Finite Group Databasebeta

← #19149374

Subgroups — #19149374

Order 5504.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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
1C2×#13063371C211yesmaximal, characteristic, complemented
2#14583707C218yesmaximal, complemented
3#14583702C218yesmaximal, complemented
4#14583697C216yesmaximal, complemented
5C2×#13063350C216yesmaximal, complemented
6#14583666C211yesmaximal, characteristic, complemented
7C43×#585C211yesmaximal, characteristic, complemented
8#13063371—24no—
9#13063371C2218yescomplemented
10C2×#10621902—21no—
11C2×#10621898C2213yescomplemented
12C22×D172C2213yescomplemented
13C2×D4×D43—23no—
14#13063356C22112yescomplemented
15#13063355C2214yescomplemented
16#13063351C22112yescomplemented
17#13063350C22112yescomplemented
18#13063350C22124yescomplemented
19#13063345C22124yescomplemented
20C2×#10621884C22112yescomplemented
21C2×#10621882C22112yescomplemented
22#13063332C2218yescomplemented
23C2×#10621877C2216yescomplemented
242−1+4×C43—21no—
252−1+4×C43C2214yescomplemented
26H(5,𝔽2)×C43—23no—
27H(5,𝔽2)×C43C2214yescomplemented
28C2×#41×C43—24no—
29C2×#41×C43C2211yescharacteristic
30C2×#41×C43C2216yescomplemented
31C23×D43—23no—
32#41×C43—24no—
33#41×C43—212no—
34#41×C43—26no—
35#41×C43—26no—
36#41×C43D414yes—
37#41×C43C2314yes—
38#41×C43C2314yes—
39#41×C43C23112yescomplemented
40C2×Q8×C43—24no—
41C2×Q8×C43D411yescharacteristic
42C2×Q8×C43C2316yescomplemented
43C2×D4×C43—212no—
44C2×D4×C43—26no—
45C2×D4×C43D413yes—
46C2×D4×C43C2316yescomplemented
47C22×C4×C43—26no—
48C22×C4×C43C2313yes—
49C2×C22⋊D43—23no—
50#10621902—28no—
51D4×D43—224no—
52#10621898—26no—
53#10621898C23112yes—
54C2×D172—23no—
55C2×D172—26no—
56C2×D172C23112yes—
57C2×D172C2313yes—
58C2×C4×D43—23no—
59C2×Dic86C2311yescharacteristic
60#10621885C2318yescomplemented
61#10621884C23124yescomplemented
62#10621883C2318yescomplemented
63#10621882C23124yescomplemented
64#10621877C2314yes—
65#10621877C23112yescomplemented
66C2×C43⋊C8C23112yescomplemented
67C23×C43—26no—
68C23×C43C2×D413yes—
69C22×D43—23no—
70C22×D43—212no—
71C22×D43—86no—
72Q8×C43—26no—
73Q8×C43C2×D414yes—
74Q8×C43C2414yes—
75D4×C43—24no—
76D4×C43—212no—
77D4×C43—26no—
78D4×C43C2×D4112yes—
79D4×C43C2414yes—
80C2×C4×C43—26no—
81C2×C4×C43—24no—
82C2×C4×C43—212no—
83C2×C4×C43C2×D413yes—
84C2×C4×C43C2×D416yes—
85C2×C4×C43C2416yes—
86C2×C4×C43C2411yescharacteristic
87C22⋊D43—212no—
88C2×Dic43—21no—
89D172—23no—
90D172—212no—
91D172C2416yes—
92C4×D43—212no—
93Dic86—21no—
94Dic86C2412yes—
95C43⋊C8C2418yes—
96C22×C43—24no—
97C22×C43—43no—
98C22×C43—86no—
99C22×C43C22×D411yescharacteristic
100C22×C43C22×D416yes—
101C2×D43—26no—
102C2×D43—46no—
103C2×D43—812no—
104C4×C43—24no—
105C4×C43C22×D411yescharacteristic
106C4×C43C22×D416yes—
107C4×C43C2511yescharacteristic
108Dic43—22no—
109#3585—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—26no—
112C2×C43—44no—
113C2×C43C23×D411yescharacteristic
114D43—46no—
115#585D4311yescharacteristic, complemented
116C2×H(5,𝔽2)—431no—
117#577—438no—
118#576—438no—
119#575—436no—
120C2×AGL(1,ℤ/8)—436no—
121#568—431no—
122C43#358511yescharacteristic, complemented, Sylow
1232−1+4—21no—
1242−1+4C2×D4314yescomplemented
125H(5,𝔽2)—23no—
