Finite Group Databasebeta

← #19148007

Subgroups — #19148007

Order 5504.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 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#14583498C216yesmaximal, complemented
2#14583489C216yesmaximal, complemented
3#14583461C213yesmaximal, complemented
4#14583435C216yesmaximal, complemented
5#14583412C216yesmaximal, complemented
6C2×(C22⋊D43)⋊C4C213yesmaximal, complemented
7C43×#543C211yesmaximal, characteristic, complemented
8C2×#10621902C2212yescomplemented
9C22×C22⋊D43C2213yes—
10C23×Dic43C2211yescharacteristic
11C22×C4×D43C2213yescomplemented
12#13063320C22112yescomplemented
13#13063316C2216yescomplemented
14#13063314C2216yescomplemented
15#13063310C22112yescomplemented
16#13063309C22112yescomplemented
17#13063301C2216yescomplemented
18#13063300C2216yescomplemented
19#13063299C2216yes—
20#13063299C2216yes—
21#13063295C22112yescomplemented
22Q8×Dic43C2212yescomplemented
23#13063287C2216yescomplemented
24(C22⋊D43)⋊C4C22112yescomplemented
25(C22⋊D43)⋊C4C22112yescomplemented
26#13063283C2216yescomplemented
27C2×Dic43⋊C4C2213yescomplemented
28C2×(C2×D43)⋊C4C2213yescomplemented
29C2×C4×Dic43C2213yescomplemented
30C22⋊Q8×C43C2216yescomplemented
31C22⋊Q8×C43C2216yescomplemented
32C2×C22⋊C4×C43C2213yes—
33C24×C43C2311yescharacteristic
34C23×D43C2313yes—
35C2×Q8×C43C2312yes—
36C2×Q8×C43C2312yes—
37C22×C4×C43C2313yes—
38C22×C4×C43C2313yes—
39C2×C22⋊D43—212no—
40C2×C22⋊D43C23112yes—
41C22×Dic43—42no—
42C22×Dic43C2313yes—
43C22×Dic43C2313yes—
44C22×Dic43C2313yes—
45#10621902—44no—
46C2×D172C2316yes—
47C2×D172C2316yes—
48C2×C4×D43—46no—
49C2×C4×D43C2316yes—
50C2×C4×D43C2316yes—
51C4⋊C4×C43C2316yes—
52C4⋊C4×C43C2316yes—
53C22⋊C4×C43C23112yes—
54(C2×D43)⋊C4C23112yes—
55(C2×D43)⋊C4C23112yes—
56(C2×D43)⋊C4C23112yes—
57C4⋊Dic43C2316yes—
58C4⋊Dic43C2316yes—
59Dic43⋊C4C23112yes—
60C4×Dic43C2316yes—
61C4×Dic43C2316yes—
62C23×C43—41no—
63C23×C43—41no—
64C23×C43#4114yescomplemented
65C23×C43C2413yes—
66C22×D43—26no—
67C22×D43—43no—
68C22×D43—43no—
69C22×D43C2416yes—
70Q8×C43—42no—
71Q8×C43—42no—
72C2×C4×C43—43no—
73C2×C4×C43—43no—
74C2×C4×C43C2416yes—
75C2×C4×C43C2416yes—
76C22⋊D43—224no—
77C2×Dic43—26no—
78C2×Dic43—26no—
79C2×Dic43—43no—
80C2×Dic43C2413yes—
81C2×Dic43C2416yes—
82C2×Dic43C2411yescharacteristic
83D172—46no—
84D172—46no—
85C4×D43—212no—
86C4×D43—46no—
87C22×C43—23no—
88C22×C43—23no—
89C22×C43—44no—
90C22×C43C2×#4116yes—
91C22×C43C2511yescharacteristic
92C2×D43—26no—
93C2×D43—26no—
94C2×D43—26no—
95C2×D43—412no—
96C4×C43—26no—
97C4×C43—26no—
98Dic43—26no—
99Dic43—23no—
100Dic43H(5,𝔽2)12yes—
101#3459—431nomaximal, Sylow
102C2×C43—26no—
103C2×C43C22×#4111yescharacteristic
104C2×C43C2×H(5,𝔽2)11yescharacteristic
105C2×C43#58511yescharacteristic
106D43—46no—
107#543D4311yescharacteristic, complemented
108#539—436no—
109#538—436no—
110#534—433no—
111#529—436no—
112#525—436no—
