Finite Group Databasebeta

← #135×D103 #20268569

Subgroups — #135×D103 #20268569

Order 6592.

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×D103C212yesmaximal, complemented
2#15693044C211yesmaximal, characteristic, complemented
3#15693043C211yesmaximal, characteristic, complemented
4#15693042C212yesmaximal, complemented
5#15693041C212yesmaximal, complemented
6#15693040C211yesmaximal, characteristic, complemented
7Q16×D103C211yesmaximal, characteristic, complemented
8SD16×D103C212yesmaximal, complemented
9D8×D103C211yesmaximal, characteristic, complemented
10C2×C8×D103C211yesmaximal, characteristic, complemented
11#135×C103C211yesmaximal, characteristic, complemented
12#13110106C2212yescomplemented
13#13110105—22no—
14#13110105C2212yescomplemented
15#13110104—22no—
16#13110104C2212yescomplemented
17Q8×D103C2212yes—
18D4×D103—22no—
19D4×D103C2212yes—
20C2×C4×D103—22no—
21C2×C4×D103C2211yescharacteristic
22Dic412C2211yescharacteristic, complemented
23#13110095C2212yescomplemented
24#13110094C2212yescomplemented
25#13110093C2212yescomplemented
26#13110092C2212yescomplemented
27D824C2211yescharacteristic, complemented
28#13110090C2212yescomplemented
29C2×C103⋊C8C2211yescharacteristic, complemented
30C8×D103C2211yescharacteristic
31C8×D103C2211yescharacteristic
32C8×D103C2211yescharacteristic, complemented
33C8×D103C2211yescharacteristic, complemented
34#41×C103C2212yescomplemented
35Q16×C103C2211yescharacteristic, complemented
36SD16×C103C2212yescomplemented
37D8×C103C2211yescharacteristic, complemented
38C2×C8×C103C2211yescharacteristic, complemented
39C22×D103—22no—
40C22×D103D411yescharacteristic
41Q8×C103C2312yes—
42D4×C103—22no—
43D4×C103C2312yes—
44C2×C4×C103—22no—
45C2×C4×C103C2311yescharacteristic
46C22⋊D103—22no—
47C22⋊D103—22no—
48C22⋊D103—22no—
49C2×Dic103—22no—
50C2×Dic103D411yescharacteristic
51D412—22no—
52D412C2312yes—
53C4×D103—22no—
54C4×D103—22no—
55C4×D103—22no—
56C4×D103D411yescharacteristic
57C4×D103D411yescharacteristic
58C4×D103C2311yescharacteristic
59C4×D103C2311yescharacteristic
60Dic206—22no—
61Dic206C2312yes—
62C8×C103C2311yescharacteristic
63C8×C103C2311yescharacteristic
64C103⋊C8C2311yescharacteristic
65C103⋊C8C2311yescharacteristic
66C22×C103—22no—
67C22×C103C2×D411yescharacteristic
68C2×D103—22no—
69C2×D103—22no—
70C2×D103—44no—
71C2×D103C2×D411yescharacteristic
72C2×D103C2×D411yescharacteristic
73C4×C103—22no—
74C4×C103C2×D411yescharacteristic
75C4×C103C2411yescharacteristic
76Dic103—22no—
77Dic103C2×D411yescharacteristic
78Dic103C2×D411yescharacteristic
79C2×C103—21no—
80C2×C103—42no—
81C2×C103C22×D411yescharacteristic
82D103—21no—
83D103—42no—
84D103#13512yesdirect product factor
85C103C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—1031nomaximal, Sylow
87C2×#41—1032no—
88#135—1032no—
89#135—1031no—
90#135—1032no—
91#135—1031no—
92#135—1031no—
93#135D10311yescharacteristic, direct product factor
94C2×Q16—1031no—
95C2×SD16—1032no—
96C2×D8—1031no—
97C22×C8—1031no—
98#41—1032no—
99#41—1032no—
100#41—1032no—
101#41—2062no—
102#41—2062no—
103#41C2×D10312yescomplemented
104C2×Q8—1032no—
105C2×D4—1032no—
106C2×D4—2062no—
107C22×C4—1031no—
108C22×C4—2062no—
109Q16—1032no—
110Q16—1031no—
111Q16C2×D10311yescharacteristic, complemented
112SD16—1032no—
113SD16—1032no—
114SD16—1032no—
115SD16C2×D10312yescomplemented
116D8—1032no—
117D8—1031no—
118D8C2×D10311yescharacteristic, complemented
119C2×C8—1031no—
120C2×C8—1031no—
121C2×C8—1031no—
122C2×C8—1031no—
123C2×C8—1031no—
124C2×C8C2×D10311yescharacteristic, complemented
125C23—1031no—
126C23—2062no—
127Q8—1032no—
128Q8—2062no—
129Q8C22×D10312yes—
130D4—22no—
131D4—1032no—
132D4—2062no—
133D4—2062no—
134D4—2062no—
135D4—2062no—
136D4C22×D10312yes—
137C2×C4—22no—
138C2×C4—1031no—
139C2×C4—1031no—
140C2×C4—1031no—
141C2×C4—1031no—
142C2×C4—1031no—
143C2×C4—2062no—
144C2×C4—2062no—
145C2×C4—2062no—
146C2×C4—2062no—
147C2×C4C22×D10311yescharacteristic
148C8—1031no—
149C8—1031no—
150C8C22×D10311yescharacteristic
151C8C22×D10311yescharacteristic
152C22—22no—
153C22—1031no—
154C22—1031no—
155C22—4124no—
156C22—2062no—
157C22—2062no—
158C22D4×D10311yescharacteristic
159C4—22no—
160C4—1031no—
161C4—1031no—
162C4—2062no—
163C4D4×D10311yescharacteristic
164C4C23×D10311yescharacteristic
165C2—21no—
166C2—42no—
167C2—1032no—
168C2—4122no—
169C2—2061no—
170C2C2×D4×D10311yescharacteristic
subgroupG/H
centerC4D4×D103
commutatorC4×C103C24
FrattiniC4C23×D103
Fitting#135×C103C2
socleC2×C103C22×D4
hypercenter#135D103
hypocenterC103C2×#135
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D103C2semidirect
2. #15693044C2semidirect
3. #15693043C2semidirect
4. #15693042C2semidirect
5. #15693041C2semidirect
6. #15693040C2semidirect
7. Q16×D103C2semidirect
8. SD16×D103C2semidirect
9. D8×D103C2semidirect
10. C2×C8×D103C2semidirect
11. #135×C103C2semidirect
12. #13110106C22semidirect
14. #13110105C22semidirect
16. #13110104C22semidirect
22. Dic412C22semidirect
23. #13110095C22semidirect
24. #13110094C22semidirect
25. #13110093C22semidirect
26. #13110092C22semidirect
27. D824C22semidirect
28. #13110090C22semidirect
29. C2×C103⋊C8C22semidirect
32. C8×D103C22semidirect
33. C8×D103C22semidirect
34. #41×C103C22semidirect
35. Q16×C103C22semidirect
36. SD16×C103C22semidirect
37. D8×C103C22semidirect
38. C2×C8×C103C22semidirect
84. D103#135direct (N × H)
85. C103C2×#135semidirect
93. #135D103direct (N × H)
103. #41C2×D103semidirect
111. Q16C2×D103semidirect
115. SD16C2×D103semidirect
118. D8C2×D103semidirect
124. C2×C8C2×D103semidirect