Finite Group Databasebeta

← D31×#392 #16848905

Subgroups — D31×#392 #16848905

Order 3968.

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×D31C213yesmaximal, complemented
2C2×C22⋊C4×D31C213yesmaximal, complemented
3#14520959C211yesmaximal, characteristic, complemented
4#14520958C213yesmaximal, complemented
5#14520957C213yesmaximal, complemented
6#95×D31C211yesmaximal, characteristic, complemented
7C31×#392C211yesmaximal, characteristic, complemented
8C24×D31C2213yes—
9C22×D4×C31C2213yescomplemented
10C22×C22⋊D31C2216yescomplemented
11C2×D4×D31—224no—
12C2×D4×D31—212no—
13C22×D124C2213yescomplemented
14C22×C4×D31C2211yescharacteristic
15C22×C4×D31C2213yes—
16C2×C22⋊C4×C31C2213yescomplemented
17C2×C22⋊Dic31C2213yescomplemented
18C2×(C2×D31)⋊C4C2213yescomplemented
19C2×(C2×D31)⋊C4C2213yescomplemented
20C22⋊C4×D31—212no—
21C31×#95C2211yescharacteristic, complemented
22C31⋊#95C2213yescomplemented
23C24×C31C2313yes—
24C23×D31—26no—
25C23×D31—212no—
26C23×D31—212no—
27C23×D31—26no—
28C23×D31D4112yescomplemented
29C23×D31C2313yes—
30C23×D31C2311yescharacteristic
31C2×D4×C31—212no—
32C2×D4×C31—26no—
33C22×C4×C31C2311yescharacteristic
34C22×C4×C31C2313yes—
35C2×C22⋊D31—212no—
36C2×C22⋊D31—212no—
37C2×C22⋊D31—212no—
38C22×Dic31C2311yescharacteristic
39C22×Dic31C2313yes—
40D4×D31—296no—
41C2×D124—212no—
42C2×D124—26no—
43C2×C4×D31—212no—
44C2×C4×D31—26no—
45C2×C4×D31D4112yescomplemented
46C22⋊C4×C31—26no—
47C22⋊Dic31—26no—
48(C2×D31)⋊C4—26no—
49(C2×D31)⋊C4—26no—
50C23×C31—23no—
51C23×C31—26no—
52C23×C31—26no—
53C23×C31—23no—
54C23×C31C2×D416yescomplemented
55C23×C31C2411yescharacteristic
56C22×D31—23no—
57C22×D31—26no—
58C22×D31—26no—
59C22×D31—23no—
60C22×D31—248no—
61C22×D31—224no—
62C22×D31—412no—
63C22×D31—424no—
64C22×D31—412no—
65C22×D31C2×D416yes—
66C22×D31C2×D416yes—
67C22×D31C2×D416yescomplemented
68C22×D31#4112yes—
69D4×C31—224no—
70C2×C4×C31—26no—
71C2×C4×C31—23no—
72C2×C4×C31C2×D416yescomplemented
73C22⋊D31—248no—
74C2×Dic31—26no—
75C2×Dic31—23no—
76C2×Dic31C2×D416yescomplemented
77D124—224no—
78C4×D31—224no—
79C4×D31—44no—
80C2×#392—311nomaximal, Sylow
81C22×C31—212no—
82C22×C31—26no—
83C22×C31—43no—
84C22×C31—46no—
85C22×C31—43no—
86C22×C31C22×D413yes—
87C22×C31C22×D413yes—
88C22×C31C2×#4111yescharacteristic
89C2×D31—212no—
90C2×D31—26no—
91C2×D31—43no—
92C2×D31—46no—
93C2×D31—43no—
94C2×D31—448no—
95C2×D31#120112yes—
96C2×D31#121112yes—
97C2×D31#12714yes—
98C4×C31—26no—
99C4×C31—41no—
100Dic31—26no—
101Dic31—41no—
102C23×D4—313no—
103C22×C22⋊C4—313no—
104#392—313no—
105#392—313no—
106#392—311no—
107#392D3111yescharacteristic, direct product factor
108C2×#95—311no—
109C2×C31—46no—
110C2×C31C2×#12013yes—
111C2×C31C2×#12113yes—
112C2×C31C2×#12711yescharacteristic
113D31—46no—
114D31#39218yesdirect product factor
115C25—313no—
116C22×D4—316no—
