Finite Group Databasebeta

← #19145521

Subgroups — #19145521

Order 5504.

428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583450C211yesmaximal, characteristic
2C4⋊Q8×D43C211yesmaximal, characteristic, complemented
3#14583273C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583251C211yesmaximal, characteristic, complemented
6#14583103C214yesmaximal, complemented
7#14583039C214yesmaximal, complemented
8#14582950C211yesmaximal, characteristic, complemented
9C43×#487C211yesmaximal, characteristic, complemented
10C2×#10621902—21no—
11C2×Q8×D43C2212yes—
12C2×#10621873C2214yes—
13C2×#10621884C2214yes—
14#13063325C2211yescharacteristic
15#13063324—21no—
16#13063324—21no—
17#13063323C2212yes—
18#13063322C2211yescharacteristic
19#13063314—21no—
20#13063300—21no—
21#13063300C2212yes—
22#13063287—21no—
23#13063287C2212yes—
24C4⋊C4×D43—21no—
25C4⋊C4×D43—21no—
26C42×D43C2211yescharacteristic
27Dic43⋊C8C2212yes—
28#13063248C2214yes—
29(C2×D43)⋊C8C2212yes—
30C4×C43⋊C8C2211yescharacteristic
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#103×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43C2312yes—
37#10621902—44no—
38Q8×D43—44no—
39C2×D172—21no—
40C2×D172—21no—
41C2×D172—22no—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×C4×D43—22no—
45C2×C4×D43D411yescharacteristic
46C2×C4×D43D411yescharacteristic
47C2×C4×D43C2311yescharacteristic
48C2×Dic86—22no—
49C2×Dic86C2312yes—
50C2×C8×C43C2312yes—
51C4⋊C4×C43—21no—
52C4⋊C4×C43—21no—
53C4⋊C4×C43—21no—
54C4⋊C4×C43C2312yes—
55C42×C43C2311yescharacteristic
56#10621884—44no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43—21no—
60C4⋊Dic43—21no—
61Dic43⋊C4—22no—
62Dic43⋊C4—22no—
63C4×Dic43D411yescharacteristic
64C4×Dic43D411yescharacteristic
65C4×Dic43C2311yescharacteristic
66C2×C43⋊C8C2312yes—
67#10621873—44no—
68C22×D43—22no—
69C22×D43C2×D411yescharacteristic
70Q8×C43—24no—
71Q8×C43—42no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2411yescharacteristic
77C2×Dic43—22no—
78C2×Dic43C2×D411yescharacteristic
79C2×Dic43C2×D411yescharacteristic
80C2×Dic43C2×D411yescharacteristic
81D172—24no—
82D172—44no—
83D172—42no—
84D172—42no—
85C4×D43—22no—
86C4×D43—22no—
87C4×D43—44no—
88C4×D43—44no—
89C4×D43SD1614yescomplemented
90Dic86—24no—
91Dic86—44no—
92C8×C43—22no—
93C43⋊C8—22no—
94C22×C43C22×D411yescharacteristic
95C2×D43—21no—
96C2×D43—21no—
97C2×D43—42no—
98C2×D43—42no—
99C2×D43—42no—
100C2×D43C2×SD1612yes—
101C4×C43—42no—
102C4×C43—42no—
103C4×C43C2×SD1612yes—
104C4×C43#13712yes—
105C4×C43H(5,𝔽2)12yes—
106Dic43—21no—
107Dic43—21no—
108Dic43—42no—
109Dic43C2×SD1612yes—
110#3206—431nomaximal, Sylow
111C2×C43#53511yescharacteristic
112C2×C43C22×SD1611yescharacteristic
113C2×C43C2×#13711yescharacteristic
114D43—22no—
115D43—82no—
116#532—431no—
117C2×C4⋊Q8—431no—
118#492—431no—
119#492—431no—
120#487—431no—
121#487D4311yescharacteristic, complemented
122#461—434no—
123#448—434no—
124#431—431no—
125C43#320611yescharacteristic, complemented, Sylow
126C2×#41—861no—
127C22×Q8—432no—
128C2×SD16—434no—
129C2×SD16—434no—
130C4⋊Q8—432no—
131C4⋊Q8—431no—
132C4⋊Q8—861no—
133C4⋊Q8—861no—
134C4⋊Q8C2×D4311yescharacteristic
135C4⋊Q8C2×D4311yescharacteristic
136#127—431no—
137#124—861no—
138#121—432no—
139#121—861no—
140C4×D4—432no—
141C4×D4—861no—
142C2×C4⋊C4—861no—
143C2×C4⋊C4—861no—
144C2×C42—431no—
145C4⋊C8—432no—
146#103—434no—
147#103C2×D4314yes—
148C22⋊C8—432no—
149C4×C8—431no—
150C4×C8C2×D4311yescharacteristic
151#41—1724no—
152C2×Q8—21no—
153C2×Q8—432no—
154C2×Q8—862no—
155C2×Q8—1724no—
156C2×Q8C22×D4312yes—
157C2×D4—432no—
158C2×D4—862no—
159C2×D4—861no—
160C2×D4—861no—
161C22×C4—431no—
162C22×C4—431no—
163C22×C4—431no—
164C22×C4—862no—
165C22×C4—862no—
166SD16—1724no—
167SD16—1724no—
168C2×C8—432no—
169C2×C8C22×D4312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—862no—
174C4⋊C4—862no—
175C4⋊C4—861no—
176C4⋊C4—861no—
177C4⋊C4C22×D4312yes—
178C22⋊C4—862no—
179C22⋊C4—862no—
180C42—431no—
181C42—431no—
182C42—431no—
183C42C22×D4311yescharacteristic
184C23—431no—
185C23—862no—
186Q8—24no—
187Q8—42no—
188Q8—864no—
189Q8—1724no—
190D4—864no—
191D4—1724no—
192D4—1722no—
193D4—1722no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—431no—
197C2×C4—434no—
198C2×C4—431no—
199C2×C4—431no—
200C2×C4—862no—
201C2×C4—862no—
202C2×C4—862no—
203C2×C4—1724no—
204C2×C4—1724no—
205C2×C4D4×D4311yescharacteristic
206C2×C4D4×D4311yescharacteristic
207C2×C4C23×D4311yescharacteristic
208C8—22no—
209C8—862no—
210C22—432no—
211C22—861no—
212C22—861no—
213C22—1722no—
214C22—1722no—
215C22—1722no—
216C22C2×D4×D4311yescharacteristic
217C4—42no—
218C4—42no—
219C4—432no—
220C4—861no—
221C4—861no—
222C4—1722no—
223C4SD16×D4312yes—
224C4#1306335712yes—
225C4#1306337112yes—
226C2—862no—
227C2—3442no—
228C2#1458346711yescharacteristic
229C2C2×SD16×D4311yescharacteristic
230C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43#3206
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D43C2semidirect
3. #14583273C2semidirect
4. #14583272C2semidirect
5. #14583251C2semidirect
6. #14583103C2semidirect
7. #14583039C2semidirect
8. #14582950C2semidirect
9. C43×#487C2semidirect
89. C4×D43SD16semidirect
121. #487D43semidirect
125. C43#3206semidirect