126H(5,𝔽2)—438no—
127H(5,𝔽2)—864no—
128H(5,𝔽2)C2×D4314yescomplemented
129C2×#41—24no—
130C2×#41—433no—
131C2×#41—861no—
132C2×#41C2×D4311yescharacteristic
133C2×#41C2×D4316yescomplemented
134C22×D4—433no—
135C22×D4—863no—
136#137—434no—
137#137—4312no—
138AGL(1,ℤ/8)—4312no—
139AGL(1,ℤ/8)—4324no—
140AGL(1,ℤ/8)—4312no—
141#135—4324no—
142C2×SD16—4312no—
143C2×D8—4312no—
144#131—438no—
145C2×M16—436no—
146C24—863no—
147#41—24no—
148#41—212no—
149#41—26no—
150#41—26no—
151#41—4312no—
152#41—868no—
153#41—866no—
154#41C22⋊D4314yes—
155#41C22×D4314yes—
156#41C22×D4314yes—
157#41C22×D43112yescomplemented
158C2×Q8—24no—
159C2×Q8—431no—
160C2×Q8C22⋊D4311yescharacteristic
161C2×Q8C22×D4316yescomplemented
162C2×D4—26no—
163C2×D4—212no—
164C2×D4—4312no—
165C2×D4—433no—
166C2×D4—863no—
167C2×D4—8624no—
168C2×D4—863no—
169C2×D4—866no—
170C2×D4C22⋊D4313yes—
171C2×D4C22×D4316yescomplemented
172C22×C4—26no—
173C22×C4—863no—
174C22×C4C22×D4313yes—
175Q16—438no—
176SD16—4324no—
177SD16—438no—
178D8—4324no—
179M16—434no—
180M16—4312no—
181C2×C8—4312no—
182C23—26no—
183C23—8612no—
184C23—863no—
185C23—3446no—
186C23C2×C22⋊D4313yes—
187Q8—26no—
188Q8—432no—
189Q8—861no—
190Q8C2×C22⋊D4314yes—
191Q8C23×D4314yes—
192D4—24no—
193D4—212no—
194D4—26no—
195D4—436no—
196D4—8612no—
197D4—863no—
198D4—8612no—
199D4C2×C22⋊D43112yes—
200D4C23×D4314yes—
201C2×C4—26no—
202C2×C4—24no—
203C2×C4—212no—
204C2×C4—861no—
205C2×C4—8612no—
206C2×C4C2×C22⋊D4316yes—
207C2×C4C2×C22⋊D4313yes—
208C2×C4C23×D4316yes—
209C2×C4C23×D4311yescharacteristic
210C8—438no—
211C22—24no—
212C22—43no—
213C22—86no—
214C22—866no—
215C22—34412no—
216C22—1726no—
217C22C22×C22⋊D4316yes—
218C22C22×C22⋊D4311yescharacteristic
219C4—24no—
220C4—862no—
221C4C22×C22⋊D4311yescharacteristic
222C4C22×C22⋊D4316yes—
223C4C24×D4311yescharacteristic
224C2—21no—
225C2—26no—
226C2—44no—
227C2—1726no—
228C2C23×C22⋊D4311yescharacteristic
subgroupG/H
centerC2C23×C22⋊D43
commutatorC4×C43C25
FrattiniC4C24×D43
FittingC43×#585C2
socleC2×C43C23×D4
hypercenter#585D43
hypocenterC43#3585
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×#41 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. #14583707C2semidirect
3. #14583702C2semidirect
4. #14583697C2semidirect
5. C2×#13063350C2semidirect
6. #14583666C2semidirect
7. C43×#585C2semidirect
9. #13063371C22semidirect
11. C2×#10621898C22semidirect
12. C22×D172C22semidirect
14. #13063356C22semidirect
15. #13063355C22semidirect
16. #13063351C22semidirect
17. #13063350C22semidirect
18. #13063350C22semidirect
19. #13063345C22semidirect
20. C2×#10621884C22semidirect
21. C2×#10621882C22semidirect
22. #13063332C22semidirect
23. C2×#10621877C22semidirect
25. 2−1+4×C43C22semidirect
27. H(5,𝔽2)×C43C22semidirect
30. C2×#41×C43C22semidirect
39. #41×C43C23semidirect
42. C2×Q8×C43C23semidirect
46. C2×D4×C43C23semidirect
60. #10621885C23semidirect
61. #10621884C23semidirect
62. #10621883C23semidirect
63. #10621882C23semidirect
65. #10621877C23semidirect
66. C2×C43⋊C8C23semidirect
115. #585D43semidirect
122. C43#3585semidirect
124. 2−1+4C2×D43semidirect
128. H(5,𝔽2)C2×D43semidirect
133. C2×#41C2×D43semidirect
157. #41C22×D43semidirect
161. C2×Q8C22×D43semidirect
171. C2×D4C22×D43semidirect