Finite Group Databasebeta

← #44536993

Subgroups — #44536993

Order 31424.

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#30628362C211yesmaximal, characteristic, complemented
2C2×#21463313C211yesmaximal, characteristic, complemented
3#30628344C211yesmaximal, characteristic, complemented
4#30628272C211yesmaximal, characteristic, complemented
5#30628254C211yesmaximal, characteristic, complemented
6#30628253C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C491C211yesmaximal, characteristic, complemented
8C2×D1964C2211yescharacteristic
9#21463315—21no—
10#21463313—21no—
11#21463313—21no—
12#21463313—21no—
13#21463312—21no—
14#21463312C2211yescharacteristic
15#21463312C2211yescharacteristic
16C2×C491⋊C8—21no—
17C2×C491⋊C8C2211yescharacteristic
18#41×C491C2211yescharacteristic
19C2×D4×C491C2211yescharacteristic
20SD16×C491—21no—
21D8×C491—21no—
22M16×C491C2211yescharacteristic
23C22×D491—21no—
24D1964—21no—
25D1964—21no—
26C491⋊C8—21no—
27C491⋊C8—21no—
28C491⋊C8D411yescharacteristic
29C491⋊C8D411yescharacteristic
30C23×C491—21no—
31Q8×C491D411yescharacteristic
32D4×C491—21no—
33D4×C491—21no—
34D4×C491—21no—
35D4×C491D411yescharacteristic
36C2×C4×C491—21no—
37C2×C4×C491C2311yescharacteristic
38C8×C491—21no—
39C22×C491—21no—
40C22×C491—41no—
41C22×C491—81no—
42C22×C491#4111yescharacteristic
43C2×D491—41no—
44C2×D491—81no—
45C4×C491—21no—
46C4×C491C2×D411yescharacteristic
47C4×C491C2×D411yescharacteristic
48C2×C491—21no—
49C2×C491—41no—
50C2×C491—81no—
51C2×C491#12111yescharacteristic
52D491—81no—
53C491#47211yescharacteristic, complemented, Sylow
54#472—4911nomaximal, Sylow
55AGL(1,ℤ/8)—4911no—
56AGL(1,ℤ/8)D49111yescharacteristic, complemented
57C2×D8—4911no—
58#131—4911no—
59#108—4911no—
60#100—4911no—
61#100—4911no—
62#41C2×D49111yescharacteristic
63C2×D4—4911no—
64C2×D4C2×D49111yescharacteristic
65SD16—21no—
66SD16—9821no—
67D8—21no—
68D8—9821no—
69D8—9821no—
70D8—9821no—
71M16—9821no—
72M16—4911no—
73M16—4911no—
74M16C2×D49111yescharacteristic
75C2×C8—9821no—
76C2×C8—4911no—
77C23—21no—
78C23—9821no—
79Q8C22⋊D49111yescharacteristic
80D4—21no—
81D4—21no—
82D4—21no—
83D4—9821no—
84D4—9821no—
85D4C22⋊D49111yescharacteristic
86C2×C4—21no—
87C2×C4C22×D49111yescharacteristic
88C8—21no—
89C8—9821no—
90C8—9821no—
91C8—4911no—
92C8—4911no—
93C22—21no—
94C22—41no—
95C22—81no—
96C22—39281no—
97C22—19641no—
98C22#2146332711yescharacteristic
99C4—21no—
100C4D4×D49111yescharacteristic
101C4C2×C22⋊D49111yescharacteristic
102C2—21no—
103C2—41no—
104C2—81no—
105C2—39281no—
106C2#3062830911yescharacteristic
subgroupG/H
centerC2#30628309
commutator, cosocleC2×C4×C491C23
FrattiniC2×C4C22×D491
FittingAGL(1,ℤ/8)×C491C2
socleC2×C491#121
hypercenterAGL(1,ℤ/8)D491
hypocenterC491#472
LCSG ▷ C2×C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #30628362C2semidirect
2. C2×#21463313C2semidirect
3. #30628344C2semidirect
4. #30628272C2semidirect
5. #30628254C2semidirect
6. #30628253C2semidirect
7. AGL(1,ℤ/8)×C491C2semidirect
53. C491#472semidirect
56. AGL(1,ℤ/8)D491semidirect

Maximal subgroups

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

subgroupindex
#306283622
C2×#214633132
#306283442
#306282722
#306282542
#306282532
AGL(1,ℤ/8)×C4912
#472491