Finite Group Databasebeta

← #44417581

Subgroups — #44417581

Order 29248.

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#28410598C211yesmaximal, characteristic, complemented
2#28410597C211yesmaximal, characteristic, complemented
3#28410580C211yesmaximal, characteristic, complemented
4#28410579C212yesmaximal, complemented
5#28410576C212yesmaximal, complemented
6#28410573C212yesmaximal, complemented
7#28410572C211yesmaximal, characteristic, complemented
8C2×#20300726C211yesmaximal, characteristic, complemented
9D8×D457C212yesmaximal, complemented
10#28410560C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C457C211yesmaximal, characteristic, complemented
12#20300742C2212yescomplemented
13#20300741—21no—
14#20300741C2211yescharacteristic
15#20300741C2211yescharacteristic, complemented
16#20300740—21no—
17#20300740C2212yescomplemented
18C2×D1828—21no—
19C2×D1828C2211yescharacteristic, complemented
20C2×C22⋊D457—22no—
21D4×D457—21no—
22D4×D457—22no—
23D4×D457C2212yescomplemented
24D4×D457C2212yescomplemented
25#20300731C2211yescharacteristic, complemented
26#20300730C2212yescomplemented
27#20300729C2211yescharacteristic, complemented
28#20300728C2211yescharacteristic, complemented
29D3656C2212yescomplemented
30#20300726C2211yescharacteristic, complemented
31#20300726C2212yescomplemented
32#20300726C2212yescomplemented
33#20300724C2212yescomplemented
34C2×#16814532C2211yescharacteristic, complemented
35C8×D457C2212yescomplemented
36#41×C457C2211yescharacteristic, complemented
37C2×D4×C457C2211yescharacteristic, complemented
38SD16×C457C2212yescomplemented
39D8×C457C2212yescomplemented
40M16×C457C2211yescharacteristic, complemented
41C22×D457—21no—
42C22×D457—22no—
43C22×D457—22no—
44Dic914D411yescharacteristic
45Dic914C2311yescharacteristic
46D1828—22no—
47D1828—21no—
48D1828D411yescharacteristic
49D1828C2312yes—
50D1828C2311yescharacteristic
51C22⋊D457—21no—
52C22⋊D457—22no—
53C22⋊D457—22no—
54C22⋊D457—22no—
55C22⋊D457D412yes—
56C2×Dic457—22no—
57C4×D457—21no—
58C4×D457—22no—
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—22no—
77C2×D457—82no—
78C2×D457—82no—
79C2×D457—81no—
80C2×D457C2×D412yes—
81C4×C457—21no—
82C4×C457C2×D411yescharacteristic
83C4×C457C2411yescharacteristic
84Dic457—21no—
85Dic457C2×D412yes—
86C2×C457—21no—
87C2×C457—41no—
88C2×C457—42no—
89C2×C457C22×D411yescharacteristic
90D457—22no—
91D457—41no—
92D457—42no—
93C457#57611yescharacteristic, complemented, Sylow
94#576—4571nomaximal, Sylow
95H(5,𝔽2)—4571no—
96H(5,𝔽2)—4571no—
97AGL(1,ℤ/8)—4572no—
98AGL(1,ℤ/8)—4572no—
99AGL(1,ℤ/8)—4571no—
100AGL(1,ℤ/8)D45711yescharacteristic, complemented
101#135—4571no—
102#135—4572no—
103C2×D8—4571no—
104C2×D8—4572no—
105#131—4571no—
106#41—9141no—
107#41—9141no—
108#41—4572no—
109#41—4572no—
110#41—4571no—
111#41—4571no—
112#41C2×D45711yescharacteristic, complemented
113C2×D4—9141no—
114C2×D4—9142no—
115C2×D4—9141no—
116C2×D4—9142no—
117C2×D4—4572no—
118C2×D4—4572no—
119C2×D4—4571no—
120C2×D4C2×D45711yescharacteristic, complemented
121Q16—4571no—
122SD16—4571no—
123SD16—4571no—
124SD16—4572no—
125SD16C2×D45712yescomplemented
126D8—4572no—
127D8—4571no—
128D8—4572no—
129D8—4572no—
130D8C2×D45712yescomplemented
131M16—4572no—
132M16C2×D45711yescharacteristic, complemented
133C2×C8—4571no—
134C2×C8—4572no—
135C23—21no—
136C23—9142no—
137C23—9142no—
138C23—9141no—
139Q8—4571no—
140Q8—4571no—
141Q8C22×D45711yescharacteristic
142D4—21no—
143D4—21no—
144D4—9142no—
145D4—9142no—
146D4—9141no—
147D4—9142no—
148D4—9142no—
149D4—9141no—
150D4—4572no—
151D4—4571no—
152D4—4572no—
153D4—4571no—
154D4C22×D45712yes—
155D4C22×D45711yescharacteristic
156C2×C4—21no—
157C2×C4—9142no—
158C2×C4—9142no—
159C2×C4—9141no—
160C2×C4—4572no—
161C2×C4C22×D45711yescharacteristic
162C8—4571no—
163C8—4571no—
164C8C22×D45712yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—36561no—
169C22—36562no—
170C22—36562no—
171C22—9142no—
172C22—9141no—
173C22—4572no—
174C22D4×D45711yescharacteristic
175C4—21no—
176C4—9141no—
177C4—4572no—
178C4D4×D45711yescharacteristic
179C4C23×D45711yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—18282no—
184C2—18281no—
185C2—9142no—
186C2C2×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#576
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. #28410598C2semidirect
2. #28410597C2semidirect
3. #28410580C2semidirect
4. #28410579C2semidirect
5. #28410576C2semidirect
6. #28410573C2semidirect
7. #28410572C2semidirect
8. C2×#20300726C2semidirect
9. D8×D457C2semidirect
10. #28410560C2semidirect
11. AGL(1,ℤ/8)×C457C2semidirect
12. #20300742C22semidirect
15. #20300741C22semidirect
17. #20300740C22semidirect
19. C2×D1828C22semidirect
23. D4×D457C22semidirect
24. D4×D457C22semidirect
25. #20300731C22semidirect
26. #20300730C22semidirect
27. #20300729C22semidirect
28. #20300728C22semidirect
29. D3656C22semidirect
30. #20300726C22semidirect
31. #20300726C22semidirect
32. #20300726C22semidirect
33. #20300724C22semidirect
34. C2×#16814532C22semidirect
35. C8×D457C22semidirect
36. #41×C457C22semidirect
37. C2×D4×C457C22semidirect
38. SD16×C457C22semidirect
39. D8×C457C22semidirect
40. M16×C457C22semidirect
93. C457#576semidirect
100. AGL(1,ℤ/8)D457semidirect
112. #41C2×D457semidirect
120. C2×D4C2×D457semidirect
125. SD16C2×D457semidirect
130. D8C2×D457semidirect
132. M16C2×D457semidirect

Maximal subgroups

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

subgroupindex
#284105982
#284105972
#284105802
#284105792
#284105762
#284105732
#284105722
C2×#203007262
D8×D4572
#284105602
AGL(1,ℤ/8)×C4572
#576457