Finite Group Databasebeta

← #19133121

Subgroups — #19133121

Order 5504.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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#14583433C211yesmaximal, characteristic
2C4×C4⋊Dic43C211yesmaximal, characteristic, complemented
3#14582637C212yesmaximal, complemented
4#14582634C212yesmaximal
5C43×#432C211yesmaximal, characteristic, complemented
6#13063319—21no—
7#13063317C411yescharacteristic, complemented
8#13063313C411yescharacteristic, complemented
9#13063308—21no—
10#13063304C2211yescharacteristic
11#13063299C2211yescharacteristic
12C4×Dic86C411yescharacteristic, complemented
13C4×D172C411yescharacteristic, complemented
14C4×C22⋊D43—21no—
15#13063282—21no—
16C2×C4⋊Dic43—21no—
17C2×C4×Dic43—21no—
18C43⋊#95C2212yes—
19C2×C42×C43C2211yescharacteristic
20C4⋊C8×C43—21no—
21C22⋊C8×C43C2212yes—
22#97×C43—21no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43D411yescharacteristic
25C22×C4×C43C2311yescharacteristic
26C2×C22⋊D43—21no—
27C22×Dic43—22no—
28C2×D172C2×C411yescharacteristic
29C2×C4×D43—21no—
30C2×Dic86C2×C411yescharacteristic
31C2×C8×C43—22no—
32C42×C43C2×C411yescharacteristic
33C42×C43C2×C411yescharacteristic
34C42×C43D411yescharacteristic
35C42×C43D411yescharacteristic
36C22⋊Dic43—21no—
37(C2×D43)⋊C4—21no—
38(C2×D43)⋊C4—21no—
39(C2×D43)⋊C4—21no—
40(C2×D43)⋊C4—21no—
41C4⋊Dic43—24no—
42C4⋊Dic43C2×C411yescharacteristic
43C4⋊Dic43C2×C411yescharacteristic
44Dic43⋊C4—21no—
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48C4×Dic43—21no—
49C4×Dic43—42no—
50C23×C43C2×D411yescharacteristic
51C22×D43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—22no—
55C2×C4×C43—41no—
56C2×C4×C43C22⋊C411yescharacteristic
57C2×C4×C43C22⋊C411yescharacteristic
58C2×C4×C43C22⋊C411yescharacteristic
59C2×C4×C43C22⋊C411yescharacteristic
60C2×C4×C43C22×C411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C22⋊D43—41no—
63C22⋊D43—41no—
64C2×Dic43—24no—
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—42no—
69C2×Dic43—42no—
70D172—41no—
71C4×D43—42no—
72Dic86—41no—
73C8×C43—42no—
74C22×C43—21no—
75C22×C43—21no—
76C22×C43C2×C22⋊C411yescharacteristic
77C22×C43AGL(1,ℤ/8)11yescharacteristic
78C22×C43#13711yescharacteristic
79C2×D43—41no—
80C2×D43—41no—
81C2×D43—41no—
82C4×C43—21no—
83C4×C43—21no—
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—21no—
87C4×C43#10412yes—
88Dic43—44no—
89Dic43—41no—
90Dic43—41no—
91Dic43—41no—
92#1509—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—21no—
95C2×C43#41011yescharacteristic
96C2×C43#41711yescharacteristic
97C2×C43C2×#10411yescharacteristic
98D43—81no—
99#529—431no—
100#432D4311yescharacteristic, complemented
101C4×C4⋊C4—431no—
102#328—432no—
103#327—432no—
104C43#150911yescharacteristic, complemented, Sylow
105#126—861no—
106#125—431no—
107#124—431no—
108#123—861no—
109C22⋊Q8—431no—
110#121—431no—
111C4×Q8—431no—
112C4×D4—431no—
113C4×D4—861no—
114#117—861no—
115C2×C4⋊C4—861no—
116C2×C42—861no—
117C2×C42C2×D4311yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C2×D4312yes—
120#97—21no—
121#95—432no—
122C2×Q8—431no—
123C2×D4—431no—
124C2×D4—861no—
125C22×C4—862no—
126C22×C4—861no—
127C22×C4D17211yescharacteristic
128C22×C4D17211yescharacteristic
129C22×C4C22×D4311yescharacteristic
130C2×C8—22no—
131C4⋊C4—431no—
132C4⋊C4—431no—
133C4⋊C4—864no—
134C4⋊C4—861no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C4⋊C4—861no—
138C22⋊C4—861no—
139C22⋊C4—861no—
140C22⋊C4—861no—
141C22⋊C4—861no—
142C22⋊C4—861no—
143C42—861no—
144C42—1722no—
145C42C4×D4311yescharacteristic
146C42C4×D4311yescharacteristic
147C42C22⋊D4311yescharacteristic
148C42C22⋊D4311yescharacteristic
149C23—861no—
150C23C2×D17211yescharacteristic
151Q8—1721no—
152D4—1721no—
153D4—1721no—
154D4—1721no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—864no—
160C2×C4—861no—
161C2×C4—861no—
162C2×C4—861no—
163C2×C4—1722no—
164C2×C4—1722no—
165C2×C4—1722no—
166C2×C4(C2×D43)⋊C411yescharacteristic
167C2×C4(C2×D43)⋊C411yescharacteristic
168C2×C4(C2×D43)⋊C411yescharacteristic
169C2×C4(C2×D43)⋊C411yescharacteristic
170C2×C4C2×C4×D4311yescharacteristic
171C2×C4C2×C22⋊D4311yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—1721no—
176C22—1721no—
177C22—1721no—
178C22C2×(C2×D43)⋊C411yescharacteristic
179C22#1306335311yescharacteristic
180C22#1306335811yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—1724no—
187C4—1721no—
188C4—1721no—
189C4—1721no—
190C4#1306325112yes—
191C2—21no—
192C2—21no—
193C2—3441no—
194C2#1458287211yescharacteristic
195C2#1458290111yescharacteristic
196C2C2×#1306325111yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#432C2
socleC22×C43C2×C22⋊C4
hypercenter#432D43
hypocenterC43#1509
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊Dic43C2semidirect
3. #14582637C2semidirect
5. C43×#432C2semidirect
7. #13063317C4semidirect
8. #13063313C4semidirect
12. C4×Dic86C4semidirect
13. C4×D172C4semidirect
100. #432D43semidirect
104. C43#1509semidirect