Finite Group Databasebeta

← #49120553

Subgroups — #49120553

Order 36224.

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

normal subgroups only

This group has 230 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, complemented
2#31826852C212yesmaximal, complemented
3#31826207C211yesmaximal, characteristic, complemented
4#31826204C212yesmaximal, complemented
5#490×C283C211yesmaximal, characteristic, complemented
6C2×#17985380—22no—
7C2×#17985377—22no—
8#22583598C2212yes—
9#22583595—22no—
10#22583588—22no—
11#22583585—22no—
12#22583521C2212yes—
13#127×C283C2211yescharacteristic
14#125×C283C2211yescharacteristic
15#102×C283—22no—
16#97×C283C2211yescharacteristic
17C2×Dic566D412yes—
18C2×D1132—22no—
19C2×D1132D412yes—
20C2×C4×D283—22no—
21#17985380—44no—
22#17985377—44no—
23C2×C283⋊C8—22no—
24Dic283⋊C4—22no—
25(C2×D283)⋊C4—22no—
26(C2×D283)⋊C4—22no—
27(C2×D283)⋊C4—22no—
28C2×D4×C283—22no—
29C2×D4×C283—21no—
30C2×C8×C283—21no—
31C4⋊C4×C283—22no—
32C4⋊C4×C283D412yes—
33C42×C283C2311yescharacteristic
34C22×D283—22no—
35Dic566—42no—
36D1132—42no—
37D1132—82no—
38C2×Dic283—22no—
39C4×D283—82no—
40C283⋊C8—24no—
41C23×C283—41no—
42D4×C283—42no—
43D4×C283—42no—
44D4×C283—42no—
45C2×C4×C283—22no—
46C2×C4×C283C2×D412yes—
47C2×C4×C283C2×D411yescharacteristic
48C8×C283—41no—
49C22×C283—82no—
50C22×C283—81no—
51C22×C283#12011yescharacteristic
52C2×D283—42no—
53C2×D283—42no—
54C2×D283—42no—
55C4×C283—22no—
56C4×C283—21no—
57C4×C283—42no—
58Dic283—42no—
59C2×C283—161no—
60C2×C283#45312yes—
61C2×C283#45411yescharacteristic
62D283—82no—
63C283#165611yescharacteristic, complemented, Sylow
64#1656—2831nomaximal, Sylow
65#562—2831no—
66#496—2832no—
67#490D28311yescharacteristic, complemented
68#330—2831no—
69#329—2832no—
70C2×SD16—5662no—
71C2×D8—5662no—
72#127C2×D28311yescharacteristic
73#125C2×D28311yescharacteristic
74#124—2832no—
75#123—5662no—
76C22⋊Q8—5662no—
77#121—5662no—
78#102—22no—
79#97—2832no—
80#97C2×D28311yescharacteristic
81C2×Q8—2832no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—2832no—
85C2×D4—5662no—
86C22×C4—5662no—
87SD16—11324no—
88D8—11324no—
89C2×C8—21no—
90C2×C8—5662no—
91C4⋊C4—22no—
92C4⋊C4—5662no—
93C4⋊C4C22⋊D28312yes—
94C22⋊C4—5662no—
95C22⋊C4—5662no—
96C22⋊C4—5662no—
97C42C22×D28311yescharacteristic
98C23—41no—
99C23—5662no—
100Q8—11322no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—11322no—
105D4—22642no—
106C2×C4—22no—
107C2×C4—5662no—
108C2×C4—22642no—
109C2×C4D4×D28312yes—
110C2×C4C2×C22⋊D28311yescharacteristic
111C8—41no—
112C8—5664no—
113C22—82no—
114C22—81no—
115C22—11322no—
116C22—11322no—
117C22—11322no—
118C22#2258357811yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—11322no—
123C2—161no—
124C2—22642no—
125C2#3182663112yes—
126C2#3182663711yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#490×C283C2
socleC22×C283#120
hypercenter#490D283
hypocenterC283#1656
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. #31827213C2semidirect
2. #31826852C2semidirect
3. #31826207C2semidirect
4. #31826204C2semidirect
5. #490×C283C2semidirect
63. C283#1656semidirect
67. #490D283semidirect

Maximal subgroups

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

subgroupindex
#318272132
#318268522
#318262072
#318262042
#490×C2832
#1656283