Finite Group Databasebeta

← #20244330

Subgroups — #20244330

Order 6016.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#15689676C211yesmaximal, characteristic
2M16×Dic47C211yesmaximal, characteristic
3C4×Dic47⋊C4C211yesmaximal, characteristic
4#15688884C211yesmaximal, characteristic
5#15688883C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094023C411yescharacteristic, complemented
10#13094023C411yescharacteristic, complemented
11#13094015C411yescharacteristic, complemented
12#13094015C411yescharacteristic, complemented
13#13094001—21no—
14#13094001—21no—
15C4×Dic94—21no—
16C4×Dic94—21no—
17#13093983C2211yescharacteristic
18C2×Dic47⋊C4—21no—
19C2×C4×Dic47C2211yescharacteristic
20C2×C4×Dic47C2211yescharacteristic
21#13093934—21no—
22C8×Dic47—21no—
23C47⋊#95—21no—
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C22×Dic47—21no—
30C22×Dic47D411yescharacteristic
31C22×Dic47D411yescharacteristic
32C2×Dic94—21no—
33C2×Dic94—21no—
34M16×C47—21no—
35M16×C47Q812yescomplemented
36C2×C8×C47—21no—
37C4⋊C4×C47C2×C411yescharacteristic
38C4⋊C4×C47C2×C411yescharacteristic
39C22⋊C4×C47—21no—
40C42×C47—21no—
41C42×C47—21no—
42C42×C47—21no—
43C22⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47C2×C411yescharacteristic
47C4⋊Dic47C2×C411yescharacteristic
48Dic47⋊C4—24no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53C4×Dic47—21no—
54C4×Dic47—21no—
55C4×Dic47—21no—
56C4×Dic47C2×C411yescharacteristic
57C4×Dic47C2×C411yescharacteristic
58C4×Dic47D411yescharacteristic
59C4×Dic47D411yescharacteristic
60#10625329—21no—
61#10625329Q812yescomplemented
62C2×C47⋊C8—21no—
63C23×C47C2×D411yescharacteristic
64C2×C4×C47—22no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×Q811yescharacteristic
72C2×C4×C47C2×Q811yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47C22⋊C411yescharacteristic
83C2×Dic47C22⋊C411yescharacteristic
84C2×Dic47C22⋊C411yescharacteristic
85C2×Dic47C22⋊C411yescharacteristic
86Dic94—42no—
87Dic94—42no—
88C8×C47—22no—
89C47⋊C8—22no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47C2×C22⋊C411yescharacteristic
93C22×C47#12411yescharacteristic
94C22×C47C4⋊Q811yescharacteristic
95C4×C47—42no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47C4×Q811yescharacteristic
99C4×C47C4×Q811yescharacteristic
100C4×C47C22⋊Q811yescharacteristic
101C4×C47C22⋊Q811yescharacteristic
102Dic47—21no—
103Dic47—21no—
104Dic47—21no—
105Dic47—42no—
106Dic47—41no—
107Dic47—41no—
108Dic47#10412yes—
109#1986—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47#39111yescharacteristic
113C2×C47C2×#10411yescharacteristic
114C2×C47#42111yescharacteristic
115#533—471no—
116C4×M16—471no—
117C4×C4⋊C4—471no—
118#339—471no—
119#339—471no—
120#339—471no—
121#339D4711yescharacteristic
122C47#198611yescharacteristic, complemented, Sylow
123C2×M16—471no—
124C2×M16C2×D4711yescharacteristic
125C4⋊Q8—471no—
126C4⋊Q8—471no—
127#125—471no—
128#125—471no—
129C22⋊Q8—941no—
130C22⋊Q8—941no—
131C4×Q8—941no—
132C4×Q8—941no—
133#117—471no—
134#117C2×D4711yescharacteristic
135C2×C4⋊C4—941no—
136C2×C42—471no—
137C2×C42—471no—
138C2×C42C2×D4711yescharacteristic
139#97—941no—
140C4×C8—941no—
141#95—941no—
142C2×Q8—941no—
143C2×Q8—941no—
144C22×C4—21no—
145C22×C4—471no—
146C22×C4—471no—
147C22×C4—941no—
148C22×C4C22×D4711yescharacteristic
149M16—21no—
150M16—472no—
151M16—941no—
152M16Dic9412yescomplemented
153C2×C8—21no—
154C2×C8—941no—
155C4⋊C4—471no—
156C4⋊C4—471no—
157C4⋊C4—941no—
158C4⋊C4—941no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—944no—
164C4⋊C4C4×D4711yescharacteristic
165C4⋊C4C4×D4711yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—941no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—471no—
172C42—471no—
173C42—471no—
174C42—471no—
175C42—941no—
176C42—941no—
177C42—941no—
178C23D4×D4711yescharacteristic
179Q8—1882no—
180Q8—1882no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—471no—
187C2×C4—471no—
188C2×C4—471no—
189C2×C4—471no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4C2×Dic9411yescharacteristic
198C2×C4C2×C4×D4711yescharacteristic
199C2×C4#1062535011yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4#1062535211yescharacteristic
202C2×C4Q8×D4711yescharacteristic
203C8—22no—
204C8—942no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D4711yescharacteristic
208C22#1309401011yescharacteristic
209C22#1309402311yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—472no—
214C4—941no—
215C4—941no—
216C4—941no—
217C4—1882no—
218C4—1881no—
219C4—1881no—
220C4#1309398911yescharacteristic
221C4C4×Dic9411yescharacteristic
222C4#1309400111yescharacteristic
223C4#1309400211yescharacteristic
224C2—21no—
225C2—21no—
226C2#1568902711yescharacteristic
227C2#104×D4711yescharacteristic
228C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1986
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #13094023C4semidirect
10. #13094023C4semidirect
11. #13094015C4semidirect
12. #13094015C4semidirect
35. M16×C47Q8semidirect
61. #10625329Q8semidirect
122. C47#1986semidirect
152. M16Dic94semidirect