Finite Group Databasebeta

← #327×D47 #20241863

Subgroups — #327×D47 #20241863

Order 6016.

388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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#121×D47C211yesmaximal, characteristic
2C22⋊C8×D47C211yesmaximal, characteristic, complemented
3#95×D47C211yesmaximal, characteristic, complemented
4#15688858C211yesmaximal, characteristic, complemented
5#15688857C211yesmaximal, characteristic, complemented
6#15688856C211yesmaximal, characteristic, complemented
7C47×#327C211yesmaximal, characteristic, complemented
8C2×D4×D47—21no—
9C2×D4×D47C411yescharacteristic, complemented
10C22×C4×D47—21no—
11C22×C4×D47C2211yescharacteristic
12C2×C8×D47—21no—
13#13093999C411yescharacteristic, complemented
14#13093998C2211yescharacteristic
15#13093997—21no—
16#13093996—21no—
17#13093995C411yescharacteristic, complemented
18C4⋊C4×D47C411yescharacteristic, complemented
19C22⋊C4×D47—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic, complemented
21(C2×D47)⋊C8—21no—
22C47⋊#95—21no—
23C47⋊#95C2211yescharacteristic, complemented
24#121×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic, complemented
26#95×C47C2211yescharacteristic, complemented
27C23×D47—21no—
28C23×D47D411yescharacteristic
29C2×D4×C47—21no—
30C2×D4×C47C2×C411yescharacteristic, complemented
31C22×C4×C47—21no—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C2×C22⋊D47—21no—
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38D4×D47—42no—
39D4×D47—42no—
40D4×D47—42no—
41C2×D188—21no—
42C2×D188C2×C411yescharacteristic, complemented
43C2×C4×D47—24no—
44C2×C4×D47—21no—
45C2×C4×D47—42no—
46C2×C4×D47—42no—
47C2×C4×D47—42no—
48C2×C4×D47C2×C411yescharacteristic
49C2×C4×D47C2×C411yescharacteristic
50C2×C4×D47D411yescharacteristic
51C2×C4×D47D411yescharacteristic
52C2×C8×C47—21no—
53C4⋊C4×C47C2×C411yescharacteristic, complemented
54C22⋊C4×C47—21no—
55C22⋊Dic47—21no—
56(C2×D47)⋊C4—21no—
57(C2×D47)⋊C4—21no—
58C4⋊Dic47C2×C411yescharacteristic, complemented
59Dic47⋊C4—21no—
60C2×C47⋊C8—21no—
61C8×D47—42no—
62C23×C47—21no—
63C23×C47C2×D411yescharacteristic
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—21no—
67C22×D47—42no—
68C22×D47—42no—
69C22×D47—42no—
70C22×D47C22⋊C411yescharacteristic
71C22×D47C22⋊C411yescharacteristic
72C22×D47D812yes—
73C22×D47SD1612yes—
74D4×C47—41no—
75D4×C47—41no—
76D4×C47—41no—
77C2×C4×C47—22no—
78C2×C4×C47—21no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47C22×C411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C22⋊D47—42no—
85C22⋊D47—41no—
86C22⋊D47—41no—
87C22⋊D47—42no—
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47C22⋊C411yescharacteristic
94C2×Dic47C22⋊C411yescharacteristic
95D188—41no—
96D188—42no—
97C4×D47—22no—
98C4×D47—22no—
99C4×D47—41no—
100C4×D47—41no—
101C4×D47—48no—
102C4×D47—42no—
103C8×C47—41no—
104C47⋊C8—41no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—41no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47C2×C22⋊C411yescharacteristic
111C22×C47C2×D811yescharacteristic
112C22×C47C2×SD1611yescharacteristic
113C2×D47—21no—
114C2×D47—21no—
115C2×D47—24no—
116C2×D47—24no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—41no—
120C2×D47—84no—
121C2×D47#9912yes—
122C2×D47#10212yes—
123C2×D47#10212yes—
124C2×D47#10412yes—
125C4×C47—21no—
126C4×C47—21no—
127C4×C47—42no—
128C4×C47—41no—
129Dic47—21no—
130Dic47—21no—
131Dic47—42no—
132Dic47—41no—
133C2×#327—471nomaximal, Sylow
134C2×C47—21no—
135C2×C47—21no—
136C2×C47—81no—
