Finite Group Databasebeta

← #19146372

Subgroups — #19146372

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#14583714C212yesmaximal, complemented
2#14583709C212yesmaximal, complemented
3#14583294C211yesmaximal, characteristic, complemented
4#14583173C212yesmaximal, complemented
5#14583160C212yesmaximal, complemented
6#14583083C212yesmaximal, complemented
7#14583076C211yesmaximal, characteristic, complemented
8#14583018C212yesmaximal, complemented
9C43×#454C211yesmaximal, characteristic, complemented
10#13063372C2212yes—
11#13063370C2211yescharacteristic
12#13063358C2212yes—
13#13063356—22no—
14#13063356C2212yes—
15#13063355—22no—
16#13063355C2212yescomplemented
17#13063354—22no—
18#13063349—22no—
19#13063345—22no—
20#13063345C2212yes—
21#13063344—22no—
22C2×#10621885—22no—
23C2×#10621885C2212yescomplemented
24C2×#10621883C2212yes—
25SD16×D43—22no—
26#13063333C2212yes—
27#13063332C2212yescomplemented
28#13063325C2211yescharacteristic, complemented
29#13063260C2212yescomplemented
30#13063253C2212yes—
31#13063243C2212yescomplemented
32#13063242C2211yescharacteristic
33#13063236C2211yescharacteristic, complemented
342−1+4×C43C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C43C2212yes—
36#124×C43C2211yescharacteristic
37#104×C43C2212yescomplemented
38#101×C43C2211yescharacteristic, complemented
39#41×C43—22no—
40#41×C43—41no—
41#41×C43C2312yes—
42C2×Q8×C43—22no—
43C2×Q8×C43C2311yescharacteristic
44C2×D4×C43C2311yescharacteristic
45C2×C22⋊D43—41no—
46Q8×D43—22no—
47#10621900—22no—
48#10621900—22no—
49#10621900—42no—
50D4×D43—22no—
51#10621898—22no—
52#10621898C2312yes—
53C2×Dic86—22no—
54C2×Dic86C2312yes—
55SD16×C43—22no—
56D8×C43—22no—
57M16×C43C2312yes—
58C22⋊C4×C43—41no—
59C42×C43C2311yescharacteristic
60#10621885—22no—
61#10621885—22no—
62#10621885—22no—
63#10621885—22no—
64#10621885D412yes—
65#10621884—22no—
66#10621884D412yes—
67#10621883—22no—
68#10621883—22no—
69#10621883—22no—
70#10621883D412yes—
71#10621882D412yes—
72C4⋊Dic43—41no—
73#10621877—22no—
74#10621877C2312yes—
75C2×C43⋊C8—22no—
76C2×C43⋊C8C2312yes—
77Dic172—22no—
78#10621873—22no—
79#10621872—22no—
80C8×D43—22no—
81C23×C43—21no—
82C22×D43—41no—
83Q8×C43—22no—
84Q8×C43—41no—
85Q8×C43C2×D412yes—
86D4×C43—22no—
87D4×C43—22no—
88D4×C43—41no—
89D4×C43C2×D412yes—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—42no—
94C2×C4×C43C2411yescharacteristic
95C22⋊D43—22no—
96C22⋊D43—42no—
97C22⋊D43—42no—
98C2×Dic43—22no—
99C2×Dic43—41no—
100C2×Dic43—42no—
101D172C2×D412yes—
102C4×D43—22no—
103C4×D43—42no—
104Dic86—22no—
105Dic86—22no—
106Dic86—42no—
107Dic86C2×D412yes—
108C8×C43—22no—
109C43⋊C8—22no—
110C43⋊C8C2×D412yes—
111C43⋊C8C2×D412yes—
112C22×C43—22no—
113C22×C43—41no—
114C22×C43—81no—
115C22×C43H(5,𝔽2)11yescharacteristic
116C2×D43—22no—
117C2×D43—161no—
118C4×C43—22no—
119C4×C43—41no—
120C4×C43—41no—
121C4×C43C22×D412yes—
122Dic43—22no—
123Dic43—42no—
124#3289—431nomaximal, Sylow
125C2×C43—21no—
126C2×C43—42no—
