Finite Group Databasebeta

← #19146363

Subgroups — #19146363

Order 5504.

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

normal subgroups only

This group has 464 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#14583707C212yesmaximal, complemented
2#14583703C212yesmaximal, complemented
3#14583289C211yesmaximal, characteristic, complemented
4#14583167C212yesmaximal, complemented
5#14583165C212yesmaximal, complemented
6#14583076C211yesmaximal, characteristic, complemented
7#14583068C212yesmaximal, complemented
8#14583018C212yesmaximal, complemented
9C43×#454C211yesmaximal, characteristic, complemented
10#13063371C2212yescomplemented
11#13063370C2211yescharacteristic
12#13063356—22no—
13#13063356C2212yescomplemented
14#13063353C2212yes—
15#13063352—22no—
16#13063350—22no—
17#13063350C2212yescomplemented
18#13063349—22no—
19#13063346—22no—
20#13063345—22no—
21#13063345C2212yes—
22C2×#10621884—22no—
23C2×#10621884C2212yescomplemented
24C2×#10621882C2212yescomplemented
25D8×D43—22no—
26#13063333C2212yescomplemented
27#13063332C2212yescomplemented
28#13063322C2211yescharacteristic, complemented
29#13063260C2212yescomplemented
30#13063253C2212yescomplemented
31#13063242C2211yescharacteristic, complemented
32#13063241C2212yescomplemented
33#13063236C2211yescharacteristic, complemented
342−1+4×C43C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C43C2212yescomplemented
36#124×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×D4×C43C2311yescharacteristic
45C2×C22⋊D43—41no—
46#10621902—22no—
47#10621900—22no—
48D4×D43—22no—
49D4×D43—22no—
50D4×D43—42no—
51#10621898—22no—
52#10621898C2312yes—
53C2×D172—22no—
54C2×D172—41no—
55C2×D172C2312yes—
56SD16×C43—22no—
57D8×C43—22no—
58M16×C43C2312yes—
59C22⋊C4×C43—41no—
60C42×C43C2311yescharacteristic
61#10621885—22no—
62#10621885D412yescomplemented
63#10621884—22no—
64#10621884—22no—
65#10621884—22no—
66#10621884—22no—
67#10621884D412yescomplemented
68#10621883D412yescomplemented
69#10621882—22no—
70#10621882—22no—
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—
81C23×C43—21no—
82C22×D43—22no—
83C22×D43—41no—
84C22×D43—42no—
85Q8×C43—22no—
86Q8×C43—41no—
87Q8×C43C2×D412yes—
88D4×C43—22no—
89D4×C43—22no—
90D4×C43—41no—
91D4×C43C2×D412yes—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—42no—
96C2×C4×C43C2411yescharacteristic
97C22⋊D43—22no—
98C22⋊D43—42no—
99C22⋊D43—42no—
100C2×Dic43—41no—
101D172—22no—
102D172—22no—
103D172—42no—
104D172—82no—
105D172C2×D412yes—
106C4×D43—22no—
107C4×D43—42no—
108Dic86C2×D412yes—
109C8×C43—22no—
110C43⋊C8—22no—
111C43⋊C8C2×D412yes—
112C43⋊C8C2×D412yes—
113C22×C43—22no—
114C22×C43—41no—
115C22×C43—81no—
116C22×C43H(5,𝔽2)11yescharacteristic
117C2×D43—22no—
118C2×D43—42no—
119C2×D43—82no—
120C2×D43—161no—
121C2×D43—162no—
122C4×C43—22no—
123C4×C43—41no—
124C4×C43—41no—
125C4×C43C22×D412yes—
126Dic43—22no—
127#3288—431nomaximal, Sylow
128C2×C43—21no—
129C2×C43—42no—
130C2×C43—81no—
131C2×C43D4211yescharacteristic
132D43—42no—
133D43—82no—
134#577—432no—
135#576—432no—
136#496—431no—
137#472—432no—
138#471—432no—
139#455—431no—
140#454D4311yescharacteristic, complemented
141#453—432no—
142#444—432no—
143C43#328811yescharacteristic, complemented, Sylow
1442−1+4C2×D4311yescharacteristic, complemented
