Finite Group Databasebeta

← #135×D443 #43248495

Subgroups — #135×D443 #43248495

Order 28352.

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×D443C212yesmaximal, complemented
2#28381909C211yesmaximal, characteristic, complemented
3#28381908C211yesmaximal, characteristic, complemented
4#28381907C212yesmaximal, complemented
5#28381906C212yesmaximal, complemented
6#28381905C211yesmaximal, characteristic, complemented
7Q16×D443C211yesmaximal, characteristic, complemented
8SD16×D443C212yesmaximal, complemented
9D8×D443C211yesmaximal, characteristic, complemented
10C2×C8×D443C211yesmaximal, characteristic, complemented
11#135×C443C211yesmaximal, characteristic, complemented
12#20296788C2212yescomplemented
13#20296787—22no—
14#20296787C2212yescomplemented
15#20296786—22no—
16#20296786C2212yescomplemented
17Q8×D443C2212yes—
18D4×D443—22no—
19D4×D443C2212yes—
20C2×C4×D443—22no—
21C2×C4×D443C2211yescharacteristic
22Dic1772C2211yescharacteristic, complemented
23#20296777C2212yescomplemented
24#20296776C2212yescomplemented
25#20296775C2212yescomplemented
26#20296774C2212yescomplemented
27D3544C2211yescharacteristic, complemented
28#20296772C2212yescomplemented
29C2×C443⋊C8C2211yescharacteristic, complemented
30C8×D443C2211yescharacteristic
31C8×D443C2211yescharacteristic
32C8×D443C2211yescharacteristic, complemented
33C8×D443C2211yescharacteristic, complemented
34#41×C443C2212yescomplemented
35Q16×C443C2211yescharacteristic, complemented
36SD16×C443C2212yescomplemented
37D8×C443C2211yescharacteristic, complemented
38C2×C8×C443C2211yescharacteristic, complemented
39C22×D443—22no—
40C22×D443D411yescharacteristic
41Dic886—22no—
42Dic886C2312yes—
43D1772—22no—
44D1772C2312yes—
45C22⋊D443—22no—
46C22⋊D443—22no—
47C22⋊D443—22no—
48C2×Dic443—22no—
49C2×Dic443D411yescharacteristic
50C4×D443—22no—
51C4×D443—22no—
52C4×D443—22no—
53C4×D443D411yescharacteristic
54C4×D443D411yescharacteristic
55C4×D443C2311yescharacteristic
56C4×D443C2311yescharacteristic
57C443⋊C8C2311yescharacteristic
58C443⋊C8C2311yescharacteristic
59Q8×C443C2312yes—
60D4×C443—22no—
61D4×C443C2312yes—
62C2×C4×C443—22no—
63C2×C4×C443C2311yescharacteristic
64C8×C443C2311yescharacteristic
65C8×C443C2311yescharacteristic
66C22×C443—22no—
67C22×C443C2×D411yescharacteristic
68C2×D443—22no—
69C2×D443—22no—
70C2×D443—44no—
71C2×D443C2×D411yescharacteristic
72C2×D443C2×D411yescharacteristic
73C4×C443—22no—
74C4×C443C2×D411yescharacteristic
75C4×C443C2411yescharacteristic
76Dic443—22no—
77Dic443C2×D411yescharacteristic
78Dic443C2×D411yescharacteristic
79C2×C443—21no—
80C2×C443—42no—
81C2×C443C22×D411yescharacteristic
82D443—21no—
83D443—42no—
84D443#13512yesdirect product factor
85C443C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—4431nomaximal, Sylow
87C2×#41—4432no—
88#135—4432no—
89#135—4431no—
90#135—4432no—
91#135—4431no—
92#135—4431no—
