Finite Group Databasebeta

← #20241750

Subgroups — #20241750

Order 6016.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C2×#13094002C211yesmaximal, characteristic
2#15689085C211yesmaximal, characteristic
3C22⋊C8×D47C211yesmaximal, characteristic
4#15688849C211yesmaximal, characteristic, complemented
5#15688848C211yesmaximal, characteristic, complemented
6#15688848C211yesmaximal, characteristic, complemented
7C47×#324C211yesmaximal, characteristic, complemented
8C22×Dic94C411yescharacteristic
9C22×C4×D47C2211yescharacteristic
10C2×#10625324—21no—
11C2×C8×D47—21no—
12#13094002—21no—
13#13094002—21no—
14#13094002—21no—
15#13094002—21no—
16C2×Dic47⋊C4C411yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×(C2×D47)⋊C4C411yescharacteristic
19C2×(C2×D47)⋊C4C411yescharacteristic
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22(C2×D47)⋊C8—21no—
23(C2×D47)⋊C8—21no—
24C2×C4⋊C4×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26C22⋊C8×C47C2211yescharacteristic
27C23×D47C2×C411yescharacteristic
28C22×C4×C47C2×C411yescharacteristic
29C22×C4×C47C2×C411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×Dic47C2×C411yescharacteristic
32C22×Dic47C2×C411yescharacteristic
33C22×Dic47C2×C411yescharacteristic
34C2×C4×D47—42no—
35C2×C4×D47D411yescharacteristic
36C2×C4×D47D411yescharacteristic
37C2×C4×D47D411yescharacteristic
38C2×C4×D47D411yescharacteristic
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—42no—
42C2×C8×C47—21no—
43C2×C8×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49(C2×D47)⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53Dic47⋊C4—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56#10625324—42no—
57C8×D47—42no—
58C23×C47C22×C411yescharacteristic
59C22×D47—21no—
60C22×D47—21no—
61C22×D47—22no—
62C22×D47—41no—
63C22×D47C22⋊C411yescharacteristic
64C22×D47C22⋊C411yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×Dic47—22no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—41no—
79C2×Dic47C22⋊C411yescharacteristic
80C2×Dic47C22⋊C411yescharacteristic
81C4×D47—22no—
82C4×D47—22no—
83C4×D47—41no—
84C4×D47—41no—
85Dic94—42no—
86Dic94—42no—
87C8×C47—41no—
88C8×C47—41no—
89C47⋊C8—41no—
90C47⋊C8—41no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47C2×C22⋊C411yescharacteristic
94C22×C47#13111yescharacteristic
95C22×C47#13111yescharacteristic
96C2×D47—21no—
97C2×D47—21no—
98C2×D47—21no—
99C2×D47—21no—
100C2×D47—21no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47#10112yes—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—41no—
107C4×C47—41no—
108Dic47—21no—
109Dic47—41no—
110Dic47—41no—
111Dic47#9912yes—
112#1472—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47#40811yescharacteristic
116C2×C47C2×#9911yescharacteristic
117C2×C47C2×#10111yescharacteristic
118D47—22no—
119D47—41no—
120C2×C22⋊Q8—471no—
121#407—471no—
122C2×C22⋊C8—471no—
123#324—471no—
124#324—471no—
125#324—471no—
126#324D4711yescharacteristic, complemented
127C47#147211yescharacteristic, complemented, Sylow
128C22×Q8—471no—
129C23×C4—471no—
130C2×M16—941no—
131C22×C8—941no—
132C22⋊Q8—941no—
133C22⋊Q8—941no—
134C22⋊Q8—941no—
135C22⋊Q8—941no—
136C2×C4⋊C4—471no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4C2×D4711yescharacteristic
139C2×C22⋊C4—471no—
140C2×C22⋊C4—471no—
141C22⋊C8—471no—
142C22⋊C8—471no—
143C22⋊C8—941no—
144C22⋊C8—941no—
145C22⋊C8C2×D4711yescharacteristic
146C22⋊C8C2×D4711yescharacteristic
147C24—471no—
148C2×Q8—941no—
149C2×Q8—941no—
150C2×Q8—1882no—
151C22×C4—471no—
152C22×C4—471no—
153C22×C4—471no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—1882no—
159C22×C4C4×D4711yescharacteristic
160C22×C4C4×D4711yescharacteristic
161C22×C4C22×D4711yescharacteristic
162M16—1882no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—941no—
166C2×C8—941no—
167C2×C8—1882no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—941no—
171C4⋊C4—941no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C22⋊C4—941no—
175C22⋊C4—941no—
176C22⋊C4—941no—
177C22⋊C4—941no—
178C23—471no—
179C23—471no—
180C23—942no—
181C23—941no—
182C23—941no—
183C23—1881no—
184C23C2×C4×D4711yescharacteristic
185Q8—1882no—
186Q8—1882no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—471no—
194C2×C4—471no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—941no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4D4×D4711yescharacteristic
206C2×C4D4×D4711yescharacteristic
207C8—41no—
208C8—41no—
209C8—1881no—
210C8—1881no—
211C22—21no—
212C22—21no—
213C22—472no—
214C22—941no—
215C22—941no—
216C22—941no—
217C22—941no—
218C22—941no—
219C22—1882no—
220C22—1882no—
221C22C22⋊C4×D4711yescharacteristic
222C22#1309403011yescharacteristic
223C22#1309403211yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—472no—
229C4—941no—
230C4—1881no—
231C4—1881no—
232C2—21no—
233C2—21no—
234C2—942no—
235C2—1881no—
236C2#1568908811yescharacteristic
237C2#99×D4711yescharacteristic
238C2#101×D4711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#324C2
socleC22×C47C2×C22⋊C4
hypercenter#324D47
hypocenterC47#1472
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
4. #15688849C2semidirect
5. #15688848C2semidirect
6. #15688848C2semidirect
7. C47×#324C2semidirect
126. #324D47semidirect
127. C47#1472semidirect