Finite Group Databasebeta

← C37×#8722 #22629975

Subgroups — C37×#8722 #22629975

Order 9472.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2285C211yesmaximal, characteristic
2C37×#1749C212yesmaximal
3C37×#1295C214yesmaximal, complemented
4C2×#117×C37C412yes—
5C22×C42×C37C2211yescharacteristic
6C2×C22⋊C8×C37—22no—
7C2×#97×C37C2214yes—
8C37×#384C412yes—
9C37×#382C2212yes—
10C37×#380—22no—
11C4×C4⋊C4×C37—22no—
12C37×#336—22no—
13C23×C4×C37C2×C411yescharacteristic
14C23×C4×C37D412yes—
15C22×C8×C37—24no—
16#117×C37—44no—
17C2×C4⋊C4×C37—22no—
18C2×C4⋊C4×C37—22no—
19C2×C4⋊C4×C37C2×C414yes—
20C2×C22⋊C4×C37—22no—
21C2×C42×C37—24no—
22C2×C42×C37—22no—
23C2×C42×C37C2×C411yescharacteristic
24C2×C42×C37D412yes—
25C2×C42×C37C2311yescharacteristic
26C22⋊C8×C37—28no—
27#97×C37—28no—
28#95×C37—24no—
29C24×C37C22⋊C411yescharacteristic
30C22×C4×C37—22no—
31C22×C4×C37—22no—
32C22×C4×C37—22no—
33C22×C4×C37—24no—
34C22×C4×C37—24no—
35C22×C4×C37—24no—
36C22×C4×C37—42no—
37C22×C4×C37C22⋊C411yescharacteristic
38C22×C4×C37C22⋊C412yes—
39C22×C4×C37C22×C411yescharacteristic
40C22×C4×C37C2×D412yes—
41C2×C8×C37—28no—
42C2×C8×C37—44no—
43C2×C8×C37—44no—
44C4⋊C4×C37—44no—
45C4⋊C4×C37—44no—
46C4⋊C4×C37—44no—
47C22⋊C4×C37—44no—
48C42×C37—22no—
49C42×C37—24no—
50C42×C37—44no—
51C42×C37#4114yes—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37—22no—
55C23×C37—22no—
56C23×C37#10012yes—
57C23×C37C2×C22⋊C411yescharacteristic
58C2×C4×C37—28no—
59C2×C4×C37—21no—
60C2×C4×C37—22no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37—48no—
68C2×C4×C37—44no—
69C2×C4×C37—44no—
70C2×C4×C37—44no—
71C2×C4×C37#10112yes—
72C2×C4×C37#10414yes—
73C2×C4×C37#11712yes—
74C2×C4×C37#12314yes—
75C8×C37—48no—
76#8722C3711yesmaximal, characteristic, direct product factor, Sylow
77C22×C37—22no—
78C22×C37—24no—
79C22×C37—41no—
80C22×C37—42no—
81C22×C37—41no—
82C22×C37#38111yescharacteristic
83C22×C37C2×#10011yescharacteristic
84C22×C37C2×#10111yescharacteristic
85C22×C37C2×#10412yes—
86C22×C37#42112yes—
87C4×C37—22no—
88C4×C37—22no—
89C4×C37—24no—
90C4×C37—24no—
91C4×C37—84no—
92#2285C2×C3711yescharacteristic
93#1749C2×C3712yes—
94#1295C2×C3714yescomplemented
95C2×C37—42no—
96C2×C37#152611yescharacteristic
97C2×C37#153012yes—
98C2×C37#153711yescharacteristic
99C2×C37#182111yescharacteristic
100C2×C37#182612yes—
101C2×#117C4×C3712yes—
102C22×C42C22×C3711yescharacteristic
103C2×C22⋊C8—22no—
104C2×#97C22×C3714yes—
105#384C4×C3712yes—
106#382C22×C3712yes—
107#380—22no—
108C4×C4⋊C4—22no—
109#336—22no—
110C37#872211yescharacteristic, direct product factor, Sylow
111C23×C4C2×C4×C3711yescharacteristic
112C23×C4D4×C3712yes—
113C22×C8—24no—
114#117—44no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—22no—
117C2×C4⋊C4C2×C4×C3714yes—
118C2×C22⋊C4—22no—
119C2×C42—24no—
120C2×C42—22no—
121C2×C42C2×C4×C3711yescharacteristic
122C2×C42D4×C3712yes—
123C2×C42C23×C3711yescharacteristic
124C22⋊C8—28no—
125#97—28no—
126#95—24no—
127C24C22⋊C4×C3711yescharacteristic
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—24no—
132C22×C4—24no—
133C22×C4—24no—
134C22×C4—42no—
135C22×C4C22⋊C4×C3711yescharacteristic
136C22×C4C22⋊C4×C3712yes—
137C22×C4C22×C4×C3711yescharacteristic
138C22×C4C2×D4×C3712yes—
139C2×C8—28no—
140C2×C8—44no—
141C2×C8—44no—
142C4⋊C4—44no—
143C4⋊C4—44no—
144C4⋊C4—44no—
145C22⋊C4—44no—
146C42—22no—
147C42—24no—
148C42—44no—
149C42#41×C3714yes—
150C23—21no—
151C23—21no—
152C23—22no—
153C23—22no—
154C23#100×C3712yes—
155C23C2×C22⋊C4×C3711yescharacteristic
156C2×C4—28no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—48no—
166C2×C4—44no—
167C2×C4—44no—
168C2×C4—44no—
169C2×C4#101×C3712yes—
170C2×C4#104×C3714yes—
171C2×C4#117×C3712yes—
172C2×C4#123×C3714yes—
173C8—48no—
174C22—24no—
175C22—22no—
176C22—41no—
177C22—41no—
178C22—42no—
179C22C37×#38111yescharacteristic
180C22C2×#100×C3711yescharacteristic
181C22C2×#101×C3711yescharacteristic
182C22C2×#104×C3712yes—
183C22C37×#42112yes—
184C4—22no—
185C4—22no—
186C4—24no—
187C4—24no—
188C4—84no—
189C2—42no—
190C2C37×#152611yescharacteristic
191C2C37×#153012yes—
192C2C37×#153711yescharacteristic
193C2C37×#182111yescharacteristic
194C2C37×#182612yes—
subgroupG/H
center, socleC23×C37C2×C22⋊C4
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×C42C23×C37
prime radicalC24×C37C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C37 ◁ C22×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C37×#1295C2semidirect
76. #8722C37direct (N × H)
94. #1295C2×C37semidirect
110. C37#8722direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#22852
C37×#17492
C37×#12952
#872237