Finite Group Databasebeta

← #44501199

Subgroups — #44501199

Order 30656.

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#29506428C211yesmaximal, characteristic, complemented
2#29506427C211yesmaximal, characteristic, complemented
3#29506410C211yesmaximal, characteristic, complemented
4#29506409C212yesmaximal, complemented
5#29506406C212yesmaximal, complemented
6#29506403C212yesmaximal, complemented
7#29506402C211yesmaximal, characteristic, complemented
8C2×#21440147C211yesmaximal, characteristic, complemented
9D8×D479C212yesmaximal, complemented
10#29506390C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C479C211yesmaximal, characteristic, complemented
12#21440163C2212yescomplemented
13#21440162—21no—
14#21440162C2211yescharacteristic
15#21440162C2211yescharacteristic, complemented
16#21440161—21no—
17#21440161C2212yescomplemented
18C2×D1916—21no—
19C2×D1916C2211yescharacteristic, complemented
20C2×C22⋊D479—22no—
21D4×D479—21no—
22D4×D479—22no—
23D4×D479C2212yescomplemented
24D4×D479C2212yescomplemented
25#21440152C2211yescharacteristic, complemented
26#21440151C2212yescomplemented
27#21440150C2211yescharacteristic, complemented
28#21440149C2211yescharacteristic, complemented
29D3832C2212yescomplemented
30#21440147C2211yescharacteristic, complemented
31#21440147C2212yescomplemented
32#21440147C2212yescomplemented
33#21440145C2212yescomplemented
34C2×C479⋊C8C2211yescharacteristic, complemented
35C8×D479C2212yescomplemented
36#41×C479C2211yescharacteristic, complemented
37C2×D4×C479C2211yescharacteristic, complemented
38SD16×C479C2212yescomplemented
39D8×C479C2212yescomplemented
40M16×C479C2211yescharacteristic, complemented
41C22×D479—21no—
42C22×D479—22no—
43C22×D479—22no—
44Dic958D411yescharacteristic
45Dic958C2311yescharacteristic
46D1916—22no—
47D1916—21no—
48D1916D411yescharacteristic
49D1916C2312yes—
50D1916C2311yescharacteristic
51C22⋊D479—21no—
52C22⋊D479—22no—
53C22⋊D479—22no—
54C22⋊D479—22no—
55C22⋊D479D412yes—
56C2×Dic479—22no—
57C4×D479—21no—
58C4×D479—22no—
59C4×D479C2312yes—
60C479⋊C8C2311yescharacteristic
61C479⋊C8C2311yescharacteristic
62C23×C479—21no—
63Q8×C479C2311yescharacteristic
64D4×C479—21no—
65D4×C479—21no—
66D4×C479C2311yescharacteristic
67D4×C479C2312yes—
68C2×C4×C479—21no—
69C2×C4×C479C2311yescharacteristic
70C8×C479C2312yes—
71C22×C479—21no—
72C22×C479—22no—
73C22×C479—81no—
74C22×C479C2×D411yescharacteristic
75C2×D479—21no—
76C2×D479—22no—
77C2×D479—82no—
78C2×D479—82no—
79C2×D479—81no—
80C2×D479C2×D412yes—
81C4×C479—21no—
82C4×C479C2×D411yescharacteristic
83C4×C479C2411yescharacteristic
84Dic479—21no—
85Dic479C2×D412yes—
86C2×C479—21no—
87C2×C479—41no—
88C2×C479—42no—
89C2×C479C22×D411yescharacteristic
90D479—22no—
91D479—41no—
92D479—42no—
93C479#57611yescharacteristic, complemented, Sylow
94#576—4791nomaximal, Sylow
95H(5,𝔽2)—4791no—
96H(5,𝔽2)—4791no—
97AGL(1,ℤ/8)—4792no—
98AGL(1,ℤ/8)—4792no—
99AGL(1,ℤ/8)—4791no—
100AGL(1,ℤ/8)D47911yescharacteristic, complemented
101#135—4791no—
102#135—4792no—
103C2×D8—4791no—
