Finite Group Databasebeta

← #44543366

Subgroups — #44543366

Order 31936.

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#30630376C211yesmaximal, characteristic, complemented
2C2×#22547796C211yesmaximal, characteristic, complemented
3#30630358C211yesmaximal, characteristic, complemented
4#30630286C211yesmaximal, characteristic, complemented
5#30630268C211yesmaximal, characteristic, complemented
6#30630267C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C499C211yesmaximal, characteristic, complemented
8C2×D1996C2211yescharacteristic
9#22547798—21no—
10#22547796—21no—
11#22547796—21no—
12#22547796—21no—
13#22547795—21no—
14#22547795C2211yescharacteristic
15#22547795C2211yescharacteristic
16C2×C499⋊C8—21no—
17C2×C499⋊C8C2211yescharacteristic
18#41×C499C2211yescharacteristic
19C2×D4×C499C2211yescharacteristic
20SD16×C499—21no—
21D8×C499—21no—
22M16×C499C2211yescharacteristic
23C22×D499—21no—
24D1996—21no—
25D1996—21no—
26C499⋊C8—21no—
27C499⋊C8—21no—
28C499⋊C8D411yescharacteristic
29C499⋊C8D411yescharacteristic
30C23×C499—21no—
31Q8×C499D411yescharacteristic
32D4×C499—21no—
33D4×C499—21no—
34D4×C499—21no—
35D4×C499D411yescharacteristic
36C2×C4×C499—21no—
37C2×C4×C499C2311yescharacteristic
38C8×C499—21no—
39C22×C499—21no—
40C22×C499—41no—
41C22×C499—81no—
42C22×C499#4111yescharacteristic
43C2×D499—41no—
44C2×D499—81no—
45C4×C499—21no—
46C4×C499C2×D411yescharacteristic
47C4×C499C2×D411yescharacteristic
48C2×C499—21no—
49C2×C499—41no—
50C2×C499—81no—
51C2×C499#12111yescharacteristic
52D499—81no—
53C499#47211yescharacteristic, complemented, Sylow
54#472—4991nomaximal, Sylow
55AGL(1,ℤ/8)—4991no—
56AGL(1,ℤ/8)D49911yescharacteristic, complemented
57C2×D8—4991no—
58#131—4991no—
59#108—4991no—
60#100—4991no—
61#100—4991no—
62#41C2×D49911yescharacteristic
63C2×D4—4991no—
64C2×D4C2×D49911yescharacteristic
65SD16—21no—
66SD16—9981no—
67D8—21no—
68D8—9981no—
69D8—9981no—
70D8—9981no—
71M16—9981no—
72M16—4991no—
73M16—4991no—
74M16C2×D49911yescharacteristic
75C2×C8—9981no—
76C2×C8—4991no—
77C23—21no—
78C23—9981no—
79Q8C22⋊D49911yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—9981no—
84D4—9981no—
85D4C22⋊D49911yescharacteristic
86C2×C4—21no—
87C2×C4C22×D49911yescharacteristic
88C8—21no—
89C8—9981no—
90C8—9981no—
91C8—4991no—
92C8—4991no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—39921no—
97C22—19961no—
98C22#2254781011yescharacteristic
99C4—21no—
100C4D4×D49911yescharacteristic
101C4C2×C22⋊D49911yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—39921no—
106C2#3063032311yescharacteristic
subgroupG/H
centerC2#30630323
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
FittingAGL(1,ℤ/8)×C499C2
socleC2×C499#121
hypercenterAGL(1,ℤ/8)D499
hypocenterC499#472
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30630376C2semidirect
2. C2×#22547796C2semidirect
3. #30630358C2semidirect
4. #30630286C2semidirect
5. #30630268C2semidirect
6. #30630267C2semidirect
7. AGL(1,ℤ/8)×C499C2semidirect
53. C499#472semidirect
56. AGL(1,ℤ/8)D499semidirect

Maximal subgroups

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

subgroupindex
#306303762
C2×#225477962
#306303582
#306302862
#306302682
#306302672
AGL(1,ℤ/8)×C4992
#472499