Finite Group Databasebeta

← D47×#1322 #26125407

Subgroups — D47×#1322 #26125407

Order 12032.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×C4⋊C8×D47C211yesmaximal, characteristic
2C22⋊C16×D47C212yesmaximal
3#20241328C211yesmaximal, characteristic, complemented
4#20241327C212yesmaximal, complemented
5C47×#1322C211yesmaximal, characteristic, complemented
6C22×C8×D47C411yescharacteristic
7C22×C8×D47C2211yescharacteristic
8C2×C42×D47C411yescharacteristic
9C2×C16×D47—22no—
10C2×C4⋊(C47⋊C8)C411yescharacteristic
11C2×Dic47⋊C8C411yescharacteristic
12C2×Dic47⋊C8C2211yescharacteristic
13C4⋊C8×D47—22no—
14C4⋊C8×D47—22no—
15C22⋊(C47⋊C16)C2212yes—
16(C2×D47)⋊C16—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C47×C22⋊C16C2212yes—
19C22×C4×D47C811yescharacteristic
20C22×C4×D47C811yescharacteristic
21C22×C4×D47C2×C411yescharacteristic
22C22×C47⋊C8C2×C411yescharacteristic
23C22×C47⋊C8C2×C411yescharacteristic
24C2×C8×D47—21no—
25C2×C8×D47—21no—
26C2×C8×D47—42no—
27C2×C8×D47—42no—
28C2×C8×D47D412yes—
29C2×C8×D47D412yes—
30C2×C4×Dic47C811yescharacteristic
31C2×C4×Dic47C811yescharacteristic
32C2×C4×Dic47C2×C411yescharacteristic
33C42×D47—21no—
34C42×D47—21no—
35C42×D47—21no—
36C42×D47—21no—
37C2×C47⋊C16—22no—
38C16×D47—44no—
39C4⋊(C47⋊C8)—22no—
40Dic47⋊C8—22no—
41Dic47⋊C8—22no—
42C22×C8×C47C2×C411yescharacteristic
43C22×C8×C47C2311yescharacteristic
44C2×C42×C47C2×C411yescharacteristic
45C2×C16×C47—22no—
46C4⋊C8×C47—22no—
47C23×D47C2×C811yescharacteristic
48C22×C4×C47C2×C811yescharacteristic
49C22×C4×C47C2×C811yescharacteristic
50C22×C4×C47C22×C411yescharacteristic
51C22×Dic47C2×C811yescharacteristic
52C22×Dic47C2×C811yescharacteristic
53C22×Dic47C2×C811yescharacteristic
54C2×C4×D47—21no—
55C2×C4×D47—21no—
56C2×C4×D47—22no—
57C2×C4×D47—22no—
58C2×C4×D47—22no—
59C2×C4×D47—21no—
60C2×C4×D47—21no—
61C2×C4×D47—42no—
62C2×C4×D47C1614yescomplemented
63C2×C4×D47C22⋊C411yescharacteristic
64C2×C4×D47C22⋊C411yescharacteristic
65C2×C4×D47M1611yescharacteristic
66C2×C4×D47M1611yescharacteristic
67C2×C8×C47—21no—
68C2×C8×C47—41no—
69C2×C8×C47—41no—
70C2×C8×C47C2×D412yes—
71C42×C47—21no—
72C42×C47—21no—
73C4×Dic47—21no—
74C4×Dic47—21no—
75C4×Dic47—21no—
76C4×Dic47—21no—
77C4×Dic47—21no—
78C4×Dic47—21no—
79C2×C47⋊C8—21no—
80C2×C47⋊C8—41no—
81C2×C47⋊C8—41no—
82C2×C47⋊C8C22⋊C412yes—
83C8×D47—24no—
84C8×D47—42no—
85C8×D47—42no—
86C8×D47—42no—
87C16×C47—42no—
88C47⋊C16—42no—
89C23×C47C22×C811yescharacteristic
90C22×D47—22no—
91C22×D47—22no—
92C22×D47C22⋊C811yescharacteristic
93C22×D47C22⋊C811yescharacteristic
94C22×D47C2×C1612yes—
95C22×D47M3212yes—
96C2×C4×C47—21no—
97C2×C4×C47—21no—
98C2×C4×C47—21no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—41no—
102C2×C4×C47C2×C1612yescomplemented
103C2×C4×C47C2×C22⋊C411yescharacteristic
104C2×C4×C47C2×M1611yescharacteristic
105C2×Dic47—21no—
106C2×Dic47—21no—
107C2×Dic47—22no—
108C2×Dic47—21no—
109C2×Dic47—41no—
110C2×Dic47C22⋊C811yescharacteristic
111C2×Dic47C22⋊C811yescharacteristic
112C2×Dic47C2×C1612yescomplemented
113C4×D47—22no—
114C4×D47—24no—
115C4×D47—24no—
116C4×D47—21no—
117C4×D47—21no—
118C4×D47—22no—
119C4×D47—42no—
120C4×D47—42no—
121C4×D47#9912yes—
122C4×D47#10112yes—
123C8×C47—22no—
124C8×C47—41no—
125C47⋊C8—22no—
126C47⋊C8—41no—
127C2×#1322—471nomaximal, Sylow
128C22×C47—21no—
129C22×C47—21no—
130C22×C47C2×C22⋊C811yescharacteristic
131C22×C47C22×C1611yescharacteristic
132C22×C47C2×M3211yescharacteristic
133C2×D47—21no—
134C2×D47—21no—
135C2×D47—24no—
136C2×D47—24no—
137C2×D47#32412yes—
138C2×D47C22⋊C1612yes—
139C2×D47C22⋊C1612yes—
140C2×D47#34912yes—
141C4×C47—22no—
142C4×C47—21no—
143C4×C47—41no—
144C4×C47C2×#9911yescharacteristic
145C4×C47C2×#10111yescharacteristic
146Dic47—22no—
147Dic47—21no—
