Finite Group Databasebeta

← #19143832

Subgroups — #19143832

Order 5504.

738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C23×Dic86C211yesmaximal, characteristic, complemented
2C2×#13063358C212yesmaximal, complemented
3#14583410C211yesmaximal, characteristic
4#14583057C214yesmaximal, complemented
5#14583040C214yesmaximal, complemented
6#14582909C212yesmaximal, complemented
7C43×#407C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×Dic86—22no—
10C22×Dic86—21no—
11C22×Dic86—28no—
12C22×Dic86C2214yes—
13C22×Dic86C2212yes—
14C23×Dic43—21no—
15#13063358—28no—
16C2×Dic172C2214yescomplemented
17C2×#10621873C2214yescomplemented
18#13063308—21no—
19#13063304C2212yes—
20#13063299C2212yes—
21#13063294—21no—
22C4×C22⋊D43—22no—
23#13063284C2211yescharacteristic
24#13063250C2218yescomplemented
25C23×C4×C43C2211yescharacteristic
26C2×M16×C43C2212yes—
27C22⋊C8×C43C2214yes—
28C24×C43D411yescharacteristic
29C22×C4×C43—24no—
30C22×C4×C43D412yes—
31C22×C4×C43D411yescharacteristic
32C22×C4×C43C2312yes—
33C22×C4×C43C2311yescharacteristic
34C2×C22⋊D43—22no—
35C2×C22⋊D43—21no—
36C22×Dic43—28no—
37C22×Dic43—22no—
38C22×Dic43—24no—
39#10621898—24no—
40C2×D172C2311yescharacteristic
41C2×C4×D43—21no—
42C2×Dic86—28no—
43C2×Dic86—216no—
44C2×Dic86—24no—
45C2×Dic86—22no—
46C2×Dic86—24no—
47C2×Dic86—216no—
48C2×Dic86D418yescomplemented
49C2×Dic86C2311yescharacteristic
50C2×Dic86C2314yes—
51M16×C43—24no—
52C2×C8×C43C2314yes—
53C22⋊Dic43—21no—
54C22⋊Dic43—22no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43C2312yes—
57Dic43⋊C4—22no—
58C4×Dic43—21no—
59Dic172—28no—
60#10621873—28no—
61C23×C43—22no—
62C23×C43—24no—
63C23×C43C2×D411yescharacteristic
64C23×C43C2×D412yes—
65C22×D43—21no—
66C2×C4×C43—22no—
67C2×C4×C43—24no—
68C2×C4×C43—24no—
69C2×C4×C43C2×D412yes—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×D414yes—
72C2×C4×C43C2411yescharacteristic
73C22⋊D43—42no—
74C22⋊D43—44no—
75C2×Dic43—216no—
76C2×Dic43—28no—
77C2×Dic43—24no—
78C2×Dic43—22no—
79C2×Dic43—21no—
80D172—22no—
81C4×D43—42no—
82Dic86—216no—
83Dic86—28no—
84Dic86—24no—
85Dic86—22no—
86Dic86C2×D418yes—
87C8×C43—24no—
88C22×C43—28no—
89C22×C43—22no—
90C22×C43—22no—
91C22×C43—22no—
92C22×C43#12012yes—
93C22×C43#13714yescomplemented
94C22×C43C22×D411yescharacteristic
95C2×D43—41no—
96C2×D43—42no—
97C4×C43—22no—
98C4×C43#12012yes—
99C4×C43C22×D412yes—
100Dic43—28no—
101Dic43—41no—
102Dic43—42no—
103#3004—431nomaximal, Sylow
104C2×C43—22no—
105C2×C43—24no—
106C2×C43C2×#12011yescharacteristic
107C2×C43C2×#13712yes—
108D43—81no—
109C23×Q8—431no—
110C2×#137—432no—
111#525—431no—
112#451—434no—
113#448—434no—
114#419—432no—
115#407D4311yescharacteristic, complemented
116C43#300411yescharacteristic, complemented, Sylow
117C2×#41—431no—
118C22×Q8—432no—
119C22×Q8—434no—
120C22×Q8—868no—
121C22×Q8—862no—
122C22×Q8—861no—
123C23×C4—861no—
124C23×C4C2×D4311yescharacteristic
125#137—868no—
126C2×Q16—434no—
127C2×SD16—434no—
128C2×M16C2×D4312yes—
129#123—861no—
130C22⋊Q8—432no—
131#121—432no—
132#120—861no—
133C4×D4—862no—
134#117—431no—
135#103—438no—
136C22⋊C8C2×D4314yes—
137C24D17211yescharacteristic
138#41—864no—
139C2×Q8—438no—
140C2×Q8—434no—
141C2×Q8—431no—
142C2×Q8—8616no—
143C2×Q8—868no—
144C2×Q8—8616no—
145C2×Q8—864no—
146C2×Q8—862no—
147C2×Q8—864no—
148C2×D4—431no—
149C2×D4—862no—
150C2×D4—861no—
151C22×C4—24no—
152C22×C4—868no—
153C22×C4—864no—
154C22×C4—862no—
155C22×C4—861no—
156C22×C4D17212yes—
157C22×C4D17211yescharacteristic
158C22×C4C22×D4312yes—
159C22×C4C22×D4311yescharacteristic
160Q16—868no—
161SD16—868no—
162M16—24no—
163C2×C8C22×D4314yes—
164C4⋊C4—432no—
165C4⋊C4—862no—
166C22⋊C4—861no—
167C22⋊C4—862no—
168C22⋊C4—862no—
169C42—861no—
170C23—22no—
171C23—24no—
172C23—861no—
173C23C2×D17211yescharacteristic
174C23C2×D17212yes—
175Q8—438no—
176Q8—8616no—
177Q8—868no—
178Q8—864no—
179Q8—862no—
180D4—862no—
181D4—1722no—
182D4—1724no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—8616no—
187C2×C4—868no—
188C2×C4—864no—
189C2×C4—862no—
190C2×C4—861no—
191C2×C4—1722no—
192C2×C4C2×D17212yes—
193C2×C4C2×D17211yescharacteristic
194C2×C4D4×D4314yes—
195C2×C4C23×D4311yescharacteristic
196C8—24no—
197C22—28no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—1721no—
202C22—1722no—
203C22#1306329512yes—
204C22#1306335814yescomplemented
205C22C22×D17211yescharacteristic
206C4—22no—
207C4—868no—
208C4—1721no—
209C4—1722no—
210C4#1306329512yes—
211C4C2×D4×D4312yes—
212C2—22no—
213C2—24no—
214C2—3441no—
215C2C2×#1306329511yescharacteristic
216C2C2×#1306335812yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3004
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C23×Dic86C2semidirect
2. C2×#13063358C2semidirect
4. #14583057C2semidirect
5. #14583040C2semidirect
6. #14582909C2semidirect
7. C43×#407C2semidirect
16. C2×Dic172C22semidirect
17. C2×#10621873C22semidirect
24. #13063250C22semidirect
48. C2×Dic86D4semidirect
93. C22×C43#137semidirect
115. #407D43semidirect
116. C43#3004semidirect
204. C22#13063358semidirect