137C2×C47C2×#9911yescharacteristic
138C2×C47C2×#10211yescharacteristic
139C2×C47C2×#10411yescharacteristic
140D47—22no—
141D47—81no—
142D47#32714yesdirect product factor
143C2×#121—471no—
144C2×C22⋊C8—471no—
145C2×#95—471no—
146#327—471no—
147#327—471no—
148#327—471no—
149#327D4711yescharacteristic, direct product factor
150C47C2×#32711yescharacteristic, complemented, Sylow
151C22×D4—471no—
152C22×D4—941no—
153C23×C4—471no—
154C23×C4—941no—
155C22×C8—941no—
156#121—471no—
157#121—471no—
158#121—471no—
159#121—941no—
160#121—941no—
161#121C2×D4711yescharacteristic
162C2×C4⋊C4—471no—
163C2×C22⋊C4—941no—
164C22⋊C8—471no—
165C22⋊C8—941no—
166C22⋊C8C2×D4711yescharacteristic, complemented
167#95—471no—
168#95—941no—
169#95C2×D4711yescharacteristic, complemented
170C24—471no—
171C24—941no—
172C2×D4—21no—
173C2×D4—471no—
174C2×D4—941no—
175C2×D4—941no—
176C2×D4—941no—
177C2×D4—941no—
178C2×D4—1882no—
179C2×D4—1882no—
180C2×D4—1882no—
181C2×D4C4×D4711yescharacteristic, complemented
182C22×C4—21no—
183C22×C4—471no—
184C22×C4—471no—
185C22×C4—471no—
186C22×C4—471no—
187C22×C4—471no—
188C22×C4—941no—
189C22×C4—944no—
190C22×C4—941no—
191C22×C4—1882no—
192C22×C4—1882no—
193C22×C4—1882no—
194C22×C4C22×D4711yescharacteristic
195C2×C8—21no—
196C2×C8—941no—
197C2×C8—1882no—
198C4⋊C4—471no—
199C4⋊C4—941no—
200C4⋊C4C4×D4711yescharacteristic, complemented
201C22⋊C4—21no—
202C22⋊C4—941no—
203C22⋊C4—941no—
204C22⋊C4—941no—
205C23—21no—
206C23—471no—
207C23—471no—
208C23—472no—
209C23—472no—
210C23—942no—
211C23—942no—
212C23—941no—
213C23—1882no—
214C23—1882no—
215C23—1882no—
216C23D4×D4711yescharacteristic
217D4—41no—
218D4—41no—
219D4—41no—
220D4—1881no—
221D4—1882no—
222D4—1882no—
223D4—1882no—
224D4—1881no—
225D4—1881no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—471no—
232C2×C4—471no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—941no—
237C2×C4—1881no—
238C2×C4—1881no—
239C2×C4—1882no—
240C2×C4—1888no—
241C2×C4—1881no—
242C2×C4—1881no—
243C2×C4—1881no—
244C2×C4C2×C4×D4711yescharacteristic
245C2×C4D4×D4711yescharacteristic
246C8—41no—
247C8—1881no—
248C22—21no—
249C22—21no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—472no—
254C22—472no—
255C22—472no—
256C22—472no—
257C22—944no—
258C22—944no—
259C22—941no—
260C22—941no—
261C22—3764no—
262C22—1881no—
263C22—1881no—
264C22—1881no—
265C22C22⋊C4×D4711yescharacteristic
266C22D8×D4711yescharacteristic
267C22SD16×D4711yescharacteristic
268C4—21no—
269C4—21no—
270C4—42no—
271C4—41no—
272C4—941no—
273C4—941no—
274C4—1882no—
275C4—1881no—
276C2—21no—
277C2—21no—
278C2—81no—
279C2—474no—
280C2—942no—
281C2—3761no—
282C2#99×D4711yescharacteristic
283C2#102×D4711yescharacteristic
284C2#104×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#327C2
socleC22×C47C2×C22⋊C4
hypercenter#327D47
hypocenterC47C2×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D47C2semidirect
3. #95×D47C2semidirect
4. #15688858C2semidirect
5. #15688857C2semidirect
6. #15688856C2semidirect
7. C47×#327C2semidirect
9. C2×D4×D47C4semidirect
13. #13093999C4semidirect
17. #13093995C4semidirect
18. C4⋊C4×D47C4semidirect
20. C22⋊(C47⋊C8)C22semidirect
23. C47⋊#95C22semidirect
25. C22⋊C8×C47C22semidirect
26. #95×C47C22semidirect
30. C2×D4×C47C2×C4semidirect
42. C2×D188C2×C4semidirect
53. C4⋊C4×C47C2×C4semidirect
58. C4⋊Dic47C2×C4semidirect
142. D47#327direct (N × H)
149. #327D47direct (N × H)
150. C47C2×#327semidirect
166. C22⋊C8C2×D47semidirect
169. #95C2×D47semidirect
181. C2×D4C4×D47semidirect
200. C4⋊C4C4×D47semidirect