Finite Group Databasebeta

← #18009574

Subgroups — #18009574

Order 4736.

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

normal subgroups only

This group has 222 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, complemented
2#14558377C211yesmaximal, characteristic, complemented
3#14557441C211yesmaximal, characteristic
4C2×C22⋊#3866—21no—
5C22⋊#64438—21no—
6C22×C22⋊D37—21no—
7C2×C22⋊Dic37—21no—
8C2×#10596938C2211yescharacteristic
9#11924443C411yescharacteristic, complemented
10C22×D4×C37C411yescharacteristic, complemented
11C24×C37—21no—
12C23×D37D411yescharacteristic
13C22×#3866—41no—
14C2×D4×C37—41no—
15C2×D4×C37—42no—
16C22×C4×C37C2×C411yescharacteristic
17C2×C22⋊D37—42no—
18C2×C22⋊D37—42no—
19C2×C22⋊D37—41no—
20C2×C22⋊D37—41no—
21C22×Dic37—21no—
22C22×Dic37D411yescharacteristic
23C22⋊#3866—22no—
24C22⋊#3866—41no—
25C2×#64438—41no—
26C22⋊Dic37—42no—
27#10596938—41no—
28C23×C37—22no—
29C23×C37—41no—
30C23×C37—41no—
31C23×C37—41no—
32C23×C37—41no—
33C23×C37—41no—
34C23×C37—41no—
35C23×C37C22⋊C411yescharacteristic
36C22×D37—21no—
37C22×D37—21no—
38C22×D37—41no—
39C22×D37—41no—
40C22×D37D811yescharacteristic
41C22×D37SD1611yescharacteristic
42C2×#3866—42no—
43C2×#3866—81no—
44C2×#3866—81no—
45D4×C37—42no—
46D4×C37—42no—
47C2×C4×C37—21no—
48C2×C4×C37—41no—
49C22⋊D37—44no—
50C22⋊D37—44no—
51C2×Dic37—22no—
52C2×Dic37—21no—
53C2×Dic37—41no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56#64438—81no—
57C22×C37—21no—
58C22×C37—21no—
59C22×C37—42no—
60C22×C37—42no—
61C22×C37—42no—
62C22×C37—81no—
63C22×C37—81no—
64C22×C37—81no—
65C22×C37—81no—
66C22×C37#9911yescharacteristic
67C22×C37#10211yescharacteristic
68C22×C37#10411yescharacteristic
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—41no—
72C2×D37—41no—
73C2×D37—41no—
74C2×D37—41no—
75C2×D37—81no—
76#3866—82no—
77C4×C37—41no—
78Dic37—42no—
79Dic37—41no—
80#1343—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—21no—
83C2×C37—82no—
84C2×C37#32711yescharacteristic
85C2×C37AΣL(1,𝔽16)11yescharacteristic
86C2×C37#35311yescharacteristic
87D37—41no—
88D37—41no—
89#392—371no—
90#342—371no—
91#323—371no—
92C37#134311yescharacteristic, complemented, Sylow
93C22×D4—741no—
94C22×D4#386611yescharacteristic, complemented
95C2×C22⋊C4—371no—
96C2×C22⋊C4—741no—
97C2×C22⋊C4—741no—
98C22⋊C8—741no—
99#95—371no—
100C24—21no—
101C24—371no—
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—1482no—
105C2×D4—1482no—
106C2×D4—1481no—
107C2×D4—1481no—
108C22×C4—371no—
109C22×C4—741no—
110C22×C4—1481no—
111C22×C4C2×#386611yescharacteristic
112C2×C8—1481no—
113C22⋊C4—742no—
114C22⋊C4—1481no—
115C22⋊C4—1482no—
116C22⋊C4—1481no—
117C23—22no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—371no—
125C23—371no—
126C23—741no—
127C23—741no—
128C23—1481no—
129C23—1481no—
130C23C22⋊#386611yescharacteristic
131D4—42no—
132D4—42no—
133D4—1484no—
134D4—1484no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—2961no—
138C2×C4—2961no—
139C2×C4—742no—
140C2×C4—741no—
141C2×C4—1482no—
142C2×C4—1481no—
143C2×C4—1481no—
144C2×C4—1481no—
145C8—2961no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—2961no—
156C22—741no—
157C22—741no—
158C22—1481no—
159C22—1481no—
160C22—1481no—
161C22—1481no—
162C22#1192459411yescharacteristic
163C22#1192459811yescharacteristic
164C22#1192460011yescharacteristic
165C4—41no—
166C4—2962no—
167C4—1482no—
168C4—1481no—
169C2—21no—
170C2—21no—
171C2—82no—
172C2—1481no—
173C2—1481no—
174C2#1455838411yescharacteristic
175C2#1455843311yescharacteristic
176C2#1455843711yescharacteristic
subgroupG/H
centerC22#11924594
commutatorC22×C4×C37C2×C4
FrattiniC22×C4C2×#3866
FittingC22×D4×C37C4
socleC22×C37#99
prime radical#14557441C2
cosocleC2×#10596938C22
hypercenterC22×D4#3866
hypocenterC37#1343
LCSG ▷ C22×C4×C37 ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558411C2semidirect
2. #14558377C2semidirect
9. #11924443C4semidirect
10. C22×D4×C37C4semidirect
92. C37#1343semidirect
94. C22×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584112
#145583772
#145574412
#134337