104C2×D8—4792no—
105#131—4791no—
106#41—9581no—
107#41—9581no—
108#41—4792no—
109#41—4792no—
110#41—4791no—
111#41—4791no—
112#41C2×D47911yescharacteristic, complemented
113C2×D4—9581no—
114C2×D4—9582no—
115C2×D4—9581no—
116C2×D4—9582no—
117C2×D4—4792no—
118C2×D4—4792no—
119C2×D4—4791no—
120C2×D4C2×D47911yescharacteristic, complemented
121Q16—4791no—
122SD16—4791no—
123SD16—4791no—
124SD16—4792no—
125SD16C2×D47912yescomplemented
126D8—4792no—
127D8—4791no—
128D8—4792no—
129D8—4792no—
130D8C2×D47912yescomplemented
131M16—4792no—
132M16C2×D47911yescharacteristic, complemented
133C2×C8—4791no—
134C2×C8—4792no—
135C23—21no—
136C23—9582no—
137C23—9582no—
138C23—9581no—
139Q8—4791no—
140Q8—4791no—
141Q8C22×D47911yescharacteristic
142D4—21no—
143D4—21no—
144D4—9582no—
145D4—9582no—
146D4—9581no—
147D4—9582no—
148D4—9582no—
149D4—9581no—
150D4—4792no—
151D4—4791no—
152D4—4792no—
153D4—4791no—
154D4C22×D47912yes—
155D4C22×D47911yescharacteristic
156C2×C4—21no—
157C2×C4—9582no—
158C2×C4—9582no—
159C2×C4—9581no—
160C2×C4—4792no—
161C2×C4C22×D47911yescharacteristic
162C8—4791no—
163C8—4791no—
164C8C22×D47912yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—9582no—
169C22—9581no—
170C22—4792no—
171C22—38321no—
172C22—38322no—
173C22—38322no—
174C22D4×D47911yescharacteristic
175C4—21no—
176C4—9581no—
177C4—4792no—
178C4D4×D47911yescharacteristic
179C4C23×D47911yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—19162no—
184C2—19161no—
185C2—9582no—
186C2C2×D4×D47911yescharacteristic
subgroupG/H
centerC2C2×D4×D479
commutator, cosocleC4×C479C24
FrattiniC4C23×D479
FittingAGL(1,ℤ/8)×C479C2
socleC2×C479C22×D4
hypercenterAGL(1,ℤ/8)D479
hypocenterC479#576
LCSG ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #29506428C2semidirect
2. #29506427C2semidirect
3. #29506410C2semidirect
4. #29506409C2semidirect
5. #29506406C2semidirect
6. #29506403C2semidirect
7. #29506402C2semidirect
8. C2×#21440147C2semidirect
9. D8×D479C2semidirect
10. #29506390C2semidirect
11. AGL(1,ℤ/8)×C479C2semidirect
12. #21440163C22semidirect
15. #21440162C22semidirect
17. #21440161C22semidirect
19. C2×D1916C22semidirect
23. D4×D479C22semidirect
24. D4×D479C22semidirect
25. #21440152C22semidirect
26. #21440151C22semidirect
27. #21440150C22semidirect
28. #21440149C22semidirect
29. D3832C22semidirect
30. #21440147C22semidirect
31. #21440147C22semidirect
32. #21440147C22semidirect
33. #21440145C22semidirect
34. C2×C479⋊C8C22semidirect
35. C8×D479C22semidirect
36. #41×C479C22semidirect
37. C2×D4×C479C22semidirect
38. SD16×C479C22semidirect
39. D8×C479C22semidirect
40. M16×C479C22semidirect
93. C479#576semidirect
100. AGL(1,ℤ/8)D479semidirect
112. #41C2×D479semidirect
120. C2×D4C2×D479semidirect
125. SD16C2×D479semidirect
130. D8C2×D479semidirect
132. M16C2×D479semidirect

Maximal subgroups

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

subgroupindex
#295064282
#295064272
#295064102
#295064092
#295064062
#295064032
#295064022
C2×#214401472
D8×D4792
#295063902
AGL(1,ℤ/8)×C4792
#576479