Finite Group Databasebeta

← #17992923

Subgroups — #17992923

Order 4736.

440 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 93 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#14557497C212yesmaximal, complemented
2#14557257C214yesmaximal, complemented
3C22×C22⋊C4×C37C211yesmaximal, characteristic
4C2×#10596934—22no—
5C22⋊#64436—22no—
6C22⋊#64436C2214yescomplemented
7C25×C37C411yescharacteristic
8C23×C4×C37C411yescharacteristic
9C23×C4×C37C2211yescharacteristic
10C2×C22⋊C4×C37—22no—
11C2×C22⋊C4×C37—22no—
12C2×C22⋊C4×C37C412yes—
13C2×C22⋊C4×C37C2212yes—
14C24×C37—21no—
15C24×C37—21no—
16C24×C37—24no—
17C24×C37—42no—
18C24×C37—42no—
19C24×C37C2×C411yescharacteristic
20C24×C37C2×C412yes—
21C22×C4×C37—21no—
22C22×C4×C37—21no—
23C22×C4×C37—42no—
24C22×C4×C37—42no—
25C22×C4×C37C2×C412yes—
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37D412yes—
28C22×C4×C37D412yes—
29C22×C4×C37C2311yescharacteristic
30C22⋊C4×C37—24no—
31C22⋊C4×C37—24no—
32#10596934—44no—
33C2×#64436—24no—
34C23×C37—22no—
35C23×C37—22no—
36C23×C37—22no—
37C23×C37—24no—
38C23×C37—24no—
39C23×C37—22no—
40C23×C37—22no—
41C23×C37—42no—
42C23×C37—42no—
43C23×C37—416no—
44C23×C37—42no—
45C23×C37—42no—
46C23×C37—42no—
47C23×C37—42no—
48C23×C37C22⋊C411yescharacteristic
49C23×C37C22⋊C411yescharacteristic
50C23×C37M1614yescomplemented
51C23×C37C22×C411yescharacteristic
52C2×C4×C37—24no—
53C2×C4×C37—22no—
54C2×C4×C37—41no—
55C2×C4×C37—42no—
56C2×C4×C37—41no—
57C2×C4×C37—42no—
58C2×C4×C37—42no—
59C2×C4×C37—42no—
60C2×C4×C37C22⋊C412yes—
61C2×C4×C37C2×D412yes—
62#64436—44no—
63C22×C37—28no—
64C22×C37—21no—
65C22×C37—21no—
66C22×C37—21no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37—24no—
71C22×C37—44no—
72C22×C37—48no—
73C22×C37—48no—
74C22×C37—44no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37#9912yes—
78C22×C37#10012yes—
79C22×C37C2×C22⋊C411yescharacteristic
80C22×C37C2×M1612yes—
81C4×C37—22no—
82C4×C37—22no—
83C4×C37—42no—
84#1462—371nomaximal, Sylow
85C2×C37—22no—
86C2×C37—22no—
87C2×C37—22no—
88C2×C37—44no—
89C2×C37#40711yescharacteristic
90C2×C37C2×#9911yescharacteristic
91C2×C37C2×#10011yescharacteristic
92C22×C22⋊C4D3711yescharacteristic
93#407—372no—
94#323—374no—
95C37#146211yescharacteristic, complemented, Sylow
96C25Dic3711yescharacteristic
97C23×C4Dic3711yescharacteristic
98C23×C4C2×D3711yescharacteristic
99C2×M16—742no—
100C2×C22⋊C4—22no—
101C2×C22⋊C4—22no—
102C2×C22⋊C4Dic3712yes—
103C2×C22⋊C4C2×D3712yes—
104C22⋊C8—374no—
105C22⋊C8—742no—
106C24—24no—
107C24—21no—
108C24—21no—
109C24—42no—
110C24—42no—
111C24C2×Dic3711yescharacteristic
112C24C2×Dic3712yes—
113C22×C4—21no—
114C22×C4—21no—
115C22×C4—42no—
116C22×C4—42no—
117C22×C4C2×Dic3712yes—
118C22×C4C2×Dic3711yescharacteristic
119C22×C4C22⋊D3712yes—
120C22×C4C22⋊D3712yes—
121C22×C4C22×D3711yescharacteristic
122M16—1484no—
123C2×C8—744no—
124C22⋊C4—24no—
125C22⋊C4—24no—
126C23—22no—
127C23—22no—
128C23—22no—
129C23—24no—
130C23—24no—
131C23—22no—
132C23—22no—
133C23—42no—
134C23—42no—
135C23—416no—
136C23—42no—
137C23—42no—
138C23—42no—
139C23—42no—
140C23#1059693414yescomplemented
141C23C22⋊Dic3711yescharacteristic
142C23C22⋊Dic3711yescharacteristic
143C23C22×Dic3711yescharacteristic
144C2×C4—24no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4C22⋊Dic3712yes—
153C2×C4C2×C22⋊D3712yes—
154C8—1484no—
155C22—28no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—24no—
163C22—44no—
164C22—44no—
165C22—48no—
166C22—48no—
167C22—42no—
168C22—42no—
169C22#1192445112yes—
170C22#1192445312yes—
171C22C2×C22⋊Dic3711yescharacteristic
172C22C2×#1059693412yes—
173C4—22no—
174C4—22no—
175C4—42no—
176C2—22no—
177C2—22no—
178C2—22no—
179C2—44no—
180C2#1455749711yescharacteristic
181C2C2×#1192445111yescharacteristic
182C2C2×#1192445311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC22×C22⋊C4×C37C2
socleC22×C37C2×C22⋊C4
prime radicalC25×C37C4
cosocleC22×C4×C37C23
hypercenterC22×C22⋊C4D37
hypocenterC37#1462
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14557497C2semidirect
2. #14557257C2semidirect
6. C22⋊#64436C22semidirect
50. C23×C37M16semidirect
95. C37#1462semidirect
140. C23#10596934semidirect

Maximal subgroups

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

subgroupindex
#145574972
#145572572
C22×C22⋊C4×C372
#146237