Finite Group Databasebeta

← #20241883

Subgroups — #20241883

Order 6016.

284 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 97 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#15689176C211yesmaximal, characteristic, complemented
2C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
3#15688857C214yesmaximal, complemented
4C47×#532C211yesmaximal, characteristic
5C2×C4⋊Dic47—21no—
6C2×C4×Dic47—21no—
7C4⋊(C47⋊C8)—21no—
8C22⋊(C47⋊C8)C2212yes—
9C4×C47⋊C8—21no—
10C47⋊#95C2212yes—
11C2×#41×C47—21no—
12C4⋊Q8×C47C411yescharacteristic, complemented
13#127×C47C411yescharacteristic, complemented
14#124×C47—21no—
15#121×C47—21no—
16#121×C47C2212yes—
17C4×D4×C47—21no—
18C4×D4×C47C412yescomplemented
19C2×C42×C47C2211yescharacteristic
20#41×C47—42no—
21#41×C47—42no—
22C2×Q8×C47—21no—
23C2×D4×C47—22no—
24C2×D4×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47C2×C412yes—
27C22×C4×C47—22no—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—22no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47C2×C412yes—
34C22⋊C4×C47—22no—
35C22⋊C4×C47—22no—
36C42×C47C2×C411yescharacteristic
37C42×C47C2×C411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47D411yescharacteristic
40C4⋊Dic47—24no—
41C4×Dic47—42no—
42C2×C47⋊C8—22no—
43C23×C47—22no—
44C23×C47C2×D411yescharacteristic
45Q8×C47—42no—
46D4×C47—42no—
47D4×C47—42no—
48D4×C47—42no—
49D4×C47—42no—
50D4×C47—42no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47—44no—
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47D812yes—
60C2×C4×C47SD1612yes—
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×Dic47—24no—
64C2×Dic47—42no—
65C2×Dic47—42no—
66C47⋊C8—42no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47—42no—
70C22×C47—42no—
71C22×C47—42no—
72C22×C47C2×C22⋊C411yescharacteristic
73C22×C47C2×D811yescharacteristic
74C22×C47C2×SD1611yescharacteristic
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—42no—
79C4×C47#10212yes—
80C4×C47#10212yes—
81C4×C47#10412yes—
82Dic47—44no—
83#1502—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—21no—
86C2×C47—82no—
87C2×C47#41011yescharacteristic
88C2×C47C2×#10211yescharacteristic
89C2×C47C2×#10411yescharacteristic
90#532D4711yescharacteristic
91#431—471no—
92C4×C4⋊C4—471no—
93#327—474no—
94C47#150211yescharacteristic, complemented, Sylow
95C2×#41—21no—
96C4⋊Q8Dic4711yescharacteristic, complemented
97#127Dic4711yescharacteristic, complemented
98#124—21no—
99#121—21no—
100#121C2×D4712yes—
101C4×D4—21no—
102C4×D4Dic4712yescomplemented
103C2×C4⋊C4—941no—
104C2×C42—941no—
105C2×C42C2×D4711yescharacteristic
106C4⋊C8—941no—
107C22⋊C8—472no—
108C4×C8—941no—
109#95—472no—
110#41—42no—
111#41—42no—
112C2×Q8—21no—
113C2×D4—22no—
114C2×D4—21no—
115C2×D4—21no—
116C2×D4C2×Dic4712yes—
117C22×C4—22no—
118C22×C4—942no—
119C22×C4C22⋊D4711yescharacteristic
120C22×C4C22⋊D4711yescharacteristic
121C22×C4C22×D4711yescharacteristic
122C2×C8—942no—
123C4⋊C4—21no—
124C4⋊C4—944no—
125C4⋊C4C2×Dic4712yes—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C42—1882no—
129C42C2×Dic4711yescharacteristic
130C42C2×Dic4711yescharacteristic
131C42C22⋊D4711yescharacteristic
132C42C22⋊D4711yescharacteristic
133C23—22no—
134C23C2×C22⋊D4711yescharacteristic
135Q8—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—42no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—44no—
145C2×C4—944no—
146C2×C4—1882no—
147C2×C4—1882no—
148C2×C4#1062533412yes—
149C2×C4#1062533512yes—
150C2×C4C22⋊Dic4711yescharacteristic
151C2×C4C22⋊Dic4711yescharacteristic
152C2×C4C22⋊Dic4711yescharacteristic
153C2×C4C22⋊Dic4711yescharacteristic
154C2×C4C22×Dic4711yescharacteristic
155C2×C4C2×C22⋊D4711yescharacteristic
156C8—1882no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22C2×C22⋊Dic4711yescharacteristic
163C22C2×#1062533411yescharacteristic
164C22C2×#1062533511yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—42no—
169C4—1884no—
170C4#1309394512yes—
171C4#1309394512yes—
172C4#1309395112yes—
173C2—21no—
174C2—21no—
175C2—82no—
176C2#1568909711yescharacteristic
177C2C2×#1309394511yescharacteristic
178C2C2×#1309395111yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#532C2
socleC22×C47C2×C22⋊C4
hypercenter#532D47
hypocenterC47#1502
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689176C2semidirect
2. C4×C4⋊Dic47C2semidirect
3. #15688857C2semidirect
12. C4⋊Q8×C47C4semidirect
13. #127×C47C4semidirect
18. C4×D4×C47C4semidirect
94. C47#1502semidirect
96. C4⋊Q8Dic47semidirect
97. #127Dic47semidirect
102. C4×D4Dic47semidirect