Finite Group Databasebeta

← #49120342

Subgroups — #49120342

Order 36224.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#31827181C211yesmaximal, characteristic, complemented
2#31826657C212yesmaximal, complemented
3#31826214C211yesmaximal, characteristic, complemented
4#31826194C212yesmaximal, complemented
5#492×C283C211yesmaximal, characteristic, complemented
6C2×#17985377—22no—
7#22583599—22no—
8#22583585—22no—
9C4×D1132C2212yes—
10#22583568—22no—
11C4⋊(C283⋊C8)C2212yes—
12#22583531—22no—
13C2×SD16×C283—22no—
14C4⋊Q8×C283C2211yescharacteristic
15#127×C283C2211yescharacteristic
16C4×C8×C283C2211yescharacteristic
17C2×D1132—22no—
18C2×D1132D412yes—
19C2×C4×D283—22no—
20#17985377—44no—
21C2×C283⋊C8—22no—
22C4⋊Dic283D412yes—
23(C2×D283)⋊C4—24no—
24(C2×D283)⋊C4—22no—
25C4×Dic283—22no—
26C2×Q8×C283D412yes—
27C2×D4×C283—22no—
28C2×D4×C283—21no—
29SD16×C283—44no—
30C2×C8×C283—21no—
31C4⋊C4×C283—22no—
32C42×C283C2311yescharacteristic
33C22×D283—22no—
34D1132—22no—
35D1132—22no—
36D1132—82no—
37C2×Dic283—22no—
38C4×D283—42no—
39C4×D283—42no—
40C283⋊C8—42no—
41C23×C283—41no—
42Q8×C283—42no—
43D4×C283—42no—
44D4×C283—42no—
45D4×C283—42no—
46C2×C4×C283—22no—
47C2×C4×C283C2×D412yes—
48C2×C4×C283C2×D411yescharacteristic
49C8×C283—22no—
50C22×C283—82no—
51C22×C283—81no—
52C22×C283#12011yescharacteristic
53C2×D283—42no—
54C2×D283—42no—
55C2×D283—42no—
56C4×C283—21no—
57C4×C283—42no—
58C4×C283#13512yes—
59C4×C283AGL(1,ℤ/8)12yes—
60Dic283—42no—
61C2×C283—161no—
62C2×C283#44912yes—
63C2×C283#45311yescharacteristic
64D283—82no—
65C283#162411yescharacteristic, complemented, Sylow
66#1624—2831nomaximal, Sylow
67#555—2831no—
68#492D28311yescharacteristic, complemented
69#459—2832no—
70#333—2831no—
71D4⋊C8—2832no—
72C2×SD16—22no—
73C2×D8—5662no—
74C4⋊Q8C2×D28311yescharacteristic
75#127C2×D28311yescharacteristic
76#124—5662no—
77#121—5662no—
78C4×D4—2832no—
79#117—5662no—
80C4⋊C8—2832no—
81#102—5662no—
82C4×C8C2×D28311yescharacteristic
83C2×Q8C22⋊D28312yes—
84C2×D4—22no—
85C2×D4—21no—
86C2×D4—2832no—
87C2×D4—5662no—
88C22×C4—5662no—
89SD16—44no—
90D8—11324no—
91C2×C8—21no—
92C2×C8—5662no—
93C4⋊C4—22no—
94C4⋊C4—2832no—
95C22⋊C4—5664no—
96C22⋊C4—5662no—
97C42—5662no—
98C42C22×D28311yescharacteristic
99C23—41no—
100C23—5662no—
101Q8—42no—
102D4—42no—
103D4—42no—
104D4—42no—
105D4—5662no—
106D4—5662no—
107D4—22642no—
108C2×C4—22no—
109C2×C4—5662no—
110C2×C4—11322no—
111C2×C4—11322no—
112C2×C4D4×D28312yes—
113C2×C4C2×C22⋊D28311yescharacteristic
114C8—22no—
115C8—11322no—
116C22—82no—
117C22—81no—
118C22—11322no—
119C22—11322no—
120C22—11322no—
121C22#2258357811yescharacteristic
122C4—21no—
123C4—42no—
124C4—11322no—
125C4#2258363112yes—
126C4#2258363712yes—
127C2—161no—
128C2—22642no—
129C2#3182660912yes—
130C2#3182663211yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#492×C283C2
socleC22×C283#120
hypercenter#492D283
hypocenterC283#1624
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #31827181C2semidirect
2. #31826657C2semidirect
3. #31826214C2semidirect
4. #31826194C2semidirect
5. #492×C283C2semidirect
65. C283#1624semidirect
68. #492D283semidirect

Maximal subgroups

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

subgroupindex
#318271812
#318266572
#318262142
#318261942
#492×C2832
#1624283