354C2#510×D4711yescharacteristic
subgroupG/H
centerC22C2×D8×D47
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#2255C2
socleC22×C47C22×D8
prime radicalC22×D47C2×D8
hypercenter#2255D47
hypocenterC47C2×#2255
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #20245675C2semidirect
4. #20245674C2semidirect
5. #20245673C2semidirect
6. #20245672C2semidirect
7. #20245671C2semidirect
11. C47×#2255C2semidirect
63. C16×D47Q8semidirect
127. C16×C47C2×Q8semidirect
128. C47⋊C16C2×Q8semidirect
181. #2255D47direct (N × H)
188. D47#2255direct (N × H)
220. C47C2×#2255semidirect
306. C16Q8×D47semidirect

Maximal subgroups

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

subgroupindex
#500×D472
#499×D472
#202456752
#202456742
#202456732
#202456722
#202456712
#367×D472
#366×D472
#346×D472
C47×#22552
C2×#225547