Finite Group Databasebeta

← #20244484

Subgroups — #20244484

Order 6016.

390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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×Dic188C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic
3C2×#13094011C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10C2×Dic188—22no—
11C2×Dic188—22no—
12C2×Dic188—22no—
13C2×#10625335—22no—
14C2×#10625335—22no—
15C2×#10625335—22no—
16C22×C47⋊C8C2211yescharacteristic
17#13094011—22no—
18#13094011—22no—
19C2×C22⋊Dic47—22no—
20C2×C4×Dic47C2211yescharacteristic
21#13093947—22no—
22C47⋊#95—22no—
23C22×D4×C47C2211yescharacteristic
24C22×C8×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26#102×C47—22no—
27C24×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47D412yes—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C22×Dic47D412yes—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94D412yes—
50C2×Dic94D412yes—
51C2×C8×C47—21no—
52C2×C8×C47—21no—
53C2×C8×C47D412yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—21no—
56C22⋊Dic47—28no—
57#10625335—28no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8D412yes—
63Dic188—28no—
64C23×C47—22no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—42no—
68C23×C47—42no—
69C23×C47C2×D411yescharacteristic
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—41no—
73D4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—42no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91Dic94—22no—
92Dic94—22no—
93Dic94—22no—
94Dic94—22no—
95Dic94—41no—
96Dic94—41no—
97Dic94—41no—
98Dic94—41no—
99C8×C47—22no—
100C47⋊C8—22no—
101C22×C47—42no—
102C22×C47—44no—
103C22×C47—82no—
104C22×C47—81no—
105C22×C47—81no—
106C22×C47#12011yescharacteristic
107C22×C47#12111yescharacteristic
108C22×C47#12711yescharacteristic
109C22×C47#13512yes—
110C22×C47#13712yes—
111C4×C47—81no—
112C4×C47#12011yescharacteristic
113C4×C47#12011yescharacteristic
114C4×C47#12111yescharacteristic
115C4×C47#12111yescharacteristic
116Dic47—42no—
117Dic47—42no—
118Dic47—42no—
119#2015—471nomaximal, Sylow
120C2×C47—82no—
121C2×C47#39211yescharacteristic
122C2×C47#45212yes—
123C2×C47#46412yes—
124C2×C47#49511yescharacteristic
125C2×C47#49711yescharacteristic
126C22×Q16—471no—
127C22×SD16—471no—
128C2×#124—471no—
129C2×#103—471no—
130C2×#102D4711yescharacteristic
131#391—471no—
132#336—471no—
133C47#201511yescharacteristic, complemented, Sylow
134C22×Q8—471no—
135C22×Q8—471no—
136C22×D4C2×D4711yescharacteristic
137C2×Q16—942no—
138C2×Q16—942no—
139C2×Q16—942no—
140C2×SD16—942no—
141C2×SD16—942no—
142C2×SD16—942no—
143C22×C8—471no—
144C22×C8C2×D4711yescharacteristic
145#124—942no—
146#124—942no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C22⋊C4—942no—
149C2×C42—471no—
150#103—942no—
151#102—22no—
152#95—942no—
153C24—21no—
154C2×Q8—472no—
155C2×Q8—472no—
156C2×Q8—941no—
157C2×Q8—941no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×Q8—941no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4D18812yes—
172C22×C4—21no—
173C22×C4—472no—
174C22×C4—941no—
175C22×C4—941no—
176C22×C4C22×D4711yescharacteristic
177Q16—948no—
178SD16—948no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—472no—
182C2×C8—941no—
183C2×C8—941no—
184C2×C8C22⋊D4712yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C22⋊C4—948no—
188C42—941no—
189C42—941no—
190C23—22no—
191C23—41no—
192C23—41no—
193C23—42no—
194C23—42no—
195C23D4×D4711yescharacteristic
196Q8—942no—
197Q8—942no—
198Q8—942no—
199Q8—942no—
200Q8—1881no—
201Q8—1881no—
202Q8—1881no—
203Q8—1881no—
204D4—22no—
205D4—22no—
206D4—41no—
207D4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4C2×D18811yescharacteristic
220C2×C4#1062535011yescharacteristic
221C2×C4D4×D4711yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4C2×C22⋊D4711yescharacteristic
225C8—22no—
226C8—942no—
227C22—44no—
228C22—42no—
229C22—81no—
230C22—81no—
231C22—82no—
232C22#1309399411yescharacteristic
233C22#1309399711yescharacteristic
234C22#1309402011yescharacteristic
235C22#1309404312yes—
236C22#1309405312yes—
237C4—81no—
238C4—1882no—
239C4—1882no—
240C4—1882no—
241C4#1309399211yescharacteristic
242C4#1309399411yescharacteristic
243C4#1309399711yescharacteristic
244C4#1309399811yescharacteristic
245C2—82no—
246C2#1568903211yescharacteristic
247C2#1568928612yes—
248C2#1568934412yes—
249C2#1568950611yescharacteristic
250C2#1568951411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#2015
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×Dic188C2semidirect
4. C2×#13093947C2semidirect
5. #15689028C2semidirect
6. #15688877C2semidirect
133. C47#2015semidirect