Finite Group Databasebeta

← #44543313

Subgroups — #44543313

Order 31936.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#22547799C211yesmaximal, characteristic, complemented
2C2×#22547796C211yesmaximal, characteristic
3#30630339C211yesmaximal, characteristic, complemented
4C4⋊(C499⋊C8)C211yesmaximal, characteristic, complemented
5#30630274C211yesmaximal, characteristic, complemented
6#30630271C211yesmaximal, characteristic, complemented
7C4×D4×C499C211yesmaximal, characteristic, complemented
8C2×Dic998C2211yescharacteristic
9C2×D1996C2211yescharacteristic
10#22547799—22no—
11#22547796—22no—
12C2×C499⋊C8C2211yescharacteristic
13C2×C499⋊C8C2211yescharacteristic
14(C2×D499)⋊C4—21no—
15(C2×D499)⋊C4—21no—
16C2×D4×C499C2211yescharacteristic
17C22×C4×C499—21no—
18C4⋊C4×C499C2211yescharacteristic
19C22⋊C4×C499—21no—
20C42×C499C2211yescharacteristic
21C22×D499—21no—
22Dic998—21no—
23Dic998—21no—
24D1996—21no—
25D1996—21no—
26C2×Dic499—21no—
27C499⋊C8—21no—
28C499⋊C8—21no—
29C23×C499—21no—
30D4×C499—21no—
31D4×C499D412yes—
32C2×C4×C499—21no—
33C2×C4×C499—42no—
34C2×C4×C499D411yescharacteristic
35C2×C4×C499D411yescharacteristic
36C2×C4×C499C2311yescharacteristic
37C22×C499—22no—
38C22×C499—41no—
39C22×C499—41no—
40C22×C499C2×D411yescharacteristic
41C2×D499—41no—
42C2×D499—41no—
43C2×D499—41no—
44C4×C499—21no—
45C4×C499—21no—
46C4×C499—41no—
47C4×C499C2×D411yescharacteristic
48C4×C499#4111yescharacteristic
49Dic499—41no—
50C2×C499—42no—
51C2×C499#12111yescharacteristic
52C2×C499#13511yescharacteristic
53C2×C499AGL(1,ℤ/8)11yescharacteristic
54D499—81no—
55C499#46311yescharacteristic, complemented, Sylow
56#463—4991nomaximal, Sylow
57C2×SD16—4991no—
58C2×D8—4991no—
59#124—4991no—
60C4×D4D49911yescharacteristic, complemented
61C4⋊C8—4991no—
62#103—4991no—
63#102—4991no—
64C2×Q8—4991no—
65C2×D4—4991no—
66C2×D4C2×D49911yescharacteristic
67C22×C4—21no—
68SD16—9982no—
69D8—9982no—
70C2×C8—4991no—
71C2×C8—4991no—
72C4⋊C4C2×D49911yescharacteristic
73C22⋊C4—21no—
74C22⋊C4—9981no—
75C22⋊C4—9981no—
76C42C2×D49911yescharacteristic
77C23—21no—
78C23—9981no—
79Q8—9981no—
80Q8—9981no—
81D4—21no—
82D4—9981no—
83D4—9981no—
84D4D199612yes—
85C2×C4—21no—
86C2×C4—42no—
87C2×C4—9981no—
88C2×C4C22⋊D49911yescharacteristic
89C2×C4C22⋊D49911yescharacteristic
90C2×C4C22×D49911yescharacteristic
91C8—9981no—
92C8—9981no—
93C22—22no—
94C22—41no—
95C22—41no—
96C22—19961no—
97C22—19961no—
98C22—19961no—
99C22C2×C22⋊D49911yescharacteristic
100C4—21no—
101C4—21no—
102C4—41no—
103C4—19961no—
104C4C2×D199611yescharacteristic
105C4#2254781111yescharacteristic
106C2—42no—
107C2—39921no—
108C2#3063032511yescharacteristic
109C2#3063037111yescharacteristic
110C2#3063037711yescharacteristic
subgroupG/H
centerC22C2×C22⋊D499
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
FittingC4×D4×C499C2
socleC22×C499C2×D4
prime radicalC2×#22547796C2
hypercenterC4×D4D499
hypocenterC499#463
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22547799C2semidirect
3. #30630339C2semidirect
4. C4⋊(C499⋊C8)C2semidirect
5. #30630274C2semidirect
6. #30630271C2semidirect
7. C4×D4×C499C2semidirect
55. C499#463semidirect
60. C4×D4D499semidirect

Maximal subgroups

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

subgroupindex
C2×#225477992
C2×#225477962
#306303392
C4⋊(C499⋊C8)2
#306302742
#306302712
C4×D4×C4992
#463499