Finite Group Databasebeta

← #44501191

Subgroups — #44501191

Order 30656.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 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
1C2×#21440161C211yesmaximal, characteristic, complemented
2#41×D479C211yesmaximal, characteristic, complemented
3#29506415C211yesmaximal, characteristic, complemented
4#29506412C211yesmaximal, characteristic, complemented
5#29506411C212yesmaximal, complemented
6#29506408C211yesmaximal, characteristic, complemented
7#29506406C212yesmaximal, complemented
8#29506403C212yesmaximal, complemented
9#29506401C212yesmaximal, complemented
10M16×D479C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C479C211yesmaximal, characteristic, complemented
12#21440163C2211yescharacteristic, complemented
13#21440162—21no—
14#21440162C2211yescharacteristic
15#21440161—21no—
16#21440161—21no—
17#21440161—21no—
18#21440161C2212yes—
19#21440161C2211yescharacteristic, complemented
20#21440161C2212yescomplemented
21C2×Dic958C2211yescharacteristic, complemented
22Q8×D479C2211yescharacteristic, complemented
23C2×C22⋊D479—21no—
24D4×D479—21no—
25D4×D479C2211yescharacteristic, complemented
26C22×Dic479—21no—
27C2×C4×D479—21no—
28C2×C4×D479C2211yescharacteristic
29Dic1916C2212yescomplemented
30#21440152C2212yescomplemented
31#21440151C2212yescomplemented
32#21440150C2212yescomplemented
33#21440150C2212yescomplemented
34#21440147C2212yescomplemented
35#21440146C2211yescharacteristic, complemented
36#21440145C2212yescomplemented
37C8×D479C2212yescomplemented
38#41×C479C2211yescharacteristic
39C2×D4×C479C2211yescharacteristic, complemented
40SD16×C479C2212yescomplemented
41D8×C479C2212yescomplemented
42M16×C479C2211yescharacteristic, complemented
43C22×D479—21no—
44C22×D479D411yescharacteristic
45Dic958—21no—
46Dic958—21no—
47Dic958C2311yescharacteristic
48Dic958C2312yes—
49D1916—21no—
50D1916C2311yescharacteristic
51C22⋊D479—21no—
52C22⋊D479—21no—
53C22⋊D479—22no—
54C22⋊D479—22no—
55C22⋊D479—21no—
56C2×Dic479—21no—
57C2×Dic479—21no—
58C2×Dic479—22no—
59C2×Dic479—22no—
60C2×Dic479D411yescharacteristic
61C4×D479—21no—
62C4×D479—21no—
63C4×D479—21no—
64C4×D479D411yescharacteristic
65C4×D479D411yescharacteristic
66C4×D479C2311yescharacteristic
67C4×D479C2311yescharacteristic
68C479⋊C8C2312yes—
69C23×C479—21no—
70Q8×C479C2311yescharacteristic
71D4×C479—21no—
72D4×C479—21no—
73D4×C479C2311yescharacteristic
74D4×C479C2312yes—
75C2×C4×C479—21no—
76C2×C4×C479C2311yescharacteristic
77C8×C479C2312yes—
78C22×C479—21no—
79C22×C479—22no—
80C22×C479—42no—
81C22×C479C2×D411yescharacteristic
82C2×D479—21no—
83C2×D479—41no—
84C2×D479—42no—
85C2×D479C2×D411yescharacteristic
86C2×D479C2×D411yescharacteristic
87C4×C479—21no—
88C4×C479C2×D411yescharacteristic
89C4×C479C2411yescharacteristic
90Dic479—21no—
91Dic479—22no—
92Dic479C2×D411yescharacteristic
93Dic479C2×D411yescharacteristic
94C2×C479—21no—
95C2×C479—41no—
96C2×C479—42no—
97C2×C479C22×D411yescharacteristic
98D479—21no—
99D479—21no—
100D479—41no—
101C479#57511yescharacteristic, complemented, Sylow
102#575—4791nomaximal, Sylow
