Finite Group Databasebeta

← #20244477

Subgroups — #20244477

Order 6016.

474 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10625325C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3C2×#13094020C211yesmaximal, characteristic
4C2×#13093944C211yesmaximal, characteristic, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×D188C2211yescharacteristic
10C22×C22⋊D47—22no—
11C2×#10625325—22no—
12C2×#10625325—22no—
13C2×#10625325—22no—
14C2×#10625335—22no—
15C2×#10625335—22no—
16C2×#10625335—22no—
17C22×C47⋊C8C2211yescharacteristic
18#13094020—22no—
19#13094020—22no—
20C2×C4×Dic47C2211yescharacteristic
21#13093944—22no—
22C47⋊#95—22no—
23C22×D4×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26#102×C47—22no—
27C24×C47—21no—
28C23×D47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47D412yes—
35C22×C4×C47—21no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—28no—
38C2×C22⋊D47—44no—
39C2×C22⋊D47—44no—
40C22×Dic47—21no—
41C22×Dic47D412yes—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—21no—
47C2×D188D412yes—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94—21no—
52C2×Dic94—21no—
53C2×Dic94D412yescomplemented
54C2×C8×C47—21no—
55C2×C8×C47—21no—
56C2×C8×C47D412yescomplemented
57C4⋊C4×C47—21no—
58C4⋊C4×C47—21no—
59#10625335—28no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8D412yescomplemented
65#10625325—28no—
66C23×C47—22no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47—42no—
70C23×C47—42no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C22×D47—41no—
74C22×D47—41no—
75C22×D47—42no—
76C22×D47—42no—
77D4×C47—22no—
78D4×C47—22no—
79D4×C47—41no—
80D4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—42no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C22⋊D47—416no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95C2×Dic47SD1614yescomplemented
96D188—22no—
97D188—22no—
98D188—41no—
99D188—41no—
100Dic94—22no—
101Dic94—22no—
102Dic94—41no—
103Dic94—41no—
104C8×C47—22no—
105C47⋊C8—22no—
106C22×C47—42no—
107C22×C47—44no—
108C22×C47—82no—
109C22×C47—81no—
110C22×C47—81no—
111C22×C47#12011yescharacteristic
112C22×C47#12111yescharacteristic
113C22×C47#12711yescharacteristic
114C22×C47C2×SD1612yes—
115C22×C47AGL(1,ℤ/8)12yes—
116C2×D47—42no—
117C2×D47—44no—
118C2×D47—82no—
119C2×D47—81no—
120C2×D47—81no—
121C4×C47—81no—
122C4×C47#12011yescharacteristic
123C4×C47#12011yescharacteristic
124C4×C47#12111yescharacteristic
125C4×C47#12111yescharacteristic
126Dic47—24no—
127Dic47—42no—
128#2014—471nomaximal, Sylow
129C2×C47—82no—
130C2×C47#39211yescharacteristic
131C2×C47#45012yes—
132C2×C47#46012yes—
133C2×C47#49211yescharacteristic
134C2×C47#49611yescharacteristic
135D47—82no—
136C22×SD16—471no—
137C22×SD16—471no—
138C2×#127—471no—
139C2×#102—471no—
140C2×#102D4711yescharacteristic, complemented
141#391—471no—
142#336—471no—
143C47#201411yescharacteristic, complemented, Sylow
144C22×Q8—471no—
145C22×D4—471no—
146C22×D4—942no—
147C22×D4C2×D4711yescharacteristic
148C2×SD16—942no—
149C2×SD16—942no—
150C2×SD16—942no—
151C2×SD16—942no—
152C2×SD16—942no—
153C2×SD16—942no—
154C22×C8—471no—
155C22×C8C2×D4711yescharacteristic
156#127—942no—
157#127—942no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C42—471no—
160#102—22no—
161#102—942no—
162#95—942no—
163C24—21no—
164C24—941no—
165C2×Q8—472no—
166C2×Q8—941no—
167C2×Q8—941no—
168C2×Q8—941no—
169C2×Q8—941no—
170C2×Q8—941no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—472no—
177C2×D4—948no—
178C2×D4—941no—
179C2×D4—941no—
180C2×D4—941no—
181C2×D4—941no—
182C2×D4—941no—
183C2×D4—1884no—
184C2×D4—1884no—
185C2×D4D18812yes—
186C22×C4—21no—
187C22×C4—472no—
188C22×C4—941no—
189C22×C4C22×D4711yescharacteristic
190SD16—948no—
191SD16—948no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—472no—
195C2×C8—941no—
196C2×C8—941no—
197C2×C8C22⋊D4712yescomplemented
198C4⋊C4—21no—
199C4⋊C4—21no—
200C42—941no—
201C42—941no—
202C23—22no—
203C23—41no—
204C23—41no—
205C23—42no—
206C23—42no—
207C23—942no—
208C23—1881no—
209C23—1881no—
210C23—1882no—
211C23—1882no—
212C23D4×D4711yescharacteristic
213Q8—942no—
214Q8—942no—
215Q8—1881no—
216Q8—1881no—
217D4—22no—
218D4—22no—
219D4—41no—
220D4—41no—
221D4—942no—
222D4—942no—
223D4—18816no—
224D4—1881no—
225D4—1881no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—474no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—1881no—
233C2×C4—1881no—
234C2×C4C2×D18811yescharacteristic
235C2×C4#1062535011yescharacteristic
236C2×C4D4×D4711yescharacteristic
237C2×C4D4×D4711yescharacteristic
238C2×C4D4×D4711yescharacteristic
239C2×C4C2×C22⋊D4711yescharacteristic
240C8—22no—
241C8—942no—
242C22—44no—
243C22—42no—
244C22—81no—
245C22—81no—
246C22—82no—
247C22—3761no—
248C22—3761no—
249C22—3762no—
250C22—1884no—
251C22—1882no—
252C22#1309399411yescharacteristic
253C22#1309399711yescharacteristic
254C22#1309402011yescharacteristic
255C22SD16×D4712yes—
256C22#1309404812yes—
257C4—81no—
258C4—944no—
259C4—1882no—
260C4#1309399211yescharacteristic
261C4#1309399411yescharacteristic
262C4#1309399711yescharacteristic
263C4#1309399811yescharacteristic
264C2—82no—
265C2—3762no—
266C2#1568903211yescharacteristic
267C2#1568927512yes—
268C2#1568932212yes—
269C2#1568949411yescharacteristic
270C2#1568951111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2014
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#10625325C2semidirect
2. C22×#10625335C2semidirect
4. C2×#13093944C2semidirect
5. #15689028C2semidirect
6. #15688877C2semidirect
7. C2×#102×C47C2semidirect
53. C2×Dic94D4semidirect
56. C2×C8×C47D4semidirect
64. C2×C47⋊C8D4semidirect
95. C2×Dic47SD16semidirect
140. C2×#102D47semidirect
143. C47#2014semidirect
197. C2×C8C22⋊D47semidirect