Finite Group Databasebeta

← C37×#9005 #22630258

Subgroups — C37×#9005 #22630258

Order 9472.

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

normal subgroups only

This group has 416 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×#3135C211yesmaximal, characteristic
2C37×#2980C211yesmaximal, characteristic
3C37×#1543C211yesmaximal, characteristic
4C37×#1497C212yesmaximal, complemented
5C37×#1302C212yesmaximal, complemented
6C37×#533C2211yescharacteristic
7C37×#532C2211yescharacteristic
8C37×#491—21no—
9C37×#490—21no—
10C37×#489C414yes—
11C37×#435—24no—
12C37×#432C2212yes—
13C37×#431C2212yes—
14C37×#416—22no—
15C37×#408—22no—
16C2×#97×C37C2211yescharacteristic
17C37×#333—21no—
18C37×#331—21no—
19C37×Q8⋊C8—24no—
20C2×#41×C37D412yes—
21C2×M16×C37—22no—
22C22×C8×C37—21no—
23C22×C8×C37—22no—
24C4⋊Q8×C37C2×C412yes—
25C4⋊Q8×C37D411yescharacteristic
26#127×C37D411yescharacteristic
27#125×C37—21no—
28#124×C37C2×C412yes—
29C22⋊Q8×C37—22no—
30#121×C37—22no—
31C4×Q8×C37—22no—
32C4×D4×C37—22no—
33#117×C37—21no—
34C2×C42×C37C2311yescharacteristic
35C4⋊C8×C37—22no—
36C4⋊C8×C37D414yes—
37#103×C37—24no—
38#102×C37—24no—
39C22⋊C8×C37—24no—
40C22⋊C8×C37—22no—
41C22⋊C8×C37—22no—
42#97×C37—21no—
43#97×C37—22no—
44#97×C37C2×C412yes—
45C4×C8×C37—22no—
46#41×C37—42no—
47#41×C37—42no—
48C2×Q8×C37—22no—
49C2×Q8×C37C22⋊C412yes—
50C2×D4×C37—22no—
51C2×D4×C37—22no—
52C2×D4×C37C22⋊C412yes—
53C22×C4×C37—22no—
54C22×C4×C37C2×D411yescharacteristic
55C22×C4×C37#4112yes—
56M16×C37—82no—
57C2×C8×C37—22no—
58C2×C8×C37—24no—
59C2×C8×C37—42no—
60C2×C8×C37—42no—
61C2×C8×C37—82no—
62C4⋊C4×C37—22no—
63C4⋊C4×C37—22no—
64C4⋊C4×C37—22no—
65C4⋊C4×C37—42no—
66C22⋊C4×C37—24no—
67C22⋊C4×C37—41no—
68C42×C37—41no—
69C42×C37C22×C411yescharacteristic
70C42×C37C2×D411yescharacteristic
71C42×C37C2×D412yes—
72C23×C37—22no—
73C23×C37#12311yescharacteristic
74Q8×C37—42no—
75Q8×C37—44no—
76D4×C37—42no—
77D4×C37—82no—
78D4×C37—82no—
79C2×C4×C37—22no—
80C2×C4×C37—22no—
81C2×C4×C37—42no—
82C2×C4×C37—42no—
83C2×C4×C37—42no—
84C2×C4×C37—42no—
85C2×C4×C37C2×C22⋊C411yescharacteristic
86C2×C4×C37C4×D412yes—
87C2×C4×C37#12011yescharacteristic
88C2×C4×C37#12112yes—
89C8×C37—42no—
90C8×C37—44no—
91C8×C37—82no—
92#9005C3711yesmaximal, characteristic, direct product factor, Sylow
93C22×C37—22no—
94C22×C37—21no—
95C22×C37—44no—
96C22×C37—42no—
97C22×C37#38611yescharacteristic
98C4×C37—22no—
99C4×C37—22no—
100C4×C37—21no—
101C4×C37—42no—
102C4×C37—82no—
103C4×C37#45512yes—
104#3135C2×C3711yescharacteristic
105#2980C2×C3711yescharacteristic
106#1543C2×C3711yescharacteristic
107#1497C2×C3712yescomplemented
108#1302C2×C3712yescomplemented
109C2×C37—41no—
110C2×C37—82no—
111C2×C37#188112yes—
112C2×C37#188511yescharacteristic
113#533C22×C3711yescharacteristic
114#532C22×C3711yescharacteristic
115#491—21no—
116#490—21no—
117#489C4×C3714yes—
118#435—24no—
119#432C22×C3712yes—
120#431C22×C3712yes—
121#416—22no—
122#408—22no—
123C2×#97C22×C3711yescharacteristic
124#333—21no—
125#331—21no—
126Q8⋊C8—24no—
127C37#900511yescharacteristic, direct product factor, Sylow
128C2×#41D4×C3712yes—
129C2×M16—22no—
130C22×C8—21no—
131C22×C8—22no—
132C4⋊Q8C2×C4×C3712yes—
133C4⋊Q8D4×C3711yescharacteristic
134#127D4×C3711yescharacteristic
135#125—21no—
136#124C2×C4×C3712yes—
137C22⋊Q8—22no—
138#121—22no—
139C4×Q8—22no—
140C4×D4—22no—
141#117—21no—
142C2×C42C23×C3711yescharacteristic
143C4⋊C8—22no—
144C4⋊C8D4×C3714yes—
145#103—24no—
146#102—24no—
147C22⋊C8—24no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150#97—21no—
151#97—22no—
152#97C2×C4×C3712yes—
153C4×C8—22no—
154#41—42no—
155#41—42no—
156C2×Q8—22no—
157C2×Q8C22⋊C4×C3712yes—
158C2×D4—22no—
159C2×D4—22no—
160C2×D4C22⋊C4×C3712yes—
161C22×C4—22no—
162C22×C4C2×D4×C3711yescharacteristic
163C22×C4#41×C3712yes—
164M16—82no—
165C2×C8—22no—
166C2×C8—24no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—82no—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C22⋊C4—24no—
175C22⋊C4—41no—
176C42—41no—
177C42C22×C4×C3711yescharacteristic
178C42C2×D4×C3711yescharacteristic
179C42C2×D4×C3712yes—
180C23—22no—
181C23#123×C3711yescharacteristic
182Q8—42no—
183Q8—44no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4C2×C22⋊C4×C3711yescharacteristic
194C2×C4C4×D4×C3712yes—
195C2×C4#120×C3711yescharacteristic
196C2×C4#121×C3712yes—
197C8—42no—
198C8—44no—
199C8—82no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22C37×#38611yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—82no—
210C4C37×#45512yes—
211C2—41no—
212C2—82no—
213C2C37×#188112yes—
214C2C37×#188511yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutatorC42C22×C4×C37
Frattini, cosocleC2×C42C23×C37
socleC22×C37#386
prime radicalC37×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
4. C37×#1497C2semidirect
5. C37×#1302C2semidirect
92. #9005C37direct (N × H)
107. #1497C2×C37semidirect
108. #1302C2×C37semidirect
127. C37#9005direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#31352
C37×#29802
C37×#15432
C37×#14972
C37×#13022
#900537