Finite Group Databasebeta

← #20242470

Subgroups — #20242470

Order 6016.

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

normal subgroups only

This group has 240 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#15689838C211yesmaximal, characteristic, complemented
2#15689495C211yesmaximal, characteristic, complemented
3#15689315C211yesmaximal, characteristic, complemented
4#15688871C211yesmaximal, characteristic, complemented
5D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#15688850C211yesmaximal, characteristic, complemented
7C47×#459C211yesmaximal, characteristic, complemented
8C2×#10625335—22no—
9C2×#10625334—21no—
10#13094024C2211yescharacteristic
11#13094010—22no—
12#13093998—21no—
13#13093995—21no—
14C4×D188C2211yescharacteristic
15#13093983—21no—
16#13093982—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18#13093945—21no—
19C4×C47⋊C8C2211yescharacteristic
20C2×D8×C47—21no—
21#127×C47C2211yescharacteristic
22C4×D4×C47C2211yescharacteristic
23C4⋊C8×C47C2211yescharacteristic
24#102×C47—21no—
25C2×D4×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47D411yescharacteristic
29C22×C4×C47—21no—
30C2×C22⋊D47—22no—
31C2×D188D411yescharacteristic
32C2×C4×D47—21no—
33C2×Dic94D412yes—
34D8×C47—42no—
35C2×C8×C47—21no—
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—22no—
40#10625335—44no—
41#10625334—42no—
42(C2×D47)⋊C4—22no—
43(C2×D47)⋊C4—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47D411yescharacteristic
47C4×Dic47—22no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47—21no—
51C23×C47—41no—
52C22×D47—21no—
53D4×C47—21no—
54D4×C47—21no—
55D4×C47—42no—
56D4×C47—41no—
57D4×C47—41no—
58D4×C47—41no—
59D4×C47—41no—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C22⋊D47—82no—
67C2×Dic47—21no—
68C2×Dic47—22no—
69D188—21no—
70D188—21no—
71C4×D47—41no—
72C4×D47—41no—
73Dic94—42no—
74C8×C47—41no—
75C47⋊C8—22no—
76C47⋊C8—41no—
77C22×C47—41no—
78C22×C47—41no—
79C22×C47—41no—
80C22×C47—81no—
81C22×C47—81no—
82C22×C47—81no—
83C22×C47#12011yescharacteristic
84C2×D47—41no—
85C2×D47—41no—
86C2×D47—41no—
87C4×C47—21no—
88C4×C47—41no—
89C4×C47#13511yescharacteristic
90C4×C47#13511yescharacteristic
91C4×C47AGL(1,ℤ/8)11yescharacteristic
92C4×C47AGL(1,ℤ/8)11yescharacteristic
93Dic47—41no—
94Dic47—42no—
95#1624—471nomaximal, Sylow
96C2×C47—81no—
97C2×C47—161no—
98C2×C47#44911yescharacteristic
99C2×C47#44911yescharacteristic
100C2×C47#45311yescharacteristic
101D47—81no—
102#555—471no—
103#492—471no—
104#459—471no—
105#459D4711yescharacteristic, complemented
106#333—471no—
107D4⋊C8—471no—
108D4⋊C8—471no—
109C47#162411yescharacteristic, complemented, Sylow
110C2×SD16—942no—
111C2×D8—21no—
112C2×D8—941no—
113C4⋊Q8—471no—
114#127C2×D4711yescharacteristic
115#124—942no—
116#121—941no—
117#121—941no—
118C4×D4—471no—
119C4×D4C2×D4711yescharacteristic
120#117—941no—
121#117—941no—
122C4⋊C8—471no—
123C4⋊C8C2×D4711yescharacteristic
124#102—21no—
125#102—941no—
126C4×C8—471no—
127C2×Q8—472no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—471no—
132C2×D4—942no—
133C2×D4C22⋊D4711yescharacteristic
134C22×C4—21no—
135C22×C4—941no—
136SD16—1884no—
137D8—42no—
138D8—1882no—
139C2×C8—21no—
140C2×C8—941no—
141C2×C8—941no—
142C4⋊C4—471no—
143C4⋊C4—941no—
144C4⋊C4—941no—
145C4⋊C4C22⋊D4711yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—942no—
148C22⋊C4—942no—
149C22⋊C4—941no—
150C42—942no—
151C42C22×D4711yescharacteristic
152C23—21no—
153C23—41no—
154C23—941no—
155Q8—1882no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—941no—
164D4—941no—
165D4—3762no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—941no—
170C2×C4—942no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4711yescharacteristic
175C2×C4C2×C22⋊D4711yescharacteristic
176C8—41no—
177C8—942no—
178C8—1881no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—1881no—
186C22—1881no—
187C22—1881no—
188C22#1309399211yescharacteristic
189C4—21no—
190C4—41no—
191C4—1881no—
192C4—1882no—
193C4#1309404311yescharacteristic
194C4#1309404411yescharacteristic
195C4#1309404811yescharacteristic
196C4#1309405011yescharacteristic
197C2—81no—
198C2—161no—
199C2—3761no—
200C2#1568926511yescharacteristic
201C2#1568926611yescharacteristic
202C2#1568928911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#459C2
socleC22×C47#120
hypercenter#459D47
hypocenterC47#1624
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #15689838C2semidirect
2. #15689495C2semidirect
3. #15689315C2semidirect
4. #15688871C2semidirect
5. D4⋊(C47⋊C8)C2semidirect
6. #15688850C2semidirect
7. C47×#459C2semidirect
105. #459D47semidirect
109. C47#1624semidirect