Finite Group Databasebeta

← C37×#11522 #22632775

Subgroups — C37×#11522 #22632775

Order 9472.

284 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2921C211yesmaximal, characteristic
2C37×#2165C212yesmaximal, complemented
3C37×#1327C212yesmaximal, complemented
4C37×#1320C212yesmaximal
5C2×#117×C37C411yescharacteristic
6C37×#433—22no—
7C37×#433—22no—
8C37×#423C411yescharacteristic
9C37×#423C2211yescharacteristic
10C37×#407C411yescharacteristic
11C37×#407C2211yescharacteristic
12C4×M16×C37C411yescharacteristic
13C4×M16×C37C2211yescharacteristic
14C37×#364—22no—
15C37×#349C2214yes—
16C37×#347—22no—
17C23×C4×C37C2×C411yescharacteristic
18C2×M16×C37C2×C411yescharacteristic
19C2×M16×C37C2×C411yescharacteristic
20C2×M16×C37C2×C411yescharacteristic
21C2×M16×C37C2311yescharacteristic
22#117×C37—21no—
23#117×C37—21no—
24#117×C37—22no—
25C2×C4⋊C4×C37—21no—
26C2×C22⋊C4×C37—21no—
27C2×C42×C37C2×C411yescharacteristic
28C2×C42×C37C2×C411yescharacteristic
29M32×C37—24no—
30C4⋊C8×C37—22no—
31C4⋊C8×C37—22no—
32C22⋊C8×C37—22no—
33C22⋊C8×C37—22no—
34#97×C37—21no—
35#97×C37D412yes—
36C4×C8×C37—21no—
37C4×C8×C37D412yes—
38C24×C37M1611yescharacteristic
39C22×C4×C37—21no—
40C22×C4×C37—21no—
41C22×C4×C37—21no—
42C22×C4×C37—21no—
43C22×C4×C37—41no—
44C22×C4×C37—41no—
45C22×C4×C37M1611yescharacteristic
46C22×C4×C37C22×C411yescharacteristic
47M16×C37—41no—
48M16×C37—41no—
49M16×C37—41no—
50M16×C37—41no—
51C2×C8×C37—21no—
52C2×C8×C37—21no—
53C2×C8×C37C22⋊C412yes—
54C2×C8×C37C2×D412yes—
55C4⋊C4×C37—22no—
56C4⋊C4×C37—22no—
57C22⋊C4×C37—22no—
58C22⋊C4×C37—22no—
59C42×C37—21no—
60C42×C37—21no—
61C42×C37C22⋊C411yescharacteristic
62C42×C37C22⋊C411yescharacteristic
63C42×C37M1612yes—
64C16×C37—44no—
65C23×C37—21no—
66C23×C37—41no—
67C23×C37—81no—
68C23×C37C2×M1611yescharacteristic
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—22no—
74C2×C4×C37—21no—
75C2×C4×C37—42no—
76C2×C4×C37—41no—
77C2×C4×C37—41no—
78C2×C4×C37—41no—
79C2×C4×C37—81no—
80C2×C4×C37—81no—
81C2×C4×C37C2×C22⋊C411yescharacteristic
82C2×C4×C37C2×M1611yescharacteristic
83C8×C37—22no—
84C8×C37—22no—
85C8×C37—41no—
86C8×C37—41no—
87#11522C3711yesmaximal, characteristic, direct product factor, Sylow
88C22×C37—21no—
89C22×C37—41no—
90C22×C37—42no—
91C22×C37—41no—
92C22×C37—82no—
93C22×C37#40711yescharacteristic
94C4×C37—21no—
95C4×C37—41no—
96C4×C37—41no—
97C4×C37—42no—
98C4×C37—41no—
99C4×C37#41011yescharacteristic
100C4×C37#41311yescharacteristic
101#2921C2×C3711yescharacteristic
102#2165C2×C3712yescomplemented
103#1327C2×C3712yescomplemented
104#1320C2×C3712yes—
105C2×C37—21no—
106C2×C37—41no—
107C2×C37—81no—
108C2×C37#146411yescharacteristic
109C2×#117C4×C3711yescharacteristic
110#433—22no—
111#433—22no—
112#423C4×C3711yescharacteristic
113#423C22×C3711yescharacteristic
114#407C4×C3711yescharacteristic
115#407C22×C3711yescharacteristic
116C4×M16C4×C3711yescharacteristic
117C4×M16C22×C3711yescharacteristic
118#364—22no—
119#349C22×C3714yes—
120#347—22no—
121C37#1152211yescharacteristic, direct product factor, Sylow
122C23×C4C2×C4×C3711yescharacteristic
123C2×M16C2×C4×C3711yescharacteristic
124C2×M16C2×C4×C3711yescharacteristic
125C2×M16C2×C4×C3711yescharacteristic
126C2×M16C23×C3711yescharacteristic
127#117—21no—
128#117—21no—
129#117—22no—
130C2×C4⋊C4—21no—
131C2×C22⋊C4—21no—
132C2×C42C2×C4×C3711yescharacteristic
133C2×C42C2×C4×C3711yescharacteristic
134M32—24no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C22⋊C8—22no—
138C22⋊C8—22no—
139#97—21no—
140#97D4×C3712yes—
141C4×C8—21no—
142C4×C8D4×C3712yes—
143C24M16×C3711yescharacteristic
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4M16×C3711yescharacteristic
151C22×C4C22×C4×C3711yescharacteristic
152M16—41no—
153M16—41no—
154M16—41no—
155M16—41no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8C22⋊C4×C3712yes—
159C2×C8C2×D4×C3712yes—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C42—21no—
165C42—21no—
166C42C22⋊C4×C3711yescharacteristic
167C42C22⋊C4×C3711yescharacteristic
168C42M16×C3712yes—
169C16—44no—
170C23—21no—
171C23—41no—
172C23—81no—
173C23C2×M16×C3711yescharacteristic
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—81no—
185C2×C4—81no—
186C2×C4C2×C22⋊C4×C3711yescharacteristic
187C2×C4C2×M16×C3711yescharacteristic
188C8—22no—
189C8—22no—
190C8—41no—
191C8—41no—
192C22—21no—
193C22—41no—
194C22—42no—
195C22—41no—
196C22—82no—
197C22C37×#40711yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4C37×#41011yescharacteristic
204C4C37×#41311yescharacteristic
205C2—21no—
206C2—41no—
207C2—81no—
208C2C37×#146411yescharacteristic
subgroupG/H
centerC4×C37#410
commutatorC22×C4C22×C4×C37
Frattini, cosocleC2×M16C23×C37
socleC2×C37#1464
prime radicalC24×C37M16
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C37 ◁ C42×C37 ◁ C4×M16×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#2165C2semidirect
3. C37×#1327C2semidirect
87. #11522C37direct (N × H)
102. #2165C2×C37semidirect
103. #1327C2×C37semidirect
121. C37#11522direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#29212
C37×#21652
C37×#13272
C37×#13202
#1152237