Finite Group Databasebeta

← #17993570

Subgroups — #17993570

Order 4736.

238 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557688C212yesmaximal
2#14557453C211yesmaximal, characteristic
3#14557270C212yesmaximal
4#14557259C211yesmaximal, characteristic
5C37×#544C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7C2×#10596942—22no—
8C2×#10596936—21no—
9#11924459—22no—
10C22⋊#64436C2212yes—
11#11924443—21no—
12#11924443C2211yescharacteristic
13C4⋊Q8×C37—22no—
14#125×C37—22no—
15C22⋊Q8×C37—21no—
16C22⋊Q8×C37C2212yes—
17#117×C37—21no—
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×Q8×C37—21no—
20C2×Q8×C37D412yes—
21C22×C4×C37D411yescharacteristic
22C22×C4×C37D411yescharacteristic
23C22×C4×C37C2311yescharacteristic
24C22×Dic37—21no—
25C22×Dic37—21no—
26C2×Dic74—22no—
27C2×Dic74—42no—
28C4⋊C4×C37—21no—
29C4⋊C4×C37—21no—
30C4⋊C4×C37—21no—
31C4⋊C4×C37—22no—
32C4⋊C4×C37—22no—
33C4⋊C4×C37—22no—
34C4⋊C4×C37D412yes—
35C22⋊C4×C37—22no—
36C42×C37—22no—
37#10596942—44no—
38#10596936—42no—
39C2×#64436—22no—
40C23×C37C2×D411yescharacteristic
41Q8×C37—42no—
42Q8×C37—81no—
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×C37Q1612yescomplemented
51C2×C4×C37C2×D412yes—
52C2×Dic37—22no—
53C2×Dic37—22no—
54C2×Dic37—41no—
55C2×Dic37—41no—
56C2×Dic37—41no—
57C2×Dic37—41no—
58Dic74—24no—
59Dic74—42no—
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#544D3711yescharacteristic
80#451—372no—
81#395—371no—
82#328—372no—
83#324—371no—
84C37#160511yescharacteristic, complemented, Sylow
85C22×Q8—371no—
86C2×Q16—742no—
87C4⋊Q8—22no—
88#125—22no—
89C22⋊Q8—21no—
90C22⋊Q8C2×D3712yes—
91#117—21no—
92C2×C4⋊C4—741no—
93C2×C4⋊C4C2×D3711yescharacteristic
94#103—742no—
95C22⋊C8—372no—
96#95—371no—
97#95—741no—
98C2×Q8—21no—
99C2×Q8—742no—
100C2×Q8—1482no—
101C2×Q8C22⋊D3712yes—
102C22×C4—741no—
103C22×C4—741no—
104C22×C4C22⋊D3711yescharacteristic
105C22×C4C22⋊D3711yescharacteristic
106C22×C4C22×D3711yescharacteristic
107Q16—1484no—
108C2×C8—742no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—1482no—
116C4⋊C4C22⋊D3712yes—
117C22⋊C4—22no—
118C42—22no—
119C23C2×C22⋊D3711yescharacteristic
120Q8—42no—
121Q8—81no—
122Q8—744no—
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—742no—
132C2×C4—742no—
133C2×C4—1481no—
134C2×C4—1481no—
135C2×C4—1481no—
136C2×C4—1481no—
137C2×C4#1059694212yescomplemented
138C2×C4C2×C22⋊D3712yes—
139C8—1482no—
140C22—21no—
141C22—21no—
142C22#1192450511yescharacteristic
143C22C2×#1059694211yescharacteristic
144C22#1192456711yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—1482no—
151C4—1482no—
152C2—21no—
153C2—21no—
154C2#1455768911yescharacteristic
155C2#1455771611yescharacteristic
156C2#1455772011yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#544C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#544D37
hypocenterC37#1605
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
50. 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
#145576882
#145574532
#145572702
#145572592
C37×#5442
#160537