Finite Group Databasebeta

← #14583703

Subgroups — #14583703

Order 2752.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#13063371C211yesmaximal, characteristic, complemented
2#13063370C211yesmaximal, characteristic, complemented
3#13063353C211yesmaximal, characteristic, complemented
4#13063352C212yesmaximal, complemented
5#13063349C212yesmaximal, complemented
6#13063346C212yesmaximal, complemented
7#13063345C211yesmaximal, characteristic, complemented
8C2×#10621882C211yesmaximal, characteristic, complemented
9D8×D43C212yesmaximal, complemented
10#13063333C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
12#41×C43C2211yescharacteristic, complemented
13C2×D4×C43C2211yescharacteristic, complemented
14C2×C22⋊D43—22no—
15#10621902C2212yescomplemented
16#10621900—21no—
17#10621900C2212yescomplemented
18D4×D43—22no—
19D4×D43—21no—
20D4×D43C2212yescomplemented
21D4×D43C2212yescomplemented
22#10621898—21no—
23#10621898C2211yescharacteristic
24#10621898C2211yescharacteristic, complemented
25C2×D172—21no—
26C2×D172C2211yescharacteristic, complemented
27SD16×C43C2212yescomplemented
28D8×C43C2212yescomplemented
29M16×C43C2211yescharacteristic, complemented
30#10621885C2211yescharacteristic, complemented
31#10621884C2211yescharacteristic, complemented
32#10621883C2211yescharacteristic, complemented
33#10621882C2211yescharacteristic, complemented
34#10621882C2212yescomplemented
35#10621882C2212yescomplemented
36C2×C43⋊C8C2211yescharacteristic, complemented
37D344C2212yescomplemented
38#10621873C2212yescomplemented
39#10621872C2212yescomplemented
40C8×D43C2212yescomplemented
41C23×C43—21no—
42C22×D43—21no—
43C22×D43—22no—
44C22×D43—22no—
45Q8×C43C2311yescharacteristic
46D4×C43—21no—
47D4×C43—21no—
48D4×C43C2312yes—
49D4×C43C2311yescharacteristic
50C2×C4×C43—21no—
51C2×C4×C43C2311yescharacteristic
52C22⋊D43—21no—
53C22⋊D43—22no—
54C22⋊D43—22no—
55C22⋊D43—22no—
56C22⋊D43D412yes—
57C2×Dic43—22no—
58D172—22no—
59D172—21no—
60D172D411yescharacteristic
61D172C2312yes—
62D172C2311yescharacteristic
63C4×D43—21no—
64C4×D43—22no—
65C4×D43C2312yes—
66Dic86D411yescharacteristic
67Dic86C2311yescharacteristic
68C8×C43C2312yes—
69C43⋊C8C2311yescharacteristic
70C43⋊C8C2311yescharacteristic
71C22×C43—21no—
72C22×C43—22no—
73C22×C43—81no—
74C22×C43C2×D411yescharacteristic
75C2×D43—22no—
76C2×D43—21no—
77C2×D43—82no—
78C2×D43—82no—
79C2×D43—81no—
80C2×D43C2×D412yes—
81C4×C43—21no—
82C4×C43C2×D411yescharacteristic
83C4×C43C2411yescharacteristic
84Dic43—21no—
85Dic43C2×D412yes—
86C2×C43—21no—
87C2×C43—41no—
88C2×C43—42no—
89C2×C43C22×D411yescharacteristic
90D43—22no—
91D43—42no—
92D43—41no—
93#576—431nomaximal, Sylow
94C43#57611yescharacteristic, complemented, Sylow
95H(5,𝔽2)—431no—
96H(5,𝔽2)—431no—
97AGL(1,ℤ/8)—432no—
98AGL(1,ℤ/8)—432no—
99AGL(1,ℤ/8)—431no—
100AGL(1,ℤ/8)D4311yescharacteristic, complemented
101#135—431no—
102#135—432no—
103C2×D8—431no—
104C2×D8—432no—
105#131—431no—
106#41—431no—
107#41—432no—
108#41—432no—
109#41—431no—
110#41—861no—
111#41—861no—
112#41C2×D4311yescharacteristic, complemented
113C2×D4—432no—
114C2×D4—432no—
115C2×D4—431no—
116C2×D4—861no—
117C2×D4—862no—
118C2×D4—861no—
119C2×D4—862no—
120C2×D4C2×D4311yescharacteristic, complemented
121Q16—431no—
122SD16—431no—
123SD16—431no—
124SD16—432no—
125SD16C2×D4312yescomplemented
126D8—432no—
127D8—431no—
128D8—432no—
129D8—432no—
130D8C2×D4312yescomplemented
131M16—432no—
132M16C2×D4311yescharacteristic, complemented
133C2×C8—431no—
134C2×C8—432no—
135C23—21no—
136C23—862no—
137C23—862no—
138C23—861no—
139Q8—431no—
140Q8—431no—
141Q8C22×D4311yescharacteristic
142D4—21no—
143D4—21no—
144D4—432no—
145D4—431no—
146D4—432no—
147D4—431no—
148D4—862no—
149D4—862no—
150D4—862no—
151D4—862no—
152D4—861no—
153D4—861no—
154D4C22×D4312yes—
155D4C22×D4311yescharacteristic
156C2×C4—21no—
157C2×C4—432no—
158C2×C4—862no—
159C2×C4—862no—
160C2×C4—861no—
161C2×C4C22×D4311yescharacteristic
162C8—431no—
163C8—431no—
164C8C22×D4312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—432no—
169C22—862no—
170C22—861no—
171C22—3441no—
172C22—3442no—
173C22—3442no—
174C22D4×D4311yescharacteristic
175C4—21no—
176C4—432no—
177C4—861no—
178C4D4×D4311yescharacteristic
179C4C23×D4311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—862no—
184C2—1722no—
185C2—1721no—
186C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingAGL(1,ℤ/8)×C43C2
socleC2×C43C22×D4
hypercenterAGL(1,ℤ/8)D43
hypocenterC43#576
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #13063371C2semidirect
2. #13063370C2semidirect
3. #13063353C2semidirect
4. #13063352C2semidirect
5. #13063349C2semidirect
6. #13063346C2semidirect
7. #13063345C2semidirect
8. C2×#10621882C2semidirect
9. D8×D43C2semidirect
10. #13063333C2semidirect
11. AGL(1,ℤ/8)×C43C2semidirect
12. #41×C43C22semidirect
13. C2×D4×C43C22semidirect
15. #10621902C22semidirect
17. #10621900C22semidirect
20. D4×D43C22semidirect
21. D4×D43C22semidirect
24. #10621898C22semidirect
26. C2×D172C22semidirect
27. SD16×C43C22semidirect
28. D8×C43C22semidirect
29. M16×C43C22semidirect
30. #10621885C22semidirect
31. #10621884C22semidirect
32. #10621883C22semidirect
33. #10621882C22semidirect
34. #10621882C22semidirect
35. #10621882C22semidirect
36. C2×C43⋊C8C22semidirect
37. D344C22semidirect
38. #10621873C22semidirect
39. #10621872C22semidirect
40. C8×D43C22semidirect
94. C43#576semidirect
100. AGL(1,ℤ/8)D43semidirect
112. #41C2×D43semidirect
120. C2×D4C2×D43semidirect
125. SD16C2×D43semidirect
130. D8C2×D43semidirect
132. M16C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633712
#130633702
#130633532
#130633522
#130633492
#130633462
#130633452
C2×#106218822
D8×D432
#130633332
AGL(1,ℤ/8)×C432
#57643