Finite Group Databasebeta

← #46855269

Subgroups — #46855269

Order 35008.

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#31776027C211yesmaximal, characteristic, complemented
2C2×#22576761C211yesmaximal, characteristic, complemented
3#31776009C211yesmaximal, characteristic, complemented
4#31775937C211yesmaximal, characteristic, complemented
5#31775919C211yesmaximal, characteristic, complemented
6#31775918C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C547C211yesmaximal, characteristic, complemented
8C2×D2188C2211yescharacteristic
9#22576763—21no—
10#22576761—21no—
11#22576761—21no—
12#22576761—21no—
13#22576760—21no—
14#22576760C2211yescharacteristic
15#22576760C2211yescharacteristic
16C2×C547⋊C8—21no—
17C2×C547⋊C8C2211yescharacteristic
18#41×C547C2211yescharacteristic
19C2×D4×C547C2211yescharacteristic
20SD16×C547—21no—
21D8×C547—21no—
22M16×C547C2211yescharacteristic
23C22×D547—21no—
24D2188—21no—
25D2188—21no—
26C547⋊C8—21no—
27C547⋊C8—21no—
28C547⋊C8D411yescharacteristic
29C547⋊C8D411yescharacteristic
30C23×C547—21no—
31Q8×C547D411yescharacteristic
32D4×C547—21no—
33D4×C547—21no—
34D4×C547—21no—
35D4×C547D411yescharacteristic
36C2×C4×C547—21no—
37C2×C4×C547C2311yescharacteristic
38C8×C547—21no—
39C22×C547—21no—
40C22×C547—41no—
41C22×C547—81no—
42C22×C547#4111yescharacteristic
43C2×D547—41no—
44C2×D547—81no—
45C4×C547—21no—
46C4×C547C2×D411yescharacteristic
47C4×C547C2×D411yescharacteristic
48C2×C547—21no—
49C2×C547—41no—
50C2×C547—81no—
51C2×C547#12111yescharacteristic
52D547—81no—
53C547#47211yescharacteristic, complemented, Sylow
54#472—5471nomaximal, Sylow
55AGL(1,ℤ/8)—5471no—
56AGL(1,ℤ/8)D54711yescharacteristic, complemented
57C2×D8—5471no—
58#131—5471no—
59#108—5471no—
60#100—5471no—
61#100—5471no—
62#41C2×D54711yescharacteristic
63C2×D4—5471no—
64C2×D4C2×D54711yescharacteristic
65SD16—21no—
66SD16—10941no—
67D8—21no—
68D8—10941no—
69D8—10941no—
70D8—10941no—
71M16—5471no—
72M16—5471no—
73M16—10941no—
74M16C2×D54711yescharacteristic
75C2×C8—5471no—
76C2×C8—10941no—
77C23—21no—
78C23—10941no—
79Q8C22⋊D54711yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—10941no—
84D4—10941no—
85D4C22⋊D54711yescharacteristic
86C2×C4—21no—
87C2×C4C22×D54711yescharacteristic
88C8—21no—
89C8—5471no—
90C8—5471no—
91C8—10941no—
92C8—10941no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—43761no—
97C22—21881no—
98C22#2257677511yescharacteristic
99C4—21no—
100C4D4×D54711yescharacteristic
101C4C2×C22⋊D54711yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—43761no—
106C2#3177597411yescharacteristic
subgroupG/H
centerC2#31775974
commutator, cosocleC2×C4×C547C23
FrattiniC2×C4C22×D547
FittingAGL(1,ℤ/8)×C547C2
socleC2×C547#121
hypercenterAGL(1,ℤ/8)D547
hypocenterC547#472
LCSG ▷ C2×C4×C547 ▷ C2×C547 ▷ C547
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #31776027C2semidirect
2. C2×#22576761C2semidirect
3. #31776009C2semidirect
4. #31775937C2semidirect
5. #31775919C2semidirect
6. #31775918C2semidirect
7. AGL(1,ℤ/8)×C547C2semidirect
53. C547#472semidirect
56. AGL(1,ℤ/8)D547semidirect

Maximal subgroups

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

subgroupindex
#317760272
C2×#225767612
#317760092
#317759372
#317759192
#317759182
AGL(1,ℤ/8)×C5472
#472547