Finite Group Databasebeta

← #49120589

Subgroups — #49120589

Order 36224.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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#31826875C212yesmaximal
2#31826835C211yesmaximal, characteristic
3#31826207C211yesmaximal, characteristic
4#31826207C212yesmaximal
5#564×C283C211yesmaximal, characteristic
6#22583610C2211yescharacteristic
7#22583543—22no—
8#22583541—22no—
9#22583533—22no—
10#22583521C2211yescharacteristic
11#22583521C2212yes—
12#125×C283—22no—
13#125×C283—22no—
14#125×C283—22no—
15#125×C283C2211yescharacteristic
16#125×C283C2212yes—
17C2×Dic566—21no—
18C2×C283⋊C8—22no—
19C2×C283⋊C8—21no—
20C4⋊Dic283—22no—
21C4⋊C4×C283—22no—
22C4⋊C4×C283—22no—
23C4⋊C4×C283—22no—
24C4⋊C4×C283—22no—
25C4⋊C4×C283—22no—
26C4⋊C4×C283—22no—
27C4⋊C4×C283D412yes—
28C4⋊C4×C283D412yes—
29C4⋊C4×C283D412yes—
30C42×C283—22no—
31C42×C283C2311yescharacteristic
32Dic566—42no—
33C2×Dic283—41no—
34C283⋊C8—24no—
35C283⋊C8—41no—
36C2×C4×C283—22no—
37C2×C4×C283—22no—
38C2×C4×C283—22no—
39C2×C4×C283C2×D412yes—
40C2×C4×C283C2×D411yescharacteristic
41C22×C283#12011yescharacteristic
42C4×C283—21no—
43C4×C283—22no—
44C4×C283—42no—
45C4×C283—42no—
46C4×C283—42no—
47Dic283—81no—
48C2×C283#45411yescharacteristic
49C2×C283#45612yes—
50C283#166311yescharacteristic, complemented, Sylow
51#1663—2831nomaximal, Sylow
52#564D28311yescharacteristic
53#501—2832no—
54#491—2831no—
55#330—2832no—
56#330—2831no—
57C4⋊Q8—2831no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D28311yescharacteristic
62#125C2×D28312yes—
63#107—5662no—
64#106—5662no—
65#103—5662no—
66#97—2831no—
67#97—2832no—
68C2×Q8—5661no—
69C2×C8—5662no—
70C2×C8—5661no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—5662no—
78C4⋊C4C22⋊D28312yes—
79C4⋊C4C22⋊D28312yes—
80C4⋊C4C22⋊D28312yes—
81C42—22no—
82C42C22×D28311yescharacteristic
83Q8—11322no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—11321no—
88C2×C4C2×C22⋊D28312yes—
89C2×C4C2×C22⋊D28311yescharacteristic
90C8—5664no—
91C8—11321no—
92C22#2258357911yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—22641no—
99C2#3182663811yescharacteristic
100C2#3182664812yes—
subgroupG/H
centerC22#22583579
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#564×C283C2
socle, prime radicalC22×C283#120
hypercenter#564D283
hypocenterC283#1663
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C283#1663semidirect

Maximal subgroups

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

subgroupindex
#318268752
#318268352
#318262072
#564×C2832
#1663283