Finite Group Databasebeta

← #20254181

Subgroups — #20254181

Order 6016.

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

normal subgroups only

This group has 424 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
1#15689634C212yesmaximal, complemented
2#15689465C212yesmaximal, complemented
3#15689448C212yesmaximal, complemented
4#15689364C211yesmaximal, characteristic, complemented
5#15689359C211yesmaximal, characteristic, complemented
6#15689352C212yesmaximal, complemented
7#15689287C212yesmaximal, complemented
8#15689270C212yesmaximal, complemented
9C2×C22⋊C8×C47C211yesmaximal, characteristic, complemented
10C2×#10625350C2212yes—
11C2×Dic188C2211yescharacteristic, complemented
12C2×#10625325C2212yescomplemented
13C2×D376C2211yescharacteristic, complemented
14#13094007—22no—
15#13094003C2212yes—
16#13094003C2212yes—
17#13093998C2212yes—
18#13093998C2212yes—
19#13093993—22no—
20C4×C22⋊D47—22no—
21C4×C22⋊D47—22no—
22#13093983C2212yes—
23#13093958C2211yescharacteristic, complemented
24#13093958C2211yescharacteristic, complemented
25#13093956C2212yescomplemented
26#13093949C2212yescomplemented
27#13093949C2212yescomplemented
28#13093946C2212yescomplemented
29#13093946C2212yescomplemented
30C23×C4×C47C2211yescharacteristic
31C22×C8×C47C2211yescharacteristic
32C22×C8×C47C2211yescharacteristic
33C22⋊C8×C47C2212yes—
34C22⋊C8×C47C2212yes—
35C24×C47D411yescharacteristic
36C22×C4×C47—41no—
37C22×C4×C47—41no—
38C22×C4×C47D411yescharacteristic
39C22×C4×C47D412yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C2×C22⋊D47—22no—
43C2×C22⋊D47—22no—
44C2×C22⋊D47—22no—
45#10625350—42no—
46#10625350—42no—
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×Dic94C2312yes—
50C2×C8×C47—41no—
51C2×C8×C47—41no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2312yes—
54C2×C8×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47C2312yes—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65Dic188—41no—
66D376—41no—
67#10625325—42no—
68C23×C47—22no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47C2×D412yes—
72C23×C47C2×D411yescharacteristic
73C22×D47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—41no—
79C2×C4×C47—42no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—44no—
84C22⋊D47—44no—
85C22⋊D47—44no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89D188—22no—
90D188—22no—
91C4×D47—44no—
92Dic94—22no—
93Dic94—22no—
94C8×C47—22no—
95C8×C47—21no—
96C8×C47—21no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—22no—
100C22×C47—22no—
101C22×C47—22no—
102C22×C47—44no—
103C22×C47#13512yes—
104C22×C47C22×D411yescharacteristic
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C4×C47—22no—
109C4×C47—21no—
110C4×C47H(5,𝔽2)11yescharacteristic
111C4×C47H(5,𝔽2)11yescharacteristic
112Dic47—42no—
113Dic47—42no—
114Dic47—42no—
115#3191—471nomaximal, Sylow
116C2×C47—22no—
117C2×C47—42no—
118C2×C47#53411yescharacteristic
119C2×C47C2×#13511yescharacteristic
120C2×C47#57511yescharacteristic
121D47—82no—
122#525—472no—
123#485—472no—
124#482—472no—
125#467—471no—
126#466—471no—
127#465—472no—
128#452—472no—
129#449—472no—
130C2×C22⋊C8D4711yescharacteristic, complemented
131C47#319111yescharacteristic, complemented, Sylow
132C2×#41—472no—
133C23×C4C2×D4711yescharacteristic
134C2×Q16—471no—
135C2×SD16—472no—
136C2×D8—471no—
137C22×C8C2×D4711yescharacteristic
138C22×C8C2×D4711yescharacteristic
139#123—942no—
140C22⋊Q8—472no—
141C22⋊Q8—472no—
142#121—472no—
143#121—472no—
144#120—942no—
145C4×D4—942no—
146C4×D4—942no—
147#117—472no—
148#107—471no—
149#107—471no—
150#106—472no—
151#103—472no—
152#103—472no—
153#102—472no—
154#102—472no—
155C22⋊C8C2×D4712yes—
156C22⋊C8C2×D4712yes—
157C24D18811yescharacteristic
158#41—1882no—
159#41—1882no—
160C2×Q8—472no—
161C2×D4—472no—
162C2×D4—942no—
163C2×D4—942no—
164C2×D4—942no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—942no—
168C22×C4D18811yescharacteristic
169C22×C4D18812yes—
170C22×C4C22×D4712yes—
171C22×C4C22×D4711yescharacteristic
172Q16—1881no—
173SD16—1882no—
174D8—1881no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8C22×D4711yescharacteristic
178C2×C8C22×D4712yes—
179C2×C8C22×D4711yescharacteristic
180C4⋊C4—472no—
181C4⋊C4—472no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C42—942no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—942no—
194C23C2×D18812yes—
195C23C2×D18811yescharacteristic
196Q8—942no—
197Q8—942no—
198D4—942no—
199D4—942no—
200D4—1884no—
201D4—1884no—
202D4—1884no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—1884no—
213C2×C4C2×D18812yes—
214C2×C4C2×D18811yescharacteristic
215C2×C4C23×D4711yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C22—21no—
220C22—21no—
221C22—22no—
222C22—22no—
223C22—22no—
224C22—44no—
225C22—1882no—
226C22—1882no—
227C22—1882no—
228C22#1309404612yes—
229C22C22×D18811yescharacteristic
230C4—22no—
231C4—21no—
232C4—1882no—
233C4—1882no—
234C4—1882no—
235C4#1309406911yescharacteristic
236C4#1309406911yescharacteristic
237C2—22no—
238C2—42no—
239C2—3762no—
240C2#1568968511yescharacteristic
241C2C2×#1309404611yescharacteristic
242C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C22⋊C8×C47C2
socleC22×C47C22×D4
hypercenterC2×C22⋊C8D47
hypocenterC47#3191
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #15689634C2semidirect
2. #15689465C2semidirect
3. #15689448C2semidirect
4. #15689364C2semidirect
5. #15689359C2semidirect
6. #15689352C2semidirect
7. #15689287C2semidirect
8. #15689270C2semidirect
9. C2×C22⋊C8×C47C2semidirect
11. C2×Dic188C22semidirect
12. C2×#10625325C22semidirect
13. C2×D376C22semidirect
23. #13093958C22semidirect
24. #13093958C22semidirect
25. #13093956C22semidirect
26. #13093949C22semidirect
27. #13093949C22semidirect
28. #13093946C22semidirect
29. #13093946C22semidirect
130. C2×C22⋊C8D47semidirect
131. C47#3191semidirect