Finite Group Databasebeta

← #44501205

Subgroups — #44501205

Order 30656.

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#29506429C211yesmaximal, characteristic, complemented
2#29506427C211yesmaximal, characteristic, complemented
3#29506415C211yesmaximal, characteristic, complemented
4#29506411C212yesmaximal, complemented
5#29506406C212yesmaximal, complemented
6#29506402C211yesmaximal, characteristic, complemented
7#29506401C212yesmaximal, complemented
8C2×#21440150C211yesmaximal, characteristic, complemented
9SD16×D479C212yesmaximal, complemented
10#29506390C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C479C211yesmaximal, characteristic, complemented
12#21440162—21no—
13#21440162C2211yescharacteristic
14#21440162C2211yescharacteristic
15#21440161—21no—
16#21440161—22no—
17#21440161C2212yes—
18#21440161C2212yescomplemented
19C2×Dic958—21no—
20C2×Dic958C2211yescharacteristic, complemented
21Q8×D479C2212yescomplemented
22C2×C22⋊D479—22no—
23D4×D479—21no—
24D4×D479C2212yes—
25Dic1916C2212yescomplemented
26#21440152C2211yescharacteristic, complemented
27#21440151C2212yescomplemented
28#21440150C2212yescomplemented
29#21440150C2212yescomplemented
30#21440150C2211yescharacteristic, complemented
31#21440149C2211yescharacteristic, complemented
32#21440147C2211yescharacteristic, complemented
33#21440145C2212yescomplemented
34C2×C479⋊C8C2211yescharacteristic, complemented
35C8×D479C2212yescomplemented
36#41×C479C2211yescharacteristic, complemented
37C2×D4×C479C2211yescharacteristic
38SD16×C479C2212yescomplemented
39D8×C479C2212yescomplemented
40M16×C479C2211yescharacteristic, complemented
41C22×D479—22no—
42Dic958—21no—
43Dic958—22no—
44Dic958D411yescharacteristic
45Dic958C2312yes—
46Dic958C2311yescharacteristic
47D1916D411yescharacteristic
48D1916C2311yescharacteristic
49C22⋊D479—21no—
50C22⋊D479—22no—
51C22⋊D479—22no—
52C22⋊D479—22no—
53C22⋊D479D412yes—
54C2×Dic479—21no—
55C2×Dic479—22no—
56C2×Dic479—22no—
57C4×D479—22no—
58C4×D479—21no—
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—82no—
77C2×D479C2×D412yes—
78C4×C479—21no—
79C4×C479C2×D411yescharacteristic
80C4×C479C2411yescharacteristic
81Dic479—21no—
82Dic479—22no—
83Dic479C2×D412yes—
84C2×C479—21no—
85C2×C479—42no—
86C2×C479—41no—
87C2×C479C22×D411yescharacteristic
88D479—22no—
89D479—41no—
90C479#57711yescharacteristic, complemented, Sylow
91#577—4791nomaximal, Sylow
922−1+4—4791no—
93H(5,𝔽2)—4791no—
94#137—4792no—
95#137—4791no—
96AGL(1,ℤ/8)—4792no—
97AGL(1,ℤ/8)D47911yescharacteristic, complemented
98#135—4791no—
99#135—4792no—
100C2×SD16—4791no—
101C2×SD16—4792no—
102#131—4791no—
103#41—9581no—
104#41—9581no—
105#41—9582no—
106#41—4792no—
107#41—4792no—
108#41—4791no—
109#41—4791no—
110#41C2×D47911yescharacteristic, complemented
111C2×Q8—9581no—
112C2×Q8—4792no—
113C2×Q8—4791no—
114C2×D4—9581no—
115C2×D4—9582no—
116C2×D4—4792no—
117C2×D4C2×D47911yescharacteristic
118Q16—4791no—
119Q16—4792no—
120SD16—4791no—
121SD16—4792no—
122SD16—4792no—
123SD16—4791no—
124SD16—4792no—
125SD16C2×D47912yescomplemented
126D8—4791no—
127D8C2×D47912yescomplemented
128M16—4792no—
129M16C2×D47911yescharacteristic, complemented
130C2×C8—4791no—
131C2×C8—4792no—
132C23—21no—
133C23—9582no—
134Q8—9582no—
135Q8—9581no—
136Q8—4792no—
137Q8—4791no—
138Q8—4791no—
139Q8C22×D47911yescharacteristic
140D4—21no—
141D4—21no—
142D4—9582no—
143D4—9582no—
144D4—9581no—
145D4—9582no—
146D4—4792no—
147D4—4791no—
148D4—4791no—
149D4C22×D47911yescharacteristic
150D4C22×D47912yes—
151C2×C4—21no—
152C2×C4—9582no—
153C2×C4—9581no—
154C2×C4—9582no—
155C2×C4—9582no—
156C2×C4—9581no—
157C2×C4—4792no—
158C2×C4C22×D47911yescharacteristic
159C8—4791no—
160C8—4791no—
161C8C22×D47912yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—9581no—
166C22—4792no—
167C22—38322no—
168C22D4×D47911yescharacteristic
169C4—21no—
170C4—9581no—
171C4—9582no—
172C4—4792no—
173C4D4×D47911yescharacteristic
174C4C23×D47911yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—19161no—
179C2—9582no—
180C2C2×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#577
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. #29506429C2semidirect
2. #29506427C2semidirect
3. #29506415C2semidirect
4. #29506411C2semidirect
5. #29506406C2semidirect
6. #29506402C2semidirect
7. #29506401C2semidirect
8. C2×#21440150C2semidirect
9. SD16×D479C2semidirect
10. #29506390C2semidirect
11. AGL(1,ℤ/8)×C479C2semidirect
18. #21440161C22semidirect
20. C2×Dic958C22semidirect
21. Q8×D479C22semidirect
25. Dic1916C22semidirect
26. #21440152C22semidirect
27. #21440151C22semidirect
28. #21440150C22semidirect
29. #21440150C22semidirect
30. #21440150C22semidirect
31. #21440149C22semidirect
32. #21440147C22semidirect
33. #21440145C22semidirect
34. C2×C479⋊C8C22semidirect
35. C8×D479C22semidirect
36. #41×C479C22semidirect
38. SD16×C479C22semidirect
39. D8×C479C22semidirect
40. M16×C479C22semidirect
90. C479#577semidirect
97. AGL(1,ℤ/8)D479semidirect
110. #41C2×D479semidirect
125. SD16C2×D479semidirect
127. D8C2×D479semidirect
129. M16C2×D479semidirect

Maximal subgroups

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

subgroupindex
#295064292
#295064272
#295064152
#295064112
#295064062
#295064022
#295064012
C2×#214401502
SD16×D4792
#295063902
AGL(1,ℤ/8)×C4792
#577479