Finite Group Databasebeta

← #135×D113 #20299376

Subgroups — #135×D113 #20299376

Order 7232.

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×D113C212yesmaximal, complemented
2#16813645C211yesmaximal, characteristic, complemented
3#16813644C211yesmaximal, characteristic, complemented
4#16813643C212yesmaximal, complemented
5#16813642C212yesmaximal, complemented
6#16813641C211yesmaximal, characteristic, complemented
7Q16×D113C211yesmaximal, characteristic, complemented
8SD16×D113C212yesmaximal, complemented
9D8×D113C211yesmaximal, characteristic, complemented
10C2×C8×D113C211yesmaximal, characteristic, complemented
11#135×C113C211yesmaximal, characteristic, complemented
12#14268648C2212yescomplemented
13#14268647—22no—
14#14268647C2212yescomplemented
15#14268646—22no—
16#14268646C2212yescomplemented
17Q8×D113C2212yes—
18D4×D113—22no—
19D4×D113C2212yes—
20C2×C4×D113—22no—
21C2×C4×D113C2211yescharacteristic
22Dic452C2211yescharacteristic, complemented
23#14268637C2212yescomplemented
24#14268636C2212yescomplemented
25#14268635C2212yescomplemented
26#14268634C2212yescomplemented
27D904C2211yescharacteristic, complemented
28#14268632C2212yescomplemented
29C2×#11744751C2211yescharacteristic, complemented
30C8×D113C2211yescharacteristic
31C8×D113C2211yescharacteristic
32C8×D113C2211yescharacteristic, complemented
33C8×D113C2211yescharacteristic, complemented
34#41×C113C2212yescomplemented
35Q16×C113C2211yescharacteristic, complemented
36SD16×C113C2212yescomplemented
37D8×C113C2211yescharacteristic, complemented
38C2×C8×C113C2211yescharacteristic, complemented
39C22×D113—22no—
40C22×D113D411yescharacteristic
41Q8×C113C2312yes—
42D4×C113—22no—
43D4×C113C2312yes—
44C2×C4×C113—22no—
45C2×C4×C113C2311yescharacteristic
46C22⋊D113—22no—
47C22⋊D113—22no—
48C22⋊D113—22no—
49C2×Dic113—22no—
50C2×Dic113D411yescharacteristic
51D452—22no—
52D452C2312yes—
53C4×D113—22no—
54C4×D113—22no—
55C4×D113—22no—
56C4×D113D411yescharacteristic
57C4×D113D411yescharacteristic
58C4×D113C2311yescharacteristic
59C4×D113C2311yescharacteristic
60Dic226—22no—
61Dic226C2312yes—
62C8×C113C2311yescharacteristic
63C8×C113C2311yescharacteristic
64#11744751C2311yescharacteristic
65#11744751C2311yescharacteristic
66C22×C113—22no—
67C22×C113C2×D411yescharacteristic
68C2×D113—22no—
69C2×D113—22no—
70C2×D113—44no—
71C2×D113C2×D411yescharacteristic
72C2×D113C2×D411yescharacteristic
73C4×C113—22no—
74C4×C113C2×D411yescharacteristic
75C4×C113C2411yescharacteristic
76Dic113—22no—
77Dic113C2×D411yescharacteristic
78Dic113C2×D411yescharacteristic
79C2×C113—21no—
80C2×C113—42no—
81C2×C113C22×D411yescharacteristic
82D113—21no—
83D113—42no—
84D113#13512yesdirect product factor
85C113C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—1131nomaximal, Sylow
87C2×#41—1132no—
88#135—1132no—
89#135—1131no—
90#135—1132no—
91#135—1131no—
92#135—1131no—
93#135D11311yescharacteristic, direct product factor
94C2×Q16—1131no—
95C2×SD16—1132no—
96C2×D8—1131no—
97C22×C8—1131no—
98#41—1132no—
99#41—1132no—
100#41—1132no—
101#41—2262no—
102#41—2262no—
103#41C2×D11312yescomplemented
104C2×Q8—1132no—
105C2×D4—1132no—
106C2×D4—2262no—
107C22×C4—1131no—
108C22×C4—2262no—
109Q16—1132no—
110Q16—1131no—
111Q16C2×D11311yescharacteristic, complemented
112SD16—1132no—
113SD16—1132no—
114SD16—1132no—
115SD16C2×D11312yescomplemented
116D8—1132no—
117D8—1131no—
118D8C2×D11311yescharacteristic, complemented
119C2×C8—1131no—
120C2×C8—1131no—
121C2×C8—1131no—
122C2×C8—1131no—
123C2×C8—1131no—
124C2×C8C2×D11311yescharacteristic, complemented
125C23—1131no—
126C23—2262no—
127Q8—1132no—
128Q8—2262no—
129Q8C22×D11312yes—
130D4—22no—
131D4—1132no—
132D4—2262no—
133D4—2262no—
134D4—2262no—
135D4—2262no—
136D4C22×D11312yes—
137C2×C4—22no—
138C2×C4—1131no—
139C2×C4—1131no—
140C2×C4—1131no—
141C2×C4—1131no—
142C2×C4—1131no—
143C2×C4—2262no—
144C2×C4—2262no—
145C2×C4—2262no—
146C2×C4—2262no—
147C2×C4C22×D11311yescharacteristic
148C8—1131no—
149C8—1131no—
150C8C22×D11311yescharacteristic
151C8C22×D11311yescharacteristic
152C22—22no—
153C22—1131no—
154C22—1131no—
155C22—4524no—
156C22—2262no—
157C22—2262no—
158C22D4×D11311yescharacteristic
159C4—22no—
160C4—1131no—
161C4—1131no—
162C4—2262no—
163C4D4×D11311yescharacteristic
164C4C23×D11311yescharacteristic
165C2—21no—
166C2—42no—
167C2—1132no—
168C2—4522no—
169C2—2261no—
170C2C2×D4×D11311yescharacteristic
subgroupG/H
centerC4D4×D113
commutatorC4×C113C24
FrattiniC4C23×D113
Fitting#135×C113C2
socleC2×C113C22×D4
hypercenter#135D113
hypocenterC113C2×#135
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D113C2semidirect
2. #16813645C2semidirect
3. #16813644C2semidirect
4. #16813643C2semidirect
5. #16813642C2semidirect
6. #16813641C2semidirect
7. Q16×D113C2semidirect
8. SD16×D113C2semidirect
9. D8×D113C2semidirect
10. C2×C8×D113C2semidirect
11. #135×C113C2semidirect
12. #14268648C22semidirect
14. #14268647C22semidirect
16. #14268646C22semidirect
22. Dic452C22semidirect
23. #14268637C22semidirect
24. #14268636C22semidirect
25. #14268635C22semidirect
26. #14268634C22semidirect
27. D904C22semidirect
28. #14268632C22semidirect
29. C2×#11744751C22semidirect
32. C8×D113C22semidirect
33. C8×D113C22semidirect
34. #41×C113C22semidirect
35. Q16×C113C22semidirect
36. SD16×C113C22semidirect
37. D8×C113C22semidirect
38. C2×C8×C113C22semidirect
84. D113#135direct (N × H)
85. C113C2×#135semidirect
93. #135D113direct (N × H)
103. #41C2×D113semidirect
111. Q16C2×D113semidirect
115. SD16C2×D113semidirect
118. D8C2×D113semidirect
124. C2×C8C2×D113semidirect