Finite Group Databasebeta

← #17996671

Subgroups — #17996671

Order 4736.

170 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 43 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#14557971C211yesmaximal, characteristic, complemented
2#14557969C211yesmaximal, characteristic, complemented
3#14557908C211yesmaximal, characteristic, complemented
4#14557649C211yesmaximal, characteristic, complemented
5#14557353C211yesmaximal, characteristic, complemented
6#14557345C211yesmaximal, characteristic, complemented
7C37×#361C211yesmaximal, characteristic, complemented
8#11924558C2211yescharacteristic
9C2×D296C2211yescharacteristic
10C2×#10596939—21no—
11#11924544—21no—
12#11924532—21no—
13#11924481—21no—
14#11924480—21no—
15D592—21no—
16#11924477—21no—
17#11924476C2211yescharacteristic
18#11924462—21no—
19C8×Dic37C2211yescharacteristic
20C2×D8×C37C2211yescharacteristic
21M32×C37C2211yescharacteristic
22#108×C37C2211yescharacteristic
23C2×D4×C37—21no—
24C2×C22⋊D37—42no—
25#10596962—21no—
26C2×D148—21no—
27D8×C37—21no—
28D8×C37—21no—
29M16×C37—21no—
30C2×C8×C37C2311yescharacteristic
31#10596939—41no—
32#10596939—41no—
33C4×Dic37D411yescharacteristic
34C2×#64436D411yescharacteristic
35Dic148D411yescharacteristic, complemented
36D296—21no—
37D296—21no—
38D296D411yescharacteristic, complemented
39#10596930—21no—
40#10596929—41no—
41C8×D37—41no—
42C16×C37—21no—
43#10596925—21no—
44C23×C37—41no—
45C22×D37—41no—
46D4×C37—41no—
47D4×C37—41no—
48C2×C4×C37C2×D411yescharacteristic
49C22⋊D37—41no—
50C22⋊D37—84no—
51C2×Dic37—21no—
52D148—21no—
53D148—41no—
54D148—41no—
55C4×D37—41no—
56Dic74—21no—
57C8×C37—41no—
58C8×C37C2×D411yescharacteristic
59C8×C37#4111yescharacteristic
60#64436D811yescharacteristic
61#64436D811yescharacteristic
62C22×C37—82no—
63C22×C37—81no—
64C22×C37AGL(1,ℤ/8)11yescharacteristic
65C2×D37—41no—
66C2×D37—82no—
67C2×D37—81no—
68C4×C37#12111yescharacteristic
69C4×C37C2×D811yescharacteristic
70Dic37—22no—
71Dic37—41no—
72#2213—371nomaximal, Sylow
73C2×C37—21no—
74C2×C37—161no—
75C2×C37#45911yescharacteristic
76D37—81no—
77D37—161no—
78#509—371no—
79#509—371no—
80#493—371no—
81#443—371no—
82#364—371no—
83#361—371no—
84#361D3711yescharacteristic, complemented
85C37#221311yescharacteristic, complemented, Sylow
86#135—371no—
87C2×D8—371no—
88C2×D8—741no—
89C2×D8C2×D3711yescharacteristic
90#131—741no—
91#127—741no—
92SD32—741no—
93SD32—741no—
94D16—741no—
95D16—741no—
96M32—371no—
97M32C2×D3711yescharacteristic
98#108C2×D3711yescharacteristic
99#104—741no—
100C4×C8—371no—
101#41—741no—
102C2×D4—21no—
103C2×D4—741no—
104C2×D4—1482no—
105Q16—371no—
106SD16—741no—
107D8—21no—
108D8—21no—
109D8—371no—
110D8—741no—
111D8—741no—
112D8—1481no—
113D8—1481no—
114M16—21no—
115M16—1481no—
116C2×C8—371no—
117C2×C8—1481no—
118C2×C8C22×D3711yescharacteristic
119C42—371no—
120C16—21no—
121C16—741no—
122C23—41no—
123C23—1481no—
124Q8—741no—
125D4—41no—
126D4—41no—
127D4—2964no—
128D4—741no—
129D4—1481no—
130D4—1481no—
131D4—1481no—
132C2×C4—741no—
133C2×C4—1481no—
134C2×C4D4×D3711yescharacteristic
135C8—41no—
136C8—371no—
137C8—371no—
138C8#1059696211yescharacteristic
139C8D4×D3711yescharacteristic
140C22—82no—
141C22—81no—
142C22—2962no—
143C22—2961no—
144C22—1481no—
145C22#1192456311yescharacteristic
146C4—742no—
147C4—1481no—
148C4#1192450911yescharacteristic
149C4D8×D3711yescharacteristic
150C2—21no—
151C2—161no—
152C2—2961no—
153C2—5921no—
154C2#1455772711yescharacteristic
subgroupG/H
centerC2#14557727
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#361C2
socleC2×C37#459
hypercenter#361D37
hypocenterC37#2213
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #14557971C2semidirect
2. #14557969C2semidirect
3. #14557908C2semidirect
4. #14557649C2semidirect
5. #14557353C2semidirect
6. #14557345C2semidirect
7. C37×#361C2semidirect
35. Dic148D4semidirect
38. D296D4semidirect
84. #361D37semidirect
85. C37#2213semidirect

Maximal subgroups

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

subgroupindex
#145579712
#145579692
#145579082
#145576492
#145573532
#145573452
C37×#3612
#221337