Finite Group Databasebeta

← #20251651

Subgroups — #20251651

Order 6016.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689060C211yesmaximal, characteristic, complemented
2#15689058C213yesmaximal, complemented
3#15689047C211yesmaximal, characteristic, complemented
4#15689046C213yesmaximal, complemented
5#15689045C213yesmaximal, complemented
6#15688978C213yesmaximal
7C47×#396C211yesmaximal, characteristic, complemented
8C24×D47C2211yescharacteristic
9C2×C4⋊Dic47C2213yescomplemented
10C2×Dic47⋊C4C2213yescomplemented
11C2×Dic47⋊C4C2213yescomplemented
12C2×C22⋊Dic47C2213yes—
13C2×(C2×D47)⋊C4C2213yes—
14C2×(C2×D47)⋊C4C2213yes—
15C2×(C2×D47)⋊C4C2213yes—
16C2×(C2×D47)⋊C4C2213yes—
17C47⋊#95C2213yescomplemented
18C2×C4⋊C4×C47C2213yescomplemented
19C2×C22⋊C4×C47C2213yes—
20#95×C47C2211yescharacteristic, complemented
21C24×C47C2311yescharacteristic
22C23×D47—43no—
23C23×D47—43no—
24C23×D47Q814yes—
25C23×D47C2311yescharacteristic
26C23×D47C2311yescharacteristic
27C22×C4×C47C2313yes—
28C22×C4×C47C2313yes—
29C22×Dic47C2313yes—
30C22×Dic47C2313yes—
31C4⋊C4×C47—43no—
32C22⋊C4×C47—43no—
33C22⋊Dic47—43no—
34(C2×D47)⋊C4—43no—
35(C2×D47)⋊C4—43no—
36(C2×D47)⋊C4—43no—
37(C2×D47)⋊C4—43no—
38C4⋊Dic47—43no—
39Dic47⋊C4—43no—
40Dic47⋊C4—43no—
41C23×C47—23no—
42C23×C47—23no—
43C23×C47C2×Q812yes—
44C23×C47C2411yescharacteristic
45C22×D47—23no—
46C22×D47—23no—
47C22×D47—23no—
48C22×D47—23no—
49C22×D47—412no—
50C22×D47—412no—
51C22×D47—44no—
52C22×D47C2×Q812yes—
53C22×D47C2×Q812yes—
54C2×C4×C47—23no—
55C2×C4×C47—23no—
56C2×C4×C47—23no—
57C2×C4×C47—23no—
58C2×C4×C47—23no—
59C2×C4×C47—23no—
60C2×Dic47—23no—
61C2×Dic47—23no—
62C2×Dic47—23no—
63C2×Dic47—23no—
64C2×Dic47—23no—
65C2×Dic47—23no—
66C22×C47—26no—
67C22×C47—43no—
68C22×C47—41no—
69C22×C47C22×Q811yescharacteristic
70C22×C47H(5,𝔽2)13yes—
71C22×C47H(5,𝔽2)13yes—
72C2×D47—26no—
73C2×D47—26no—
74C2×D47—416no—
75C2×D47—43no—
76C2×D47—43no—
77C2×D47—41no—
78C2×D47—41no—
79C4×C47—43no—
80C4×C47—43no—
81Dic47—43no—
82Dic47—43no—
83#2842—471nomaximal, Sylow
84C2×C47—42no—
85C2×C47#54313yes—
86C2×C47#56013yes—
87C2×C47#56011yescharacteristic
88D47—42no—
89D47—42no—
90#399—473no—
91#399—471no—
92#396—473no—
93#396—473no—
94#396—471no—
95#396D4711yescharacteristic, complemented
96#379—473no—
97C47#284211yescharacteristic, complemented, Sylow
98C25—471no—
99C2×C4⋊C4—473no—
100C2×C4⋊C4—473no—
101C2×C4⋊C4—473no—
102C2×C4⋊C4C2×D4713yescomplemented
103C2×C22⋊C4—473no—
104C2×C22⋊C4—473no—
105C2×C22⋊C4—473no—
106C2×C22⋊C4—473no—
107C2×C22⋊C4—473no—
108C2×C22⋊C4C2×D4713yes—
109#95—473no—
110#95C2×D4711yescharacteristic, complemented
111C24—471no—
112C24—471no—
113C24—474no—
114C24—1883no—
115C24—1883no—
116C24C22×D4711yescharacteristic
117C22×C4—473no—
118C22×C4—473no—
119C22×C4C22×D4713yes—
120C22×C4C22×D4713yes—
121C4⋊C4—43no—
122C4⋊C4—1883no—
123C4⋊C4—1883no—
124C4⋊C4—1883no—
125C22⋊C4—43no—
126C22⋊C4—1883no—
127C22⋊C4—1883no—
128C22⋊C4—1883no—
129C22⋊C4—1883no—
130C22⋊C4—1883no—
131C23—23no—
132C23—23no—
133C23—472no—
134C23—472no—
135C23—943no—
136C23—943no—
137C23—943no—
138C23—943no—
139C23—18812no—
140C23—18812no—
141C23—1884no—
142C23Q8×D4712yes—
143C23C23×D4711yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—943no—
151C2×C4—943no—
152C2×C4—943no—
153C2×C4—943no—
154C2×C4—943no—
155C2×C4—943no—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—946no—
160C22—946no—
161C22—18816no—
162C22—1883no—
163C22—1883no—
164C22—1881no—
165C22—1881no—
166C22C2×Q8×D4711yescharacteristic
167C22#1309406913yes—
168C22#1309407013yes—
169C4—43no—
170C4—43no—
171C4—1883no—
172C4—1883no—
173C2—42no—
174C2—1882no—
175C2—1882no—
176C2#1568974813yes—
177C2#1568986113yes—
178C2#1568986411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#396C2
hypercenter#396D47
hypocenterC47#2842
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #15689060C2semidirect
2. #15689058C2semidirect
3. #15689047C2semidirect
4. #15689046C2semidirect
5. #15689045C2semidirect
7. C47×#396C2semidirect
9. C2×C4⋊Dic47C22semidirect
10. C2×Dic47⋊C4C22semidirect
11. C2×Dic47⋊C4C22semidirect
17. C47⋊#95C22semidirect
18. C2×C4⋊C4×C47C22semidirect
20. #95×C47C22semidirect
95. #396D47semidirect
97. C47#2842semidirect
102. C2×C4⋊C4C2×D47semidirect
110. #95C2×D47semidirect