Finite Group Databasebeta

← #19144528

Subgroups — #19144528

Order 5504.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#14583410C211yesmaximal, characteristic
2C2×#13063284C211yesmaximal, characteristic, complemented
3#14583241C214yesmaximal, complemented
4#14583224C214yesmaximal, complemented
5#14582941C212yesmaximal, complemented
6#14582901C212yesmaximal, complemented
7C43×#407C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063308—21no—
10#13063304C2212yes—
11#13063299C2212yes—
12#13063294—21no—
13C4×C22⋊D43—22no—
14#13063284—22no—
15#13063284C2214yes—
16#13063284C2211yescharacteristic
17C2×C4⋊Dic43C2212yes—
18C2×C22⋊Dic43—21no—
19C2×C4×Dic43—21no—
20#13063259C2214yescomplemented
21#13063257C2214yescomplemented
22#13063250C2214yescomplemented
23#13063247C2214yescomplemented
24C23×C4×C43C2211yescharacteristic
25C2×M16×C43C2212yes—
26C22⋊C8×C43C2214yes—
27C24×C43D411yescharacteristic
28C22×C4×C43—24no—
29C22×C4×C43D411yescharacteristic
30C22×C4×C43D412yes—
31C22×C4×C43C2312yes—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—22no—
34C2×C22⋊D43—21no—
35C22×Dic43—22no—
36#10621898—24no—
37C2×D172C2311yescharacteristic
38C2×C4×D43—21no—
39C2×Dic86C2311yescharacteristic
40M16×C43—24no—
41C2×C8×C43C2314yes—
42C22⋊Dic43—24no—
43C22⋊Dic43—21no—
44C22⋊Dic43—22no—
45(C2×D43)⋊C4—22no—
46C4⋊Dic43—22no—
47C4⋊Dic43C2314yes—
48C4⋊Dic43C2312yes—
49Dic43⋊C4—22no—
50C4×Dic43—24no—
51C4×Dic43—21no—
52C23×C43—22no—
53C23×C43—42no—
54C23×C43C2×D412yes—
55C23×C43C2×D411yescharacteristic
56C22×D43—21no—
57C2×C4×C43—22no—
58C2×C4×C43—24no—
59C2×C4×C43—24no—
60C2×C4×C43C2×D412yes—
61C2×C4×C43C2×D411yescharacteristic
62C2×C4×C43#4114yes—
63C2×C4×C43C2411yescharacteristic
64C22⋊D43—44no—
65C22⋊D43—42no—
66C2×Dic43—24no—
67C2×Dic43—22no—
68C2×Dic43—21no—
69C2×Dic43—44no—
70D172—22no—
71C4×D43—42no—
72Dic86—22no—
73C8×C43—24no—
74C22×C43—22no—
75C22×C43—22no—
76C22×C43—22no—
77C22×C43—22no—
78C22×C43—44no—
79C22×C43#12312yes—
80C22×C43C22×D411yescharacteristic
81C2×D43—41no—
82C2×D43—42no—
83C4×C43—22no—
84C4×C43#12312yes—
85C4×C43C2×#4112yes—
86Dic43—41no—
87Dic43—44no—
88Dic43—42no—
89#3093—431nomaximal, Sylow
90C2×C43—22no—
91C2×C43—42no—
92C2×C43C2×#12311yescharacteristic
93C2×C43#57512yes—
94D43—81no—
95#525—431no—
96C2×#117—431no—
97#485—434no—
98#482—434no—
99#428—432no—
100#417—432no—
101#407D4311yescharacteristic, complemented
102C43#309311yescharacteristic, complemented, Sylow
103C2×#41—431no—
104C23×C4C2×D4311yescharacteristic
105C2×M16C2×D4312yes—
106#123—861no—
107C22⋊Q8—432no—
108#121—432no—
109#120—861no—
110C4×D4—862no—
111#117—434no—
112#117—431no—
113#117—862no—
114C2×C4⋊C4—432no—
115C2×C22⋊C4—861no—
116C2×C42—861no—
117#107—434no—
118#106—434no—
119#103—434no—
120#102—434no—
121C22⋊C8C2×D4314yes—
122C24D17211yescharacteristic
123#41—864no—
124C2×Q8—431no—
125C2×D4—431no—
126C2×D4—862no—
127C2×D4—861no—
128C22×C4—24no—
129C22×C4—862no—
130C22×C4—861no—
131C22×C4D17211yescharacteristic
132C22×C4D17212yes—
133C22×C4C22×D4312yes—
134C22×C4C22×D4311yescharacteristic
135M16—24no—
136C2×C8C22×D4314yes—
137C4⋊C4—434no—
138C4⋊C4—432no—
139C4⋊C4—862no—
140C4⋊C4—862no—
141C22⋊C4—864no—
142C22⋊C4—861no—
143C22⋊C4—862no—
144C22⋊C4—862no—
145C42—864no—
146C42—861no—
147C23—22no—
148C23—42no—
149C23—861no—
150C23C2×D17212yes—
151C23C2×D17211yescharacteristic
152Q8—862no—
153D4—862no—
154D4—1724no—
155D4—1722no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—864no—
160C2×C4—862no—
161C2×C4—861no—
162C2×C4—1724no—
163C2×C4—1722no—
164C2×C4C2×D17212yes—
165C2×C4C2×D17211yescharacteristic
166C2×C4#1062190014yes—
167C2×C4C23×D4311yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—1721no—
175C22—1722no—
176C22#1306330912yes—
177C22C22×D17211yescharacteristic
178C4—22no—
179C4—1721no—
180C4—1724no—
181C4—1722no—
182C4#1306330912yes—
183C4C2×#1062190012yes—
184C2—22no—
185C2—42no—
186C2—3441no—
187C2C2×#1306330911yescharacteristic
188C2#1458369912yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#407C2
socleC22×C43C22×D4
hypercenter#407D43
hypocenterC43#3093
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
2. C2×#13063284C2semidirect
3. #14583241C2semidirect
4. #14583224C2semidirect
5. #14582941C2semidirect
6. #14582901C2semidirect
7. C43×#407C2semidirect
20. #13063259C22semidirect
21. #13063257C22semidirect
22. #13063250C22semidirect
23. #13063247C22semidirect
101. #407D43semidirect
102. C43#3093semidirect