Finite Group Databasebeta

← #17993889

Subgroups — #17993889

Order 4736.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#14557923C212yesmaximal, complemented
2#14557899C211yesmaximal, characteristic, complemented
3#14557275C211yesmaximal, characteristic, complemented
4#14557273C212yesmaximal, complemented
5C37×#562C211yesmaximal, characteristic, complemented
6C2×#10596941—22no—
7C2×#10596939—22no—
8#11924533C2211yescharacteristic
9#11924456—22no—
10#11924447C2211yescharacteristic
11#11924447C2212yes—
12#125×C37C2211yescharacteristic
13#124×C37C2212yes—
14#123×C37—22no—
15C22⋊Q8×C37—22no—
16#121×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×C37—22no—
25C4⋊C4×C37D412yes—
26C22⋊C4×C37—22no—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C42×C37C2311yescharacteristic
30#10596941—44no—
31#10596939—44no—
32C2×#64436—22no—
33C2×#64436—21no—
34C23×C37—22no—
35C22×D37—41no—
36Q8×C37—42no—
37D4×C37—42no—
38D4×C37—82no—
39C2×C4×C37—22no—
40C2×C4×C37—22no—
41C2×C4×C37—82no—
42C2×C4×C37C2×D411yescharacteristic
43C2×C4×C37C2×D412yes—
44D148—42no—
45D148—42no—
46D148—42no—
47#64436—24no—
48#64436—41no—
49C22×C37—42no—
50C22×C37—42no—
51C22×C37—42no—
52C22×C37#12011yescharacteristic
53C2×D37—82no—
54C2×D37—81no—
55C4×C37—22no—
56C4×C37—21no—
57C4×C37—42no—
58C4×C37—42no—
59#1656—371nomaximal, Sylow
60C2×C37—82no—
61C2×C37#45312yes—
62C2×C37#45411yescharacteristic
63D37—161no—
64#562D3711yescharacteristic, complemented
65#496—372no—
66#490—371no—
67#330—371no—
68#329—372no—
69C37#165611yescharacteristic, complemented, Sylow
70C2×SD16—742no—
71C2×D8—742no—
72#127—371no—
73#125C2×D3711yescharacteristic
74#124C2×D3712yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—742no—
79#97—371no—
80#97—372no—
81C2×Q8C22⋊D3712yes—
82C2×D4—22no—
83C2×D4—741no—
84C2×D4—742no—
85C2×D4C22⋊D3712yes—
86C22×C4—22no—
87SD16—1484no—
88D8—1484no—
89C2×C8—742no—
90C2×C8—741no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D3712yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D3711yescharacteristic
98C23—22no—
99C23—1481no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—1482no—
104D4—1482no—
105D4—1482no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D3711yescharacteristic
110C2×C4C2×C22⋊D3712yes—
111C8—744no—
112C8—1481no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—2962no—
117C22—2961no—
118C22#1192450511yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—5921no—
125C2#1455770112yes—
126C2#1455770611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#562C2
socleC22×C37#120
hypercenter#562D37
hypocenterC37#1656
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14557923C2semidirect
2. #14557899C2semidirect
3. #14557275C2semidirect
4. #14557273C2semidirect
5. C37×#562C2semidirect
64. #562D37semidirect
69. C37#1656semidirect

Maximal subgroups

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

subgroupindex
#145579232
#145578992
#145572752
#145572732
C37×#5622
#165637