Finite Group Databasebeta

← #20242347

Subgroups — #20242347

Order 6016.

256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689749C211yesmaximal, characteristic
2#15689281C212yesmaximal, complemented
3#15689035C211yesmaximal, characteristic
4#15688861C212yesmaximal, complemented
5C47×#323C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×Dic188—22no—
8#13094003—21no—
9#13094003C2212yes—
10#13094001—22no—
11#13094001—22no—
12C2×C22⋊Dic47—21no—
13C2×C22⋊Dic47—21no—
14#13093949—22no—
15C47⋊#95—21no—
16C47⋊#95C2211yescharacteristic
17C2×C22⋊C4×C47C2211yescharacteristic
18C22⋊C8×C47C2212yes—
19C24×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C22×Dic47—21no—
25C22×Dic47—21no—
26C2×Dic94—22no—
27C2×Dic94—21no—
28C2×Dic94—42no—
29C2×Dic94D412yes—
30C2×C8×C47—22no—
31C22⋊C4×C47—22no—
32C22⋊Dic47—22no—
33C22⋊Dic47—22no—
34C22⋊Dic47—42no—
35C4⋊Dic47—21no—
36C4⋊Dic47D412yes—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39Dic188—44no—
40C23×C47—21no—
41C23×C47—21no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47Q1612yescomplemented
45C23×C47C2×D411yescharacteristic
46C2×C4×C47—21no—
47C2×C4×C47—41no—
48C2×C4×C47—41no—
49C2×C4×C47C2×D412yes—
50C2×Dic47—22no—
51C2×Dic47—22no—
52C2×Dic47—22no—
53C2×Dic47—41no—
54C2×Dic47—41no—
55C2×Dic47—41no—
56C2×Dic47—41no—
57C2×Dic47—41no—
58C2×Dic47—81no—
59C2×Dic47—81no—
60Dic94—24no—
61Dic94—42no—
62Dic94—42no—
63Dic94—81no—
64C8×C47—42no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47—22no—
68C22×C47—42no—
69C22×C47—41no—
70C22×C47—41no—
71C22×C47—81no—
72C22×C47#12011yescharacteristic
73C22×C47C2×Q1611yescharacteristic
74C22×C47#13711yescharacteristic
75C4×C47—22no—
76C4×C47—41no—
77Dic47—42no—
78Dic47—42no—
79Dic47—42no—
80Dic47—81no—
81#1602—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—21no—
84C2×C47—42no—
85C2×C47#45111yescharacteristic
86C2×C47#45511yescharacteristic
87C2×C47B(4,𝔽2)11yescharacteristic
88#543—471no—
89#451—472no—
90#393—471no—
91#328—472no—
92#323D4711yescharacteristic
93C47#160211yescharacteristic, complemented, Sylow
94C22×Q8—471no—
95C2×Q16—942no—
96C22⋊Q8—472no—
97C22⋊Q8—942no—
98C22⋊Q8—942no—
99C22⋊Q8—941no—
100C2×C22⋊C4—941no—
101C2×C22⋊C4—941no—
102C2×C22⋊C4C2×D4711yescharacteristic
103#103—942no—
104C22⋊C8C2×D4712yes—
105#95—471no—
106#95—941no—
107C24D18811yescharacteristic
108C2×Q8—472no—
109C2×Q8—941no—
110C2×Q8—942no—
111C2×Q8—1882no—
112C22×C4—941no—
113C22×C4—941no—
114C22×C4—941no—
115C22×C4—941no—
116C22×C4D18811yescharacteristic
117C22×C4C22×D4711yescharacteristic
118Q16—1884no—
119C2×C8—22no—
120C4⋊C4—472no—
121C4⋊C4—942no—
122C4⋊C4—941no—
123C4⋊C4—942no—
124C22⋊C4—22no—
125C22⋊C4—942no—
126C22⋊C4—942no—
127C22⋊C4—1882no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23Dic18812yescomplemented
133C23C2×D18811yescharacteristic
134Q8—944no—
135Q8—3761no—
136Q8—1882no—
137Q8—1882no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—942no—
142C2×C4—942no—
143C2×C4—942no—
144C2×C4—3761no—
145C2×C4—3761no—
146C2×C4—1881no—
147C2×C4—1881no—
148C2×C4—1881no—
149C2×C4—1881no—
150C2×C4—1881no—
151C2×C4D4×D4712yes—
152C8—42no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#1309399411yescharacteristic
161C22C2×Dic18811yescharacteristic
162C22#1309405711yescharacteristic
163C4—22no—
164C4—41no—
165C4—3761no—
166C4—1882no—
167C4—1882no—
168C4—1882no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#1568928111yescharacteristic
173C2#1568930311yescharacteristic
174C2#1568931111yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#323C2
socleC22×C47#120
hypercenter#323D47
hypocenterC47#1602
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #15689281C2semidirect
4. #15688861C2semidirect
44. C23×C47Q16semidirect
93. C47#1602semidirect
132. C23Dic188semidirect