Finite Group Databasebeta

← #19145592

Subgroups — #19145592

Order 5504.

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

normal subgroups only

This group has 434 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#14583449C211yesmaximal, characteristic, complemented
2#14583449C211yesmaximal, characteristic, complemented
3#14583288C212yesmaximal, complemented
4#14583259C212yesmaximal, complemented
5#14583105C212yesmaximal, complemented
6#14583095C212yesmaximal, complemented
7#14583046C214yesmaximal, complemented
8C43×#432C211yesmaximal, characteristic, complemented
9C2×#10621898—21no—
10C2×#10621898C2212yes—
11C2×#10621873C2214yes—
12C2×D344C2214yes—
13#13063325C2211yescharacteristic
14#13063325C2211yescharacteristic
15#13063322C2211yescharacteristic
16#13063322C2211yescharacteristic
17#13063313—21no—
18#13063313C2212yes—
19#13063299—21no—
20#13063299—21no—
21#13063299—21no—
22#13063299C2212yes—
23C4×D172—21no—
24C4×D172—21no—
25C4×D172—21no—
26C4×D172C2212yes—
27#13063250C2214yes—
28#13063247C2214yes—
29C2×C42×C43C2211yescharacteristic
30C4⋊C8×C43C2212yes—
31C22⋊C8×C43C2212yes—
32#97×C43C2212yes—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43D411yescharacteristic
35C22×C4×C43C2311yescharacteristic
36C2×C22⋊D43—22no—
37C2×C22⋊D43—22no—
38#10621898—44no—
39#10621898—44no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172—21no—
43C2×D172—21no—
44C2×D172C2312yes—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×C4×D43—22no—
48C2×Dic86—21no—
49C2×Dic86C2312yes—
50C2×C8×C43C2314yes—
51C42×C43D411yescharacteristic
52C42×C43D411yescharacteristic
53C42×C43C2311yescharacteristic
54C42×C43C2311yescharacteristic
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—21no—
60C4⋊Dic43—21no—
61C4⋊Dic43—21no—
62C4⋊Dic43C2312yes—
63D344—44no—
64#10621873—44no—
65C23×C43C2×D411yescharacteristic
66C22×D43—22no—
67C22×D43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—41no—
71C2×C4×C43C2×D411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2411yescharacteristic
77C22⋊D43—44no—
78C22⋊D43—44no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81D172—22no—
82D172—22no—
83D172—24no—
84D172—42no—
85D172—42no—
86D172—42no—
87D172—42no—
88C4×D43—44no—
89C4×D43—44no—
90Dic86—24no—
91Dic86—42no—
92C8×C43—24no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—21no—
96C22×C43C22×D411yescharacteristic
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43—42no—
101C2×D43—42no—
102C2×D43—42no—
103C4×C43—21no—
104C4×C43—21no—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43AGL(1,ℤ/8)12yes—
108C4×C43H(5,𝔽2)12yes—
109Dic43—42no—
110Dic43—42no—
111#3214—431nomaximal, Sylow
112C2×C43—41no—
113C2×C43#53511yescharacteristic
114C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C43#57511yescharacteristic
116D43—82no—
117D43—82no—
118#532—431no—
119#532—431no—
120#496—432no—
121#489—432no—
122#461—432no—
123#459—432no—
124#449—434no—
125#432D4311yescharacteristic, complemented
126C43#321411yescharacteristic, complemented, Sylow
127C2×#41—432no—
128C2×#41—861no—
129C2×SD16—434no—
130C2×D8—434no—
131C4⋊Q8—431no—
132C4⋊Q8—431no—
133#127—431no—
134#127—431no—
135#124—432no—
136#124—861no—
137#121—432no—
138#121—861no—
139#121—861no—
140#121—861no—
141C4×D4—432no—
142C4×D4—861no—
143C4×D4—861no—
144C4×D4—861no—
145C2×C42C2×D4311yescharacteristic
146C4⋊C8C2×D4312yes—
147#103—434no—
148#102—434no—
149C22⋊C8C2×D4312yes—
150#97C2×D4312yes—
151#41—1724no—
152#41—1724no—
153C2×Q8—432no—
154C2×Q8—861no—
155C2×D4—432no—
156C2×D4—432no—
157C2×D4—862no—
158C2×D4—862no—
159C2×D4—861no—
160C2×D4—861no—
161C2×D4—861no—
162C2×D4—861no—
163C22×C4—862no—
164C22×C4—862no—
165C22×C4D17211yescharacteristic
166C22×C4D17211yescharacteristic
167C22×C4C22×D4311yescharacteristic
168SD16—1724no—
169D8—1724no—
170C2×C8C22×D4314yes—
171C4⋊C4—432no—
172C4⋊C4—861no—
173C4⋊C4—861no—
174C4⋊C4—861no—
175C22⋊C4—862no—
176C22⋊C4—862no—
177C22⋊C4—862no—
178C22⋊C4—862no—
179C42D17211yescharacteristic
180C42D17211yescharacteristic
181C42C22×D4311yescharacteristic
182C42C22×D4311yescharacteristic
183C23—862no—
184C23—862no—
185C23C2×D17211yescharacteristic
186Q8—864no—
187Q8—1722no—
188D4—862no—
189D4—864no—
190D4—862no—
191D4—1722no—
192D4—1722no—
193D4—1722no—
194D4—1724no—
195D4—1724no—
196D4—1722no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—1724no—
203C2×C4—1724no—
204C2×C4C2×D17211yescharacteristic
205C2×C4C2×D17211yescharacteristic
206C2×C4C2×D17211yescharacteristic
207C2×C4C2×D17211yescharacteristic
208C2×C4C2×D17211yescharacteristic
209C2×C4C23×D4311yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—1722no—
215C22—1722no—
216C22—1722no—
217C22—1722no—
218C22—1722no—
219C22—1722no—
220C22C22×D17211yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—1722no—
226C4—1722no—
227C4#1306335312yes—
228C4#1306337112yes—
229C2—41no—
230C2—3442no—
231C2—3442no—
232C2#1458346811yescharacteristic
233C2C2×#1306335311yescharacteristic
234C2#1458369911yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#432C2
socleC22×C43C22×D4
hypercenter#432D43
hypocenterC43#3214
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. #14583449C2semidirect
2. #14583449C2semidirect
3. #14583288C2semidirect
4. #14583259C2semidirect
5. #14583105C2semidirect
6. #14583095C2semidirect
7. #14583046C2semidirect
8. C43×#432C2semidirect
125. #432D43semidirect
126. C43#3214semidirect