Finite Group Databasebeta

← #14583544

Subgroups — #14583544

Order 2752.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×#10621900C211yesmaximal, characteristic, complemented
2C2×D4×D43C211yesmaximal, characteristic, complemented
3#13063313C211yesmaximal, characteristic, complemented
4#13063309C212yesmaximal, complemented
5#13063305C211yesmaximal, characteristic, complemented
6#13063300C211yesmaximal, characteristic, complemented
7#13063299C212yesmaximal, complemented
8#13063295C212yesmaximal, complemented
9C4×D172C211yesmaximal, characteristic, complemented
10C2×(C2×D43)⋊C4C212yesmaximal, complemented
11C4×D4×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yes—
13C2×D4×C43C2211yescharacteristic
14C22×C4×C43C2212yescomplemented
15C2×C22⋊D43C2212yes—
16C2×C22⋊D43C2212yescomplemented
17C22×Dic43C2212yescomplemented
18#10621900—24no—
19D4×D43—24no—
20C2×D172C2211yescharacteristic
21C2×D172C2211yescharacteristic
22C2×D172C2212yescomplemented
23C2×C4×D43C2211yescharacteristic
24C2×C4×D43C2211yescharacteristic, complemented
25C2×Dic86C2211yescharacteristic, complemented
26C4⋊C4×C43C2211yescharacteristic, complemented
27C22⋊C4×C43C2212yescomplemented
28C42×C43C2211yescharacteristic, complemented
29(C2×D43)⋊C4C2211yescharacteristic
30(C2×D43)⋊C4C2212yes—
31(C2×D43)⋊C4C2212yescomplemented
32(C2×D43)⋊C4C2212yescomplemented
33(C2×D43)⋊C4C2211yescharacteristic, complemented
34(C2×D43)⋊C4C2212yescomplemented
35C4⋊Dic43C2211yescharacteristic, complemented
36C4⋊Dic43C2212yescomplemented
37C23×C43C2312yes—
38C22×D43—24no—
39C22×D43—24no—
40C22×D43—42no—
41C22×D43C2312yes—
42C22×D43C2311yescharacteristic
43C22×D43C2311yescharacteristic
44D4×C43D414yescomplemented
45C2×C4×C43—42no—
46C2×C4×C43C2312yes—
47C2×C4×C43C2311yescharacteristic
48C2×C4×C43C2311yescharacteristic
49C2×C4×C43C2311yescharacteristic
50C22⋊D43—24no—
51C22⋊D43—24no—
52C2×Dic43—24no—
53C2×Dic43C2311yescharacteristic
54C2×Dic43C2312yes—
55C2×Dic43C2311yescharacteristic
56D172—22no—
57D172—22no—
58D172—42no—
59C4×D43—22no—
60C4×D43—22no—
61Dic86—22no—
62C22×C43—22no—
63C22×C43—22no—
64C22×C43C2×D414yes—
65C22×C43C2411yescharacteristic
66C2×D43—21no—
67C2×D43—21no—
68C2×D43—22no—
69C2×D43—21no—
70C2×D43—22no—
71C2×D43—21no—
72C2×D43—22no—
73C2×D43—21no—
74C2×D43—48no—
75C2×D43#4112yescomplemented
76C4×C43—21no—
77C4×C43—22no—
78C4×C43—21no—
79C4×C43C2×D412yes—
80Dic43—22no—
81Dic43—21no—
82Dic43—21no—
83C2×C43—24no—
84C2×C43C22×D411yescharacteristic
85C2×C43C2×#4111yescharacteristic
86C2×C43H(5,𝔽2)11yescharacteristic
87D43—22no—
88D43—41no—
89D43—42no—
90#546—431nomaximal, Sylow
91C43#54611yescharacteristic, complemented, Sylow
92C2×#41—431no—
93C22×D4—431no—
94#124—431no—
95#123—432no—
96C22⋊Q8—431no—
97#121—432no—
98#121—431no—
