Finite Group Databasebeta

← #49120406

Subgroups — #49120406

Order 36224.

218 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 57 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#31826844C211yesmaximal, characteristic, complemented
2#31826755C212yesmaximal, complemented
3#31826214C211yesmaximal, characteristic, complemented
4D4⋊(C283⋊C8)C212yesmaximal, complemented
5#555×C283C211yesmaximal, characteristic
6C2×#17985382—22no—
7#22583610C2211yescharacteristic
8#22583541—22no—
9C4⋊(C283⋊C8)C2212yes—
10#22583531—22no—
11C4×C283⋊C8C2211yescharacteristic
12C4⋊Q8×C283C2211yescharacteristic
13#124×C283—22no—
14#121×C283—22no—
15C4×D4×C283C2212yes—
16#117×C283—22no—
17C2×Dic566—21no—
18#17985382—44no—
19C2×C283⋊C8—21no—
20C2×C283⋊C8—22no—
21C4⋊Dic283—22no—
22C2×Q8×C283D412yes—
23C2×D4×C283—22no—
24C2×D4×C283D412yes—
25C22×C4×C283—22no—
26C4⋊C4×C283—22no—
27C4⋊C4×C283D412yes—
28C22⋊C4×C283—24no—
29C22⋊C4×C283—22no—
30C42×C283—22no—
31C42×C283C2311yescharacteristic
32Dic566—42no—
33C2×Dic283—41no—
34C283⋊C8—22no—
35C283⋊C8—42no—
36C23×C283—22no—
37Q8×C283—42no—
38D4×C283—22no—
39D4×C283—22no—
40D4×C283—82no—
41C2×C4×C283—22no—
42C2×C4×C283—22no—
43C2×C4×C283—42no—
44C2×C4×C283—42no—
45C2×C4×C283C2×D411yescharacteristic
46C2×C4×C283C2×D412yes—
47C22×C283—42no—
48C22×C283—42no—
49C22×C283—42no—
50C22×C283#12011yescharacteristic
51C4×C283—21no—
52C4×C283—42no—
53C4×C283—42no—
54C4×C283#13512yes—
55C4×C283#13712yes—
56Dic283—81no—
57C2×C283—82no—
58C2×C283#45212yes—
59C2×C283#45311yescharacteristic
60C283#163411yescharacteristic, complemented, Sylow
61#1634—2831nomaximal, Sylow
62#555D28311yescharacteristic
63#494—2831no—
64#476—2832no—
65#333—2831no—
66D4⋊C8—2832no—
67C2×Q16—5662no—
68C4⋊Q8—2831no—
69C4⋊Q8C2×D28311yescharacteristic
70#124—22no—
71#121—22no—
72C4×D4C2×D28312yes—
73#117—22no—
74#106—5662no—
75C4⋊C8—2832no—
76#102—5662no—
77C4×C8—2831no—
78C2×Q8—5661no—
79C2×Q8C22⋊D28312yes—
80C2×D4—22no—
81C2×D4C22⋊D28312yes—
82C22×C4—22no—
83Q16—11324no—
84C2×C8—5661no—
85C2×C8—5662no—
86C4⋊C4—22no—
87C4⋊C4—5662no—
88C4⋊C4C22⋊D28312yes—
89C22⋊C4—24no—
90C22⋊C4—22no—
91C42—22no—
92C42C22×D28311yescharacteristic
93C23—22no—
94Q8—42no—
95Q8—11322no—
96D4—22no—
97D4—22no—
98D4—82no—
99C2×C4—22no—
100C2×C4—22no—
101C2×C4—42no—
102C2×C4—42no—
103C2×C4—11321no—
104C2×C4C2×C22⋊D28311yescharacteristic
105C2×C4C2×C22⋊D28312yes—
106C8—5662no—
107C8—11322no—
108C22—42no—
109C22—42no—
110C22—42no—
111C22#2258357911yescharacteristic
112C4—21no—
113C4—42no—
114C4—42no—
115C4—22641no—
116C4#2258363012yes—
117C4#2258364012yes—
118C2—82no—
119C2#3182662712yes—
120C2#3182663311yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting, prime radical#555×C283C2
socleC22×C283#120
hypercenter#555D283
hypocenterC283#1634
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #31826844C2semidirect
2. #31826755C2semidirect
3. #31826214C2semidirect
4. D4⋊(C283⋊C8)C2semidirect
60. C283#1634semidirect

Maximal subgroups

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

subgroupindex
#318268442
#318267552
#318262142
D4⋊(C283⋊C8)2
#555×C2832
#1634283