Finite Group Databasebeta

← #19144967

Subgroups — #19144967

Order 5504.

484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#14583452C211yesmaximal, characteristic, complemented
2C2×#13063321C211yesmaximal, characteristic
3#14583262C214yesmaximal, complemented
4#14583244C214yesmaximal, complemented
5#14582905C211yesmaximal, characteristic, complemented
6#14582904C211yesmaximal, characteristic, complemented
7#14582903C211yesmaximal, characteristic, complemented
8M16×Dic43C211yesmaximal, characteristic, complemented
9C43×#418C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C22×C22⋊D43—22no—
12C2×#10621877C2211yescharacteristic
13#13063324C2212yescomplemented
14#13063321—22no—
15#13063321C2212yes—
16#13063321C2212yes—
17#13063316C2212yescomplemented
18#13063302—22no—
19C4×Dic86—22no—
20#13063284C2211yescharacteristic
21C2×C4×Dic43C2211yescharacteristic
22#13063247C2214yescomplemented
23#13063246C2214yescomplemented
24#13063245C2214yescomplemented
25#13063235C2212yescomplemented
26C8×Dic43C2212yescomplemented
27C22×D4×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic
29#117×C43C2211yescharacteristic
30#102×C43C2214yescomplemented
31C24×C43—21no—
32C23×D43—21no—
33C2×D4×C43—21no—
34C2×D4×C43—22no—
35C2×D4×C43—22no—
36C2×D4×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—24no—
39C2×C22⋊D43—24no—
40C2×C22⋊D43—48no—
41C22×Dic43D412yes—
42C2×D172—21no—
43C2×D172—22no—
44C2×D172—22no—
45C2×D172C2312yes—
46C2×Dic86—22no—
47M16×C43—22no—
48C2×C8×C43C2312yes—
49C4⋊C4×C43C2312yes—
50C22⋊C4×C43—21no—
51C42×C43—21no—
52C22⋊Dic43—21no—
53C4⋊Dic43—22no—
54C4⋊Dic43C2312yes—
55Dic43⋊C4—22no—
56Dic43⋊C4—22no—
57C4×Dic43—21no—
58C4×Dic43D412yes—
59C4×Dic43C2311yescharacteristic
60C4×Dic43C2311yescharacteristic
61#10621877—22no—
62C2×C43⋊C8C2312yes—
63C23×C43—22no—
64C23×C43—44no—
65C23×C43—42no—
66C23×C43C2×D411yescharacteristic
67C22×D43—22no—
68C22×D43—44no—
69C22×D43—42no—
70D4×C43—22no—
71D4×C43—22no—
72D4×C43—42no—
73C2×C4×C43—22no—
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43#4112yes—
76C2×C4×C43#4112yes—
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—48no—
79C22⋊D43—48no—
80C2×Dic43—24no—
81C2×Dic43—22no—
82C2×Dic43C2×D412yes—
83C2×Dic43C2×D412yes—
84D172—22no—
85D172—22no—
86D172—42no—
87Dic86—44no—
88C8×C43—22no—
89C43⋊C8—22no—
90C22×C43—22no—
91C22×C43—42no—
92C22×C43—44no—
93C22×C43—84no—
94C22×C43#12412yes—
95C22×C43C22×D411yescharacteristic
96C2×D43—42no—
97C2×D43—44no—
98C2×D43—84no—
99C4×C43—42no—
100C4×C43#12412yes—
101C4×C43C2×#4111yescharacteristic
102C4×C43C2×#4111yescharacteristic
103Dic43—22no—
104Dic43—42no—
105Dic43AGL(1,ℤ/8)14yes—
106#3138—431nomaximal, Sylow
107C2×C43—22no—
108C2×C43—82no—
109C2×C43C2×#12411yescharacteristic
110C2×C43C2×AGL(1,ℤ/8)12yes—
111D43—82no—
112#533—431no—
113C2×#127—431no—
114#490—434no—
115#486—434no—
116#418—431no—
117#418—431no—
118#418—431no—
119#418D4311yescharacteristic, complemented
120C4×M16—431no—
121C43#313811yescharacteristic, complemented, Sylow
122C22×D4—431no—
123C22×D4—862no—
124C22×D4C2×D4311yescharacteristic
125C2×M16—431no—
126C2×M16C2×D4311yescharacteristic
127C4⋊Q8—432no—
128#127—432no—
129#127—432no—
130#127—862no—
131#125—432no—
132C22⋊Q8—862no—
133C4×Q8—862no—
134#117—431no—
135#117C2×D4311yescharacteristic
136C2×C42—431no—
137#102—434no—
138#102—434no—
139#102—434no—
140#102C2×D4314yescomplemented
141#97—432no—
142C4×C8—432no—
143C24—21no—
144C24—861no—
145C2×Q8—862no—
146C2×D4—22no—
147C2×D4—21no—
148C2×D4—22no—
149C2×D4—432no—
150C2×D4—864no—
151C2×D4—864no—
152C2×D4—862no—
153C2×D4—861no—
154C2×D4—862no—
155C2×D4—1728no—
156C2×D4C22×D4312yes—
157C22×C4—432no—
158C22×C4C22×D4311yescharacteristic
159M16—22no—
160M16—862no—
161C2×C8—432no—
162C2×C8C22×D4312yes—
163C4⋊C4—432no—
164C4⋊C4—862no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4C22×D4312yes—
168C22⋊C4—21no—
169C22⋊C4—861no—
170C42—21no—
171C42—432no—
172C42—431no—
173C42—431no—
174C42—861no—
175C23—22no—
176C23—44no—
177C23—42no—
178C23—862no—
179C23—1724no—
180C23—1722no—
181C23D4×D4311yescharacteristic
182Q8—1724no—
183D4—22no—
184D4—22no—
185D4—42no—
186D4—862no—
187D4—862no—
188D4—1728no—
189D4—1728no—
190D4—1722no—
191C2×C4—22no—
192C2×C4—432no—
193C2×C4—432no—
194C2×C4—864no—
195C2×C4—862no—
196C2×C4#1062189812yes—
197C2×C4D4×D4311yescharacteristic
198C2×C4#1062190012yes—
199C2×C4C23×D4311yescharacteristic
200C8—22no—
201C8—862no—
202C22—22no—
203C22—42no—
204C22—44no—
205C22—84no—
206C22—3444no—
207C22—1722no—
208C22—1724no—
209C22#1306331112yes—
210C22C2×D4×D4311yescharacteristic
211C4—42no—
212C4—434no—
213C4—862no—
214C4—1722no—
215C4#1306331112yes—
216C4C2×#1062190011yescharacteristic
217C4C2×#1062189811yescharacteristic
218C2—22no—
219C2—82no—
220C2—3442no—
221C2C2×#1306331111yescharacteristic
222C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #14583452C2semidirect
3. #14583262C2semidirect
4. #14583244C2semidirect
5. #14582905C2semidirect
6. #14582904C2semidirect
7. #14582903C2semidirect
8. M16×Dic43C2semidirect
9. C43×#418C2semidirect
13. #13063324C22semidirect
17. #13063316C22semidirect
22. #13063247C22semidirect
23. #13063246C22semidirect
24. #13063245C22semidirect
25. #13063235C22semidirect
26. C8×Dic43C22semidirect
30. #102×C43C22semidirect
119. #418D43semidirect
121. C43#3138semidirect
140. #102C2×D43semidirect