Finite Group Databasebeta

← #20255062

Subgroups — #20255062

Order 6016.

620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D376C211yesmaximal, characteristic, complemented
2C2×D8×D47C211yesmaximal, characteristic, complemented
3#15689757C212yesmaximal, complemented
4#15689498C211yesmaximal, characteristic, complemented
5#15689360C211yesmaximal, characteristic, complemented
6#15689317C212yesmaximal, complemented
7#15689258C212yesmaximal, complemented
8#15689256C212yesmaximal, complemented
9#15689205C211yesmaximal, characteristic, complemented
10C8×C22⋊D47C211yesmaximal, characteristic, complemented
11C47×#466C211yesmaximal, characteristic, complemented
12C22×D188C2212yescomplemented
13C2×D4×D47—22no—
14C2×D4×D47C2212yescomplemented
15C2×D376—24no—
16C2×D376C2211yescharacteristic
17C2×D376C2211yescharacteristic, complemented
18C2×D376C2212yescomplemented
19C2×#10625334C2212yescomplemented
20C2×#10625334C2212yescomplemented
21D8×D47—24no—
22C2×C8×D47C2211yescharacteristic, complemented
23#13094020C2212yescomplemented
24#13093999C2212yescomplemented
25#13093997—22no—
26#13093994—22no—
27#13093992—22no—
28#13093986C2212yescomplemented
29C4×C22⋊D47C2211yescharacteristic
30Dic47⋊C8C2211yescharacteristic, complemented
31#13093944C2212yescomplemented
32#13093944C2212yescomplemented
33C22⋊(C47⋊C8)C2211yescharacteristic, complemented
34(C2×D47)⋊C8C2211yescharacteristic, complemented
35C8×Dic47C2211yescharacteristic, complemented
36C2×D8×C47C2211yescharacteristic, complemented
37C22×C8×C47C2211yescharacteristic, complemented
38#121×C47C2212yescomplemented
39#107×C47C2211yescharacteristic, complemented
40#102×C47C2212yescomplemented
41C23×D47—22no—
42C23×D47—22no—
43C2×D4×C47—22no—
44C2×D4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—22no—
47C2×C22⋊D47—22no—
48C2×C22⋊D47—22no—
49C2×C22⋊D47D411yescharacteristic
50D4×D47—24no—
51D4×D47—42no—
52D4×D47—48no—
53C2×D188—24no—
54C2×D188—22no—
55C2×D188—22no—
56C2×D188—42no—
57C2×D188C2312yes—
58C2×D188C2312yes—
59C2×C4×D47—22no—
60C2×C4×D47C2311yescharacteristic
61D8×C47—22no—
62C2×C8×C47—22no—
63C2×C8×C47C2311yescharacteristic
64C2×C8×C47C2311yescharacteristic
65C4⋊C4×C47C2312yes—
66C22⋊C4×C47—22no—
67C22⋊Dic47D411yescharacteristic
68#10625334—24no—
69#10625334—42no—
70(C2×D47)⋊C4—22no—
71(C2×D47)⋊C4—22no—
72(C2×D47)⋊C4D411yescharacteristic
73Dic47⋊C4D411yescharacteristic
74C4×Dic47C2311yescharacteristic
75C2×C47⋊C8C2311yescharacteristic
76C2×C47⋊C8C2311yescharacteristic
77D376—24no—
78D376—22no—
79D376D414yescomplemented
80C8×D47—22no—
81C23×C47—22no—
82C23×C47C2×D411yescharacteristic
83C22×D47—22no—
84C22×D47—22no—
85C22×D47—44no—
86C22×D47—44no—
87C22×D47—44no—
88C22×D47—44no—
89C22×D47—82no—
90C22×D47—82no—
91C22×D47C2×D411yescharacteristic
92D4×C47—22no—
93D4×C47—22no—
94D4×C47—44no—
95C2×C4×C47—21no—
96C2×C4×C47—21no—
97C2×C4×C47—22no—
98C2×C4×C47C2×D411yescharacteristic
99C2×C4×C47C2411yescharacteristic
100C22⋊D47—44no—
101C22⋊D47—44no—
102C22⋊D47—82no—
103C22⋊D47D814yescomplemented
104C2×Dic47C2×D411yescharacteristic
105C2×Dic47C2×D411yescharacteristic
106C2×Dic47C2×D411yescharacteristic
107D188—22no—
108D188—22no—
109D188—22no—
110D188—44no—
111D188—44no—
112D188C2×D414yescomplemented
113C4×D47—21no—
114C4×D47—21no—
115C4×D47—44no—
116C8×C47—21no—
117C8×C47C2×D412yescomplemented
118C47⋊C8—21no—
119C47⋊C8—21no—
120C22×C47—21no—
121C22×C47—21no—
122C22×C47—42no—
123C22×C47—42no—
124C22×C47—42no—
125C22×C47C2×D812yescomplemented
126C22×C47C22×D411yescharacteristic
127C2×D47—21no—
128C2×D47—21no—
129C2×D47—24no—
130C2×D47—42no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—42no—
134C2×D47—42no—
135C2×D47—88no—
136C2×D47—88no—
137C2×D47C2×D812yescomplemented
138C4×C47—21no—
139C4×C47—42no—
140C4×C47C22×D411yescharacteristic
141C4×C47H(5,𝔽2)11yescharacteristic
142Dic47—21no—
143Dic47—21no—
144Dic47C2×D812yescomplemented
145D4×D8—471nomaximal, Sylow
146C2×C47—22no—
147C2×C47—82no—
148C2×C47D4211yescharacteristic
149C2×C47C22×D811yescharacteristic
150C2×C47#57611yescharacteristic
151D47—22no—
152D47—44no—
153D47—82no—
154C22×D8—471no—
