Finite Group Databasebeta

← #20254159

Subgroups — #20254159

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
1C22⋊Q8×D47C212yesmaximal
2#15689460C212yesmaximal, complemented
3#15689457C212yesmaximal, complemented
4#15689364C211yesmaximal, characteristic, complemented
5#15689362C212yesmaximal, complemented
6#15689280C212yesmaximal, complemented
7#15689277C212yesmaximal, complemented
8C2×(C2×D47)⋊C8C211yesmaximal, characteristic
9C47×#467C211yesmaximal, characteristic, complemented
10C2×Q8×D47C2212yes—
11C22×C4×D47C2211yescharacteristic
12C2×Dic188C2211yescharacteristic, complemented
13C2×#10625337C2212yescomplemented
14C22×C47⋊C8C2211yescharacteristic
15#13094004C2212yes—
16#13094003C2212yes—
17#13094002—22no—
18#13094001—22no—
19#13094000C2212yes—
20C4⋊C4×D47—22no—
21C4⋊C4×D47C2212yes—
22C22⋊C4×D47—22no—
23#13093958C2211yescharacteristic, complemented
24#13093957C2212yescomplemented
25#13093949C2212yescomplemented
26#13093948C2212yescomplemented
27#13093947C2212yescomplemented
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×Q16×C47C2211yescharacteristic, complemented
31C22×C8×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#107×C47C2211yescharacteristic, complemented
34#103×C47C2212yescomplemented
35C23×D47D411yescharacteristic
36C2×Q8×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47D411yescharacteristic
39Q8×D47—42no—
40Q8×D47—42no—
41C2×C4×D47—22no—
42C2×C4×D47—22no—
43C2×C4×D47—41no—
44C2×C4×D47—41no—
45C2×C4×D47D412yes—
46C2×C4×D47C2312yes—
47C2×Dic94—22no—
48C2×Dic94C2312yes—
49Q16×C47—41no—
50C2×C8×C47—41no—
51C2×C8×C47C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C4⋊C4×C47—22no—
54C4⋊C4×C47C2312yes—
55C22⋊C4×C47—22no—
56C22⋊Dic47—22no—
57#10625337—42no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65C2×C47⋊C8—41no—
66C2×C47⋊C8C2312yes—
67Dic188—41no—
68C23×C47C2×D411yescharacteristic
69C22×D47—41no—
70C22×D47—41no—
71C22×D47Q1614yescomplemented
72C22×D47C2×D412yes—
73Q8×C47—22no—
74Q8×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—41no—
84C2×Dic47C2×D412yes—
85C4×D47—22no—
86C4×D47—22no—
87C4×D47—42no—
88C4×D47—44no—
89C4×D47—44no—
90Dic94—22no—
91Dic94—22no—
92Dic94—44no—
93C8×C47—21no—
94C8×C47—21no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47C2×Q1612yes—
99C22×C47C22×D411yescharacteristic
100C2×D47—22no—
101C2×D47—22no—
102C2×D47—44no—
103C2×D47C2×Q1614yes—
104C4×C47—21no—
105C4×C47—42no—
106C4×C47—42no—
107C4×C47H(5,𝔽2)11yescharacteristic
108C4×C47H(5,𝔽2)11yescharacteristic
109Dic47—22no—
110Dic47—42no—
111Dic47—42no—
112#3189—471nomaximal, Sylow
113C2×C47—22no—
114C2×C47#53411yescharacteristic
115C2×C47C22×Q1611yescharacteristic
116C2×C47#57511yescharacteristic
117D47—24no—
118C2×C22⋊Q8—472no—
119#484—472no—
120#484—472no—
121#467—471no—
122#467—472no—
123#467D4711yescharacteristic, complemented
124#451—472no—
125#451—472no—
126C2×C22⋊C8—471no—
127C47#318911yescharacteristic, complemented, Sylow
128C22×Q8—472no—
129C23×C4—471no—
130C2×Q16—472no—
131C2×Q16—471no—
132C2×Q16C2×D4711yescharacteristic, complemented
133C22×C8—471no—
134C22×C8C2×D4711yescharacteristic
135C22⋊Q8—472no—
136C22⋊Q8—472no—
137C22⋊Q8—472no—
138C22⋊Q8—942no—
139C22⋊Q8—942no—
140C22⋊Q8C2×D4712yes—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—942no—
143C2×C22⋊C4—942no—
144#107—471no—
145#107—472no—
146#107C2×D4711yescharacteristic, complemented
147#103—472no—
148#103—472no—
149#103—472no—
150#103C2×D4712yescomplemented
151C22⋊C8—472no—
152C22⋊C8—472no—
153C24—471no—
154C2×Q8—472no—
155C2×Q8—942no—
156C2×Q8—1882no—
157C2×Q8—1882no—
158C2×Q8C22×D4712yes—
159C22×C4—471no—
160C22×C4—472no—
161C22×C4—472no—
162C22×C4—942no—
163C22×C4—942no—
164C22×C4—1881no—
165C22×C4—1881no—
166C22×C4C22×D4711yescharacteristic
167Q16—41no—
168Q16—1881no—
169Q16—1882no—
170C2×C8—41no—
171C2×C8—472no—
172C2×C8—1881no—
173C2×C8C22×D4711yescharacteristic
174C2×C8C22×D4711yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—472no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4C22×D4712yes—
182C22⋊C4—22no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C23—472no—
187C23—474no—
188C23—1881no—
189C23—1881no—
190C23D4×D4711yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—942no—
194Q8—942no—
195Q8—1884no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—1882no—
206C2×C4—1884no—
207C2×C4—1884no—
208C2×C4—1881no—
209C2×C4D4×D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—21no—
212C8—21no—
213C8—942no—
214C22—21no—
215C22—21no—
216C22—474no—
217C22—942no—
218C22—942no—
219C22—1884no—
220C22Q16×D4712yes—
221C22C2×D4×D4711yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—942no—
226C4—1882no—
227C4—1882no—
228C4#1309406911yescharacteristic
229C4#1309407011yescharacteristic
230C2—22no—
231C2—944no—
232C2#1568968111yescharacteristic
233C2C2×Q16×D4711yescharacteristic
234C2#1568992011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3189
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #15689460C2semidirect
3. #15689457C2semidirect
4. #15689364C2semidirect
5. #15689362C2semidirect
6. #15689280C2semidirect
7. #15689277C2semidirect
9. C47×#467C2semidirect
12. C2×Dic188C22semidirect
13. C2×#10625337C22semidirect
23. #13093958C22semidirect
24. #13093957C22semidirect
25. #13093949C22semidirect
26. #13093948C22semidirect
27. #13093947C22semidirect
30. C2×Q16×C47C22semidirect
33. #107×C47C22semidirect
34. #103×C47C22semidirect
71. C22×D47Q16semidirect
123. #467D47semidirect
127. C47#3189semidirect
132. C2×Q16C2×D47semidirect
146. #107C2×D47semidirect
150. #103C2×D47semidirect