Finite Group Databasebeta

← #18009897

Subgroups — #18009897

Order 4736.

312 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 84 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#14558549C211yesmaximal, characteristic, complemented
2#14558549C211yesmaximal, characteristic, complemented
3#14558381C214yesmaximal, complemented
4C2×#11924498C211yesmaximal, characteristic
5C4⋊#64438—21no—
6C4⋊#64438C2212yescomplemented
7C22⋊#64438—21no—
8C22⋊#64438—21no—
9C4×#64438—21no—
10C4×#64438C2212yescomplemented
11C22×D148C411yescharacteristic
12C22×C4×D37—21no—
13#11924498—21no—
14#11924498—21no—
15#11924498C412yes—
16#11924498C2212yes—
17C2×#10596938—21no—
18C2×C4×Dic37C2211yescharacteristic
19C2×C4⋊C4×C37C411yescharacteristic
20C23×D37—21no—
21C22×C4×C37—21no—
22C22×C4×C37C2×C411yescharacteristic
23C22×Dic37D411yescharacteristic
24C22×Dic37D411yescharacteristic
25C2×D148—21no—
26C2×D148—22no—
27C2×D148C814yescomplemented
28C2×D148C2×C412yes—
29C2×C4×D37—22no—
30C2×C4×D37—22no—
31C2×C4×D37—44no—
32C2×#64438—22no—
33C2×#64438—22no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37C2×C412yes—
36#10596938—22no—
37#10596938—22no—
38C4×Dic37C2×C411yescharacteristic
39C4×Dic37D411yescharacteristic
40C4×Dic37D411yescharacteristic
41C4×Dic37C2311yescharacteristic
42C23×C37C22⋊C411yescharacteristic
43C22×D37—24no—
44C22×D37—22no—
45C22×D37—42no—
46C22×D37—42no—
47C2×C4×C37—22no—
48C2×C4×C37—42no—
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C2×C812yes—
51C2×C4×C37M1612yes—
52C2×C4×C37C22×C411yescharacteristic
53C2×Dic37—22no—
54C2×Dic37—41no—
55C2×Dic37C22⋊C411yescharacteristic
56C2×Dic37C22⋊C411yescharacteristic
57C2×Dic37C2×D411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59D148—24no—
60D148—22no—
61D148C2×C814yes—
62C4×D37—44no—
63C4×D37—44no—
64#64438—42no—
65#64438—42no—
66C22×C37—21no—
67C22×C37—21no—
68C22×C37C22⋊C812yes—
69C22×C37C2×C22⋊C411yescharacteristic
70C2×D37—24no—
71C2×D37—48no—
72C2×D37—42no—
73C2×D37—42no—
74C4×C37—42no—
75C4×C37C22⋊C812yes—
76C4×C37C22×C811yescharacteristic
77C4×C37C2×M1611yescharacteristic
78Dic37—21no—
79Dic37—21no—
80Dic37—21no—
81Dic37AGL(1,ℤ/8)12yes—
82#1478—371nomaximal, Sylow
83C2×C37—22no—
84C2×C37C2×C22⋊C811yescharacteristic
85C2×C37#41811yescharacteristic
86C2×C37#42111yescharacteristic
87D37—44no—
88C2×C4×D4—371no—
89#431—371no—
90#431—371no—
91D4⋊C8—374no—
92C37#147811yescharacteristic, complemented, Sylow
93C22×D4—371no—
94C23×C4—741no—
95C4×D4—372no—
96C4×D4—372no—
97C4×D4—741no—
98C4×D4—741no—
99C2×C4⋊C4#386611yescharacteristic
100C2×C22⋊C4—741no—
101C2×C42—371no—
102C4⋊C8—372no—
103C4⋊C8—741no—
104C22⋊C8—741no—
105C22⋊C8—741no—
106C4×C8—372no—
107C4×C8—741no—
108C24—741no—
109C2×D4—374no—
110C2×D4—372no—
111C2×D4—742no—
112C2×D4—741no—
113C22×C4—21no—
114C22×C4—371no—
115C22×C4—371no—
116C22×C4—742no—
117C22×C4—742no—
118C22×C4—1484no—
119C22×C4C2×#386611yescharacteristic
120C2×C8—742no—
121C2×C8—742no—
122C4⋊C4—21no—
123C4⋊C4C2×#386612yes—
124C22⋊C4—742no—
125C22⋊C4—742no—
126C42—371no—
127C42—371no—
128C42—371no—
129C42—371no—
130C23—744no—
131C23—742no—
132C23—1482no—
133C23—1482no—
134C23C22⋊#386611yescharacteristic
135D4—374no—
136D4—744no—
137D4—742no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—371no—
141C2×C4—371no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—742no—
145C2×C4—1484no—
146C2×C4—1484no—
147C2×C4—1481no—
148C2×C4D37⋊C812yes—
149C2×C4#1059695312yes—
150C2×C4C22⋊#386611yescharacteristic
151C2×C4C22×#386611yescharacteristic
152C8—1482no—
153C8—1482no—
154C22—21no—
155C22—21no—
156C22—744no—
157C22—1488no—
158C22—1482no—
159C22—1482no—
160C22#1192459312yes—
161C22C2×C22⋊#386611yescharacteristic
162C4—42no—
163C4—372no—
164C4—741no—
165C4—741no—
166C4—741no—
167C4#1192459312yes—
168C4C2×D37⋊C811yescharacteristic
169C4C2×#1059695311yescharacteristic
170C2—22no—
171C2—1484no—
172C2C2×#1192459311yescharacteristic
173C2#1455852511yescharacteristic
174C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC4×C37C22×C8
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC4×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1478
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14558549C2semidirect
2. #14558549C2semidirect
3. #14558381C2semidirect
6. C4⋊#64438C22semidirect
10. C4×#64438C22semidirect
27. C2×D148C8semidirect
92. C37#1478semidirect

Maximal subgroups

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

subgroupindex
#145585492
#145583812
C2×#119244982
#147837