127C2×C43—81no—
128C2×C43D4211yescharacteristic
129D43—42no—
130#578—432no—
131#577—432no—
132#497—431no—
133#473—432no—
134#471—432no—
135#456—432no—
136#455—431no—
137#454D4311yescharacteristic, complemented
138#444—432no—
139C43#328911yescharacteristic, complemented, Sylow
1402−1+4—432no—
1412−1+4C2×D4311yescharacteristic, complemented
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)—862no—
150AGL(1,ℤ/8)C2×D4312yes—
151#135—432no—
152#135—862no—
153#135—862no—
154C2×Q16—432no—
155C2×Q16—862no—
156C2×SD16—432no—
157C2×SD16—862no—
158#131—432no—
159#131—432no—
160C4⋊Q8—431no—
161#124C2×D4311yescharacteristic
162#108—432no—
163#104—432no—
164#104C2×D4312yescomplemented
165#101—432no—
166#101C2×D4311yescharacteristic, complemented
167#100—431no—
168#97—431no—
169#41—22no—
170#41—41no—
171#41—432no—
172#41—862no—
173#41—862no—
174#41—862no—
175#41—1722no—
176#41C22×D4312yes—
177C2×Q8—22no—
178C2×Q8—432no—
179C2×Q8—862no—
180C2×Q8—862no—
181C2×Q8C22×D4311yescharacteristic
182C2×D4—862no—
183C2×D4—1721no—
184C2×D4C22×D4311yescharacteristic
185Q16—432no—
186Q16—862no—
187Q16—862no—
188Q16—862no—
189Q16—862no—
190Q16—862no—
191SD16—22no—
192SD16—432no—
193SD16—432no—
194SD16—862no—
195SD16—862no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199D8—22no—
200D8—432no—
201M16—432no—
202M16—862no—
203M16—862no—
204M16C22×D4312yes—
205C2×C8—432no—
206C2×C8—862no—
207C2×C8—862no—
208C4⋊C4—1721no—
209C22⋊C4—41no—
210C42C22×D4311yescharacteristic
211C23—21no—
212C23—1721no—
213Q8—22no—
214Q8—41no—
215Q8—432no—
216Q8—862no—
217Q8—862no—
218Q8—1722no—
219Q8D4×D4312yes—
220D4—22no—
221D4—22no—
222D4—41no—
223D4—432no—
224D4—862no—
225D4—1722no—
226D4—1722no—
227D4D4×D4312yes—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—862no—
233C2×C4—862no—
234C2×C4—1722no—
235C2×C4—1721no—
236C2×C4—1722no—
237C2×C4C23×D4311yescharacteristic
238C8—22no—
239C8—432no—
240C8—432no—
241C8—862no—
242C22—22no—
243C22—41no—
244C22—81no—
245C22—862no—
246C22—6881no—
247C22#1306337011yescharacteristic
248C4—22no—
249C4—41no—
250C4—41no—
251C4—862no—
252C4—1722no—
253C4C2×D4×D4312yes—
254C2—21no—
255C2—42no—
256C2—81no—
257C2—1722no—
258C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#454C2
socleC2×C43D42
hypercenter#454D43
hypocenterC43#3289
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14583714C2semidirect
2. #14583709C2semidirect
3. #14583294C2semidirect
4. #14583173C2semidirect
5. #14583160C2semidirect
6. #14583083C2semidirect
7. #14583076C2semidirect
8. #14583018C2semidirect
9. C43×#454C2semidirect
16. #13063355C22semidirect
23. C2×#10621885C22semidirect
27. #13063332C22semidirect
28. #13063325C22semidirect
29. #13063260C22semidirect
31. #13063243C22semidirect
33. #13063236C22semidirect
34. 2−1+4×C43C22semidirect
37. #104×C43C22semidirect
38. #101×C43C22semidirect
137. #454D43semidirect
139. C43#3289semidirect
141. 2−1+4C2×D43semidirect
164. #104C2×D43semidirect
166. #101C2×D43semidirect