Finite Group Databasebeta

← #26103674

Subgroups — #26103674

Order 12032.

184 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 39 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#20244364C211yesmaximal, characteristic
2#20241339C211yesmaximal, characteristic
3C47×#1327C211yesmaximal, characteristic
4#15689680C411yescharacteristic
5C42×Dic47C411yescharacteristic
6#15688905—21no—
7#15688884—21no—
8#15688884—21no—
9C47×#423C2211yescharacteristic
10C47×#349—21no—
11#13094024—21no—
12#13094016C812yes—
13#13094003—41no—
14C4×Dic94—41no—
15#13093983—21no—
16C2×C4×Dic47—21no—
17C2×C4×Dic47—41no—
18#13093964—41no—
19C2×M16×C47D411yescharacteristic
20C2×M16×C47D411yescharacteristic
21C2×C42×C47C2×C411yescharacteristic
22M32×C47—41no—
23C4⋊C8×C47—41no—
24C22×C4×C47—21no—
25C22×C4×C47C22⋊C411yescharacteristic
26C22×Dic47—41no—
27C2×Dic94—41no—
28M16×C47—41no—
29M16×C47—41no—
30C2×C8×C47—21no—
31C2×C8×C47—21no—
32C42×C47—21no—
33C42×C47C2×C811yescharacteristic
34C42×C47M1611yescharacteristic
35C22⋊Dic47—41no—
36C4⋊Dic47—22no—
37C4⋊Dic47—41no—
38Dic47⋊C4—42no—
39C4×Dic47—22no—
40C4×Dic47—41no—
41C4×Dic47—44no—
42C4×Dic47—41no—
43C16×C47—81no—
44C47⋊C16—81no—
45C23×C47#10011yescharacteristic
46C2×C4×C47—21no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—21no—
50C2×C4×C47—42no—
51C2×C4×C47C22⋊C811yescharacteristic
52C2×C4×C47#9911yescharacteristic
53C2×Dic47—42no—
54C2×Dic47—44no—
55C2×Dic47—42no—
56Dic94—82no—
57C8×C47—41no—
58C8×C47—41no—
59#7361—471nomaximal, Sylow
60C22×C47—21no—
61C22×C47—41no—
62C22×C47#32311yescharacteristic
63C4×C47—22no—
64C4×C47—21no—
65C4×C47—41no—
66C4×C47#35411yescharacteristic
67C4×C47#35611yescharacteristic
68Dic47—44no—
69Dic47—82no—
70#1994—471no—
71#1327—471no—
72#1327D4711yescharacteristic
73C2×C47—21no—
74C2×C47—41no—
75C2×C47#131911yescharacteristic
76#533—471no—
77#423C2×D4711yescharacteristic
78C43—471no—
79#349—21no—
80#349—941no—
81#339—941no—
82#339—941no—
83C47#736111yescharacteristic, complemented, Sylow
84C2×M16D18811yescharacteristic
85C2×M16C22⋊D4711yescharacteristic
86C4⋊Q8—941no—
87#125—472no—
88C22⋊Q8—1881no—
89C4×Q8—1881no—
90#117—941no—
91C2×C42—941no—
92C2×C42—1881no—
93C2×C42C4×D4711yescharacteristic
94M32—41no—
95M32—1881no—
96C4⋊C8—41no—
97C2×Q8—1881no—
98C22×C4—21no—
99C22×C4—1881no—
100C22×C4(C2×D47)⋊C411yescharacteristic
101M16—41no—
102M16—41no—
103C2×C8—21no—
104C2×C8—21no—
105C4⋊C4—942no—
106C4⋊C4—1882no—
107C4⋊C4—1881no—
108C22⋊C4—1881no—
109C42—21no—
110C42—942no—
111C42—1881no—
112C42—1884no—
113C42—1881no—
114C42C8×D4711yescharacteristic
115C42#1062532411yescharacteristic
116C16—81no—
117C16—3761no—
118C23#1309394011yescharacteristic
119Q8—3762no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—42no—
125C2×C4—1882no—
126C2×C4—1882no—
127C2×C4—1884no—
128C2×C4(C2×D47)⋊C811yescharacteristic
129C2×C4#1309393811yescharacteristic
130C8—41no—
131C8—41no—
132C22—21no—
133C22—41no—
134C22#1568884611yescharacteristic
135C4—22no—
136C4—21no—
137C4—41no—
138C4—3762no—
139C4—1884no—
140C4#1568891711yescharacteristic
141C4#1568892111yescharacteristic
142C2—21no—
143C2—41no—
144C2#2024132111yescharacteristic
subgroupG/H
centerC4#15688917
commutatorC42×C47C2×C8
Frattini#423C2×D47
FittingC47×#1327C2
socleC2×C47#1319
prime radicalC23×C47#100
cosocleC47×#423C22
hypercenter#1327D47
hypocenterC47#7361
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
83. C47#7361semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202443642
#202413392
C47×#13272
#736147