Finite Group Databasebeta

← #46830443

Subgroups — #46830443

Order 34624.

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#31772653C211yesmaximal, characteristic, complemented
2C2×#22575821C211yesmaximal, characteristic, complemented
3#31772635C211yesmaximal, characteristic, complemented
4#31772563C211yesmaximal, characteristic, complemented
5#31772545C211yesmaximal, characteristic, complemented
6#31772544C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
8C2×D2164C2211yescharacteristic
9#22575823—21no—
10#22575821—21no—
11#22575821—21no—
12#22575821—21no—
13#22575820—21no—
14#22575820C2211yescharacteristic
15#22575820C2211yescharacteristic
16C2×#16864513—21no—
17C2×#16864513C2211yescharacteristic
18#41×C541C2211yescharacteristic
19C2×D4×C541C2211yescharacteristic
20SD16×C541—21no—
21D8×C541—21no—
22M16×C541C2211yescharacteristic
23C22×D541—21no—
24D2164—21no—
25D2164—21no—
26#16864513—21no—
27#16864513—21no—
28#16864513D411yescharacteristic
29#16864513D411yescharacteristic
30C23×C541—21no—
31Q8×C541D411yescharacteristic
32D4×C541—21no—
33D4×C541—21no—
34D4×C541—21no—
35D4×C541D411yescharacteristic
36C2×C4×C541—21no—
37C2×C4×C541C2311yescharacteristic
38C8×C541—21no—
39C22×C541—21no—
40C22×C541—41no—
41C22×C541—81no—
42C22×C541#4111yescharacteristic
43C2×D541—41no—
44C2×D541—81no—
45C4×C541—21no—
46C4×C541C2×D411yescharacteristic
47C4×C541C2×D411yescharacteristic
48C2×C541—21no—
49C2×C541—41no—
50C2×C541—81no—
51C2×C541#12111yescharacteristic
52D541—81no—
53C541#47211yescharacteristic, complemented, Sylow
54#472—5411nomaximal, Sylow
55AGL(1,ℤ/8)—5411no—
56AGL(1,ℤ/8)D54111yescharacteristic, complemented
57C2×D8—5411no—
58#131—5411no—
59#108—5411no—
60#100—5411no—
61#100—5411no—
62#41C2×D54111yescharacteristic
63C2×D4—5411no—
64C2×D4C2×D54111yescharacteristic
65SD16—21no—
66SD16—10821no—
67D8—21no—
68D8—10821no—
69D8—10821no—
70D8—10821no—
71M16—5411no—
72M16—5411no—
73M16—10821no—
74M16C2×D54111yescharacteristic
75C2×C8—5411no—
76C2×C8—10821no—
77C23—21no—
78C23—10821no—
79Q8C22⋊D54111yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—10821no—
84D4—10821no—
85D4C22⋊D54111yescharacteristic
86C2×C4—21no—
87C2×C4C22×D54111yescharacteristic
88C8—21no—
89C8—5411no—
90C8—5411no—
91C8—10821no—
92C8—10821no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—21641no—
97C22—43281no—
98C22#2257583511yescharacteristic
99C4—21no—
100C4D4×D54111yescharacteristic
101C4C2×C22⋊D54111yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—43281no—
106C2#3177260011yescharacteristic
subgroupG/H
centerC2#31772600
commutator, cosocleC2×C4×C541C23
FrattiniC2×C4C22×D541
FittingAGL(1,ℤ/8)×C541C2
socleC2×C541#121
hypercenterAGL(1,ℤ/8)D541
hypocenterC541#472
LCSG ▷ C2×C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #31772653C2semidirect
2. C2×#22575821C2semidirect
3. #31772635C2semidirect
4. #31772563C2semidirect
5. #31772545C2semidirect
6. #31772544C2semidirect
7. AGL(1,ℤ/8)×C541C2semidirect
53. C541#472semidirect
56. AGL(1,ℤ/8)D541semidirect

Maximal subgroups

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

subgroupindex
#317726532
C2×#225758212
#317726352
#317725632
#317725452
#317725442
AGL(1,ℤ/8)×C5412
#472541