Finite Group Databasebeta

← #17992639

Subgroups — #17992639

Order 4736.

102 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 41 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
1C4⋊#10596925C211yesmaximal, characteristic, complemented
2#14557284C211yesmaximal, characteristic, complemented
3C37×#495C211yesmaximal, characteristic
4C2×#10596925—21no—
5C4⋊#64436—21no—
6C2×Q16×C37C411yescharacteristic
7C2×SD16×C37—21no—
8C2×D8×C37C411yescharacteristic
9#124×C37—21no—
10C4×C8×C37C2211yescharacteristic
11C2×Q8×C37—21no—
12C2×D4×C37—21no—
13Q16×C37—41no—
14SD16×C37—41no—
15SD16×C37—41no—
16D8×C37—41no—
17C2×C8×C37C2×C411yescharacteristic
18C2×C8×C37D411yescharacteristic
19C22⋊C4×C37—41no—
20C22⋊C4×C37—41no—
21C42×C37D411yescharacteristic
22C2×#64436—41no—
23#10596925—41no—
24C23×C37—41no—
25Q8×C37—41no—
26Q8×C37—41no—
27D4×C37—41no—
28D4×C37—41no—
29C2×C4×C37—41no—
30C2×C4×C37C22⋊C411yescharacteristic
31C2×C4×C37D811yescharacteristic
32C2×C4×C37SD1611yescharacteristic
33C8×C37—21no—
34C8×C37D811yescharacteristic
35C8×C37SD1611yescharacteristic
36#64436—81no—
37C22×C37—81no—
38C22×C37—81no—
39C22×C37—81no—
40C22×C37#10211yescharacteristic
41C4×C37—21no—
42C4×C37—21no—
43C4×C37—81no—
44C4×C37#10011yescharacteristic
45C4×C37#10211yescharacteristic
46#1360—371nomaximal, Sylow
47C2×C37—161no—
48C2×C37#33111yescharacteristic
49C2×C37#35911yescharacteristic
50C2×C37#36011yescharacteristic
51#495D3711yescharacteristic
52C4⋊C16—371no—
53#334—371no—
54C37#136011yescharacteristic, complemented, Sylow
55C2×Q16Dic3711yescharacteristic
56C2×SD16—21no—
57C2×D8Dic3711yescharacteristic
58#124—21no—
59C2×C16—741no—
60C4⋊C8—741no—
61C4×C8C2×D3711yescharacteristic
62C2×Q8—21no—
63C2×D4—21no—
64Q16—41no—
65SD16—41no—
66SD16—41no—
67D8—41no—
68C2×C8—1481no—
69C2×C8C2×Dic3711yescharacteristic
70C2×C8C22⋊D3711yescharacteristic
71C22⋊C4—41no—
72C22⋊C4—41no—
73C42C22⋊D3711yescharacteristic
74C16—1481no—
75C23—41no—
76Q8—41no—
77Q8—41no—
78D4—41no—
79D4—41no—
80C2×C4—41no—
81C2×C4#1059693911yescharacteristic
82C2×C4#1059694011yescharacteristic
83C2×C4C22⋊Dic3711yescharacteristic
84C8—21no—
85C8—2961no—
86C8#1059693911yescharacteristic
87C8#1059694011yescharacteristic
88C22—81no—
89C22—81no—
90C22—81no—
91C22#1192445711yescharacteristic
92C4—21no—
93C4—21no—
94C4—81no—
95C4#1192445311yescharacteristic
96C4#1192445711yescharacteristic
97C2—161no—
98C2#1455727711yescharacteristic
99C2#1455734011yescharacteristic
100C2#1455734311yescharacteristic
subgroupG/H
centerC22#11924457
commutatorC2×C8×C37C2×C4
FrattiniC4×C8C2×D37
FittingC37×#495C2
socleC22×C37#102
prime radicalC2×D8×C37C4
cosocleC4×C8×C37C22
hypercenter#495D37
hypocenterC37#1360
LCSG ▷ C2×C8×C37 ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C4⋊#10596925C2semidirect
2. #14557284C2semidirect
54. C37#1360semidirect

Maximal subgroups

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

subgroupindex
C4⋊#105969252
#145572842
C37×#4952
#136037