Finite Group Databasebeta

← #20241884

Subgroups — #20241884

Order 6016.

284 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
3#15688858C214yesmaximal, complemented
4C47×#431C211yesmaximal, characteristic, complemented
5C2×#10625350—21no—
6#13094024C411yescharacteristic, complemented
7#13094021C411yescharacteristic, complemented
8#13094012—21no—
9#13093998—21no—
10#13093998C2212yes—
11C4×D188—21no—
12C4×D188C412yescomplemented
13C2×C4⋊Dic47—21no—
14C2×C4×Dic47—21no—
15C47⋊#95C2212yes—
16C2×C42×C47C2211yescharacteristic
17C4⋊C8×C47—21no—
18C22⋊C8×C47C2212yes—
19C4×C8×C47—21no—
20C22×C4×C47D411yescharacteristic
21C22×C4×C47D411yescharacteristic
22C22×C4×C47C2311yescharacteristic
23C2×C22⋊D47—22no—
24C22×Dic47—22no—
25#10625350—42no—
26#10625350—42no—
27C2×D188—21no—
28C2×D188—21no—
29C2×D188C2×C412yes—
30C2×C4×D47—22no—
31C2×Dic94—21no—
32C2×C8×C47—22no—
33C42×C47C2×C411yescharacteristic
34C42×C47C2×C411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4⋊Dic47—24no—
40C4⋊Dic47—21no—
41C4⋊Dic47C2×C412yes—
42C4×Dic47—42no—
43C23×C47C2×D411yescharacteristic
44C22×D47—22no—
45C2×C4×C47—22no—
46C2×C4×C47—41no—
47C2×C4×C47C22⋊C411yescharacteristic
48C2×C4×C47C22⋊C411yescharacteristic
49C2×C4×C47C22⋊C411yescharacteristic
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47D812yes—
52C2×C4×C47SD1612yes—
53C2×C4×C47C22×C411yescharacteristic
54C2×C4×C47C2×D411yescharacteristic
55C22⋊D47—42no—
56C22⋊D47—42no—
57C2×Dic47—24no—
58C2×Dic47—22no—
59C2×Dic47—42no—
60C2×Dic47—42no—
61D188—42no—
62D188—42no—
63D188—42no—
64C4×D47—44no—
65Dic94—42no—
66C8×C47—42no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47C2×C22⋊C411yescharacteristic
70C22×C47C2×D811yescharacteristic
71C22×C47C2×SD1611yescharacteristic
72C2×D47—42no—
73C2×D47—42no—
74C2×D47—42no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47#10212yes—
79C4×C47#10212yes—
80C4×C47#10412yes—
81Dic47—44no—
82Dic47—42no—
83#1502—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—21no—
86C2×C47#41011yescharacteristic
87C2×C47C2×#10211yescharacteristic
88C2×C47C2×#10411yescharacteristic
89D47—82no—
90#532—471no—
91#431D4711yescharacteristic, complemented
92C4×C4⋊C4—471no—
93#327—474no—
94C47#150211yescharacteristic, complemented, Sylow
95C2×#41—941no—
96C4⋊Q8—471no—
97#127—471no—
98#124—941no—
99#121—472no—
100#121—941no—
101C4×D4—472no—
102C4×D4—941no—
103C2×C4⋊C4—941no—
104C2×C42—941no—
105C2×C42C2×D4711yescharacteristic
106C4⋊C8—21no—
107C22⋊C8C2×D4712yes—
108C4×C8—21no—
109#95—472no—
110#41—1882no—
111#41—1882no—
112C2×Q8—941no—
113C2×D4—472no—
114C2×D4—942no—
115C2×D4—941no—
116C2×D4—941no—
117C22×C4—942no—
118C22×C4—942no—
119C22×C4D18811yescharacteristic
120C22×C4D18811yescharacteristic
121C22×C4C22×D4711yescharacteristic
122C2×C8—22no—
123C4⋊C4—472no—
124C4⋊C4—944no—
125C4⋊C4—941no—
126C22⋊C4—942no—
127C22⋊C4—942no—
128C42—1882no—
129C42C4×D4711yescharacteristic
130C42C4×D4711yescharacteristic
131C42C22⋊D4711yescharacteristic
132C42C22⋊D4711yescharacteristic
133C23—942no—
134C23C2×D18811yescharacteristic
135Q8—1882no—
136D4—1882no—
137D4—1882no—
138D4—1882no—
139D4—1882no—
140D4—1882no—
141C2×C4—22no—
142C2×C4—41no—
143C2×C4—944no—
144C2×C4—942no—
145C2×C4—1882no—
146C2×C4—1882no—
147C2×C4—1884no—
148C2×C4#1062532512yes—
149C2×C4D37612yes—
150C2×C4(C2×D47)⋊C411yescharacteristic
151C2×C4(C2×D47)⋊C411yescharacteristic
152C2×C4(C2×D47)⋊C411yescharacteristic
153C2×C4(C2×D47)⋊C411yescharacteristic
154C2×C4C2×C4×D4711yescharacteristic
155C2×C4C2×C22⋊D4711yescharacteristic
156C8—42no—
157C22—21no—
158C22—21no—
159C22—1882no—
160C22—1882no—
161C22—1882no—
162C22C2×(C2×D47)⋊C411yescharacteristic
163C22C2×D37611yescharacteristic
164C22C2×#1062532511yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—1884no—
169C4—1882no—
170C4#1309394612yes—
171C4#1309394612yes—
172C4#1309395012yes—
173C2—21no—
174C2—21no—
175C2—3762no—
176C2#1568909611yescharacteristic
177C2C2×#1309394611yescharacteristic
178C2C2×#1309395011yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#431C2
socleC22×C47C2×C22⋊C4
hypercenter#431D47
hypocenterC47#1502
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic47C2semidirect
3. #15688858C2semidirect
4. C47×#431C2semidirect
6. #13094024C4semidirect
7. #13094021C4semidirect
12. C4×D188C4semidirect
91. #431D47semidirect
94. C47#1502semidirect