Finite Group Databasebeta

← #20254162

Subgroups — #20254162

Order 6016.

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

normal subgroups only

This group has 416 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×#13094004C211yesmaximal, characteristic
2C22⋊Q8×D47C211yesmaximal, characteristic
3#15689460C212yesmaximal, complemented
4#15689458C211yesmaximal, characteristic, complemented
5#15689365C212yesmaximal, complemented
6#15689363C212yesmaximal, complemented
7#15689281C211yesmaximal, characteristic, complemented
8#15689280C212yesmaximal, complemented
9#15689278C211yesmaximal, characteristic, complemented
10C22⋊C8×D47C211yesmaximal, characteristic
11C47×#484C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C2×Q8×D47C2211yescharacteristic
14C22×C4×D47C2211yescharacteristic
15C2×Dic188C2212yescomplemented
16C2×#10625337C2212yescomplemented
17C2×C8×D47C2212yes—
18#13094004—21no—
19#13094004—21no—
20#13094004C2212yes—
21#13094004C2211yescharacteristic
22#13094004C2212yes—
23#13094003C2211yescharacteristic
24#13094002—21no—
25#13094001—21no—
26#13094000C2211yescharacteristic
27C2×C4⋊Dic47—21no—
28C4⋊C4×D47—21no—
29C4⋊C4×D47C2211yescharacteristic
30C2×(C2×D47)⋊C4—21no—
31C22⋊C4×D47—21no—
32#13093957C2212yescomplemented
33#13093949C2212yescomplemented
34#13093947C2212yescomplemented
35#13093947C2212yescomplemented
36C22⋊(C47⋊C8)C2211yescharacteristic
37(C2×D47)⋊C8C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#107×C47C2212yescomplemented
41#103×C47C2212yescomplemented
42C22⋊C8×C47C2211yescharacteristic
43C23×D47D411yescharacteristic
44C2×Q8×C47C2311yescharacteristic
45C22×C4×C47—21no—
46C22×C4×C47C2311yescharacteristic
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49Q8×D47—42no—
50C2×C4×D47—21no—
51C2×C4×D47—21no—
52C2×C4×D47—42no—
53C2×C4×D47D411yescharacteristic
54C2×C4×D47D411yescharacteristic
55C2×C4×D47C2311yescharacteristic
56C2×C4×D47C2311yescharacteristic
57C2×Dic94—21no—
58C2×Dic94—21no—
59C2×Dic94—42no—
60C2×Dic94C2311yescharacteristic
61C2×Dic94C2312yes—
62C2×C8×C47C2312yes—
63C4⋊C4×C47—21no—
64C4⋊C4×C47—21no—
65C4⋊C4×C47C2312yes—
66C4⋊C4×C47C2311yescharacteristic
67C22⋊C4×C47—21no—
68C22⋊Dic47—21no—
69#10625337—42no—
70(C2×D47)⋊C4—21no—
71(C2×D47)⋊C4—21no—
72(C2×D47)⋊C4—22no—
73(C2×D47)⋊C4—22no—
74C4⋊Dic47—21no—
75C4⋊Dic47—22no—
76C4⋊Dic47—22no—
77C4⋊Dic47C2311yescharacteristic
78Dic47⋊C4—21no—
79Dic47⋊C4—21no—
80Dic47⋊C4—21no—
81C2×C47⋊C8C2312yes—
82Dic188—42no—
83C8×D47—42no—
84C23×C47C2×D411yescharacteristic
85C22×D47—41no—
86C22×D47—41no—
87C22×D47Q1614yescomplemented
88C22×D47C2×D411yescharacteristic
89C22×D47C2×D411yescharacteristic
90Q8×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—22no—
95C2×C4×C47—42no—
96C2×C4×C47C2×D411yescharacteristic
97C2×C4×C47C2411yescharacteristic
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—22no—
101C2×Dic47—41no—
102C2×Dic47—42no—
103C2×Dic47C2×D411yescharacteristic
104C2×Dic47C2×D411yescharacteristic
105C4×D47—22no—
106C4×D47—22no—
107C4×D47—41no—
108C4×D47—41no—
109C4×D47—42no—
110C4×D47—42no—
111Dic94—22no—
112Dic94—22no—
113Dic94—22no—
114Dic94—42no—
115Dic94—42no—
116C8×C47—22no—
117C47⋊C8—22no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47C2×Q1612yes—
121C22×C47C22×D411yescharacteristic
122C2×D47—21no—
123C2×D47—21no—
124C2×D47—21no—
125C2×D47—21no—
126C2×D47—44no—
127C2×D47C2×Q1612yes—
128C2×D47C2×Q1612yes—
129C4×C47—21no—
130C4×C47—41no—
131C4×C47—41no—
132C4×C47—42no—
133C4×C47H(5,𝔽2)12yes—
134Dic47—21no—
135Dic47—21no—
136Dic47—41no—
