Finite Group Databasebeta

← #17993891

Subgroups — #17993891

Order 4736.

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

normal subgroups only

This group has 230 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, complemented
2#14557922C212yesmaximal, complemented
3#14557899C211yesmaximal, characteristic, complemented
4#14557272C212yesmaximal, complemented
5C37×#330C211yesmaximal, characteristic, complemented
6C2×#10596930—22no—
7C2×D296—22no—
8#11924533C2211yescharacteristic
9#11924524C2212yes—
10#11924521—22no—
11#11924514—22no—
12#11924511—22no—
13#11924456—22no—
14#11924447C2211yescharacteristic
15#125×C37C2211yescharacteristic
16#97×C37C2212yes—
17C2×D148—22no—
18C2×D148—21no—
19C2×D148—22no—
20C2×D148D412yes—
21C2×C4×D37—22no—
22C2×Dic74D412yes—
23C2×C8×C37—22no—
24C4⋊C4×C37—22no—
25C4⋊C4×C37D412yes—
26C42×C37C2311yescharacteristic
27#10596938—22no—
28#10596938—22no—
29#10596938—22no—
30#10596936—22no—
31C2×#64436—21no—
32D296—44no—
33#10596930—44no—
34C22×D37—22no—
35C22×D37—41no—
36C2×C4×C37—22no—
37C2×C4×C37C2×D411yescharacteristic
38C2×C4×C37C2×D412yes—
39C2×Dic37—22no—
40D148—42no—
41D148—42no—
42D148—42no—
43D148—42no—
44D148—82no—
45C4×D37—82no—
46Dic74—42no—
47C8×C37—24no—
48#64436—41no—
49C22×C37#12011yescharacteristic
50C2×D37—42no—
51C2×D37—42no—
52C2×D37—42no—
53C2×D37—82no—
54C2×D37—81no—
55C4×C37—22no—
56C4×C37—21no—
57C4×C37—42no—
58Dic37—42no—
59#1656—371nomaximal, Sylow
60C2×C37#45312yes—
61C2×C37#45411yescharacteristic
62D37—82no—
63D37—161no—
64#562—371no—
65#496—372no—
66#490—371no—
67#330D3711yescharacteristic, complemented
68#329—372no—
69C37#165611yescharacteristic, complemented, Sylow
70C2×SD16—742no—
71C2×D8—742no—
72#127—371no—
73#125C2×D3711yescharacteristic
74#124—372no—
75#123—742no—
76C22⋊Q8—742no—
77#121—742no—
78#102—742no—
79#97—371no—
80#97C2×D3712yes—
81C2×Q8—372no—
82C2×D4—372no—
83C2×D4—742no—
84C2×D4—741no—
85C2×D4—742no—
86C22×C4—742no—
87SD16—1484no—
88D8—1484no—
89C2×C8—22no—
90C2×C8—741no—
91C4⋊C4—22no—
92C4⋊C4—742no—
93C4⋊C4D14812yes—
94C22⋊C4—742no—
95C22⋊C4—742no—
96C22⋊C4—742no—
97C42C22×D3711yescharacteristic
98C23—742no—
99C23—1481no—
100Q8—1482no—
101D4—2962no—
102D4—1482no—
103D4—1482no—
104D4—1482no—
105D4—1482no—
106C2×C4—22no—
107C2×C4—2962no—
108C2×C4—742no—
109C2×C4C2×D14811yescharacteristic
110C2×C4D4×D3712yes—
111C8—24no—
112C8—1481no—
113C22—2962no—
114C22—2961no—
115C22—1482no—
116C22—1482no—
117C22—1482no—
118C22#1192450611yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1482no—
123C2—2962no—
124C2—5921no—
125C2#1455770212yes—
126C2#1455770811yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37#120
hypercenter#330D37
hypocenterC37#1656
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #14558281C2semidirect
2. #14557922C2semidirect
3. #14557899C2semidirect
4. #14557272C2semidirect
5. C37×#330C2semidirect
67. #330D37semidirect
69. C37#1656semidirect

Maximal subgroups

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

subgroupindex
#145582812
#145579222
#145578992
#145572722
C37×#3302
#165637