Finite Group Databasebeta

← #20245431

Subgroups — #20245431

Order 6016.

166 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#13093968C211yesmaximal, characteristic
2#15689501C211yesmaximal, characteristic, complemented
3D8×Dic47C211yesmaximal, characteristic
4Dic47⋊C16C211yesmaximal, characteristic, complemented
5#15688928C211yesmaximal, characteristic, complemented
6#15688927C211yesmaximal, characteristic, complemented
7C2×SD32×C47C211yesmaximal, characteristic
8C2×Dic188C2211yescharacteristic
9C2×#10625337—21no—
10#13094022—21no—
11D4×Dic47—21no—
12#13093968—22no—
13C2×C47⋊C16C2211yescharacteristic
14#13093958C2211yescharacteristic
15#13093945—21no—
16C8×Dic47C2211yescharacteristic
17C2×Q16×C47C2211yescharacteristic
18C2×D8×C47C2211yescharacteristic
19SD32×C47—22no—
20C2×C16×C47C2211yescharacteristic
21C2×Q8×C47—21no—
22C2×D4×C47—21no—
23C22×Dic47—41no—
24C2×Dic94—21no—
25Q16×C47—21no—
26Q16×C47—21no—
27D8×C47—21no—
28D8×C47D412yes—
29C2×C8×C47C2311yescharacteristic
30C22⋊Dic47—41no—
31#10625337—42no—
32C4⋊Dic47—21no—
33Dic47⋊C4—41no—
34Dic47⋊C4—41no—
35C4×Dic47D411yescharacteristic
36C2×C47⋊C8D411yescharacteristic
37Dic188—21no—
38Dic188—21no—
39C16×C47—21no—
40C47⋊C16—21no—
41C23×C47—41no—
42Q8×C47—41no—
43Q8×C47—41no—
44D4×C47—22no—
45D4×C47—41no—
46C2×C4×C47—41no—
47C2×C4×C47C2×D411yescharacteristic
48C2×Dic47—41no—
49C2×Dic47—41no—
50C2×Dic47—82no—
51C2×Dic47D811yescharacteristic
52C2×Dic47D811yescharacteristic
53Dic94—41no—
54Dic94—41no—
55C8×C47C2×D411yescharacteristic
56C8×C47#4111yescharacteristic
57C47⋊C8—21no—
58C22×C47—42no—
59C22×C47—81no—
60C22×C47—81no—
61C22×C47C2×D811yescharacteristic
62C4×C47—81no—
63C4×C47#12111yescharacteristic
64C4×C47AGL(1,ℤ/8)11yescharacteristic
65Dic47—21no—
66Dic47—81no—
67Dic47—81no—
68Dic47SD3212yescomplemented
69#2208—471nomaximal, Sylow
70C2×C47—82no—
71C2×C47#45911yescharacteristic
72C2×C47C2×SD3211yescharacteristic
73C2×C47#51011yescharacteristic
74C2×SD32—471no—
75C2×SD32D4711yescharacteristic
76#494—471no—
77C4×D8—471no—
78C4⋊C16—471no—
79#358—471no—
80#358—471no—
81C47#220811yescharacteristic, complemented, Sylow
82C2×Q16—471no—
83C2×Q16—941no—
84C2×Q16C2×D4711yescharacteristic
85C2×D8C2×D4711yescharacteristic
86C4⋊Q8—941no—
87C4×D4—941no—
88SD32—22no—
89SD32—942no—
90C2×C16—471no—
91C2×C16C2×D4711yescharacteristic
92#107—471no—
93#102—941no—
94C4×C8—471no—
95C2×Q8—21no—
96C2×Q8—941no—
97C2×D4—21no—
98C22×C4—1881no—
99Q16—21no—
100Q16—21no—
101Q16—941no—
102Q16—941no—
103Q16—1882no—
104D8—21no—
105D8C22⋊D4712yes—
106C2×C8—471no—
107C2×C8C22×D4711yescharacteristic
108C4⋊C4—941no—
109C4⋊C4—1881no—
110C4⋊C4—1881no—
111C22⋊C4—1881no—
112C42—471no—
113C16—21no—
114C16—941no—
115C23—41no—
116Q8—41no—
117Q8—41no—
118Q8—1881no—
119Q8—1881no—
120D4—22no—
121D4—41no—
122C2×C4—41no—
123C2×C4—471no—
124C2×C4—471no—
125C2×C4—3762no—
126C2×C4—1881no—
127C2×C4—1881no—
128C2×C4D4×D4711yescharacteristic
129C8—941no—
130C8#1062535211yescharacteristic
131C8C2×C22⋊D4711yescharacteristic
132C22—42no—
133C22—81no—
134C22—81no—
135C22D8×D4711yescharacteristic
136C4—81no—
137C4—472no—
138C4—941no—
139C4—3761no—
140C4—3761no—
141C4#1309399611yescharacteristic
142C4#1309404811yescharacteristic
143C2—82no—
144C2#1568931611yescharacteristic
145C2SD32×D4711yescharacteristic
146C2#1568956211yescharacteristic
subgroupG/H
centerC22D8×D47
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC2×SD32×C47C2
socleC22×C47C2×D8
hypercenterC2×SD32D47
hypocenterC47#2208
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #15689501C2semidirect
4. Dic47⋊C16C2semidirect
5. #15688928C2semidirect
6. #15688927C2semidirect
68. Dic47SD32semidirect
81. C47#2208semidirect