Finite Group Databasebeta

← #49120585

Subgroups — #49120585

Order 36224.

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

normal subgroups only

This group has 196 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
1#31827213C211yesmaximal, characteristic
2#31826835C211yesmaximal, characteristic, complemented
3#31826825C212yesmaximal, complemented
4#31826204C212yesmaximal, complemented
5#330×C283C211yesmaximal, characteristic, complemented
6#22583610C2211yescharacteristic
7#22583598C2212yes—
8#22583595—22no—
9#22583588—22no—
10#22583585—22no—
11#22583535—22no—
12#22583533—22no—
13#22583532—22no—
14#22583521C2211yescharacteristic
15#125×C283C2211yescharacteristic
16#97×C283C2212yes—
17C2×Dic566—21no—
18C2×Dic566D412yes—
19C2×D1132—22no—
20C2×D1132D412yes—
21C2×C4×D283—22no—
22C2×C283⋊C8—21no—
23C4⋊Dic283—22no—
24Dic283⋊C4—22no—
25(C2×D283)⋊C4—22no—
26(C2×D283)⋊C4—22no—
27(C2×D283)⋊C4—22no—
28C2×C8×C283—22no—
29C4⋊C4×C283—22no—
30C4⋊C4×C283D412yes—
31C42×C283C2311yescharacteristic
32C22×D283—22no—
33Dic566—42no—
34Dic566—42no—
35D1132—42no—
36D1132—82no—
37C2×Dic283—22no—
38C2×Dic283—41no—
39C4×D283—82no—
40C283⋊C8—41no—
41C2×C4×C283—22no—
42C2×C4×C283C2×D412yes—
43C2×C4×C283C2×D411yescharacteristic
44C8×C283—42no—
45C22×C283#12011yescharacteristic
46C2×D283—42no—
47C2×D283—42no—
48C2×D283—42no—
49C4×C283—21no—
50C4×C283—22no—
51C4×C283—42no—
52Dic283—42no—
53Dic283—81no—
54C2×C283#45411yescharacteristic
55C2×C283#45512yes—
56D283—82no—
57C283#166211yescharacteristic, complemented, Sylow
58#1662—2831nomaximal, Sylow
59#562—2831no—
60#491—2831no—
61#489—2832no—
62#330D28311yescharacteristic, complemented
63#329—2832no—
64C4⋊Q8—2831no—
65#125C2×D28311yescharacteristic
66#124—2832no—
67#123—5662no—
68C22⋊Q8—5662no—
69#121—5662no—
70#103—5662no—
71#103—5662no—
72#102—5662no—
73#97—2831no—
74#97C2×D28312yes—
75C2×Q8—2832no—
76C2×Q8—5661no—
77C2×D4—2832no—
78C2×D4—5662no—
79C22×C4—5662no—
80C2×C8—22no—
81C2×C8—5661no—
82C4⋊C4—22no—
83C4⋊C4—5662no—
84C4⋊C4—5662no—
85C4⋊C4D113212yes—
86C22⋊C4—5662no—
87C22⋊C4—5662no—
88C22⋊C4—5662no—
89C42C22×D28311yescharacteristic
90C23—5662no—
91Q8—11322no—
92Q8—11322no—
93D4—11322no—
94D4—22642no—
95C2×C4—22no—
96C2×C4—5662no—
97C2×C4—11321no—
98C2×C4—22642no—
99C2×C4D4×D28312yes—
100C2×C4C2×D113211yescharacteristic
101C8—42no—
102C8—11321no—
103C22—11322no—
104C22—11322no—
105C22—11322no—
106C22#2258358011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—11322no—
111C4—22641no—
112C2—22642no—
113C2#3182664011yescharacteristic
114C2#3182664412yes—
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#330×C283C2
socleC22×C283#120
prime radical#31827213C2
hypercenter#330D283
hypocenterC283#1662
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #31826835C2semidirect
3. #31826825C2semidirect
4. #31826204C2semidirect
5. #330×C283C2semidirect
57. C283#1662semidirect
62. #330D283semidirect

Maximal subgroups

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

subgroupindex
#318272132
#318268352
#318268252
#318262042
#330×C2832
#1662283