155C22×D8—471no—
156D42—472no—
157#493—471no—
158#466—471no—
159#466D4711yescharacteristic, complemented
160#459—472no—
161#447—472no—
162#447—472no—
163C4×D8—471no—
164C8×D4—471no—
165C47D4×D811yescharacteristic, complemented, Sylow
166C22×D4—472no—
167C22×D4—472no—
168C22×D4—942no—
169C2×D8—472no—
170C2×D8—472no—
171C2×D8—471no—
172C2×D8—472no—
173C2×D8—471no—
174C2×D8—944no—
175C2×D8—944no—
176C2×D8C2×D4711yescharacteristic, complemented
177C22×C8—471no—
178C22×C8C2×D4711yescharacteristic, complemented
179#127—472no—
180#121—472no—
181#121—942no—
182#121C2×D4712yescomplemented
183#120—942no—
184#120—942no—
185C4×D4—471no—
186C4×D4—472no—
187#107C2×D4711yescharacteristic, complemented
188C4⋊C8—471no—
189#102—472no—
190#102—472no—
191#102C2×D4712yescomplemented
192C22⋊C8—471no—
193C22⋊C8—471no—
194C4×C8—471no—
195C24—942no—
196C24—942no—
197C2×D4—22no—
198C2×D4—471no—
199C2×D4—472no—
200C2×D4—472no—
201C2×D4—944no—
202C2×D4—942no—
203C2×D4—942no—
204C2×D4—942no—
205C2×D4—942no—
206C2×D4—944no—
207C2×D4—942no—
208C2×D4—1882no—
209C2×D4—1882no—
210C2×D4—1888no—
211C2×D4C22×D4712yes—
212C22×C4—471no—
213C22×C4—942no—
214C22×C4C22×D4711yescharacteristic
215D8—22no—
216D8—474no—
217D8—944no—
218D8—944no—
219D8—942no—
220D8—1882no—
221C2×C8—22no—
222C2×C8—471no—
223C2×C8—471no—
224C2×C8—942no—
225C2×C8C22×D4711yescharacteristic
226C2×C8C22×D4711yescharacteristic
227C4⋊C4—471no—
228C4⋊C4C22×D4712yes—
229C22⋊C4—22no—
230C22⋊C4—471no—
231C22⋊C4—471no—
232C22⋊C4—942no—
233C22⋊C4—942no—
234C42—471no—
235C23—22no—
236C23—471no—
237C23—942no—
238C23—942no—
239C23—3762no—
240C23—3762no—
241C23—1884no—
242C23—1884no—
243C23—1884no—
244C23—1884no—
245C23D4×D4711yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—474no—
250D4—474no—
251D4—942no—
252D4—942no—
253D4—942no—
254D4—3762no—
255D4—1884no—
256D4—1884no—
257D4—1884no—
258D4—1884no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—471no—
263C2×C4—471no—
264C2×C4—471no—
265C2×C4—941no—
266C2×C4—941no—
267C2×C4—1884no—
268C2×C4D4×D4711yescharacteristic
269C2×C4C23×D4711yescharacteristic
270C8—21no—
271C8—941no—
272C8—941no—
273C8D4×D4712yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—472no—
280C22—941no—
281C22—941no—
282C22—944no—
283C22—3768no—
284C22—3768no—
285C22—1882no—
286C22—1882no—
287C22—1882no—
288C22—1882no—
289C22—1882no—
290C22D8×D4712yescomplemented
291C22C2×D4×D4711yescharacteristic
292C4—21no—
293C4—42no—
294C4—472no—
295C4—941no—
296C4—941no—
297C4C2×D4×D4711yescharacteristic
298C4#1309407011yescharacteristic
299C2—22no—
300C2—82no—
301C2—942no—
302C2—3762no—
303C2—1884no—
304C2#1568975711yescharacteristic
305C2C2×D8×D4711yescharacteristic
306C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#466C2
socleC22×C47C22×D4
hypercenter#466D47
hypocenterC47D4×D8
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D376C2semidirect
2. C2×D8×D47C2semidirect
3. #15689757C2semidirect
4. #15689498C2semidirect
5. #15689360C2semidirect
6. #15689317C2semidirect
7. #15689258C2semidirect
8. #15689256C2semidirect
9. #15689205C2semidirect
10. C8×C22⋊D47C2semidirect
11. C47×#466C2semidirect
12. C22×D188C22semidirect
14. C2×D4×D47C22semidirect
17. C2×D376C22semidirect
18. C2×D376C22semidirect
19. C2×#10625334C22semidirect
20. C2×#10625334C22semidirect
22. C2×C8×D47C22semidirect
23. #13094020C22semidirect
24. #13093999C22semidirect
28. #13093986C22semidirect
30. Dic47⋊C8C22semidirect
31. #13093944C22semidirect
32. #13093944C22semidirect
33. C22⋊(C47⋊C8)C22semidirect
34. (C2×D47)⋊C8C22semidirect
35. C8×Dic47C22semidirect
36. C2×D8×C47C22semidirect
37. C22×C8×C47C22semidirect
38. #121×C47C22semidirect
39. #107×C47C22semidirect
40. #102×C47C22semidirect
79. D376D4semidirect
103. C22⋊D47D8semidirect
112. D188C2×D4semidirect
117. C8×C47C2×D4semidirect
125. C22×C47C2×D8semidirect
137. C2×D47C2×D8semidirect
144. Dic47C2×D8semidirect
159. #466D47semidirect
165. C47D4×D8semidirect
176. C2×D8C2×D47semidirect
178. C22×C8C2×D47semidirect
182. #121C2×D47semidirect
187. #107C2×D47semidirect
191. #102C2×D47semidirect
273. C8D4×D47semidirect
290. C22D8×D47semidirect