Finite Group Databasebeta

← #19146370

Subgroups — #19146370

Order 5504.

448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583712C212yesmaximal, complemented
2#14583705C212yesmaximal, complemented
3#14583171C212yesmaximal, complemented
4#14583159C212yesmaximal, complemented
5#14583081C212yesmaximal, complemented
6#14583076C211yesmaximal, characteristic, complemented
7#14583071C211yesmaximal, characteristic, complemented
8#14583022C212yesmaximal, complemented
9C43×#497C211yesmaximal, characteristic, complemented
10#13063373C2212yes—
11#13063373C2211yescharacteristic, complemented
12#13063370C2211yescharacteristic
13#13063357—22no—
14#13063357—22no—
15#13063356C2212yes—
16#13063356C2212yes—
17#13063356C2212yescomplemented
18#13063354—22no—
19#13063352—22no—
20#13063351C2212yes—
21#13063348—22no—
22#13063347C2212yes—
23#13063346—22no—
24Q16×D43—22no—
25SD16×D43—22no—
26#13063331C2212yes—
27#13063331C2212yescomplemented
28#13063261C2212yescomplemented
29#13063253C2212yes—
30#13063253C2212yescomplemented
31#13063244C2211yescharacteristic, complemented
32#13063244C2212yescomplemented
33#13063242C2211yescharacteristic
34C2×Q16×C43C2212yescomplemented
35C2×SD16×C43C2212yes—
36C4⋊Q8×C43C2211yescharacteristic, complemented
37#124×C43C2211yescharacteristic
38#97×C43C2211yescharacteristic, complemented
39C2×Q8×C43C2311yescharacteristic
40C2×Q8×C43C2312yes—
41C2×D4×C43C2311yescharacteristic
42C2×C22⋊D43—41no—
43#10621902—22no—
44#10621902—22no—
45#10621902—22no—
46Q8×D43—22no—
47Q8×D43—22no—
48Q8×D43—22no—
49#10621900—22no—
50D4×D43—22no—
51#10621898—42no—
52#10621898—41no—
53#10621898C2312yes—
54#10621898C2312yes—
55Q16×C43—22no—
56Q16×C43—22no—
57SD16×C43—22no—
58SD16×C43—22no—
59C2×C8×C43C2312yes—
60C4⋊C4×C43—41no—
61C22⋊C4×C43—41no—
62C42×C43C2311yescharacteristic
63#10621885—22no—
64#10621885—22no—
65#10621885—22no—
66#10621884—22no—
67#10621884—22no—
68#10621884—22no—
69#10621883—22no—
70#10621882—22no—
71#10621877C2312yes—
72#10621877C2312yes—
73Dic172D412yes—
74D344D412yes—
75#10621873D412yes—
76#10621873D412yes—
77#10621872—22no—
78#10621872—22no—
79C8×D43—22no—
80C8×D43—22no—
81C23×C43—21no—
82C22×D43—41no—
83Q8×C43—22no—
84Q8×C43—22no—
85Q8×C43—22no—
86D4×C43—22no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43C2411yescharacteristic
91C22⋊D43—22no—
92C22⋊D43—22no—
93C22⋊D43—42no—
94C2×Dic43—41no—
95D172—42no—
96D172—41no—
97D172C2×D412yes—
98D172C2×D412yes—
99C4×D43—22no—
100C4×D43—22no—
101C4×D43—42no—
102C4×D43—42no—
103C4×D43—42no—
104Dic86—41no—
105Dic86—42no—
106Dic86C2×D412yes—
107Dic86C2×D412yes—
108C8×C43C2×D412yes—
109C8×C43C2×D412yes—
110C43⋊C8—22no—
111C43⋊C8—22no—
112C22×C43—41no—
113C22×C43—81no—
114C22×C43H(5,𝔽2)11yescharacteristic
115C2×D43—22no—
116C2×D43—22no—
117C2×D43—161no—
118C4×C43—41no—
119C4×C43—41no—
120C4×C43—42no—
121C4×C43C22×D412yes—
122Dic43—22no—
123Dic43—22no—
124#3289—431nomaximal, Sylow
125C2×C43—21no—
126C2×C43—81no—
127C2×C43D4211yescharacteristic
128D43—42no—
129D43—42no—
130#578—432no—
