Finite Group Databasebeta

← #18009695

Subgroups — #18009695

Order 4736.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#14558520C211yesmaximal, characteristic
2#14558507C211yesmaximal, characteristic
3#14557505C211yesmaximal, characteristic
4C2×#10596953C411yescharacteristic, complemented
5C2×#10596957—21no—
6C2×D37⋊C8C411yescharacteristic, complemented
7#11924597C412yescomplemented
8#11924596—21no—
9C22⋊#64438—21no—
10C22⋊#64438—21no—
11C2×#10596964C2211yescharacteristic
12#11924492—21no—
13#11924451C411yescharacteristic
14#11924450—21no—
15#99×C37C411yescharacteristic
16C2×D4×C37C2×C411yescharacteristic
17C2×C22⋊D37D411yescharacteristic
18C2×C22⋊D37Q811yescharacteristic
19C22×Dic37D411yescharacteristic
20C22×Dic37D411yescharacteristic
21#10596964—41no—
22#10596964—41no—
23C2×C4×D37C2×C411yescharacteristic
24C2×Dic74C2×C411yescharacteristic
25#10596957—22no—
26#10596957—41no—
27C2×#64438—21no—
28C2×#64438—21no—
29C2×#64438—41no—
30#10596953—41no—
31D37⋊C8—41no—
32C22⋊C4×C37—21no—
33C22⋊Dic37—21no—
34#10596936—41no—
35C4×Dic37—41no—
36C23×C37C22⋊C411yescharacteristic
37C23×C37C4⋊C411yescharacteristic
38C22×D37C4⋊C411yescharacteristic
39D4×C37—41no—
40C2×C4×C37—41no—
41C2×C4×C37C4211yescharacteristic
42C22⋊D37—41no—
43C22⋊D37—41no—
44C2×Dic37—21no—
45C2×Dic37—21no—
46C2×Dic37—21no—
47C2×Dic37—21no—
48C2×Dic37—41no—
49C2×Dic37C22⋊C411yescharacteristic
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C4⋊C411yescharacteristic
52C4×D37—21no—
53C4×D37—21no—
54Dic74—41no—
55#64438—42no—
56#64438—41no—
57#64438—41no—
58C22×C37—21no—
59C22×C37—21no—
60C22×C37—41no—
61C22×C37—41no—
62C22×C37#9511yescharacteristic
63C2×D37—21no—
64C2×D37—41no—
65C4×C37—21no—
66C4×C37—81no—
67Dic37—21no—
68Dic37—21no—
69Dic37—81no—
70Dic37#9911yescharacteristic
71Dic37#9911yescharacteristic
72#1395—371nomaximal, Sylow
73C2×C37—21no—
74C2×C37—41no—
75C2×C37—41no—
76C2×C37#34211yescharacteristic
77D37—41no—
78#413—371no—
79#410—371no—
80#408—371no—
81C37#139511yescharacteristic, complemented, Sylow
82C2×#41—371no—
83C2×M16—371no—
84C2×M16—741no—
85C22×C8—371no—
86#117—741no—
87#101—372no—
88#100—741no—
89#99—371no—
90#99—741no—
91#99#386611yescharacteristic
92C22⋊C8—741no—
93C22⋊C8—741no—
94#41—1481no—
95#41—1481no—
96C2×Q8—371no—
97C2×D4—371no—
98C2×D4—371no—
99C2×D4C2×#386611yescharacteristic
100C22×C4—371no—
101C22×C4—371no—
102C22×C4—371no—
103M16—742no—
104M16—1481no—
105M16—1481no—
106C2×C8—741no—
107C2×C8—741no—
108C2×C8—1481no—
109C2×C8—1481no—
110C4⋊C4—1481no—
111C22⋊C4—21no—
112C22⋊C4—741no—
113C42—1481no—
114C23—371no—
115C23C4⋊#386611yescharacteristic
116C23C22⋊#386611yescharacteristic
117Q8—1481no—
118D4—41no—
119D4—1481no—
120D4—1481no—
121C2×C4—41no—
122C2×C4—371no—
123C2×C4—371no—
124C2×C4—371no—
125C2×C4—741no—
126C2×C4—741no—
127C2×C4—741no—
128C2×C4—741no—
129C2×C4—741no—
130C2×C4—741no—
131C2×C4—1481no—
132C2×C4C4×#386611yescharacteristic
133C8—1481no—
134C8—1481no—
135C8—1482no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—741no—
141C22—1481no—
142C22(C2×#3866)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—371no—
146C4—371no—
147C4—2961no—
148C4—741no—
149C4—741no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—1481no—
154C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC2×C4×C37C42
FrattiniC2×D4C2×#3866
Fitting#99×C37C4
socleC2×C37#342
prime radical, cosocleC2×#10596964C22
hypercenter#99#3866
hypocenterC37#1395
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#10596953C4semidirect
6. C2×D37⋊C8C4semidirect
7. #11924597C4semidirect
81. C37#1395semidirect

Maximal subgroups

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

subgroupindex
#145585202
#145585072
#145575052
#139537