Finite Group Databasebeta

← #14271544

Subgroups — #14271544

Order 1856.

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

normal subgroups only

This group has 130 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×SD16×C29C211yesmaximal, characteristic, complemented
2#11745309C211yesmaximal, characteristic, complemented
3C2×#90785C211yesmaximal, characteristic, complemented
4#11745298C211yesmaximal, characteristic, complemented
5C2×#90782C211yesmaximal, characteristic
6C2×#90773C211yesmaximal, characteristic, complemented
7C8×Dic29C211yesmaximal, characteristic, complemented
8C2×Q8×C29C2211yescharacteristic
9C2×D4×C29C2211yescharacteristic
10C2×D116C2211yescharacteristic
11C2×Dic58C2211yescharacteristic
12SD16×C29—22no—
13C2×C8×C29C2211yescharacteristic
14C22⋊Dic29—22no—
15#90785—22no—
16#90782—22no—
17#90781—22no—
18C4×Dic29C2211yescharacteristic
19C2×#6597C2211yescharacteristic
20#90773—22no—
21C23×C29—21no—
22C22×D29—21no—
23Q8×C29—21no—
24Q8×C29—21no—
25D4×C29—21no—
26D4×C29—21no—
27C2×C4×C29—21no—
28C2×C4×C29C2311yescharacteristic
29C2×Dic29—21no—
30C2×Dic29D412yes—
31D116—21no—
32D116—21no—
33Dic58—21no—
34Dic58—21no—
35C8×C29D412yes—
36#6597D412yes—
37C22×C29—41no—
38C22×C29—42no—
39C22×C29C2×D411yescharacteristic
40C2×D29—41no—
41C2×D29—42no—
42C4×C29—41no—
43C4×C29C2×D411yescharacteristic
44C4×C29C2×D411yescharacteristic
45Dic29—22no—
46Dic29—41no—
47#495—291nomaximal, Sylow
48C2×C29—81no—
49C2×C29#12711yescharacteristic
50C2×C29#13512yes—
51D29—81no—
52C2×Q16—291no—
53C2×SD16—291no—
54C2×SD16D2911yescharacteristic, complemented
55C2×D8—291no—
56#124—291no—
57#124—291no—
58C4×C8—291no—
59C29#49511yescharacteristic, complemented, Sylow
60C2×Q8—291no—
61C2×Q8C2×D2911yescharacteristic
62C2×D4—291no—
63C2×D4C2×D2911yescharacteristic
64Q16—582no—
65SD16—22no—
66SD16—582no—
67D8—582no—
68C2×C8—291no—
69C2×C8C2×D2911yescharacteristic
70C22⋊C4—582no—
71C22⋊C4—582no—
72C42—291no—
73C23—21no—
74C23—581no—
75Q8—21no—
76Q8—21no—
77Q8—581no—
78Q8—581no—
79D4—21no—
80D4—21no—
81D4—581no—
82D4—581no—
83C2×C4—21no—
84C2×C4—292no—
85C2×C4—581no—
86C2×C4C22×D2911yescharacteristic
87C8—292no—
88C8C22⋊D2912yes—
89C22—41no—
90C22—42no—
91C22—1161no—
92C22—1162no—
93C22D4×D2911yescharacteristic
94C4—41no—
95C4—582no—
96C4—1161no—
97C4D4×D2911yescharacteristic
98C4C2×C22⋊D2911yescharacteristic
99C2—81no—
100C2—2321no—
101C2#1174527812yes—
102C2#1174530211yescharacteristic
subgroupG/H
centerC22D4×D29
commutator, cosocleC2×C4×C29C23
FrattiniC2×C4C22×D29
FittingC2×SD16×C29C2
socleC22×C29C2×D4
prime radicalC2×#90782C2
hypercenterC2×SD16D29
hypocenterC29#495
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×C29C2semidirect
2. #11745309C2semidirect
3. C2×#90785C2semidirect
4. #11745298C2semidirect
6. C2×#90773C2semidirect
7. C8×Dic29C2semidirect
54. C2×SD16D29semidirect
59. C29#495semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C292
#117453092
C2×#907852
#117452982
C2×#907822
C2×#907732
C8×Dic292
#49529