Finite Group Databasebeta

← #44417587

Subgroups — #44417587

Order 29248.

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#28410599C211yesmaximal, characteristic, complemented
2#28410597C211yesmaximal, characteristic, complemented
3#28410585C211yesmaximal, characteristic, complemented
4#28410581C212yesmaximal, complemented
5#28410576C212yesmaximal, complemented
6#28410572C211yesmaximal, characteristic, complemented
7#28410571C212yesmaximal, complemented
8C2×#20300729C211yesmaximal, characteristic, complemented
9SD16×D457C212yesmaximal, complemented
10#28410560C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C457C211yesmaximal, characteristic, complemented
12#20300741—21no—
13#20300741C2211yescharacteristic
14#20300741C2211yescharacteristic
15#20300740—21no—
16#20300740—22no—
17#20300740C2212yes—
18#20300740C2212yescomplemented
19C2×Dic914—21no—
20C2×Dic914C2211yescharacteristic, complemented
21Q8×D457C2212yescomplemented
22C2×C22⋊D457—22no—
23D4×D457—21no—
24D4×D457C2212yes—
25Dic1828C2212yescomplemented
26#20300731C2211yescharacteristic, complemented
27#20300730C2212yescomplemented
28#20300729C2212yescomplemented
29#20300729C2212yescomplemented
30#20300729C2211yescharacteristic, complemented
31#20300728C2211yescharacteristic, complemented
32#20300726C2211yescharacteristic, complemented
33#20300724C2212yescomplemented
34C2×#16814532C2211yescharacteristic, complemented
35C8×D457C2212yescomplemented
36#41×C457C2211yescharacteristic, complemented
37C2×D4×C457C2211yescharacteristic
38SD16×C457C2212yescomplemented
39D8×C457C2212yescomplemented
40M16×C457C2211yescharacteristic, complemented
41C22×D457—22no—
42Dic914—21no—
43Dic914—22no—
44Dic914D411yescharacteristic
45Dic914C2312yes—
46Dic914C2311yescharacteristic
47D1828D411yescharacteristic
48D1828C2311yescharacteristic
49C22⋊D457—21no—
50C22⋊D457—22no—
51C22⋊D457—22no—
52C22⋊D457—22no—
53C22⋊D457D412yes—
54C2×Dic457—21no—
55C2×Dic457—22no—
56C2×Dic457—22no—
57C4×D457—22no—
58C4×D457—21no—
59C4×D457C2312yes—
60#16814532C2311yescharacteristic
61#16814532C2311yescharacteristic
62C23×C457—21no—
63Q8×C457C2311yescharacteristic
64D4×C457—21no—
65D4×C457—21no—
66D4×C457C2311yescharacteristic
67D4×C457C2312yes—
68C2×C4×C457—21no—
69C2×C4×C457C2311yescharacteristic
70C8×C457C2312yes—
71C22×C457—21no—
72C22×C457—22no—
73C22×C457—81no—
74C22×C457C2×D411yescharacteristic
75C2×D457—21no—
76C2×D457—82no—
77C2×D457C2×D412yes—
78C4×C457—21no—
79C4×C457C2×D411yescharacteristic
80C4×C457C2411yescharacteristic
81Dic457—21no—
82Dic457—22no—
83Dic457C2×D412yes—
84C2×C457—21no—
85C2×C457—42no—
86C2×C457—41no—
87C2×C457C22×D411yescharacteristic
88D457—22no—
89D457—41no—
90C457#57711yescharacteristic, complemented, Sylow
91#577—4571nomaximal, Sylow
922−1+4—4571no—
93H(5,𝔽2)—4571no—
94#137—4572no—
95#137—4571no—
96AGL(1,ℤ/8)—4572no—
97AGL(1,ℤ/8)D45711yescharacteristic, complemented
