Finite Group Databasebeta

← #44543325

Subgroups — #44543325

Order 31936.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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
2C22×C499⋊C8C211yesmaximal, characteristic, complemented
3#30630330C211yesmaximal, characteristic, complemented
4#30630282C211yesmaximal, characteristic, complemented
5#30630274C211yesmaximal, characteristic, complemented
6#30630272C211yesmaximal, characteristic, complemented
7#121×C499C211yesmaximal, characteristic
8C2×Dic998C2211yescharacteristic
9#22547799—22no—
10C2×C499⋊C8—22no—
11C2×C499⋊C8C2211yescharacteristic
12C2×C499⋊C8C2211yescharacteristic
13C4⋊Dic499C2211yescharacteristic
14Dic499⋊C4—21no—
15C22⋊Dic499—21no—
16C2×D4×C499—21no—
17C2×D4×C499C2211yescharacteristic
18C22×C4×C499C2211yescharacteristic
19C4⋊C4×C499C2211yescharacteristic
20C22⋊C4×C499—21no—
21Dic998—21no—
22Dic998—21no—
23C2×Dic499—21no—
24C2×Dic499—21no—
25C499⋊C8—21no—
26C499⋊C8D412yescomplemented
27C23×C499—21no—
28C23×C499D411yescharacteristic
29D4×C499—21no—
30D4×C499—21no—
31D4×C499—42no—
32C2×C4×C499—21no—
33C2×C4×C499—21no—
34C2×C4×C499—21no—
35C2×C4×C499D411yescharacteristic
36C2×C4×C499C2311yescharacteristic
37C22×C499—21no—
38C22×C499—21no—
39C22×C499—41no—
40C22×C499—41no—
41C22×C499—41no—
42C22×C499SD1612yescomplemented
43C22×C499C2×D411yescharacteristic
44C4×C499—21no—
45C4×C499—41no—
46C4×C499C2×D411yescharacteristic
47C4×C499#4111yescharacteristic
48Dic499—41no—
49Dic499—41no—
50C2×C499—22no—
51C2×C499—81no—
52C2×C499#12111yescharacteristic
53C2×C499C2×SD1611yescharacteristic
54C2×C499#13511yescharacteristic
55C499#46511yescharacteristic, complemented, Sylow
56#465—4991nomaximal, Sylow
57C2×SD16—4991no—
58C22×C8—4991no—
59C22⋊Q8—4991no—
60#121D49911yescharacteristic
61#106—4991no—
62#103—4991no—
63#102—4991no—
64C2×Q8—4991no—
65C2×D4—21no—
66C2×D4C2×D49911yescharacteristic
67C22×C4C2×D49911yescharacteristic
68SD16—9982no—
69C2×C8—9982no—
70C2×C8—4991no—
71C2×C8—4991no—
72C4⋊C4—9981no—
73C4⋊C4—4991no—
74C4⋊C4C2×D49911yescharacteristic
75C22⋊C4—21no—
76C22⋊C4—9981no—
77C23—21no—
78C23C22⋊D49911yescharacteristic
79Q8—9981no—
80Q8—9981no—
81D4—21no—
82D4—21no—
83D4—42no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—9981no—
88C2×C4—9981no—
89C2×C4C22⋊D49911yescharacteristic
90C2×C4C22×D49911yescharacteristic
91C8—9981no—
92C8—4992no—
93C22—21no—
94C22—21no—
95C22—41no—
96C22—41no—
97C22—41no—
98C22#2254779912yescomplemented
99C22C2×C22⋊D49911yescharacteristic
100C4—21no—
101C4—41no—
102C4—19961no—
103C4—19961no—
104C4D4×D49911yescharacteristic
105C4#2254781011yescharacteristic
106C2—22no—
107C2—81no—
108C2#3063032311yescharacteristic
109C2C2×#2254779911yescharacteristic
110C2#3063037111yescharacteristic
subgroupG/H
centerC22C2×C22⋊D499
commutator, cosocleC2×C4×C499C23
FrattiniC2×C4C22×D499
Fitting, prime radical#121×C499C2
socleC22×C499C2×D4
hypercenter#121D499
hypocenterC499#465
LCSG ▷ C2×C4×C499 ▷ C2×C499 ▷ C499
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22547799C2semidirect
2. C22×C499⋊C8C2semidirect
3. #30630330C2semidirect
4. #30630282C2semidirect
5. #30630274C2semidirect
6. #30630272C2semidirect
26. C499⋊C8D4semidirect
42. C22×C499SD16semidirect
55. C499#465semidirect
98. C22#22547799semidirect

Maximal subgroups

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

subgroupindex
C2×#225477992
C22×C499⋊C82
#306303302
#306302822
#306302742
#306302722
#121×C4992
#465499