Finite Group Databasebeta

← #342×D43 #19134323

Subgroups — #342×D43 #19134323

Order 5504.

680 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×C22⋊C4×D43C211yesmaximal, characteristic
2C2×C22⋊C4×D43C212yesmaximal
3#14582666C211yesmaximal, characteristic, complemented
4#14582665C212yesmaximal, complemented
5C43×#342C211yesmaximal, characteristic, complemented
6C24×D43C2211yescharacteristic
7C22×C4×D43—22no—
8C22×C4×D43C412yescomplemented
9C2×C22⋊Dic43C2211yescharacteristic
10C2×C22⋊Dic43C2212yes—
11C2×(C2×D43)⋊C4—22no—
12C2×(C2×D43)⋊C4C412yescomplemented
13C22⋊C4×D43—22no—
14C22⋊C4×D43—22no—
15C22⋊C4×D43—24no—
16C22⋊C4×D43C418yescomplemented
17C2×C22⋊C4×C43C2211yescharacteristic
18C2×C22⋊C4×C43C2212yes—
19C24×C43C2311yescharacteristic
20C23×D43—44no—
21C23×D43C2×C411yescharacteristic
22C23×D43C2×C414yes—
23C23×D43C2×C411yescharacteristic
24C23×D43D412yes—
25C23×D43D412yes—
26C23×D43D412yes—
27C23×D43Q812yes—
28C22×C4×C43—22no—
29C22×C4×C43C2×C412yescomplemented
30C22×Dic43—22no—
31C22×Dic43C2×C412yescomplemented
32C2×C4×D43—22no—
33C2×C4×D43—22no—
34C2×C4×D43—28no—
35C2×C4×D43—48no—
36C2×C4×D43—44no—
37C22⋊C4×C43—22no—
38C22⋊C4×C43—22no—
39C22⋊C4×C43C2×C414yescomplemented
40C22⋊Dic43—22no—
41C22⋊Dic43—22no—
42C22⋊Dic43C2×C414yescomplemented
43(C2×D43)⋊C4—24no—
44(C2×D43)⋊C4—28no—
45C23×C43—42no—
46C23×C43C22×C411yescharacteristic
47C23×C43C22×C412yes—
48C23×C43C2×D412yes—
49C23×C43C2×D411yescharacteristic
50C23×C43C2×Q811yescharacteristic
51C22×D43—24no—
52C22×D43—28no—
53C22×D43—48no—
54C22×D43—44no—
55C22×D43—44no—
56C22×D43—42no—
57C22×D43—44no—
58C22×D43C4212yes—
59C22×D43C4212yes—
60C22×D43C22⋊C412yes—
61C22×D43C22⋊C414yes—
62C22×D43C22⋊C411yescharacteristic
63C22×D43C22⋊C414yes—
64C22×D43C22⋊C411yescharacteristic
65C22×D43C4⋊C412yes—
66C22×D43C4⋊C414yes—
67C22×D43C4⋊C414yes—
68C22×D43C4⋊C412yes—
69C2×C4×C43—22no—
70C2×C4×C43—24no—
71C2×C4×C43—44no—
72C2×C4×C43—42no—
73C2×Dic43—22no—
74C2×Dic43—24no—
75C2×Dic43—44no—
76C2×Dic43—42no—
77C4×D43—416no—
78C4×D43—44no—
79C4×D43—44no—
80C22×C43—22no—
81C22×C43—24no—
82C22×C43—42no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43C2×C4211yescharacteristic
86C22×C43C2×C22⋊C412yes—
87C22×C43C2×C22⋊C411yescharacteristic
88C22×C43C2×C4⋊C411yescharacteristic
89C22×C43C2×C4⋊C412yes—
90C2×D43—24no—
91C2×D43—22no—
92C2×D43—24no—
93C2×D43—28no—
94C2×D43—24no—
95C2×D43—28no—
96C2×D43—42no—
97C2×D43—44no—
98C2×D43—44no—
99C2×D43—42no—
100C2×D43#9512yes—
101C2×D43#9514yes—
102C2×D43#9512yes—
103C2×D43#9914yes—
104C4×C43—44no—
105C4×C43—42no—
106Dic43—44no—
107Dic43—42no—
108C2×#342—431nomaximal, Sylow
109C2×C43—22no—
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—22no—
113C2×C43C2×#9511yescharacteristic
114C2×C43C2×#9912yes—
115D43—24no—
116D43—22no—
