Finite Group Databasebeta

← #135×D479 #44501173

Subgroups — #135×D479 #44501173

Order 30656.

266 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D479C212yesmaximal, complemented
2#29506405C211yesmaximal, characteristic, complemented
3#29506404C211yesmaximal, characteristic, complemented
4#29506403C212yesmaximal, complemented
5#29506402C212yesmaximal, complemented
6#29506401C211yesmaximal, characteristic, complemented
7Q16×D479C211yesmaximal, characteristic, complemented
8SD16×D479C212yesmaximal, complemented
9D8×D479C211yesmaximal, characteristic, complemented
10C2×C8×D479C211yesmaximal, characteristic, complemented
11#135×C479C211yesmaximal, characteristic, complemented
12#21440163C2212yescomplemented
13#21440162—22no—
14#21440162C2212yescomplemented
15#21440161—22no—
16#21440161C2212yescomplemented
17Q8×D479C2212yes—
18D4×D479—22no—
19D4×D479C2212yes—
20C2×C4×D479—22no—
21C2×C4×D479C2211yescharacteristic
22Dic1916C2211yescharacteristic, complemented
23#21440152C2212yescomplemented
24#21440151C2212yescomplemented
25#21440150C2212yescomplemented
26#21440149C2212yescomplemented
27D3832C2211yescharacteristic, complemented
28#21440147C2212yescomplemented
29C2×C479⋊C8C2211yescharacteristic, complemented
30C8×D479C2211yescharacteristic
31C8×D479C2211yescharacteristic
32C8×D479C2211yescharacteristic, complemented
33C8×D479C2211yescharacteristic, complemented
34#41×C479C2212yescomplemented
35Q16×C479C2211yescharacteristic, complemented
36SD16×C479C2212yescomplemented
37D8×C479C2211yescharacteristic, complemented
38C2×C8×C479C2211yescharacteristic, complemented
39C22×D479—22no—
40C22×D479D411yescharacteristic
41Dic958—22no—
42Dic958C2312yes—
43D1916—22no—
44D1916C2312yes—
45C22⋊D479—22no—
46C22⋊D479—22no—
47C22⋊D479—22no—
48C2×Dic479—22no—
49C2×Dic479D411yescharacteristic
50C4×D479—22no—
51C4×D479—22no—
52C4×D479—22no—
53C4×D479D411yescharacteristic
54C4×D479D411yescharacteristic
55C4×D479C2311yescharacteristic
56C4×D479C2311yescharacteristic
57C479⋊C8C2311yescharacteristic
58C479⋊C8C2311yescharacteristic
59Q8×C479C2312yes—
60D4×C479—22no—
61D4×C479C2312yes—
62C2×C4×C479—22no—
63C2×C4×C479C2311yescharacteristic
64C8×C479C2311yescharacteristic
65C8×C479C2311yescharacteristic
66C22×C479—22no—
67C22×C479C2×D411yescharacteristic
68C2×D479—22no—
69C2×D479—22no—
70C2×D479—44no—
71C2×D479C2×D411yescharacteristic
72C2×D479C2×D411yescharacteristic
73C4×C479—22no—
74C4×C479C2×D411yescharacteristic
75C4×C479C2411yescharacteristic
76Dic479—22no—
77Dic479C2×D411yescharacteristic
78Dic479C2×D411yescharacteristic
79C2×C479—21no—
80C2×C479—42no—
81C2×C479C22×D411yescharacteristic
82D479—21no—
83D479—42no—
84D479#13512yesdirect product factor
85C479C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4791nomaximal, Sylow
87C2×#41—4792no—
88#135—4792no—
89#135—4791no—
90#135—4792no—
91#135—4791no—
92#135—4791no—
