Finite Group Databasebeta

← #19140939

Subgroups — #19140939

Order 5504.

568 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063310C212yesmaximal
2C2×#13063301C212yesmaximal, complemented
3#14582832C212yesmaximal, complemented
4#14582828C212yesmaximal, complemented
5#14582816C211yesmaximal, characteristic
6#14582791C212yesmaximal, complemented
7#14582773C212yesmaximal, complemented
8#14582768C211yesmaximal, characteristic, complemented
9C43×#395C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C22×C4×D43C2212yes—
12#13063310—28no—
13#13063301—28no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×(C2×D43)⋊C4C2212yes—
20C2×(C2×D43)⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×(C2×D43)⋊C4C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2211yescharacteristic
27C43⋊#95C2212yes—
28C22×Q8×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2212yes—
30C2×C4⋊C4×C43C2211yescharacteristic
31#95×C43C2212yes—
32#95×C43C2211yescharacteristic
33C23×D43C2312yes—
34C2×Q8×C43—24no—
35C2×Q8×C43—41no—
36C22×C4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C2×D172—24no—
45C2×D172—41no—
46C2×C4×D43—24no—
47C2×C4×D43—24no—
48C2×C4×D43—42no—
49C4⋊C4×C43—24no—
50C4⋊C4×C43—41no—
51(C2×D43)⋊C4—24no—
52(C2×D43)⋊C4—24no—
53(C2×D43)⋊C4—24no—
54(C2×D43)⋊C4—24no—
55(C2×D43)⋊C4D418yes—
56C4⋊Dic43—24no—
57C4⋊Dic43—41no—
58Dic43⋊C4—24no—
59Dic43⋊C4—24no—
60Dic43⋊C4—24no—
61C4×Dic43—22no—
62C23×C43C2411yescharacteristic
63C22×D43—22no—
64C22×D43—22no—
65C22×D43—22no—
66C22×D43—22no—
67C22×D43—22no—
68C22×D43—22no—
69C22×D43C2×D414yes—
70Q8×C43—44no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—22no—
74C2×C4×C43—21no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43C2×D414yes—
83C2×C4×C43#4112yes—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43C2×D414yes—
93D172—44no—
94C4×D43—48no—
95C22×C43C22×D412yes—
96C22×C43C2×#4111yescharacteristic
97C22×C43H(5,𝔽2)11yescharacteristic
98C22×C432−1+411yescharacteristic
99C22×C432−1+412yes—
100C2×D43—24no—
101C2×D43—24no—
102C2×D43—24no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C4×C43—22no—
108C4×C43—24no—
109C4×C43—42no—
110C4×C43—41no—
111C4×C43—41no—
112Dic43—24no—
113Dic43—42no—
114Dic43—42no—
115#2680—431nomaximal, Sylow
116C2×C43#53612yes—
117C2×C43#53911yescharacteristic
118C2×C43D4211yescharacteristic
119C2×C43#54712yes—
120C2×C43#56311yescharacteristic
121D43—44no—
122C2×#123—432no—
123C2×C22⋊Q8—432no—
124#398—432no—
125#397—432no—
126#395D4311yescharacteristic, complemented
127#394—431no—
128#388—432no—
129#385—432no—
130#384—431no—
131C43#268011yescharacteristic, complemented, Sylow
132C22×Q8C2×D4311yescharacteristic
133C22×D4—431no—
134C23×C4—432no—
135#123—868no—
136C22⋊Q8—868no—
137C2×C4⋊C4—432no—
138C2×C4⋊C4—432no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—431no—
142C2×C4⋊C4C2×D4312yes—
143C2×C4⋊C4C2×D4311yescharacteristic
144C2×C22⋊C4—432no—
145C2×C22⋊C4—432no—
146C2×C22⋊C4—432no—
147C2×C22⋊C4—432no—
148C2×C22⋊C4—432no—
149C2×C42—431no—
150#95—432no—
151#95—432no—
152#95—431no—
153#95C2×D4312yes—
154#95C2×D4311yescharacteristic
155C24—432no—
156C2×Q8—24no—
157C2×Q8—41no—
158C2×D4—864no—
159C2×D4—1721no—
160C22×C4—432no—
161C22×C4—432no—
162C22×C4—432no—
163C22×C4—864no—
164C22×C4—864no—
165C22×C4—1722no—
166C22×C4C22×D4312yes—
167C22×C4C22×D4311yescharacteristic
168C22×C4C22×D4311yescharacteristic
169C22×C4C22×D4312yes—
170C22×C4C22×D4311yescharacteristic
171C4⋊C4—24no—
172C4⋊C4—41no—
173C4⋊C4—864no—
174C4⋊C4—864no—
175C4⋊C4—864no—
176C4⋊C4—864no—
177C4⋊C4—1721no—
178C22⋊C4—438no—
179C22⋊C4—864no—
180C22⋊C4—864no—
181C22⋊C4—864no—
182C22⋊C4—864no—
183C42—862no—
184C23—434no—
185C23—862no—
186C23—862no—
187C23—862no—
188C23—862no—
189C23—862no—
190C23—862no—
191C23C23×D4311yescharacteristic
192Q8—44no—
193D4—1724no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—434no—
206C2×C4—862no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—1728no—
215C2×C4D4×D4314yes—
216C2×C4#1062190212yes—
217C22—864no—
218C22—864no—
219C22—864no—
220C22—1722no—
221C22—1722no—
222C22—1722no—
223C22—1722no—
224C22C2×D4×D4312yes—
225C22C2×#1062190211yescharacteristic
226C22#1306337011yescharacteristic
227C22#1306337211yescharacteristic
228C22#1306337312yes—
229C4—22no—
230C4—24no—
231C4—42no—
232C4—41no—
233C4—41no—
234C4—864no—
235C4—1722no—
236C4—1722no—
237C2—1724no—
238C2#1458347212yes—
239C2#1458349811yescharacteristic
240C2#1458353111yescharacteristic
241C2#1458355212yes—
242C2#1458364811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2680
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#13063301C2semidirect
3. #14582832C2semidirect
4. #14582828C2semidirect
6. #14582791C2semidirect
7. #14582773C2semidirect
8. #14582768C2semidirect
9. C43×#395C2semidirect
126. #395D43semidirect
131. C43#2680semidirect