Finite Group Databasebeta

← #392×D43 #19137789

Subgroups — #392×D43 #19137789

Order 5504.

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×D43C213yesmaximal, complemented
2C2×C22⋊C4×D43C213yesmaximal, complemented
3#14582809C211yesmaximal, characteristic, complemented
4#14582808C213yesmaximal, complemented
5#14582807C213yesmaximal, complemented
6#95×D43C211yesmaximal, characteristic, complemented
7C43×#392C211yesmaximal, characteristic, complemented
8C24×D43C2213yes—
9C22×D172C2213yescomplemented
10C22×C22⋊D43C2216yescomplemented
11C2×D4×D43—224no—
12C2×D4×D43—212no—
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2213yes—
15C2×C22⋊Dic43C2213yescomplemented
16C2×(C2×D43)⋊C4C2213yescomplemented
17C2×(C2×D43)⋊C4C2213yescomplemented
18C22⋊C4×D43—212no—
19C43⋊#95C2213yescomplemented
20C22×D4×C43C2213yescomplemented
21C2×C22⋊C4×C43C2213yescomplemented
22#95×C43C2211yescharacteristic, complemented
23C24×C43C2313yes—
24C23×D43—26no—
25C23×D43—212no—
26C23×D43—212no—
27C23×D43—26no—
28C23×D43D4112yescomplemented
29C23×D43C2313yes—
30C23×D43C2311yescharacteristic
31C2×D4×C43—26no—
32C2×D4×C43—212no—
33C22×C4×C43C2311yescharacteristic
34C22×C4×C43C2313yes—
35C2×C22⋊D43—212no—
36C2×C22⋊D43—212no—
37C2×C22⋊D43—212no—
38C22×Dic43C2311yescharacteristic
39C22×Dic43C2313yes—
40D4×D43—296no—
41C2×D172—26no—
42C2×D172—212no—
43C2×C4×D43—212no—
44C2×C4×D43—26no—
45C2×C4×D43D4112yescomplemented
46C22⋊C4×C43—26no—
47C22⋊Dic43—26no—
48(C2×D43)⋊C4—26no—
49(C2×D43)⋊C4—26no—
50C23×C43—23no—
51C23×C43—26no—
52C23×C43—26no—
53C23×C43—23no—
54C23×C43C2×D416yescomplemented
55C23×C43C2411yescharacteristic
56C22×D43—23no—
57C22×D43—26no—
58C22×D43—26no—
59C22×D43—23no—
60C22×D43—248no—
61C22×D43—224no—
62C22×D43—412no—
63C22×D43—424no—
64C22×D43—412no—
65C22×D43C2×D416yes—
66C22×D43C2×D416yes—
67C22×D43C2×D416yescomplemented
68C22×D43#4112yes—
69D4×C43—224no—
70C2×C4×C43—26no—
71C2×C4×C43—23no—
72C2×C4×C43C2×D416yescomplemented
73C22⋊D43—248no—
74C2×Dic43—26no—
75C2×Dic43—23no—
76C2×Dic43C2×D416yescomplemented
77D172—224no—
78C4×D43—224no—
79C4×D43—44no—
80C22×C43—212no—
81C22×C43—26no—
82C22×C43—43no—
83C22×C43—46no—
84C22×C43—43no—
85C22×C43C22×D413yes—
86C22×C43C22×D413yes—
87C22×C43C2×#4111yescharacteristic
88C2×D43—212no—
89C2×D43—26no—
90C2×D43—43no—
91C2×D43—46no—
92C2×D43—43no—
93C2×D43—448no—
94C2×D43#120112yes—
95C2×D43#121112yes—
96C2×D43#12714yes—
97C4×C43—26no—
98C4×C43—41no—
99Dic43—26no—
100Dic43—41no—
101C2×#392—431nomaximal, Sylow
102C2×C43—46no—
103C2×C43C2×#12013yes—
104C2×C43C2×#12113yes—
105C2×C43C2×#12711yescharacteristic
106D43—46no—
107D43#39218yesdirect product factor
108C23×D4—433no—
109C22×C22⋊C4—433no—
110#392—433no—
111#392—433no—
112#392—431no—
