Finite Group Databasebeta

← #20241932

Subgroups — #20241932

Order 6016.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689634C211yesmaximal, characteristic
2#15688983C211yesmaximal, characteristic, complemented
3#15688861C212yesmaximal, complemented
4#15688858C212yesmaximal, complemented
5C47×#407C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic, complemented
7#13094007—21no—
8#13094003C411yescharacteristic, complemented
9#13094003C2211yescharacteristic
10#13093998C411yescharacteristic, complemented
11#13093998C2211yescharacteristic
12#13093993—21no—
13C4×C22⋊D47—21no—
14C4×C22⋊D47—21no—
15#13093983C411yescharacteristic, complemented
16C2×C4⋊Dic47—21no—
17C2×C22⋊Dic47—21no—
18C47⋊#95C2212yes—
19C23×C4×C47C2211yescharacteristic
20C2×M16×C47—21no—
21C22⋊C8×C47—21no—
22C22⋊C8×C47C2212yes—
23C24×C47D411yescharacteristic
24C22×C4×C47—42no—
25C22×C4×C47C2×C411yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—21no—
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C22×Dic47—22no—
35#10625350—42no—
36C2×D188C2×C411yescharacteristic
37C2×C4×D47—21no—
38C2×Dic94C2×C411yescharacteristic
39M16×C47—42no—
40C2×C8×C47—22no—
41C22⋊Dic47—21no—
42C22⋊Dic47—21no—
43C22⋊Dic47—21no—
44C22⋊Dic47—42no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47C4⋊Dic47—42no—
48C4⋊Dic47C2×C411yescharacteristic
49C4⋊Dic47C2×C411yescharacteristic
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C23×C47—21no—
54C23×C47—21no—
55C23×C47—41no—
56C23×C47—41no—
57C23×C47C22⋊C411yescharacteristic
58C23×C47C22⋊C411yescharacteristic
59C23×C47C2×D411yescharacteristic
60C22×D47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C22⋊C411yescharacteristic
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22×C411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C22⋊D47—42no—
72C22⋊D47—42no—
73C22⋊D47—41no—
74C22⋊D47—41no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—42no—
79C2×Dic47—42no—
80C2×Dic47—42no—
81D188—41no—
82C4×D47—42no—
83Dic94—41no—
84C8×C47—42no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47C2×C22⋊C411yescharacteristic
96C22×C47AGL(1,ℤ/8)11yescharacteristic
97C22×C47#13711yescharacteristic
98C2×D47—41no—
99C2×D47—41no—
100C2×D47—41no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47#9912yes—
105Dic47—41no—
106Dic47—41no—
107Dic47—41no—
108Dic47—82no—
109#1513—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—41no—
113C2×C47—41no—
114C2×C47C2×#9911yescharacteristic
115C2×C47#41711yescharacteristic
116C2×C47#42111yescharacteristic
117D47—81no—
118#525—471no—
119#407D4711yescharacteristic, complemented
120#380—471no—
121#328—472no—
122#327—472no—
123C47#151311yescharacteristic, complemented, Sylow
124C2×#41—471no—
125C23×C4C2×D4711yescharacteristic
126C2×M16—21no—
127#123—941no—
128C22⋊Q8—471no—
129C22⋊Q8—471no—
130#121—471no—
131#121—471no—
132#120—941no—
133C4×D4—941no—
134C4×D4—941no—
135#117—471no—
136C2×C4⋊C4—941no—
137C2×C22⋊C4—941no—
138C22⋊C8—21no—
139C22⋊C8C2×D4712yes—
140#95—472no—
141C24D18811yescharacteristic
142#41—1882no—
143C2×Q8—471no—
144C2×D4—471no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C22×C4—42no—
149C22×C4—941no—
150C22×C4—942no—
151C22×C4C4×D4711yescharacteristic
152C22×C4C4×D4711yescharacteristic
153C22×C4D18811yescharacteristic
154C22×C4C22⋊D4711yescharacteristic
155C22×C4C22⋊D4711yescharacteristic
156C22×C4C22×D4711yescharacteristic
157M16—42no—
158C2×C8—22no—
159C4⋊C4—471no—
160C4⋊C4—471no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—1882no—
164C22⋊C4—941no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C22⋊C4—941no—
169C22⋊C4—1882no—
170C42—941no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—941no—
176C23(C2×D47)⋊C411yescharacteristic
177C23(C2×D47)⋊C411yescharacteristic
178C23C2×D18811yescharacteristic
179Q8—1881no—
180D4—1881no—
181D4—1882no—
182D4—1882no—
183D4—1881no—
184D4—1881no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4(C2×D47)⋊C411yescharacteristic
199C2×C4(C2×D47)⋊C411yescharacteristic
200C2×C4C2×C4×D4711yescharacteristic
201C2×C4C2×C22⋊D4711yescharacteristic
202C8—42no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—1881no—
214C22—1881no—
215C22—1881no—
216C22C2×(C2×D47)⋊C411yescharacteristic
217C22#1309405211yescharacteristic
218C22#1309405711yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—3762no—
223C4—1881no—
224C4—1881no—
225C4—1881no—
226C4#1309393812yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—3761no—
232C2C2×#1309393811yescharacteristic
233C2#1568912511yescharacteristic
234C2#1568913911yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#407C2
socleC22×C47C2×C22⋊C4
hypercenter#407D47
hypocenterC47#1513
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #15688983C2semidirect
3. #15688861C2semidirect
4. #15688858C2semidirect
5. C47×#407C2semidirect
6. C2×#10625350C4semidirect
8. #13094003C4semidirect
10. #13093998C4semidirect
15. #13093983C4semidirect
119. #407D47semidirect
123. C47#1513semidirect