103C2×#41—4791no—
104C2×#41—4791no—
105#137—4791no—
106#137—4792no—
107#137—4791no—
108AGL(1,ℤ/8)—4791no—
109AGL(1,ℤ/8)—4792no—
110AGL(1,ℤ/8)D47911yescharacteristic, complemented
111#135—4792no—
112#135—4792no—
113C2×M16—4791no—
114#41—9581no—
115#41—9581no—
116#41—9581no—
117#41—9581no—
118#41—4791no—
119#41—4792no—
120#41—4791no—
121#41—4792no—
122#41—4791no—
123#41C2×D47911yescharacteristic
124C2×Q8—4791no—
125C2×Q8—4791no—
126C2×D4—9581no—
127C2×D4—9581no—
128C2×D4—4791no—
129C2×D4C2×D47911yescharacteristic, complemented
130C22×C4—9581no—
131C22×C4—9581no—
132C22×C4—4791no—
133Q16—4792no—
134Q16—4792no—
135SD16—4792no—
136SD16—4792no—
137SD16—4792no—
138SD16C2×D47912yescomplemented
139D8—4792no—
140D8C2×D47912yescomplemented
141M16—4791no—
142M16—4792no—
143M16C2×D47911yescharacteristic, complemented
144C2×C8—4792no—
145C23—21no—
146C23—9581no—
147C23—4791no—
148Q8—9581no—
149Q8—9581no—
150Q8—4791no—
151Q8—4792no—
152Q8C22×D47911yescharacteristic
153D4—21no—
154D4—21no—
155D4—9581no—
156D4—9581no—
157D4—9582no—
158D4—9582no—
159D4—9581no—
160D4—9581no—
161D4—4791no—
162D4C22×D47912yes—
163D4C22×D47911yescharacteristic
164C2×C4—21no—
165C2×C4—9581no—
166C2×C4—9581no—
167C2×C4—9581no—
168C2×C4—9581no—
169C2×C4—9582no—
170C2×C4—9582no—
171C2×C4—9581no—
172C2×C4—4791no—
173C2×C4—4791no—
174C2×C4—4791no—
175C2×C4—4791no—
176C2×C4—4791no—
177C2×C4C22×D47911yescharacteristic
178C8—4792no—
179C8C22×D47912yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—19161no—
184C22—19162no—
185C22—9581no—
186C22—4791no—
187C22—4791no—
188C22D4×D47911yescharacteristic
189C4—21no—
190C4—9581no—
191C4—9582no—
192C4—4791no—
193C4—4791no—
194C4D4×D47911yescharacteristic
195C4C23×D47911yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—19161no—
200C2—9581no—
201C2—9581no—
202C2C2×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#575
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. C2×#21440161C2semidirect
2. #41×D479C2semidirect
3. #29506415C2semidirect
4. #29506412C2semidirect
5. #29506411C2semidirect
6. #29506408C2semidirect
7. #29506406C2semidirect
8. #29506403C2semidirect
9. #29506401C2semidirect
10. M16×D479C2semidirect
11. AGL(1,ℤ/8)×C479C2semidirect
12. #21440163C22semidirect
19. #21440161C22semidirect
20. #21440161C22semidirect
21. C2×Dic958C22semidirect
22. Q8×D479C22semidirect
25. D4×D479C22semidirect
29. Dic1916C22semidirect
30. #21440152C22semidirect
31. #21440151C22semidirect
32. #21440150C22semidirect
33. #21440150C22semidirect
34. #21440147C22semidirect
35. #21440146C22semidirect
36. #21440145C22semidirect
37. C8×D479C22semidirect
39. C2×D4×C479C22semidirect
40. SD16×C479C22semidirect
41. D8×C479C22semidirect
42. M16×C479C22semidirect
101. C479#575semidirect
110. AGL(1,ℤ/8)D479semidirect
129. C2×D4C2×D479semidirect
138. SD16C2×D479semidirect
140. D8C2×D479semidirect
143. M16C2×D479semidirect

Maximal subgroups

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

subgroupindex
C2×#214401612
#41×D4792
#295064152
#295064122
#295064112
#295064082
#295064062
#295064032
#295064012
M16×D4792
AGL(1,ℤ/8)×C4792
#575479