Finite Group Databasebeta

← #31823652

Subgroups — #31823652

Order 17984.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#22582924C211yesmaximal, characteristic
2#22582862C212yesmaximal, complemented
3#22582794C211yesmaximal, characteristic, complemented
4#22582793C212yesmaximal, complemented
5#123×C281C211yesmaximal, characteristic, complemented
6#17985138—21no—
7#17985137—22no—
8C2×C22⋊D281—21no—
9C2×C22⋊D281C2212yes—
10D4×D281—22no—
11#17985117—22no—
12C22⋊Dic281C2212yescomplemented
13#17985115—22no—
14C2×D4×C281C2211yescharacteristic
15C22×C4×C281C2211yescharacteristic, complemented
16C4⋊C4×C281—21no—
17C22⋊C4×C281—21no—
18C22⋊C4×C281C2211yescharacteristic, complemented
19C22×D281—21no—
20C22×D281D412yes—
21Dic562—21no—
22D1124—21no—
23C22⋊D281—22no—
24C22⋊D281—22no—
25C22⋊D281—22no—
26C2×Dic281—21no—
27C2×Dic281—22no—
28C2×Dic281D412yes—
29C4×D281—22no—
30C23×C281D411yescharacteristic
31C23×C281C2311yescharacteristic
32D4×C281—22no—
33C2×C4×C281—21no—
34C2×C4×C281—21no—
35C2×C4×C281—22no—
36C2×C4×C281D411yescharacteristic
37C22×C281—21no—
38C22×C281—41no—
39C22×C281—41no—
40C22×C281C2×D412yes—
41C22×C281C2×D411yescharacteristic
42C2×D281—22no—
43C2×D281—42no—
44C2×D281—81no—
45C4×C281—21no—
46C4×C281—41no—
47C4×C281—41no—
48Dic281—22no—
49Dic281—42no—
50C2×C281—22no—
51C2×C281—21no—
52C2×C281—41no—
53C2×C281#12011yescharacteristic
54D281—42no—
55C281#45811yescharacteristic, complemented, Sylow
56#458—2811nomaximal, Sylow
57H(5,𝔽2)—2811no—
58#123—2812no—
59#123D28111yescharacteristic, complemented
60#99—2811no—
61#99—2812no—
62#41—5622no—
63#41—5621no—
64C2×D4—2812no—
65C2×D4—5622no—
66C2×D4—5621no—
67C2×D4C2×D28111yescharacteristic
68C22×C4C2×D28111yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—5622no—
71C22⋊C4—21no—
72C22⋊C4—2812no—
73C22⋊C4—5622no—
74C22⋊C4C2×D28111yescharacteristic, complemented
75C23—2812no—
76C23—5621no—
77C23C22⋊D28111yescharacteristic
78C23C22×D28111yescharacteristic
79Q8—5621no—
80D4—22no—
81D4—5621no—
82D4—5622no—
83D4—5622no—
84D4—5622no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—2812no—
89C2×C4—5622no—
90C2×C4—5621no—
91C2×C4—5622no—
92C2×C4C22⋊D28111yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—5622no—
97C22—11242no—
98C22—22481no—
99C22D4×D28112yes—
100C22C2×C22⋊D28111yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—5622no—
105C4—11242no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—11242no—
110C2#2258284711yescharacteristic
subgroupG/H
centerC2#22582847
commutator, cosocleC23×C281C23
FrattiniC23C22×D281
Fitting#123×C281C2
socleC2×C281#120
prime radical#22582924C2
hypercenter#123D281
hypocenterC281#458
LCSG ▷ C23×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #22582862C2semidirect
3. #22582794C2semidirect
4. #22582793C2semidirect
5. #123×C281C2semidirect
12. C22⋊Dic281C22semidirect
15. C22×C4×C281C22semidirect
18. C22⋊C4×C281C22semidirect
55. C281#458semidirect
59. #123D281semidirect
68. C22×C4C2×D281semidirect
74. C22⋊C4C2×D281semidirect

Maximal subgroups

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

subgroupindex
#225829242
#225828622
#225827942
#225827932
#123×C2812
#458281