Finite Group Databasebeta

← #20244463

Subgroups — #20244463

Order 6016.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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×#10625335C211yesmaximal, characteristic, complemented
2C2×#13094011C211yesmaximal, characteristic, complemented
3C2×#13093949C211yesmaximal, characteristic, complemented
4C2×#13093945C211yesmaximal, characteristic, complemented
5#15689026C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C22×D8×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625335—22no—
10C2×#10625335—22no—
11C2×#10625335—22no—
12C22×C47⋊C8C2211yescharacteristic
13#13094011—22no—
14#13094011—22no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47—22no—
17C2×C22⋊Dic47—22no—
18C2×C4×Dic47C2211yescharacteristic
19#13093949—22no—
20#13093945—22no—
21C22×D4×C47C2211yescharacteristic
22C22×D4×C47C2211yescharacteristic
23C2×D8×C47—22no—
24C2×D8×C47—22no—
25C2×D8×C47—22no—
26C22×C8×C47C2211yescharacteristic
27C24×C47—21no—
28C24×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47—21no—
33C2×D4×C47—21no—
34C2×D4×C47—21no—
35C2×D4×C47—21no—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47D412yes—
40C2×D4×C47D412yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—21no—
43C22×Dic47—21no—
44C22×Dic47D412yes—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×Dic94D412yes—
51D8×C47—28no—
52C2×C8×C47—21no—
53C2×C8×C47—21no—
54C2×C8×C47D412yes—
55C22⋊Dic47—28no—
56C22⋊Dic47—44no—
57#10625335—28no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C2×C47⋊C8D412yes—
65C23×C47—22no—
66C23×C47—22no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47—41no—
70C23×C47—41no—
71C23×C47—42no—
72C23×C47—42no—
73C23×C47—42no—
74C23×C47—42no—
75C23×C47C2×D411yescharacteristic
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—22no—
79D4×C47—22no—
80D4×C47—41no—
81D4×C47—41no—
82D4×C47—41no—
83D4×C47—41no—
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97C2×Dic47—42no—
98Dic94—22no—
99Dic94—22no—
100Dic94—41no—
101Dic94—41no—
102C8×C47—22no—
103C47⋊C8—22no—
104C22×C47—42no—
105C22×C47—42no—
106C22×C47—44no—
107C22×C47—44no—
108C22×C47—82no—
109C22×C47—82no—
110C22×C47—81no—
111C22×C47—81no—
112C22×C47—81no—
113C22×C47—81no—
114C22×C47#12011yescharacteristic
115C22×C47#12111yescharacteristic
116C22×C47#12711yescharacteristic
117C22×C47#13512yes—
118C22×C47AGL(1,ℤ/8)12yes—
119C4×C47#12011yescharacteristic
120C4×C47#12011yescharacteristic
121C4×C47#12111yescharacteristic
122C4×C47#12111yescharacteristic
123Dic47—42no—
124Dic47—42no—
125Dic47—81no—
126#2012—471nomaximal, Sylow
127C2×C47—82no—
128C2×C47—82no—
129C2×C47#39211yescharacteristic
130C2×C47#44912yes—
131C2×C47#46312yes—
132C2×C47#49511yescharacteristic
133C2×C47#49611yescharacteristic
134C22×SD16—471no—
135C22×D8D4711yescharacteristic
136C2×#124—471no—
137C2×#103—471no—
138C2×#102—471no—
139#390—471no—
140#336—471no—
141C47#201211yescharacteristic, complemented, Sylow
142C22×Q8—471no—
143C22×D4C2×D4711yescharacteristic
144C22×D4C2×D4711yescharacteristic
145C2×SD16—942no—
146C2×SD16—942no—
147C2×SD16—942no—
148C2×D8—22no—
149C2×D8—22no—
150C2×D8—22no—
151C22×C8—471no—
152C22×C8C2×D4711yescharacteristic
153#124—942no—
154#124—942no—
155C2×C4⋊C4—471no—
156C2×C22⋊C4—942no—
157C2×C22⋊C4—942no—
158C2×C42—471no—
159#103—942no—
160#102—942no—
161C24—21no—
162C24—21no—
163C2×Q8—472no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×Q8—941no—
168C2×Q8—941no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4C22⋊D4712yes—
180C2×D4C22⋊D4712yes—
181C22×C4—472no—
182C22×C4—941no—
183C22×C4—941no—
184C22×C4C22×D4711yescharacteristic
185SD16—948no—
186D8—28no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—472no—
190C2×C8—941no—
191C2×C8—941no—
192C2×C8C22⋊D4712yes—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C22⋊C4—948no—
196C22⋊C4—1884no—
197C42—941no—
198C42—941no—
199C23—22no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—42no—
206C23—42no—
207C23—42no—
208C23—42no—
209C23D4×D4711yescharacteristic
210Q8—942no—
211Q8—942no—
212Q8—1881no—
213Q8—1881no—
214D4—22no—
215D4—22no—
216D4—22no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—41no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—1881no—
227C2×C4—1882no—
228C2×C4—1881no—
229C2×C4—1881no—
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4#1062535211yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C2×C4C2×C22⋊D4711yescharacteristic
235C2×C4C2×C22⋊D4711yescharacteristic
236C8—22no—
237C8—942no—
238C22—44no—
239C22—42no—
240C22—42no—
241C22—44no—
242C22—81no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22—82no—
247C22—82no—
248C22#1309399211yescharacteristic
249C22#1309399611yescharacteristic
250C22#1309402011yescharacteristic
251C22#1309404312yes—
252C22#1309404812yes—
253C4—3761no—
254C4—1882no—
255C4—1882no—
256C4#1309399211yescharacteristic
257C4#1309399311yescharacteristic
258C4#1309399511yescharacteristic
259C4#1309399611yescharacteristic
260C2—82no—
261C2—82no—
262C2#1568903111yescharacteristic
263C2#1568926512yes—
264C2#1568933612yes—
265C2#1568950611yescharacteristic
266C2#1568951111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC22×D8×C47C2
socleC23×C47C2×D4
hypercenterC22×D8D47
hypocenterC47#2012
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#10625335C2semidirect
2. C2×#13094011C2semidirect
3. C2×#13093949C2semidirect
4. C2×#13093945C2semidirect
5. #15689026C2semidirect
6. #15688877C2semidirect
141. C47#2012semidirect