Finite Group Databasebeta

← #17993553

Subgroups — #17993553

Order 4736.

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

normal subgroups only

This group has 256 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, complemented
2#14557445C211yesmaximal, characteristic
3#14557270C212yesmaximal, complemented
4#14557257C211yesmaximal, characteristic
5C37×#543C211yesmaximal, characteristic
6C22×Dic74C2211yescharacteristic
7C2×#10596942—22no—
8C2×C22⋊Dic37—21no—
9#11924459—22no—
10C22⋊#64436C2212yes—
11#11924443—21no—
12#11924443C2211yescharacteristic
13C22⋊Q8×C37—22no—
14C22⋊Q8×C37—21no—
15C22⋊Q8×C37—22no—
16C22⋊Q8×C37C2212yes—
17C2×C22⋊C4×C37—21no—
18C2×C22⋊C4×C37C2211yescharacteristic
19C24×C37D411yescharacteristic
20C2×Q8×C37—21no—
21C2×Q8×C37D412yes—
22C22×C4×C37—21no—
23C22×C4×C37—21no—
24C22×C4×C37D411yescharacteristic
25C22×C4×C37C2311yescharacteristic
26C22×Dic37—21no—
27C22×Dic37—21no—
28C2×Dic74—22no—
29C2×Dic74—42no—
30C4⋊C4×C37—21no—
31C4⋊C4×C37—22no—
32C4⋊C4×C37—22no—
33C4⋊C4×C37D412yes—
34C22⋊C4×C37—22no—
35C22⋊C4×C37—22no—
36C22⋊C4×C37—22no—
37C22⋊Dic37—42no—
38#10596942—44no—
39C2×#64436—22no—
40C23×C37—21no—
41C23×C37—21no—
42C23×C37—41no—
43C23×C37—41no—
44C23×C37Q1612yescomplemented
45C23×C37C2×D411yescharacteristic
46Q8×C37—42no—
47Q8×C37—81no—
48C2×C4×C37—22no—
49C2×C4×C37—21no—
50C2×C4×C37—22no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37—81no—
54C2×C4×C37—81no—
55C2×C4×C37C2×D412yes—
56C2×Dic37—22no—
57C2×Dic37—41no—
58C2×Dic37—41no—
59C2×Dic37—41no—
60C2×Dic37—41no—
61C2×Dic37—41no—
62Dic74—24no—
63Dic74—42no—
64#64436—42no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37—22no—
68C22×C37—42no—
69C22×C37—41no—
70C22×C37—41no—
71C22×C37—81no—
72C22×C37#12011yescharacteristic
73C22×C37C2×Q1611yescharacteristic
74C22×C37#13711yescharacteristic
75C4×C37—22no—
76C4×C37—41no—
77C4×C37—42no—
78C4×C37—42no—
79Dic37—42no—
80Dic37—81no—
81#1602—371nomaximal, Sylow
82C2×C37—21no—
83C2×C37—21no—
84C2×C37—42no—
85C2×C37#45111yescharacteristic
86C2×C37#45511yescharacteristic
87C2×C37B(4,𝔽2)11yescharacteristic
88#543D3711yescharacteristic
89#451—372no—
90#393—371no—
91#328—372no—
92#323—371no—
93C37#160211yescharacteristic, complemented, Sylow
94C22×Q8—371no—
95C2×Q16—742no—
96C22⋊Q8—22no—
97C22⋊Q8—21no—
98C22⋊Q8—22no—
99C22⋊Q8C2×D3712yes—
100C2×C22⋊C4—21no—
101C2×C22⋊C4—741no—
102C2×C22⋊C4C2×D3711yescharacteristic
103#103—742no—
104C22⋊C8—372no—
105#95—371no—
106#95—741no—
107C24C22⋊D3711yescharacteristic
108C2×Q8—21no—
109C2×Q8—742no—
110C2×Q8—1482no—
111C2×Q8C22⋊D3712yes—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—741no—
115C22×C4—741no—
116C22×C4C22⋊D3711yescharacteristic
117C22×C4C22×D3711yescharacteristic
118Q16—1484no—
119C2×C8—742no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4C22⋊D3712yes—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C22⋊C4—1482no—
128C23—21no—
129C23—21no—
130C23—41no—
131C23—41no—
132C23#1059694212yescomplemented
133C23C2×C22⋊D3711yescharacteristic
134Q8—42no—
135Q8—81no—
136Q8—744no—
137Q8—1482no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—742no—
146C2×C4—1481no—
147C2×C4—1481no—
148C2×C4—1481no—
149C2×C4—1481no—
150C2×C4—1481no—
151C2×C4C2×C22⋊D3712yes—
152C8—1482no—
153C22—21no—
154C22—21no—
155C22—22no—
156C22—42no—
157C22—41no—
158C22—41no—
159C22—81no—
160C22#1192450511yescharacteristic
161C22C2×#1059694211yescharacteristic
162C22#1192456711yescharacteristic
163C4—22no—
164C4—41no—
165C4—42no—
166C4—42no—
167C4—2961no—
168C4—1482no—
169C2—21no—
170C2—21no—
171C2—42no—
172C2#1455768911yescharacteristic
173C2#1455771111yescharacteristic
174C2#1455772011yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#543C2
socleC22×C37#120
prime radicalC24×C37D4
hypercenter#543D37
hypocenterC37#1602
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #14557688C2semidirect
3. #14557270C2semidirect
44. C23×C37Q16semidirect
93. C37#1602semidirect
132. C23#10596942semidirect

Maximal subgroups

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

subgroupindex
#145576882
#145574452
#145572702
#145572572
C37×#5432
#160237