Finite Group Databasebeta

← #18009593

Subgroups — #18009593

Order 4736.

154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 30 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#14558411C211yesmaximal, characteristic
2#14558377C211yesmaximal, characteristic
3#14557468C211yesmaximal, characteristic
4C2×C22⋊#3866—21no—
5C22⋊#64438—21no—
6C2×#10596936—21no—
7C2×#10596938—21no—
8C2×#10596938C2211yescharacteristic
9#11924443C411yescharacteristic, complemented
10C2×C4⋊C4×C37C411yescharacteristic, complemented
11C23×D37D411yescharacteristic
12C22×#3866—41no—
13C22×C4×C37—21no—
14C22×C4×C37C2×C411yescharacteristic
15C22×Dic37—21no—
16C22×Dic37D411yescharacteristic
17C22⋊#3866—22no—
18C22⋊#3866—41no—
19C2×#64438—41no—
20C4⋊C4×C37—41no—
21#10596938—41no—
22#10596938—42no—
23#10596936—42no—
24C23×C37C22⋊C411yescharacteristic
25C22×D37—21no—
26C22×D37—21no—
27C22×D37—41no—
28C22×D37—41no—
29C22×D37SD1611yescharacteristic
30C22×D37Q1611yescharacteristic
31C2×#3866—42no—
32C2×#3866—81no—
33C2×#3866—81no—
34C2×C4×C37—21no—
35C2×C4×C37—41no—
36C2×C4×C37—41no—
37C2×C4×C37—41no—
38C2×C4×C37—41no—
39C2×Dic37—22no—
40C2×Dic37—21no—
41C2×Dic37—41no—
42C2×Dic37—41no—
43C2×Dic37—41no—
44#64438—81no—
45C22×C37—21no—
46C22×C37—21no—
47C22×C37#9911yescharacteristic
48C22×C37#10311yescharacteristic
49C22×C37#10411yescharacteristic
50C2×D37—21no—
51C2×D37—21no—
52C2×D37—41no—
53C2×D37—41no—
54C2×D37—41no—
55C2×D37—41no—
56C2×D37—81no—
57#3866—82no—
58C4×C37—41no—
59C4×C37—81no—
60Dic37—42no—
61Dic37—41no—
62#1352—371nomaximal, Sylow
63C2×C37—21no—
64C2×C37—21no—
65C2×C37#32811yescharacteristic
66C2×C37#35211yescharacteristic
67C2×C37#35311yescharacteristic
68D37—41no—
69D37—41no—
70#399—371no—
71#342—371no—
72#323—371no—
73C37#135211yescharacteristic, complemented, Sylow
74C2×C4⋊C4—741no—
75C2×C4⋊C4#386611yescharacteristic, complemented
76C2×C22⋊C4—371no—
77C2×C22⋊C4—741no—
78C2×C22⋊C4—741no—
79C22⋊C8—741no—
80#95—371no—
81C24—371no—
82C22×C4—21no—
83C22×C4—371no—
84C22×C4—741no—
85C22×C4—1481no—
86C22×C4C2×#386611yescharacteristic
87C2×C8—1481no—
88C4⋊C4—41no—
89C4⋊C4—1482no—
90C22⋊C4—742no—
91C22⋊C4—1481no—
92C22⋊C4—1482no—
93C22⋊C4—1481no—
94C23—371no—
95C23—371no—
96C23—741no—
97C23—741no—
98C23—1481no—
99C23—1481no—
100C23C22⋊#386611yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—2961no—
107C2×C4—2961no—
108C2×C4—742no—
109C2×C4—741no—
110C2×C4—1482no—
111C2×C4—1481no—
112C2×C4—1481no—
113C2×C4—1481no—
114C8—2961no—
115C22—21no—
116C22—21no—
117C22—2961no—
118C22—741no—
119C22—741no—
120C22—1481no—
121C22—1481no—
122C22—1481no—
123C22—1481no—
124C22#1192459411yescharacteristic
125C22#1192459911yescharacteristic
126C22#1192460111yescharacteristic
127C4—41no—
128C4—81no—
129C4—2962no—
130C4—1482no—
131C4—1481no—
132C2—21no—
133C2—21no—
134C2—1481no—
135C2—1481no—
136C2#1455838711yescharacteristic
137C2#1455843511yescharacteristic
138C2#1455843711yescharacteristic
subgroupG/H
centerC22#11924594
commutatorC22×C4×C37C2×C4
FrattiniC22×C4C2×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37#99
prime radicalC23×D37D4
cosocleC2×#10596938C22
hypercenterC2×C4⋊C4#3866
hypocenterC37#1352
LCSG ▷ C22×C4×C37 ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #11924443C4semidirect
10. C2×C4⋊C4×C37C4semidirect
73. C37#1352semidirect
75. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584112
#145583772
#145574682
#135237