Finite Group Databasebeta

← #17994239

Subgroups — #17994239

Order 4736.

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

normal subgroups only

This group has 164 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#14557936C211yesmaximal, characteristic
2#14557929C211yesmaximal, characteristic
3#14557885C211yesmaximal, characteristic
4#14557884C211yesmaximal, characteristic
5#14557883C211yesmaximal, characteristic
6#14557254C211yesmaximal, characteristic
7C37×#487C211yesmaximal, characteristic
8#11924536C2211yescharacteristic
9#11924536C2211yescharacteristic
10#11924469—22no—
11#11924467—22no—
12#11924461—22no—
13#11924460—22no—
14#11924459—22no—
15C4×#64436C2211yescharacteristic
16C4×#64436C2211yescharacteristic
17C4⋊Q8×C37C2211yescharacteristic
18C4⋊Q8×C37C2211yescharacteristic
19#103×C37—22no—
20C4×C8×C37C2211yescharacteristic
21C2×Q8×C37—21no—
22C2×Q8×C37—21no—
23C2×Dic74—21no—
24C2×Dic74—21no—
25C2×C8×C37D412yes—
26C4⋊C4×C37—21no—
27C4⋊C4×C37—21no—
28C4⋊C4×C37—21no—
29C4⋊C4×C37—21no—
30C42×C37C2311yescharacteristic
31C4⋊Dic37—21no—
32C4⋊Dic37—21no—
33C4⋊Dic37—21no—
34C4⋊Dic37—21no—
35C2×#64436D412yes—
36C2×#64436D412yes—
37Q8×C37—42no—
38Q8×C37—42no—
39C2×C4×C37—41no—
40C2×C4×C37—41no—
41C2×C4×C37C2×D411yescharacteristic
42C2×C4×C37C2×D411yescharacteristic
43C2×C4×C37C2×D411yescharacteristic
44C2×Dic37—41no—
45C2×Dic37—41no—
46Dic74—42no—
47Dic74—42no—
48C8×C37—22no—
49#64436—22no—
50#64436—22no—
51C22×C37#12711yescharacteristic
52C4×C37—81no—
53C4×C37—81no—
54C4×C37#13512yes—
55C4×C37#13712yes—
56C4×C37#13712yes—
57Dic37—81no—
58Dic37—81no—
59#1718—371nomaximal, Sylow
60C2×C37#49511yescharacteristic
61C2×C37#49711yescharacteristic
62C2×C37#49711yescharacteristic
63#500—371no—
64#498—371no—
65#487—371no—
66#487—371no—
67#487—371no—
68#487D3711yescharacteristic
69#322—371no—
70C37#171811yescharacteristic, complemented, Sylow
71C4⋊Q8—371no—
72C4⋊Q8—371no—
73C4⋊Q8C2×D3711yescharacteristic
74C4⋊Q8C2×D3711yescharacteristic
75#107—742no—
76#106—742no—
77#103—22no—
78#103—742no—
79#103—742no—
80#103—742no—
81C4×C8—371no—
82C4×C8—371no—
83C4×C8C2×D3711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—741no—
87C2×Q8—741no—
88C2×C8—372no—
89C2×C8—372no—
90C2×C8C22⋊D3712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—741no—
96C4⋊C4—741no—
97C4⋊C4—741no—
98C4⋊C4—741no—
99C42C22×D3711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—1482no—
103Q8—1482no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—1481no—
107C2×C4—1481no—
108C2×C4D4×D3711yescharacteristic
109C2×C4D4×D3711yescharacteristic
110C2×C4C2×C22⋊D3711yescharacteristic
111C8—22no—
112C8—742no—
113C8—742no—
114C22#1192453211yescharacteristic
115C4—81no—
116C4—81no—
117C4—2961no—
118C4—2961no—
119C4#1192455612yes—
120C4#1192456512yes—
121C4#1192456812yes—
122C2#1455791511yescharacteristic
123C2#1455792411yescharacteristic
124C2#1455792611yescharacteristic
subgroupG/H
centerC22#11924532
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#487C2
socle, prime radicalC22×C37#127
hypercenter#487D37
hypocenterC37#1718
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
70. C37#1718semidirect

Maximal subgroups

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

subgroupindex
#145579362
#145579292
#145578852
#145578842
#145578832
#145572542
C37×#4872
#171837