Finite Group Databasebeta

← #20241771

Subgroups — #20241771

Order 6016.

276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C4×#10625350C211yesmaximal, characteristic
2#15689176C211yesmaximal, characteristic, complemented
3#15688855C212yesmaximal, complemented
4#15688852C212yesmaximal, complemented
5C2×C4×C8×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C411yescharacteristic
7C4×Dic94C411yescharacteristic
8C4×Dic94C2211yescharacteristic
9C4×D188C411yescharacteristic
10C4×D188C2211yescharacteristic
11C4×C22⋊D47—21no—
12C4×C22⋊D47—21no—
13#13093983C411yescharacteristic
14#13093981—21no—
15C42×D47—21no—
16C4⋊(C47⋊C8)C2212yes—
17C22⋊(C47⋊C8)—21no—
18C4×C47⋊C8—21no—
19C22×C8×C47—21no—
20C2×C42×C47C2211yescharacteristic
21C4×C8×C47—21no—
22C4×C8×C47C2212yes—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C2×C22⋊D47—21no—
27#10625350—22no—
28#10625350C814yescomplemented
29C2×D188C2×C411yescharacteristic
30C2×C4×D47—21no—
31C2×C4×D47—21no—
32C2×C4×D47—21no—
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—24no—
35C2×C8×C47—22no—
36C42×C47C2×C411yescharacteristic
37C42×C47D411yescharacteristic
38C42×C47D411yescharacteristic
39C42×C47C2311yescharacteristic
40C22⋊Dic47—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47C2×C411yescharacteristic
44C4⋊Dic47C2×C411yescharacteristic
45Dic47⋊C4—21no—
46Dic47⋊C4—21no—
47C4×Dic47—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C2×C47⋊C8—22no—
51C23×C47C22⋊C411yescharacteristic
52C22×D47—21no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47C22⋊C411yescharacteristic
56C2×C4×C47C22⋊C411yescharacteristic
57C2×C4×C47C22⋊C411yescharacteristic
58C2×C4×C47C2×C812yes—
59C2×C4×C47M1612yes—
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C22⋊D47—24no—
64C2×Dic47—21no—
65C2×Dic47—21no—
66C2×Dic47—21no—
67D188—21no—
68D188C2×C812yescomplemented
69C4×D47—24no—
70C4×D47—42no—
71C4×D47—42no—
72Dic94—21no—
73Dic94C2×C812yescomplemented
74C8×C47—24no—
75C47⋊C8—42no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47C22⋊C812yes—
79C22×C47C2×C22⋊C411yescharacteristic
80C2×D47—22no—
81C2×D47—41no—
82C2×D47—41no—
83C4×C47—21no—
84C4×C47—21no—
85C4×C47C22⋊C812yes—
86C4×C47#10412yes—
87C4×C47C22×C811yescharacteristic
88C4×C47C2×M1611yescharacteristic
89C4×C47#13512yes—
90Dic47—22no—
91Dic47—41no—
92Dic47—41no—
93#1476—471nomaximal, Sylow
94C2×C47—22no—
95C2×C47C2×C22⋊C811yescharacteristic
96C2×C47#41611yescharacteristic
97C2×C47C2×#10411yescharacteristic
98D47—42no—
99C4×#41—471no—
100#431—471no—
101C2×C4×C8D4711yescharacteristic, complemented
102Q8⋊C8—472no—
103D4⋊C8—472no—
104C47#147611yescharacteristic, complemented, Sylow
105C2×#41—471no—
106C22×C8—21no—
107C4×Q8—471no—
108C4×Q8—471no—
109C4×D4—471no—
110C4×D4—471no—
111C4×D4—941no—
112C4×D4—941no—
113#117—471no—
114#117—941no—
115C2×C42—941no—
116C2×C42C2×D4711yescharacteristic
117C4⋊C8—472no—
118C22⋊C8—941no—
119C4×C8—21no—
120C4×C8—941no—
121C4×C8C2×D4712yes—
122#41—474no—
123#41—942no—
124C2×Q8—471no—
125C2×D4—471no—
126C2×D4—941no—
127C22×C4—941no—
128C22×C4—941no—
129C22×C4—941no—
130C22×C4C4×D4711yescharacteristic
131C22×C4D18811yescharacteristic
132C22×C4C22⋊D4711yescharacteristic
133C2×C8—24no—
134C2×C8—22no—
135C2×C8—942no—
136C4⋊C4—471no—
137C4⋊C4—471no—
138C4⋊C4—941no—
139C4⋊C4—941no—
140C22⋊C4—941no—
141C22⋊C4—941no—
142C22⋊C4—941no—
143C42—941no—
144C42—941no—
145C42—941no—
146C42C4×D4711yescharacteristic
147C42D18811yescharacteristic
148C42C22⋊D4711yescharacteristic
149C42C22×D4711yescharacteristic
150C23—941no—
151C23(C2×D47)⋊C411yescharacteristic
152Q8—472no—
153Q8—941no—
154D4—472no—
155D4—944no—
156D4—941no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—941no—
160C2×C4—944no—
161C2×C4—941no—
162C2×C4—941no—
163C2×C4—1882no—
164C2×C4—1882no—
165C2×C4C8×D4712yes—
166C2×C4#1062532412yes—
167C2×C4(C2×D47)⋊C411yescharacteristic
168C2×C4(C2×D47)⋊C411yescharacteristic
169C2×C4(C2×D47)⋊C411yescharacteristic
170C2×C4C2×C4×D4711yescharacteristic
171C2×C4C2×D18811yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—24no—
174C8—1882no—
175C22—21no—
176C22—21no—
177C22—942no—
178C22—1881no—
179C22—1881no—
180C22(C2×D47)⋊C812yes—
181C22C2×(C2×D47)⋊C411yescharacteristic
182C4—21no—
183C4—21no—
184C4—942no—
185C4—1881no—
186C4—1881no—
187C4(C2×D47)⋊C812yes—
188C4#1309395212yes—
189C4C2×C8×D4711yescharacteristic
190C4C2×#1062532411yescharacteristic
191C4#1309404612yes—
192C2—22no—
193C2—1882no—
194C2C2×(C2×D47)⋊C811yescharacteristic
195C2#1568912011yescharacteristic
196C2C2×#1309395211yescharacteristic
subgroupG/H
centerC42D188
commutatorC4×C47C22×C8
FrattiniC42C22×D47
FittingC2×C4×C8×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC2×C4×C8D47
hypocenterC47#1476
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #15689176C2semidirect
3. #15688855C2semidirect
4. #15688852C2semidirect
5. C2×C4×C8×C47C2semidirect
28. #10625350C8semidirect
68. D188C2×C8semidirect
73. Dic94C2×C8semidirect
101. C2×C4×C8D47semidirect
104. C47#1476semidirect