Finite Group Databasebeta

← #19146385

Subgroups — #19146385

Order 5504.

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

normal subgroups only

This group has 460 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#14583708C212yesmaximal, complemented
2#14583707C212yesmaximal, complemented
3#14583273C211yesmaximal, characteristic, complemented
4#14583165C212yesmaximal, complemented
5#14583164C212yesmaximal, complemented
6#14583081C211yesmaximal, characteristic, complemented
7#14583068C212yesmaximal, complemented
8#14583013C212yesmaximal, complemented
9C43×#456C211yesmaximal, characteristic, complemented
10#13063373C2211yescharacteristic
11#13063371C2212yescomplemented
12#13063357—22no—
13#13063356—22no—
14#13063356C2212yescomplemented
15#13063353C2212yes—
16#13063352—22no—
17#13063350—22no—
18#13063350C2212yes—
19#13063348—22no—
20#13063345—22no—
21#13063345C2212yes—
22C2×#10621884—22no—
23C2×#10621884C2212yescomplemented
24C2×#10621884C2212yescomplemented
25SD16×D43—22no—
26#13063333C2212yescomplemented
27#13063332C2212yescomplemented
28#13063322C2211yescharacteristic
29#13063260C2212yescomplemented
30#13063253C2212yescomplemented
31#13063244C2211yescharacteristic, complemented
32#13063241C2212yescomplemented
33C4×C43⋊C8C2211yescharacteristic, complemented
342−1+4×C43C2211yescharacteristic
35#137×C43C2212yescomplemented
36C4⋊Q8×C43C2211yescharacteristic, complemented
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×Q8×C43C2311yescharacteristic
45#10621902—22no—
46#10621902—22no—
47Q8×D43—22no—
48D4×D43—22no—
49D4×D43—42no—
50#10621898—22no—
51#10621898—41no—
52#10621898C2312yes—
53C2×D172—22no—
54C2×D172—41no—
55C2×D172C2312yes—
56Q16×C43—22no—
57SD16×C43—22no—
58M16×C43C2312yes—
59C4⋊C4×C43—41no—
60C42×C43C2311yescharacteristic
61#10621885—22no—
62#10621885D412yescomplemented
63#10621884—22no—
64#10621884—22no—
65#10621884—22no—
66#10621884—22no—
67#10621884—22no—
68#10621884—22no—
69#10621884D412yescomplemented
70#10621883D412yescomplemented
71#10621882—22no—
72#10621882D412yescomplemented
73#10621877—22no—
74#10621877C2312yes—
75C2×C43⋊C8—22no—
76C2×C43⋊C8C2312yes—
77D344—22no—
78#10621873—22no—
79#10621872—22no—
80C8×D43—22no—
81C22×D43—22no—
82C22×D43—42no—
83Q8×C43—22no—
84Q8×C43—22no—
85Q8×C43—41no—
86Q8×C43C2×D412yes—
87D4×C43—22no—
88D4×C43—41no—
89D4×C43C2×D412yes—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—21no—
93C2×C4×C43—21no—
94C2×C4×C43—42no—
95C2×C4×C43C2411yescharacteristic
96C22⋊D43—22no—
97C22⋊D43—42no—
98D172—22no—
99D172—22no—
100D172—42no—
101D172—41no—
102D172—82no—
103D172C2×D412yes—
104C4×D43—22no—
105C4×D43—42no—
106C4×D43—42no—
107Dic86—41no—
108Dic86C2×D412yes—
109C8×C43—22no—
110C43⋊C8—22no—
111C43⋊C8C2×D412yes—
112C43⋊C8C2×D412yes—
113C22×C43—22no—
114C22×C43H(5,𝔽2)11yescharacteristic
115C2×D43—22no—
116C2×D43—42no—
117C2×D43—82no—
118C2×D43—162no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—41no—
122C4×C43—41no—
123C4×C43C22×D412yes—
124Dic43—22no—
125#3291—431nomaximal, Sylow
126C2×C43—21no—
127C2×C43—42no—
128C2×C43D4211yescharacteristic
129D43—42no—
130D43—82no—
131#577—432no—
132#577—432no—
133#492—431no—
134#471—432no—
135#471—432no—
