Finite Group Databasebeta

← #14583537

Subgroups — #14583537

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×D4×D43C211yesmaximal, characteristic, complemented
2#13063314C211yesmaximal, characteristic, complemented
3#13063308C212yesmaximal, complemented
4#13063301C211yesmaximal, characteristic, complemented
5#13063299C211yesmaximal, characteristic, complemented
6#13063297C212yesmaximal, complemented
7#13063293C212yesmaximal, complemented
8D4×Dic43C211yesmaximal, characteristic, complemented
9C4×C22⋊D43C211yesmaximal, characteristic, complemented
10C2×(C2×D43)⋊C4C212yesmaximal, complemented
11C2×#41×C43C211yesmaximal, characteristic, complemented
12C23×D43C2212yes—
13#41×C43—24no—
14C2×Q8×C43C2211yescharacteristic, complemented
15C2×D4×C43C2211yescharacteristic
16C2×D4×C43C2212yescomplemented
17C22×C4×C43C2212yescomplemented
18C22×C4×C43C2211yescharacteristic, complemented
19C2×C22⋊D43C2211yescharacteristic
20C2×C22⋊D43C2212yes—
21C2×C22⋊D43C2212yescomplemented
22C22×Dic43C2212yescomplemented
23D4×D43—24no—
24C2×D172C2211yescharacteristic
25C2×C4×D43C2211yescharacteristic
26C22⋊Dic43C2211yescharacteristic, complemented
27C22⋊Dic43C2212yescomplemented
28(C2×D43)⋊C4C2211yescharacteristic
29(C2×D43)⋊C4C2212yes—
30(C2×D43)⋊C4C2212yescomplemented
31(C2×D43)⋊C4C2212yescomplemented
32(C2×D43)⋊C4C2212yescomplemented
33C4⋊Dic43C2211yescharacteristic, complemented
34Dic43⋊C4C2211yescharacteristic, complemented
35Dic43⋊C4C2212yescomplemented
36C4×Dic43C2211yescharacteristic, complemented
37C23×C43C2311yescharacteristic
38C23×C43C2312yes—
39C22×D43—24no—
40C22×D43—24no—
41C22×D43—42no—
42C22×D43C2312yes—
43C22×D43C2311yescharacteristic
44Q8×C43—22no—
45D4×C43—24no—
46D4×C43D414yescomplemented
47C2×C4×C43—24no—
48C2×C4×C43—22no—
49C2×C4×C43C2311yescharacteristic
50C2×C4×C43C2312yes—
51C2×C4×C43C2311yescharacteristic
52C22⋊D43—24no—
53C22⋊D43—22no—
54C22⋊D43—42no—
55C2×Dic43—42no—
56C2×Dic43C2311yescharacteristic
57C2×Dic43C2311yescharacteristic
58C2×Dic43C2311yescharacteristic
59C2×Dic43C2312yes—
60D172—22no—
61C4×D43—22no—
62C22×C43—22no—
63C22×C43—22no—
64C22×C43—21no—
65C22×C43—21no—
66C22×C43—21no—
67C22×C43C2×D414yes—
68C22×C43C2411yescharacteristic
69C2×D43—21no—
70C2×D43—21no—
71C2×D43—22no—
72C2×D43—22no—
73C2×D43—22no—
74C2×D43—48no—
75C2×D43#4112yescomplemented
76C4×C43—21no—
77C4×C43—22no—
78C4×C43C2×D412yes—
79Dic43—21no—
80Dic43—21no—
81Dic43—21no—
82Dic43—22no—
83C2×C43—24no—
84C2×C43—41no—
85C2×C43C22×D411yescharacteristic
86C2×C43C2×#4111yescharacteristic
87C2×C43H(5,𝔽2)11yescharacteristic
88D43—22no—
89D43—42no—
90#546—431nomaximal, Sylow
91C43#54611yescharacteristic, complemented, Sylow
92C2×#41D4311yescharacteristic, complemented
