Finite Group Databasebeta

← #451×D47 #20252579

Subgroups — #451×D47 #20252579

Order 6016.

740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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
1C22×Q8×D47C211yesmaximal, characteristic
2C2×Q16×D47C212yesmaximal, complemented
3C22⋊Q8×D47C211yesmaximal, characteristic
4#15689281C211yesmaximal, characteristic, complemented
5#15689280C212yesmaximal, complemented
6#15689279C211yesmaximal, characteristic, complemented
7#15689278C211yesmaximal, characteristic, complemented
8#15689277C212yesmaximal, complemented
9#103×D47C212yesmaximal, complemented
10C22⋊C8×D47C211yesmaximal, characteristic
11C47×#451C211yesmaximal, characteristic, complemented
12C22×Dic94—21no—
13C22×Dic94C2211yescharacteristic
14C2×Q8×D47—28no—
15C2×Q8×D47—21no—
16C2×Q8×D47—21no—
17C2×Q8×D47C2212yes—
18C2×Q8×D47C2211yescharacteristic
19C2×Q8×D47C2212yes—
20C22×C4×D47—21no—
21C22×C4×D47C2211yescharacteristic
22C2×Dic188C2212yescomplemented
23C2×#10625337C2212yescomplemented
24C2×#10625337C2212yescomplemented
25Q16×D47—28no—
26C2×C8×D47C2212yes—
27#13094004C2211yescharacteristic
28#13094003C2211yescharacteristic
29#13094002—21no—
30#13094001—21no—
31#13094000C2211yescharacteristic
32C4⋊C4×D47—21no—
33C4⋊C4×D47C2211yescharacteristic
34C22⋊C4×D47—21no—
35#13093949C2212yescomplemented
36#13093948C2212yescomplemented
37#13093947C2212yescomplemented
38C22⋊(C47⋊C8)C2211yescharacteristic
39(C2×D47)⋊C8C2212yes—
40C22×Q8×C47C2211yescharacteristic
41C2×Q16×C47C2212yescomplemented
42C22⋊Q8×C47C2211yescharacteristic
43#103×C47C2212yescomplemented
44C22⋊C8×C47C2211yescharacteristic
45C23×D47D411yescharacteristic
46C2×Q8×C47—24no—
47C2×Q8×C47—21no—
48C2×Q8×C47C2311yescharacteristic
49C2×Q8×C47C2312yes—
50C22×C4×C47—21no—
51C22×C4×C47C2311yescharacteristic
52C22×Dic47—21no—
53C22×Dic47D411yescharacteristic
54Q8×D47—28no—
55Q8×D47—28no—
56Q8×D47—24no—
57Q8×D47—24no—
58Q8×D47—24no—
59Q8×D47—24no—
60Q8×D47D418yes—
61C2×C4×D47—28no—
62C2×C4×D47—22no—
63C2×C4×D47—22no—
64C2×C4×D47—24no—
65C2×C4×D47—21no—
66C2×C4×D47—21no—
67C2×C4×D47D411yescharacteristic
68C2×C4×D47D411yescharacteristic
69C2×C4×D47C2311yescharacteristic
70C2×C4×D47C2311yescharacteristic
71C2×Dic94—28no—
72C2×Dic94—21no—
73C2×Dic94—22no—
74C2×Dic94—22no—
75C2×Dic94—24no—
76C2×Dic94—21no—
77C2×Dic94C2311yescharacteristic
78C2×Dic94C2312yes—
79Q16×C47—24no—
80C2×C8×C47C2312yes—
81C4⋊C4×C47—21no—
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊Dic47—21no—
85#10625337—24no—
86#10625337—24no—
87(C2×D47)⋊C4—21no—
88(C2×D47)⋊C4—21no—
89C4⋊Dic47—21no—
90C4⋊Dic47C2311yescharacteristic
91Dic47⋊C4—21no—
92Dic47⋊C4—21no—
93Dic47⋊C4—21no—