113C2×C4×D4—433no—
114C43#345911yescharacteristic, complemented, Sylow
115C2×#41—432no—
116C22×D4—433no—
117C23×C4—431no—
118C23×C4—433no—
119#126—4312no—
120#125—436no—
121#124—436no—
122#123—4312no—
123#123—4312no—
124C22⋊Q8—436no—
125C22⋊Q8C2×D4316yescomplemented
126C22⋊Q8C2×D4316yescomplemented
127#121—436no—
128#121—436no—
129#121—436no—
130#120—4312no—
131C4×Q8—432no—
132C4×D4—436no—
133C4×D4—4312no—
134C4×D4—4312no—
135#117—436no—
136C2×C4⋊C4—433no—
137C2×C22⋊C4—433no—
138C2×C22⋊C4C2×D4313yes—
139C2×C42—433no—
140C24—433no—
141C24C22×D4311yescharacteristic
142#41—1724no—
143C2×Q8C22×D4312yes—
144C2×Q8C22×D4312yes—
145C2×D4—4312no—
146C2×D4—436no—
147C2×D4—436no—
148C2×D4—8612no—
149C22×C4—433no—
150C22×C4—433no—
151C22×C4—433no—
152C22×C4—436no—
153C22×C4—436no—
154C22×C4—1726no—
155C22×C4—1722no—
156C22×C4C22×D4313yes—
157C22×C4C22×D4313yes—
158C4⋊C4—4312no—
159C4⋊C4—436no—
160C4⋊C4—436no—
161C4⋊C4C22×D4316yes—
162C4⋊C4C22×D4316yes—
163C22⋊C4—4312no—
164C22⋊C4—4312no—
165C22⋊C4—4312no—
166C22⋊C4C22×D43112yes—
167C42—436no—
168C42—436no—
169C23—41no—
170C23—41no—
171C23—436no—
172C23—866no—
173C23—1723no—
174C23—1723no—
175C23#1062190214yescomplemented
176C23C23×D4313yes—
177Q8—42no—
178Q8—42no—
179D4—8624no—
180D4—1726no—
181D4—1726no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—431no—
185C2×C4—436no—
186C2×C4—433no—
187C2×C4—8612no—
188C2×C4—866no—
189C2×C4—866no—
190C2×C4—1726no—
191C2×C4—1723no—
192C2×C4C23×D4316yes—
193C2×C4C23×D4316yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—866no—
198C22—866no—
199C22—866no—
200C22—17212no—
201C22C2×#1062190216yes—
202C22C24×D4311yescharacteristic
203C4—26no—
204C4—26no—
205C4—432no—
206C4—866no—
207C4—863no—
208C2—26no—
209C2—1726no—
210C2C22×#1062190211yescharacteristic
211C2H(5,𝔽2)×D4311yescharacteristic
212C2#1458373411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#543C2
hypercenter#543D43
hypocenterC43#3459
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #14583498C2semidirect
2. #14583489C2semidirect
3. #14583461C2semidirect
4. #14583435C2semidirect
5. #14583412C2semidirect
6. C2×(C22⋊D43)⋊C4C2semidirect
7. C43×#543C2semidirect
8. C2×#10621902C22semidirect
11. C22×C4×D43C22semidirect
12. #13063320C22semidirect
13. #13063316C22semidirect
14. #13063314C22semidirect
15. #13063310C22semidirect
16. #13063309C22semidirect
17. #13063301C22semidirect
18. #13063300C22semidirect
21. #13063295C22semidirect
22. Q8×Dic43C22semidirect
23. #13063287C22semidirect
24. (C22⋊D43)⋊C4C22semidirect
25. (C22⋊D43)⋊C4C22semidirect
26. #13063283C22semidirect
27. C2×Dic43⋊C4C22semidirect
28. C2×(C2×D43)⋊C4C22semidirect
29. C2×C4×Dic43C22semidirect
30. C22⋊Q8×C43C22semidirect
31. C22⋊Q8×C43C22semidirect
64. C23×C43#41semidirect
107. #543D43semidirect
114. C43#3459semidirect
125. C22⋊Q8C2×D43semidirect
126. C22⋊Q8C2×D43semidirect
175. C23#10621902semidirect