Finite Group Databasebeta

← #392×D37 #17997790

Subgroups — #392×D37 #17997790

Order 4736.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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
1C22×D4×D37C213yesmaximal, complemented
2C2×C22⋊C4×D37C213yesmaximal, complemented
3#14557443C211yesmaximal, characteristic, complemented
4#14557442C213yesmaximal, complemented
5#14557441C213yesmaximal, complemented
6#95×D37C211yesmaximal, characteristic, complemented
7C37×#392C211yesmaximal, characteristic, complemented
8C24×D37C2213yes—
9C22×D148C2213yescomplemented
10C22×C22⋊D37C2216yescomplemented
11C2×D4×D37—224no—
12C2×D4×D37—212no—
13C22×C4×D37C2211yescharacteristic
14C22×C4×D37C2213yes—
15C2×C22⋊Dic37C2213yescomplemented
16C2×#10596938C2213yescomplemented
17C2×#10596938C2213yescomplemented
18C22⋊C4×D37—212no—
19#11924443C2213yescomplemented
20C22×D4×C37C2213yescomplemented
21C2×C22⋊C4×C37C2213yescomplemented
22#95×C37C2211yescharacteristic, complemented
23C24×C37C2313yes—
24C23×D37—26no—
25C23×D37—212no—
26C23×D37—212no—
27C23×D37—26no—
28C23×D37D4112yescomplemented
29C23×D37C2313yes—
30C23×D37C2311yescharacteristic
31C2×D4×C37—212no—
32C2×D4×C37—26no—
33C22×C4×C37C2311yescharacteristic
34C22×C4×C37C2313yes—
35C2×C22⋊D37—212no—
36C2×C22⋊D37—212no—
37C2×C22⋊D37—212no—
38C22×Dic37C2311yescharacteristic
39C22×Dic37C2313yes—
40D4×D37—296no—
41C2×D148—212no—
42C2×D148—26no—
43C2×C4×D37—212no—
44C2×C4×D37—26no—
45C2×C4×D37D4112yescomplemented
46C22⋊C4×C37—26no—
47C22⋊Dic37—26no—
48#10596938—26no—
49#10596938—26no—
50C23×C37—23no—
51C23×C37—26no—
52C23×C37—26no—
53C23×C37—23no—
54C23×C37C2×D416yescomplemented
55C23×C37C2411yescharacteristic
56C22×D37—23no—
57C22×D37—26no—
58C22×D37—26no—
59C22×D37—23no—
60C22×D37—248no—
61C22×D37—224no—
62C22×D37—412no—
63C22×D37—424no—
64C22×D37—412no—
65C22×D37C2×D416yes—
66C22×D37C2×D416yes—
67C22×D37C2×D416yescomplemented
68C22×D37#4112yes—
69D4×C37—224no—
70C2×C4×C37—26no—
71C2×C4×C37—23no—
72C2×C4×C37C2×D416yescomplemented
73C22⋊D37—248no—
74C2×Dic37—26no—
75C2×Dic37—23no—
76C2×Dic37C2×D416yescomplemented
77D148—224no—
78C4×D37—224no—
79C4×D37—44no—
80C22×C37—212no—
81C22×C37—26no—
82C22×C37—43no—
83C22×C37—46no—
84C22×C37—43no—
85C22×C37C22×D413yes—
86C22×C37C22×D413yes—
87C22×C37C2×#4111yescharacteristic
88C2×D37—212no—
89C2×D37—26no—
90C2×D37—43no—
91C2×D37—46no—
92C2×D37—43no—
93C2×D37—448no—
94C2×D37#120112yes—
95C2×D37#121112yes—
96C2×D37#12714yes—
97C4×C37—26no—
98C4×C37—41no—
99Dic37—26no—
100Dic37—41no—
101C2×#392—371nomaximal, Sylow
102C2×C37—46no—
103C2×C37C2×#12013yes—
104C2×C37C2×#12113yes—
105C2×C37C2×#12711yescharacteristic
106D37—46no—
107D37#39218yesdirect product factor
108C23×D4—373no—
109C22×C22⋊C4—373no—
110#392—373no—
111#392—373no—
112#392—371no—
113#392D3711yescharacteristic, direct product factor
114C2×#95—371no—
