Finite Group Databasebeta

← #20244519

Subgroups — #20244519

Order 6016.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#15689685C211yesmaximal, characteristic
2C2×#13094007C212yesmaximal, complemented
3C2×#13093938C212yesmaximal, complemented
4#15688890C211yesmaximal, characteristic, complemented
5C47×#381C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C2212yes—
7#13094008—22no—
8#13094007—24no—
9#13094007—24no—
10#13093998—22no—
11#13093994—22no—
12C2×Dic47⋊C4—22no—
13C2×C22⋊Dic47C2212yes—
14C2×(C2×D47)⋊C4—22no—
15#13093938—24no—
16C23×C4×C47C2211yescharacteristic
17C2×C22⋊C4×C47C2211yescharacteristic
18C2×C22⋊C4×C47C2211yescharacteristic
19#95×C47—22no—
20C24×C47C2311yescharacteristic
21C23×D47D412yes—
22C22×C4×C47—22no—
23C22×C4×C47—22no—
24C22×C4×C47—21no—
25C22×C4×C47—21no—
26C22×C4×C47—21no—
27C22×C4×C47D412yes—
28C22×C4×C47D412yescomplemented
29C2×C22⋊D47—22no—
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32C2×C22⋊D47—22no—
33C2×C22⋊D47—22no—
34C2×C22⋊D47—22no—
35C22×Dic47—22no—
36C22×Dic47D412yes—
37C2×D188—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—22no—
40C22⋊Dic47—22no—
41C22⋊Dic47D414yescomplemented
42(C2×D47)⋊C4—28no—
43(C2×D47)⋊C4—24no—
44C4⋊Dic47—22no—
45Dic47⋊C4—28no—
46C23×C47—42no—
47C23×C47C2×D411yescharacteristic
48C23×C47C2×D412yes—
49C23×C47C2×D412yes—
50C23×C47C2×D411yescharacteristic
51C23×C47#4111yescharacteristic
52C22×D47—22no—
53C22×D47—22no—
54C22×D47—22no—
55C22×D47—44no—
56C2×C4×C47—24no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—41no—
60C2×C4×C47—42no—
61C2×C4×C47—41no—
62C2×C4×C47—42no—
63C2×C4×C47—42no—
64C2×C4×C47—41no—
65C22⋊D47—42no—
66C22⋊D47—42no—
67C22⋊D47—42no—
68C22⋊D47—42no—
69C2×Dic47—22no—
70C2×Dic47—24no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—44no—
74D188—82no—
75C22×C47—24no—
76C22×C47—22no—
77C22×C47—41no—
78C22×C47—42no—
79C22×C47—41no—
80C22×C47#12011yescharacteristic
81C22×C47#12012yes—
82C22×C47#12112yes—
83C22×C47#12111yescharacteristic
84C22×C47#12711yescharacteristic
85C2×D47—44no—
86C2×D47—42no—
87C2×D47—44no—
88C2×D47—82no—
89C4×C47—42no—
90C4×C47—42no—
91C4×C47—81no—
92Dic47—44no—
93Dic47—42no—
94#2022—471nomaximal, Sylow
95C2×C47—22no—
96C2×C47—21no—
97C2×C47—22no—
98C2×C47—21no—
99C2×C47#39211yescharacteristic
100C2×C47#45812yes—
101D47—82no—
102#534—471no—
103C2×#123—472no—
104C2×#99—472no—
105#381D4711yescharacteristic, complemented
106#342—471no—
107C47#202211yescharacteristic, complemented, Sylow
108C22×D4—472no—
109C23×C4C2×D4711yescharacteristic
110#123—942no—
111#123—944no—
112#123—944no—
113#121—942no—
114#120—942no—
115C2×C4⋊C4—942no—
116C2×C22⋊C4—472no—
117C2×C22⋊C4—942no—
118C2×C22⋊C4C2×D4711yescharacteristic
119C2×C22⋊C4C2×D4711yescharacteristic
120#99—944no—
121#95—22no—
122C24—472no—
123C24C22×D4711yescharacteristic
124C2×D4—942no—
125C2×D4—942no—
126C2×D4—942no—
127C2×D4—942no—
128C2×D4—942no—
129C2×D4—942no—
130C2×D4—942no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—472no—
137C22×C4—942no—
138C22×C4D18812yescomplemented
139C22×C4C22⋊D4712yes—
140C4⋊C4—948no—
141C4⋊C4—942no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—474no—
145C22⋊C4—948no—
146C22⋊C4—944no—
147C22⋊C4—942no—
148C23—42no—
149C23—942no—
150C23—942no—
151C23—942no—
152C23—1884no—
153C23C2×D18811yescharacteristic
154C23#1062535011yescharacteristic
155C23D4×D4712yes—
156C23D4×D4712yes—
157C23C2×C22⋊D4711yescharacteristic
158D4—3762no—
159D4—1882no—
160D4—1882no—
161D4—1882no—
162D4—1882no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—942no—
173C2×C4—944no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—1884no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—3762no—
183C22—1884no—
184C22—1882no—
185C22—1884no—
186C22#1309399211yescharacteristic
187C22#1309399412yes—
188C22#1309399712yes—
189C22#1309399811yescharacteristic
190C22#1309402011yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—1884no—
195C4—1882no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—3762no—
201C2#1568903211yescharacteristic
202C2#1568931212yes—
subgroupG/H
centerC22#13093992
commutatorC24×C47C23
FrattiniC24C22×D47
FittingC47×#381C2
socleC22×C47#120
hypercenter#381D47
hypocenterC47#2022
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#13094007C2semidirect
3. C2×#13093938C2semidirect
4. #15688890C2semidirect
5. C47×#381C2semidirect
28. C22×C4×C47D4semidirect
41. C22⋊Dic47D4semidirect
105. #381D47semidirect
107. C47#2022semidirect
138. C22×C4D188semidirect