Finite Group Databasebeta

← D47×#1298 #26106416

Subgroups — D47×#1298 #26106416

Order 12032.

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

normal subgroups only

This group has 938 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
2C2×C22⋊C8×D47C212yesmaximal
3#20241276C212yesmaximal, complemented
4#20241275C211yesmaximal, characteristic, complemented
5C47×#1298C211yesmaximal, characteristic, complemented
6C23×C4×D47C2211yescharacteristic
7C2×M16×D47C412yes—
8C22×C8×D47—22no—
9#15689087C2211yescharacteristic
10#15689086C412yes—
11#15689085—22no—
12C2×C22⋊(C47⋊C8)C2212yes—
13C2×(C2×D47)⋊C8—22no—
14C22⋊C8×D47—22no—
15C22⋊C8×D47—22no—
16C22⋊C8×D47—22no—
17C22⋊C8×D47C414yes—
18C22⋊C8×D47C414yes—
19C47×#407C2211yescharacteristic
20C2×C22⋊C8×C47C2212yes—
21C24×D47Q811yescharacteristic
22C23×Dic47Q811yescharacteristic
23C22×C4×D47—44no—
24C22×C4×D47C2×C411yescharacteristic
25C22×C4×D47C2×C412yes—
26C22×C4×D47C2×C412yes—
27C22×C4×D47C2×C411yescharacteristic
28C22×C4×D47D412yes—
29C22×C4×D47D411yescharacteristic
30C22×C4×D47D411yescharacteristic
31C22×C4×D47D412yes—
32C2×#10625329C2×C412yes—
33C2×#10625324—22no—
34M16×D47—44no—
35C22×C47⋊C8—22no—
36C2×C8×D47—22no—
37C2×C8×D47—24no—
38C2×C8×D47—24no—
39C2×C8×D47—48no—
40C22⋊(C47⋊C8)—22no—
41C22⋊(C47⋊C8)—22no—
42C22⋊(C47⋊C8)C2×C414yes—
43(C2×D47)⋊C8—24no—
44(C2×D47)⋊C8—24no—
45(C2×D47)⋊C8—24no—
46C23×C4×C47C2311yescharacteristic
47C2×M16×C47C2×C412yes—
48C22×C8×C47—22no—
49C22⋊C8×C47—22no—
50C22⋊C8×C47—22no—
51C22⋊C8×C47C2×C414yes—
52C24×C47C2×Q811yescharacteristic
53C23×D47—28no—
54C23×D47—42no—
55C23×D47C4⋊C411yescharacteristic
56C23×D47C4⋊C412yes—
57C23×D47C4⋊C411yescharacteristic
58C23×D47C4⋊C412yes—
59C22×C4×C47—42no—
60C22×C4×C47C22×C411yescharacteristic
61C22×C4×C47C22×C412yes—
62C22×C4×C47C2×D412yes—
63C22×C4×C47C2×D411yescharacteristic
64C22×Dic47—42no—
65C22×Dic47C4⋊C411yescharacteristic
66C22×Dic47C4⋊C412yes—
67C22×Dic47C4⋊C411yescharacteristic
68C22×Dic47C4⋊C412yes—
69C2×C4×D47—28no—
70C2×C4×D47—24no—
71C2×C4×D47—44no—
72C2×C4×D47—42no—
73C2×C4×D47—42no—
74C2×C4×D47—44no—
75C2×C4×D47—44no—
76C2×C4×D47—42no—
77C2×C4×D47C4211yescharacteristic
78C2×C4×D47C4211yescharacteristic
79C2×C4×D47C4212yes—
80C2×C4×D47C22⋊C412yes—
81C2×C4×D47C22⋊C412yes—
82C2×C4×D47C22⋊C412yes—
83C2×C4×D47C22⋊C411yescharacteristic
84C2×C4×D47C22⋊C412yes—
85C2×C4×D47C22⋊C412yes—
86C2×C4×D47C22⋊C411yescharacteristic
87M16×C47—42no—
88C2×C8×C47—24no—
89C2×C8×C47—22no—
90C2×C8×C47—44no—
91#10625329—42no—
92C2×C47⋊C8—22no—
93C2×C47⋊C8—24no—
94C2×C47⋊C8—44no—
95#10625324—44no—
96C8×D47—48no—
97C8×D47—48no—
98C8×D47—44no—
99C23×C47—24no—
100C23×C47—41no—
