Finite Group Databasebeta

← #135×D97 #20261513

Subgroups — #135×D97 #20261513

Order 6208.

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×D97C212yesmaximal, complemented
2#15690833C211yesmaximal, characteristic, complemented
3#15690832C211yesmaximal, characteristic, complemented
4#15690831C212yesmaximal, complemented
5#15690830C212yesmaximal, complemented
6#15690829C211yesmaximal, characteristic, complemented
7Q16×D97C211yesmaximal, characteristic, complemented
8SD16×D97C212yesmaximal, complemented
9D8×D97C211yesmaximal, characteristic, complemented
10C2×C8×D97C211yesmaximal, characteristic, complemented
11#135×C97C211yesmaximal, characteristic, complemented
12#13095512C2212yescomplemented
13#13095511—22no—
14#13095511C2212yescomplemented
15#13095510—22no—
16#13095510C2212yescomplemented
17Q8×D97C2212yes—
18D4×D97—22no—
19D4×D97C2212yes—
20C2×C4×D97—22no—
21C2×C4×D97C2211yescharacteristic
22Dic388C2211yescharacteristic, complemented
23#13095501C2212yescomplemented
24#13095500C2212yescomplemented
25#13095499C2212yescomplemented
26#13095498C2212yescomplemented
27D776C2211yescharacteristic, complemented
28#13095496C2212yescomplemented
29C2×#11715895C2211yescharacteristic, complemented
30C8×D97C2211yescharacteristic
31C8×D97C2211yescharacteristic
32C8×D97C2211yescharacteristic, complemented
33C8×D97C2211yescharacteristic, complemented
34#41×C97C2212yescomplemented
35Q16×C97C2211yescharacteristic, complemented
36SD16×C97C2212yescomplemented
37D8×C97C2211yescharacteristic, complemented
38C2×C8×C97C2211yescharacteristic, complemented
39C22×D97—22no—
40C22×D97D411yescharacteristic
41Q8×C97C2312yes—
42D4×C97—22no—
43D4×C97C2312yes—
44C2×C4×C97—22no—
45C2×C4×C97C2311yescharacteristic
46C22⋊D97—22no—
47C22⋊D97—22no—
48C22⋊D97—22no—
49C2×Dic97—22no—
50C2×Dic97D411yescharacteristic
51D388—22no—
52D388C2312yes—
53C4×D97—22no—
54C4×D97—22no—
55C4×D97—22no—
56C4×D97D411yescharacteristic
57C4×D97D411yescharacteristic
58C4×D97C2311yescharacteristic
59C4×D97C2311yescharacteristic
60Dic194—22no—
61Dic194C2312yes—
62C8×C97C2311yescharacteristic
63C8×C97C2311yescharacteristic
64#11715895C2311yescharacteristic
65#11715895C2311yescharacteristic
66C22×C97—22no—
67C22×C97C2×D411yescharacteristic
68C2×D97—22no—
69C2×D97—22no—
70C2×D97—44no—
71C2×D97C2×D411yescharacteristic
72C2×D97C2×D411yescharacteristic
73C4×C97—22no—
74C4×C97C2×D411yescharacteristic
75C4×C97C2411yescharacteristic
76Dic97—22no—
77Dic97C2×D411yescharacteristic
78Dic97C2×D411yescharacteristic
79C2×C97—21no—
80C2×C97—42no—
81C2×C97C22×D411yescharacteristic
82D97—21no—
83D97—42no—
84D97#13512yesdirect product factor
85C97C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—971nomaximal, Sylow
87C2×#41—972no—
88#135—972no—
89#135—971no—
90#135—972no—
91#135—971no—
92#135—971no—
93#135D9711yescharacteristic, direct product factor
94C2×Q16—971no—
95C2×SD16—972no—
96C2×D8—971no—
97C22×C8—971no—
98#41—972no—
99#41—972no—
100#41—972no—
101#41—1942no—
102#41—1942no—
103#41C2×D9712yescomplemented
104C2×Q8—972no—
105C2×D4—972no—
106C2×D4—1942no—
107C22×C4—971no—
108C22×C4—1942no—
109Q16—972no—
110Q16—971no—
111Q16C2×D9711yescharacteristic, complemented
112SD16—972no—
113SD16—972no—
114SD16—972no—
115SD16C2×D9712yescomplemented
116D8—972no—
117D8—971no—
118D8C2×D9711yescharacteristic, complemented
119C2×C8—971no—
120C2×C8—971no—
121C2×C8—971no—
122C2×C8—971no—
123C2×C8—971no—
124C2×C8C2×D9711yescharacteristic, complemented
125C23—971no—
126C23—1942no—
127Q8—972no—
128Q8—1942no—
129Q8C22×D9712yes—
130D4—22no—
131D4—972no—
132D4—1942no—
133D4—1942no—
134D4—1942no—
135D4—1942no—
136D4C22×D9712yes—
137C2×C4—22no—
138C2×C4—971no—
139C2×C4—971no—
140C2×C4—971no—
141C2×C4—971no—
142C2×C4—971no—
143C2×C4—1942no—
144C2×C4—1942no—
145C2×C4—1942no—
146C2×C4—1942no—
147C2×C4C22×D9711yescharacteristic
148C8—971no—
149C8—971no—
150C8C22×D9711yescharacteristic
151C8C22×D9711yescharacteristic
152C22—22no—
153C22—971no—
154C22—971no—
155C22—3884no—
156C22—1942no—
157C22—1942no—
158C22D4×D9711yescharacteristic
159C4—22no—
160C4—971no—
161C4—971no—
162C4—1942no—
163C4D4×D9711yescharacteristic
164C4C23×D9711yescharacteristic
165C2—21no—
166C2—42no—
167C2—972no—
168C2—3882no—
169C2—1941no—
170C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC4D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
Fitting#135×C97C2
socleC2×C97C22×D4
hypercenter#135D97
hypocenterC97C2×#135
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D97C2semidirect
2. #15690833C2semidirect
3. #15690832C2semidirect
4. #15690831C2semidirect
5. #15690830C2semidirect
6. #15690829C2semidirect
7. Q16×D97C2semidirect
8. SD16×D97C2semidirect
9. D8×D97C2semidirect
10. C2×C8×D97C2semidirect
11. #135×C97C2semidirect
12. #13095512C22semidirect
14. #13095511C22semidirect
16. #13095510C22semidirect
22. Dic388C22semidirect
23. #13095501C22semidirect
24. #13095500C22semidirect
25. #13095499C22semidirect
26. #13095498C22semidirect
27. D776C22semidirect
28. #13095496C22semidirect
29. C2×#11715895C22semidirect
32. C8×D97C22semidirect
33. C8×D97C22semidirect
34. #41×C97C22semidirect
35. Q16×C97C22semidirect
36. SD16×C97C22semidirect
37. D8×C97C22semidirect
38. C2×C8×C97C22semidirect
84. D97#135direct (N × H)
85. C97C2×#135semidirect
93. #135D97direct (N × H)
103. #41C2×D97semidirect
111. Q16C2×D97semidirect
115. SD16C2×D97semidirect
118. D8C2×D97semidirect
124. C2×C8C2×D97semidirect