Finite Group Databasebeta

← #19133131

Subgroups — #19133131

Order 5504.

222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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
2#14582956C211yesmaximal, characteristic, complemented
3#14582635C212yesmaximal, complemented
4#14582632C212yesmaximal
5C43×#382C211yesmaximal, 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—
16C4⋊(C43⋊C8)—21no—
17C22⋊(C43⋊C8)C2212yes—
18#13063236—21no—
19C2×C4⋊C4×C43—21no—
20C2×C42×C43C2211yescharacteristic
21#95×C43—21no—
22#95×C43C2212yes—
23C22×C4×C43—22no—
24C22×C4×C43D411yescharacteristic
25C22×C4×C43D411yescharacteristic
26C22×C4×C43C2311yescharacteristic
27C2×C22⋊D43—21no—
28C2×D172C2×C411yescharacteristic
29C2×C4×D43—21no—
30C2×Dic86C2×C411yescharacteristic
31C4⋊C4×C43—42no—
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⋊Dic43C2×C411yescharacteristic
42C4⋊Dic43C2×C411yescharacteristic
43Dic43⋊C4—21no—
44Dic43⋊C4—21no—
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47C4×Dic43—21no—
48C2×C43⋊C8—22no—
49C23×C43C2×D411yescharacteristic
50C22×D43—21no—
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43—42no—
56C2×C4×C43—42no—
57C2×C4×C43—42no—
58C2×C4×C43C22⋊C411yescharacteristic
59C2×C4×C43C22⋊C411yescharacteristic
60C2×C4×C43C22⋊C411yescharacteristic
61C2×C4×C43C22⋊C411yescharacteristic
62C2×C4×C43C22×C411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C22⋊D43—41no—
65C22⋊D43—41no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69D172—41no—
70C4×D43—42no—
71Dic86—41no—
72C43⋊C8—42no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43C2×C22⋊C411yescharacteristic
76C22×C43AGL(1,ℤ/8)11yescharacteristic
77C22×C43#13711yescharacteristic
78C2×D43—41no—
79C2×D43—41no—
80C2×D43—41no—
81C4×C43—21no—
82C4×C43—21no—
83C4×C43—21no—
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—21no—
87C4×C43—82no—
88Dic43—41no—
89Dic43—41no—
90Dic43—41no—
91#1512—431nomaximal, Sylow
92C2×C43—21no—
93C2×C43—21no—
94C2×C43#41011yescharacteristic
95C2×C43#41711yescharacteristic
96C2×C43#42111yescharacteristic
97D43—81no—
98#529—431no—
99#432—431no—
100#382D4311yescharacteristic, complemented
101#328—432no—
102#327—432no—
103C43#151211yescharacteristic, complemented, Sylow
104#126—861no—
105#125—431no—
106#124—431no—
107#123—861no—
108C22⋊Q8—431no—
109#121—431no—
110C4×Q8—431no—
111C4×D4—431no—
112C4×D4—861no—
113#117—861no—
114C2×C4⋊C4—21no—
115C2×C42C2×D4311yescharacteristic
116C4⋊C8—861no—
117C22⋊C8—432no—
118#97—861no—
119#95—21no—
120#95C2×D4312yes—
121C2×Q8—431no—
122C2×D4—431no—
123C2×D4—861no—
124C22×C4—22no—
125C22×C4—861no—
126C22×C4C22⋊D4311yescharacteristic
127C22×C4C22⋊D4311yescharacteristic
128C22×C4C22×D4311yescharacteristic
129C2×C8—862no—
130C4⋊C4—42no—
131C4⋊C4—431no—
132C4⋊C4—431no—
133C4⋊C4—861no—
134C4⋊C4—861no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C22⋊C4—861no—
138C22⋊C4—861no—
139C22⋊C4—861no—
140C22⋊C4—861no—
141C22⋊C4—861no—
142C42—861no—
143C42C4×D4311yescharacteristic
144C42C4×D4311yescharacteristic
145C42D17211yescharacteristic
146C42D17211yescharacteristic
147C23—861no—
148C23C2×C22⋊D4311yescharacteristic
149Q8—1721no—
150D4—1721no—
151D4—1721no—
152D4—1721no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—861no—
161C2×C4—861no—
162C2×C4—861no—
163C2×C4—1722no—
164C2×C4(C2×D43)⋊C411yescharacteristic
165C2×C4(C2×D43)⋊C411yescharacteristic
166C2×C4(C2×D43)⋊C411yescharacteristic
167C2×C4(C2×D43)⋊C411yescharacteristic
168C2×C4C2×C4×D4311yescharacteristic
169C2×C4C2×D17211yescharacteristic
170C8—1722no—
171C22—21no—
172C22—21no—
173C22—1721no—
174C22—1721no—
175C22—1721no—
176C22C2×(C2×D43)⋊C411yescharacteristic
177C22#1306335111yescharacteristic
178C22#1306335611yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—82no—
186C4—1721no—
187C4—1721no—
188C4—1721no—
189C2—21no—
190C2—21no—
191C2—3441no—
192C2#1458287211yescharacteristic
193C2#1458289811yescharacteristic
194C2#1458291711yescharacteristic
subgroupG/H
centerC22C2×(C2×D43)⋊C4
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#382C2
socleC22×C43C2×C22⋊C4
hypercenter#382D43
hypocenterC43#1512
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #14582956C2semidirect
3. #14582635C2semidirect
5. C43×#382C2semidirect
7. #13063317C4semidirect
8. #13063313C4semidirect
12. C4×Dic86C4semidirect
13. C4×D172C4semidirect
100. #382D43semidirect
103. C43#1512semidirect