99#120—432no—
100C4×D4—431no—
101C4×D4D4311yescharacteristic, complemented
102C2×C22⋊C4—432no—
103C24—432no—
104#41—864no—
105C2×Q8—431no—
106C2×D4—432no—
107C2×D4—432no—
108C2×D4—431no—
109C2×D4—431no—
110C2×D4—432no—
111C2×D4—864no—
112C2×D4C2×D4311yescharacteristic
113C22×C4—432no—
114C22×C4—431no—
115C22×C4—431no—
116C22×C4C2×D4312yescomplemented
117C4⋊C4—431no—
118C4⋊C4—432no—
119C4⋊C4C2×D4311yescharacteristic, complemented
120C22⋊C4—431no—
121C22⋊C4—432no—
122C22⋊C4—432no—
123C22⋊C4—432no—
124C22⋊C4—431no—
125C22⋊C4—432no—
126C22⋊C4C2×D4312yescomplemented
127C42C2×D4311yescharacteristic, complemented
128C23—431no—
129C23—432no—
130C23—431no—
131C23—864no—
132C23—864no—
133C23—1722no—
134C23C22×D4312yes—
135Q8—862no—
136D4—862no—
137D4—864no—
138D4—864no—
139D4—862no—
140D4—1722no—
141D4D17214yescomplemented
142C2×C4—42no—
143C2×C4—431no—
144C2×C4—432no—
145C2×C4—431no—
146C2×C4—864no—
147C2×C4—862no—
148C2×C4—862no—
149C2×C4C22×D4311yescharacteristic
150C2×C4C22×D4311yescharacteristic
151C2×C4C22×D4312yes—
152C2×C4C22×D4311yescharacteristic
153C22—22no—
154C22—22no—
155C22—432no—
156C22—861no—
157C22—861no—
158C22—861no—
159C22—862no—
160C22—861no—
161C22—862no—
162C22—861no—
163C22—862no—
164C22—1728no—
165C22C2×D17214yes—
166C22C23×D4311yescharacteristic
167C4—21no—
168C4—21no—
169C4—22no—
170C4—861no—
171C4—861no—
172C4—862no—
173C4C2×D17212yes—
174C2—24no—
175C2—862no—
176C2—1722no—
177C2—1721no—
178C2C22×D17211yescharacteristic
179C2#41×D4311yescharacteristic
180C2#1306337011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC4×D4×C43C2
hypercenterC4×D4D43
hypocenterC43#546
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10621900C2semidirect
2. C2×D4×D43C2semidirect
3. #13063313C2semidirect
4. #13063309C2semidirect
5. #13063305C2semidirect
6. #13063300C2semidirect
7. #13063299C2semidirect
8. #13063295C2semidirect
9. C4×D172C2semidirect
10. C2×(C2×D43)⋊C4C2semidirect
11. C4×D4×C43C2semidirect
14. C22×C4×C43C22semidirect
16. C2×C22⋊D43C22semidirect
17. C22×Dic43C22semidirect
22. C2×D172C22semidirect
24. C2×C4×D43C22semidirect
25. C2×Dic86C22semidirect
26. C4⋊C4×C43C22semidirect
27. C22⋊C4×C43C22semidirect
28. C42×C43C22semidirect
31. (C2×D43)⋊C4C22semidirect
32. (C2×D43)⋊C4C22semidirect
33. (C2×D43)⋊C4C22semidirect
34. (C2×D43)⋊C4C22semidirect
35. C4⋊Dic43C22semidirect
36. C4⋊Dic43C22semidirect
44. D4×C43D4semidirect
75. C2×D43#41semidirect
91. C43#546semidirect
101. C4×D4D43semidirect
116. C22×C4C2×D43semidirect
119. C4⋊C4C2×D43semidirect
126. C22⋊C4C2×D43semidirect
127. C42C2×D43semidirect
141. D4D172semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106219002
C2×D4×D432
#130633132
#130633092
#130633052
#130633002
#130632992
#130632952
C4×D1722
C2×(C2×D43)⋊C42
C4×D4×C432
#54643