Finite Group Databasebeta

← #49120564

Subgroups — #49120564

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#31826831C211yesmaximal, characteristic
3#31826830C212yesmaximal
4#31826206C212yesmaximal, complemented
5#330×C283C211yesmaximal, characteristic, complemented
6#22583607C2211yescharacteristic
7#22583602C2212yes—
8#22583601—22no—
9#22583600—22no—
10#22583600—22no—
11#22583532—22no—
12#22583532—22no—
13#22583530—22no—
14#22583521C2211yescharacteristic
15#125×C283C2211yescharacteristic
16#97×C283C2212yes—
17C2×D1132—21no—
18C2×D1132—22no—
19C2×C283⋊C8—21no—
20C4⋊Dic283—22no—
21C4⋊Dic283D412yes—
22C4⋊Dic283D412yes—
23Dic283⋊C4—22no—
24Dic283⋊C4—22no—
25Dic283⋊C4—22no—
26Dic283⋊C4—22no—
27C4×Dic283—22no—
28C2×C8×C283—22no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283D412yes—
31C42×C283C2311yescharacteristic
32C22×D283—41no—
33D1132—44no—
34D1132—42no—
35C2×Dic283—22no—
36C2×Dic283—22no—
37C283⋊C8—41no—
38C2×C4×C283—22no—
39C2×C4×C283C2×D412yes—
40C2×C4×C283C2×D411yescharacteristic
41C8×C283—42no—
42C22×C283#12011yescharacteristic
43C2×D283—82no—
44C2×D283—81no—
45C4×C283—22no—
46C4×C283—21no—
47C4×C283—42no—
48Dic283—42no—
49Dic283—42no—
50C2×C283#45412yes—
51C2×C283#45411yescharacteristic
52D283—161no—
53C283#165811yescharacteristic, complemented, Sylow
54#1658—2831nomaximal, Sylow
55#564—2831no—
56#490—2831no—
57#490—2832no—
58#330—2832no—
59#330D28311yescharacteristic, complemented
60#127—2831no—
61#125—2832no—
62#125—5662no—
63#125—5662no—
64#125—5662no—
65#125C2×D28311yescharacteristic
66#102—5662no—
67#102—5662no—
68#102—5662no—
69#97—2831no—
70#97C2×D28312yes—
71C2×D4—5662no—
72C2×D4—5661no—
73C2×C8—22no—
74C2×C8—5661no—
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⋊C4D113212yes—
84C42—5662no—
85C42C22×D28311yescharacteristic
86C23—11321no—
87D4—11324no—
88D4—11322no—
89C2×C4—22no—
90C2×C4—5662no—
91C2×C4—5662no—
92C2×C4D4×D28312yes—
93C2×C4C2×D113211yescharacteristic
94C8—42no—
95C8—11321no—
96C22—22642no—
97C22—22641no—
98C22#2258358011yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—11322no—
103C4—11322no—
104C2—45281no—
105C2#3182663912yes—
106C2#3182664011yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#330×C283C2
socleC22×C283#120
prime radical#22583607C22
hypercenter#330D283
hypocenterC283#1658
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C283⋊#564C2semidirect
4. #31826206C2semidirect
5. #330×C283C2semidirect
53. C283#1658semidirect
59. #330D283semidirect

Maximal subgroups

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

subgroupindex
C283⋊#5642
#318268312
#318268302
#318262062
#330×C2832
#1658283