Finite Group Databasebeta

← #20241741

Subgroups — #20241741

Order 6016.

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

normal subgroups only

This group has 256 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
2#15689176C211yesmaximal, characteristic, complemented
3#15688846C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic, complemented
5C22×Dic94C411yescharacteristic
6C22×D188C411yescharacteristic
7#13094012—21no—
8#13094012—21no—
9#13094012—21no—
10#13094012—21no—
11C2×(C2×D47)⋊C4C412yes—
12C2×(C2×D47)⋊C4C2212yes—
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)C2212yes—
15C4×C47⋊C8—21no—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47C2212yes—
19#97×C47—21no—
20C23×D47C2×C412yes—
21C22×C4×C47C2×C411yescharacteristic
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47C2×C412yes—
25C2×D188—21no—
26C2×D188—21no—
27C2×D188—42no—
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—42no—
31C2×C8×C47—22no—
32C42×C47D411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—22no—
40C2×C47⋊C8—22no—
41C23×C47C22×C411yescharacteristic
42C22×D47—22no—
43C22×D47—24no—
44C22×D47—42no—
45C22×D47—42no—
46C2×C4×C47—22no—
47C2×C4×C47—22no—
48C2×C4×C47—41no—
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C2×Dic47—22no—
56C2×Dic47—42no—
57D188—42no—
58D188—42no—
59Dic94—42no—
60Dic94—42no—
61C8×C47—42no—
62C47⋊C8—42no—
63C22×C47—21no—
64C22×C47—21no—
65C22×C47C2×C22⋊C411yescharacteristic
66C22×C47#13112yes—
67C2×D47—42no—
68C2×D47—42no—
69C2×D47—42no—
70C2×D47—84no—
71C4×C47—21no—
72C4×C47—21no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47#10012yes—
77Dic47—42no—
78#1469—471nomaximal, Sylow
79C2×C47—22no—
80C2×C47#40811yescharacteristic
81C2×C47#41011yescharacteristic
82C2×C47C2×#10011yescharacteristic
83D47—82no—
84C2×#124—471no—
85#432D4711yescharacteristic, complemented
86#431—471no—
87#323—474no—
88C47#146911yescharacteristic, complemented, Sylow
89C22×Q8—471no—
90C22×D4—471no—
91#124—941no—
92#124—941no—
93#124—941no—
94#124—941no—
95C2×C22⋊C4—472no—
96C2×C22⋊C4—472no—
97C2×C42C2×D4711yescharacteristic
98C4⋊C8—21no—
99C4⋊C8—941no—
100C22⋊C8—472no—
101C22⋊C8C2×D4712yes—
102#97—21no—
103C4×C8—941no—
104C24—472no—
105C2×Q8—941no—
106C2×Q8—941no—
107C2×Q8—1882no—
108C2×D4—941no—
109C2×D4—941no—
110C2×D4—1882no—
111C22×C4—472no—
112C22×C4C4×D4711yescharacteristic
113C22×C4C4×D4711yescharacteristic
114C22×C4C22×D4711yescharacteristic
115C2×C8—22no—
116C2×C8—942no—
117C22⋊C4—942no—
118C22⋊C4—942no—
119C22⋊C4—942no—
120C22⋊C4—942no—
121C42D18811yescharacteristic
122C42D18811yescharacteristic
123C42C22⋊D4711yescharacteristic
124C42C22⋊D4711yescharacteristic
125C23—944no—
126C23—942no—
127C23—1882no—
128C23—1882no—
129C23C2×C4×D4711yescharacteristic
130Q8—1882no—
131Q8—1882no—
132D4—1882no—
133D4—1882no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—942no—
138C2×C4—1882no—
139C2×C4(C2×D47)⋊C411yescharacteristic
140C2×C4(C2×D47)⋊C411yescharacteristic
141C2×C4(C2×D47)⋊C411yescharacteristic
142C2×C4(C2×D47)⋊C411yescharacteristic
143C2×C4C2×D18811yescharacteristic
144C2×C4C2×C22⋊D4711yescharacteristic
145C8—42no—
146C8—1882no—
147C22—21no—
148C22—21no—
149C22—3764no—
150C22—1882no—
151C22—1882no—
152C22—1882no—
153C22C2×(C2×D47)⋊C411yescharacteristic
154C22#1309403212yes—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—1882no—
161C4#1309394012yes—
162C2—22no—
163C2—3762no—
164C2#1568909111yescharacteristic
165C2#1568909611yescharacteristic
166C2C2×#1309394011yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1469
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #15689176C2semidirect
3. #15688846C2semidirect
4. C47×#432C2semidirect
85. #432D47semidirect
88. C47#1469semidirect