Finite Group Databasebeta

← #43247906

Subgroups — #43247906

Order 28352.

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#28381931C211yesmaximal, characteristic
2#28381869C212yesmaximal, complemented
3#28381801C211yesmaximal, characteristic, complemented
4#28381800C212yesmaximal, complemented
5#123×C443C211yesmaximal, characteristic, complemented
6#20296787—21no—
7#20296786—22no—
8C2×C22⋊D443—21no—
9C2×C22⋊D443C2212yes—
10D4×D443—22no—
11Dic443⋊C4—22no—
12C22⋊Dic443C2212yescomplemented
13(C2×D443)⋊C4—22no—
14C2×D4×C443C2211yescharacteristic
15C22×C4×C443C2211yescharacteristic, complemented
16C4⋊C4×C443—21no—
17C22⋊C4×C443—21no—
18C22⋊C4×C443C2211yescharacteristic, complemented
19C22×D443—21no—
20C22×D443D412yes—
21Dic886—21no—
22D1772—21no—
23C22⋊D443—22no—
24C22⋊D443—22no—
25C22⋊D443—22no—
26C2×Dic443—21no—
27C2×Dic443—22no—
28C2×Dic443D412yes—
29C4×D443—22no—
30C23×C443D411yescharacteristic
31C23×C443C2311yescharacteristic
32D4×C443—22no—
33C2×C4×C443—21no—
34C2×C4×C443—21no—
35C2×C4×C443—22no—
36C2×C4×C443D411yescharacteristic
37C22×C443—21no—
38C22×C443—41no—
39C22×C443—41no—
40C22×C443C2×D412yes—
41C22×C443C2×D411yescharacteristic
42C2×D443—22no—
43C2×D443—42no—
44C2×D443—81no—
45C4×C443—21no—
46C4×C443—41no—
47C4×C443—41no—
48Dic443—22no—
49Dic443—42no—
50C2×C443—22no—
51C2×C443—21no—
52C2×C443—41no—
53C2×C443#12011yescharacteristic
54D443—42no—
55C443#45811yescharacteristic, complemented, Sylow
56#458—4431nomaximal, Sylow
57H(5,𝔽2)—4431no—
58#123—4432no—
59#123D44311yescharacteristic, complemented
60#99—4431no—
61#99—4432no—
62#41—8862no—
63#41—8861no—
64C2×D4—8862no—
65C2×D4—8861no—
66C2×D4—4432no—
67C2×D4C2×D44311yescharacteristic
68C22×C4C2×D44311yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—8862no—
71C22⋊C4—21no—
72C22⋊C4—8862no—
73C22⋊C4—4432no—
74C22⋊C4C2×D44311yescharacteristic, complemented
75C23—8861no—
76C23—4432no—
77C23C22⋊D44311yescharacteristic
78C23C22×D44311yescharacteristic
79Q8—8861no—
80D4—22no—
81D4—8861no—
82D4—8862no—
83D4—8862no—
84D4—8862no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—8862no—
89C2×C4—8861no—
90C2×C4—8862no—
91C2×C4—4432no—
92C2×C4C22⋊D44311yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—8862no—
97C22—35441no—
98C22—17722no—
99C22D4×D44312yes—
100C22C2×C22⋊D44311yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—8862no—
105C4—17722no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—17722no—
110C2#2838185411yescharacteristic
subgroupG/H
centerC2#28381854
commutator, cosocleC23×C443C23
FrattiniC23C22×D443
Fitting#123×C443C2
socleC2×C443#120
prime radical#28381931C2
hypercenter#123D443
hypocenterC443#458
LCSG ▷ C23×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #28381869C2semidirect
3. #28381801C2semidirect
4. #28381800C2semidirect
5. #123×C443C2semidirect
12. C22⋊Dic443C22semidirect
15. C22×C4×C443C22semidirect
18. C22⋊C4×C443C22semidirect
55. C443#458semidirect
59. #123D443semidirect
68. C22×C4C2×D443semidirect
74. C22⋊C4C2×D443semidirect

Maximal subgroups

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

subgroupindex
#283819312
#283818692
#283818012
#283818002
#123×C4432
#458443