Finite Group Databasebeta

← #20243989

Subgroups — #20243989

Order 6016.

186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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#15689150C211yesmaximal, characteristic
2#15689079C211yesmaximal, characteristic
3#15688888C211yesmaximal, characteristic
4#15688882C211yesmaximal, characteristic
5#15688882C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C47×#427C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12C4⋊(C47⋊C8)—21no—
13C4⋊(C47⋊C8)—21no—
14#13093935—21no—
15C4×C47⋊C8—21no—
16C22×C8×C47C2211yescharacteristic
17#117×C47C2211yescharacteristic
18#117×C47C2211yescharacteristic
19#107×C47C411yescharacteristic, complemented
20#107×C47C411yescharacteristic, complemented
21#106×C47C411yescharacteristic, complemented
22#106×C47C411yescharacteristic, complemented
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C2×C8×C47—21no—
26C2×C8×C47—21no—
27C2×C8×C47C2×C411yescharacteristic
28C2×C8×C47C2×C411yescharacteristic
29C4⋊C4×C47C2×C411yescharacteristic
30C4⋊C4×C47C2×C411yescharacteristic
31C4⋊C4×C47C2×C411yescharacteristic
32C4⋊C4×C47C2×C411yescharacteristic
33C22⋊C4×C47—21no—
34C22⋊C4×C47—21no—
35C42×C47—21no—
36C42×C47—21no—
37C4×Dic47—21no—
38C4×Dic47—21no—
39#10625329—21no—
40#10625329—21no—
41#10625329—21no—
42#10625329Q812yes—
43C2×C47⋊C8—21no—
44C2×C47⋊C8—21no—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8D411yescharacteristic
48C2×C47⋊C8D411yescharacteristic
49C23×C47#4111yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×Q811yescharacteristic
57C2×C4×C47#4111yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C2×Dic47—22no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63C8×C47—21no—
64C8×C47—21no—
65C47⋊C8—22no—
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—41no—
75C4×C47—41no—
76C4×C47—41no—
77C4×C47—41no—
78C4×C47#11711yescharacteristic
79C4×C47C4×Q811yescharacteristic
80C4×C47C22⋊Q811yescharacteristic
81C4×C47#12311yescharacteristic
82Dic47—42no—
83#1922—471nomaximal, Sylow
84C2×C47—21no—
85C2×C47—21no—
86C2×C47#38711yescharacteristic
87C2×C47#44311yescharacteristic
88C2×C47#44411yescharacteristic
89#427D4711yescharacteristic
90#424—471no—
91#405—471no—
92#341—471no—
93#339—471no—
94#339—471no—
95#336—471no—
96C47#192211yescharacteristic, complemented, Sylow
97C2×M16—471no—
98C2×M16—471no—
99C22×C8—471no—
100C22×C8C2×D4711yescharacteristic
101#117C2×D4711yescharacteristic
102#117C2×D4711yescharacteristic
103C2×C42—471no—
104#107Dic4711yescharacteristic, complemented
105#107Dic4711yescharacteristic, complemented
106#106Dic4711yescharacteristic, complemented
107#106Dic4711yescharacteristic, complemented
108C4⋊C8—941no—
109C4⋊C8—941no—
110#97—941no—
111C4×C8—941no—
112C22×C4—941no—
113C22×C4C22×D4711yescharacteristic
114M16—472no—
115M16—941no—
116M16—941no—
117M16—941no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—471no—
121C2×C8—471no—
122C2×C8—941no—
123C2×C8—941no—
124C2×C8—941no—
125C2×C8—941no—
126C2×C8C2×Dic4711yescharacteristic
127C2×C8C2×Dic4711yescharacteristic
128C4⋊C4C2×Dic4711yescharacteristic
129C4⋊C4C2×Dic4711yescharacteristic
130C4⋊C4C2×Dic4711yescharacteristic
131C4⋊C4C2×Dic4711yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—21no—
134C42—21no—
135C42—21no—
136C42—941no—
137C42—941no—
138C23#1062535211yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—942no—
144C2×C4—1881no—
145C2×C4—1881no—
146C2×C4#1062535011yescharacteristic
147C2×C4#1062535011yescharacteristic
148C2×C4D4×D4711yescharacteristic
149C2×C4Q8×D4711yescharacteristic
150C2×C4#1062535411yescharacteristic
151C2×C4C22×Dic4711yescharacteristic
152C8—21no—
153C8—21no—
154C8—942no—
155C8—941no—
156C8—941no—
157C8—1881no—
158C22—21no—
159C22—21no—
160C22D4×Dic4711yescharacteristic
161C22#1309401411yescharacteristic
162C22#1309401911yescharacteristic
163C4—41no—
164C4—41no—
165C4—41no—
166C4—41no—
167C4—1882no—
168C4#1309398311yescharacteristic
169C4Q8×Dic4711yescharacteristic
170C4#1309400211yescharacteristic
171C4#1309400911yescharacteristic
172C2—21no—
173C2—21no—
174C2#1568900911yescharacteristic
175C2#1568924011yescharacteristic
176C2#1568924511yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#427C2
socleC22×C47C4×D4
hypercenter#427D47
hypocenterC47#1922
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
19. #107×C47C4semidirect
20. #107×C47C4semidirect
21. #106×C47C4semidirect
22. #106×C47C4semidirect
96. C47#1922semidirect
104. #107Dic47semidirect
105. #107Dic47semidirect
106. #106Dic47semidirect
107. #106Dic47semidirect