Finite Group Databasebeta

← #135×D439 #43244382

Subgroups — #135×D439 #43244382

Order 28096.

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×D439C212yesmaximal, complemented
2#28380766C211yesmaximal, characteristic, complemented
3#28380765C211yesmaximal, characteristic, complemented
4#28380764C212yesmaximal, complemented
5#28380763C212yesmaximal, complemented
6#28380762C211yesmaximal, characteristic, complemented
7Q16×D439C211yesmaximal, characteristic, complemented
8SD16×D439C212yesmaximal, complemented
9D8×D439C211yesmaximal, characteristic, complemented
10C2×C8×D439C211yesmaximal, characteristic, complemented
11#135×C439C211yesmaximal, characteristic, complemented
12#20296330C2212yescomplemented
13#20296329—22no—
14#20296329C2212yescomplemented
15#20296328—22no—
16#20296328C2212yescomplemented
17Q8×D439C2212yes—
18D4×D439—22no—
19D4×D439C2212yes—
20C2×C4×D439—22no—
21C2×C4×D439C2211yescharacteristic
22Dic1756C2211yescharacteristic, complemented
23#20296319C2212yescomplemented
24#20296318C2212yescomplemented
25#20296317C2212yescomplemented
26#20296316C2212yescomplemented
27D3512C2211yescharacteristic, complemented
28#20296314C2212yescomplemented
29C2×C439⋊C8C2211yescharacteristic, complemented
30C8×D439C2211yescharacteristic
31C8×D439C2211yescharacteristic
32C8×D439C2211yescharacteristic, complemented
33C8×D439C2211yescharacteristic, complemented
34#41×C439C2212yescomplemented
35Q16×C439C2211yescharacteristic, complemented
36SD16×C439C2212yescomplemented
37D8×C439C2211yescharacteristic, complemented
38C2×C8×C439C2211yescharacteristic, complemented
39C22×D439—22no—
40C22×D439D411yescharacteristic
41Dic878—22no—
42Dic878C2312yes—
43D1756—22no—
44D1756C2312yes—
45C22⋊D439—22no—
46C22⋊D439—22no—
47C22⋊D439—22no—
48C2×Dic439—22no—
49C2×Dic439D411yescharacteristic
50C4×D439—22no—
51C4×D439—22no—
52C4×D439—22no—
53C4×D439D411yescharacteristic
54C4×D439D411yescharacteristic
55C4×D439C2311yescharacteristic
56C4×D439C2311yescharacteristic
57C439⋊C8C2311yescharacteristic
58C439⋊C8C2311yescharacteristic
59Q8×C439C2312yes—
60D4×C439—22no—
61D4×C439C2312yes—
62C2×C4×C439—22no—
63C2×C4×C439C2311yescharacteristic
64C8×C439C2311yescharacteristic
65C8×C439C2311yescharacteristic
66C22×C439—22no—
67C22×C439C2×D411yescharacteristic
68C2×D439—22no—
69C2×D439—22no—
70C2×D439—44no—
71C2×D439C2×D411yescharacteristic
72C2×D439C2×D411yescharacteristic
73C4×C439—22no—
74C4×C439C2×D411yescharacteristic
75C4×C439C2411yescharacteristic
76Dic439—22no—
77Dic439C2×D411yescharacteristic
78Dic439C2×D411yescharacteristic
79C2×C439—21no—
80C2×C439—42no—
81C2×C439C22×D411yescharacteristic
82D439—21no—
83D439—42no—
84D439#13512yesdirect product factor
85C439C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4391nomaximal, Sylow
87C2×#41—4392no—
88#135—4392no—
89#135—4391no—
90#135—4392no—
91#135—4391no—
92#135—4391no—
93#135D43911yescharacteristic, direct product factor
94C2×Q16—4391no—
95C2×SD16—4392no—
96C2×D8—4391no—
97C22×C8—4391no—
98#41—8782no—
99#41—8782no—
100#41—4392no—
101#41—4392no—
102#41—4392no—
103#41C2×D43912yescomplemented
104C2×Q8—4392no—
105C2×D4—8782no—
106C2×D4—4392no—
107C22×C4—8782no—
108C22×C4—4391no—
109Q16—4392no—
110Q16—4391no—
111Q16C2×D43911yescharacteristic, complemented
112SD16—4392no—
113SD16—4392no—
114SD16—4392no—
115SD16C2×D43912yescomplemented
116D8—4392no—
117D8—4391no—
118D8C2×D43911yescharacteristic, complemented
119C2×C8—4391no—
120C2×C8—4391no—
121C2×C8—4391no—
122C2×C8—4391no—
123C2×C8—4391no—
124C2×C8C2×D43911yescharacteristic, complemented
125C23—8782no—
126C23—4391no—
127Q8—8782no—
128Q8—4392no—
129Q8C22×D43912yes—
130D4—22no—
131D4—8782no—
132D4—8782no—
133D4—8782no—
134D4—8782no—
135D4—4392no—
136D4C22×D43912yes—
137C2×C4—22no—
138C2×C4—8782no—
139C2×C4—8782no—
140C2×C4—8782no—
141C2×C4—8782no—
142C2×C4—4391no—
143C2×C4—4391no—
144C2×C4—4391no—
145C2×C4—4391no—
146C2×C4—4391no—
147C2×C4C22×D43911yescharacteristic
148C8—4391no—
149C8—4391no—
150C8C22×D43911yescharacteristic
151C8C22×D43911yescharacteristic
152C22—22no—
153C22—8782no—
154C22—8782no—
155C22—4391no—
156C22—4391no—
157C22—17564no—
158C22D4×D43911yescharacteristic
159C4—22no—
160C4—8782no—
161C4—4391no—
162C4—4391no—
163C4D4×D43911yescharacteristic
164C4C23×D43911yescharacteristic
165C2—21no—
166C2—42no—
167C2—8781no—
168C2—4392no—
169C2—17562no—
170C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC4D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
Fitting#135×C439C2
socleC2×C439C22×D4
hypercenter#135D439
hypocenterC439C2×#135
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D439C2semidirect
2. #28380766C2semidirect
3. #28380765C2semidirect
4. #28380764C2semidirect
5. #28380763C2semidirect
6. #28380762C2semidirect
7. Q16×D439C2semidirect
8. SD16×D439C2semidirect
9. D8×D439C2semidirect
10. C2×C8×D439C2semidirect
11. #135×C439C2semidirect
12. #20296330C22semidirect
14. #20296329C22semidirect
16. #20296328C22semidirect
22. Dic1756C22semidirect
23. #20296319C22semidirect
24. #20296318C22semidirect
25. #20296317C22semidirect
26. #20296316C22semidirect
27. D3512C22semidirect
28. #20296314C22semidirect
29. C2×C439⋊C8C22semidirect
32. C8×D439C22semidirect
33. C8×D439C22semidirect
34. #41×C439C22semidirect
35. Q16×C439C22semidirect
36. SD16×C439C22semidirect
37. D8×C439C22semidirect
38. C2×C8×C439C22semidirect
84. D439#135direct (N × H)
85. C439C2×#135semidirect
93. #135D439direct (N × H)
103. #41C2×D439semidirect
111. Q16C2×D439semidirect
115. SD16C2×D439semidirect
118. D8C2×D439semidirect
124. C2×C8C2×D439semidirect

Maximal subgroups

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

subgroupindex
#41×D4392
#283807662
#283807652
#283807642
#283807632
#283807622
Q16×D4392
SD16×D4392
D8×D4392
C2×C8×D4392
#135×C4392
C2×#135439