Finite Group Databasebeta

← D47×#1297 #26106396

Subgroups — D47×#1297 #26106396

Order 12032.

1226 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 1226 conjugacy classes of subgroups — too many to draw. Only its 179 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#407×D47C211yesmaximal, characteristic
2C4×C22⋊C4×D47C212yesmaximal
3#20241274C212yesmaximal, complemented
4#20241273C211yesmaximal, characteristic, complemented
5C47×#1297C211yesmaximal, characteristic, complemented
6C23×C4×D47C2211yescharacteristic
7C2×M16×D47C412yescomplemented
8C2×C22⋊C4×D47—22no—
9C2×C42×D47—22no—
10#15689087C2211yescharacteristic
11#15689086C412yescomplemented
12#15689085—22no—
13C22⋊C8×D47—22no—
14C22⋊C4×Dic47—22no—
15C4×(C2×D47)⋊C4—22no—
16C4×C22⋊Dic47C2212yes—
17#15688970C414yescomplemented
18#95×D47C414yescomplemented
19C47×#407C2211yescharacteristic
20C4×C22⋊C4×C47C2212yes—
21C24×D47D411yescharacteristic
22C23×Dic47D411yescharacteristic
23C22×C4×D47—24no—
24C22×C4×D47—44no—
25C22×C4×D47C2×C411yescharacteristic
26C22×C4×D47C2×C411yescharacteristic
27C22×C4×D47C2×C412yes—
28C22×C4×D47C2×C412yes—
29C22×C4×D47D412yes—
30C22×C4×D47D412yes—
31C22×C4×D47Q811yescharacteristic
32C22×C4×D47Q811yescharacteristic
33C2×#10625329C2×C412yescomplemented
34C2×#10625324—22no—
35M16×D47—44no—
36C2×C8×D47—22no—
37C2×C22⋊Dic47—22no—
38C2×(C2×D47)⋊C4—24no—
39C22⋊C4×D47—216no—
40C2×C4×Dic47—22no—
41C2×C4×Dic47—24no—
42C42×D47—48no—
43C22⋊(C47⋊C8)—22no—
44(C2×D47)⋊C8—24no—
45C47⋊#95—24no—
46C47⋊#95C2×C414yescomplemented
47C23×C4×C47C2311yescharacteristic
48C2×M16×C47C2×C412yescomplemented
49C2×C22⋊C4×C47—22no—
50C2×C42×C47—22no—
51C22⋊C8×C47—22no—
52#95×C47C2×C414yescomplemented
53C24×C47C2×D411yescharacteristic
54C23×D47—28no—
55C23×D47—42no—
56C23×D47C22⋊C412yes—
57C23×D47C22⋊C412yes—
58C23×D47C4⋊C411yescharacteristic
59C23×D47C4⋊C411yescharacteristic
60C22×C4×C47—24no—
61C22×C4×C47—42no—
62C22×C4×C47C22×C411yescharacteristic
63C22×C4×C47C22×C412yes—
64C22×C4×C47C2×D412yes—
65C22×C4×C47C2×Q811yescharacteristic
66C22×Dic47—24no—
67C22×Dic47—42no—
68C22×Dic47C22⋊C412yes—
69C22×Dic47C22⋊C412yes—
70C22×Dic47C4⋊C411yescharacteristic
71C22×Dic47C4⋊C411yescharacteristic
72C2×C4×D47—28no—
73C2×C4×D47—24no—
74C2×C4×D47—216no—
75C2×C4×D47—44no—
76C2×C4×D47—42no—
77C2×C4×D47—42no—
78C2×C4×D47—44no—
79C2×C4×D47—44no—
80C2×C4×D47—42no—
81C2×C4×D47—48no—
82C2×C4×D47—48no—
83C2×C4×D47C4211yescharacteristic
84C2×C4×D47C4211yescharacteristic
85C2×C4×D47C4212yes—
86C2×C4×D47C22⋊C412yes—
87C2×C4×D47C22⋊C411yescharacteristic
88C2×C4×D47C22⋊C411yescharacteristic
89C2×C4×D47C4⋊C412yes—
90C2×C4×D47C4⋊C412yes—
91C2×C4×D47C4⋊C412yes—
92C2×C4×D47C4⋊C412yes—
93M16×C47—42no—
94C2×C8×C47—22no—
95C22⋊C4×C47—28no—
96C42×C47—44no—
97C22⋊Dic47—28no—
98(C2×D47)⋊C4—216no—
99C4×Dic47—48no—
100C4×Dic47—44no—
101#10625329—42no—
102C2×C47⋊C8—22no—
103#10625324—44no—
104C8×D47—44no—
105C23×C47—24no—
106C23×C47—41no—
107C23×C47C2×C22⋊C412yes—
