Finite Group Databasebeta

← #18010898

Subgroups — #18010898

Order 4736.

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

normal subgroups only

This group has 230 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
2#14558443C214yesmaximal, complemented
3#14558107C211yesmaximal, characteristic
4D37⋊M16—22no—
5#11924597C2214yes—
6#11924596—22no—
7C2×#10596962C2211yescharacteristic
8#11924534C2212yes—
9#11924525C412yes—
10#11924519—22no—
11#11924512—22no—
12#11924495C411yescharacteristic
13C22×Q8×C37C411yescharacteristic
14C2×Q8×C37—21no—
15C2×Q8×C37—42no—
16C2×Q8×C37C2×C412yes—
17C22×C4×C37—21no—
18C22×C4×C37C2×C411yescharacteristic
19C2×C22⋊D37D412yes—
20#10596962—42no—
21C2×D148C2×C411yescharacteristic
22C2×C4×D37D412yes—
23C2×Dic74C2311yescharacteristic
24#10596957—24no—
25#10596953—42no—
26D37⋊C8—42no—
27C22⋊Dic37—21no—
28#10596938—24no—
29C4⋊Dic37—21no—
30#10596936—24no—
31C4×Dic37C2×C412yes—
32C23×C37C22⋊C411yescharacteristic
33C22×D37C22⋊C412yes—
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
41C22⋊D37—42no—
42C2×Dic37—22no—
43C2×Dic37C2×D412yes—
44D148—41no—
45C4×D37—22no—
46C4×D37—22no—
47Dic74—41no—
48#64438—44no—
49C22×C37—21no—
50C22×C37—41no—
51C22×C37C2×C22⋊C411yescharacteristic
52C2×D37—22no—
53C2×D37—42no—
54C4×C37—21no—
55C4×C37—42no—
56C4×C37#9912yes—
57Dic37—22no—
58Dic37—42no—
59#2135—371nomaximal, Sylow
60C2×C37—21no—
61C2×C37—41no—
62C2×C37C2×#9911yescharacteristic
63D37—42no—
64#536—371no—
65#413—372no—
66#356—374no—
67C37#213511yescharacteristic, complemented, Sylow
68C2×#41—371no—
69C22×Q8#386611yescharacteristic
70C2×M16—742no—
71C4⋊Q8—372no—
72#124—372no—
73#123—742no—
74C22⋊Q8—742no—
75#117—371no—
76#101—374no—
77#100—742no—
78#41—1482no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—371no—
82C2×Q8C2×#386612yes—
83C2×D4—372no—
84C2×D4—371no—
85C22×C4—21no—
86C22×C4—372no—
87C22×C4C2×#386611yescharacteristic
88M16—744no—
89M16—1482no—
90C2×C8—1482no—
91C4⋊C4—744no—
92C4⋊C4—741no—
93C22⋊C4—744no—
94C22⋊C4—741no—
95C42—372no—
96C23—372no—
97C23C22⋊#386611yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—1481no—
101D4—1481no—
102D4—1482no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—372no—
107C2×C4—742no—
108C2×C4—742no—
109C2×C4—742no—
110C2×C4C22⋊#386611yescharacteristic
111C2×C4C22×#386611yescharacteristic
112C8—1484no—
113C22—21no—
114C22—41no—
115C22—742no—
116C22—1482no—
117C22C2×C22⋊#386611yescharacteristic
118C4—21no—
119C4—42no—
120C4—742no—
121C4—1482no—
122C4#1192459412yes—
123C2—21no—
124C2—41no—
125C2—1482no—
126C2C2×#1192459411yescharacteristic
subgroupG/H
centerC2C2×#11924594
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×Q8×C37C4
socleC2×C37C2×#99
prime radicalC2×#10596962C22
cosocleC2×Dic74C23
hypercenterC22×Q8#3866
hypocenterC37#2135
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #14558443C2semidirect
67. C37#2135semidirect

Maximal subgroups

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

subgroupindex
#145585192
#145584432
#145581072
#213537