Finite Group Databasebeta

← #44543367

Subgroups — #44543367

Order 31936.

108 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 35 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#30630379C211yesmaximal, characteristic, complemented
2#30630377C211yesmaximal, characteristic, complemented
3C2×#22547796C211yesmaximal, characteristic, complemented
4#30630359C211yesmaximal, characteristic, complemented
5#30630286C211yesmaximal, characteristic, complemented
6#30630267C211yesmaximal, characteristic, complemented
7#100×C499C211yesmaximal, characteristic, complemented
8#22547811C2211yescharacteristic
9C2×D1996C2211yescharacteristic
10#22547800—21no—
11#22547799—21no—
12D3992—21no—
13#22547796—21no—
14#22547796—21no—
15#22547796—21no—
16#22547795C2211yescharacteristic
17#22547794—21no—
18C2×C499⋊C8C2211yescharacteristic
19C8×D499—21no—
20C2×D4×C499C2211yescharacteristic
21M16×C499C2211yescharacteristic
22M16×C499C2211yescharacteristic
23C22×D499—21no—
24Dic998D411yescharacteristic
25D1996—21no—
26D1996—21no—
27D1996D411yescharacteristic
28C22⋊D499—21no—
29C4×D499—21no—
30C499⋊C8—21no—
31C499⋊C8D411yescharacteristic
32C499⋊C8D411yescharacteristic
33C23×C499—21no—
34D4×C499—21no—
35D4×C499—21no—
36C2×C4×C499C2311yescharacteristic
37C8×C499—21no—
38C8×C499—21no—
39C22×C499—41no—
40C22×C499—81no—
41C22×C499#4111yescharacteristic
42C2×D499—21no—
43C2×D499—41no—
44C2×D499—81no—
45C4×C499C2×D411yescharacteristic
46C4×C499C2×D411yescharacteristic
47Dic499—21no—
48C2×C499—21no—
49C2×C499—81no—
50C2×C499#12111yescharacteristic
51D499—41no—
52D499—81no—
53C499#47211yescharacteristic, complemented, Sylow
54#472—4991nomaximal, Sylow
55AGL(1,ℤ/8)—4991no—
56AGL(1,ℤ/8)—4991no—
57C2×D8—4991no—
58#131—4991no—
59#108—4991no—
60#100—4991no—
61#100D49911yescharacteristic, complemented
62#41—4991no—
63C2×D4—4991no—
64C2×D4C2×D49911yescharacteristic
65SD16—9981no—
66SD16—9981no—
67D8—9981no—
68D8—9981no—
69D8—9981no—
70D8—9981no—
71M16—9981no—
72M16—4991no—
73M16C2×D49911yescharacteristic
74M16C2×D49911yescharacteristic
75C2×C8—9981no—
76C2×C8—4991no—
77C23—21no—
78C23—9981no—
79Q8—4991no—
80D4—21no—
81D4—21no—
82D4—9981no—
83D4—9981no—
84D4—9981no—
85D4—4991no—
86C2×C4—9981no—
87C2×C4C22×D49911yescharacteristic
88C8—21no—
89C8—21no—
90C8—9981no—
91C8—4991no—
92C8—4991no—
93C22—41no—
94C22—81no—
95C22—39921no—
96C22—19961no—
97C22—9981no—
98C22#2254781111yescharacteristic
99C4—9981no—
100C4D4×D49911yescharacteristic
101C4D4×D49911yescharacteristic
102C2—21no—
103C2—81no—
104C2—39921no—
105C2—19961no—
106C2#3063032411yescharacteristic
subgroupG/H
centerC2#30630324
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
Fitting#100×C499C2
socleC2×C499#121
hypercenter#100D499
hypocenterC499#472
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #30630379C2semidirect
2. #30630377C2semidirect
3. C2×#22547796C2semidirect
4. #30630359C2semidirect
5. #30630286C2semidirect
6. #30630267C2semidirect
7. #100×C499C2semidirect
53. C499#472semidirect
61. #100D499semidirect

Maximal subgroups

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

subgroupindex
#306303792
#306303772
C2×#225477962
#306303592
#306302862
#306302672
#100×C4992
#472499