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×D4—431no—
102C2×C22⋊C4—432no—
103C24—432no—
104#41—24no—
105C2×Q8C2×D4311yescharacteristic, complemented
106C2×D4—431no—
107C2×D4—432no—
108C2×D4—432no—
109C2×D4—431no—
110C2×D4—864no—
111C2×D4C2×D4311yescharacteristic
112C2×D4C2×D4312yescomplemented
113C22×C4—432no—
114C22×C4—431no—
115C22×C4C2×D4312yescomplemented
116C22×C4C2×D4311yescharacteristic, complemented
117C4⋊C4—431no—
118C4⋊C4—431no—
119C4⋊C4—432no—
120C22⋊C4—432no—
121C22⋊C4—431no—
122C22⋊C4—431no—
123C22⋊C4—432no—
124C22⋊C4—432no—
125C22⋊C4—432no—
126C22⋊C4—432no—
127C42—431no—
128C23—431no—
129C23—432no—
130C23—864no—
131C23—864no—
132C23—1722no—
133C23C22×D4311yescharacteristic
134C23C22×D4312yes—
135Q8—22no—
136D4—24no—
137D4—862no—
138D4—864no—
139D4—862no—
140D4—1722no—
141D4C22⋊D4314yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—431no—
145C2×C4—431no—
146C2×C4—432no—
147C2×C4—431no—
148C2×C4—862no—
149C2×C4—1722no—
150C2×C4C22×D4311yescharacteristic
151C2×C4C22×D4312yes—
152C2×C4C22×D4311yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—432no—
159C22—861no—
160C22—861no—
161C22—862no—
162C22—862no—
163C22—862no—
164C22—1728no—
165C22C2×C22⋊D4314yes—
166C22C23×D4311yescharacteristic
167C4—21no—
168C4—22no—
169C4—861no—
170C4—861no—
171C4—861no—
172C4—862no—
173C4C2×C22⋊D4312yes—
174C2—24no—
175C2—41no—
176C2—862no—
177C2—1722no—
178C2C22×C22⋊D4311yescharacteristic
179C2#41×D4311yescharacteristic
180C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC2×#41×C43C2
hypercenterC2×#41D43
hypocenterC43#546
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D43C2semidirect
2. #13063314C2semidirect
3. #13063308C2semidirect
4. #13063301C2semidirect
5. #13063299C2semidirect
6. #13063297C2semidirect
7. #13063293C2semidirect
8. D4×Dic43C2semidirect
9. C4×C22⋊D43C2semidirect
10. C2×(C2×D43)⋊C4C2semidirect
11. C2×#41×C43C2semidirect
14. C2×Q8×C43C22semidirect
16. C2×D4×C43C22semidirect
17. C22×C4×C43C22semidirect
18. C22×C4×C43C22semidirect
21. C2×C22⋊D43C22semidirect
22. C22×Dic43C22semidirect
26. C22⋊Dic43C22semidirect
27. C22⋊Dic43C22semidirect
30. (C2×D43)⋊C4C22semidirect
31. (C2×D43)⋊C4C22semidirect
32. (C2×D43)⋊C4C22semidirect
33. C4⋊Dic43C22semidirect
34. Dic43⋊C4C22semidirect
35. Dic43⋊C4C22semidirect
36. C4×Dic43C22semidirect
46. D4×C43D4semidirect
75. C2×D43#41semidirect
91. C43#546semidirect
92. C2×#41D43semidirect
105. C2×Q8C2×D43semidirect
112. C2×D4C2×D43semidirect
115. C22×C4C2×D43semidirect
116. C22×C4C2×D43semidirect
141. D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D432
#130633142
#130633082
#130633012
#130632992
#130632972
#130632932
D4×Dic432
C4×C22⋊D432
C2×(C2×D43)⋊C42
C2×#41×C432
#54643