Finite Group Databasebeta

← #17993680

Subgroups — #17993680

Order 4736.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558249C211yesmaximal, characteristic, complemented
2#14557907C211yesmaximal, characteristic, complemented
3#14557729C212yesmaximal, complemented
4#14557260C212yesmaximal, complemented
5C37×#333C211yesmaximal, characteristic, complemented
6C2×#10596941—22no—
7C2×D296—22no—
8#11924533C2211yescharacteristic
9#11924525—22no—
10#11924511—22no—
11C4×D148C2212yes—
12#11924494—22no—
13#11924458—22no—
14C4×#64436C2211yescharacteristic
15C4⋊Q8×C37C2211yescharacteristic
16C4⋊C8×C37C2212yes—
17C2×Q8×C37D412yes—
18C2×D148—22no—
19C2×D148—21no—
20C2×D148—22no—
21C2×D148D412yes—
22C2×C4×D37—22no—
23C2×C8×C37—22no—
24C4⋊C4×C37—22no—
25C42×C37C2311yescharacteristic
26#10596941—44no—
27#10596938—24no—
28#10596938—22no—
29C4⋊Dic37D412yes—
30C4×Dic37—22no—
31C2×#64436—21no—
32D296—44no—
33C22×D37—22no—
34C22×D37—41no—
35Q8×C37—42no—
36C2×C4×C37—22no—
37C2×C4×C37C2×D411yescharacteristic
38C2×C4×C37C2×D412yes—
39C2×Dic37—22no—
40D148—22no—
41D148—22no—
42D148—42no—
43D148—42no—
44D148—42no—
45D148—82no—
46C4×D37—42no—
47C4×D37—42no—
48C8×C37—42no—
49#64436—22no—
50C22×C37#12011yescharacteristic
51C2×D37—42no—
52C2×D37—42no—
53C2×D37—42no—
54C2×D37—82no—
55C2×D37—81no—
56C4×C37—21no—
57C4×C37—42no—
58C4×C37#13512yes—
59C4×C37AGL(1,ℤ/8)12yes—
60Dic37—42no—
61#1624—371nomaximal, Sylow
62C2×C37#44912yes—
63C2×C37#45311yescharacteristic
64D37—82no—
65D37—161no—
66#555—371no—
67#492—371no—
68#459—372no—
69#333D3711yescharacteristic, complemented
70D4⋊C8—372no—
71C37#162411yescharacteristic, complemented, Sylow
72C2×SD16—742no—
73C2×D8—742no—
74C4⋊Q8C2×D3711yescharacteristic
75#127—371no—
76#124—742no—
77#121—742no—
78C4×D4—372no—
79#117—742no—
80C4⋊C8C2×D3712yes—
81#102—742no—
82C4×C8—371no—
83C2×Q8D14812yes—
84C2×D4—372no—
85C2×D4—742no—
86C2×D4—741no—
87C2×D4—742no—
88C22×C4—742no—
89SD16—1484no—
90D8—1484no—
91C2×C8—22no—
92C2×C8—741no—
93C4⋊C4—22no—
94C4⋊C4—372no—
95C22⋊C4—744no—
96C22⋊C4—742no—
97C42—742no—
98C42C22×D3711yescharacteristic
99C23—742no—
100C23—1481no—
101Q8—42no—
102D4—2962no—
103D4—742no—
104D4—742no—
105D4—1482no—
106D4—1482no—
107D4—1482no—
108C2×C4—22no—
109C2×C4—742no—
110C2×C4—1482no—
111C2×C4—1482no—
112C2×C4C2×D14811yescharacteristic
113C2×C4D4×D3712yes—
114C8—42no—
115C8—742no—
116C22—2961no—
117C22—2962no—
118C22—1482no—
119C22—1482no—
120C22—1482no—
121C22#1192450611yescharacteristic
122C4—21no—
123C4—42no—
124C4—1482no—
125C4#1192455912yes—
126C4#1192456312yes—
127C2—2962no—
128C2—5921no—
129C2#1455768112yes—
130C2#1455770311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#333C2
socleC22×C37#120
hypercenter#333D37
hypocenterC37#1624
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #14558249C2semidirect
2. #14557907C2semidirect
3. #14557729C2semidirect
4. #14557260C2semidirect
5. C37×#333C2semidirect
69. #333D37semidirect
71. C37#1624semidirect

Maximal subgroups

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

subgroupindex
#145582492
#145579072
#145577292
#145572602
C37×#3332
#162437