Finite Group Databasebeta

← #49120587

Subgroups — #49120587

Order 36224.

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

normal subgroups only

This group has 172 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
2#31826871C212yesmaximal
3#31826207C211yesmaximal, characteristic
4#31826206C212yesmaximal
5#491×C283C211yesmaximal, characteristic
6#22583602C2212yes—
7#22583601—22no—
8#22583600—22no—
9#22583600—22no—
10#22583543—22no—
11#22583541—22no—
12#22583521C2212yes—
13C4⋊Q8×C283C2211yescharacteristic
14#125×C283C2211yescharacteristic
15#103×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×Q8×C283—21no—
27C2×C8×C283—21no—
28C4⋊C4×C283—22no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283D412yes—
31C42×C283C2311yescharacteristic
32C2×Dic283—22no—
33C2×Dic283—22no—
34C283⋊C8—24no—
35Q8×C283—42no—
36C2×C4×C283—22no—
37C2×C4×C283—41no—
38C2×C4×C283C2×D412yes—
39C2×C4×C283C2×D411yescharacteristic
40C8×C283—41no—
41C22×C283#12011yescharacteristic
42C4×C283—21no—
43C4×C283—22no—
44C4×C283—42no—
45C4×C283—81no—
46Dic283—42no—
47Dic283—42no—
48C2×C283#45411yescharacteristic
49C2×C283#45612yes—
50C283#166311yescharacteristic, complemented, Sylow
51#1663—2831nomaximal, Sylow
52#564—2831no—
53#501—2832no—
54#491D28311yescharacteristic
55#330—2831no—
56#330—2832no—
57C4⋊Q8C2×D28311yescharacteristic
58#125—2832no—
59#125—5662no—
60#125—5662no—
61#125—5662no—
62#125C2×D28311yescharacteristic
63#107—5662no—
64#106—5662no—
65#103—22no—
66#97—2832no—
67#97C2×D28311yescharacteristic
68C2×Q8—21no—
69C2×C8—21no—
70C2×C8—5662no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—2832no—
74C4⋊C4—2832no—
75C4⋊C4—5662no—
76C4⋊C4—5662no—
77C4⋊C4—5662no—
78C4⋊C4—5662no—
79C4⋊C4—5662no—
80C4⋊C4C22⋊D28312yes—
81C42—5662no—
82C42C22×D28311yescharacteristic
83Q8—42no—
84C2×C4—22no—
85C2×C4—41no—
86C2×C4—5662no—
87C2×C4—5662no—
88C2×C4D4×D28312yes—
89C2×C4C2×C22⋊D28311yescharacteristic
90C8—41no—
91C8—5664no—
92C22#2258357811yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—81no—
97C4—11322no—
98C4—11322no—
99C2#3182663711yescharacteristic
100C2#3182664612yes—
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#491×C283C2
socle, prime radicalC22×C283#120
hypercenter#491D283
hypocenterC283#1663
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #491

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
C283⋊#5642
#318268712
#318262072
#318262062
#491×C2832
#1663283