Finite Group Databasebeta

← #20244517

Subgroups — #20244517

Order 6016.

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

normal subgroups only

This group has 430 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
1C2×#13094005C212yesmaximal, complemented
2C2×#13093939C212yesmaximal, complemented
3#15688984C211yesmaximal, characteristic, complemented
4#15688890C211yesmaximal, characteristic, complemented
5C47×#534C211yesmaximal, characteristic
6C23×Dic47C2211yescharacteristic
7#13094005—24no—
8#13094005—24no—
9C2×Dic47⋊C4—22no—
10C2×C22⋊Dic47—22no—
11C2×C22⋊Dic47C2211yescharacteristic
12C2×C22⋊Dic47C2212yes—
13#13093939—24no—
14C47⋊#95—22no—
15C22×D4×C47C2212yes—
16#123×C47—22no—
17#121×C47—22no—
18#120×C47—22no—
19C2×C22⋊C4×C47C2211yescharacteristic
20C24×C47D412yes—
21C24×C47C2311yescharacteristic
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47—22no—
25C2×D4×C47—22no—
26C2×D4×C47—22no—
27C2×D4×C47—22no—
28C2×D4×C47—22no—
29C22×C4×C47D412yes—
30C22×C4×C47D412yes—
31C22×Dic47—21no—
32C22×Dic47—22no—
33C22×Dic47—22no—
34C22×Dic47—22no—
35C22×Dic47—21no—
36C22×Dic47—21no—
37C22×Dic47D412yescomplemented
38C4⋊C4×C47—22no—
39C22⋊C4×C47—24no—
40C22⋊C4×C47—22no—
41C22⋊Dic47—28no—
42C22⋊Dic47—22no—
43C22⋊Dic47—22no—
44C22⋊Dic47D414yescomplemented
45Dic47⋊C4—28no—
46C23×C47—22no—
47C23×C47—22no—
48C23×C47—22no—
49C23×C47—42no—
50C23×C47—44no—
51C23×C47C2×D411yescharacteristic
52C23×C47C2×D412yes—
53C23×C47C2×D412yes—
54C23×C47C2×D411yescharacteristic
55C23×C47#4111yescharacteristic
56D4×C47—42no—
57D4×C47—42no—
58D4×C47—42no—
59D4×C47—42no—
60D4×C47—82no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—42no—
66C2×Dic47—24no—
67C2×Dic47—24no—
68C2×Dic47—22no—
69C2×Dic47—44no—
70C2×Dic47—41no—
71C2×Dic47—42no—
72C2×Dic47—41no—
73C2×Dic47—42no—
74C2×Dic47—41no—
75C22×C47—22no—
76C22×C47—24no—
77C22×C47—41no—
78C22×C47—42no—
79C22×C47—41no—
80C22×C47—44no—
81C22×C47—42no—
82C22×C47—44no—
83C22×C47—82no—
84C22×C47#12012yes—
85C22×C47#12011yescharacteristic
86C22×C47#12111yescharacteristic
87C22×C47#12112yes—
88C22×C47#12711yescharacteristic
89C4×C47—42no—
90C4×C47—42no—
91Dic47—44no—
92Dic47—42no—
93Dic47—81no—
94#2022—471nomaximal, Sylow
95C2×C47—22no—
96C2×C47—21no—
97C2×C47—22no—
98C2×C47—21no—
99C2×C47—82no—
100C2×C47#39211yescharacteristic
101C2×C47#45812yes—
102#534D4711yescharacteristic
103C2×#123—472no—
104C2×#99—472no—
105#381—471no—
106#342—471no—
107C47#202211yescharacteristic, complemented, Sylow
108C22×D4C2×D4712yes—
109C23×C4—471no—
110#123—22no—
111#123—944no—
112#123—944no—
113#121—22no—
114#120—22no—
115C2×C4⋊C4—942no—
116C2×C22⋊C4—472no—
117C2×C22⋊C4—471no—
118C2×C22⋊C4—942no—
119C2×C22⋊C4C2×D4711yescharacteristic
120#99—944no—
121#95—942no—
122C24C22⋊D4712yes—
123C24C22×D4711yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C22×C4—472no—
132C22×C4—942no—
133C22×C4—941no—
134C22×C4—941no—
135C22×C4—942no—
136C22×C4—942no—
137C22×C4—941no—
138C22×C4C22⋊D4712yes—
139C22×C4C22⋊D4712yes—
140C4⋊C4—22no—
141C4⋊C4—948no—
142C22⋊C4—24no—
143C22⋊C4—22no—
144C22⋊C4—474no—
145C22⋊C4—948no—
146C22⋊C4—942no—
147C22⋊C4—942no—
148C23—22no—
149C23—22no—
150C23—22no—
151C23—42no—
152C23—44no—
153C23D4×D4711yescharacteristic
154C23D4×D4712yes—
155C23#1062535211yescharacteristic
156C23C2×C22⋊D4712yes—
157C23C2×C22⋊D4711yescharacteristic
158D4—42no—
159D4—42no—
160D4—42no—
161D4—42no—
162D4—82no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—944no—
169C2×C4—944no—
170C2×C4—942no—
171C2×C4—1882no—
172C2×C4—1881no—
173C2×C4—1884no—
174C2×C4—1881no—
175C2×C4—1882no—
176C2×C4—1881no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—44no—
183C22—42no—
184C22—44no—
185C22—82no—
186C22#1309399212yes—
187C22#1309399311yescharacteristic
188C22#1309399511yescharacteristic
189C22#1309399612yes—
190C22#1309402011yescharacteristic
191C4—42no—
192C4—42no—
193C4—3761no—
194C4—1884no—
195C4—1882no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—82no—
201C2#1568903111yescharacteristic
202C2#1568931312yes—
subgroupG/H
centerC22#13093993
commutatorC24×C47C23
FrattiniC24C22×D47
FittingC47×#534C2
socleC22×C47#120
hypercenter#534D47
hypocenterC47#2022
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. C2×#13094005C2semidirect
2. C2×#13093939C2semidirect
3. #15688984C2semidirect
4. #15688890C2semidirect
37. C22×Dic47D4semidirect
44. C22⋊Dic47D4semidirect
107. C47#2022semidirect