Finite Group Databasebeta

← #487×D43 #19144903

Subgroups — #487×D43 #19144903

Order 5504.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D43C211yesmaximal, characteristic
2C4⋊Q8×D43C211yesmaximal, characteristic
3#14583251C211yesmaximal, characteristic, complemented
4#14583250C211yesmaximal, characteristic, complemented
5#14583249C211yesmaximal, characteristic, complemented
6#14583248C214yesmaximal, complemented
7#103×D43C214yesmaximal
8C4×C8×D43C211yesmaximal, characteristic
9C43×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D43—21no—
11C2×Q8×D43C2212yes—
12C2×C8×D43C2212yes—
13#13063325C2211yescharacteristic
14#13063325C2211yescharacteristic
15#13063324—21no—
16#13063324—21no—
17#13063324—21no—
18#13063324C2212yes—
19#13063323—21no—
20#13063323C2212yes—
21C4⋊C4×D43—21no—
22C4⋊C4×D43—21no—
23C4⋊C4×D43—21no—
24C4⋊C4×D43C2212yes—
25C42×D43C2211yescharacteristic
26#13063250C2214yes—
27#13063249C2214yes—
28#13063248C2214yes—
29C4×C43⋊C8C2211yescharacteristic
30C8×Dic43C2212yes—
31C4⋊Q8×C43C2211yescharacteristic
32C4⋊Q8×C43C2211yescharacteristic
33#103×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×Q8×C43C2312yes—
37Q8×D43—28no—
38Q8×D43—44no—
39C2×C4×D43—22no—
40C2×C4×D43—22no—
41C2×C4×D43D411yescharacteristic
42C2×C4×D43D411yescharacteristic
43C2×C4×D43C2311yescharacteristic
44C2×Dic86—21no—
45C2×Dic86—22no—
46C2×Dic86—22no—
47C2×Dic86C2312yes—
48C2×C8×C43C2312yes—
49C4⋊C4×C43—21no—
50C4⋊C4×C43—21no—
51C4⋊C4×C43—21no—
52C4⋊C4×C43C2312yes—
53C42×C43C2311yescharacteristic
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43C2312yes—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60Dic43⋊C4—22no—
61Dic43⋊C4—22no—
62C4×Dic43D411yescharacteristic
63C4×Dic43D411yescharacteristic
64C4×Dic43C2311yescharacteristic
65C2×C43⋊C8C2312yes—
66C8×D43—24no—
67C22×D43C2×D411yescharacteristic
68Q8×C43—24no—
69Q8×C43—42no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2411yescharacteristic
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43C2×D411yescharacteristic
78C2×Dic43C2×D411yescharacteristic
79C2×Dic43C2×D411yescharacteristic
80C4×D43—44no—
81C4×D43—44no—
82C4×D43SD1614yes—
83C4×D43Q1614yes—
84C4×D43#4114yes—
85Dic86—24no—
86Dic86—42no—
87Dic86—44no—
88Dic86—44no—
89C8×C43—22no—
90C43⋊C8—22no—
91C22×C43C22×D411yescharacteristic
92C2×D43#12412yes—
93C2×D43C2×SD1612yes—
94C2×D43C2×Q1612yes—
95C4×C43—42no—
96C4×C43—42no—
97C4×C43C2×SD1612yes—
98C4×C43C2×Q1612yes—
99C4×C43C2×#4112yes—
100Dic43—42no—
101Dic43—42no—
102Dic43#12412yes—
103Dic43C2×SD1612yes—
104Dic43C2×Q1612yes—
105C2×#487—431nomaximal, Sylow
106C2×C43C2×#12411yescharacteristic
107C2×C43C22×SD1611yescharacteristic
108C2×C43C22×Q1611yescharacteristic
109D43#48714yesdirect product factor
110C2×C4⋊Q8—431no—
111C2×C4⋊Q8—431no—
112#487—431no—
113#487—431no—
114#487—434no—
115#487—431no—
116#487D4311yescharacteristic, direct product factor
117C2×#103—434no—
118C2×C4×C8—431no—
119C43C2×#48711yescharacteristic, complemented, Sylow
120C22×Q8—432no—
121C22×Q8—861no—
122C22×C8—432no—
123C4⋊Q8—432no—
124C4⋊Q8—432no—
125C4⋊Q8—431no—
126C4⋊Q8—431no—
127C4⋊Q8—861no—
128C4⋊Q8—861no—
129C4⋊Q8—861no—
130C4⋊Q8—861no—
131C4⋊Q8C2×D4311yescharacteristic
132C4⋊Q8C2×D4311yescharacteristic
133C2×C4⋊C4—432no—
134C2×C4⋊C4—861no—
135C2×C4⋊C4—861no—
136C2×C4⋊C4—861no—
137C2×C42—431no—
138#103—434no—
139#103—434no—
140#103—434no—
141#103C2×D4314yes—
142C4×C8—432no—
143C4×C8—431no—
144C4×C8C2×D4311yescharacteristic
145C2×Q8—21no—
146C2×Q8—432no—
147C2×Q8—862no—
148C2×Q8—862no—
149C2×Q8—868no—
150C2×Q8—861no—
151C2×Q8—1724no—
152C2×Q8C22×D4312yes—
153C22×C4—431no—
154C22×C4—431no—
155C22×C4—431no—
156C22×C4—862no—
157C22×C4—862no—
158C2×C8—432no—
159C2×C8—864no—
160C2×C8C22×D4312yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—432no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—862no—
169C4⋊C4—861no—
170C4⋊C4—861no—
171C4⋊C4—861no—
172C4⋊C4C22×D4312yes—
173C42—431no—
174C42—431no—
175C42—431no—
176C42C22×D4311yescharacteristic
177C23—431no—
178Q8—24no—
179Q8—42no—
180Q8—864no—
181Q8—1724no—
182Q8—1724no—
183Q8—1722no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—431no—
187C2×C4—431no—
188C2×C4—431no—
189C2×C4—434no—
190C2×C4—434no—
191C2×C4—434no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—1724no—
195C2×C4—1724no—
196C2×C4D4×D4311yescharacteristic
197C2×C4D4×D4311yescharacteristic
198C2×C4C23×D4311yescharacteristic
199C8—22no—
200C8—862no—
201C22—432no—
202C22—432no—
203C22—432no—
204C22C2×D4×D4311yescharacteristic
205C4—42no—
206C4—42no—
207C4—432no—
208C4—432no—
209C4—432no—
210C4—1722no—
211C4—1722no—
212C4SD16×D4312yes—
213C4Q16×D4312yes—
214C4#41×D4312yes—
215C2—434no—
216C2#124×D4311yescharacteristic
217C2C2×SD16×D4311yescharacteristic
218C2C2×Q16×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#487C2
socleC22×C43C22×D4
hypercenter#487D43
hypocenterC43C2×#487
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
3. #14583251C2semidirect
4. #14583250C2semidirect
5. #14583249C2semidirect
6. #14583248C2semidirect
9. C43×#487C2semidirect
109. D43#487direct (N × H)
116. #487D43direct (N × H)
119. C43C2×#487semidirect