Finite Group Databasebeta

← #20241987

Subgroups — #20241987

Order 6016.

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

normal subgroups only

This group has 264 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
1C2×#13094012C211yesmaximal, characteristic
2C4×#10625329C211yesmaximal, characteristic, complemented
3#15688862C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic, complemented
5C22×Dic94C411yescharacteristic
6C22×D188C411yescharacteristic
7C2×#10625329—21no—
8#13094012—21no—
9#13094012—21no—
10#13094012C412yes—
11#13094012C2212yes—
12C2×(C2×D47)⋊C4—21no—
13C2×(C2×D47)⋊C4—21no—
14#13093935C2212yescomplemented
15C4×C47⋊C8—21no—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47—21no—
19#97×C47C2212yescomplemented
20C23×D47—21no—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×Dic47—21no—
25C2×D188—21no—
26C2×D188—42no—
27C2×D188C2×C412yes—
28C2×Dic94—21no—
29C2×Dic94—42no—
30C2×Dic94C2×C412yes—
31C2×C8×C47—22no—
32C42×C47C2×C411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47C2311yescharacteristic
36(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40#10625329—24no—
41C2×C47⋊C8—22no—
42C23×C47C22⋊C411yescharacteristic
43C22×D47—22no—
44C22×D47—42no—
45C22×D47—42no—
46C22×D47—42no—
47C2×C4×C47—22no—
48C2×C4×C47—22no—
49C2×C4×C47—41no—
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×Dic47—22no—
57C2×Dic47—42no—
58D188—42no—
59D188—42no—
60Dic94—42no—
61Dic94—42no—
62C8×C47—42no—
63C47⋊C8—24no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47#10412yes—
67C22×C47C2×C22⋊C411yescharacteristic
68C2×D47—42no—
69C2×D47—42no—
70C2×D47—42no—
71C2×D47—84no—
72C4×C47—21no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47#10012yes—
78Dic47—42no—
79#1527—471nomaximal, Sylow
80C2×C47—22no—
81C2×C47C2×#10011yescharacteristic
82C2×C47C2×#10411yescharacteristic
83C2×C47#42111yescharacteristic
84D47—82no—
85C2×#124—471no—
86#432D4711yescharacteristic, complemented
87C4×M16—471no—
88#329—474no—
89C47#152711yescharacteristic, complemented, Sylow
90C22×Q8—471no—
91C22×D4—471no—
92C2×M16—941no—
93#124—472no—
94#124—472no—
95#124—941no—
96#124—941no—
97C2×C22⋊C4—941no—
98C2×C22⋊C4—941no—
99C2×C42C2×D4711yescharacteristic
100C4⋊C8—21no—
101C22⋊C8—21no—
102#97—472no—
103#97C2×D4712yescomplemented
104C4×C8—941no—
105C24—941no—
106C2×Q8—472no—
107C2×Q8—941no—
108C2×Q8—1882no—
109C2×D4—472no—
110C2×D4—941no—
111C2×D4—1882no—
112C22×C4—941no—
113C22×C4C4×D4711yescharacteristic
114C22×C4D18811yescharacteristic
115C22×C4C22⋊D4711yescharacteristic
116M16—944no—
117C2×C8—22no—
118C2×C8—942no—
119C22⋊C4—942no—
120C22⋊C4—942no—
121C22⋊C4—942no—
122C22⋊C4—942no—
123C42C4×D4711yescharacteristic
124C42D18811yescharacteristic
125C42C22⋊D4711yescharacteristic
126C42C22×D4711yescharacteristic
127C23—942no—
128C23—1882no—
129C23—1882no—
130C23—1882no—
131C23(C2×D47)⋊C411yescharacteristic
132Q8—1882no—
133Q8—1882no—
134D4—1882no—
135D4—1882no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—41no—
139C2×C4—942no—
140C2×C4—1882no—
141C2×C4(C2×D47)⋊C411yescharacteristic
142C2×C4(C2×D47)⋊C411yescharacteristic
143C2×C4(C2×D47)⋊C411yescharacteristic
144C2×C4C2×C4×D4711yescharacteristic
145C2×C4C2×D18811yescharacteristic
146C2×C4C2×C22⋊D4711yescharacteristic
147C8—42no—
148C8—944no—
149C22—21no—
150C22—21no—
151C22—3764no—
152C22—1882no—
153C22—1882no—
154C22—1882no—
155C22#1309395012yes—
156C22C2×(C2×D47)⋊C411yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—1882no—
163C4#1309394012yes—
164C2—22no—
165C2—3762no—
166C2C2×#1309394011yescharacteristic
167C2C2×#1309395011yescharacteristic
168C2#1568914111yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1527
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#10625329C2semidirect
3. #15688862C2semidirect
4. C47×#432C2semidirect
14. #13093935C22semidirect
19. #97×C47C22semidirect
86. #432D47semidirect
89. C47#1527semidirect
103. #97C2×D47semidirect