117C22×D4—313no—
118C22×D4—6212no—
119C22×D4—6224no—
120C22×D4C2×D3113yescomplemented
121C23×C4—313no—
122C23×C4—311no—
123C2×C22⋊C4—313no—
124C2×C22⋊C4—313no—
125C2×C22⋊C4—313no—
126C2×C22⋊C4—6212no—
127C2×C22⋊C4C2×D3113yescomplemented
128#95—313no—
129#95C2×D3111yescharacteristic, complemented
130C31C2×#39211yescharacteristic, complemented, Sylow
131C24—311no—
132C24—3112no—
133C24—313no—
134C24—626no—
135C24—6212no—
136C24—6212no—
137C24—626no—
138C24C22×D3113yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—6212no—
142C2×D4—6212no—
143C2×D4—6296no—
144C2×D4—6212no—
145C2×D4—6212no—
146C2×D4—626no—
147C22×C4—313no—
148C22×C4—3112no—
149C22×C4—311no—
150C22×C4—6212no—
151C22×C4—626no—
152C22×C4C22×D3111yescharacteristic
153C22×C4C22×D3113yes—
154C22⋊C4—26no—
155C22⋊C4—626no—
156C22⋊C4—626no—
157C22⋊C4—626no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—316no—
163C23—316no—
164C23—312no—
165C23—316no—
166C23—6248no—
167C23—6224no—
168C23—623no—
169C23—626no—
170C23—626no—
171C23—623no—
172C23—12412no—
173C23—12424no—
174C23—12412no—
175C23D4×D3116yescomplemented
176C23C23×D3111yescharacteristic
177D4—224no—
178D4—6224no—
179D4—6248no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—316no—
183C2×C4—6224no—
184C2×C4—626no—
185C2×C4—623no—
186C2×C4—1244no—
187C2×C4D4×D3116yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—3112no—
194C22—3112no—
195C22—314no—
196C22—6212no—
197C22—626no—
198C22—12448no—
199C22—1243no—
200C22—1246no—
201C22—1243no—
202C22C2×D4×D3113yes—
203C22C2×D4×D3113yes—
204C22#41×D3111yescharacteristic
205C4—26no—
206C4—41no—
207C4—626no—
208C4—1241no—
209C2—46no—
210C2—318no—
211C2—1246no—
212C2#120×D3113yes—
213C2#121×D3113yes—
214C2#127×D3111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#392C2
hypercenter#392D31
hypocenterC31C2×#392
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D31C2semidirect
2. C2×C22⋊C4×D31C2semidirect
3. #14520959C2semidirect
4. #14520958C2semidirect
5. #14520957C2semidirect
6. #95×D31C2semidirect
7. C31×#392C2semidirect
9. C22×D4×C31C22semidirect
10. C22×C22⋊D31C22semidirect
13. C22×D124C22semidirect
16. C2×C22⋊C4×C31C22semidirect
17. C2×C22⋊Dic31C22semidirect
18. C2×(C2×D31)⋊C4C22semidirect
19. C2×(C2×D31)⋊C4C22semidirect
21. C31×#95C22semidirect
22. C31⋊#95C22semidirect
28. C23×D31D4semidirect
45. C2×C4×D31D4semidirect
54. C23×C31C2×D4semidirect
67. C22×D31C2×D4semidirect
72. C2×C4×C31C2×D4semidirect
76. C2×Dic31C2×D4semidirect
107. #392D31direct (N × H)
114. D31#392direct (N × H)
120. C22×D4C2×D31semidirect
127. C2×C22⋊C4C2×D31semidirect
129. #95C2×D31semidirect
130. C31C2×#392semidirect
175. C23D4×D31semidirect
187. C2×C4D4×D31semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D312
C2×C22⋊C4×D312
#145209592
#145209582
#145209572
#95×D312
C31×#3922
C2×#39231