Finite Group Databasebeta

← #43272198

Subgroups — #43272198

Order 28736.

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#28385385C211yesmaximal, characteristic
2#28385324C212yesmaximal, complemented
3#28385321C211yesmaximal, characteristic, complemented
4#28385254C212yesmaximal, complemented
5#99×C449C211yesmaximal, characteristic, complemented
6#20297736—21no—
7#20297735—22no—
8C2×C22⋊D449—21no—
9C2×C22⋊D449C2212yes—
10D4×D449—22no—
11C22×Dic449C2211yescharacteristic, complemented
12C4⋊Dic449—22no—
13#20297715—21no—
14C22⋊Dic449—21no—
15C22⋊Dic449C2211yescharacteristic, complemented
16#20297713—22no—
17C2×D4×C449C2211yescharacteristic
18C22⋊C4×C449C2212yescomplemented
19C22×D449—21no—
20C22×D449D412yes—
21Dic898—21no—
22D1796—21no—
23C22⋊D449—22no—
24C22⋊D449—22no—
25C22⋊D449—22no—
26C2×Dic449—21no—
27C2×Dic449—22no—
28C2×Dic449—21no—
29C2×Dic449—21no—
30C2×Dic449D412yes—
31C4×D449—22no—
32C23×C449D411yescharacteristic
33C23×C449C2311yescharacteristic
34D4×C449—22no—
35C2×C4×C449—22no—
36C2×C4×C449D411yescharacteristic
37C22×C449—21no—
38C22×C449—41no—
39C22×C449—41no—
40C22×C449C2×D412yes—
41C22×C449C2×D411yescharacteristic
42C2×D449—22no—
43C2×D449—42no—
44C2×D449—81no—
45C4×C449—21no—
46C4×C449—42no—
47Dic449—22no—
48Dic449—41no—
49Dic449—41no—
50C2×C449—21no—
51C2×C449—22no—
52C2×C449—41no—
53C2×C449#12011yescharacteristic
54D449—42no—
55C449#45811yescharacteristic, complemented, Sylow
56#458—4491nomaximal, Sylow
57H(5,𝔽2)—4491no—
58#123—4491no—
59#123—4492no—
60#99—4492no—
61#99D44911yescharacteristic, complemented
62#41—8982no—
63#41—8981no—
64C2×D4—8982no—
65C2×D4—8981no—
66C2×D4—4492no—
67C2×D4C2×D44911yescharacteristic
68C22×C4—4491no—
69C4⋊C4—8982no—
70C4⋊C4—8981no—
71C22⋊C4—8982no—
72C22⋊C4—8981no—
73C22⋊C4—4491no—
74C22⋊C4C2×D44912yescomplemented
75C23—8981no—
76C23—4492no—
77C23D179611yescharacteristic
78C23C22×D44911yescharacteristic
79Q8—8981no—
80D4—22no—
81D4—8981no—
82D4—8982no—
83D4—8982no—
84D4—8982no—
85C2×C4—22no—
86C2×C4—8982no—
87C2×C4—8982no—
88C2×C4—8981no—
89C2×C4—8981no—
90C2×C4—8981no—
91C2×C4—4492no—
92C2×C4D179611yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—17962no—
97C22—35921no—
98C22—8982no—
99C22D4×D44912yes—
100C22C2×D179611yescharacteristic
101C4—21no—
102C4—42no—
103C4—17961no—
104C4—17961no—
105C4—8982no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—17962no—
110C2#2838531011yescharacteristic
subgroupG/H
centerC2#28385310
commutator, cosocleC23×C449C23
FrattiniC23C22×D449
Fitting#99×C449C2
socleC2×C449#120
prime radical#28385385C2
hypercenter#99D449
hypocenterC449#458
LCSG ▷ C23×C449 ▷ C2×C449 ▷ C449
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #28385324C2semidirect
3. #28385321C2semidirect
4. #28385254C2semidirect
5. #99×C449C2semidirect
11. C22×Dic449C22semidirect
15. C22⋊Dic449C22semidirect
18. C22⋊C4×C449C22semidirect
55. C449#458semidirect
61. #99D449semidirect
74. C22⋊C4C2×D449semidirect

Maximal subgroups

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

subgroupindex
#283853852
#283853242
#283853212
#283852542
#99×C4492
#458449