Finite Group Databasebeta

← #20241505

Subgroups — #20241505

Order 6016.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13093941C211yesmaximal, characteristic
2#15689003C211yesmaximal, characteristic
3C2×#99×C47C211yesmaximal, characteristic
4C23×Dic47C411yescharacteristic, complemented
5C2×#10625329—21no—
6C2×C22⋊Dic47—21no—
7C2×C22⋊Dic47C411yescharacteristic, complemented
8#13093941—21no—
9#13093941C412yescomplemented
10C47⋊#95—21no—
11C22×D4×C47C2211yescharacteristic
12C2×C22⋊C4×C47—21no—
13#99×C47—21no—
14#99×C47C412yescomplemented
15C24×C47C2×C411yescharacteristic
16C24×C47D411yescharacteristic
17C2×D4×C47—41no—
18C2×D4×C47—41no—
19C2×D4×C47C2×C411yescharacteristic
20C2×D4×C47C2×C411yescharacteristic
21C2×D4×C47D411yescharacteristic
22C2×D4×C47Q811yescharacteristic
23C22×C4×C47—41no—
24C22×C4×C47D411yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47—42no—
28C22×Dic47—41no—
29C22⋊C4×C47—22no—
30C22⋊C4×C47—41no—
31C22⋊Dic47—42no—
32C22⋊Dic47—41no—
33#10625329—22no—
34#10625329—41no—
35C2×C47⋊C8—41no—
36C23×C47—21no—
37C23×C47—21no—
38C23×C47—21no—
39C23×C47—21no—
40C23×C47—41no—
41C23×C47—41no—
42C23×C47—41no—
43C23×C47—41no—
44C23×C47C4211yescharacteristic
45C23×C47C22⋊C411yescharacteristic
46C23×C47C22⋊C411yescharacteristic
47C23×C47C4⋊C411yescharacteristic
48C23×C47C4⋊C411yescharacteristic
49D4×C47—41no—
50D4×C47—41no—
51D4×C47—41no—
52D4×C47—41no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—42no—
56C2×C4×C47—81no—
57C2×C4×C47—81no—
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C4⋊C411yescharacteristic
60C2×Dic47—22no—
61C2×Dic47—41no—
62C2×Dic47—42no—
63C2×Dic47—41no—
64C2×Dic47—42no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C47⋊C8—42no—
69C22×C47—21no—
70C22×C47—21no—
71C22×C47—21no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47—42no—
80C22×C47—41no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47—81no—
85C22×C47#9511yescharacteristic
86C22×C47#9911yescharacteristic
87C22×C47#9911yescharacteristic
88C4×C47—21no—
89C4×C47—21no—
90C4×C47—82no—
91Dic47—42no—
92Dic47—81no—
93#1390—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—21no—
96C2×C47—41no—
97C2×C47—41no—
98C2×C47—41no—
99C2×C47—41no—
100C2×C47#34211yescharacteristic
101C2×C47AΣL(1,𝔽16)11yescharacteristic
102C2×C47#35211yescharacteristic
103C2×#100—471no—
104C2×#99D4711yescharacteristic
105#386—471no—
106C47#139011yescharacteristic, complemented, Sylow
107C22×D4C2×D4711yescharacteristic
108C23×C4—471no—
109C2×M16—941no—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—471no—
112C2×C22⋊C4—941no—
113#100—472no—
114#100—941no—
115#99—21no—
116#99Dic4712yescomplemented
117#95—941no—
118C24C4×D4711yescharacteristic
119C24C22⋊D4711yescharacteristic
120C2×D4—41no—
121C2×D4—41no—
122C2×D4Dic9411yescharacteristic
123C2×D4C4×D4711yescharacteristic
124C2×D4C2×Dic4711yescharacteristic
125C2×D4C22⋊D4711yescharacteristic
126C22×C4—41no—
127C22×C4—941no—
128C22×C4—941no—
129C22×C4—1882no—
130C22×C4—1881no—
131C22×C4D18811yescharacteristic
132M16—942no—
133M16—1881no—
134C2×C8—1881no—
135C22⋊C4—22no—
136C22⋊C4—41no—
137C22⋊C4—1882no—
138C22⋊C4—1881no—
139C23—21no—
140C23—21no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—41no—
146C23—41no—
147C23C4×Dic4711yescharacteristic
148C23Dic47⋊C411yescharacteristic
149C23Dic47⋊C411yescharacteristic
150C23(C2×D47)⋊C411yescharacteristic
151C23C22⋊Dic4711yescharacteristic
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—42no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—942no—
162C2×C4—1881no—
163C2×C4—1881no—
164C2×C4—1881no—
165C2×C4—1881no—
166C2×C4—1882no—
167C2×C4—1881no—
168C2×C4—1882no—
169C2×C4C4⋊Dic4711yescharacteristic
170C2×C4(C2×D47)⋊C411yescharacteristic
171C8—1882no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—81no—
188C22C47⋊#9511yescharacteristic
189C22#1309393811yescharacteristic
190C22#1309393811yescharacteristic
191C4—21no—
192C4—21no—
193C4—82no—
194C4—3761no—
195C4—1882no—
196C2—21no—
197C2—21no—
198C2—41no—
199C2—41no—
200C2—41no—
201C2—41no—
202C2#1568888911yescharacteristic
203C2#1568890911yescharacteristic
204C2#1568891211yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC23×C47C42
FrattiniC22×D4C2×D47
FittingC2×#99×C47C2
socleC22×C47#99
hypercenterC2×#99D47
hypocenterC47#1390
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. C23×Dic47C4semidirect
7. C2×C22⋊Dic47C4semidirect
9. #13093941C4semidirect
14. #99×C47C4semidirect
106. C47#1390semidirect
116. #99Dic47semidirect