Finite Group Databasebeta

← #49122953

Subgroups — #49122953

Order 36224.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#31826449C212yesmaximal, complemented
2#31826262C214yesmaximal, complemented
3#535×C283C211yesmaximal, characteristic
4C2×#17985376—22no—
5#22583529C2214yescomplemented
6#22583527—22no—
7C2×#41×C283C2211yescharacteristic
8C22×D4×C283C411yescharacteristic
9#127×C283C412yes—
10#124×C283C2212yes—
11#121×C283—22no—
12#120×C283—22no—
13#117×C283C411yescharacteristic
14#17985376—24no—
15#17985376—42no—
16C2×C283⋊C8—42no—
17C24×C283—21no—
18#41×C283—42no—
19C2×Q8×C283C2311yescharacteristic
20C2×D4×C283—24no—
21C2×D4×C283—21no—
22C2×D4×C283—42no—
23C2×D4×C283C2×C412yes—
24C2×D4×C283C2×C411yescharacteristic
25C2×D4×C283D412yes—
26C22×C4×C283C2×C411yescharacteristic
27C22×C4×C283D412yes—
28C4⋊C4×C283—21no—
29C22⋊C4×C283—21no—
30C22⋊C4×C283—24no—
31C42×C283C2×C412yes—
32C283⋊C8—44no—
33C23×C283—22no—
34C23×C283—42no—
35C23×C283—82no—
36C23×C283C22⋊C411yescharacteristic
37C23×C283C22⋊C412yes—
38Q8×C283—41no—
39D4×C283—41no—
40D4×C283—42no—
41D4×C283—42no—
42D4×C283—42no—
43D4×C283—84no—
44C2×C4×C283—22no—
45C2×C4×C283—22no—
46C2×C4×C283—22no—
47C2×C4×C283—22no—
48C2×C4×C283C22⋊C411yescharacteristic
49C2×C4×C283C22×C411yescharacteristic
50C2×C4×C283C2×D412yes—
51C22×C283—21no—
52C22×C283—22no—
53C22×C283—42no—
54C22×C283—41no—
55C22×C283—44no—
56C22×C283—42no—
57C22×C283—84no—
58C22×C283C2×C22⋊C411yescharacteristic
59C4×C283—21no—
60C4×C283—22no—
61C4×C283—42no—
62C4×C283#9912yes—
63C2×C283—21no—
64C2×C283—42no—
65C2×C283—41no—
66C2×C283—82no—
67C2×C283C2×#9911yescharacteristic
68C283#213411yescharacteristic, complemented, Sylow
69#2134—2831nomaximal, Sylow
70#535D28311yescharacteristic
71#413—2832no—
72#355—2834no—
73C2×#41C2×D28311yescharacteristic
74C22×D4Dic28311yescharacteristic
75C2×M16—5662no—
76#127Dic28312yes—
77#124C2×D28312yes—
78#121—22no—
79#120—22no—
80#117Dic28311yescharacteristic
81#101—2834no—
82#100—5662no—
83C24—21no—
84#41—42no—
85C2×Q8C22×D28311yescharacteristic
86C2×D4—24no—
87C2×D4—21no—
88C2×D4—42no—
89C2×D4C2×Dic28312yes—
90C2×D4C2×Dic28311yescharacteristic
91C2×D4C22⋊D28312yes—
92C22×C4C2×Dic28311yescharacteristic
93C22×C4C22⋊D28312yes—
94M16—5664no—
95M16—11322no—
96C2×C8—11322no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—24no—
100C42C2×Dic28312yes—
101C23—22no—
102C23—42no—
103C23—82no—
104C23C22⋊Dic28311yescharacteristic
105C23C22⋊Dic28312yes—
106Q8—41no—
107D4—41no—
108D4—42no—
109D4—42no—
110D4—42no—
111D4—84no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—22no—
116C2×C4C22⋊Dic28311yescharacteristic
117C2×C4C22×Dic28311yescharacteristic
118C2×C4C2×C22⋊D28312yes—
119C8—11324no—
120C22—21no—
121C22—22no—
122C22—42no—
123C22—41no—
124C22—44no—
125C22—42no—
126C22—84no—
127C22C2×C22⋊Dic28311yescharacteristic
128C4—22no—
129C4—21no—
130C4—42no—
131C4#2258352512yes—
132C2—21no—
133C2—41no—
134C2—42no—
135C2—82no—
136C2C2×#2258352511yescharacteristic
subgroupG/H
centerC2C2×#22583525
commutatorC2×C4×C283C22×C4
FrattiniC2×Q8C22×D283
Fitting, prime radical#535×C283C2
socleC2×C283C2×#99
cosocleC2×Q8×C283C23
hypercenter#535D283
hypocenterC283#2134
LCSG ▷ C2×C4×C283 ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #31826449C2semidirect
2. #31826262C2semidirect
5. #22583529C22semidirect
68. C283#2134semidirect

Maximal subgroups

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

subgroupindex
#318264492
#318262622
#535×C2832
#2134283