Finite Group Databasebeta

← #14557801

Subgroups — #14557801

Order 2368.

108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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#11924561C211yesmaximal, characteristic, complemented
2C2×#10596939C211yesmaximal, characteristic, complemented
3#11924543C211yesmaximal, characteristic, complemented
4#11924471C211yesmaximal, characteristic, complemented
5#11924453C211yesmaximal, characteristic, complemented
6#11924452C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
8#41×C37C2211yescharacteristic
9C2×D4×C37C2211yescharacteristic
10C2×D148C2211yescharacteristic
11SD16×C37—21no—
12D8×C37—21no—
13M16×C37C2211yescharacteristic
14#10596941—21no—
15#10596939—21no—
16#10596939—21no—
17#10596939—21no—
18#10596934—21no—
19#10596934C2211yescharacteristic
20#10596934C2211yescharacteristic
21C2×#64436—21no—
22C2×#64436C2211yescharacteristic
23C23×C37—21no—
24C22×D37—21no—
25Q8×C37D411yescharacteristic
26D4×C37—21no—
27D4×C37—21no—
28D4×C37—21no—
29D4×C37D411yescharacteristic
30C2×C4×C37—21no—
31C2×C4×C37C2311yescharacteristic
32D148—21no—
33D148—21no—
34C8×C37—21no—
35#64436—21no—
36#64436—21no—
37#64436D411yescharacteristic
38#64436D411yescharacteristic
39C22×C37—21no—
40C22×C37—41no—
41C22×C37—81no—
42C22×C37#4111yescharacteristic
43C2×D37—41no—
44C2×D37—81no—
45C4×C37—21no—
46C4×C37C2×D411yescharacteristic
47C4×C37C2×D411yescharacteristic
48C2×C37—21no—
49C2×C37—41no—
50C2×C37—81no—
51C2×C37#12111yescharacteristic
52D37—81no—
53#472—371nomaximal, Sylow
54C37#47211yescharacteristic, complemented, Sylow
55AGL(1,ℤ/8)—371no—
56AGL(1,ℤ/8)D3711yescharacteristic, complemented
57C2×D8—371no—
58#131—371no—
59#108—371no—
60#100—371no—
61#100—371no—
62#41C2×D3711yescharacteristic
63C2×D4—371no—
64C2×D4C2×D3711yescharacteristic
65SD16—21no—
66SD16—741no—
67D8—21no—
68D8—741no—
69D8—741no—
70D8—741no—
71M16—371no—
72M16—371no—
73M16—741no—
74M16C2×D3711yescharacteristic
75C2×C8—371no—
76C2×C8—741no—
77C23—21no—
78C23—741no—
79Q8C22⋊D3711yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—741no—
84D4—741no—
85D4C22⋊D3711yescharacteristic
86C2×C4—21no—
87C2×C4C22×D3711yescharacteristic
88C8—21no—
89C8—371no—
90C8—371no—
91C8—741no—
92C8—741no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—2961no—
97C22—1481no—
98C22#1059696411yescharacteristic
99C4—21no—
100C4D4×D3711yescharacteristic
101C4C2×C22⋊D3711yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—2961no—
106C2#1192450811yescharacteristic
subgroupG/H
centerC2#11924508
commutator, cosocleC2×C4×C37C23
FrattiniC2×C4C22×D37
FittingAGL(1,ℤ/8)×C37C2
socleC2×C37#121
hypercenterAGL(1,ℤ/8)D37
hypocenterC37#472
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #11924561C2semidirect
2. C2×#10596939C2semidirect
3. #11924543C2semidirect
4. #11924471C2semidirect
5. #11924453C2semidirect
6. #11924452C2semidirect
7. AGL(1,ℤ/8)×C37C2semidirect
54. C37#472semidirect
56. AGL(1,ℤ/8)D37semidirect

Maximal subgroups

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

subgroupindex
#119245612
C2×#105969392
#119245432
#119244712
#119244532
#119244522
AGL(1,ℤ/8)×C372
#47237