Finite Group Databasebeta

← #135×D283 #31827243

Subgroups — #135×D283 #31827243

Order 18112.

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×D283C212yesmaximal, complemented
2#22583633C211yesmaximal, characteristic, complemented
3#22583632C211yesmaximal, characteristic, complemented
4#22583631C212yesmaximal, complemented
5#22583630C212yesmaximal, complemented
6#22583629C211yesmaximal, characteristic, complemented
7Q16×D283C211yesmaximal, characteristic, complemented
8SD16×D283C212yesmaximal, complemented
9D8×D283C211yesmaximal, characteristic, complemented
10C2×C8×D283C211yesmaximal, characteristic, complemented
11#135×C283C211yesmaximal, characteristic, complemented
12#17985393C2212yescomplemented
13#17985392—22no—
14#17985392C2212yescomplemented
15#17985391—22no—
16#17985391C2212yescomplemented
17Q8×D283C2212yes—
18D4×D283—22no—
19D4×D283C2212yes—
20C2×C4×D283—22no—
21C2×C4×D283C2211yescharacteristic
22Dic1132C2211yescharacteristic, complemented
23#17985382C2212yescomplemented
24#17985381C2212yescomplemented
25#17985380C2212yescomplemented
26#17985379C2212yescomplemented
27D2264C2211yescharacteristic, complemented
28#17985377C2212yescomplemented
29C2×C283⋊C8C2211yescharacteristic, complemented
30C8×D283C2211yescharacteristic
31C8×D283C2211yescharacteristic
32C8×D283C2211yescharacteristic, complemented
33C8×D283C2211yescharacteristic, complemented
34#41×C283C2212yescomplemented
35Q16×C283C2211yescharacteristic, complemented
36SD16×C283C2212yescomplemented
37D8×C283C2211yescharacteristic, complemented
38C2×C8×C283C2211yescharacteristic, complemented
39C22×D283—22no—
40C22×D283D411yescharacteristic
41Dic566—22no—
42Dic566C2312yes—
43D1132—22no—
44D1132C2312yes—
45C22⋊D283—22no—
46C22⋊D283—22no—
47C22⋊D283—22no—
48C2×Dic283—22no—
49C2×Dic283D411yescharacteristic
50C4×D283—22no—
51C4×D283—22no—
52C4×D283—22no—
53C4×D283D411yescharacteristic
54C4×D283D411yescharacteristic
55C4×D283C2311yescharacteristic
56C4×D283C2311yescharacteristic
57C283⋊C8C2311yescharacteristic
58C283⋊C8C2311yescharacteristic
59Q8×C283C2312yes—
60D4×C283—22no—
61D4×C283C2312yes—
62C2×C4×C283—22no—
63C2×C4×C283C2311yescharacteristic
64C8×C283C2311yescharacteristic
65C8×C283C2311yescharacteristic
66C22×C283—22no—
67C22×C283C2×D411yescharacteristic
68C2×D283—22no—
69C2×D283—22no—
70C2×D283—44no—
71C2×D283C2×D411yescharacteristic
72C2×D283C2×D411yescharacteristic
73C4×C283—22no—
74C4×C283C2×D411yescharacteristic
75C4×C283C2411yescharacteristic
76Dic283—22no—
77Dic283C2×D411yescharacteristic
78Dic283C2×D411yescharacteristic
79C2×C283—21no—
80C2×C283—42no—
81C2×C283C22×D411yescharacteristic
82D283—21no—
83D283—42no—
84D283#13512yesdirect product factor
85C283C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—2831nomaximal, Sylow
87C2×#41—2832no—
88#135—2832no—
89#135—2831no—
90#135—2832no—
91#135—2831no—
92#135—2831no—
93#135D28311yescharacteristic, direct product factor
94C2×Q16—2831no—
95C2×SD16—2832no—
96C2×D8—2831no—
97C22×C8—2831no—
98#41—2832no—
99#41—2832no—
100#41—2832no—
101#41—5662no—
102#41—5662no—
103#41C2×D28312yescomplemented
104C2×Q8—2832no—
105C2×D4—2832no—
106C2×D4—5662no—
107C22×C4—2831no—
108C22×C4—5662no—
109Q16—2832no—
110Q16—2831no—
111Q16C2×D28311yescharacteristic, complemented
112SD16—2832no—
113SD16—2832no—
114SD16—2832no—
115SD16C2×D28312yescomplemented
116D8—2832no—
117D8—2831no—
118D8C2×D28311yescharacteristic, complemented
119C2×C8—2831no—
120C2×C8—2831no—
121C2×C8—2831no—
122C2×C8—2831no—
123C2×C8—2831no—
124C2×C8C2×D28311yescharacteristic, complemented
125C23—2831no—
126C23—5662no—
127Q8—2832no—
128Q8—5662no—
129Q8C22×D28312yes—
130D4—22no—
131D4—2832no—
132D4—5662no—
133D4—5662no—
134D4—5662no—
135D4—5662no—
136D4C22×D28312yes—
137C2×C4—22no—
138C2×C4—2831no—
139C2×C4—2831no—
140C2×C4—2831no—
141C2×C4—2831no—
142C2×C4—2831no—
143C2×C4—5662no—
144C2×C4—5662no—
145C2×C4—5662no—
146C2×C4—5662no—
147C2×C4C22×D28311yescharacteristic
148C8—2831no—
149C8—2831no—
150C8C22×D28311yescharacteristic
151C8C22×D28311yescharacteristic
152C22—22no—
153C22—2831no—
154C22—2831no—
155C22—5662no—
156C22—5662no—
157C22—11324no—
158C22D4×D28311yescharacteristic
159C4—22no—
160C4—2831no—
161C4—2831no—
162C4—5662no—
163C4D4×D28311yescharacteristic
164C4C23×D28311yescharacteristic
165C2—21no—
166C2—42no—
167C2—2832no—
168C2—5661no—
169C2—11322no—
170C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC4D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
Fitting#135×C283C2
socleC2×C283C22×D4
hypercenter#135D283
hypocenterC283C2×#135
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D283C2semidirect
2. #22583633C2semidirect
3. #22583632C2semidirect
4. #22583631C2semidirect
5. #22583630C2semidirect
6. #22583629C2semidirect
7. Q16×D283C2semidirect
8. SD16×D283C2semidirect
9. D8×D283C2semidirect
10. C2×C8×D283C2semidirect
11. #135×C283C2semidirect
12. #17985393C22semidirect
14. #17985392C22semidirect
16. #17985391C22semidirect
22. Dic1132C22semidirect
23. #17985382C22semidirect
24. #17985381C22semidirect
25. #17985380C22semidirect
26. #17985379C22semidirect
27. D2264C22semidirect
28. #17985377C22semidirect
29. C2×C283⋊C8C22semidirect
32. C8×D283C22semidirect
33. C8×D283C22semidirect
34. #41×C283C22semidirect
35. Q16×C283C22semidirect
36. SD16×C283C22semidirect
37. D8×C283C22semidirect
38. C2×C8×C283C22semidirect
84. D283#135direct (N × H)
85. C283C2×#135semidirect
93. #135D283direct (N × H)
103. #41C2×D283semidirect
111. Q16C2×D283semidirect
115. SD16C2×D283semidirect
118. D8C2×D283semidirect
124. C2×C8C2×D283semidirect

Maximal subgroups

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

subgroupindex
#41×D2832
#225836332
#225836322
#225836312
#225836302
#225836292
Q16×D2832
SD16×D2832
D8×D2832
C2×C8×D2832
#135×C2832
C2×#135283