Finite Group Databasebeta

← #17993679

Subgroups — #17993679

Order 4736.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557907C211yesmaximal, characteristic, complemented
2#14557728C212yesmaximal, complemented
3#14557282C211yesmaximal, characteristic, complemented
4D4⋊#64436C212yesmaximal, complemented
5C37×#555C211yesmaximal, characteristic, complemented
6C2×#10596941—22no—
7C2×#10596939—22no—
8#11924533C2211yescharacteristic
9C4⋊#64436C2212yes—
10#11924456—22no—
11C4×#64436C2211yescharacteristic
12C4⋊Q8×C37C2211yescharacteristic
13#124×C37—22no—
14#121×C37—22no—
15C4×D4×C37C2212yes—
16#117×C37—22no—
17C2×Q8×C37D412yes—
18C2×D4×C37—22no—
19C2×D4×C37D412yes—
20C22×C4×C37—22no—
21C2×D148—22no—
22C2×D148—21no—
23C4⋊C4×C37—22no—
24C4⋊C4×C37D412yes—
25C22⋊C4×C37—24no—
26C22⋊C4×C37—22no—
27C42×C37—22no—
28C42×C37C2311yescharacteristic
29#10596941—44no—
30#10596939—44no—
31C2×#64436—21no—
32C2×#64436—22no—
33C23×C37—22no—
34C22×D37—41no—
35Q8×C37—42no—
36D4×C37—22no—
37D4×C37—22no—
38D4×C37—82no—
39C2×C4×C37—22no—
40C2×C4×C37—22no—
41C2×C4×C37—42no—
42C2×C4×C37—42no—
43C2×C4×C37C2×D411yescharacteristic
44C2×C4×C37C2×D412yes—
45D148—42no—
46D148—42no—
47D148—42no—
48#64436—22no—
49#64436—42no—
50C22×C37—42no—
51C22×C37—42no—
52C22×C37—42no—
53C22×C37#12011yescharacteristic
54C2×D37—82no—
55C2×D37—81no—
56C4×C37—21no—
57C4×C37—42no—
58C4×C37—42no—
59C4×C37#13512yes—
60C4×C37AGL(1,ℤ/8)12yes—
61#1624—371nomaximal, Sylow
62C2×C37—82no—
63C2×C37#44912yes—
64C2×C37#45311yescharacteristic
65D37—161no—
66#555D3711yescharacteristic, complemented
67#492—371no—
68#459—372no—
69#333—371no—
70D4⋊C8—372no—
71C37#162411yescharacteristic, complemented, Sylow
72C2×SD16—742no—
73C2×D8—742no—
74C4⋊Q8C2×D3711yescharacteristic
75#127—371no—
76#124—22no—
77#121—22no—
78C4×D4C2×D3712yes—
79#117—22no—
80C4⋊C8—372no—
81#102—742no—
82C4×C8—371no—
83C2×Q8C22⋊D3712yes—
84C2×D4—22no—
85C2×D4—742no—
86C2×D4—741no—
87C2×D4C22⋊D3712yes—
88C22×C4—22no—
89SD16—1484no—
90D8—1484no—
91C2×C8—741no—
92C2×C8—742no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D3712yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D3711yescharacteristic
99C23—22no—
100C23—1481no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—1482no—
106D4—1482no—
107D4—1482no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D3711yescharacteristic
113C2×C4C2×C22⋊D3712yes—
114C8—742no—
115C8—1482no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—2961no—
120C22—2962no—
121C22#1192450511yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#1192455612yes—
126C4#1192456112yes—
127C2—82no—
128C2—5921no—
129C2#1455767812yes—
130C2#1455770111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#555C2
socleC22×C37#120
hypercenter#555D37
hypocenterC37#1624
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #14557907C2semidirect
2. #14557728C2semidirect
3. #14557282C2semidirect
4. D4⋊#64436C2semidirect
5. C37×#555C2semidirect
66. #555D37semidirect
71. C37#1624semidirect

Maximal subgroups

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

subgroupindex
#145579072
#145577282
#145572822
D4⋊#644362
C37×#5552
#162437