93#135D47911yescharacteristic, direct product factor
94C2×Q16—4791no—
95C2×SD16—4792no—
96C2×D8—4791no—
97C22×C8—4791no—
98#41—9582no—
99#41—9582no—
100#41—4792no—
101#41—4792no—
102#41—4792no—
103#41C2×D47912yescomplemented
104C2×Q8—4792no—
105C2×D4—9582no—
106C2×D4—4792no—
107C22×C4—9582no—
108C22×C4—4791no—
109Q16—4792no—
110Q16—4791no—
111Q16C2×D47911yescharacteristic, complemented
112SD16—4792no—
113SD16—4792no—
114SD16—4792no—
115SD16C2×D47912yescomplemented
116D8—4792no—
117D8—4791no—
118D8C2×D47911yescharacteristic, complemented
119C2×C8—4791no—
120C2×C8—4791no—
121C2×C8—4791no—
122C2×C8—4791no—
123C2×C8—4791no—
124C2×C8C2×D47911yescharacteristic, complemented
125C23—9582no—
126C23—4791no—
127Q8—9582no—
128Q8—4792no—
129Q8C22×D47912yes—
130D4—22no—
131D4—9582no—
132D4—9582no—
133D4—9582no—
134D4—9582no—
135D4—4792no—
136D4C22×D47912yes—
137C2×C4—22no—
138C2×C4—9582no—
139C2×C4—9582no—
140C2×C4—9582no—
141C2×C4—9582no—
142C2×C4—4791no—
143C2×C4—4791no—
144C2×C4—4791no—
145C2×C4—4791no—
146C2×C4—4791no—
147C2×C4C22×D47911yescharacteristic
148C8—4791no—
149C8—4791no—
150C8C22×D47911yescharacteristic
151C8C22×D47911yescharacteristic
152C22—22no—
153C22—19164no—
154C22—9582no—
155C22—9582no—
156C22—4791no—
157C22—4791no—
158C22D4×D47911yescharacteristic
159C4—22no—
160C4—9582no—
161C4—4791no—
162C4—4791no—
163C4D4×D47911yescharacteristic
164C4C23×D47911yescharacteristic
165C2—21no—
166C2—42no—
167C2—19162no—
168C2—9581no—
169C2—4792no—
170C2C2×D4×D47911yescharacteristic
subgroupG/H
centerC4D4×D479
commutator, cosocleC4×C479C24
FrattiniC4C23×D479
Fitting#135×C479C2
socleC2×C479C22×D4
hypercenter#135D479
hypocenterC479C2×#135
LCSG ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D479C2semidirect
2. #29506405C2semidirect
3. #29506404C2semidirect
4. #29506403C2semidirect
5. #29506402C2semidirect
6. #29506401C2semidirect
7. Q16×D479C2semidirect
8. SD16×D479C2semidirect
9. D8×D479C2semidirect
10. C2×C8×D479C2semidirect
11. #135×C479C2semidirect
12. #21440163C22semidirect
14. #21440162C22semidirect
16. #21440161C22semidirect
22. Dic1916C22semidirect
23. #21440152C22semidirect
24. #21440151C22semidirect
25. #21440150C22semidirect
26. #21440149C22semidirect
27. D3832C22semidirect
28. #21440147C22semidirect
29. C2×C479⋊C8C22semidirect
32. C8×D479C22semidirect
33. C8×D479C22semidirect
34. #41×C479C22semidirect
35. Q16×C479C22semidirect
36. SD16×C479C22semidirect
37. D8×C479C22semidirect
38. C2×C8×C479C22semidirect
84. D479#135direct (N × H)
85. C479C2×#135semidirect
93. #135D479direct (N × H)
103. #41C2×D479semidirect
111. Q16C2×D479semidirect
115. SD16C2×D479semidirect
118. D8C2×D479semidirect
124. C2×C8C2×D479semidirect

Maximal subgroups

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

subgroupindex
#41×D4792
#295064052
#295064042
#295064032
#295064022
#295064012
Q16×D4792
SD16×D4792
D8×D4792
C2×C8×D4792
#135×C4792
C2×#135479