Finite Group Databasebeta

← #17993569

Subgroups — #17993569

Order 4736.

238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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#14558164C211yesmaximal, characteristic
2#14557689C212yesmaximal
3#14557269C212yesmaximal
4#14557259C211yesmaximal, characteristic
5C37×#395C211yesmaximal, characteristic
6C2×#10596942—22no—
7#11924535—22no—
8#11924527—22no—
9#11924515—21no—
10#11924515C2212yes—
11#11924495—21no—
12#11924460—22no—
13C22⋊#64436C2212yes—
14C22×Q8×C37C2211yescharacteristic
15C2×C4⋊C4×C37—21no—
16C2×C4⋊C4×C37C2211yescharacteristic
17#95×C37—21no—
18#95×C37C2211yescharacteristic
19C2×Q8×C37—22no—
20C2×Q8×C37—42no—
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37D411yescharacteristic
24C22×C4×C37D411yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C2×Dic74—21no—
27C2×Dic74D412yes—
28C4⋊C4×C37—22no—
29C4⋊C4×C37—42no—
30C22⋊Dic37—22no—
31#10596942—44no—
32C4⋊Dic37—21no—
33C4⋊Dic37—21no—
34C4⋊Dic37—21no—
35C4⋊Dic37D412yes—
36#10596936—22no—
37#10596936—22no—
38C4×Dic37—22no—
39C2×#64436—22no—
40C23×C37C2×D411yescharacteristic
41Q8×C37—24no—
42Q8×C37—42no—
43C2×C4×C37—21no—
44C2×C4×C37—21no—
45C2×C4×C37—22no—
46C2×C4×C37—22no—
47C2×C4×C37—21no—
48C2×C4×C37—41no—
49C2×C4×C37—41no—
50C2×C4×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—41no—
54C2×C4×C37Q1612yescomplemented
55C2×C4×C37C2×D412yes—
56C2×Dic37—22no—
57C2×Dic37—22no—
58Dic74—42no—
59Dic74—81no—
60#64436—42no—
61C22×C37—21no—
62C22×C37—21no—
63C22×C37#12011yescharacteristic
64C22×C37C2×Q1611yescharacteristic
65C22×C37#13711yescharacteristic
66C4×C37—22no—
67C4×C37—22no—
68C4×C37—42no—
69C4×C37—41no—
70C4×C37—42no—
71Dic37—42no—
72Dic37—42no—
73#1605—371nomaximal, Sylow
74C2×C37—21no—
75C2×C37—21no—
76C2×C37#45111yescharacteristic
77C2×C37#45611yescharacteristic
78C2×C37B(4,𝔽2)11yescharacteristic
79#544—371no—
80#451—372no—
81#395D3711yescharacteristic
82#328—372no—
83#324—371no—
84C37#160511yescharacteristic, complemented, Sylow
85C22×Q8C2×D3711yescharacteristic
86C2×Q16—742no—
87C4⋊Q8—742no—
88#125—742no—
89C22⋊Q8—372no—
90C22⋊Q8—741no—
91#117—741no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4C2×D3711yescharacteristic
94#103—742no—
95C22⋊C8—372no—
96#95—21no—
97#95C2×D3711yescharacteristic
98C2×Q8—22no—
99C2×Q8—42no—
100C2×Q8—372no—
101C2×Q8—741no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4C22⋊D3711yescharacteristic
105C22×C4C22⋊D3711yescharacteristic
106C22×C4C22×D3711yescharacteristic
107Q16—1484no—
108C2×C8—742no—
109C4⋊C4—22no—
110C4⋊C4—42no—
111C4⋊C4—372no—
112C4⋊C4—742no—
113C4⋊C4—741no—
114C4⋊C4—741no—
115C4⋊C4—741no—
116C4⋊C4—742no—
117C22⋊C4—742no—
118C42—742no—
119C23C2×C22⋊D3711yescharacteristic
120Q8—24no—
121Q8—42no—
122Q8—2961no—
123Q8—1482no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—742no—
136C2×C4—742no—
137C2×C4#1059694212yescomplemented
138C2×C4D4×D3712yes—
139C8—1482no—
140C22—21no—
141C22—21no—
142C22#1192450411yescharacteristic
143C22C2×#1059694211yescharacteristic
144C22#1192456611yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—42no—
149C4—41no—
150C4—1482no—
151C4—1482no—
152C2—21no—
153C2—21no—
154C2#1455768811yescharacteristic
155C2#1455771511yescharacteristic
156C2#1455771911yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#395C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#395D37
hypocenterC37#1605
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×C4×C37Q16semidirect
84. C37#1605semidirect
137. C2×C4#10596942semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145576892
#145572692
#145572592
C37×#3952
#160537