Finite Group Databasebeta

← #135×D101 #20265955

Subgroups — #135×D101 #20265955

Order 6464.

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×D101C212yesmaximal, complemented
2#15692278C211yesmaximal, characteristic, complemented
3#15692277C211yesmaximal, characteristic, complemented
4#15692276C212yesmaximal, complemented
5#15692275C212yesmaximal, complemented
6#15692274C211yesmaximal, characteristic, complemented
7Q16×D101C211yesmaximal, characteristic, complemented
8SD16×D101C212yesmaximal, complemented
9D8×D101C211yesmaximal, characteristic, complemented
10C2×C8×D101C211yesmaximal, characteristic, complemented
11#135×C101C211yesmaximal, characteristic, complemented
12#13108075C2212yescomplemented
13#13108074—22no—
14#13108074C2212yescomplemented
15#13108073—22no—
16#13108073C2212yescomplemented
17Q8×D101C2212yes—
18D4×D101—22no—
19D4×D101C2212yes—
20C2×C4×D101—22no—
21C2×C4×D101C2211yescharacteristic
22Dic404C2211yescharacteristic, complemented
23#13108064C2212yescomplemented
24#13108063C2212yescomplemented
25#13108062C2212yescomplemented
26#13108061C2212yescomplemented
27D808C2211yescharacteristic, complemented
28#13108059C2212yescomplemented
29C2×#11717579C2211yescharacteristic, complemented
30C8×D101C2211yescharacteristic
31C8×D101C2211yescharacteristic
32C8×D101C2211yescharacteristic, complemented
33C8×D101C2211yescharacteristic, complemented
34#41×C101C2212yescomplemented
35Q16×C101C2211yescharacteristic, complemented
36SD16×C101C2212yescomplemented
37D8×C101C2211yescharacteristic, complemented
38C2×C8×C101C2211yescharacteristic, complemented
39C22×D101—22no—
40C22×D101D411yescharacteristic
41Q8×C101C2312yes—
42D4×C101—22no—
43D4×C101C2312yes—
44C2×C4×C101—22no—
45C2×C4×C101C2311yescharacteristic
46C22⋊D101—22no—
47C22⋊D101—22no—
48C22⋊D101—22no—
49C2×Dic101—22no—
50C2×Dic101D411yescharacteristic
51D404—22no—
52D404C2312yes—
53C4×D101—22no—
54C4×D101—22no—
55C4×D101—22no—
56C4×D101D411yescharacteristic
57C4×D101D411yescharacteristic
58C4×D101C2311yescharacteristic
59C4×D101C2311yescharacteristic
60Dic202—22no—
61Dic202C2312yes—
62C8×C101C2311yescharacteristic
63C8×C101C2311yescharacteristic
64#11717579C2311yescharacteristic
65#11717579C2311yescharacteristic
66C22×C101—22no—
67C22×C101C2×D411yescharacteristic
68C2×D101—22no—
69C2×D101—22no—
70C2×D101—44no—
71C2×D101C2×D411yescharacteristic
72C2×D101C2×D411yescharacteristic
73C4×C101—22no—
74C4×C101C2×D411yescharacteristic
75C4×C101C2411yescharacteristic
76Dic101—22no—
77Dic101C2×D411yescharacteristic
78Dic101C2×D411yescharacteristic
79C2×C101—21no—
80C2×C101—42no—
81C2×C101C22×D411yescharacteristic
82D101—21no—
83D101—42no—
84D101#13512yesdirect product factor
85C101C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—1011nomaximal, Sylow
87C2×#41—1012no—
88#135—1012no—
89#135—1011no—
90#135—1012no—
91#135—1011no—
92#135—1011no—
93#135D10111yescharacteristic, direct product factor
94C2×Q16—1011no—
95C2×SD16—1012no—
96C2×D8—1011no—
97C22×C8—1011no—
98#41—1012no—
99#41—1012no—
100#41—1012no—
101#41—2022no—
102#41—2022no—
103#41C2×D10112yescomplemented
104C2×Q8—1012no—
105C2×D4—1012no—
106C2×D4—2022no—
107C22×C4—1011no—
108C22×C4—2022no—
109Q16—1012no—
110Q16—1011no—
111Q16C2×D10111yescharacteristic, complemented
112SD16—1012no—
113SD16—1012no—
114SD16—1012no—
115SD16C2×D10112yescomplemented
116D8—1012no—
117D8—1011no—
118D8C2×D10111yescharacteristic, complemented
119C2×C8—1011no—
120C2×C8—1011no—
121C2×C8—1011no—
122C2×C8—1011no—
123C2×C8—1011no—
124C2×C8C2×D10111yescharacteristic, complemented
125C23—1011no—
126C23—2022no—
127Q8—1012no—
128Q8—2022no—
129Q8C22×D10112yes—
130D4—22no—
131D4—1012no—
132D4—2022no—
133D4—2022no—
134D4—2022no—
135D4—2022no—
136D4C22×D10112yes—
137C2×C4—22no—
138C2×C4—1011no—
139C2×C4—1011no—
140C2×C4—1011no—
141C2×C4—1011no—
142C2×C4—1011no—
143C2×C4—2022no—
144C2×C4—2022no—
145C2×C4—2022no—
146C2×C4—2022no—
147C2×C4C22×D10111yescharacteristic
148C8—1011no—
149C8—1011no—
150C8C22×D10111yescharacteristic
151C8C22×D10111yescharacteristic
152C22—22no—
153C22—1011no—
154C22—1011no—
155C22—4044no—
156C22—2022no—
157C22—2022no—
158C22D4×D10111yescharacteristic
159C4—22no—
160C4—1011no—
161C4—1011no—
162C4—2022no—
163C4D4×D10111yescharacteristic
164C4C23×D10111yescharacteristic
165C2—21no—
166C2—42no—
167C2—1012no—
168C2—4042no—
169C2—2021no—
170C2C2×D4×D10111yescharacteristic
subgroupG/H
centerC4D4×D101
commutatorC4×C101C24
FrattiniC4C23×D101
Fitting#135×C101C2
socleC2×C101C22×D4
hypercenter#135D101
hypocenterC101C2×#135
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D101C2semidirect
2. #15692278C2semidirect
3. #15692277C2semidirect
4. #15692276C2semidirect
5. #15692275C2semidirect
6. #15692274C2semidirect
7. Q16×D101C2semidirect
8. SD16×D101C2semidirect
9. D8×D101C2semidirect
10. C2×C8×D101C2semidirect
11. #135×C101C2semidirect
12. #13108075C22semidirect
14. #13108074C22semidirect
16. #13108073C22semidirect
22. Dic404C22semidirect
23. #13108064C22semidirect
24. #13108063C22semidirect
25. #13108062C22semidirect
26. #13108061C22semidirect
27. D808C22semidirect
28. #13108059C22semidirect
29. C2×#11717579C22semidirect
32. C8×D101C22semidirect
33. C8×D101C22semidirect
34. #41×C101C22semidirect
35. Q16×C101C22semidirect
36. SD16×C101C22semidirect
37. D8×C101C22semidirect
38. C2×C8×C101C22semidirect
84. D101#135direct (N × H)
85. C101C2×#135semidirect
93. #135D101direct (N × H)
103. #41C2×D101semidirect
111. Q16C2×D101semidirect
115. SD16C2×D101semidirect
118. D8C2×D101semidirect
124. C2×C8C2×D101semidirect