98#135—4571no—
99#135—4572no—
100C2×SD16—4571no—
101C2×SD16—4572no—
102#131—4571no—
103#41—9141no—
104#41—9141no—
105#41—9142no—
106#41—4572no—
107#41—4572no—
108#41—4571no—
109#41—4571no—
110#41C2×D45711yescharacteristic, complemented
111C2×Q8—9141no—
112C2×Q8—4572no—
113C2×Q8—4571no—
114C2×D4—9141no—
115C2×D4—9142no—
116C2×D4—4572no—
117C2×D4C2×D45711yescharacteristic
118Q16—4571no—
119Q16—4572no—
120SD16—4571no—
121SD16—4572no—
122SD16—4572no—
123SD16—4571no—
124SD16—4572no—
125SD16C2×D45712yescomplemented
126D8—4571no—
127D8C2×D45712yescomplemented
128M16—4572no—
129M16C2×D45711yescharacteristic, complemented
130C2×C8—4571no—
131C2×C8—4572no—
132C23—21no—
133C23—9142no—
134Q8—9142no—
135Q8—9141no—
136Q8—4572no—
137Q8—4571no—
138Q8—4571no—
139Q8C22×D45711yescharacteristic
140D4—21no—
141D4—21no—
142D4—9142no—
143D4—9142no—
144D4—9141no—
145D4—9142no—
146D4—4572no—
147D4—4571no—
148D4—4571no—
149D4C22×D45711yescharacteristic
150D4C22×D45712yes—
151C2×C4—21no—
152C2×C4—9142no—
153C2×C4—9141no—
154C2×C4—9142no—
155C2×C4—9142no—
156C2×C4—9141no—
157C2×C4—4572no—
158C2×C4C22×D45711yescharacteristic
159C8—4571no—
160C8—4571no—
161C8C22×D45712yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—36562no—
166C22—9141no—
167C22—4572no—
168C22D4×D45711yescharacteristic
169C4—21no—
170C4—9141no—
171C4—9142no—
172C4—4572no—
173C4D4×D45711yescharacteristic
174C4C23×D45711yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—18281no—
179C2—9142no—
180C2C2×D4×D45711yescharacteristic
subgroupG/H
centerC2C2×D4×D457
commutator, cosocleC4×C457C24
FrattiniC4C23×D457
FittingAGL(1,ℤ/8)×C457C2
socleC2×C457C22×D4
hypercenterAGL(1,ℤ/8)D457
hypocenterC457#577
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28410599C2semidirect
2. #28410597C2semidirect
3. #28410585C2semidirect
4. #28410581C2semidirect
5. #28410576C2semidirect
6. #28410572C2semidirect
7. #28410571C2semidirect
8. C2×#20300729C2semidirect
9. SD16×D457C2semidirect
10. #28410560C2semidirect
11. AGL(1,ℤ/8)×C457C2semidirect
18. #20300740C22semidirect
20. C2×Dic914C22semidirect
21. Q8×D457C22semidirect
25. Dic1828C22semidirect
26. #20300731C22semidirect
27. #20300730C22semidirect
28. #20300729C22semidirect
29. #20300729C22semidirect
30. #20300729C22semidirect
31. #20300728C22semidirect
32. #20300726C22semidirect
33. #20300724C22semidirect
34. C2×#16814532C22semidirect
35. C8×D457C22semidirect
36. #41×C457C22semidirect
38. SD16×C457C22semidirect
39. D8×C457C22semidirect
40. M16×C457C22semidirect
90. C457#577semidirect
97. AGL(1,ℤ/8)D457semidirect
110. #41C2×D457semidirect
125. SD16C2×D457semidirect
127. D8C2×D457semidirect
129. M16C2×D457semidirect

Maximal subgroups

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

subgroupindex
#284105992
#284105972
#284105852
#284105812
#284105762
#284105722
#284105712
C2×#203007292
SD16×D4572
#284105602
AGL(1,ℤ/8)×C4572
#577457