131#577—432no—
132#497D4311yescharacteristic, complemented
133#473—432no—
134#471—432no—
135#456—432no—
136#455—431no—
137#454—431no—
138#444—432no—
139C43#328911yescharacteristic, complemented, Sylow
1402−1+4—432no—
1412−1+4—431no—
142H(5,𝔽2)—431no—
143#137—432no—
144#137—432no—
145#137—432no—
146#137—862no—
147#137—862no—
148#137—862no—
149AGL(1,ℤ/8)—432no—
150AGL(1,ℤ/8)—862no—
151#135—432no—
152#135—862no—
153#135—862no—
154C2×Q16—862no—
155C2×Q16C2×D4312yescomplemented
156C2×SD16—862no—
157C2×SD16C2×D4312yes—
158#131—432no—
159#131—432no—
160C4⋊Q8C2×D4311yescharacteristic, complemented
161#124C2×D4311yescharacteristic
162#108—432no—
163#104—432no—
164#104—432no—
165#101—431no—
166#101—432no—
167#100—431no—
168#97C2×D4311yescharacteristic, complemented
169#41—432no—
170#41—432no—
171#41—862no—
172#41—862no—
173#41—862no—
174#41—862no—
175#41—1721no—
176#41—1722no—
177C2×Q8—862no—
178C2×Q8—862no—
179C2×Q8—862no—
180C2×Q8C22×D4311yescharacteristic
181C2×Q8C22×D4312yes—
182C2×D4—862no—
183C2×D4—1721no—
184C2×D4C22×D4311yescharacteristic
185Q16—22no—
186Q16—22no—
187Q16—432no—
188Q16—862no—
189Q16—862no—
190Q16—862no—
191SD16—22no—
192SD16—22no—
193SD16—432no—
194SD16—432no—
195SD16—862no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199D8—432no—
200D8—862no—
201M16—432no—
202M16—432no—
203M16—862no—
204M16—862no—
205C2×C8—862no—
206C2×C8—862no—
207C2×C8C22×D4312yes—
208C4⋊C4—41no—
209C22⋊C4—41no—
210C42C22×D4311yescharacteristic
211C23—21no—
212C23—1721no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—432no—
217Q8—432no—
218Q8—1722no—
219Q8—1721no—
220D4—22no—
221D4—432no—
222D4—432no—
223D4—862no—
224D4—862no—
225D4—1721no—
226D4—1722no—
227D4—1722no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—862no—
232C2×C4—862no—
233C2×C4—1722no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1721no—
237C2×C4C23×D4311yescharacteristic
238C8—862no—
239C8—862no—
240C8D4×D4312yes—
241C8D4×D4312yes—
242C22—41no—
243C22—81no—
244C22—862no—
245C22—862no—
246C22—6881no—
247C22#1306337011yescharacteristic
248C4—41no—
249C4—41no—
250C4—42no—
251C4—862no—
252C4—862no—
253C4C2×D4×D4312yes—
254C2—21no—
255C2—81no—
256C2—1722no—
257C2—1722no—
258C2#1458353411yescharacteristic
subgroupG/H
centerC2#14583534
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#497C2
socleC2×C43D42
hypercenter#497D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #14583712C2semidirect
2. #14583705C2semidirect
3. #14583171C2semidirect
4. #14583159C2semidirect
5. #14583081C2semidirect
6. #14583076C2semidirect
7. #14583071C2semidirect
8. #14583022C2semidirect
9. C43×#497C2semidirect
11. #13063373C22semidirect
17. #13063356C22semidirect
27. #13063331C22semidirect
28. #13063261C22semidirect
30. #13063253C22semidirect
31. #13063244C22semidirect
32. #13063244C22semidirect
34. C2×Q16×C43C22semidirect
36. C4⋊Q8×C43C22semidirect
38. #97×C43C22semidirect
132. #497D43semidirect
139. C43#3289semidirect
155. C2×Q16C2×D43semidirect
160. C4⋊Q8C2×D43semidirect
168. #97C2×D43semidirect