Finite Group Databasebeta

← #49120562

Subgroups — #49120562

Order 36224.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C283⋊#564C211yesmaximal, characteristic, complemented
2#31826829C212yesmaximal
3#31826207C211yesmaximal, characteristic, complemented
4#31826206C212yesmaximal, complemented
5#490×C283C211yesmaximal, characteristic
6#22583602C2212yes—
7#22583601—22no—
8#22583600—22no—
9#22583600—22no—
10#22583531—22no—
11#22583531—22no—
12#22583521C2212yes—
13#127×C283C2211yescharacteristic
14#125×C283C2211yescharacteristic
15#102×C283—22no—
16#97×C283C2211yescharacteristic
17C2×C283⋊C8—22no—
18C4⋊Dic283—22no—
19C4⋊Dic283D412yes—
20C4⋊Dic283D412yes—
21Dic283⋊C4—22no—
22Dic283⋊C4—22no—
23Dic283⋊C4—22no—
24Dic283⋊C4—22no—
25C4×Dic283—22no—
26C2×D4×C283—21no—
27C2×D4×C283—22no—
28C2×C8×C283—21no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283D412yes—
31C42×C283C2311yescharacteristic
32C2×Dic283—22no—
33C2×Dic283—22no—
34C283⋊C8—42no—
35C23×C283—41no—
36D4×C283—42no—
37D4×C283—44no—
38C2×C4×C283—22no—
39C2×C4×C283C2×D412yes—
40C2×C4×C283C2×D411yescharacteristic
41C8×C283—41no—
42C22×C283—82no—
43C22×C283—81no—
44C22×C283#12011yescharacteristic
45C4×C283—21no—
46C4×C283—22no—
47C4×C283—42no—
48Dic283—42no—
49Dic283—42no—
50C2×C283—161no—
51C2×C283#45412yes—
52C2×C283#45411yescharacteristic
53C283#165811yescharacteristic, complemented, Sylow
54#1658—2831nomaximal, Sylow
55#564—2831no—
56#490—2832no—
57#490D28311yescharacteristic
58#330—2831no—
59#330—2832no—
60#127C2×D28311yescharacteristic
61#125—2832no—
62#125—5662no—
63#125—5662no—
64#125—5662no—
65#125C2×D28311yescharacteristic
66#102—22no—
67#102—5662no—
68#102—5662no—
69#97—2832no—
70#97C2×D28311yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—5662no—
75C4⋊C4—22no—
76C4⋊C4—2832no—
77C4⋊C4—2832no—
78C4⋊C4—5662no—
79C4⋊C4—5662no—
80C4⋊C4—5662no—
81C4⋊C4—5662no—
82C4⋊C4—5662no—
83C4⋊C4C22⋊D28312yes—
84C42—5662no—
85C42C22×D28311yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—5662no—
91C2×C4—5662no—
92C2×C4D4×D28312yes—
93C2×C4C2×C22⋊D28311yescharacteristic
94C8—41no—
95C8—11322no—
96C22—82no—
97C22—81no—
98C22#2258357811yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—11322no—
103C4—11322no—
104C2—161no—
105C2#3182663612yes—
106C2#3182663711yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#490×C283C2
socleC22×C283#120
prime radical#127×C283C22
hypercenter#490D283
hypocenterC283#1658
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C283⋊#564C2semidirect
3. #31826207C2semidirect
4. #31826206C2semidirect
53. C283#1658semidirect

Maximal subgroups

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

subgroupindex
C283⋊#5642
#318268292
#318262072
#318262062
#490×C2832
#1658283