101C23×C47C2×C4⋊C411yescharacteristic
102C23×C47C2×C4⋊C412yes—
103C22×D47—24no—
104C22×D47—24no—
105C22×D47—24no—
106C22×D47—24no—
107C22×D47—24no—
108C22×D47—24no—
109C22×D47—22no—
110C22×D47—41no—
111C22×D47—42no—
112C22×D47—416no—
113C22×D47#9511yescharacteristic
114C22×D47#9512yes—
115C22×D47#9511yescharacteristic
116C22×D47#10818yes—
117C2×C4×C47—24no—
118C2×C4×C47—22no—
119C2×C4×C47—42no—
120C2×C4×C47—41no—
121C2×C4×C47C2×C4211yescharacteristic
122C2×C4×C47C2×C22⋊C412yes—
123C2×C4×C47C2×C22⋊C411yescharacteristic
124C2×Dic47—24no—
125C2×Dic47—22no—
126C2×Dic47—42no—
127C2×Dic47—41no—
128C2×Dic47#9511yescharacteristic
129C2×Dic47#9512yes—
130C2×Dic47#9511yescharacteristic
131C4×D47—24no—
132C4×D47—22no—
133C4×D47—22no—
134C4×D47—24no—
135C4×D47—24no—
136C4×D47—22no—
137C4×D47—42no—
138C4×D47—42no—
139C4×D47—42no—
140C4×D47#9914yes—
141C8×C47—44no—
142C8×C47—42no—
143C47⋊C8—44no—
144C47⋊C8—42no—
145C2×#1298—471nomaximal, Sylow
146C22×C47—22no—
147C22×C47—22no—
148C22×C47—22no—
149C22×C47—21no—
150C22×C47—44no—
151C22×C47C2×#9511yescharacteristic
152C22×C47C2×#10814yes—
153C2×D47—22no—
154C2×D47—22no—
155C2×D47—216no—
156C2×D47—22no—
157C2×D47—21no—
158C2×D47—44no—
159C2×D47—48no—
160C2×D47—44no—
161C2×D47#34114yes—
162C2×D47#34114yes—
163C2×D47#34212yes—
164C4×C47—22no—
165C4×C47—21no—
166C4×C47C2×#9912yes—
167Dic47—22no—
168Dic47—21no—
169Dic47#34212yes—
170C2×#407—471no—
171C22×C22⋊C8—472no—
172#1298—471no—
173#1298—472no—
174#1298D4711yescharacteristic, direct product factor
175C2×C47—24no—
176C2×C47—41no—
177C2×C47C2×#34112yes—
178C2×C47C2×#34211yescharacteristic
179D47—24no—
180D47—41no—
181D47#129814yesdirect product factor
182C24×C4—471no—
183C22×M16—472no—
184C23×C8—942no—
185#407—471no—
186#407—472no—
187#407—942no—
188#407C2×D4711yescharacteristic
189C2×C22⋊C8—472no—
190C2×C22⋊C8—474no—
191C2×C22⋊C8—474no—
192C2×C22⋊C8—942no—
193C2×C22⋊C8—942no—
194C2×C22⋊C8—942no—
195C2×C22⋊C8—942no—
196C2×C22⋊C8C2×D4712yes—
197C47C2×#129811yescharacteristic, complemented, Sylow
198C25—471no—
199C23×C4—471no—
200C23×C4—471no—
201C23×C4—472no—
202C23×C4—472no—
203C23×C4—472no—
204C23×C4—471no—
205C23×C4—471no—
206C23×C4—471no—
207C23×C4—472no—
208C23×C4—1884no—
209C23×C4C22×D4711yescharacteristic
210C2×M16—472no—
211C2×M16—942no—
212C2×M16—1884no—
213C2×M16C4×D4712yes—
214C22×C8—22no—
215C22×C8—944no—
216C22×C8—944no—
217C22×C8—942no—
218C22×C8—942no—
219C22×C8—1888no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222C22⋊C8—474no—
223C22⋊C8—944no—
224C22⋊C8—944no—
225C22⋊C8—944no—
226C22⋊C8—942no—
227C22⋊C8—942no—
228C22⋊C8C4×D4714yes—
229C24—472no—
230C24—471no—
