Finite Group Databasebeta

← #20243990

Subgroups — #20243990

Order 6016.

186 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 75 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#15689159C211yesmaximal, characteristic
2#15689150C211yesmaximal, characteristic
3#15689081C211yesmaximal, characteristic
4#15688887C211yesmaximal, characteristic
5#15688883C211yesmaximal, characteristic
6#15688878C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13093983C2211yescharacteristic
12#13093957C411yescharacteristic, complemented
13#13093957C411yescharacteristic, complemented
14#13093955C411yescharacteristic, complemented
15#13093955C411yescharacteristic, complemented
16C4⋊(C47⋊C8)—21no—
17C4⋊(C47⋊C8)—21no—
18#13093934—21no—
19C8×Dic47—21no—
20C2×M16×C47C2211yescharacteristic
21#117×C47C2211yescharacteristic
22C2×C42×C47C2211yescharacteristic
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25M16×C47—21no—
26M16×C47Q812yes—
27C2×C8×C47—21no—
28C4⋊C4×C47C2×C411yescharacteristic
29C4⋊C4×C47C2×C411yescharacteristic
30C22⋊C4×C47—21no—
31C42×C47—21no—
32C42×C47—21no—
33C42×C47—21no—
34C22⋊Dic47—21no—
35C4⋊Dic47C2×C411yescharacteristic
36C4⋊Dic47C2×C411yescharacteristic
37C4×Dic47—21no—
38#10625329—21no—
39#10625329—21no—
40C2×C47⋊C8—21no—
41C2×C47⋊C8—21no—
42C2×C47⋊C8—21no—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8C2×C411yescharacteristic
46C2×C47⋊C8C2×C411yescharacteristic
47C2×C47⋊C8D411yescharacteristic
48C2×C47⋊C8D411yescharacteristic
49C23×C47#4111yescharacteristic
50C2×C4×C47—22no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47C22×C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×Q811yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×Dic47—21no—
62C2×Dic47—21no—
63C8×C47—22no—
64C47⋊C8—21no—
65C47⋊C8—21no—
66C47⋊C8—21no—
67C47⋊C8—21no—
68C47⋊C8—41no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47C4×D411yescharacteristic
72C22×C47#12511yescharacteristic
73C22×C47#12611yescharacteristic
74C4×C47—42no—
75C4×C47—41no—
76C4×C47—41no—
77C4×C47#11711yescharacteristic
78C4×C47C4×Q811yescharacteristic
79C4×C47C22⋊Q811yescharacteristic
80C4×C47#12311yescharacteristic
81Dic47—41no—
82Dic47—41no—
83#1922—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—21no—
86C2×C47#38711yescharacteristic
87C2×C47#44311yescharacteristic
88C2×C47#44411yescharacteristic
89#427—471no—
90#424—471no—
91#405—471no—
92#341—471no—
93#339—471no—
94#339D4711yescharacteristic
95#336—471no—
96C47#192211yescharacteristic, complemented, Sylow
97C2×M16—471no—
98C2×M16C2×D4711yescharacteristic
99C22×C8—471no—
100C22×C8—471no—
101#117—471no—
102#117C2×D4711yescharacteristic
103C2×C42C2×D4711yescharacteristic
104#107—471no—
105#107—471no—
106#106—471no—
107#106—471no—
108C4⋊C8—941no—
109C4⋊C8—941no—
110#97—941no—
111C4×C8—941no—
112C22×C4—21no—
113C22×C4C22×D4711yescharacteristic
114M16—21no—
115M16—941no—
116M16—941no—
117M16Dic9412yes—
118C2×C8—21no—
119C2×C8—471no—
120C2×C8—471no—
121C2×C8—471no—
122C2×C8—471no—
123C2×C8—941no—
124C2×C8—941no—
125C2×C8—941no—
126C2×C8—941no—
127C2×C8—941no—
128C4⋊C4—471no—
129C4⋊C4—471no—
130C4⋊C4C4×D4711yescharacteristic
131C4⋊C4C4×D4711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—941no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—941no—
138C23#1062535211yescharacteristic
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—941no—
145C2×C4—941no—
146C2×C4C2×Dic9411yescharacteristic
147C2×C4C2×C4×D4711yescharacteristic
148C2×C4#1062535011yescharacteristic
149C2×C4D4×D4711yescharacteristic
150C2×C4#1062535211yescharacteristic
151C2×C4#1062535411yescharacteristic
152C8—22no—
153C8—941no—
154C8—941no—
155C8—941no—
156C8—941no—
157C8—1881no—
158C22—21no—
159C22—21no—
160C22(C22⋊D47)⋊C411yescharacteristic
161C22#1309401511yescharacteristic
162C22#1309401711yescharacteristic
163C4—42no—
164C4—41no—
165C4—41no—
166C4—1881no—
167C4—1881no—
168C4#1309398211yescharacteristic
169C4C4×Dic9411yescharacteristic
170C4#1309400111yescharacteristic
171C4#1309400911yescharacteristic
172C2—21no—
173C2—21no—
174C2#1568901011yescharacteristic
175C2#1568923711yescharacteristic
176C2#1568924211yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C4×D4
hypercenter#339D47
hypocenterC47#1922
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #13093957C4semidirect
13. #13093957C4semidirect
14. #13093955C4semidirect
15. #13093955C4semidirect
96. C47#1922semidirect