Finite Group Databasebeta

← #20241948

Subgroups — #20241948

Order 6016.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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
2#15688989C211yesmaximal, characteristic, complemented
3#15688857C214yesmaximal, complemented
4C47×#532C211yesmaximal, characteristic
5C2×C4⋊Dic47—21no—
6C4⋊(C47⋊C8)—21no—
7C22⋊(C47⋊C8)C2212yes—
8C4×C47⋊C8—21no—
9C47⋊#95—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—42no—
41C2×C47⋊C8—22no—
42C23×C47—22no—
43C23×C47C2×D411yescharacteristic
44Q8×C47—42no—
45D4×C47—42no—
46D4×C47—42no—
47D4×C47—42no—
48D4×C47—42no—
49D4×C47—42no—
50C2×C4×C47—22no—
51C2×C4×C47—41no—
52C2×C4×C47—41no—
53C2×C4×C47—44no—
54C2×C4×C47C22⋊C411yescharacteristic
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47D812yes—
59C2×C4×C47SD1612yes—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×Dic47—42no—
63C2×Dic47—42no—
64C2×Dic47—42no—
65C47⋊C8—42no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47—42no—
69C22×C47—42no—
70C22×C47—42no—
71C22×C47C2×C22⋊C411yescharacteristic
72C22×C47C2×D811yescharacteristic
73C22×C47C2×SD1611yescharacteristic
74C4×C47—21no—
75C4×C47—21no—
76C4×C47—21no—
77C4×C47—21no—
78C4×C47—42no—
79C4×C47#10212yes—
80C4×C47#10212yes—
81Dic47—82no—
82#1517—471nomaximal, Sylow
83C2×C47—21no—
84C2×C47—21no—
85C2×C47—82no—
86C2×C47#41011yescharacteristic
87C2×C47C2×#10211yescharacteristic
88C2×C47#42111yescharacteristic
89#532D4711yescharacteristic
90#431—471no—
91#382—471no—
92#327—474no—
93C47#151711yescharacteristic, complemented, Sylow
94C2×#41—21no—
95C4⋊Q8Dic4711yescharacteristic, complemented
96#127Dic4711yescharacteristic, complemented
97#124—21no—
98#121—21no—
99#121C2×D4712yes—
100C4×D4—21no—
101C4×D4Dic4712yescomplemented
102C2×C4⋊C4—941no—
103C2×C42C2×D4711yescharacteristic
104C4⋊C8—941no—
105C22⋊C8—472no—
106C4×C8—941no—
107#95—472no—
108#95—941no—
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×Dic4712yes—
116C22×C4—22no—
117C22×C4—942no—
118C22×C4C22⋊D4711yescharacteristic
119C22×C4C22⋊D4711yescharacteristic
120C22×C4C22×D4711yescharacteristic
121C2×C8—942no—
122C4⋊C4—21no—
123C4⋊C4—1882no—
124C4⋊C4C2×Dic4712yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×Dic4711yescharacteristic
128C42C2×Dic4711yescharacteristic
129C42C22⋊D4711yescharacteristic
130C42C22⋊D4711yescharacteristic
131C23—22no—
132C23C2×C22⋊D4711yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—1882no—
144C2×C4—1882no—
145C2×C4—1882no—
146C2×C4#1062533412yes—
147C2×C4#1062533512yes—
148C2×C4C22⋊Dic4711yescharacteristic
149C2×C4C22⋊Dic4711yescharacteristic
150C2×C4C22⋊Dic4711yescharacteristic
151C2×C4C22⋊Dic4711yescharacteristic
152C2×C4C22×Dic4711yescharacteristic
153C2×C4C2×C22⋊D4711yescharacteristic
154C8—1882no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C22⋊Dic4711yescharacteristic
161C22C2×#1062533411yescharacteristic
162C22C2×#1062533511yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—3762no—
169C4#1309394512yes—
170C4#1309394512yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1568909711yescharacteristic
175C2C2×#1309394511yescharacteristic
176C2#1568914011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#532C2
socleC22×C47C2×C22⋊C4
hypercenter#532D47
hypocenterC47#1517
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #15689176C2semidirect
2. #15688989C2semidirect
3. #15688857C2semidirect
12. C4⋊Q8×C47C4semidirect
13. #127×C47C4semidirect
18. C4×D4×C47C4semidirect
93. C47#1517semidirect
95. C4⋊Q8Dic47semidirect
96. #127Dic47semidirect
101. C4×D4Dic47semidirect