94C2×C47⋊C8C2312yes—
95Dic188—24no—
96C8×D47—24no—
97C23×C47C2×D411yescharacteristic
98C22×D47—22no—
99C22×D47—22no—
100C22×D47Q1614yescomplemented
101C22×D47C2×D411yescharacteristic
102C22×D47C2×D411yescharacteristic
103Q8×C47—24no—
104Q8×C47—22no—
105Q8×C47—22no—
106Q8×C47C2×D414yes—
107C2×C4×C47—24no—
108C2×C4×C47—22no—
109C2×C4×C47—22no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47C2×D411yescharacteristic
113C2×C4×C47C2411yescharacteristic
114C2×Dic47—24no—
115C2×Dic47—22no—
116C2×Dic47—22no—
117C2×Dic47—21no—
118C2×Dic47—21no—
119C2×Dic47C2×D411yescharacteristic
120C2×Dic47C2×D411yescharacteristic
121C4×D47—28no—
122C4×D47—28no—
123C4×D47—22no—
124C4×D47—22no—
125C4×D47—22no—
126C4×D47—42no—
127C4×D47—42no—
128C4×D47C2×D414yes—
129Dic94—28no—
130Dic94—24no—
131Dic94—22no—
132Dic94—28no—
133Dic94—22no—
134Dic94—42no—
135Dic94C2×D414yes—
136C8×C47—22no—
137C47⋊C8—22no—
138C22×C47—21no—
139C22×C47—21no—
140C22×C47C2×Q1612yescomplemented
141C22×C47C22×D411yescharacteristic
142C2×D47—21no—
143C2×D47—21no—
144C2×D47—28no—
145C2×D47#12012yes—
146C2×D47C2×Q1612yes—
147C2×D47C2×Q1612yescomplemented
148C2×D47#13712yes—
149C4×C47—24no—
150C4×C47—21no—
151C4×C47—41no—
152C4×C47—41no—
153C4×C47C22×D412yes—
154Dic47—21no—
155Dic47—24no—
156Dic47—41no—
157Dic47—41no—
158Dic47#12012yes—
159C2×#451—471nomaximal, Sylow
160C2×C47—22no—
161C2×C47C2×#12011yescharacteristic
162C2×C47C22×Q1611yescharacteristic
163C2×C47C2×#13711yescharacteristic
164D47—22no—
165D47#45114yesdirect product factor
166C23×Q8—471no—
167C22×Q16—472no—
168C2×C22⋊Q8—471no—
169#451—471no—
170#451—472no—
171#451—471no—
172#451—472no—
173#451—471no—
174#451D4711yescharacteristic, direct product factor
175C2×#103—472no—
176C2×C22⋊C8—471no—
177C47C2×#45111yescharacteristic, complemented, Sylow
178C22×Q8—472no—
179C22×Q8—471no—
180C22×Q8—472no—
181C22×Q8—471no—
182C22×Q8—941no—
183C22×Q8—941no—
184C22×Q8—941no—
185C22×Q8—948no—
186C22×Q8C2×D4711yescharacteristic
187C23×C4—471no—
188C23×C4—941no—
189C2×Q16—472no—
190C2×Q16—472no—
191C2×Q16—472no—
192C2×Q16—948no—
193C2×Q16C2×D4712yescomplemented
194C22×C8—472no—
195C22⋊Q8—471no—
196C22⋊Q8—471no—
197C22⋊Q8—471no—
198C22⋊Q8—941no—
199C22⋊Q8—941no—
200C22⋊Q8C2×D4711yescharacteristic
201C2×C4⋊C4—471no—
202C2×C4⋊C4—941no—
203C2×C22⋊C4—941no—
204#103—472no—
205#103—472no—
206#103—472no—
207#103C2×D4712yescomplemented
208C22⋊C8—471no—
209C22⋊C8—472no—
210C22⋊C8C2×D4711yescharacteristic
211C24—471no—
212C2×Q8—24no—
213C2×Q8—21no—
214C2×Q8—478no—
215C2×Q8—472no—
216C2×Q8—471no—
217C2×Q8—942no—
218C2×Q8—942no—
219C2×Q8—941no—
220C2×Q8—944no—
221C2×Q8—948no—
222C2×Q8—944no—
223C2×Q8—944no—