148Dic47—41no—
149Dic47#32412yes—
150C22×C4⋊C8—471no—
151C2×C22⋊C16—472no—
152#1322—471no—
153#1322—472no—
154#1322D4711yescharacteristic, direct product factor
155C2×C47—21no—
156C2×C47—21no—
157C2×C47C2×#32411yescharacteristic
158C2×C47C2×C22⋊C1611yescharacteristic
159C2×C47C2×#34911yescharacteristic
160D47—22no—
161D47#132214yesdirect product factor
162C23×C8—471no—
163C23×C8—471no—
164C22×C42—471no—
165C22×C16—942no—
166C2×C4⋊C8—471no—
167C2×C4⋊C8—471no—
168C2×C4⋊C8—471no—
169C2×C4⋊C8—942no—
170C2×C4⋊C8—942no—
171C2×C4⋊C8C2×D4711yescharacteristic
172C22⋊C16—472no—
173C22⋊C16—942no—
174C22⋊C16C2×D4712yes—
175C47C2×#132211yescharacteristic, complemented, Sylow
176C23×C4—471no—
177C23×C4—471no—
178C23×C4—471no—
179C22×C8—471no—
180C22×C8—472no—
181C22×C8—472no—
182C22×C8—471no—
183C22×C8—941no—
184C22×C8—941no—
185C22×C8—1882no—
186C22×C8—1882no—
187C22×C8C4×D4711yescharacteristic
188C22×C8C22×D4711yescharacteristic
189C2×C42—471no—
190C2×C42—471no—
191C2×C42—471no—
192C2×C42—941no—
193C2×C42—941no—
194C2×C42—941no—
195C2×C42—941no—
196C2×C42C4×D4711yescharacteristic
197C2×C16—22no—
198C2×C16—942no—
199C2×C16—1884no—
200C4⋊C8—22no—
201C4⋊C8—942no—
202C4⋊C8—942no—
203C4⋊C8—942no—
204C24—471no—
205C22×C4—471no—
206C22×C4—471no—
207C22×C4—471no—
208C22×C4—474no—
209C22×C4—471no—
210C22×C4—471no—
211C22×C4—471no—
212C22×C4—471no—
213C22×C4—942no—
214C22×C4—942no—
215C22×C4—941no—
216C22×C4—941no—
217C22×C4—942no—
218C22×C4—941no—
219C22×C4—941no—
220C22×C4—1882no—
221C22×C4C8×D4711yescharacteristic
222C22×C4C8×D4711yescharacteristic
223C22×C4C2×C4×D4711yescharacteristic
224C2×C8—21no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—472no—
228C2×C8—944no—
229C2×C8—941no—
230C2×C8—1882no—
231C2×C8—1882no—
232C2×C8—1882no—
233C2×C8—1881no—
234C2×C8—1881no—
235C2×C8D4×D4712yes—
236C42—21no—
237C42—21no—
238C42—941no—
239C42—941no—
240C42—941no—
241C42—941no—
242C42—941no—
243C42—941no—
244C16—42no—
245C16—1882no—
246C23—471no—
247C23—472no—
248C23—472no—
249C23—471no—
250C23—942no—
251C23—942no—
252C23C2×C8×D4711yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—471no—
260C2×C4—472no—
261C2×C4—472no—
262C2×C4—472no—
263C2×C4—471no—
264C2×C4—942no—
265C2×C4—944no—
266C2×C4—944no—
267C2×C4—942no—
268C2×C4—942no—
269C2×C4—941no—
270C2×C4—941no—
271C2×C4—941no—
272C2×C4—941no—
273C2×C4—941no—
274C2×C4—1882no—
275C2×C4—1882no—
276C2×C4—1881no—
277C2×C4C16×D4712yescomplemented
278C2×C4C22⋊C4×D4711yescharacteristic
279C2×C4M16×D4711yescharacteristic
280C8—22no—
281C8—41no—
282C8—942no—
283C8—1881no—
284C22—21no—
285C22—21no—
286C22—472no—
287C22—472no—
288C22—472no—
289C22—472no—
290C22—944no—
291C22—944no—
292C22—941no—
293C22—941no—
294C22C22⋊C8×D4711yescharacteristic
295C22C2×C16×D4711yescharacteristic
296C22M32×D4711yescharacteristic
297C4—22no—
298C4—21no—
299C4—41no—
300C4—472no—
301C4—942no—
302C4—941no—
303C4—1881no—
304C4#99×D4711yescharacteristic
305C4#101×D4711yescharacteristic
306C2—21no—
307C2—21no—
308C2—474no—
309C2—942no—
310C2#324×D4711yescharacteristic
311C2C22⋊C16×D4711yescharacteristic
312C2#349×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C16
FrattiniC22×C8C22×D47
FittingC47×#1322C2
socleC22×C47C2×C22⋊C8
prime radicalC23×D47C2×C8
cosocleC22×C8×C47C23
hypercenter#1322D47
hypocenterC47C2×#1322
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
3. #20241328C2semidirect
4. #20241327C2semidirect
5. C47×#1322C2semidirect
62. C2×C4×D47C16semidirect
102. C2×C4×C47C2×C16semidirect
112. C2×Dic47C2×C16semidirect
154. #1322D47direct (N × H)
161. D47#1322direct (N × H)
175. C47C2×#1322semidirect
277. C2×C4C16×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C8×D472
C22⋊C16×D472
#202413282
#202413272
C47×#13222
C2×#132247