Finite Group Databasebeta

← #20241934

Subgroups — #20241934

Order 6016.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689673C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688856C214yesmaximal, complemented
4C47×#383C211yesmaximal, characteristic, complemented
5C2×#10625350—21no—
6#13094024C411yescharacteristic, complemented
7#13094021C411yescharacteristic, complemented
8#13094012—21no—
9#13093998—21no—
10#13093998C2212yes—
11C4×D188—21no—
12C4×D188C412yescomplemented
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)C2212yes—
15#13093935—21no—
16C2×C42×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47—21no—
19#95×C47C2212yes—
20C22×C4×C47—22no—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C2×C22⋊D47—22no—
25#10625350—44no—
26C2×D188—21no—
27C2×D188—21no—
28C2×D188C2×C412yes—
29C2×C4×D47—22no—
30C2×Dic94—21no—
31C42×C47C2×C411yescharacteristic
32C42×C47C2×C411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4⋊Dic47—21no—
38C4⋊Dic47C2×C412yes—
39C2×C47⋊C8—22no—
40C23×C47C2×D411yescharacteristic
41C22×D47—22no—
42C2×C4×C47—22no—
43C2×C4×C47—41no—
44C2×C4×C47—41no—
45C2×C4×C47—42no—
46C2×C4×C47—42no—
47C2×C4×C47—42no—
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22×C411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C22⋊D47—44no—
55C2×Dic47—22no—
56D188—42no—
57D188—42no—
58D188—42no—
59C4×D47—44no—
60Dic94—42no—
61C47⋊C8—42no—
62C22×C47—21no—
63C22×C47—21no—
64C22×C47C2×C22⋊C411yescharacteristic
65C22×C47AGL(1,ℤ/8)12yes—
66C2×D47—42no—
67C2×D47—42no—
68C2×D47—42no—
69C4×C47—21no—
70C4×C47—21no—
71C4×C47—21no—
72C4×C47—21no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—82no—
76Dic47—42no—
77#1514—471nomaximal, Sylow
78C2×C47—22no—
79C2×C47#41011yescharacteristic
80C2×C47#41811yescharacteristic
81C2×C47#42111yescharacteristic
82D47—82no—
83#532—471no—
84#432—471no—
85#383D4711yescharacteristic, complemented
86#327—474no—
87C47#151411yescharacteristic, complemented, Sylow
88C2×#41—941no—
89C4⋊Q8—471no—
90#127—471no—
91#124—941no—
92#121—472no—
93#121—941no—
94C4×D4—472no—
95C4×D4—941no—
96C2×C42C2×D4711yescharacteristic
97C4⋊C8—941no—
98C22⋊C8—472no—
99#97—941no—
100#95—21no—
101#95—21no—
102#95C2×D4712yes—
103#41—1884no—
104C2×Q8—941no—
105C2×D4—472no—
106C2×D4—942no—
107C2×D4—941no—
108C2×D4—941no—
109C22×C4—22no—
110C22×C4—942no—
111C22×C4C22⋊D4711yescharacteristic
112C22×C4C22⋊D4711yescharacteristic
113C22×C4C22×D4711yescharacteristic
114C2×C8—942no—
115C4⋊C4—472no—
116C4⋊C4—941no—
117C22⋊C4—942no—
118C22⋊C4—942no—
119C42C4×D4711yescharacteristic
120C42C4×D4711yescharacteristic
121C42D18811yescharacteristic
122C42D18811yescharacteristic
123C23—942no—
124C23C2×C22⋊D4711yescharacteristic
125Q8—1882no—
126D4—1882no—
127D4—1882no—
128D4—1882no—
129D4—1884no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—42no—
135C2×C4—42no—
136C2×C4—942no—
137C2×C4—1884no—
138C2×C4(C2×D47)⋊C411yescharacteristic
139C2×C4(C2×D47)⋊C411yescharacteristic
140C2×C4(C2×D47)⋊C411yescharacteristic
141C2×C4(C2×D47)⋊C411yescharacteristic
142C2×C4C2×C4×D4711yescharacteristic
143C2×C4C2×D18811yescharacteristic
144C8—1882no—
145C22—21no—
146C22—21no—
147C22—1882no—
148C22—1882no—
149C22—1882no—
150C22C2×(C2×D47)⋊C411yescharacteristic
151C22#1309404912yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—82no—
159C4—1882no—
160C2—22no—
161C2—3762no—
162C2#1568909611yescharacteristic
163C2#1568912711yescharacteristic
164C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#383C2
socleC22×C47C2×C22⋊C4
hypercenter#383D47
hypocenterC47#1514
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #15689180C2semidirect
3. #15688856C2semidirect
4. C47×#383C2semidirect
6. #13094024C4semidirect
7. #13094021C4semidirect
12. C4×D188C4semidirect
85. #383D47semidirect
87. C47#1514semidirect