Finite Group Databasebeta

← #20241728

Subgroups — #20241728

Order 6016.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×D188C211yesmaximal, characteristic
2#15689180C211yesmaximal, characteristic, complemented
3#15688846C214yesmaximal, complemented
4C47×#432C211yesmaximal, characteristic, complemented
5C22×D188C411yescharacteristic
6C22×C4×D47C412yes—
7C4×D188—21no—
8C4×D188—21no—
9C4×D188—21no—
10C4×D188—21no—
11C2×C4⋊Dic47C411yescharacteristic
12C2×(C2×D47)⋊C4C2212yes—
13C4⋊(C47⋊C8)—21no—
14C22⋊(C47⋊C8)C2212yes—
15#13093935—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—24no—
26C2×D188—21no—
27C2×D188—21no—
28C2×C4×D47—22no—
29C2×C4×D47—22no—
30C2×C4×D47—44no—
31C2×C8×C47—22no—
32C42×C47D411yescharacteristic
33C42×C47D411yescharacteristic
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36(C2×D47)⋊C4—22no—
37(C2×D47)⋊C4—22no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C2×C47⋊C8—22no—
41C23×C47C22×C411yescharacteristic
42C22×D47—22no—
43C22×D47—22no—
44C22×D47—42no—
45C22×D47—42no—
46C22×D47M1614yes—
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—24no—
59D188—24no—
60C4×D47—44no—
61C4×D47—44no—
62C8×C47—42no—
63C47⋊C8—42no—
64C22×C47—21no—
65C22×C47—21no—
66C22×C47C2×C22⋊C411yescharacteristic
67C22×C47C2×M1612yes—
68C2×D47—24no—
69C2×D47—44no—
70C2×D47—42no—
71C2×D47—42no—
72C2×D47—44no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47#10012yes—
79Dic47—42no—
80#1466—471nomaximal, Sylow
81C2×C47—22no—
82C2×C47#40711yescharacteristic
83C2×C47#41011yescharacteristic
84C2×C47C2×#10011yescharacteristic
85D47—44no—
86C2×C4×D4—471no—
87#432—471no—
88#432D4711yescharacteristic, complemented
89#323—474no—
90C47#146611yescharacteristic, complemented, Sylow
91C22×D4—471no—
92C23×C4—472no—
93C4×D4—941no—
94C4×D4—941no—
95C4×D4—941no—
96C4×D4—941no—
97C2×C4⋊C4—471no—
98C2×C22⋊C4—472no—
99C2×C42C2×D4711yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—941no—
102C22⋊C8—472no—
103C22⋊C8C2×D4712yes—
104#97—21no—
105#97—941no—
106C24—472no—
107C2×D4—944no—
108C2×D4—941no—
109C2×D4—941no—
110C22×C4—472no—
111C22×C4—942no—
112C22×C4—942no—
113C22×C4—1884no—
114C22×C4C4×D4711yescharacteristic
115C22×C4C4×D4711yescharacteristic
116C22×C4C22×D4711yescharacteristic
117C2×C8—22no—
118C2×C8—942no—
119C4⋊C4—941no—
120C4⋊C4—941no—
121C22⋊C4—942no—
122C22⋊C4—942no—
123C42D18811yescharacteristic
124C42D18811yescharacteristic
125C42C22⋊D4711yescharacteristic
126C42C22⋊D4711yescharacteristic
127C23—474no—
128C23—942no—
129C23—942no—
130C23—1882no—
131C23—1882no—
132C23C2×C4×D4711yescharacteristic
133D4—944no—
134D4—944no—
135C2×C4—22no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—942no—
139C2×C4—1884no—
140C2×C4—1884no—
141C2×C4—1882no—
142C2×C4(C2×D47)⋊C411yescharacteristic
143C2×C4(C2×D47)⋊C411yescharacteristic
144C2×C4(C2×D47)⋊C411yescharacteristic
145C2×C4(C2×D47)⋊C411yescharacteristic
146C2×C4C2×D18811yescharacteristic
147C2×C4C2×C22⋊D4711yescharacteristic
148C8—42no—
149C8—1882no—
150C22—21no—
151C22—21no—
152C22—944no—
153C22—1884no—
154C22—1884no—
155C22—1882no—
156C22—1882no—
157C22C2×(C2×D47)⋊C411yescharacteristic
158C22M16×D4712yes—
159C4—21no—
160C4—21no—
161C4—21no—
162C4—21no—
163C4—21no—
164C4—1882no—
165C4#1309394012yes—
166C2—22no—
167C2—1884no—
168C2#1568908611yescharacteristic
169C2#1568909611yescharacteristic
170C2C2×#1309394011yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#432C2
socleC22×C47C2×C22⋊C4
hypercenter#432D47
hypocenterC47#1466
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. #15689180C2semidirect
3. #15688846C2semidirect
4. C47×#432C2semidirect
88. #432D47semidirect
90. C47#1466semidirect