Finite Group Databasebeta

← #471×C373 #37559025

Subgroups — #471×C373 #37559025

Order 23872.

104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 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#137×C373C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×C373C211yesmaximal, characteristic
3C2×SD16×C373C211yesmaximal, characteristic, complemented
4#131×C373C211yesmaximal, characteristic, complemented
5#108×C373C211yesmaximal, characteristic, complemented
6#101×C373C211yesmaximal, characteristic, complemented
7#100×C373C211yesmaximal, characteristic, complemented
8#41×C373C2211yescharacteristic
9C2×Q8×C373C2211yescharacteristic
10C2×D4×C373C2211yescharacteristic
11Q16×C373—21no—
12SD16×C373—21no—
13SD16×C373—21no—
14SD16×C373—21no—
15SD16×C373—21no—
16D8×C373—21no—
17M16×C373—21no—
18M16×C373C2211yescharacteristic
19M16×C373C2211yescharacteristic
20M16×C373C2211yescharacteristic
21C2×C8×C373—21no—
22C2×C8×C373C2211yescharacteristic
23C23×C373—21no—
24Q8×C373—21no—
25Q8×C373—21no—
26Q8×C373D411yescharacteristic
27D4×C373—21no—
28D4×C373—21no—
29D4×C373—21no—
30D4×C373D411yescharacteristic
31C2×C4×C373—21no—
32C2×C4×C373—21no—
33C2×C4×C373C2311yescharacteristic
34C8×C373—21no—
35C8×C373—21no—
36C8×C373—21no—
37C8×C373D411yescharacteristic
38C8×C373D411yescharacteristic
39C22×C373—21no—
40C22×C373—41no—
41C22×C373—81no—
42C22×C373#4111yescharacteristic
43C4×C373—21no—
44C4×C373—41no—
45C4×C373C2×D411yescharacteristic
46C4×C373C2×D411yescharacteristic
47C2×C373—21no—
48C2×C373—41no—
49C2×C373—81no—
50C2×C373#12111yescharacteristic
51C373#47111yescharacteristic, direct product factor, Sylow
52#471C37311yesmaximal, characteristic, direct product factor, Sylow
53#137C2×C37311yescharacteristic, complemented
54AGL(1,ℤ/8)C2×C37311yescharacteristic
55C2×SD16C2×C37311yescharacteristic, complemented
56#131C2×C37311yescharacteristic, complemented
57#108C2×C37311yescharacteristic, complemented
58#101C2×C37311yescharacteristic, complemented
59#100C2×C37311yescharacteristic, complemented
60#41C22×C37311yescharacteristic
61C2×Q8C22×C37311yescharacteristic
62C2×D4C22×C37311yescharacteristic
63Q16—21no—
64SD16—21no—
65SD16—21no—
66SD16—21no—
67SD16—21no—
68D8—21no—
69M16—21no—
70M16C22×C37311yescharacteristic
71M16C22×C37311yescharacteristic
72M16C22×C37311yescharacteristic
73C2×C8—21no—
74C2×C8C22×C37311yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8D4×C37311yescharacteristic
79D4—21no—
80D4—21no—
81D4—21no—
82D4D4×C37311yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4C23×C37311yescharacteristic
86C8—21no—
87C8—21no—
88C8—21no—
89C8D4×C37311yescharacteristic
90C8D4×C37311yescharacteristic
91C22—21no—
92C22—41no—
93C22—81no—
94C22#41×C37311yescharacteristic
95C4—21no—
96C4—41no—
97C4C2×D4×C37311yescharacteristic
98C4C2×D4×C37311yescharacteristic
99C2—21no—
100C2—41no—
101C2—81no—
102C2#121×C37311yescharacteristic
subgroupG/H
center, socleC2×C373#121
commutator, Frattini, cosocleC2×C4C23×C373
prime radicalAGL(1,ℤ/8)×C373C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C373 ◁ C2×C4×C373 ◁ G

Complements

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

NH ≅ G/Ntype
1. #137×C373C2semidirect
3. C2×SD16×C373C2semidirect
4. #131×C373C2semidirect
5. #108×C373C2semidirect
6. #101×C373C2semidirect
7. #100×C373C2semidirect
51. C373#471direct (N × H)
52. #471C373direct (N × H)
53. #137C2×C373semidirect
55. C2×SD16C2×C373semidirect
56. #131C2×C373semidirect
57. #108C2×C373semidirect
58. #101C2×C373semidirect
59. #100C2×C373semidirect

Maximal subgroups

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

subgroupindex
#137×C3732
AGL(1,ℤ/8)×C3732
C2×SD16×C3732
#131×C3732
#108×C3732
#101×C3732
#100×C3732
#471373