Finite Group Databasebeta

← C37×#8749 #22630002

Subgroups — C37×#8749 #22630002

Order 9472.

786 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C37×#2309C211yesmaximal, characteristic
2C37×#1781C212yesmaximal
3C37×#1304C214yesmaximal, complemented
4C23×D4×C37C2211yescharacteristic
5C2×#117×C37C412yescomplemented
6C2×#99×C37—24no—
7C37×#390—24no—
8C37×#379C412yescomplemented
9C37×#379C2214yes—
10C37×#379C2212yes—
11C25×C37C2×C411yescharacteristic
12C25×C37C2311yescharacteristic
13C22×D4×C37—24no—
14C22×D4×C37—44no—
15C22×D4×C37D414yes—
16C23×C4×C37C2×C411yescharacteristic
17#117×C37—44no—
18C2×C4⋊C4×C37—22no—
19C2×C22⋊C4×C37—24no—
20C2×C22⋊C4×C37—24no—
21C2×C22⋊C4×C37—24no—
22C2×C22⋊C4×C37—28no—
23C2×C22⋊C4×C37C2×C414yes—
24C2×C42×C37—22no—
25#99×C37—48no—
26C24×C37—22no—
27C24×C37—42no—
28C24×C37—42no—
29C24×C37—82no—
30C24×C37—82no—
31C24×C37C22⋊C412yes—
32C24×C37C22×C411yescharacteristic
33C24×C37C2×D412yes—
34C24×C37#4114yes—
35C2×D4×C37—28no—
36C2×D4×C37—28no—
37C2×D4×C37—44no—
38C2×D4×C37—416no—
39C22×C4×C37—22no—
40C22×C4×C37—24no—
41C22×C4×C37—24no—
42C22×C4×C37—44no—
43C22×C4×C37C22⋊C412yes—
44C4⋊C4×C37—44no—
45C22⋊C4×C37—44no—
46C22⋊C4×C37—48no—
47C22⋊C4×C37—84no—
48C22⋊C4×C37—84no—
49C22⋊C4×C37—88no—
50C42×C37—44no—
51C23×C37—22no—
52C23×C37—24no—
53C23×C37—22no—
54C23×C37—24no—
55C23×C37—42no—
56C23×C37—44no—
57C23×C37—48no—
58C23×C37—44no—
59C23×C37—44no—
60C23×C37—44no—
61C23×C37—84no—
62C23×C37—88no—
63C23×C37—88no—
64C23×C37C2×C22⋊C411yescharacteristic
65C23×C37#11712yes—
66C23×C37#12314yes—
67D4×C37—416no—
68C2×C4×C37—28no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—48no—
72C2×C4×C37—44no—
73C2×C4×C37—84no—
74C2×C4×C37—88no—
75C2×C4×C37#9914yes—
76#8749C3711yesmaximal, characteristic, direct product factor, Sylow
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—24no—
80C22×C37—28no—
81C22×C37—24no—
82C22×C37—44no—
83C22×C37—42no—
84C22×C37—44no—
85C22×C37—84no—
86C22×C37—84no—
87C22×C37—88no—
88C22×C37—88no—
89C22×C37#38111yescharacteristic
90C22×C37C2×#9912yes—
91C4×C37—24no—
92C4×C37—84no—
93C4×C37—164no—
94#2309C2×C3711yescharacteristic
95#1781C2×C3712yes—
96#1304C2×C3714yescomplemented
97C2×C37—22no—
98C2×C37—44no—
99C2×C37—42no—
100C2×C37—82no—
101C2×C37#181911yescharacteristic
102C2×C37#182812yes—
103C23×D4C22×C3711yescharacteristic
104C2×#117C4×C3712yescomplemented
105C2×#99—24no—
106#390—24no—
107#379C4×C3712yescomplemented
108#379C22×C3714yes—
109#379C22×C3712yes—
110C37#874911yescharacteristic, direct product factor, Sylow
111C25C2×C4×C3711yescharacteristic
112C25C23×C3711yescharacteristic
113C22×D4—24no—
114C22×D4—44no—
115C22×D4D4×C3714yes—
116C23×C4C2×C4×C3711yescharacteristic
117#117—44no—
118C2×C4⋊C4—22no—
119C2×C22⋊C4—24no—
120C2×C22⋊C4—24no—
121C2×C22⋊C4—24no—
122C2×C22⋊C4—28no—
123C2×C22⋊C4C2×C4×C3714yes—
124C2×C42—22no—
125#99—48no—
126C24—22no—
127C24—42no—
128C24—42no—
129C24—82no—
130C24—82no—
131C24C22⋊C4×C3712yes—
132C24C22×C4×C3711yescharacteristic
133C24C2×D4×C3712yes—
134C24#41×C3714yes—
135C2×D4—28no—
136C2×D4—28no—
137C2×D4—44no—
138C2×D4—416no—
139C22×C4—22no—
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—44no—
143C22×C4C22⋊C4×C3712yes—
144C4⋊C4—44no—
145C22⋊C4—44no—
146C22⋊C4—48no—
147C22⋊C4—84no—
148C22⋊C4—84no—
149C22⋊C4—88no—
150C42—44no—
151C23—22no—
152C23—24no—
153C23—22no—
154C23—24no—
155C23—42no—
156C23—44no—
157C23—48no—
158C23—44no—
159C23—44no—
160C23—44no—
161C23—84no—
162C23—88no—
163C23—88no—
164C23C2×C22⋊C4×C3711yescharacteristic
165C23#117×C3712yes—
166C23#123×C3714yes—
167D4—416no—
168C2×C4—28no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—84no—
174C2×C4—88no—
175C2×C4#99×C3714yes—
176C22—22no—
177C22—22no—
178C22—24no—
179C22—28no—
180C22—24no—
181C22—44no—
182C22—42no—
183C22—44no—
184C22—84no—
185C22—84no—
186C22—88no—
187C22—88no—
188C22C37×#38111yescharacteristic
189C22C2×#99×C3712yes—
190C4—24no—
191C4—84no—
192C4—164no—
193C2—22no—
194C2—44no—
195C2—42no—
196C2—82no—
197C2C37×#181911yescharacteristic
198C2C37×#182812yes—
subgroupG/H
center, socleC22×C37#381
commutatorC24C22×C4×C37
Frattini, cosocleC25C23×C37
prime radicalC23×D4×C37C22
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C25×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1304C2semidirect
5. C2×#117×C37C4semidirect
8. C37×#379C4semidirect
76. #8749C37direct (N × H)
96. #1304C2×C37semidirect
104. C2×#117C4×C37semidirect
107. #379C4×C37semidirect
110. C37#8749direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#23092
C37×#17812
C37×#13042
#874937