231C24—471no—
232C24—472no—
233C24—948no—
234C24—1882no—
235C24Q8×D4711yescharacteristic
236C22×C4—42no—
237C22×C4—471no—
238C22×C4—471no—
239C22×C4—472no—
240C22×C4—471no—
241C22×C4—472no—
242C22×C4—471no—
243C22×C4—471no—
244C22×C4—472no—
245C22×C4—472no—
246C22×C4—472no—
247C22×C4—471no—
248C22×C4—472no—
249C22×C4—472no—
250C22×C4—472no—
251C22×C4—948no—
252C22×C4—944no—
253C22×C4—1884no—
254C22×C4—1882no—
255C22×C4—1884no—
256C22×C4—1882no—
257C22×C4—1884no—
258C22×C4—1882no—
259C22×C4—1882no—
260C22×C4C2×C4×D4711yescharacteristic
261C22×C4C2×C4×D4712yes—
262C22×C4D4×D4712yes—
263C22×C4D4×D4711yescharacteristic
264M16—42no—
265M16—1884no—
266M16—1882no—
267C2×C8—24no—
268C2×C8—22no—
269C2×C8—44no—
270C2×C8—944no—
271C2×C8—942no—
272C2×C8—1884no—
273C2×C8—1888no—
274C2×C8—1888no—
275C2×C8—1884no—
276C23—24no—
277C23—41no—
278C23—471no—
279C23—472no—
280C23—478no—
281C23—471no—
282C23—944no—
283C23—944no—
284C23—942no—
285C23—944no—
286C23—944no—
287C23—944no—
288C23—944no—
289C23—1882no—
290C23—1881no—
291C23—18816no—
292C23C4⋊C4×D4711yescharacteristic
293C23C4⋊C4×D4712yes—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—471no—
299C2×C4—474no—
300C2×C4—471no—
301C2×C4—472no—
302C2×C4—944no—
303C2×C4—942no—
304C2×C4—944no—
305C2×C4—942no—
306C2×C4—944no—
307C2×C4—942no—
308C2×C4—942no—
309C2×C4—944no—
310C2×C4—1882no—
311C2×C4—1882no—
312C2×C4—1882no—
313C2×C4—1882no—
314C2×C4—1881no—
315C2×C4C42×D4711yescharacteristic
316C2×C4C22⋊C4×D4712yes—
317C2×C4C22⋊C4×D4711yescharacteristic
318C8—44no—
319C8—42no—
320C8—1884no—
321C8—1882no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—44no—
327C22—474no—
328C22—472no—
329C22—474no—
330C22—9416no—
331C22—942no—
332C22—942no—
333C22—942no—
334C22—941no—
335C22—1888no—
336C22—1884no—
337C22—1884no—
338C22#95×D4711yescharacteristic
339C22#108×D4714yes—
340C4—22no—
341C4—21no—
342C4—472no—
343C4—942no—
344C4—941no—
345C4#99×D4712yes—
346C2—24no—
347C2—41no—
348C2—474no—
349C2—944no—
350C2—1881no—
351C2#341×D4712yes—
352C2#342×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1298C2
socleC22×C47C2×#95
prime radicalC24×D47Q8
cosocleC23×C4×C47C23
hypercenter#1298D47
hypocenterC47C2×#1298
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1298

Complements

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

NH ≅ G/Ntype
3. #20241276C2semidirect
4. #20241275C2semidirect
5. C47×#1298C2semidirect
174. #1298D47direct (N × H)
181. D47#1298direct (N × H)
197. C47C2×#1298semidirect

Maximal subgroups

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

subgroupindex
#407×D472
C2×C22⋊C8×D472
#202412762
#202412752
C47×#12982
C2×#129847