Finite Group Databasebeta

← #18009496

Subgroups — #18009496

Order 4736.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#14558504C211yesmaximal, characteristic
2#14558475C211yesmaximal, characteristic
3#14557496C211yesmaximal, characteristic
4C2×#10596953—21no—
5C2×C4⋊#3866—21no—
6C2×C22⋊#3866C412yes—
7#11924593—21no—
8C22⋊#64438C412yescomplemented
9(C2×#3866)⋊C4—21no—
10C22×C4×D37C2211yescharacteristic
11C2×#10596934C411yescharacteristic, complemented
12#11924448—21no—
13#11924448—21no—
14C2×M16×C37C411yescharacteristic, complemented
15C23×D37C2×C411yescharacteristic
16C22×#3866—22no—
17C22×C4×C37C2×C411yescharacteristic
18C22×Dic37C2×C411yescharacteristic
19C2×C4×D37—41no—
20C2×C4×D37—41no—
21C2×C4×D37D411yescharacteristic
22C2×C4×D37D411yescharacteristic
23C2×C4×D37D411yescharacteristic
24C2×C4×D37Q811yescharacteristic
25C22⋊#3866—42no—
26C2×#64438—22no—
27C4⋊#3866—41no—
28C4⋊#3866—41no—
29#10596953—41no—
30#10596953—41no—
31M16×C37—41no—
32C2×C8×C37—21no—
33#10596934—41no—
34C2×#64436—21no—
35C23×C37C4211yescharacteristic
36C22×D37—21no—
37C22×D37—21no—
38C22×D37—41no—
39C22×D37—41no—
40C22×D37C22⋊C411yescharacteristic
41C22×D37C4⋊C411yescharacteristic
42C2×#3866—42no—
43C2×#3866—42no—
44C2×#3866—42no—
45C2×C4×C37—21no—
46C2×C4×C37—21no—
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C4⋊C411yescharacteristic
49C2×Dic37—41no—
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C4⋊C411yescharacteristic
52C4×D37—21no—
53C4×D37—21no—
54C4×D37—21no—
55C4×D37—21no—
56C4×D37—41no—
57C4×D37—41no—
58#64438—42no—
59C8×C37—41no—
60#64436—41no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37—21no—
64C22×C37#9511yescharacteristic
65C2×D37—21no—
66C2×D37—21no—
67C2×D37—21no—
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—42no—
71C2×D37—42no—
72C2×D37#10011yescharacteristic
73C2×D37#10111yescharacteristic
74#3866—82no—
75C4×C37—21no—
76C4×C37#9911yescharacteristic
77C4×C37#9911yescharacteristic
78Dic37—21no—
79Dic37—21no—
80#1305—371nomaximal, Sylow
81C2×C37—41no—
82C2×C37#34211yescharacteristic
83C2×C37#34311yescharacteristic
84C2×C37#34411yescharacteristic
85D37—21no—
86D37—21no—
87D37—41no—
88#407—371no—
89#407—371no—
90#380—371no—
91C37#130511yescharacteristic, complemented, Sylow
92C23×C4—371no—
93C2×M16—371no—
94C2×M16—741no—
95C2×M16#386611yescharacteristic, complemented
96C2×C4⋊C4—741no—
97C2×C22⋊C4—372no—
98C22⋊C8—372no—
99C22⋊C8—741no—
100C22⋊C8—741no—
101C22⋊C8—741no—
102#95—741no—
103C24—371no—
104C22×C4—371no—
105C22×C4—371no—
106C22×C4—371no—
107C22×C4—371no—
108C22×C4—371no—
109C22×C4—742no—
110C22×C4—1481no—
111C22×C4—1481no—
112C22×C4C2×#386611yescharacteristic
113M16—41no—
114M16—1481no—
115M16—1481no—
116M16—1481no—
117C2×C8—21no—
118C2×C8—742no—
119C2×C8—741no—
120C4⋊C4—1481no—
121C4⋊C4—1481no—
122C22⋊C4—1482no—
123C23—371no—
124C23—371no—
125C23—741no—
126C23—741no—
127C23—1481no—
128C23—1481no—
129C23C4×#386611yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—371no—
133C2×C4—371no—
134C2×C4—741no—
135C2×C4—741no—
136C2×C4—741no—
137C2×C4—741no—
138C2×C4—1481no—
139C2×C4—1481no—
140C2×C4—1482no—
141C2×C4—1482no—
142C2×C4—1482no—
143C2×C4—1481no—
144C2×C4C4⋊#386611yescharacteristic
145C2×C4C22⋊#386611yescharacteristic
146C8—41no—
147C8—1482no—
148C8—1481no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—371no—
153C22—371no—
154C22—741no—
155C22—741no—
156C22—741no—
157C22—741no—
158C22—741no—
159C22—1482no—
160C22—1482no—
161C22(C2×#3866)⋊C411yescharacteristic
162C4—21no—
163C4—2962no—
164C4—741no—
165C4—741no—
166C4#1192459411yescharacteristic
167C4#1192459511yescharacteristic
168C2—41no—
169C2—741no—
170C2—741no—
171C2—1481no—
172C2#1455841111yescharacteristic
173C2#1455841211yescharacteristic
174C2#1455841611yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC23×C37C42
FrattiniC22×C4C2×#3866
FittingC2×M16×C37C4
socleC22×C37#95
prime radicalC23×D37C2×C4
cosocleC22×C4×D37C22
hypercenterC2×M16#3866
hypocenterC37#1305
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#64438C4semidirect
11. C2×#10596934C4semidirect
14. C2×M16×C37C4semidirect
91. C37#1305semidirect
95. C2×M16#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
#145584752
#145574962
#130537