117D43#34214yesdirect product factor
118C22×C22⋊C4—432no—
119C22×C22⋊C4—431no—
120#342—432no—
121#342—431no—
122#342D4311yescharacteristic, direct product factor
123C43C2×#34211yescharacteristic, complemented, Sylow
124C25—431no—
125C23×C4—432no—
126C23×C4—862no—
127C2×C22⋊C4—432no—
128C2×C22⋊C4—438no—
129C2×C22⋊C4—431no—
130C2×C22⋊C4—432no—
131C2×C22⋊C4—864no—
132C2×C22⋊C4—862no—
133C2×C22⋊C4—862no—
134C2×C22⋊C4—862no—
135C2×C22⋊C4C2×D4311yescharacteristic
136C2×C22⋊C4C2×D4312yes—
137C24—431no—
138C24—432no—
139C24—434no—
140C24—431no—
141C24—432no—
142C24—432no—
143C24—432no—
144C24—1724no—
145C24C22×D4311yescharacteristic
146C22×C4—22no—
147C22×C4—432no—
148C22×C4—868no—
149C22×C4—862no—
150C22×C4—862no—
151C22×C4—862no—
152C22×C4—1728no—
153C22×C4—1724no—
154C22×C4C4×D4312yescomplemented
155C22⋊C4—22no—
156C22⋊C4—22no—
157C22⋊C4—434no—
158C22⋊C4—868no—
159C22⋊C4—864no—
160C22⋊C4—862no—
161C22⋊C4—862no—
162C22⋊C4C4×D4314yescomplemented
163C23—42no—
164C23—431no—
165C23—432no—
166C23—434no—
167C23—432no—
168C23—431no—
169C23—432no—
170C23—434no—
171C23—432no—
172C23—434no—
173C23—434no—
174C23—432no—
175C23—864no—
176C23—868no—
177C23—1722no—
178C23—1724no—
179C23—1728no—
180C23—1724no—
181C23—1724no—
182C23C2×C4×D4311yescharacteristic
183C23C2×C4×D4312yes—
184C23D4×D4312yes—
185C23D4×D4311yescharacteristic
186C23Q8×D4311yescharacteristic
187C2×C4—24no—
188C2×C4—22no—
189C2×C4—44no—
190C2×C4—42no—
191C2×C4—864no—
192C2×C4—862no—
193C2×C4—1724no—
194C2×C4—17216no—
195C2×C4—1724no—
196C2×C4—1724no—
197C2×C4—1722no—
198C22—22no—
199C22—24no—
200C22—42no—
201C22—41no—
202C22—41no—
203C22—434no—
204C22—432no—
205C22—432no—
206C22—434no—
207C22—868no—
208C22—864no—
209C22—864no—
210C22—868no—
211C22—862no—
212C22—864no—
213C22—1724no—
214C22—1722no—
215C22—1722no—
216C22—1724no—
217C22C42×D4311yescharacteristic
218C22C22⋊C4×D4312yes—
219C22C22⋊C4×D4311yescharacteristic
220C22C4⋊C4×D4311yescharacteristic
221C22C4⋊C4×D4312yes—
222C4—44no—
223C4—42no—
224C4—1724no—
225C4—1722no—
226C2—22no—
227C2—21no—
228C2—21no—
229C2—22no—
230C2—434no—
231C2—864no—
232C2—862no—
233C2#95×D4311yescharacteristic
234C2#99×D4312yes—
subgroupG/H
centerC22C22⋊C4×D43
commutatorC22×C43C2×C42
FrattiniC24C22×D43
FittingC43×#342C2
socleC22×C43C2×C22⋊C4
hypercenter#342D43
hypocenterC43C2×#342
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #14582666C2semidirect
4. #14582665C2semidirect
5. C43×#342C2semidirect
8. C22×C4×D43C4semidirect
12. C2×(C2×D43)⋊C4C4semidirect
16. C22⋊C4×D43C4semidirect
29. C22×C4×C43C2×C4semidirect
31. C22×Dic43C2×C4semidirect
39. C22⋊C4×C43C2×C4semidirect
42. C22⋊Dic43C2×C4semidirect
117. D43#342direct (N × H)
122. #342D43direct (N × H)
123. C43C2×#342semidirect
154. C22×C4C4×D43semidirect
162. C22⋊C4C4×D43semidirect