108C23×C47C2×C4⋊C411yescharacteristic
109C22×D47—24no—
110C22×D47—24no—
111C22×D47—24no—
112C22×D47—24no—
113C22×D47—24no—
114C22×D47—24no—
115C22×D47—22no—
116C22×D47—42no—
117C22×D47—41no—
118C22×D47—416no—
119C22×D47#9511yescharacteristic
120C22×D47#9512yes—
121C22×D47#9511yescharacteristic
122C22×D47#10418yes—
123C2×C4×C47—22no—
124C2×C4×C47—24no—
125C2×C4×C47—28no—
126C2×C4×C47—42no—
127C2×C4×C47—41no—
128C2×C4×C47—44no—
129C2×C4×C47—44no—
130C2×C4×C47C2×C4211yescharacteristic
131C2×C4×C47C2×C22⋊C411yescharacteristic
132C2×C4×C47C2×C4⋊C412yes—
133C2×Dic47—24no—
134C2×Dic47—22no—
135C2×Dic47—28no—
136C2×Dic47—42no—
137C2×Dic47—41no—
138C2×Dic47—44no—
139C2×Dic47—44no—
140C2×Dic47#9511yescharacteristic
141C2×Dic47#9512yes—
142C2×Dic47#9511yescharacteristic
143C4×D47—22no—
144C4×D47—24no—
145C4×D47—22no—
146C4×D47—24no—
147C4×D47—22no—
148C4×D47—24no—
149C4×D47—42no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47—432no—
153C4×D47#9914yes—
154C8×C47—42no—
155C47⋊C8—42no—
156C2×#1297—471nomaximal, Sylow
157C22×C47—22no—
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—21no—
161C22×C47—44no—
162C22×C47C2×#9511yescharacteristic
163C22×C47C2×#10414yes—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—216no—
167C2×D47—22no—
168C2×D47—21no—
169C2×D47—44no—
170C2×D47—48no—
171C2×D47—44no—
172C2×D47#33914yes—
173C2×D47#33914yes—
174C2×D47#34212yes—
175C4×C47—21no—
176C4×C47—22no—
177C4×C47—48no—
178C4×C47C2×#9912yes—
179Dic47—21no—
180Dic47—22no—
181Dic47—48no—
182Dic47#34212yes—
183C2×#407—471no—
184C2×C4×C22⋊C4—472no—
185#1297—471no—
186#1297—472no—
187#1297D4711yescharacteristic, direct product factor
188C2×C47—24no—
189C2×C47—41no—
190C2×C47C2×#33912yes—
191C2×C47C2×#34211yescharacteristic
192D47—24no—
193D47—41no—
194D47#129714yesdirect product factor
195C24×C4—471no—
196C22×M16—472no—
197C22×C22⋊C4—942no—
198C22×C42—942no—
199#407—471no—
200#407—472no—
201#407—942no—
202#407C2×D4711yescharacteristic
203C2×C22⋊C8—942no—
204C4×C22⋊C4—472no—
205C4×C22⋊C4—474no—
206C4×C22⋊C4—942no—
207C4×C22⋊C4—942no—
208C4×C22⋊C4C2×D4712yes—
209C2×#95—474no—
210C47C2×#129711yescharacteristic, complemented, Sylow
211C25—471no—
212C23×C4—471no—
213C23×C4—471no—
214C23×C4—472no—
215C23×C4—472no—
216C23×C4—472no—
217C23×C4—471no—
218C23×C4—472no—
219C23×C4—471no—
220C23×C4—471no—
221C23×C4—944no—
222C23×C4—1884no—
223C23×C4C22×D4711yescharacteristic
224C2×M16—472no—
225C2×M16—942no—
226C2×M16—1884no—
227C2×M16C4×D4712yescomplemented
228C22×C8—942no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—9416no—
231C2×C22⋊C4—944no—
232C2×C22⋊C4—942no—
233C2×C42—22no—
234C2×C42—944no—
235C2×C42—942no—
236C2×C42—1888no—
237C22⋊C8—22no—
238C22⋊C8—944no—
239C22⋊C8—942no—
240#95—474no—
241#95—944no—
242#95C4×D4714yescomplemented
243C24—472no—
244C24—471no—
245C24—472no—
246C24—471no—
247C24—948no—
248C24—1882no—
249C24D4×D4711yescharacteristic
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—471no—
