Finite Group Databasebeta

← #135×D461 #44442854

Subgroups — #135×D461 #44442854

Order 29504.

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×D461C212yesmaximal, complemented
2#28414141C211yesmaximal, characteristic, complemented
3#28414140C211yesmaximal, characteristic, complemented
4#28414139C212yesmaximal, complemented
5#28414138C212yesmaximal, complemented
6#28414137C211yesmaximal, characteristic, complemented
7Q16×D461C211yesmaximal, characteristic, complemented
8SD16×D461C212yesmaximal, complemented
9D8×D461C211yesmaximal, characteristic, complemented
10C2×C8×D461C211yesmaximal, characteristic, complemented
11#135×C461C211yesmaximal, characteristic, complemented
12#20301502C2212yescomplemented
13#20301501—22no—
14#20301501C2212yescomplemented
15#20301500—22no—
16#20301500C2212yescomplemented
17Q8×D461C2212yes—
18D4×D461—22no—
19D4×D461C2212yes—
20C2×C4×D461—22no—
21C2×C4×D461C2211yescharacteristic
22Dic1844C2211yescharacteristic, complemented
23#20301491C2212yescomplemented
24#20301490C2212yescomplemented
25#20301489C2212yescomplemented
26#20301488C2212yescomplemented
27D3688C2211yescharacteristic, complemented
28#20301486C2212yescomplemented
29C2×#16814779C2211yescharacteristic, complemented
30C8×D461C2211yescharacteristic
31C8×D461C2211yescharacteristic
32C8×D461C2211yescharacteristic, complemented
33C8×D461C2211yescharacteristic, complemented
34#41×C461C2212yescomplemented
35Q16×C461C2211yescharacteristic, complemented
36SD16×C461C2212yescomplemented
37D8×C461C2211yescharacteristic, complemented
38C2×C8×C461C2211yescharacteristic, complemented
39C22×D461—22no—
40C22×D461D411yescharacteristic
41Dic922—22no—
42Dic922C2312yes—
43D1844—22no—
44D1844C2312yes—
45C22⋊D461—22no—
46C22⋊D461—22no—
47C22⋊D461—22no—
48C2×Dic461—22no—
49C2×Dic461D411yescharacteristic
50C4×D461—22no—
51C4×D461—22no—
52C4×D461—22no—
53C4×D461D411yescharacteristic
54C4×D461D411yescharacteristic
55C4×D461C2311yescharacteristic
56C4×D461C2311yescharacteristic
57#16814779C2311yescharacteristic
58#16814779C2311yescharacteristic
59Q8×C461C2312yes—
60D4×C461—22no—
61D4×C461C2312yes—
62C2×C4×C461—22no—
63C2×C4×C461C2311yescharacteristic
64C8×C461C2311yescharacteristic
65C8×C461C2311yescharacteristic
66C22×C461—22no—
67C22×C461C2×D411yescharacteristic
68C2×D461—22no—
69C2×D461—22no—
70C2×D461—44no—
71C2×D461C2×D411yescharacteristic
72C2×D461C2×D411yescharacteristic
73C4×C461—22no—
74C4×C461C2×D411yescharacteristic
75C4×C461C2411yescharacteristic
76Dic461—22no—
77Dic461C2×D411yescharacteristic
78Dic461C2×D411yescharacteristic
79C2×C461—21no—
80C2×C461—42no—
81C2×C461C22×D411yescharacteristic
82D461—21no—
83D461—42no—
84D461#13512yesdirect product factor
85C461C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4611nomaximal, Sylow
87C2×#41—4612no—
88#135—4612no—
89#135—4611no—
90#135—4612no—
91#135—4611no—
92#135—4611no—
93#135D46111yescharacteristic, direct product factor
94C2×Q16—4611no—
95C2×SD16—4612no—
96C2×D8—4611no—
97C22×C8—4611no—
98#41—9222no—
99#41—9222no—
100#41—4612no—
101#41—4612no—
102#41—4612no—
103#41C2×D46112yescomplemented
104C2×Q8—4612no—
105C2×D4—9222no—
106C2×D4—4612no—
107C22×C4—9222no—
108C22×C4—4611no—
109Q16—4612no—
110Q16—4611no—
111Q16C2×D46111yescharacteristic, complemented
112SD16—4612no—
113SD16—4612no—
114SD16—4612no—
115SD16C2×D46112yescomplemented
116D8—4612no—
117D8—4611no—
118D8C2×D46111yescharacteristic, complemented
119C2×C8—4611no—
120C2×C8—4611no—
121C2×C8—4611no—
122C2×C8—4611no—
123C2×C8—4611no—
124C2×C8C2×D46111yescharacteristic, complemented
125C23—9222no—
126C23—4611no—
127Q8—9222no—
128Q8—4612no—
129Q8C22×D46112yes—
130D4—22no—
131D4—9222no—
132D4—9222no—
133D4—9222no—
134D4—9222no—
135D4—4612no—
136D4C22×D46112yes—
137C2×C4—22no—
138C2×C4—9222no—
139C2×C4—9222no—
140C2×C4—9222no—
141C2×C4—9222no—
142C2×C4—4611no—
143C2×C4—4611no—
144C2×C4—4611no—
145C2×C4—4611no—
146C2×C4—4611no—
147C2×C4C22×D46111yescharacteristic
148C8—4611no—
149C8—4611no—
150C8C22×D46111yescharacteristic
151C8C22×D46111yescharacteristic
152C22—22no—
153C22—18444no—
154C22—9222no—
155C22—9222no—
156C22—4611no—
157C22—4611no—
158C22D4×D46111yescharacteristic
159C4—22no—
160C4—9222no—
161C4—4611no—
162C4—4611no—
163C4D4×D46111yescharacteristic
164C4C23×D46111yescharacteristic
165C2—21no—
166C2—42no—
167C2—18442no—
168C2—9221no—
169C2—4612no—
170C2C2×D4×D46111yescharacteristic
subgroupG/H
centerC4D4×D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
Fitting#135×C461C2
socleC2×C461C22×D4
hypercenter#135D461
hypocenterC461C2×#135
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D461C2semidirect
2. #28414141C2semidirect
3. #28414140C2semidirect
4. #28414139C2semidirect
5. #28414138C2semidirect
6. #28414137C2semidirect
7. Q16×D461C2semidirect
8. SD16×D461C2semidirect
9. D8×D461C2semidirect
10. C2×C8×D461C2semidirect
11. #135×C461C2semidirect
12. #20301502C22semidirect
14. #20301501C22semidirect
16. #20301500C22semidirect
22. Dic1844C22semidirect
23. #20301491C22semidirect
24. #20301490C22semidirect
25. #20301489C22semidirect
26. #20301488C22semidirect
27. D3688C22semidirect
28. #20301486C22semidirect
29. C2×#16814779C22semidirect
32. C8×D461C22semidirect
33. C8×D461C22semidirect
34. #41×C461C22semidirect
35. Q16×C461C22semidirect
36. SD16×C461C22semidirect
37. D8×C461C22semidirect
38. C2×C8×C461C22semidirect
84. D461#135direct (N × H)
85. C461C2×#135semidirect
93. #135D461direct (N × H)
103. #41C2×D461semidirect
111. Q16C2×D461semidirect
115. SD16C2×D461semidirect
118. D8C2×D461semidirect
124. C2×C8C2×D461semidirect

Maximal subgroups

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

subgroupindex
#41×D4612
#284141412
#284141402
#284141392
#284141382
#284141372
Q16×D4612
SD16×D4612
D8×D4612
C2×C8×D4612
#135×C4612
C2×#135461