224C2×Q8—944no—
225C2×Q8—948no—
226C2×Q8—948no—
227C2×Q8—944no—
228C2×Q8—941no—
229C2×Q8C22×D4711yescharacteristic
230C2×Q8C22×D4712yes—
231C22×C4—21no—
232C22×C4—471no—
233C22×C4—471no—
234C22×C4—471no—
235C22×C4—471no—
236C22×C4—471no—
237C22×C4—944no—
238C22×C4—942no—
239C22×C4—942no—
240C22×C4—948no—
241C22×C4—941no—
242C22×C4—941no—
243C22×C4—941no—
244C22×C4C22×D4711yescharacteristic
245Q16—24no—
246Q16—944no—
247Q16—944no—
248Q16—944no—
249C2×C8—472no—
250C2×C8—944no—
251C2×C8C22×D4712yes—
252C4⋊C4—21no—
253C4⋊C4—471no—
254C4⋊C4—941no—
255C4⋊C4—941no—
256C4⋊C4—941no—
257C4⋊C4—941no—
258C4⋊C4C22×D4711yescharacteristic
259C22⋊C4—21no—
260C22⋊C4—941no—
261C22⋊C4—941no—
262C22⋊C4—941no—
263C23—471no—
264C23—474no—
265C23—471no—
266C23—942no—
267C23—942no—
268C23D4×D4711yescharacteristic
269Q8—24no—
270Q8—22no—
271Q8—22no—
272Q8—474no—
273Q8—948no—
274Q8—948no—
275Q8—944no—
276Q8—942no—
277Q8—942no—
278Q8—1882no—
279Q8D4×D4714yes—
280C2×C4—24no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—471no—
286C2×C4—474no—
287C2×C4—471no—
288C2×C4—942no—
289C2×C4—942no—
290C2×C4—948no—
291C2×C4—948no—
292C2×C4—942no—
293C2×C4—944no—
294C2×C4—942no—
295C2×C4—942no—
296C2×C4—941no—
297C2×C4—941no—
298C2×C4—1882no—
299C2×C4—1882no—
300C2×C4D4×D4711yescharacteristic
301C2×C4C23×D4711yescharacteristic
302C8—22no—
303C8—942no—
304C22—21no—
305C22—21no—
306C22—472no—
307C22—472no—
308C22—472no—
309C22—472no—
310C22—948no—
311C22—941no—
312C22—941no—
313C22Q16×D4712yescomplemented
314C22C2×D4×D4711yescharacteristic
315C4—24no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—472no—
320C4—941no—
321C4—944no—
322C4—1881no—
323C4—1881no—
324C4C2×D4×D4712yes—
325C2—22no—
326C2—474no—
327C2—942no—
328C2#120×D4711yescharacteristic
329C2C2×Q16×D4711yescharacteristic
330C2#137×D4711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#451C2
socleC22×C47C22×D4
hypercenter#451D47
hypocenterC47C2×#451
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×Q16×D47C2semidirect
4. #15689281C2semidirect
5. #15689280C2semidirect
6. #15689279C2semidirect
7. #15689278C2semidirect
8. #15689277C2semidirect
9. #103×D47C2semidirect
11. C47×#451C2semidirect
22. C2×Dic188C22semidirect
23. C2×#10625337C22semidirect
24. C2×#10625337C22semidirect
35. #13093949C22semidirect
36. #13093948C22semidirect
37. #13093947C22semidirect
41. C2×Q16×C47C22semidirect
43. #103×C47C22semidirect
100. C22×D47Q16semidirect
140. C22×C47C2×Q16semidirect
147. C2×D47C2×Q16semidirect
165. D47#451direct (N × H)
174. #451D47direct (N × H)
177. C47C2×#451semidirect
193. C2×Q16C2×D47semidirect
207. #103C2×D47semidirect
313. C22Q16×D47semidirect