Finite Group Databasebeta

← #20242419

Subgroups — #20242419

Order 6016.

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

normal subgroups only

This group has 208 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#15689456C211yesmaximal, characteristic, complemented
2#15689439C211yesmaximal, characteristic
3#15689062C211yesmaximal, characteristic, complemented
4#15688860C211yesmaximal, characteristic, complemented
5#15688857C211yesmaximal, characteristic
6#15688849C211yesmaximal, characteristic, complemented
7C47×#539C211yesmaximal, characteristic
8C2×C4⋊Dic47C2211yescharacteristic
9#13093957—21no—
10#13093955—21no—
11#13093948—21no—
12#13093945—21no—
13C22⋊(C47⋊C8)C2211yescharacteristic
14C22⋊(C47⋊C8)C2211yescharacteristic
15C47⋊#95—21no—
16C47⋊#95—21no—
17C47⋊#95C2211yescharacteristic
18#126×C47—21no—
19#125×C47—21no—
20#123×C47—21no—
21#123×C47—21no—
22C22⋊Q8×C47—21no—
23C22⋊Q8×C47C2211yescharacteristic
24#121×C47C2211yescharacteristic
25C4×D4×C47—21no—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C2×D4×C47—21no—
29C2×D4×C47D411yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47D411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47D411yescharacteristic
43C4⋊C4×C47D411yescharacteristic
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C42×C47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47—21no—
55C23×C47C2×D411yescharacteristic
56Q8×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59D4×C47—41no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—81no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—42no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C47⋊C8—41no—
78C47⋊C8—41no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—41no—
82C22×C47—41no—
83C22×C47—41no—
84C22×C47#12011yescharacteristic
85C22×C47#13511yescharacteristic
86C22×C47#13711yescharacteristic
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—41no—
90C4×C47—41no—
91C4×C47—41no—
92C4×C47—41no—
93C4×C47—41no—
94Dic47—81no—
95Dic47—81no—
96#1615—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—21no—
99C2×C47—81no—
100C2×C47#45211yescharacteristic
101C2×C47#45411yescharacteristic
102C2×C47#45811yescharacteristic
103#539D4711yescharacteristic
104#484—471no—
105#481—471no—
106#400—471no—
107#328—471no—
108#327—471no—
109#324—471no—
110C47#161511yescharacteristic, complemented, Sylow
111#126—21no—
112#125—21no—
113#123—21no—
114#123—21no—
115C22⋊Q8—21no—
116C22⋊Q8C2×D4711yescharacteristic
117#121C2×D4711yescharacteristic
118C4×D4—21no—
119C2×C4⋊C4—471no—
120C2×C4⋊C4C2×D4711yescharacteristic
121#107—941no—
122#106—941no—
123#103—941no—
124#102—941no—
125C22⋊C8—471no—
126C22⋊C8—471no—
127#95—471no—
128#95—941no—
129#95—941no—
130C2×Q8C22⋊D4711yescharacteristic
131C2×D4—21no—
132C2×D4C22⋊D4711yescharacteristic
133C22×C4—21no—
134C22×C4—941no—
135C22×C4—941no—
136C22×C4C22⋊D4711yescharacteristic
137C22×C4C22⋊D4711yescharacteristic
138C22×C4C22×D4711yescharacteristic
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4C22⋊D4711yescharacteristic
150C4⋊C4C22⋊D4711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×C22⋊D4711yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4—1882no—
176C2×C4—1881no—
177C2×C4—1881no—
178C2×C4C2×C22⋊D4711yescharacteristic
179C2×C4C2×C22⋊D4711yescharacteristic
180C8—1881no—
181C8—1881no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1309399311yescharacteristic
188C22#1309404411yescharacteristic
189C22#1309405411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—3761no—
198C4—3761no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#1568928511yescharacteristic
203C2#1568929611yescharacteristic
204C2#1568931311yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#539C2
socleC22×C47#120
hypercenter#539D47
hypocenterC47#1615
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #15689456C2semidirect
3. #15689062C2semidirect
4. #15688860C2semidirect
6. #15688849C2semidirect
110. C47#1615semidirect