145H(5,𝔽2)—432no—
146H(5,𝔽2)—431no—
147#137—432no—
148#137—862no—
149AGL(1,ℤ/8)—432no—
150AGL(1,ℤ/8)—432no—
151AGL(1,ℤ/8)—862no—
152AGL(1,ℤ/8)—862no—
153AGL(1,ℤ/8)—862no—
154AGL(1,ℤ/8)C2×D4312yescomplemented
155#135—432no—
156#135—862no—
157#135—862no—
158C2×SD16—432no—
159C2×SD16—862no—
160C2×D8—432no—
161C2×D8—862no—
162#131—432no—
163#131—432no—
164#127—431no—
165#124C2×D4311yescharacteristic, complemented
166#108—432no—
167#104—432no—
168#104C2×D4312yescomplemented
169#101C2×D4311yescharacteristic, complemented
170#100—431no—
171#100—432no—
172#97—431no—
173#41—22no—
174#41—41no—
175#41—432no—
176#41—862no—
177#41—862no—
178#41—862no—
179#41C22×D4312yes—
180C2×Q8—22no—
181C2×Q8C22×D4311yescharacteristic
182C2×D4—432no—
183C2×D4—862no—
184C2×D4—862no—
185C2×D4—862no—
186C2×D4—1721no—
187C2×D4—1722no—
188C2×D4—1721no—
189C2×D4C22×D4311yescharacteristic
190Q16—432no—
191Q16—862no—
192SD16—22no—
193SD16—432no—
194SD16—432no—
195SD16—862no—
196SD16—862no—
197SD16—862no—
198SD16—862no—
199SD16—862no—
200D8—22no—
201D8—432no—
202D8—862no—
203D8—862no—
204D8—862no—
205D8—862no—
206M16—432no—
207M16—862no—
208M16—862no—
209M16C22×D4312yes—
210C2×C8—432no—
211C2×C8—862no—
212C2×C8—862no—
213C22⋊C4—41no—
214C42C22×D4311yescharacteristic
215C23—21no—
216C23—862no—
217C23—1722no—
218C23—1721no—
219Q8—22no—
220Q8—41no—
221Q8—432no—
222Q8D4×D4312yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—432no—
227D4—862no—
228D4—862no—
229D4—862no—
230D4—3442no—
231D4—1722no—
232D4—1722no—
233D4—1722no—
234D4D4×D4312yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—862no—
240C2×C4—1722no—
241C2×C4—1721no—
242C2×C4C23×D4311yescharacteristic
243C8—22no—
244C8—432no—
245C8—432no—
246C8—862no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—862no—
251C22—3442no—
252C22—1722no—
253C22—6882no—
254C22—6881no—
255C22#1306337011yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—862no—
260C4C2×D4×D4312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—3442no—
265C2—1722no—
266C2#1458353111yescharacteristic
subgroupG/H
centerC2#14583531
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#454C2
socleC2×C43D42
hypercenter#454D43
hypocenterC43#3288
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. #14583707C2semidirect
2. #14583703C2semidirect
3. #14583289C2semidirect
4. #14583167C2semidirect
5. #14583165C2semidirect
6. #14583076C2semidirect
7. #14583068C2semidirect
8. #14583018C2semidirect
9. C43×#454C2semidirect
10. #13063371C22semidirect
13. #13063356C22semidirect
17. #13063350C22semidirect
23. C2×#10621884C22semidirect
24. C2×#10621882C22semidirect
26. #13063333C22semidirect
27. #13063332C22semidirect
28. #13063322C22semidirect
29. #13063260C22semidirect
30. #13063253C22semidirect
31. #13063242C22semidirect
32. #13063241C22semidirect
33. #13063236C22semidirect
34. 2−1+4×C43C22semidirect
35. AGL(1,ℤ/8)×C43C22semidirect
36. #124×C43C22semidirect
37. #104×C43C22semidirect
38. #101×C43C22semidirect
62. #10621885D4semidirect
67. #10621884D4semidirect
68. #10621883D4semidirect
72. #10621882D4semidirect
140. #454D43semidirect
143. C43#3288semidirect
144. 2−1+4C2×D43semidirect
154. AGL(1,ℤ/8)C2×D43semidirect
165. #124C2×D43semidirect
168. #104C2×D43semidirect
169. #101C2×D43semidirect