93#135D44311yescharacteristic, direct product factor
94C2×Q16—4431no—
95C2×SD16—4432no—
96C2×D8—4431no—
97C22×C8—4431no—
98#41—8862no—
99#41—8862no—
100#41—4432no—
101#41—4432no—
102#41—4432no—
103#41C2×D44312yescomplemented
104C2×Q8—4432no—
105C2×D4—8862no—
106C2×D4—4432no—
107C22×C4—8862no—
108C22×C4—4431no—
109Q16—4432no—
110Q16—4431no—
111Q16C2×D44311yescharacteristic, complemented
112SD16—4432no—
113SD16—4432no—
114SD16—4432no—
115SD16C2×D44312yescomplemented
116D8—4432no—
117D8—4431no—
118D8C2×D44311yescharacteristic, complemented
119C2×C8—4431no—
120C2×C8—4431no—
121C2×C8—4431no—
122C2×C8—4431no—
123C2×C8—4431no—
124C2×C8C2×D44311yescharacteristic, complemented
125C23—8862no—
126C23—4431no—
127Q8—8862no—
128Q8—4432no—
129Q8C22×D44312yes—
130D4—22no—
131D4—8862no—
132D4—8862no—
133D4—8862no—
134D4—8862no—
135D4—4432no—
136D4C22×D44312yes—
137C2×C4—22no—
138C2×C4—8862no—
139C2×C4—8862no—
140C2×C4—8862no—
141C2×C4—8862no—
142C2×C4—4431no—
143C2×C4—4431no—
144C2×C4—4431no—
145C2×C4—4431no—
146C2×C4—4431no—
147C2×C4C22×D44311yescharacteristic
148C8—4431no—
149C8—4431no—
150C8C22×D44311yescharacteristic
151C8C22×D44311yescharacteristic
152C22—22no—
153C22—8862no—
154C22—8862no—
155C22—4431no—
156C22—4431no—
157C22—17724no—
158C22D4×D44311yescharacteristic
159C4—22no—
160C4—8862no—
161C4—4431no—
162C4—4431no—
163C4D4×D44311yescharacteristic
164C4C23×D44311yescharacteristic
165C2—21no—
166C2—42no—
167C2—8861no—
168C2—4432no—
169C2—17722no—
170C2C2×D4×D44311yescharacteristic
subgroupG/H
centerC4D4×D443
commutator, cosocleC4×C443C24
FrattiniC4C23×D443
Fitting#135×C443C2
socleC2×C443C22×D4
hypercenter#135D443
hypocenterC443C2×#135
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D443C2semidirect
2. #28381909C2semidirect
3. #28381908C2semidirect
4. #28381907C2semidirect
5. #28381906C2semidirect
6. #28381905C2semidirect
7. Q16×D443C2semidirect
8. SD16×D443C2semidirect
9. D8×D443C2semidirect
10. C2×C8×D443C2semidirect
11. #135×C443C2semidirect
12. #20296788C22semidirect
14. #20296787C22semidirect
16. #20296786C22semidirect
22. Dic1772C22semidirect
23. #20296777C22semidirect
24. #20296776C22semidirect
25. #20296775C22semidirect
26. #20296774C22semidirect
27. D3544C22semidirect
28. #20296772C22semidirect
29. C2×C443⋊C8C22semidirect
32. C8×D443C22semidirect
33. C8×D443C22semidirect
34. #41×C443C22semidirect
35. Q16×C443C22semidirect
36. SD16×C443C22semidirect
37. D8×C443C22semidirect
38. C2×C8×C443C22semidirect
84. D443#135direct (N × H)
85. C443C2×#135semidirect
93. #135D443direct (N × H)
103. #41C2×D443semidirect
111. Q16C2×D443semidirect
115. SD16C2×D443semidirect
118. D8C2×D443semidirect
124. C2×C8C2×D443semidirect

Maximal subgroups

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

subgroupindex
#41×D4432
#283819092
#283819082
#283819072
#283819062
#283819052
Q16×D4432
SD16×D4432
D8×D4432
C2×C8×D4432
#135×C4432
C2×#135443