Finite Group Databasebeta

← #19149289

Subgroups — #19149289

Order 5504.

958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.

normal subgroups only

This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 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#14583649C213yesmaximal, complemented
2#14583618C216yesmaximal, complemented
3#14583580C216yesmaximal, complemented
4#14583513C216yesmaximal, complemented
5#14583484C216yesmaximal, complemented
6#14583428C213yesmaximal, complemented
7C43×H(3,𝔽4)C211yesmaximal, characteristic, complemented
8#13063323C2216yescomplemented
9#13063319C2212yescomplemented
10#13063318C2216yescomplemented
11#13063318C2216yescomplemented
12#13063318C2216yescomplemented
13#13063318C2216yescomplemented
14#13063317C2213yescomplemented
15#13063312C2216yes—
16#13063311C2216yescomplemented
17#13063307C2216yescomplemented
18#13063306C2216yes—
19#13063306C2216yes—
20#13063302C2216yescomplemented
21#13063302C2216yescomplemented
22#13063302C2216yescomplemented
23#13063301C2213yescomplemented
24#13063297C2216yes—
25#13063296C2213yes—
26#13063294C2212yescomplemented
27Q8×Dic43C2213yescomplemented
28C4×Dic86C2216yescomplemented
29D4×Dic43C2213yes—
30D4×Dic43C2216yes—
31(C22⋊D43)⋊C4C2216yescomplemented
32#13063281C2216yescomplemented
33#13063281C2216yescomplemented
34C2×C22⋊Dic43C2216yescomplemented
35C42×D43C2211yescharacteristic, complemented
36#124×C43C2216yes—
37#124×C43C2213yes—
38#120×C43C2216yes—
39C24×C43C2312yes—
40C2×Q8×C43C2313yes—
41C2×D4×C43C2313yes—
42C2×D4×C43C2316yes—
43C2×C22⋊D43C2316yes—
44C22×Dic43C2316yes—
45C22×Dic43C2316yes—
46C2×C4×D43C2313yes—
47C2×Dic86C2316yes—
48C22⋊C4×C43C2316yes—
49C22⋊C4×C43C2316yes—
50C22⋊C4×C43C2316yes—
51C42×C43C2311yescharacteristic
52C42×C43C2312yes—
53C22⋊Dic43C2316yes—
54C22⋊Dic43C2316yes—
55C22⋊Dic43C2316yes—
56C22⋊Dic43C2316yes—
57C22⋊Dic43C2316yes—
58(C2×D43)⋊C4C2316yes—
59C4⋊Dic43C2316yes—
60C4⋊Dic43C2313yes—
61C4⋊Dic43C2313yes—
62Dic43⋊C4C2316yes—
63Dic43⋊C4C2316yes—
64Dic43⋊C4C2316yes—
65Dic43⋊C4C2316yes—
66Dic43⋊C4C2316yes—
67C4×Dic43C2313yes—
68C4×Dic43C2316yes—
69C4×Dic43C2316yes—
70C23×C43—46no—
71C23×C43C2416yes—
72C22×D43C2411yescharacteristic
73Q8×C43—43no—
74D4×C43—46no—
75D4×C43—43no—
76C2×C4×C43C2416yes—
77C2×C4×C43C2413yes—
78C22⋊D43—46no—
79C2×Dic43—46no—
80C2×Dic43—46no—
81C2×Dic43C2413yes—
82C2×Dic43C2416yes—
83C2×Dic43C2416yes—
84C4×D43—43no—
85Dic86—46no—
86C22×C43—26no—
87C22×C43—26no—
88C22×C43—26no—
89C22×C43—84no—
90C22×C43C2511yescharacteristic
91C2×D43—23no—
92C4×C43—26no—
93C4×C43—23no—
94Dic43—26no—
95Dic43—26no—
96Dic43—23no—
97#3568—431nomaximal, Sylow
98C2×C43—46no—
99C2×C43#58513yes—
100D43—41no—
101#563—433no—
102H(3,𝔽4)D4311yescharacteristic, complemented