253C22×C4—472no—
254C22×C4—471no—
255C22×C4—472no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—472no—
260C22×C4—471no—
261C22×C4—472no—
262C22×C4—472no—
263C22×C4—472no—
264C22×C4—472no—
265C22×C4—472no—
266C22×C4—948no—
267C22×C4—944no—
268C22×C4—9416no—
269C22×C4—944no—
270C22×C4—1884no—
271C22×C4—1882no—
272C22×C4—1884no—
273C22×C4—1882no—
274C22×C4—1884no—
275C22×C4—1882no—
276C22×C4—1888no—
277C22×C4—1888no—
278C22×C4—1882no—
279C22×C4C2×C4×D4711yescharacteristic
280C22×C4C2×C4×D4712yes—
281C22×C4D4×D4712yes—
282C22×C4Q8×D4711yescharacteristic
283M16—42no—
284M16—1884no—
285M16—1882no—
286C2×C8—22no—
287C2×C8—942no—
288C2×C8—1884no—
289C22⋊C4—28no—
290C22⋊C4—9416no—
291C22⋊C4—948no—
292C42—44no—
293C42—1884no—
294C42—1888no—
295C23—24no—
296C23—41no—
297C23—471no—
298C23—472no—
299C23—478no—
300C23—471no—
301C23—944no—
302C23—944no—
303C23—944no—
304C23—942no—
305C23—944no—
306C23—944no—
307C23—944no—
308C23—1882no—
309C23—1881no—
310C23—18816no—
311C23C22⋊C4×D4712yes—
312C23C4⋊C4×D4711yescharacteristic
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—28no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—471no—
321C2×C4—474no—
322C2×C4—472no—
323C2×C4—471no—
324C2×C4—942no—
325C2×C4—944no—
326C2×C4—942no—
327C2×C4—944no—
328C2×C4—944no—
329C2×C4—942no—
330C2×C4—942no—
331C2×C4—944no—
332C2×C4—948no—
333C2×C4—1882no—
334C2×C4—1882no—
335C2×C4—1882no—
336C2×C4—18832no—
337C2×C4—1882no—
338C2×C4—1881no—
339C2×C4—1884no—
340C2×C4—1884no—
341C2×C4C42×D4711yescharacteristic
342C2×C4C22⋊C4×D4711yescharacteristic
343C2×C4C4⋊C4×D4712yes—
344C8—42no—
345C8—1882no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—21no—
350C22—44no—
351C22—474no—
352C22—472no—
353C22—474no—
354C22—9416no—
355C22—942no—
356C22—942no—
357C22—942no—
358C22—941no—
359C22—1888no—
360C22—1884no—
361C22—1884no—
362C22#95×D4711yescharacteristic
363C22#104×D4714yes—
364C4—21no—
365C4—22no—
366C4—48no—
367C4—472no—
368C4—942no—
369C4—941no—
370C4—1888no—
371C4#99×D4712yes—
372C2—24no—
373C2—41no—
374C2—474no—
375C2—944no—
376C2—1881no—
377C2#339×D4712yes—
378C2#342×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1297C2
socleC22×C47C2×#95
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenter#1297D47
hypocenterC47C2×#1297
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
3. #20241274C2semidirect
4. #20241273C2semidirect
5. C47×#1297C2semidirect
7. C2×M16×D47C4semidirect
11. #15689086C4semidirect
17. #15688970C4semidirect
18. #95×D47C4semidirect
33. C2×#10625329C2×C4semidirect
46. C47⋊#95C2×C4semidirect
48. C2×M16×C47C2×C4semidirect
52. #95×C47C2×C4semidirect
187. #1297D47direct (N × H)
194. D47#1297direct (N × H)
210. C47C2×#1297semidirect
227. C2×M16C4×D47semidirect
242. #95C4×D47semidirect

Maximal subgroups

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

subgroupindex
#407×D472
C4×C22⋊C4×D472
#202412742
#202412732
C47×#12972
C2×#129747