Finite Group Databasebeta

← #17996670

Subgroups — #17996670

Order 4736.

170 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 45 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#14557968C211yesmaximal, characteristic, complemented
2#14557908C211yesmaximal, characteristic, complemented
3#14557650C211yesmaximal, characteristic, complemented
4#14557353C211yesmaximal, characteristic, complemented
5#14557347C211yesmaximal, characteristic, complemented
6#14557346C211yesmaximal, characteristic, complemented
7C37×#509C211yesmaximal, characteristic, complemented
8C2×D296C2211yescharacteristic
9C2×#10596939—21no—
10#11924543—21no—
11#11924532—21no—
12#11924479—21no—
13#11924477—21no—
14#11924476C2211yescharacteristic
15#11924472C2211yescharacteristic
16#11924463—21no—
17C8×Dic37C2211yescharacteristic
18#135×C37C2211yescharacteristic
19C2×D8×C37C2211yescharacteristic
20SD32×C37—21no—
21D16×C37—21no—
22M32×C37C2211yescharacteristic
23#41×C37—21no—
24C2×D4×C37—21no—
25C2×C22⋊D37—42no—
26C2×D148—21no—
27Q16×C37D411yescharacteristic, complemented
28SD16×C37—21no—
29D8×C37—21no—
30D8×C37—21no—
31D8×C37D411yescharacteristic, complemented
32C2×C8×C37C2311yescharacteristic
33#10596939—41no—
34#10596939—41no—
35C4×Dic37D411yescharacteristic
36#10596934—21no—
37#10596934—41no—
38C2×#64436—41no—
39C2×#64436D411yescharacteristic
40D296—21no—
41D296—21no—
42C16×C37—21no—
43#10596925—21no—
44C23×C37—41no—
45C22×D37—41no—
46Q8×C37—21no—
47D4×C37—21no—
48D4×C37—41no—
49D4×C37—41no—
50D4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37C2×D411yescharacteristic
53C22⋊D37—84no—
54C2×Dic37—21no—
55D148—41no—
56D148—41no—
57C8×C37C2×D411yescharacteristic
58C8×C37#4111yescharacteristic
59#64436—41no—
60#64436D811yescharacteristic
61#64436D811yescharacteristic
62C22×C37—41no—
63C22×C37—82no—
64C22×C37—81no—
65C22×C37AGL(1,ℤ/8)11yescharacteristic
66C2×D37—82no—
67C2×D37—81no—
68C4×C37—41no—
69C4×C37#12111yescharacteristic
70C4×C37C2×D811yescharacteristic
71Dic37—22no—
72#2213—371nomaximal, Sylow
73C2×C37—21no—
74C2×C37—81no—
75C2×C37—161no—
76C2×C37#45911yescharacteristic
77D37—161no—
78#509—371no—
79#509D3711yescharacteristic, complemented
80#493—371no—
81#443—371no—
82#364—371no—
83#361—371no—
84#361—371no—
85C37#221311yescharacteristic, complemented, Sylow
86#135C2×D3711yescharacteristic
87C2×D8—371no—
88C2×D8—741no—
89C2×D8C2×D3711yescharacteristic
90#131—741no—
91#127—741no—
92SD32—21no—
93SD32—741no—
94D16—21no—
95D16—741no—
96M32—371no—
97M32C2×D3711yescharacteristic
98#108—371no—
99#104—741no—
100C4×C8—371no—
101#41—21no—
102C2×D4—21no—
103C2×D4—741no—
104C2×D4—1482no—
105Q16C22⋊D3711yescharacteristic, complemented
106SD16—21no—
107D8—21no—
108D8—21no—
109D8—741no—
110D8—741no—
111D8—1481no—
112D8—1481no—
113D8C22⋊D3711yescharacteristic, complemented
114M16—741no—
115M16—1481no—
116C2×C8—371no—
117C2×C8—1481no—
118C2×C8C22×D3711yescharacteristic
119C42—371no—
120C16—21no—
121C16—741no—
122C23—41no—
123C23—1481no—
124Q8—21no—
125D4—21no—
126D4—41no—
127D4—41no—
128D4—41no—
129D4—2964no—
130D4—1481no—
131D4—1481no—
132C2×C4—41no—
133C2×C4—741no—
134C2×C4D4×D3711yescharacteristic
135C8—371no—
136C8—371no—
137C8—1481no—
138C8#1059696411yescharacteristic
139C8C2×C22⋊D3711yescharacteristic
140C22—41no—
141C22—82no—
142C22—81no—
143C22—2962no—
144C22—2961no—
145C22#1192456011yescharacteristic
146C4—41no—
147C4—742no—
148C4#1192450811yescharacteristic
149C4D8×D3711yescharacteristic
150C2—21no—
151C2—81no—
152C2—161no—
153C2—5921no—
154C2#1455772611yescharacteristic
subgroupG/H
centerC2#14557726
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#509C2
socleC2×C37#459
hypercenter#509D37
hypocenterC37#2213
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #14557968C2semidirect
2. #14557908C2semidirect
3. #14557650C2semidirect
4. #14557353C2semidirect
5. #14557347C2semidirect
6. #14557346C2semidirect
7. C37×#509C2semidirect
27. Q16×C37D4semidirect
31. D8×C37D4semidirect
79. #509D37semidirect
85. C37#2213semidirect
105. Q16C22⋊D37semidirect
113. D8C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
#145579682
#145579082
#145576502
#145573532
#145573472
#145573462
C37×#5092
#221337