Finite Group Databasebeta

← #20256280

Subgroups — #20256280

Order 6016.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689851C212yesmaximal
2#15689528C211yesmaximal, characteristic
3#15689525C212yesmaximal
4#15689431C214yesmaximal
5#15689409C212yesmaximal
6C4×Dic188C212yesmaximal
7C4×Dic188C211yesmaximal, characteristic
8C8×Q8×C47C211yesmaximal, characteristic
9C2×Dic188C2211yescharacteristic
10#13094024C2212yes—
11#13094022—22no—
12#13094016C2214yes—
13#13094014—24no—
14C4×Dic94C2212yes—
15C4×Dic94C2214yes—
16#13093989—22no—
17#13093958C2211yescharacteristic
18#13093958C2212yes—
19#13093958C2212yes—
20#13093956C2214yes—
21#13093949C2214yes—
22#13093949C2212yes—
23C4×Q8×C47C2211yescharacteristic
24C4⋊C8×C47C2211yescharacteristic
25C4⋊C8×C47C2212yes—
26C4×C8×C47C2212yes—
27C4×C8×C47C2211yescharacteristic
28C2×Q8×C47D411yescharacteristic
29C2×Dic94—22no—
30C2×Dic94C2312yes—
31C2×C8×C47C2312yes—
32C2×C8×C47C2311yescharacteristic
33C2×C8×C47C2311yescharacteristic
34C4⋊C4×C47D411yescharacteristic
35C4⋊C4×C47D412yes—
36C42×C47C2312yes—
37C42×C47C2311yescharacteristic
38C4⋊Dic47—22no—
39C4⋊Dic47C2312yes—
40C4⋊Dic47C2314yes—
41Dic47⋊C4—24no—
42Dic47⋊C4—22no—
43Dic47⋊C4—24no—
44Dic47⋊C4—24no—
45C4×Dic47—24no—
46C4×Dic47—22no—
47Dic188Q814yescomplemented
48Q8×C47—22no—
49C2×C4×C47C2×D412yes—
50C2×C4×C47C2×D412yes—
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2411yescharacteristic
54C2×Dic47—22no—
55C2×Dic47—22no—
56C2×Dic47—24no—
57Dic94—22no—
58Dic94—44no—
59Dic94C2×Q814yes—
60C8×C47—22no—
61C8×C47—21no—
62C8×C47C2×Q812yes—
63C22×C47C22×D411yescharacteristic
64C4×C47—22no—
65C4×C47—22no—
66C4×C47—21no—
67C4×C47#13512yes—
68C4×C47C22×Q811yescharacteristic
69C4×C472−1+411yescharacteristic
70Dic47—24no—
71Dic47—44no—
72Dic47—42no—
73#3383—471nomaximal, Sylow
74C2×C47D4×Q811yescharacteristic
75C2×C47C2×#13511yescharacteristic
76C2×C47#57811yescharacteristic
77#557—472no—
78#500—471no—
79#499—472no—
80#479—474no—
81#475—472no—
82C8×Q8D4711yescharacteristic
83C4×Q16—472no—
84C4×Q16—471no—
85C47#338311yescharacteristic, complemented, Sylow
86C2×Q16—471no—
87C4⋊Q8—472no—
88C4⋊Q8—942no—
89#125—474no—
90#125—944no—
91C4×Q8—472no—
92C4×Q8—474no—
93C4×Q8—942no—
94C4×Q8C2×D4711yescharacteristic
95#107—471no—
96#107—472no—
97#107—472no—
98#106—474no—
99C4⋊C8C2×D4711yescharacteristic
100C4⋊C8C2×D4712yes—
101#103—474no—
102#103—472no—
103C4×C8C2×D4712yes—
104C4×C8C2×D4711yescharacteristic
105C2×Q8—472no—
106C2×Q8—942no—
107C2×Q8D18811yescharacteristic
108Q16—474no—
109C2×C8C22×D4712yes—
110C2×C8C22×D4711yescharacteristic
111C2×C8C22×D4711yescharacteristic
112C4⋊C4—472no—
113C4⋊C4—474no—
114C4⋊C4—942no—
115C4⋊C4—944no—
116C4⋊C4—944no—
117C4⋊C4—944no—
118C4⋊C4—942no—
119C4⋊C4D18811yescharacteristic
120C4⋊C4D18812yes—
121C42—944no—
122C42—942no—
123C42C22×D4712yes—
124C42C22×D4711yescharacteristic
125Q8—22no—
126Q8—474no—
127Q8—942no—
128Q8—1884no—
129C2×C4—942no—
130C2×C4—942no—
131C2×C4—944no—
132C2×C4C2×D18812yes—
133C2×C4C2×D18811yescharacteristic
134C2×C4C2×D18812yes—
135C2×C4C2×D18811yescharacteristic
136C2×C4C23×D4711yescharacteristic
137C8—22no—
138C8—21no—
139C8Q8×D4712yes—
140C22C22×D18811yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—944no—
145C4—1884no—
146C4—1882no—
147C4#1309404612yes—
148C4C2×Q8×D4711yescharacteristic
149C4#1309407111yescharacteristic
150C2Q8×D18811yescharacteristic
151C2C2×#1309404611yescharacteristic
152C2#1568994011yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×Q8×C47C2
socleC22×C47C22×D4
hypercenterC8×Q8D47
hypocenterC47#3383
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
47. Dic188Q8semidirect
85. C47#3383semidirect