Finite Group Databasebeta

← #17995763

Subgroups — #17995763

Order 4736.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#14558159C211yesmaximal, characteristic
2#14557396C212yesmaximal
3#14557300C211yesmaximal, characteristic
4#14557299C212yesmaximal
5C37×#381C211yesmaximal, characteristic
6#11924515—22no—
7#11924513—24no—
8C2×C22⋊Dic37C2212yes—
9C2×C22⋊Dic37C2212yes—
10#11924443—24no—
11C23×C4×C37C2211yescharacteristic
12C2×C22⋊C4×C37C2211yescharacteristic
13C2×C22⋊C4×C37C2211yescharacteristic
14#95×C37—22no—
15C24×C37C2311yescharacteristic
16C22×C4×C37—21no—
17C22×C4×C37—22no—
18C22×C4×C37—21no—
19C22×C4×C37—22no—
20C22×C4×C37—21no—
21C22×C4×C37D412yes—
22C22×C4×C37Q812yescomplemented
23C22×Dic37—22no—
24C22×Dic37D414yes—
25C2×Dic74—22no—
26C22⋊C4×C37—22no—
27C22⋊C4×C37—22no—
28C22⋊Dic37—22no—
29C22⋊Dic37—22no—
30C22⋊Dic37—22no—
31C22⋊Dic37—22no—
32C4⋊Dic37—22no—
33#10596936—24no—
34C23×C37—42no—
35C23×C37C2×D412yes—
36C23×C37C2×D411yescharacteristic
37C23×C37C2×Q811yescharacteristic
38C23×C37#4111yescharacteristic
39C23×C37#4112yes—
40C2×C4×C37—22no—
41C2×C4×C37—24no—
42C2×C4×C37—22no—
43C2×C4×C37—41no—
44C2×C4×C37—42no—
45C2×C4×C37—41no—
46C2×C4×C37—42no—
47C2×C4×C37—42no—
48C2×C4×C37—41no—
49C2×Dic37—24no—
50C2×Dic37—44no—
51C2×Dic37—44no—
52C2×Dic37—42no—
53Dic74—82no—
54C22×C37—24no—
55C22×C37—22no—
56C22×C37—41no—
57C22×C37—41no—
58C22×C37—42no—
59C22×C37#12011yescharacteristic
60C22×C37C22⋊Q812yes—
61C22×C37C22⋊Q811yescharacteristic
62C22×C37#12412yes—
63C22×C37#12411yescharacteristic
64C4×C37—42no—
65C4×C37—42no—
66C4×C37—81no—
67Dic37—44no—
68Dic37—82no—
69#2030—371nomaximal, Sylow
70C2×C37—22no—
71C2×C37—21no—
72C2×C37—22no—
73C2×C37—21no—
74C2×C37#39311yescharacteristic
75C2×C37#45812yes—
76#543—371no—
77#381—372no—
78#381D3711yescharacteristic
79#342—372no—
80#342—371no—
81C37#203011yescharacteristic, complemented, Sylow
82C23×C4C2×D3711yescharacteristic
83C22⋊Q8—744no—
84C22⋊Q8—742no—
85C2×C22⋊C4—372no—
86C2×C22⋊C4—372no—
87C2×C22⋊C4C2×D3711yescharacteristic
88C2×C22⋊C4C2×D3711yescharacteristic
89#95—22no—
90#95—744no—
91C24C22×D3711yescharacteristic
92C2×Q8—742no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—374no—
99C22×C4—742no—
100C22×C4Dic7412yescomplemented
101C22×C4C22⋊D3712yes—
102C4⋊C4—744no—
103C4⋊C4—742no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—742no—
107C22⋊C4—742no—
108C22⋊C4—742no—
109C22⋊C4—742no—
110C23—42no—
111C23C2×Dic7411yescharacteristic
112C23#1059696211yescharacteristic
113C23D4×D3712yes—
114C23#1059696412yes—
115C23C2×C22⋊D3711yescharacteristic
116Q8—2962no—
117C2×C4—22no—
118C2×C4—24no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—744no—
127C2×C4—1484no—
128C2×C4—1482no—
129C2×C4—1484no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1192450411yescharacteristic
136C22#1192451312yes—
137C22#1192451511yescharacteristic
138C22#1192452212yes—
139C22#1192452311yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—2962no—
144C4—1484no—
145C2—21no—
146C2—22no—
147C2—22no—
148C2—21no—
149C2#1455744511yescharacteristic
150C2#1455772212yes—
subgroupG/H
centerC22#11924504
commutator, prime radical, cosocleC24×C37C23
FrattiniC24C22×D37
FittingC37×#381C2
socleC22×C37#120
hypercenter#381D37
hypocenterC37#2030
LCSG ▷ C24×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
22. C22×C4×C37Q8semidirect
81. C37#2030semidirect
100. C22×C4Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581592
#145573962
#145573002
#145572992
C37×#3812
#203037