136#456—431no—
137#456D4311yescharacteristic, complemented
138#453—432no—
139#443—432no—
140C43#329111yescharacteristic, complemented, Sylow
1412−1+4—431no—
1422−1+4C2×D4311yescharacteristic
143H(5,𝔽2)—432no—
144#137—432no—
145#137—862no—
146#137—862no—
147#137C2×D4312yescomplemented
148AGL(1,ℤ/8)—432no—
149AGL(1,ℤ/8)—432no—
150AGL(1,ℤ/8)—862no—
151AGL(1,ℤ/8)—862no—
152#135—432no—
153#135—862no—
154#135—862no—
155C2×SD16—432no—
156C2×SD16—432no—
157C2×SD16—862no—
158C2×SD16—862no—
159#131—432no—
160#131—432no—
161C4⋊Q8C2×D4311yescharacteristic, complemented
162#127—431no—
163#108—432no—
164#104—432no—
165#104C2×D4312yescomplemented
166#101—431no—
167#101C2×D4311yescharacteristic, complemented
168#100—432no—
169C4×C8—431no—
170#41—22no—
171#41—41no—
172#41—432no—
173#41—862no—
174#41—862no—
175#41—862no—
176#41—1721no—
177#41C22×D4312yes—
178C2×Q8—22no—
179C2×Q8—862no—
180C2×Q8C22×D4311yescharacteristic
181C2×Q8C22×D4311yescharacteristic
182C2×D4—432no—
183C2×D4—862no—
184C2×D4—862no—
185C2×D4—1721no—
186C2×D4—1722no—
187Q16—22no—
188Q16—432no—
189Q16—862no—
190SD16—22no—
191SD16—432no—
192SD16—432no—
193SD16—862no—
194SD16—862no—
195SD16—862no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199SD16—862no—
200D8—432no—
201D8—862no—
202D8—862no—
203M16—432no—
204M16—862no—
205M16—862no—
206M16C22×D4312yes—
207C2×C8—432no—
208C2×C8—862no—
209C2×C8—862no—
210C4⋊C4—41no—
211C42C22×D4311yescharacteristic
212C23—862no—
213C23—1722no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—432no—
218Q8—1721no—
219Q8D4×D4312yes—
220D4—22no—
221D4—41no—
222D4—432no—
223D4—862no—
224D4—862no—
225D4—862no—
226D4—3442no—
227D4—1722no—
228D4—1721no—
229D4—1722no—
230D4D4×D4312yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—862no—
237C2×C4—1722no—
238C2×C4—1722no—
239C2×C4C23×D4311yescharacteristic
240C8—22no—
241C8—432no—
242C8—432no—
243C8—862no—
244C22—22no—
245C22—862no—
246C22—3442no—
247C22—1722no—
248C22—6882no—
249C22#1306337011yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—862no—
255C4C2×D4×D4312yes—
256C2—21no—
257C2—42no—
258C2—3442no—
259C2—1722no—
260C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#456C2
socleC2×C43D42
hypercenter#456D43
hypocenterC43#3291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14583708C2semidirect
2. #14583707C2semidirect
3. #14583273C2semidirect
4. #14583165C2semidirect
5. #14583164C2semidirect
6. #14583081C2semidirect
7. #14583068C2semidirect
8. #14583013C2semidirect
9. C43×#456C2semidirect
11. #13063371C22semidirect
14. #13063356C22semidirect
23. C2×#10621884C22semidirect
24. C2×#10621884C22semidirect
26. #13063333C22semidirect
27. #13063332C22semidirect
29. #13063260C22semidirect
30. #13063253C22semidirect
31. #13063244C22semidirect
32. #13063241C22semidirect
33. C4×C43⋊C8C22semidirect
35. #137×C43C22semidirect
36. C4⋊Q8×C43C22semidirect
37. #104×C43C22semidirect
38. #101×C43C22semidirect
62. #10621885D4semidirect
69. #10621884D4semidirect
70. #10621883D4semidirect
72. #10621882D4semidirect
137. #456D43semidirect
140. C43#3291semidirect
147. #137C2×D43semidirect
161. C4⋊Q8C2×D43semidirect
165. #104C2×D43semidirect
167. #101C2×D43semidirect