Finite Group Databasebeta

← #18010059

Subgroups — #18010059

Order 4736.

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

normal subgroups only

This group has 212 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#14558556C211yesmaximal, characteristic
2C4×#10596953C211yesmaximal, characteristic
3#14558390C212yesmaximal, complemented
4#14558390C212yesmaximal, complemented
5#125×D37C211yesmaximal, characteristic
6C2×#10596953—21no—
7#11924603—21no—
8#11924593—21no—
9#11924591C2212yes—
10#11924591C2212yes—
11C4×#64438—21no—
12#11924528C411yescharacteristic
13#11924527C2211yescharacteristic
14#11924527C2211yescharacteristic
15#11924526—21no—
16#11924526—21no—
17C4⋊C4×D37—21no—
18C4⋊C4×D37—21no—
19C4⋊C4×D37C411yescharacteristic
20C4⋊C4×D37C411yescharacteristic
21C42×D37C2211yescharacteristic
22#125×C37C411yescharacteristic
23C2×C4×D37—21no—
24C2×C4×D37—21no—
25C2×C4×D37C2×C411yescharacteristic
26C2×C4×D37D411yescharacteristic
27C2×C4×D37D411yescharacteristic
28C2×#64438—22no—
29C2×#64438—22no—
30#10596953—24no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37C2×C411yescharacteristic
34C4⋊C4×C37C2×C411yescharacteristic
35C42×C37C2×C411yescharacteristic
36C4⋊Dic37—21no—
37C4⋊Dic37—21no—
38C4⋊Dic37C2×C411yescharacteristic
39C4⋊Dic37C2×C411yescharacteristic
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C4×Dic37C2311yescharacteristic
49C22×D37C22⋊C411yescharacteristic
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37C22⋊C411yescharacteristic
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—21no—
56C2×Dic37—21no—
57C2×Dic37C22⋊C411yescharacteristic
58C2×Dic37C2×D411yescharacteristic
59C2×Dic37C2×D411yescharacteristic
60C4×D37—22no—
61C4×D37—22no—
62C4×D37—41no—
63C4×D37—42no—
64C4×D37—42no—
65#64438—24no—
66#64438—42no—
67C22×C37C2×C22⋊C411yescharacteristic
68C2×D37—21no—
69C2×D37—21no—
70C2×D37#10412yes—
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—21no—
74C4×C37—41no—
75C4×C37—41no—
76Dic37—21no—
77Dic37—21no—
78Dic37—41no—
79Dic37—41no—
80Dic37#10112yes—
81#1528—371nomaximal, Sylow
82C2×C37C2×#10111yescharacteristic
83C2×C37C2×#10411yescharacteristic
84C2×C37#42111yescharacteristic
85D37—22no—
86C2×#125—371no—
87#432—371no—
88C4×M16—371no—
89#330—372no—
90#330—372no—
91C37#152811yescharacteristic, complemented, Sylow
92C2×M16—741no—
93#125—371no—
94#125—371no—
95#125—371no—
96#125—741no—
97#125—741no—
98#125#386611yescharacteristic
99C2×C4⋊C4—371no—
100C2×C4⋊C4—371no—
101C2×C4⋊C4—741no—
102C2×C4⋊C4—741no—
103C2×C42—371no—
104C4⋊C8—741no—
105C22⋊C8—741no—
106#97—372no—
107#97—372no—
108C4×C8—741no—
109C22×C4—371no—
110C22×C4—371no—
111C22×C4—371no—
112C22×C4—741no—
113C22×C4—741no—
114M16—744no—
115C2×C8—742no—
116C2×C8—742no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—371no—
120C4⋊C4—371no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4C2×#386611yescharacteristic
130C4⋊C4C2×#386611yescharacteristic
131C42—371no—
132C42—371no—
133C42—371no—
134C42C2×#386611yescharacteristic
135C23—371no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—371no—
139C2×C4—371no—
140C2×C4—371no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—741no—
144C2×C4—741no—
145C2×C4—1481no—
146C2×C4—1482no—
147C2×C4—1482no—
148C2×C4C22⋊#386611yescharacteristic
149C2×C4C22⋊#386611yescharacteristic
150C2×C4C22×#386611yescharacteristic
151C8—744no—
152C8—1482no—
153C22—372no—
154C22—741no—
155C22—741no—
156C22C2×C22⋊#386611yescharacteristic
157C4—21no—
158C4—21no—
159C4—21no—
160C4—41no—
161C4—41no—
162C4—372no—
163C4—741no—
164C4—741no—
165C4—1481no—
166C4—1481no—
167C2—742no—
168C2D37⋊#10111yescharacteristic
169C2D37⋊#10411yescharacteristic
170C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#125×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenter#125#3866
hypocenterC37#1528
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. #14558390C2semidirect
4. #14558390C2semidirect
91. C37#1528semidirect

Maximal subgroups

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

subgroupindex
#145585562
C4×#105969532
#145583902
#125×D372
#152837