Finite Group Databasebeta

← #20255819

Subgroups — #20255819

Order 6016.

340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689843C212yesmaximal
2#15689528C211yesmaximal, characteristic, complemented
3#15689465C214yesmaximal, complemented
4#15689409C212yesmaximal, complemented
5#15689364C212yesmaximal, complemented
6C4×Dic188C211yesmaximal, characteristic, complemented
7#15689161C212yesmaximal, complemented
8C8×D4×C47C211yesmaximal, characteristic
9C2×Dic188C2211yescharacteristic
10#13094024C2212yes—
11#13094017—24no—
12#13094011—22no—
13#13094003C2214yes—
14C4×Dic94C2212yes—
15#13093989—22no—
16#13093983C2214yes—
17#13093958C2211yescharacteristic
18#13093958C2212yes—
19#13093958C2212yes—
20#13093956C2214yes—
21#13093949C2212yes—
22#13093949C2214yes—
23C22×C8×C47C2212yes—
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic
26C22⋊C8×C47C2212yes—
27C4×C8×C47C2211yescharacteristic
28C2×D4×C47D411yescharacteristic
29C22×C4×C47C2312yes—
30C2×Dic94—22no—
31C2×Dic94C2312yes—
32C2×C8×C47—24no—
33C2×C8×C47C2312yes—
34C2×C8×C47C2311yescharacteristic
35C2×C8×C47C2311yescharacteristic
36C4⋊C4×C47D411yescharacteristic
37C22⋊C4×C47D412yes—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—24no—
40C22⋊Dic47—24no—
41C4⋊Dic47—22no—
42C4⋊Dic47C2312yes—
43C4⋊Dic47C2314yes—
44Dic47⋊C4—24no—
45Dic47⋊C4—22no—
46C4×Dic47—24no—
47C4×Dic47—22no—
48Dic188—22no—
49C23×C47C2×D412yes—
50D4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47C2×D412yes—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2411yescharacteristic
57C2×Dic47—22no—
58C2×Dic47—22no—
59C2×Dic47—24no—
60Dic94—22no—
61Dic94—22no—
62Dic94—44no—
63C8×C47—22no—
64C8×C47—21no—
65C8×C47#4112yes—
66C22×C47—22no—
67C22×C47—22no—
68C22×C47—22no—
69C22×C47C22×D411yescharacteristic
70C4×C47—22no—
71C4×C47—21no—
72C4×C47#13512yes—
73C4×C47C2×#4111yescharacteristic
74C4×C472−1+411yescharacteristic
75Dic47—42no—
76Dic47—44no—
77Dic47—42no—
78#3342—471nomaximal, Sylow
79C2×C47—42no—
80C2×C47#54711yescharacteristic
81C2×C47C2×#13511yescharacteristic
82C2×C47#57811yescharacteristic
83#556—472no—
84#500—471no—
85#485—474no—
86#475—472no—
87#467—472no—
88C4×Q16—471no—
89C8×D4D4711yescharacteristic
90#427—472no—
91C47#334211yescharacteristic, complemented, Sylow
92C2×Q16—471no—
93C22×C8C2×D4712yes—
94C4⋊Q8—472no—
95#126—944no—
96#124—942no—
97C22⋊Q8—474no—
98C4×Q8—472no—
99C4×Q8—942no—
100C4×D4C2×D4711yescharacteristic
101#117—474no—
102#107—471no—
103#107—472no—
104#107—472no—
105#106—474no—
106C4⋊C8C2×D4711yescharacteristic
107#103—472no—
108#103—474no—
109C22⋊C8C2×D4712yes—
110C4×C8C2×D4711yescharacteristic
111C2×Q8—472no—
112C2×Q8—942no—
113C2×D4D18811yescharacteristic
114C22×C4C22×D4712yes—
115Q16—942no—
116C2×C8—24no—
117C2×C8C22×D4711yescharacteristic
118C2×C8C22×D4712yes—
119C2×C8C22×D4711yescharacteristic
120C4⋊C4—472no—
121C4⋊C4—474no—
122C4⋊C4—942no—
123C4⋊C4—944no—
124C4⋊C4—942no—
125C4⋊C4D18811yescharacteristic
126C22⋊C4—944no—
127C22⋊C4—944no—
128C22⋊C4D18812yes—
129C42—944no—
130C42—942no—
131C42C22×D4711yescharacteristic
132C23C2×D18812yes—
133Q8—942no—
134Q8—942no—
135Q8—1884no—
136D4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—942no—
140C2×C4—944no—
141C2×C4—942no—
142C2×C4C2×D18812yes—
143C2×C4C2×D18811yescharacteristic
144C2×C4C2×D18811yescharacteristic
145C2×C4C23×D4711yescharacteristic
146C8—22no—
147C8—21no—
148C8#1062535212yes—
149C22—22no—
150C22—22no—
151C22—22no—
152C22C22×D18811yescharacteristic
153C4—22no—
154C4—21no—
155C4—1882no—
156C4—1884no—
157C4—1882no—
158C4#1309404612yes—
159C4C2×#1062535211yescharacteristic
160C4#1309407111yescharacteristic
161C2—42no—
162C2#1568977711yescharacteristic
163C2C2×#1309404611yescharacteristic
164C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3342
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #15689528C2semidirect
3. #15689465C2semidirect
4. #15689409C2semidirect
5. #15689364C2semidirect
6. C4×Dic188C2semidirect
7. #15689161C2semidirect
91. C47#3342semidirect