Finite Group Databasebeta

← #14583705

Subgroups — #14583705

Order 2752.

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

normal subgroups only

This group has 258 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#13063373C211yesmaximal, characteristic, complemented
2#13063370C211yesmaximal, characteristic, complemented
3#13063356C211yesmaximal, characteristic, complemented
4#13063354C212yesmaximal, complemented
5#13063352C212yesmaximal, complemented
6#13063351C211yesmaximal, characteristic, complemented
7#13063347C211yesmaximal, characteristic, complemented
8#13063346C212yesmaximal, complemented
9SD16×D43C212yesmaximal, complemented
10#13063331C211yesmaximal, characteristic, complemented
11C2×SD16×C43C211yesmaximal, characteristic, complemented
12C2×Q8×C43C2211yescharacteristic, complemented
13C2×D4×C43C2211yescharacteristic
14C2×C22⋊D43—22no—
15#10621902—21no—
16#10621902C2212yescomplemented
17Q8×D43—21no—
18Q8×D43C2212yescomplemented
19#10621900—21no—
20#10621900C2212yes—
21D4×D43—21no—
22D4×D43C2212yes—
23#10621898—22no—
24#10621898C2211yescharacteristic
25#10621898C2211yescharacteristic
26#10621898C2211yescharacteristic, complemented
27SD16×C43C2212yescomplemented
28SD16×C43C2212yescomplemented
29C2×C8×C43C2211yescharacteristic, complemented
30#10621885C2212yescomplemented
31#10621884C2212yescomplemented
32#10621883C2212yescomplemented
33#10621882C2212yescomplemented
34#10621877C2211yescharacteristic, complemented
35Dic172C2211yescharacteristic, complemented
36D344C2211yescharacteristic, complemented
37#10621873C2211yescharacteristic, complemented
38#10621873C2211yescharacteristic, complemented
39#10621872C2212yescomplemented
40C8×D43C2212yescomplemented
41C23×C43—21no—
42C22×D43—22no—
43Q8×C43—21no—
44Q8×C43C2312yes—
45D4×C43—21no—
46D4×C43C2312yes—
47C2×C4×C43—21no—
48C2×C4×C43C2311yescharacteristic
49C22⋊D43—21no—
50C22⋊D43—21no—
51C22⋊D43—22no—
52C22⋊D43—22no—
53C22⋊D43D412yes—
54C2×Dic43—22no—
55D172—22no—
56D172D411yescharacteristic
57D172C2311yescharacteristic
58D172C2311yescharacteristic
59C4×D43—22no—
60C4×D43—21no—
61C4×D43—21no—
62C4×D43—22no—
63C4×D43C2312yes—
64Dic86—22no—
65Dic86D411yescharacteristic
66Dic86C2311yescharacteristic
67Dic86C2311yescharacteristic
68C8×C43C2311yescharacteristic
69C8×C43C2311yescharacteristic
70C43⋊C8C2312yes—
71C22×C43—22no—
72C22×C43—81no—
73C22×C43C2×D411yescharacteristic
74C2×D43—21no—
75C2×D43—21no—
76C2×D43—82no—
77C2×D43C2×D412yes—
78C4×C43—22no—
79C4×C43C2×D411yescharacteristic
80C4×C43C2411yescharacteristic
81Dic43—21no—
82Dic43—21no—
83Dic43C2×D412yes—
84C2×C43—21no—
85C2×C43—42no—
86C2×C43C22×D411yescharacteristic
87D43—22no—
88D43—41no—
89D43—41no—
90#577—431nomaximal, Sylow
91C43#57711yescharacteristic, complemented, Sylow
922−1+4—431no—
93H(5,𝔽2)—431no—
94#137—431no—
95#137—432no—
96AGL(1,ℤ/8)—431no—
97AGL(1,ℤ/8)—432no—
98#135—432no—
99#135—431no—
100C2×SD16—432no—
101C2×SD16D4311yescharacteristic, complemented
102#131—431no—
103#41—431no—
104#41—432no—
105#41—432no—
106#41—431no—
107#41—431no—
108#41—862no—
109#41—861no—
110#41—861no—
111C2×Q8—432no—
112C2×Q8—861no—
113C2×Q8C2×D4311yescharacteristic, complemented
114C2×D4—432no—
115C2×D4—861no—
116C2×D4—862no—
117C2×D4C2×D4311yescharacteristic
118Q16—432no—
119Q16—431no—
120SD16—432no—
121SD16—432no—
122SD16—431no—
123SD16—431no—
124SD16C2×D4312yescomplemented
125SD16C2×D4312yescomplemented
126D8—432no—
127D8—431no—
128M16—431no—
129M16—432no—
130C2×C8—432no—
131C2×C8C2×D4311yescharacteristic, complemented
132C23—21no—
133C23—862no—
134Q8—21no—
135Q8—431no—
136Q8—431no—
137Q8—431no—
138Q8—862no—
139Q8C22×D4312yes—
140D4—21no—
141D4—432no—
142D4—431no—
143D4—431no—
144D4—431no—
145D4—862no—
146D4—862no—
147D4—862no—
148D4—861no—
149D4—861no—
150D4C22×D4312yes—
151C2×C4—21no—
152C2×C4—432no—
153C2×C4—862no—
154C2×C4—862no—
155C2×C4—862no—
156C2×C4—861no—
157C2×C4—861no—
158C2×C4C22×D4311yescharacteristic
159C8—432no—
160C8C22×D4311yescharacteristic
161C8C22×D4311yescharacteristic
162C22—22no—
163C22—81no—
164C22—432no—
165C22—861no—
166C22—861no—
167C22—3442no—
168C22D4×D4311yescharacteristic
169C4—22no—
170C4—432no—
171C4—861no—
172C4—861no—
173C4D4×D4311yescharacteristic
174C4C23×D4311yescharacteristic
175C2—21no—
176C2—42no—
177C2—862no—
178C2—1721no—
179C2—1721no—
180C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingC2×SD16×C43C2
socleC2×C43C22×D4
hypercenterC2×SD16D43
hypocenterC43#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #13063373C2semidirect
2. #13063370C2semidirect
3. #13063356C2semidirect
4. #13063354C2semidirect
5. #13063352C2semidirect
6. #13063351C2semidirect
7. #13063347C2semidirect
8. #13063346C2semidirect
9. SD16×D43C2semidirect
10. #13063331C2semidirect
11. C2×SD16×C43C2semidirect
12. C2×Q8×C43C22semidirect
16. #10621902C22semidirect
18. Q8×D43C22semidirect
26. #10621898C22semidirect
27. SD16×C43C22semidirect
28. SD16×C43C22semidirect
29. C2×C8×C43C22semidirect
30. #10621885C22semidirect
31. #10621884C22semidirect
32. #10621883C22semidirect
33. #10621882C22semidirect
34. #10621877C22semidirect
35. Dic172C22semidirect
36. D344C22semidirect
37. #10621873C22semidirect
38. #10621873C22semidirect
39. #10621872C22semidirect
40. C8×D43C22semidirect
91. C43#577semidirect
101. C2×SD16D43semidirect
113. C2×Q8C2×D43semidirect
124. SD16C2×D43semidirect
125. SD16C2×D43semidirect
131. C2×C8C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633732
#130633702
#130633562
#130633542
#130633522
#130633512
#130633472
#130633462
SD16×D432
#130633312
C2×SD16×C432
#57743