113#392D4311yescharacteristic, direct product factor
114C2×#95—431no—
115C43C2×#39211yescharacteristic, complemented, Sylow
116C25—433no—
117C22×D4—436no—
118C22×D4—433no—
119C22×D4—8612no—
120C22×D4—8624no—
121C22×D4C2×D4313yescomplemented
122C23×C4—433no—
123C23×C4—431no—
124C2×C22⋊C4—433no—
125C2×C22⋊C4—433no—
126C2×C22⋊C4—433no—
127C2×C22⋊C4—8612no—
128C2×C22⋊C4C2×D4313yescomplemented
129#95—433no—
130#95C2×D4311yescharacteristic, complemented
131C24—431no—
132C24—4312no—
133C24—433no—
134C24—866no—
135C24—8612no—
136C24—8612no—
137C24—866no—
138C24C22×D4313yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—8612no—
142C2×D4—8612no—
143C2×D4—8696no—
144C2×D4—8612no—
145C2×D4—8612no—
146C2×D4—866no—
147C22×C4—433no—
148C22×C4—4312no—
149C22×C4—431no—
150C22×C4—8612no—
151C22×C4—866no—
152C22×C4C22×D4311yescharacteristic
153C22×C4C22×D4313yes—
154C22⋊C4—26no—
155C22⋊C4—866no—
156C22⋊C4—866no—
157C22⋊C4—866no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—436no—
163C23—436no—
164C23—432no—
165C23—436no—
166C23—8648no—
167C23—8624no—
168C23—863no—
169C23—866no—
170C23—866no—
171C23—863no—
172C23—17212no—
173C23—17224no—
174C23—17212no—
175C23D4×D4316yescomplemented
176C23C23×D4311yescharacteristic
177D4—224no—
178D4—8624no—
179D4—8648no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—436no—
183C2×C4—8624no—
184C2×C4—866no—
185C2×C4—863no—
186C2×C4—1724no—
187C2×C4D4×D4316yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—4312no—
194C22—4312no—
195C22—434no—
196C22—8612no—
197C22—866no—
198C22—17248no—
199C22—1723no—
200C22—1726no—
201C22—1723no—
202C22C2×D4×D4313yes—
203C22C2×D4×D4313yes—
204C22#41×D4311yescharacteristic
205C4—26no—
206C4—41no—
207C4—866no—
208C4—1721no—
209C2—46no—
210C2—438no—
211C2—1726no—
212C2#120×D4313yes—
213C2#121×D4313yes—
214C2#127×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43C2×#392
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×C22⋊C4×D43C2semidirect
3. #14582809C2semidirect
4. #14582808C2semidirect
5. #14582807C2semidirect
6. #95×D43C2semidirect
7. C43×#392C2semidirect
9. C22×D172C22semidirect
10. C22×C22⋊D43C22semidirect
15. C2×C22⋊Dic43C22semidirect
16. C2×(C2×D43)⋊C4C22semidirect
17. C2×(C2×D43)⋊C4C22semidirect
19. C43⋊#95C22semidirect
20. C22×D4×C43C22semidirect
21. C2×C22⋊C4×C43C22semidirect
22. #95×C43C22semidirect
28. C23×D43D4semidirect
45. C2×C4×D43D4semidirect
54. C23×C43C2×D4semidirect
67. C22×D43C2×D4semidirect
72. C2×C4×C43C2×D4semidirect
76. C2×Dic43C2×D4semidirect
107. D43#392direct (N × H)
113. #392D43direct (N × H)
115. C43C2×#392semidirect
121. C22×D4C2×D43semidirect
128. C2×C22⋊C4C2×D43semidirect
130. #95C2×D43semidirect
175. C23D4×D43semidirect
187. C2×C4D4×D43semidirect