Finite Group Databasebeta

← #19145600

Subgroups — #19145600

Order 5504.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583456C211yesmaximal, characteristic, complemented
2C2×#13063313C211yesmaximal, characteristic
3#14583293C212yesmaximal, complemented
4#14583259C212yesmaximal, complemented
5#14583122C214yesmaximal, complemented
6#14583057C212yesmaximal, complemented
7#14583052C212yesmaximal
8C43×#432C211yesmaximal, characteristic, complemented
9C22×Dic86C2211yescharacteristic
10C22×D172C2211yescharacteristic
11C2×Dic172C2214yescomplemented
12C2×#10621873C2214yes—
13#13063325C2211yescharacteristic, complemented
14#13063325C2211yescharacteristic, complemented
15#13063317—21no—
16#13063313—21no—
17#13063313—21no—
18#13063313C2212yes—
19#13063313C2212yes—
20#13063304—21no—
21#13063304C2212yes—
22C4×Dic86—21no—
23C4×Dic86C2212yescomplemented
24#13063284—21no—
25C2×(C2×D43)⋊C4—21no—
26C2×(C2×D43)⋊C4—21no—
27#13063250C2214yescomplemented
28#13063247C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yescomplemented
31C22⋊C8×C43C2212yes—
32#97×C43C2212yescomplemented
33C23×D43—21no—
34C22×C4×C43D411yescharacteristic
35C22×C4×C43D411yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×Dic43—21no—
38C2×D172—21no—
39C2×D172—42no—
40C2×D172C2312yes—
41C2×Dic86—21no—
42C2×Dic86—21no—
43C2×Dic86—42no—
44C2×Dic86C2312yes—
45C2×Dic86C2312yes—
46C2×C8×C43C2314yes—
47C42×C43D411yescharacteristic
48C42×C43D411yescharacteristic
49C42×C43C2311yescharacteristic
50C42×C43C2311yescharacteristic
51C22⋊Dic43—22no—
52(C2×D43)⋊C4—22no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56C4⋊Dic43—21no—
57C4⋊Dic43—21no—
58C4⋊Dic43—21no—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63Dic172—44no—
64#10621873—44no—
65C23×C43C2×D411yescharacteristic
66C22×D43—22no—
67C22×D43—42no—
68C22×D43—42no—
69C22×D43—42no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—41no—
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2411yescharacteristic
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—42no—
83D172—24no—
84D172—42no—
85Dic86—24no—
86Dic86—24no—
87Dic86—42no—
88Dic86—42no—
89C8×C43—24no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#13712yes—
93C22×C43C22×D411yescharacteristic
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C2×D43—84no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43H(5,𝔽2)12yes—
104Dic43—42no—
105Dic43—42no—
106Dic43—42no—
107#3215—431nomaximal, Sylow
108C2×C43—22no—
109C2×C43#53511yescharacteristic
110C2×C43C2×#13711yescharacteristic
111C2×C43#57511yescharacteristic
112D43—82no—
113#533—431no—
114C2×#124—431no—
115#497—432no—
116#489—432no—
117#464—434no—
118#451—432no—
119#450—432no—
120#432D4311yescharacteristic, complemented
121C43#321511yescharacteristic, complemented, Sylow
122C22×Q8—431no—
123C22×D4—431no—
124C2×Q16—434no—
125C2×SD16—434no—
126C4⋊Q8—431no—
127C4⋊Q8—431no—
128#125—861no—
129#124—432no—
130#124—432no—
131#124—861no—
132#124—861no—
133C22⋊Q8—432no—
134C22⋊Q8—861no—
135C4×Q8—432no—
136C4×Q8—861no—
137#117—861no—
138C2×C22⋊C4—861no—
139C2×C22⋊C4—861no—
140C2×C42C2×D4311yescharacteristic
141C4⋊C8C2×D4312yescomplemented
142#103—434no—
143#102—434no—
144C22⋊C8C2×D4312yes—
145#97C2×D4312yescomplemented
146C24—861no—
147C2×Q8—432no—
148C2×Q8—432no—
149C2×Q8—861no—
150C2×Q8—861no—
151C2×Q8—1722no—
152C2×D4—432no—
153C2×D4—861no—
154C2×D4—1722no—
155C22×C4—861no—
156C22×C4D17211yescharacteristic
157C22×C4D17211yescharacteristic
158C22×C4C22×D4311yescharacteristic
159Q16—1724no—
160SD16—1724no—
161C2×C8C22×D4314yes—
162C4⋊C4—432no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—861no—
168C22⋊C4—862no—
169C22⋊C4—862no—
170C22⋊C4—862no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C42—862no—
174C42D17211yescharacteristic
175C42D17211yescharacteristic
176C42C22×D4311yescharacteristic
177C42C22×D4311yescharacteristic
178C23—862no—
179C23—1722no—
180C23—1722no—
181C23—1722no—
182C23C2×D17211yescharacteristic
183Q8—864no—
184Q8—864no—
185Q8—1722no—
186Q8—1722no—
187D4—864no—
188D4—1722no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—1722no—
196C2×C4C2×D17211yescharacteristic
197C2×C4C2×D17211yescharacteristic
198C2×C4C2×D17211yescharacteristic
199C2×C4C2×D17211yescharacteristic
200C2×C4C2×D17211yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—3444no—
206C22—1722no—
207C22—1722no—
208C22—1722no—
209C22#1306335812yes—
210C22C22×D17211yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—1722no—
217C4—1722no—
218C4—1722no—
219C4#1306337112yes—
220C2—22no—
221C2—3442no—
222C2#1458346811yescharacteristic
223C2C2×#1306335811yescharacteristic
224C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3215
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #14583456C2semidirect
3. #14583293C2semidirect
4. #14583259C2semidirect
5. #14583122C2semidirect
6. #14583057C2semidirect
8. C43×#432C2semidirect
11. C2×Dic172C22semidirect
13. #13063325C22semidirect
14. #13063325C22semidirect
23. C4×Dic86C22semidirect
27. #13063250C22semidirect
30. C4⋊C8×C43C22semidirect
32. #97×C43C22semidirect
120. #432D43semidirect
121. C43#3215semidirect
141. C4⋊C8C2×D43semidirect
145. #97C2×D43semidirect