137Dic47—42no—
138Dic47—41no—
139#3189—471nomaximal, Sylow
140C2×C47—22no—
141C2×C47#53411yescharacteristic
142C2×C47C22×Q1611yescharacteristic
143C2×C47#57511yescharacteristic
144D47—22no—
145D47—22no—
146C2×C22⋊Q8—471no—
147C2×C22⋊Q8—471no—
148#484—471no—
149#484—472no—
150#484D4711yescharacteristic, complemented
151#467—472no—
152#467—472no—
153#451—471no—
154#451—472no—
155#451—471no—
156C2×C22⋊C8—471no—
157C47#318911yescharacteristic, complemented, Sylow
158C22×Q8—471no—
159C22×Q8—471no—
160C23×C4—471no—
161C2×Q16—472no—
162C2×Q16—472no—
163C22×C8—472no—
164C22⋊Q8—471no—
165C22⋊Q8—471no—
166C22⋊Q8—472no—
167C22⋊Q8—471no—
168C22⋊Q8—472no—
169C22⋊Q8—941no—
170C22⋊Q8—941no—
171C22⋊Q8—941no—
172C22⋊Q8—941no—
173C22⋊Q8C2×D4711yescharacteristic
174C2×C4⋊C4—471no—
175C2×C4⋊C4—941no—
176C2×C4⋊C4—941no—
177C2×C4⋊C4C2×D4711yescharacteristic
178C2×C22⋊C4—941no—
179C2×C22⋊C4—941no—
180#107—472no—
181#107C2×D4712yescomplemented
182#103—472no—
183#103—472no—
184#103—472no—
185#103C2×D4712yescomplemented
186C22⋊C8—471no—
187C22⋊C8—472no—
188C22⋊C8C2×D4711yescharacteristic
189C24—471no—
190C2×Q8—471no—
191C2×Q8—472no—
192C2×Q8—941no—
193C2×Q8—941no—
194C2×Q8—1882no—
195C2×Q8—1882no—
196C2×Q8C22×D4711yescharacteristic
197C22×C4—21no—
198C22×C4—471no—
199C22×C4—471no—
200C22×C4—471no—
201C22×C4—471no—
202C22×C4—471no—
203C22×C4—941no—
204C22×C4—941no—
205C22×C4—941no—
206C22×C4—1882no—
207C22×C4C22×D4711yescharacteristic
208Q16—1882no—
209Q16—1882no—
210C2×C8—472no—
211C2×C8—1882no—
212C2×C8C22×D4712yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—471no—
216C4⋊C4—941no—
217C4⋊C4—941no—
218C4⋊C4—941no—
219C4⋊C4—942no—
220C4⋊C4—942no—
221C4⋊C4—941no—
222C4⋊C4C22×D4711yescharacteristic
223C4⋊C4C22×D4712yes—
224C22⋊C4—21no—
225C22⋊C4—941no—
226C22⋊C4—941no—
227C22⋊C4—942no—
228C22⋊C4—942no—
229C22⋊C4—941no—
230C23—471no—
231C23—471no—
232C23—474no—
233C23—1881no—
234C23—1881no—
235C23D4×D4711yescharacteristic
236Q8—22no—
237Q8—942no—
238Q8—942no—
239Q8—942no—
240Q8—1882no—
241Q8—1882no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—471no—
248C2×C4—471no—
249C2×C4—942no—
250C2×C4—942no—
251C2×C4—941no—
252C2×C4—941no—
253C2×C4—942no—
254C2×C4—1881no—
255C2×C4—1881no—
256C2×C4—1882no—
257C2×C4—1882no—
258C2×C4—1881no—
259C2×C4—1882no—
260C2×C4D4×D4711yescharacteristic
261C2×C4C23×D4711yescharacteristic
262C8—22no—
263C8—942no—
264C22—21no—
265C22—21no—
266C22—472no—
267C22—472no—
268C22—941no—
269C22—941no—
270C22—941no—
271C22—941no—
272C22—1884no—
273C22Q16×D4712yes—
274C22C2×D4×D4711yescharacteristic
275C4—21no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—941no—
280C4—941no—
281C4—1881no—
282C4—1881no—
283C4—1882no—
284C4#1309407012yes—
285C2—22no—
286C2—942no—
287C2—942no—
288C2#1568968411yescharacteristic
289C2C2×Q16×D4711yescharacteristic
290C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#484C2
socleC22×C47C22×D4
hypercenter#484D47
hypocenterC47#3189
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #15689460C2semidirect
4. #15689458C2semidirect
5. #15689365C2semidirect
6. #15689363C2semidirect
7. #15689281C2semidirect
8. #15689280C2semidirect
9. #15689278C2semidirect
11. C47×#484C2semidirect
15. C2×Dic188C22semidirect
16. C2×#10625337C22semidirect
32. #13093957C22semidirect
33. #13093949C22semidirect
34. #13093947C22semidirect
35. #13093947C22semidirect
40. #107×C47C22semidirect
41. #103×C47C22semidirect
87. C22×D47Q16semidirect
150. #484D47semidirect
157. C47#3189semidirect
181. #107C2×D47semidirect
185. #103C2×D47semidirect