Finite Group Databasebeta

← #20244474

Subgroups — #20244474

Order 6016.

474 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10625336C211yesmaximal, characteristic, complemented
2C2×#13094020C211yesmaximal, characteristic
3C2×#13093946C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C22×SD16×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C22⋊D47—22no—
10C2×#10625336—22no—
11C2×#10625336—22no—
12C2×#10625336—22no—
13C22×C47⋊C8C2211yescharacteristic
14#13094020—22no—
15#13094020—22no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4×Dic47C2211yescharacteristic
18#13093946—22no—
19#13093945—22no—
20C47⋊#95—22no—
21C22×Q8×C47C2211yescharacteristic
22C22×D4×C47C2211yescharacteristic
23C2×SD16×C47—22no—
24C2×SD16×C47—22no—
25C2×SD16×C47—22no—
26C22×C8×C47C2211yescharacteristic
27C24×C47—21no—
28C23×D47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47D412yescomplemented
35C2×D4×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47D412yes—
41C22×C4×C47—21no—
42C22×C4×C47C2311yescharacteristic
43C2×C22⋊D47—28no—
44C2×C22⋊D47—44no—
45C2×C22⋊D47—44no—
46C22×Dic47—21no—
47C22×Dic47D412yes—
48C2×D188—21no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188D412yes—
54SD16×C47—28no—
55C2×C8×C47—21no—
56C2×C8×C47—21no—
57C2×C8×C47D412yescomplemented
58#10625336—28no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4×Dic47—21no—
62C4×Dic47—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8—21no—
65C2×C47⋊C8D412yescomplemented
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—
77Q8×C47—22no—
78Q8×C47—22no—
79Q8×C47—41no—
80Q8×C47—41no—
81D4×C47—22no—
82D4×C47—22no—
83D4×C47—41no—
84D4×C47—41no—
85C2×C4×C47—22no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47#4111yescharacteristic
94C22⋊D47—416no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—41no—
98C2×Dic47—42no—
99C2×Dic47SD1614yescomplemented
100D188—22no—
101D188—22no—
102D188—41no—
103D188—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—42no—
122C4×C47#12011yescharacteristic
123C4×C47#12011yescharacteristic
124C4×C47#12111yescharacteristic
125C4×C47#12111yescharacteristic
126Dic47—24no—
127Dic47—81no—
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×SD16D4711yescharacteristic, complemented
138C2×#127—471no—
139C2×#102—471no—
140C2×#102—471no—
141#391—471no—
142#336—471no—
143C47#201411yescharacteristic, complemented, Sylow
144C22×Q8C2×D4711yescharacteristic
145C22×D4—471no—
146C22×D4—942no—
147C22×D4C2×D4711yescharacteristic
148C2×SD16—22no—
149C2×SD16—22no—
150C2×SD16—22no—
151C2×SD16—942no—
152C2×SD16—942no—
153C2×SD16—942no—
154C22×C8—471no—
155C22×C8C2×D4711yescharacteristic
156#127—942no—
157#127—942no—
158C2×C4⋊C4—471no—
159C2×C42—471no—
160#102—942no—
161#102—942no—
162#95—942no—
163C24—21no—
164C24—941no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8C22⋊D4712yescomplemented
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×D4C22⋊D4712yes—
186C22×C4—21no—
187C22×C4—472no—
188C22×C4—941no—
189C22×C4C22×D4711yescharacteristic
190SD16—28no—
191SD16—948no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—472no—
195C2×C8—941no—
196C2×C8—941no—
197C2×C8C22⋊D4712yescomplemented
198C4⋊C4—941no—
199C4⋊C4—941no—
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—22no—
214Q8—22no—
215Q8—41no—
216Q8—41no—
217D4—22no—
218D4—22no—
219D4—41no—
220D4—41no—
221D4—942no—
222D4—942no—
223D4—18816no—
224D4—1881no—
225D4—1881no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—474no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—1881no—
233C2×C4—1882no—
234C2×C4D4×D4711yescharacteristic
235C2×C4D4×D4711yescharacteristic
236C2×C4#1062535211yescharacteristic
237C2×C4C2×C22⋊D4711yescharacteristic
238C2×C4C2×C22⋊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#1309399211yescharacteristic
253C22#1309399611yescharacteristic
254C22#1309402011yescharacteristic
255C22SD16×D4712yes—
256C22#1309405112yes—
257C4—42no—
258C4—944no—
259C4—3761no—
260C4#1309399211yescharacteristic
261C4#1309399311yescharacteristic
262C4#1309399511yescharacteristic
263C4#1309399611yescharacteristic
264C2—82no—
265C2—3762no—
266C2#1568903111yescharacteristic
267C2#1568927212yes—
268C2#1568932112yes—
269C2#1568949411yescharacteristic
270C2#1568950911yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC23×C47C2×D4
hypercenterC22×SD16D47
hypocenterC47#2014
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#10625336C2semidirect
3. C2×#13093946C2semidirect
4. C2×#13093945C2semidirect
5. #15689030C2semidirect
6. #15688877C2semidirect
7. C22×SD16×C47C2semidirect
34. C2×Q8×C47D4semidirect
57. C2×C8×C47D4semidirect
65. C2×C47⋊C8D4semidirect
99. C2×Dic47SD16semidirect
137. C22×SD16D47semidirect
143. C47#2014semidirect
170. C2×Q8C22⋊D47semidirect
197. C2×C8C22⋊D47semidirect