Finite Group Databasebeta

← #20242383

Subgroups — #20242383

Order 6016.

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

normal subgroups only

This group has 216 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#15689453C211yesmaximal, characteristic, complemented
3#15689436C211yesmaximal, characteristic
4#15688859C211yesmaximal, characteristic, complemented
5#15688856C211yesmaximal, characteristic
6#15688849C211yesmaximal, characteristic, complemented
7C47×#398C211yesmaximal, 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×C47—21no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
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—
40C4⋊C4×C47—42no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46C4⋊Dic47D411yescharacteristic
47C4⋊Dic47D411yescharacteristic
48Dic47⋊C4—21no—
49Dic47⋊C4—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C22⋊D47—41no—
72C22⋊D47—41no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76D188—41no—
77C4×D47—81no—
78Dic94—41no—
79C47⋊C8—41no—
80C47⋊C8—41no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47#12011yescharacteristic
84C22×C47#13511yescharacteristic
85C22×C47AGL(1,ℤ/8)11yescharacteristic
86C2×D47—41no—
87C2×D47—41no—
88C2×D47—41no—
89C4×C47—21no—
90C4×C47—21no—
91C4×C47—42no—
92C4×C47—41no—
93C4×C47—41no—
94C4×C47—81no—
95Dic47—41no—
96Dic47—41no—
97Dic47—41no—
98#1609—471nomaximal, Sylow
99C2×C47—21no—
100C2×C47—21no—
101C2×C47#44911yescharacteristic
102C2×C47#45611yescharacteristic
103C2×C47#45811yescharacteristic
104D47—81no—
105#539—471no—
106#483—471no—
107#480—471no—
108#398D4711yescharacteristic, complemented
109#328—471no—
110#327—471no—
111#324—471no—
112C47#160911yescharacteristic, complemented, Sylow
113#126—941no—
114#125—941no—
115#123—941no—
116#123—941no—
117C22⋊Q8—471no—
118C22⋊Q8—941no—
119#121—471no—
120C4×D4—941no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D4711yescharacteristic
123C2×C4⋊C4C2×D4711yescharacteristic
124#107—941no—
125#106—941no—
126#103—941no—
127#102—941no—
128C22⋊C8—471no—
129C22⋊C8—471no—
130#95—21no—
131#95C2×D4711yescharacteristic
132C2×Q8—471no—
133C2×D4—471no—
134C2×D4—941no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—941no—
138C22×C4C22⋊D4711yescharacteristic
139C22×C4C22⋊D4711yescharacteristic
140C22×C4C22×D4711yescharacteristic
141C2×C8—941no—
142C2×C8—941no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—471no—
149C4⋊C4—471no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C22⋊C4—941no—
159C42—941no—
160C23—941no—
161C23C2×C22⋊D4711yescharacteristic
162Q8—1881no—
163D4—1881no—
164D4—1881no—
165D4—1881no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—3761no—
182C2×C4D4×D4711yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C8—1881no—
185C8—1881no—
186C22—21no—
187C22—21no—
188C22—1881no—
189C22—1881no—
190C22—1881no—
191C22#1309399211yescharacteristic
192C22#1309404411yescharacteristic
193C22#1309405011yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—1881no—
201C4—1881no—
202C4—1881no—
203C2—21no—
204C2—21no—
205C2—3761no—
206C2#1568926611yescharacteristic
207C2#1568930511yescharacteristic
208C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#398C2
socleC22×C47#120
hypercenter#398D47
hypocenterC47#1609
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #15689453C2semidirect
4. #15688859C2semidirect
6. #15688849C2semidirect
7. C47×#398C2semidirect
108. #398D47semidirect
112. C47#1609semidirect