Finite Group Databasebeta

← #26104148

Subgroups — #26104148

Order 12032.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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#20243019C211yesmaximal, characteristic
2#20241557C211yesmaximal, characteristic
3C47×#1411C211yesmaximal, characteristic
4#15689521C411yescharacteristic
5#15689519—21no—
6#15689475—21no—
7#15688922—21no—
8#15688844C411yescharacteristic
9C47×#494C2211yescharacteristic
10C47×#356—21no—
11#13094024—21no—
12#13093956—41no—
13#13093955—42no—
14#13093947—42no—
15#13093943—41no—
16C4×C47⋊C8—21no—
17C2×Q16×C47—41no—
18C4⋊Q8×C47D411yescharacteristic
19C4⋊Q8×C47D411yescharacteristic
20#101×C47—41no—
21C4×C8×C47C2×C411yescharacteristic
22C2×Q8×C47—21no—
23C2×Q8×C47—21no—
24C2×Dic94—41no—
25Q16×C47—82no—
26M16×C47—81no—
27C2×C8×C47—21no—
28C4⋊C4×C47—41no—
29C4⋊C4×C47—41no—
30C42×C47C22⋊C411yescharacteristic
31C4⋊Dic47—41no—
32C4⋊Dic47—41no—
33#10625329—81no—
34C2×C47⋊C8—22no—
35Q8×C47—81no—
36Q8×C47—81no—
37C2×C4×C47—21no—
38C2×C4×C47—41no—
39C2×C4×C47—41no—
40C2×C4×C47#9911yescharacteristic
41C2×Dic47—81no—
42Dic94—82no—
43C8×C47—22no—
44C8×C47—161no—
45C47⋊C8—42no—
46C47⋊C8—161no—
47#7534—471nomaximal, Sylow
48C22×C47#35311yescharacteristic
49C4×C47—22no—
50C4×C47—21no—
51C4×C47—81no—
52C4×C47—81no—
53Dic47—161no—
54#1716—471no—
55#1411—471no—
56#1411D4711yescharacteristic
57C2×C47—21no—
58C2×C47#140911yescharacteristic
59#498—471no—
60#498—941no—
61#494C2×D4711yescharacteristic
62#487—941no—
63#356—21no—
64#356—941no—
65#322—471no—
66C47#753411yescharacteristic, complemented, Sylow
67C2×Q16—41no—
68C4⋊Q8—941no—
69C4⋊Q8D18811yescharacteristic
70C4⋊Q8C22⋊D4711yescharacteristic
71#106—1882no—
72#106—1881no—
73#103—1882no—
74#101—41no—
75#101—1881no—
76C4×C8—941no—
77C4×C8C4×D4711yescharacteristic
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—1881no—
81Q16—82no—
82M16—81no—
83M16—3761no—
84C2×C8—21no—
85C2×C8—942no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—1881no—
89C4⋊C4—1881no—
90C42(C2×D47)⋊C411yescharacteristic
91Q8—81no—
92Q8—81no—
93Q8—3762no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—3761no—
98C2×C4#1309393811yescharacteristic
99C8—22no—
100C8—161no—
101C8—1882no—
102C8—7521no—
103C22#1568891511yescharacteristic
104C4—22no—
105C4—21no—
106C4—81no—
107C4—81no—
108C4—7521no—
109C2—21no—
110C2#2024155211yescharacteristic
subgroupG/H
centerC2#20241552
commutatorC4×C8×C47C2×C4
Frattini#494C2×D47
FittingC47×#1411C2
socleC2×C47#1409
prime radicalC22×C47#353
cosocleC47×#494C22
hypercenter#1411D47
hypocenterC47#7534
LCSG ▷ C4×C8×C47 ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
66. C47#7534semidirect

Maximal subgroups

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

subgroupindex
#202430192
#202415572
C47×#14112
#753447