Finite Group Databasebeta

← #18009498

Subgroups — #18009498

Order 4736.

200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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#14558505C211yesmaximal, characteristic
2#14558475C211yesmaximal, characteristic
3#14557495C211yesmaximal, characteristic
4C2×#10596957C412yescomplemented
5C2×C4⋊#3866—21no—
6C2×C22⋊#3866C412yes—
7#11924593—21no—
8#11924593—21no—
9(C2×#3866)⋊C4—21no—
10C22×C4×D37C2211yescharacteristic
11C2×#10596929—21no—
12C22⋊#64436C411yescharacteristic, complemented
13#11924448—21no—
14C22⋊C8×C37C411yescharacteristic, complemented
15C23×D37C2×C411yescharacteristic
16C22×#3866—22no—
17C22×C4×C37C2×C411yescharacteristic
18C22×Dic37C2×C411yescharacteristic
19C2×C4×D37—42no—
20C2×C4×D37D411yescharacteristic
21C2×C4×D37D411yescharacteristic
22C2×C4×D37D411yescharacteristic
23C2×C4×D37Q811yescharacteristic
24C22⋊#3866—42no—
25#10596957—42no—
26C2×#64438—22no—
27C4⋊#3866—42no—
28C2×C8×C37—21no—
29C2×#64436—21no—
30#10596929—42no—
31C23×C37C4211yescharacteristic
32C22×D37—21no—
33C22×D37—21no—
34C22×D37—41no—
35C22×D37—41no—
36C22×D37C22⋊C411yescharacteristic
37C22×D37C4⋊C411yescharacteristic
38C2×#3866—42no—
39C2×#3866—42no—
40C2×#3866—42no—
41C2×C4×C37—41no—
42C2×C4×C37C22⋊C411yescharacteristic
43C2×C4×C37C4⋊C411yescharacteristic
44C2×Dic37—22no—
45C2×Dic37C22⋊C411yescharacteristic
46C2×Dic37C4⋊C411yescharacteristic
47C4×D37—22no—
48C4×D37—22no—
49C4×D37—41no—
50C4×D37—41no—
51#64438—42no—
52C8×C37—41no—
53#64436—41no—
54C22×C37—21no—
55C22×C37—21no—
56C22×C37—21no—
57C22×C37#9511yescharacteristic
58C2×D37—21no—
59C2×D37—21no—
60C2×D37—21no—
61C2×D37—21no—
62C2×D37—21no—
63C2×D37—42no—
64C2×D37—42no—
65C2×D37#10011yescharacteristic
66C2×D37#10111yescharacteristic
67#3866—82no—
68C4×C37—21no—
69C4×C37—21no—
70Dic37—21no—
71Dic37#9912yes—
72#1305—371nomaximal, Sylow
73C2×C37—41no—
74C2×C37#34211yescharacteristic
75C2×C37#34311yescharacteristic
76C2×C37#34411yescharacteristic
77D37—21no—
78D37—21no—
79D37—41no—
80#407—371no—
81#407—371no—
82#380—371no—
83C37#130511yescharacteristic, complemented, Sylow
84C23×C4—371no—
85C2×M16—372no—
86C2×M16—741no—
87C2×C4⋊C4—741no—
88C2×C22⋊C4—372no—
89C22⋊C8—371no—
90C22⋊C8—741no—
91C22⋊C8—741no—
92C22⋊C8—741no—
93C22⋊C8#386611yescharacteristic, complemented
94#95—741no—
95C24—371no—
96C22×C4—371no—
97C22×C4—371no—
98C22×C4—371no—
99C22×C4—371no—
100C22×C4—371no—
101C22×C4—742no—
102C22×C4—1482no—
103C22×C4C2×#386611yescharacteristic
104M16—1482no—
105M16—1482no—
106C2×C8—21no—
107C2×C8—742no—
108C2×C8—741no—
109C4⋊C4—1482no—
110C22⋊C4—1482no—
111C23—371no—
112C23—371no—
113C23—741no—
114C23—741no—
115C23—1481no—
116C23—1481no—
117C23C4×#386611yescharacteristic
118C2×C4—41no—
119C2×C4—371no—
120C2×C4—371no—
121C2×C4—742no—
122C2×C4—742no—
123C2×C4—742no—
124C2×C4—1481no—
125C2×C4—1481no—
126C2×C4—1482no—
127C2×C4—1482no—
128C2×C4—1482no—
129C2×C4C4⋊#386611yescharacteristic
130C2×C4C22⋊#386611yescharacteristic
131C8—41no—
132C8—1481no—
133C8—1482no—
134C22—21no—
135C22—21no—
136C22—21no—
137C22—371no—
138C22—371no—
139C22—741no—
140C22—741no—
141C22—741no—
142C22—741no—
143C22—741no—
144C22—1482no—
145C22—1482no—
146C22(C2×#3866)⋊C411yescharacteristic
147C4—21no—
148C4—21no—
149C4—372no—
150C4—2962no—
151C4—741no—
152C2—41no—
153C2—741no—
154C2—741no—
155C2—1481no—
156C2#1455841011yescharacteristic
157C2#1455841211yescharacteristic
158C2#1455841511yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC23×C37C42
FrattiniC22×C4C2×#3866
FittingC22⋊C8×C37C4
socleC22×C37#95
prime radicalC23×D37C2×C4
cosocleC22×C4×D37C22
hypercenterC22⋊C8#3866
hypocenterC37#1305
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#10596957C4semidirect
12. C22⋊#64436C4semidirect
14. C22⋊C8×C37C4semidirect
83. C37#1305semidirect
93. C22⋊C8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585052
#145584752
#145574952
#130537