Finite Group Databasebeta

← #18010077

Subgroups — #18010077

Order 4736.

248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558553C212yesmaximal, complemented
2#14558389C214yesmaximal, complemented
3C2×#11924525C211yesmaximal, characteristic
4#11924603—22no—
5C22⋊#64438—22no—
6#11924591C2214yescomplemented
7C22×D148C411yescharacteristic
8#11924525—22no—
9#11924525C412yes—
10#11924525C2212yes—
11C2×#10596938—22no—
12C2×C4×Dic37C2211yescharacteristic
13C22×Q8×C37C411yescharacteristic
14C23×D37—21no—
15C2×Q8×C37—21no—
16C2×Q8×C37—42no—
17C2×Q8×C37C2×C412yes—
18C22×C4×C37—21no—
19C22×C4×C37C2×C411yescharacteristic
20C22×Dic37D412yes—
21C2×D148—21no—
22C2×D148—42no—
23C2×D148C2×C412yes—
24C2×#64438—24no—
25#10596938—24no—
26#10596938—24no—
27C4×Dic37C2×C411yescharacteristic
28C4×Dic37D412yes—
29C4×Dic37C2311yescharacteristic
30C23×C37C22⋊C411yescharacteristic
31C22×D37—22no—
32C22×D37—44no—
33C22×D37—42no—
34Q8×C37—42no—
35Q8×C37—42no—
36C2×C4×C37—22no—
37C2×C4×C37—22no—
38C2×C4×C37—42no—
39C2×C4×C37C22⋊C411yescharacteristic
40C2×C4×C37C22×C411yescharacteristic
41C2×Dic37—42no—
42C2×Dic37C22⋊C412yes—
43C2×Dic37C2×D412yes—
44D148—42no—
45D148—42no—
46#64438—44no—
47C22×C37—22no—
48C22×C37#10012yes—
49C22×C37C2×C22⋊C411yescharacteristic
50C2×D37—42no—
51C2×D37—44no—
52C2×D37—84no—
53C4×C37—21no—
54C4×C37—21no—
55C4×C37—42no—
56Dic37—22no—
57Dic37—22no—
58#1533—371nomaximal, Sylow
59C2×C37—22no—
60C2×C37C2×#10011yescharacteristic
61C2×C37#42112yes—
62D37—82no—
63C2×#124—371no—
64#432—372no—
65#329—374no—
66C37#153311yescharacteristic, complemented, Sylow
67C22×Q8#386611yescharacteristic
68C22×D4—371no—
69#124—372no—
70#124—372no—
71#124—742no—
72C2×C22⋊C4—742no—
73C2×C42—371no—
74C4⋊C8—742no—
75C22⋊C8—742no—
76#97—374no—
77C24—741no—
78C2×Q8—21no—
79C2×Q8—42no—
80C2×Q8C2×#386612yes—
81C2×D4—372no—
82C2×D4—741no—
83C2×D4—1482no—
84C22×C4—21no—
85C22×C4—372no—
86C22×C4C2×#386611yescharacteristic
87C2×C8—744no—
88C22⋊C4—744no—
89C22⋊C4—744no—
90C42—372no—
91C42—371no—
92C42—371no—
93C23—742no—
94C23—1484no—
95C23—1482no—
96C23C22⋊#386611yescharacteristic
97Q8—42no—
98Q8—42no—
99D4—1482no—
100D4—1482no—
101C2×C4—22no—
102C2×C4—22no—
103C2×C4—42no—
104C2×C4—372no—
105C2×C4—372no—
106C2×C4—1482no—
107C2×C4C22⋊#386611yescharacteristic
108C2×C4C22×#386611yescharacteristic
109C8—1484no—
110C22—22no—
111C22—2964no—
112C22—1482no—
113C22—1484no—
114C22#1192459612yes—
115C22C2×C22⋊#386611yescharacteristic
116C4—21no—
117C4—21no—
118C4—42no—
119C4—742no—
120C4—742no—
121C2—22no—
122C2—2962no—
123C2C2×#1192459611yescharacteristic
124C2#1455853212yes—
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC4×Dic37C23
hypercenterC22×Q8#3866
hypocenterC37#1533
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #14558553C2semidirect
2. #14558389C2semidirect
6. #11924591C22semidirect
66. C37#1533semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145583892
C2×#119245252
#153337