Finite Group Databasebeta

← #20243986

Subgroups — #20243986

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#15689161C211yesmaximal, characteristic
2#15689151C211yesmaximal, characteristic
3#15689081C211yesmaximal, characteristic
4#15688884C211yesmaximal, characteristic
5#15688884C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#341C211yesmaximal, characteristic
8C22×C47⋊C8C2211yescharacteristic
9#13093983C2211yescharacteristic
10#13093983C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093958C411yescharacteristic, complemented
13#13093958C411yescharacteristic, complemented
14#13093956C411yescharacteristic, complemented
15#13093956C411yescharacteristic, complemented
16Dic47⋊C8—21no—
17Dic47⋊C8—21no—
18#13093934—21no—
19C8×Dic47—21no—
20C2×M16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25M16×C47—21no—
26M16×C47—21no—
27M16×C47—21no—
28M16×C47Q812yes—
29C2×C8×C47—21no—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C2×C8×C47—21no—
33C2×C8×C47C2×C411yescharacteristic
34C2×C8×C47C2×C411yescharacteristic
35C22⋊Dic47—21no—
36C22⋊Dic47—21no—
37C4⋊Dic47C2×C411yescharacteristic
38C4⋊Dic47C2×C411yescharacteristic
39C4⋊Dic47C2×C411yescharacteristic
40C4⋊Dic47C2×C411yescharacteristic
41C4×Dic47—21no—
42C4×Dic47—21no—
43C4×Dic47—21no—
44C4×Dic47—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D411yescharacteristic
48C2×C47⋊C8D411yescharacteristic
49C23×C47#4111yescharacteristic
50C2×C4×C47C22×C411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×Q811yescharacteristic
53C2×C4×C47#4111yescharacteristic
54C2×C4×C47#4111yescharacteristic
55C2×C4×C47#4111yescharacteristic
56C2×Dic47—22no—
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60C2×Dic47—21no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C8×C47—21no—
64C8×C47—21no—
65C8×C47—22no—
66C8×C47—41no—
67C47⋊C8—21no—
68C47⋊C8—21no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47C4×D411yescharacteristic
72C22×C47#12511yescharacteristic
73C22×C47#12611yescharacteristic
74C4×C47#11711yescharacteristic
75C4×C47C4×Q811yescharacteristic
76C4×C47C22⋊Q811yescharacteristic
77C4×C47#12311yescharacteristic
78Dic47—42no—
79Dic47—41no—
80Dic47—41no—
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#341D4711yescharacteristic
93#339—471no—
94#339—471no—
95#336—471no—
96C47#192211yescharacteristic, complemented, Sylow
97C2×M16C2×D4711yescharacteristic
98C2×M16C2×D4711yescharacteristic
99C22×C8—471no—
100C22×C8C2×D4711yescharacteristic
101#117—471no—
102#117—471no—
103C2×C42—471no—
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—941no—
113C22×C4C22×D4711yescharacteristic
114M16—21no—
115M16—21no—
116M16—21no—
117M16Dic9412yes—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—471no—
123C2×C8—471no—
124C2×C8—941no—
125C2×C8—941no—
126C2×C8C4×D4711yescharacteristic
127C2×C8C4×D4711yescharacteristic
128C4⋊C4—471no—
129C4⋊C4—471no—
130C4⋊C4—471no—
131C4⋊C4—471no—
132C22⋊C4—941no—
133C22⋊C4—941no—
134C42—941no—
135C42—941no—
136C42—941no—
137C42—941no—
138C23#1062535411yescharacteristic
139C2×C4—942no—
140C2×C4—941no—
141C2×C4—941no—
142C2×C4—941no—
143C2×C4—941no—
144C2×C4—1881no—
145C2×C4—1881no—
146C2×C4C2×Dic9411yescharacteristic
147C2×C4C2×C4×D4711yescharacteristic
148C2×C4#1062535011yescharacteristic
149C2×C4D4×D4711yescharacteristic
150C2×C4#1062535211yescharacteristic
151C2×C4#1062535211yescharacteristic
152C8—21no—
153C8—21no—
154C8—22no—
155C8—41no—
156C8—941no—
157C8—941no—
158C22—21no—
159C22—21no—
160C22#1309398611yescharacteristic
161C22#1309401511yescharacteristic
162C22#1309401911yescharacteristic
163C4—1882no—
164C4—1881no—
165C4—1881no—
166C4—1881no—
167C4—1881no—
168C4#1309398011yescharacteristic
169C4C4×Dic9411yescharacteristic
170C4#1309400111yescharacteristic
171C4#1309400611yescharacteristic
172C2—21no—
173C2—21no—
174C2#1568900611yescharacteristic
175C2#1568923911yescharacteristic
176C2#1568924411yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#341C2
socleC22×C47C4×D4
hypercenter#341D47
hypocenterC47#1922
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
12. #13093958C4semidirect
13. #13093958C4semidirect
14. #13093956C4semidirect
15. #13093956C4semidirect
96. C47#1922semidirect