Finite Group Databasebeta

← #17993920

Subgroups — #17993920

Order 4736.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558281C211yesmaximal, characteristic
2#14557903C211yesmaximal, characteristic, complemented
3#14557893C212yesmaximal, complemented
4#14557272C212yesmaximal, complemented
5C37×#330C211yesmaximal, characteristic, complemented
6#11924536C2211yescharacteristic
7#11924524C2212yes—
8#11924521—22no—
9#11924514—22no—
10#11924511—22no—
11#11924461—22no—
12#11924459—22no—
13#11924458—22no—
14#11924447C2211yescharacteristic
15#125×C37C2211yescharacteristic
16#97×C37C2212yes—
17C2×D148—22no—
18C2×D148D412yes—
19C2×C4×D37—22no—
20C2×Dic74—21no—
21C2×Dic74D412yes—
22C2×C8×C37—22no—
23C4⋊C4×C37—22no—
24C4⋊C4×C37D412yes—
25C42×C37C2311yescharacteristic
26#10596938—22no—
27#10596938—22no—
28#10596938—22no—
29C4⋊Dic37—22no—
30#10596936—22no—
31C2×#64436—21no—
32C22×D37—22no—
33C2×C4×C37—22no—
34C2×C4×C37C2×D411yescharacteristic
35C2×C4×C37C2×D412yes—
36C2×Dic37—22no—
37C2×Dic37—41no—
38D148—42no—
39D148—82no—
40C4×D37—82no—
41Dic74—42no—
42Dic74—42no—
43C8×C37—42no—
44#64436—41no—
45C22×C37#12011yescharacteristic
46C2×D37—42no—
47C2×D37—42no—
48C2×D37—42no—
49C4×C37—21no—
50C4×C37—22no—
51C4×C37—42no—
52Dic37—42no—
53Dic37—81no—
54#1662—371nomaximal, Sylow
55C2×C37#45411yescharacteristic
56C2×C37#45512yes—
57D37—82no—
58#562—371no—
59#491—371no—
60#489—372no—
61#330D3711yescharacteristic, complemented
62#329—372no—
63C37#166211yescharacteristic, complemented, Sylow
64C4⋊Q8—371no—
65#125C2×D3711yescharacteristic
66#124—372no—
67#123—742no—
68C22⋊Q8—742no—
69#121—742no—
70#103—742no—
71#103—742no—
72#102—742no—
73#97—371no—
74#97C2×D3712yes—
75C2×Q8—372no—
76C2×Q8—741no—
77C2×D4—372no—
78C2×D4—742no—
79C22×C4—742no—
80C2×C8—22no—
81C2×C8—741no—
82C4⋊C4—22no—
83C4⋊C4—742no—
84C4⋊C4—742no—
85C4⋊C4D14812yes—
86C22⋊C4—742no—
87C22⋊C4—742no—
88C22⋊C4—742no—
89C42C22×D3711yescharacteristic
90C23—742no—
91Q8—1482no—
92Q8—1482no—
93D4—2962no—
94D4—1482no—
95C2×C4—22no—
96C2×C4—2962no—
97C2×C4—742no—
98C2×C4—1481no—
99C2×C4C2×D14811yescharacteristic
100C2×C4D4×D3712yes—
101C8—42no—
102C8—1481no—
103C22—1482no—
104C22—1482no—
105C22—1482no—
106C22#1192450611yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—2961no—
111C4—1482no—
112C2—2962no—
113C2#1455770811yescharacteristic
114C2#1455771212yes—
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37#120
prime radical#14558281C2
hypercenter#330D37
hypocenterC37#1662
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #14557903C2semidirect
3. #14557893C2semidirect
4. #14557272C2semidirect
5. C37×#330C2semidirect
61. #330D37semidirect
63. C37#1662semidirect

Maximal subgroups

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

subgroupindex
#145582812
#145579032
#145578932
#145572722
C37×#3302
#166237