Finite Group Databasebeta

← #19132920

Subgroups — #19132920

Order 5504.

440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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
2#14582861C212yesmaximal, complemented
3#14582623C211yesmaximal, characteristic, complemented
4#14582622C212yesmaximal, complemented
5C43×#323C211yesmaximal, characteristic, complemented
6C24×D43C411yescharacteristic
7C22×C4×D43C411yescharacteristic
8C22×C4×D43C2211yescharacteristic
9C2×#10621872—22no—
10C2×C22⋊Dic43C411yescharacteristic
11C2×(C2×D43)⋊C4C411yescharacteristic
12C2×(C2×D43)⋊C4C2211yescharacteristic
13C22⋊C4×D43—22no—
14C22⋊C4×D43—22no—
15C22⋊(C43⋊C8)C2212yescomplemented
16(C2×D43)⋊C8—22no—
17C2×C22⋊C4×C43C2211yescharacteristic
18C22⋊C8×C43C2212yescomplemented
19C24×C43C2×C411yescharacteristic
20C23×D43—22no—
21C23×D43—21no—
22C23×D43—21no—
23C23×D43—22no—
24C23×D43—42no—
25C23×D43—42no—
26C23×D43C2×C411yescharacteristic
27C23×D43C2×C411yescharacteristic
28C22×C4×C43C2×C411yescharacteristic
29C22×C4×C43C2311yescharacteristic
30C22×Dic43C2×C411yescharacteristic
31C22×Dic43C2×C411yescharacteristic
32C2×C4×D43—21no—
33C2×C4×D43—21no—
34C2×C4×D43—42no—
35C2×C4×D43—42no—
36C2×C4×D43D412yes—
37C2×C4×D43D412yes—
38C2×C8×C43—22no—
39C22⋊C4×C43—22no—
40C22⋊Dic43—22no—
41(C2×D43)⋊C4—22no—
42(C2×D43)⋊C4—22no—
43C2×C43⋊C8—22no—
44#10621872—44no—
45C23×C43—21no—
46C23×C43—21no—
47C23×C43—41no—
48C23×C43—41no—
49C23×C43M1612yescomplemented
50C23×C43C22×C411yescharacteristic
51C22×D43—21no—
52C22×D43—21no—
53C22×D43—22no—
54C22×D43—22no—
55C22×D43—24no—
56C22×D43—24no—
57C22×D43—21no—
58C22×D43—21no—
59C22×D43—48no—
60C22×D43—48no—
61C22×D43—42no—
62C22×D43—42no—
63C22×D43—42no—
64C22×D43—42no—
65C22×D43—41no—
66C22×D43—41no—
67C22×D43C22⋊C411yescharacteristic
68C22×D43C22⋊C411yescharacteristic
69C22×D43M1612yescomplemented
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43—41no—
73C2×C4×C43C2×D412yes—
74C2×Dic43—21no—
75C2×Dic43—41no—
76C2×Dic43—41no—
77C2×Dic43C22⋊C412yes—
78C4×D43—24no—
79C4×D43—42no—
80C4×D43—42no—
81C4×D43—42no—
82C8×C43—42no—
83C43⋊C8—42no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—22no—
87C22×C43—42no—
88C22×C43—42no—
89C22×C43—41no—
90C22×C43—41no—
91C22×C43C2×C22⋊C411yescharacteristic
92C22×C43C2×M1611yescharacteristic
93C22×C43C2×M1611yescharacteristic
94C2×D43—24no—
95C2×D43—24no—
96C2×D43—21no—
97C2×D43—21no—
98C2×D43—21no—
99C2×D43—21no—
100C2×D43—22no—
101C2×D43—48no—
102C2×D43—48no—
103C2×D43—42no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C2×D43#9912yes—
108C2×D43#10012yes—
109C4×C43—22no—
110C4×C43—41no—
111Dic43—22no—
112Dic43—41no—
113#1462—431nomaximal, Sylow
114C2×C43—21no—
115C2×C43—21no—
116C2×C43—42no—
117C2×C43#40711yescharacteristic
118C2×C43C2×#9911yescharacteristic
119C2×C43C2×#10011yescharacteristic
120D43—22no—
121D43—22no—
122D43—42no—
123C22×C22⋊C4—431no—
124#407—432no—
125#323—431no—
126#323—432no—
127#323D4311yescharacteristic, complemented
128C43#146211yescharacteristic, complemented, Sylow
129C25—431no—
130C23×C4—431no—
131C23×C4—431no—
132C2×M16—862no—
133C2×C22⋊C4—431no—
134C2×C22⋊C4—431no—
135C2×C22⋊C4—431no—
136C2×C22⋊C4—862no—
137C2×C22⋊C4—862no—
138C2×C22⋊C4C2×D4311yescharacteristic
139C22⋊C8—432no—
140C22⋊C8—862no—
141C22⋊C8C2×D4312yescomplemented
142C24—431no—
143C24—431no—
144C24—861no—
145C24—861no—
146C24—862no—
147C24—862no—
148C24—1722no—
149C24—1722no—
150C24C4×D4311yescharacteristic
151C22×C4—431no—
152C22×C4—432no—
153C22×C4—432no—
154C22×C4—431no—
155C22×C4—861no—
156C22×C4—861no—
157C22×C4—1722no—
158C22×C4—1722no—
159C22×C4C4×D4311yescharacteristic
160C22×C4C22×D4311yescharacteristic
161M16—1724no—
162C2×C8—22no—
163C2×C8—862no—
164C22⋊C4—22no—
165C22⋊C4—862no—
166C22⋊C4—862no—
167C22⋊C4—862no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—431no—
173C23—431no—
174C23—432no—
175C23—862no—
176C23—862no—
177C23—864no—
178C23—864no—
179C23—861no—
180C23—861no—
181C23—861no—
182C23—861no—
183C23—1721no—
184C23—1721no—
185C23—1722no—
186C23—1722no—
187C23—1728no—
188C23—1728no—
189C23—1722no—
190C23—1722no—
191C23#1062187212yescomplemented
192C23C2×C4×D4311yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—432no—
197C2×C4—864no—
198C2×C4—861no—
199C2×C4—1722no—
200C2×C4—1722no—
201C2×C4—1722no—
202C2×C4—1721no—
203C2×C4—1721no—
204C2×C4D4×D4312yes—
205C8—42no—
206C8—1722no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—432no—
215C22—432no—
216C22—864no—
217C22—864no—
218C22—861no—
219C22—861no—
220C22—861no—
221C22—861no—
222C22—862no—
223C22—1722no—
224C22—1722no—
225C22—1728no—
226C22—1728no—
227C22—1721no—
228C22—1721no—
229C22C22⋊C4×D4311yescharacteristic
230C22M16×D4311yescharacteristic
231C22C2×#1062187211yescharacteristic
232C4—22no—
233C4—41no—
234C4—862no—
235C4—1721no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—862no—
240C2—862no—
241C2—1722no—
242C2#1458286111yescharacteristic
243C2#99×D4311yescharacteristic
244C2#100×D4311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#323C2
socleC22×C43C2×C22⋊C4
hypercenter#323D43
hypocenterC43#1462
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14582861C2semidirect
3. #14582623C2semidirect
4. #14582622C2semidirect
5. C43×#323C2semidirect
15. C22⋊(C43⋊C8)C22semidirect
18. C22⋊C8×C43C22semidirect
49. C23×C43M16semidirect
69. C22×D43M16semidirect
127. #323D43semidirect
128. C43#1462semidirect
141. C22⋊C8C2×D43semidirect
191. C23#10621872semidirect