Finite Group Databasebeta

← #14583706

Subgroups — #14583706

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#13063372C211yesmaximal, characteristic, complemented
2#13063371C211yesmaximal, characteristic, complemented
3#13063357C212yesmaximal, complemented
4#13063355C211yesmaximal, characteristic, complemented
5#13063350C211yesmaximal, characteristic, complemented
6#13063349C212yesmaximal, complemented
7#13063346C212yesmaximal, complemented
8C2×#10621873C211yesmaximal, characteristic, complemented
9SD16×D43C212yesmaximal, complemented
10#13063331C211yesmaximal, characteristic, complemented
11#135×C43C211yesmaximal, characteristic, complemented
12#41×C43C2211yescharacteristic
13#41×C43C2211yescharacteristic, complemented
14#10621902C2212yes—
15Q8×D43C2212yescomplemented
16#10621900—22no—
17#10621900C2212yescomplemented
18D4×D43—22no—
19D4×D43C2212yes—
20#10621898—21no—
21#10621898—21no—
22#10621898C2211yescharacteristic
23C2×D172—21no—
24C2×D172C2211yescharacteristic
25C2×Dic86—21no—
26C2×Dic86C2211yescharacteristic, complemented
27Q16×C43C2211yescharacteristic, complemented
28SD16×C43C2211yescharacteristic, complemented
29SD16×C43C2211yescharacteristic, complemented
30D8×C43C2211yescharacteristic, complemented
31C2×C8×C43C2211yescharacteristic, complemented
32#10621885C2212yescomplemented
33#10621884C2212yescomplemented
34#10621883C2212yescomplemented
35#10621882C2212yescomplemented
36#10621877C2211yescharacteristic, complemented
37#10621873C2212yescomplemented
38#10621873C2212yescomplemented
39#10621872C2212yescomplemented
40C8×D43C2212yescomplemented
41C22×D43—21no—
42C22×D43—22no—
43Q8×C43C2311yescharacteristic
44Q8×C43C2311yescharacteristic
45D4×C43—21no—
46D4×C43—21no—
47D4×C43C2311yescharacteristic
48D4×C43C2311yescharacteristic
49C2×C4×C43—21no—
50C2×C4×C43—21no—
51C2×C4×C43C2311yescharacteristic
52C22⋊D43—22no—
53C22⋊D43—22no—
54C22⋊D43D412yes—
55C2×Dic43—21no—
56C2×Dic43—22no—
57D172—22no—
58D172—21no—
59D172D411yescharacteristic
60D172C2312yes—
61C4×D43—22no—
62C4×D43—22no—
63C4×D43C2312yes—
64Dic86—21no—
65Dic86—22no—
66Dic86D411yescharacteristic
67Dic86C2312yes—
68C8×C43C2311yescharacteristic
69C8×C43C2311yescharacteristic
70C43⋊C8C2312yes—
71C22×C43—21no—
72C22×C43—21no—
73C22×C43C2×D411yescharacteristic
74C2×D43—22no—
75C2×D43—82no—
76C2×D43—81no—
77C2×D43C2×D412yes—
78C4×C43—21no—
79C4×C43—21no—
80C4×C43C2×D411yescharacteristic
81C4×C43C2411yescharacteristic
82Dic43—22no—
83Dic43C2×D412yes—
84C2×C43—21no—
85C2×C43—41no—
86C2×C43—41no—
87C2×C43C22×D411yescharacteristic
88D43—22no—
89D43—42no—
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#135D4311yescharacteristic, complemented
100C2×SD16—432no—
101C2×SD16—431no—
102#131—431no—
103#41—431no—
104#41—432no—
105#41—432no—
106#41—861no—
107#41—861no—
108#41—862no—
109#41C2×D4311yescharacteristic
110#41C2×D4311yescharacteristic, complemented
111C2×Q8—432no—
112C2×Q8—431no—
113C2×Q8—861no—
114C2×D4—432no—
115C2×D4—431no—
116C2×D4—861no—
117C2×D4—862no—
118Q16—432no—
119Q16C2×D4311yescharacteristic, complemented
120SD16—432no—
121SD16—432no—
122SD16—432no—
123SD16—432no—
124SD16C2×D4311yescharacteristic, complemented
125SD16C2×D4311yescharacteristic, complemented
126D8—432no—
127D8C2×D4311yescharacteristic, complemented
128M16—431no—
129M16—432no—
130C2×C8—432no—
131C2×C8C2×D4311yescharacteristic, complemented
132C23—862no—
133C23—861no—
134Q8—431no—
135Q8—432no—
136Q8—862no—
137Q8—861no—
138Q8C22×D4311yescharacteristic
139Q8C22×D4311yescharacteristic
140D4—21no—
141D4—21no—
142D4—432no—
143D4—431no—
144D4—432no—
145D4—862no—
146D4—862no—
147D4—862no—
148D4—861no—
149D4C22×D4311yescharacteristic
150D4C22×D4311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—432no—
154C2×C4—862no—
155C2×C4—862no—
156C2×C4—862no—
157C2×C4—861no—
158C2×C4C22×D4311yescharacteristic
159C8—432no—
160C8C22×D4311yescharacteristic
161C8C22×D4311yescharacteristic
162C22—21no—
163C22—21no—
164C22—432no—
165C22—862no—
166C22—3441no—
167C22—3442no—
168C22D4×D4311yescharacteristic
169C4—21no—
170C4—21no—
171C4—432no—
172C4—862no—
173C4D4×D4311yescharacteristic
174C4C23×D4311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—862no—
179C2—1722no—
180C2C2×D4×D4311yescharacteristic
subgroupG/H
centerC2C2×D4×D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
Fitting#135×C43C2
socleC2×C43C22×D4
hypercenter#135D43
hypocenterC43#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #13063372C2semidirect
2. #13063371C2semidirect
3. #13063357C2semidirect
4. #13063355C2semidirect
5. #13063350C2semidirect
6. #13063349C2semidirect
7. #13063346C2semidirect
8. C2×#10621873C2semidirect
9. SD16×D43C2semidirect
10. #13063331C2semidirect
11. #135×C43C2semidirect
13. #41×C43C22semidirect
15. Q8×D43C22semidirect
17. #10621900C22semidirect
26. C2×Dic86C22semidirect
27. Q16×C43C22semidirect
28. SD16×C43C22semidirect
29. SD16×C43C22semidirect
30. D8×C43C22semidirect
31. C2×C8×C43C22semidirect
32. #10621885C22semidirect
33. #10621884C22semidirect
34. #10621883C22semidirect
35. #10621882C22semidirect
36. #10621877C22semidirect
37. #10621873C22semidirect
38. #10621873C22semidirect
39. #10621872C22semidirect
40. C8×D43C22semidirect
91. C43#577semidirect
99. #135D43semidirect
110. #41C2×D43semidirect
119. Q16C2×D43semidirect
124. SD16C2×D43semidirect
125. SD16C2×D43semidirect
127. D8C2×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
#130633722
#130633712
#130633572
#130633552
#130633502
#130633492
#130633462
C2×#106218732
SD16×D432
#130633312
#135×C432
#57743