Finite Group Databasebeta

← #20242417

Subgroups — #20242417

Order 6016.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689720C211yesmaximal, characteristic
2#15689458C211yesmaximal, characteristic, complemented
3#15689441C211yesmaximal, characteristic
4#15688859C211yesmaximal, characteristic, complemented
5#15688856C211yesmaximal, characteristic
6#15688849C211yesmaximal, characteristic, complemented
7C47×#400C211yesmaximal, characteristic, complemented
8#13094019—21no—
9#13094014—21no—
10#13094009—21no—
11#13094007—21no—
12#13094003C2211yescharacteristic
13#13094002—21no—
14#13093998C2211yescharacteristic
15C4×C22⋊D47—21no—
16#13093957—21no—
17#13093955—21no—
18#13093947—21no—
19#13093944—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#95×C47—21no—
25#95×C47—21no—
26#95×C47C2211yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47D411yescharacteristic
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×D188D411yescharacteristic
34C2×C4×D47—21no—
35C2×Dic94D411yescharacteristic
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C22⋊Dic47—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47D411yescharacteristic
46C4⋊Dic47D411yescharacteristic
47Dic47⋊C4—21no—
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51C4×Dic47—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C2×D411yescharacteristic
55C22×D47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—42no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C22⋊D47—41no—
70C22⋊D47—41no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74D188—41no—
75C4×D47—81no—
76Dic94—41no—
77C47⋊C8—41no—
78C47⋊C8—41no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47#12011yescharacteristic
82C22×C47#13511yescharacteristic
83C22×C47#13711yescharacteristic
84C2×D47—41no—
85C2×D47—41no—
86C2×D47—41no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—41no—
90C4×C47—41no—
91C4×C47—81no—
92C4×C47—81no—
93Dic47—41no—
94Dic47—41no—
95Dic47—41no—
96#1615—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—21no—
99C2×C47#45211yescharacteristic
100C2×C47#45411yescharacteristic
101C2×C47#45811yescharacteristic
102D47—81no—
103#539—471no—
104#484—471no—
105#481—471no—
106#400D4711yescharacteristic, complemented
107#328—471no—
108#327—471no—
109#324—471no—
110C47#161511yescharacteristic, complemented, Sylow
111#126—941no—
112#125—941no—
113#123—941no—
114#123—941no—
115C22⋊Q8—471no—
116C22⋊Q8—941no—
117#121—471no—
118C4×D4—941no—
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C4⋊C4C2×D4711yescharacteristic
121#107—941no—
122#106—941no—
123#103—941no—
124#102—941no—
125C22⋊C8—471no—
126C22⋊C8—471no—
127#95—21no—
128#95—21no—
129#95C2×D4711yescharacteristic
130C2×Q8—471no—
131C2×D4—471no—
132C2×D4—941no—
133C22×C4—21no—
134C22×C4—21no—
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—471no—
146C4⋊C4—471no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C22⋊C4—941no—
152C22⋊C4—941no—
153C22⋊C4—941no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C42—941no—
157C23—941no—
158C23C2×C22⋊D4711yescharacteristic
159Q8—1881no—
160D4—1881no—
161D4—1881no—
162D4—1881no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—941no—
175C2×C4—941no—
176C2×C4—941no—
177C2×C4—3761no—
178C2×C4D4×D4711yescharacteristic
179C2×C4D4×D4711yescharacteristic
180C8—1881no—
181C8—1881no—
182C22—21no—
183C22—21no—
184C22—1881no—
185C22—1881no—
186C22—1881no—
187C22#1309399211yescharacteristic
188C22#1309404411yescharacteristic
189C22#1309405511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—1881no—
197C4—1881no—
198C4—1881no—
199C2—21no—
200C2—21no—
201C2—3761no—
202C2#1568928311yescharacteristic
203C2#1568929511yescharacteristic
204C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#400C2
socleC22×C47#120
hypercenter#400D47
hypocenterC47#1615
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #15689458C2semidirect
4. #15688859C2semidirect
6. #15688849C2semidirect
7. C47×#400C2semidirect
106. #400D47semidirect
110. C47#1615semidirect