Finite Group Databasebeta

← #20244520

Subgroups — #20244520

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
1#15689685C211yesmaximal, characteristic
2C2×#13094008C212yesmaximal, complemented
3C2×#13093938C212yesmaximal, complemented
4#15688984C211yesmaximal, characteristic, complemented
5C47×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D47C2212yes—
7C23×Dic47C2211yescharacteristic
8#13094008—22no—
9#13094008—24no—
10#13094008—24no—
11#13093998—22no—
12#13093994—22no—
13C2×C4⋊Dic47—22no—
14C2×C22⋊Dic47C2211yescharacteristic
15C2×(C2×D47)⋊C4—22no—
16#13093938—24no—
17C47⋊#95—22no—
18C2×C22⋊C4×C47C2211yescharacteristic
19C2×C22⋊C4×C47C2212yes—
20C24×C47C2311yescharacteristic
21C23×D47D412yes—
22C22×C4×C47—22no—
23C22×C4×C47D412yes—
24C2×C22⋊D47—22no—
25C2×C22⋊D47—22no—
26C2×C22⋊D47—22no—
27C2×C22⋊D47—22no—
28C2×C22⋊D47—22no—
29C2×C22⋊D47—22no—
30C22×Dic47—21no—
31C22×Dic47—22no—
32C22×Dic47—22no—
33C22×Dic47—21no—
34C22×Dic47—21no—
35C22×Dic47D412yes—
36C22×Dic47D412yescomplemented
37C2×D188—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47—22no—
40C22⋊C4×C47D414yescomplemented
41C22⋊Dic47—22no—
42(C2×D47)⋊C4—28no—
43(C2×D47)⋊C4—24no—
44C4⋊Dic47—28no—
45C4⋊Dic47—22no—
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—44no—
59C2×C4×C47—42no—
60C22⋊D47—42no—
61C22⋊D47—42no—
62C22⋊D47—42no—
63C22⋊D47—42no—
64C2×Dic47—22no—
65C2×Dic47—24no—
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—41no—
70C2×Dic47—42no—
71C2×Dic47—41no—
72C2×Dic47—42no—
73C2×Dic47—41no—
74D188—82no—
75C22×C47—22no—
76C22×C47—24no—
77C22×C47—42no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47#12012yes—
81C22×C47#12011yescharacteristic
82C22×C47#12111yescharacteristic
83C22×C47#12112yes—
84C22×C47#12711yescharacteristic
85C2×D47—44no—
86C2×D47—42no—
87C2×D47—44no—
88C2×D47—82no—
89C4×C47—44no—
90C4×C47—42no—
91Dic47—42no—
92Dic47—42no—
93Dic47—81no—
94#2022—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—22no—
97C2×C47—22no—
98C2×C47—21no—
99C2×C47#39211yescharacteristic
100C2×C47#45812yes—
101D47—82no—
102#534—471no—
103C2×#123—472no—
104C2×#99—472no—
105#381—471no—
106#342D4711yescharacteristic, complemented
107C47#202211yescharacteristic, complemented, Sylow
108C22×D4—472no—
109C23×C4—471no—
110#123—944no—
111#123—942no—
112#123—944no—
113#121—942no—
114#120—942no—
115C2×C4⋊C4—942no—
116C2×C22⋊C4—471no—
117C2×C22⋊C4—942no—
118C2×C22⋊C4C2×D4711yescharacteristic
119C2×C22⋊C4C2×D4712yes—
120#99—944no—
121#95—942no—
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—22no—
132C22×C4—472no—
133C22×C4—472no—
134C22×C4—941no—
135C22×C4—942no—
136C22×C4—942no—
137C22×C4—941no—
138C22×C4—941no—
139C22×C4D18812yes—
140C4⋊C4—948no—
141C4⋊C4—942no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—948no—
145C22⋊C4—944no—
146C22⋊C4—942no—
147C22⋊C4D18814yescomplemented
148C23—42no—
149C23—942no—
150C23—942no—
151C23—942no—
152C23—1884no—
153C23C2×D18811yescharacteristic
154C23C2×D18812yes—
155C23D4×D4712yes—
156C23D4×D4711yescharacteristic
157C23#1062535411yescharacteristic
158D4—3762no—
159D4—1882no—
160D4—1882no—
161D4—1882no—
162D4—1882no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—944no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—942no—
171C2×C4—942no—
172C2×C4—1882no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4—1882no—
176C2×C4—1881no—
177C22—22no—
178C22—24no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—3762no—
183C22—1884no—
184C22—1882no—
185C22—1884no—
186C22#1309399412yes—
187C22#1309399411yescharacteristic
188C22#1309399911yescharacteristic
189C22#1309399912yes—
190C22#1309402111yescharacteristic
191C4—44no—
192C4—42no—
193C4—3761no—
194C4—1882no—
195C4—1882no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—3762no—
201C2#1568903311yescharacteristic
202C2#1568931412yes—
subgroupG/H
centerC22#13093994
commutatorC24×C47C23
FrattiniC24C22×D47
FittingC47×#342C2
socleC22×C47#120
hypercenter#342D47
hypocenterC47#2022
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#13094008C2semidirect
3. C2×#13093938C2semidirect
4. #15688984C2semidirect
5. C47×#342C2semidirect
36. C22×Dic47D4semidirect
40. C22⋊C4×C47D4semidirect
106. #342D47semidirect
107. C47#2022semidirect
147. C22⋊C4D188semidirect