Finite Group Databasebeta

← #18010897

Subgroups — #18010897

Order 4736.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#14558519C212yesmaximal, complemented
2#14558442C214yesmaximal, complemented
3#14558102C211yesmaximal, characteristic
4D37⋊M16—22no—
5#11924597C2214yescomplemented
6#11924596—22no—
7C2×#10596962C2211yescharacteristic
8C22×D148C411yescharacteristic
9#11924533C412yes—
10#11924524C2212yes—
11#11924511—22no—
12#11924506—22no—
13#117×C37C411yescharacteristic
14C23×D37—21no—
15C22×C4×C37C2×C411yescharacteristic
16C2×C22⋊D37D412yes—
17#10596962—42no—
18C2×D148—21no—
19C2×D148—24no—
20C2×D148—42no—
21C2×D148C2×C412yes—
22C2×D148C2×C411yescharacteristic
23C2×C4×D37D412yes—
24C2×Dic74C2311yescharacteristic
25#10596957—24no—
26#10596953—42no—
27D37⋊C8—42no—
28C4⋊C4×C37—21no—
29C22⋊C4×C37—21no—
30C42×C37C2×C412yes—
31#10596938—24no—
32C23×C37C22⋊C411yescharacteristic
33C22×D37—22no—
34C22×D37—42no—
35C22×D37—82no—
36C22×D37C22⋊C412yes—
37C2×C4×C37—22no—
38C2×C4×C37—22no—
39C2×C4×C37C22⋊C411yescharacteristic
40C2×C4×C37C22×C411yescharacteristic
41C22⋊D37—42no—
42C2×Dic37C2×D412yes—
43D148—41no—
44D148—42no—
45D148—42no—
46D148—84no—
47C4×D37—22no—
48C4×D37—22no—
49Dic74—41no—
50#64438—44no—
51C22×C37—21no—
52C22×C37—41no—
53C22×C37C2×C22⋊C411yescharacteristic
54C2×D37—22no—
55C2×D37—42no—
56C2×D37—44no—
57C2×D37—42no—
58C2×D37—84no—
59C4×C37—21no—
60C4×C37—42no—
61C4×C37#9912yes—
62Dic37—22no—
63#2134—371nomaximal, Sylow
64C2×C37—21no—
65C2×C37—41no—
66C2×C37C2×#9911yescharacteristic
67D37—42no—
68D37—82no—
69#535—371no—
70#413—372no—
71#355—374no—
72C37#213411yescharacteristic, complemented, Sylow
73C2×#41—371no—
74C22×D4—371no—
75C2×M16—742no—
76#127—372no—
77#124—372no—
78#121—742no—
79#120—742no—
80#117#386611yescharacteristic
81#101—374no—
82#100—742no—
83C24—741no—
84#41—1482no—
85C2×Q8—371no—
86C2×D4—372no—
87C2×D4—371no—
88C2×D4—372no—
89C2×D4—744no—
90C2×D4—741no—
91C2×D4—1482no—
92C22×C4—372no—
93C22×C4C2×#386611yescharacteristic
94M16—744no—
95M16—1482no—
96C2×C8—1482no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—744no—
100C42C2×#386612yes—
101C23—372no—
102C23—2962no—
103C23—742no—
104C23—1482no—
105C23C22⋊#386611yescharacteristic
106Q8—1481no—
107D4—2964no—
108D4—1481no—
109D4—1482no—
110D4—1482no—
111D4—1482no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—372no—
115C2×C4—742no—
116C2×C4—742no—
117C2×C4C22⋊#386611yescharacteristic
118C2×C4C22×#386611yescharacteristic
119C8—1484no—
120C22—21no—
121C22—41no—
122C22—2964no—
123C22—742no—
124C22—1484no—
125C22—1482no—
126C22—1482no—
127C22C2×C22⋊#386611yescharacteristic
128C4—21no—
129C4—42no—
130C4—742no—
131C4#1192459512yes—
132C2—21no—
133C2—41no—
134C2—2962no—
135C2—1482no—
136C2C2×#1192459511yescharacteristic
subgroupG/H
centerC2C2×#11924595
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#117×C37C4
socleC2×C37C2×#99
prime radical#14558102C2
cosocleC2×Dic74C23
hypercenter#117#3866
hypocenterC37#2134
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #14558519C2semidirect
2. #14558442C2semidirect
5. #11924597C22semidirect
72. C37#2134semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145584422
#145581022
#213437