103#556—436no—
104#551—436no—
105#542—436no—
106#538—436no—
107#529—433no—
108C43#356811yescharacteristic, complemented, Sylow
109C4⋊Q8—436no—
110#126—436no—
111#126—436no—
112#126—436no—
113#126—436no—
114#126—432no—
115#125—433no—
116#124—436no—
117#124—436no—
118#124C2×D4313yes—
119#124C2×D4316yes—
120#123—436no—
121#123—436no—
122#123—436no—
123C22⋊Q8—433no—
124C22⋊Q8—436no—
125C22⋊Q8—436no—
126C22⋊Q8—436no—
127#121—433no—
128#121—436no—
129#120—432no—
130#120C2×D4316yes—
131C4×Q8—433no—
132C4×Q8—436no—
133C4×D4—433no—
134C4×D4—436no—
135C4×D4—436no—
136#117—436no—
137#117—436no—
138C2×C22⋊C4—436no—
139C2×C42—431no—
140C24C22×D4312yes—
141C2×Q8—436no—
142C2×Q8C22×D4313yes—
143C2×D4—436no—
144C2×D4C22×D4313yes—
145C2×D4C22×D4316yes—
146C22×C4—436no—
147C22×C4—436no—
148C22×C4—433no—
149C4⋊C4—436no—
150C4⋊C4—436no—
151C4⋊C4—436no—
152C4⋊C4—436no—
153C4⋊C4—433no—
154C4⋊C4—436no—
155C4⋊C4—433no—
156C4⋊C4—436no—
157C22⋊C4—436no—
158C22⋊C4—436no—
159C22⋊C4—436no—
160C22⋊C4—436no—
161C22⋊C4—436no—
162C22⋊C4—436no—
163C22⋊C4C22×D4316yes—
164C22⋊C4C22×D4316yes—
165C22⋊C4C22×D4316yes—
166C42—433no—
167C42—436no—
168C42—436no—
169C42C22×D4311yescharacteristic
170C42C22×D4312yes—
171C23—46no—
172C23—431no—
173C23C23×D4316yes—
174Q8—43no—
175Q8—1726no—
176D4—43no—
177D4—46no—
178D4—1726no—
179C2×C4—433no—
180C2×C4—436no—
181C2×C4—436no—
182C2×C4—1723no—
183C2×C4—1726no—
184C2×C4—1726no—
185C2×C4C23×D4316yes—
186C2×C4C23×D4313yes—
187C22—26no—
188C22—26no—
189C22—26no—
190C22—84no—
191C22—863no—
192C22C24×D4311yescharacteristic
193C4—23no—
194C4—26no—
195C4—863no—
196C4—866no—
197C4—866no—
198C2—46no—
199C2—1721no—
200C2#1458373413yes—
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×H(3,𝔽4)C2
hypercenterH(3,𝔽4)D43
hypocenterC43#3568
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ H(3,𝔽4)

Complements

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

NH ≅ G/Ntype
1. #14583649C2semidirect
2. #14583618C2semidirect
3. #14583580C2semidirect
4. #14583513C2semidirect
5. #14583484C2semidirect
6. #14583428C2semidirect
7. C43×H(3,𝔽4)C2semidirect
8. #13063323C22semidirect
9. #13063319C22semidirect
10. #13063318C22semidirect
11. #13063318C22semidirect
12. #13063318C22semidirect
13. #13063318C22semidirect
14. #13063317C22semidirect
16. #13063311C22semidirect
17. #13063307C22semidirect
20. #13063302C22semidirect
21. #13063302C22semidirect
22. #13063302C22semidirect
23. #13063301C22semidirect
26. #13063294C22semidirect
27. Q8×Dic43C22semidirect
28. C4×Dic86C22semidirect
31. (C22⋊D43)⋊C4C22semidirect
32. #13063281C22semidirect
33. #13063281C22semidirect
34. C2×C22⋊Dic43C22semidirect
35. C42×D43C22semidirect
102. H(3,𝔽4)D43semidirect
108. C43#3568semidirect