Finite Group Databasebeta

← #19145059

Subgroups — #19145059

Order 5504.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063356C212yesmaximal, complemented
2C2×#13063351C212yesmaximal, complemented
3#14583449C211yesmaximal, characteristic, complemented
4#14583294C212yesmaximal, complemented
5#14583289C212yesmaximal, complemented
6#14583281C214yesmaximal, complemented
7C4×#10621877C211yesmaximal, characteristic, complemented
8C2×#124×C43C211yesmaximal, characteristic, complemented
9C2×#10621898C2212yes—
10#13063356—28no—
11#13063351—28no—
12C2×#10621885C2214yescomplemented
13C2×#10621883C2214yes—
14C2×#10621884C2214yescomplemented
15C2×#10621882C2214yes—
16C2×#10621877C2212yes—
17#13063325C2211yescharacteristic, complemented
18#13063322C2211yescharacteristic, complemented
19#13063313C2212yescomplemented
20#13063299—22no—
21C4×D172—22no—
22#13063236C2212yescomplemented
23C4×C43⋊C8C2212yescomplemented
24C22×Q8×C43C2211yescharacteristic
25C22×D4×C43C2211yescharacteristic
26#124×C43—22no—
27#124×C43C2212yes—
28#124×C43C2212yes—
29C2×C22⋊C4×C43—22no—
30C2×C42×C43C2211yescharacteristic
31C24×C43—21no—
32C2×Q8×C43—21no—
33C2×Q8×C43—24no—
34C2×Q8×C43C2312yes—
35C2×D4×C43—21no—
36C2×D4×C43—24no—
37C2×D4×C43C2312yes—
38C22×C4×C43—21no—
39C22×C4×C43D412yes—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—22no—
42#10621898—24no—
43#10621898—24no—
44C2×D172—22no—
45C2×D172C2312yes—
46C2×C4×D43—22no—
47C2×Dic86C2312yes—
48C22⋊C4×C43—24no—
49C22⋊C4×C43—24no—
50C42×C43D412yes—
51C42×C43C2311yescharacteristic
52C42×C43C2311yescharacteristic
53#10621885—28no—
54#10621884—28no—
55#10621883—28no—
56#10621882—28no—
57(C2×D43)⋊C4—24no—
58C4⋊Dic43—22no—
59#10621877D418yescomplemented
60C2×C43⋊C8C2314yes—
61C23×C43—22no—
62C23×C43—44no—
63C23×C43—42no—
64C23×C43C2×D411yescharacteristic
65C22×D43—22no—
66Q8×C43—24no—
67Q8×C43—42no—
68D4×C43—24no—
69D4×C43—42no—
70C2×C4×C43—22no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43C2×D414yes—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2411yescharacteristic
78C22⋊D43—44no—
79C2×Dic43—22no—
80D172—22no—
81D172—22no—
82D172—44no—
83C4×D43—44no—
84Dic86—22no—
85Dic86—22no—
86C43⋊C8C2×D418yes—
87C22×C43—22no—
88C22×C43—42no—
89C22×C43—44no—
90C22×C43—84no—
91C22×C43#12712yes—
92C22×C43C22×D411yescharacteristic
93C2×D43—42no—
94C2×D43—44no—
95C4×C43—22no—
96C4×C43—22no—
97C4×C43—42no—
98C4×C43#12712yes—
99C4×C43C22×D412yes—
100Dic43—42no—
101#3153—431nomaximal, Sylow
102C2×C43—22no—
103C2×C43—82no—
104C2×C43C2×#12711yescharacteristic
105C2×C43#57512yes—
106D43—82no—
107C2×#137—432no—
108C2×AGL(1,ℤ/8)—432no—
109#532—431no—
110C2×#124D4311yescharacteristic, complemented
111#497—432no—
112#496—432no—
113#495—434no—
114C4×M16—431no—
115C43#315311yescharacteristic, complemented, Sylow
116C2×#41—432no—
117C22×Q8C2×D4311yescharacteristic
118C22×D4C2×D4311yescharacteristic
119#137—868no—
120AGL(1,ℤ/8)—868no—
121C2×Q16—434no—
122C2×SD16—434no—
123C2×SD16—434no—
124C2×D8—434no—
125C2×M16—432no—
126C4⋊Q8—431no—
127#127—431no—
128#124—22no—
129#124—432no—
130#124C2×D4312yes—
131#124C2×D4312yes—
132#121—862no—
133C4×D4—862no—
134C2×C22⋊C4—22no—
135C2×C42C2×D4311yescharacteristic
136#97—432no—
137C4×C8—432no—
138C24—21no—
139#41—864no—
140#41—864no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—432no—
144C2×Q8C22×D4312yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—432no—
148C2×D4—862no—
149C2×D4—862no—
150C2×D4C22×D4312yes—
151C22×C4—21no—
152C22×C4—862no—
153C22×C4C22⋊D4312yes—
154C22×C4C22×D4311yescharacteristic
155Q16—868no—
156SD16—868no—
157SD16—868no—
158D8—868no—
159M16—438no—
160C2×C8—434no—
161C4⋊C4—862no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—864no—
165C42C22⋊D4312yes—
166C42C22×D4311yescharacteristic
167C42C22×D4311yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—862no—
172C23C2×C22⋊D4311yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—862no—
176Q8—862no—
177D4—24no—
178D4—42no—
179D4—862no—
180D4—862no—
181D4—1724no—
182D4—1724no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—862no—
187C2×C4—1724no—
188C2×C4D4×D4314yes—
189C2×C4C2×C22⋊D4312yes—
190C2×C4C2×C22⋊D4312yes—
191C2×C4C2×C22⋊D4311yescharacteristic
192C2×C4C23×D4311yescharacteristic
193C8—438no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—1722no—
199C22—1724no—
200C22#1306332112yes—
201C22C22×C22⋊D4311yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—1722no—
206C4#1306332112yes—
207C4C2×D4×D4312yes—
208C2—22no—
209C2—82no—
210C2—3442no—
211C2C2×#1306332111yescharacteristic
212C2#1458369712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#124×C43C2
socleC22×C43C22×D4
hypercenterC2×#124D43
hypocenterC43#3153
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13063356C2semidirect
2. C2×#13063351C2semidirect
3. #14583449C2semidirect
4. #14583294C2semidirect
5. #14583289C2semidirect
6. #14583281C2semidirect
7. C4×#10621877C2semidirect
8. C2×#124×C43C2semidirect
12. C2×#10621885C22semidirect
14. C2×#10621884C22semidirect
17. #13063325C22semidirect
18. #13063322C22semidirect
19. #13063313C22semidirect
22. #13063236C22semidirect
23. C4×C43⋊C8C22semidirect
59. #10621877D4semidirect
110. C2×#124D43semidirect
115. C43#3153semidirect