115C37C2×#39211yescharacteristic, complemented, Sylow
116C25—373no—
117C22×D4—376no—
118C22×D4—373no—
119C22×D4—7412no—
120C22×D4—7424no—
121C22×D4C2×D3713yescomplemented
122C23×C4—373no—
123C23×C4—371no—
124C2×C22⋊C4—373no—
125C2×C22⋊C4—373no—
126C2×C22⋊C4—373no—
127C2×C22⋊C4—7412no—
128C2×C22⋊C4C2×D3713yescomplemented
129#95—373no—
130#95C2×D3711yescharacteristic, complemented
131C24—371no—
132C24—3712no—
133C24—373no—
134C24—746no—
135C24—7412no—
136C24—7412no—
137C24—746no—
138C24C22×D3713yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—7412no—
142C2×D4—7412no—
143C2×D4—7496no—
144C2×D4—7412no—
145C2×D4—7412no—
146C2×D4—746no—
147C22×C4—373no—
148C22×C4—3712no—
149C22×C4—371no—
150C22×C4—7412no—
151C22×C4—746no—
152C22×C4C22×D3711yescharacteristic
153C22×C4C22×D3713yes—
154C22⋊C4—26no—
155C22⋊C4—746no—
156C22⋊C4—746no—
157C22⋊C4—746no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—376no—
163C23—376no—
164C23—372no—
165C23—376no—
166C23—7448no—
167C23—7424no—
168C23—743no—
169C23—746no—
170C23—746no—
171C23—743no—
172C23—14812no—
173C23—14824no—
174C23—14812no—
175C23D4×D3716yescomplemented
176C23C23×D3711yescharacteristic
177D4—224no—
178D4—7424no—
179D4—7448no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—376no—
183C2×C4—7424no—
184C2×C4—746no—
185C2×C4—743no—
186C2×C4—1484no—
187C2×C4D4×D3716yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—3712no—
194C22—3712no—
195C22—374no—
196C22—7412no—
197C22—746no—
198C22—14848no—
199C22—1483no—
200C22—1486no—
201C22—1483no—
202C22C2×D4×D3713yes—
203C22C2×D4×D3713yes—
204C22#41×D3711yescharacteristic
205C4—26no—
206C4—41no—
207C4—746no—
208C4—1481no—
209C2—46no—
210C2—378no—
211C2—1486no—
212C2#120×D3713yes—
213C2#121×D3713yes—
214C2#127×D3711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#392C2
hypercenter#392D37
hypocenterC37C2×#392
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D37C2semidirect
2. C2×C22⋊C4×D37C2semidirect
3. #14557443C2semidirect
4. #14557442C2semidirect
5. #14557441C2semidirect
6. #95×D37C2semidirect
7. C37×#392C2semidirect
9. C22×D148C22semidirect
10. C22×C22⋊D37C22semidirect
15. C2×C22⋊Dic37C22semidirect
16. C2×#10596938C22semidirect
17. C2×#10596938C22semidirect
19. #11924443C22semidirect
20. C22×D4×C37C22semidirect
21. C2×C22⋊C4×C37C22semidirect
22. #95×C37C22semidirect
28. C23×D37D4semidirect
45. C2×C4×D37D4semidirect
54. C23×C37C2×D4semidirect
67. C22×D37C2×D4semidirect
72. C2×C4×C37C2×D4semidirect
76. C2×Dic37C2×D4semidirect
107. D37#392direct (N × H)
113. #392D37direct (N × H)
115. C37C2×#392semidirect
121. C22×D4C2×D37semidirect
128. C2×C22⋊C4C2×D37semidirect
130. #95C2×D37semidirect
175. C23D4×D37semidirect
187. C2×C4D4×D37semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D372
C2×C22⋊C4×D372
#145574432
#145574422
#145574412
#95×D372
C37×#3922
C2×#39237