Finite Group Databasebeta

← #20242599

Subgroups — #20242599

Order 6016.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#15689834C211yesmaximal, characteristic
2#15689400C211yesmaximal, characteristic
3#15689330C211yesmaximal, characteristic, complemented
4#15688872C211yesmaximal, characteristic, complemented
5#15688855C211yesmaximal, characteristic, complemented
6#15688852C211yesmaximal, characteristic
7C47×#487C211yesmaximal, characteristic, complemented
8C2×#10625337—21no—
9#13094015—21no—
10#13094004—21no—
11#13094000—22no—
12C4×Dic94C2211yescharacteristic
13C4×D188C2211yescharacteristic
14#13093986—21no—
15C4⋊C4×D47—21no—
16#13093957—21no—
17C4⋊(C47⋊C8)C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19#13093948—21no—
20#13093944—21no—
21C4⋊Q8×C47C2211yescharacteristic
22C4⋊Q8×C47C2211yescharacteristic
23#103×C47—22no—
24C4×C8×C47C2211yescharacteristic
25C2×Q8×C47—21no—
26C2×Q8×C47D412yes—
27C2×D188D411yescharacteristic
28C2×C4×D47—21no—
29C2×C4×D47—22no—
30C2×Dic94D411yescharacteristic
31C2×C8×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C42×C47C2311yescharacteristic
37#10625337—42no—
38(C2×D47)⋊C4—22no—
39(C2×D47)⋊C4—21no—
40C4⋊Dic47—22no—
41C4⋊Dic47D411yescharacteristic
42C4⋊Dic47D411yescharacteristic
43Dic47⋊C4—22no—
44Dic47⋊C4—21no—
45C4×Dic47—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C22×D47—21no—
49Q8×C47—42no—
50Q8×C47—41no—
51Q8×C47—41no—
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×Dic47—21no—
58C2×Dic47—21no—
59C2×Dic47—21no—
60D188—21no—
61D188Q1612yescomplemented
62C4×D47—41no—
63C4×D47—41no—
64C4×D47—82no—
65Dic94—21no—
66Dic94—21no—
67C8×C47—41no—
68C47⋊C8—41no—
69C47⋊C8—41no—
70C22×C47#12011yescharacteristic
71C2×D47—22no—
72C2×D47—41no—
73C2×D47—41no—
74C4×C47—21no—
75C4×C47—42no—
76C4×C47—81no—
77C4×C47C2×Q1611yescharacteristic
78C4×C47#13511yescharacteristic
79C4×C47AGL(1,ℤ/8)11yescharacteristic
80C4×C47#13711yescharacteristic
81Dic47—41no—
82Dic47—41no—
83Dic47—41no—
84#1644—471nomaximal, Sylow
85C2×C47#44911yescharacteristic
86C2×C47#45111yescharacteristic
87C2×C47#45511yescharacteristic
88D47—42no—
89#554—471no—
90#487D4711yescharacteristic, complemented
91#474—471no—
92#462—471no—
93#333—471no—
94Q8⋊C8—471no—
95D4⋊C8—471no—
96C47#164411yescharacteristic, complemented, Sylow
97C2×Q16—941no—
98C4⋊Q8C2×D4711yescharacteristic
99C4⋊Q8C2×D4711yescharacteristic
100#125—941no—
101C22⋊Q8—941no—
102C22⋊Q8—942no—
103C4×Q8—471no—
104C4×D4—471no—
105C4×D4—941no—
106C2×C4⋊C4—941no—
107#107—941no—
108C4⋊C8—471no—
109C4⋊C8—471no—
110#103—22no—
111#103—941no—
112#102—941no—
113C4×C8C2×D4711yescharacteristic
114C2×Q8—21no—
115C2×Q8—471no—
116C2×Q8C22⋊D4712yes—
117C2×D4—471no—
118C22×C4—942no—
119C22×C4—941no—
120Q16—1882no—
121C2×C8—21no—
122C2×C8—941no—
123C2×C8—941no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—471no—
129C4⋊C4—471no—
130C4⋊C4—942no—
131C4⋊C4—942no—
132C4⋊C4—941no—
133C22⋊C4—942no—
134C22⋊C4—941no—
135C42—941no—
136C42C22×D4711yescharacteristic
137C23—941no—
138Q8—42no—
139Q8—41no—
140Q8—41no—
141Q8—941no—
142Q8—941no—
143D4—472no—
144D4—941no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—941no—
148C2×C4—941no—
149C2×C4—941no—
150C2×C4—3762no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4D4×D4711yescharacteristic
154C2×C4D4×D4711yescharacteristic
155C2×C4C2×C22⋊D4711yescharacteristic
156C8—41no—
157C8—1881no—
158C8—1881no—
159C22—942no—
160C22—1881no—
161C22—1881no—
162C22#1309399211yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—1881no—
167C4—1881no—
168C4—1881no—
169C4Q16×D4711yescharacteristic
170C4#1309404511yescharacteristic
171C4#1309405111yescharacteristic
172C4#1309405611yescharacteristic
173C2—1882no—
174C2#1568926711yescharacteristic
175C2#1568927711yescharacteristic
176C2#1568930011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC42×C47C23
FrattiniC42C22×D47
FittingC47×#487C2
socleC22×C47#120
hypercenter#487D47
hypocenterC47#1644
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #15689330C2semidirect
4. #15688872C2semidirect
5. #15688855C2semidirect
7. C47×#487C2semidirect
61. D188Q16semidirect
90. #487D47semidirect
96. C47#1644semidirect