Finite Group Databasebeta

← #135×D107 #20293405

Subgroups — #135×D107 #20293405

Order 6848.

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×D107C212yesmaximal, complemented
2#16812132C211yesmaximal, characteristic, complemented
3#16812131C211yesmaximal, characteristic, complemented
4#16812130C212yesmaximal, complemented
5#16812129C212yesmaximal, complemented
6#16812128C211yesmaximal, characteristic, complemented
7Q16×D107C211yesmaximal, characteristic, complemented
8SD16×D107C212yesmaximal, complemented
9D8×D107C211yesmaximal, characteristic, complemented
10C2×C8×D107C211yesmaximal, characteristic, complemented
11#135×C107C211yesmaximal, characteristic, complemented
12#13133819C2212yescomplemented
13#13133818—22no—
14#13133818C2212yescomplemented
15#13133817—22no—
16#13133817C2212yescomplemented
17Q8×D107C2212yes—
18D4×D107—22no—
19D4×D107C2212yes—
20C2×C4×D107—22no—
21C2×C4×D107C2211yescharacteristic
22Dic428C2211yescharacteristic, complemented
23#13133808C2212yescomplemented
24#13133807C2212yescomplemented
25#13133806C2212yescomplemented
26#13133805C2212yescomplemented
27D856C2211yescharacteristic, complemented
28#13133803C2212yescomplemented
29C2×C107⋊C8C2211yescharacteristic, complemented
30C8×D107C2211yescharacteristic
31C8×D107C2211yescharacteristic
32C8×D107C2211yescharacteristic, complemented
33C8×D107C2211yescharacteristic, complemented
34#41×C107C2212yescomplemented
35Q16×C107C2211yescharacteristic, complemented
36SD16×C107C2212yescomplemented
37D8×C107C2211yescharacteristic, complemented
38C2×C8×C107C2211yescharacteristic, complemented
39C22×D107—22no—
40C22×D107D411yescharacteristic
41Q8×C107C2312yes—
42D4×C107—22no—
43D4×C107C2312yes—
44C2×C4×C107—22no—
45C2×C4×C107C2311yescharacteristic
46C22⋊D107—22no—
47C22⋊D107—22no—
48C22⋊D107—22no—
49C2×Dic107—22no—
50C2×Dic107D411yescharacteristic
51D428—22no—
52D428C2312yes—
53C4×D107—22no—
54C4×D107—22no—
55C4×D107—22no—
56C4×D107D411yescharacteristic
57C4×D107D411yescharacteristic
58C4×D107C2311yescharacteristic
59C4×D107C2311yescharacteristic
60Dic214—22no—
61Dic214C2312yes—
62C8×C107C2311yescharacteristic
63C8×C107C2311yescharacteristic
64C107⋊C8C2311yescharacteristic
65C107⋊C8C2311yescharacteristic
66C22×C107—22no—
67C22×C107C2×D411yescharacteristic
68C2×D107—22no—
69C2×D107—22no—
70C2×D107—44no—
71C2×D107C2×D411yescharacteristic
72C2×D107C2×D411yescharacteristic
73C4×C107—22no—
74C4×C107C2×D411yescharacteristic
75C4×C107C2411yescharacteristic
76Dic107—22no—
77Dic107C2×D411yescharacteristic
78Dic107C2×D411yescharacteristic
79C2×C107—21no—
80C2×C107—42no—
81C2×C107C22×D411yescharacteristic
82D107—21no—
83D107—42no—
84D107#13512yesdirect product factor
85C107C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—1071nomaximal, Sylow
87C2×#41—1072no—
88#135—1072no—
89#135—1071no—
90#135—1072no—
91#135—1071no—
92#135—1071no—
93#135D10711yescharacteristic, direct product factor
94C2×Q16—1071no—
95C2×SD16—1072no—
96C2×D8—1071no—
97C22×C8—1071no—
98#41—1072no—
99#41—1072no—
100#41—1072no—
101#41—2142no—
102#41—2142no—
103#41C2×D10712yescomplemented
104C2×Q8—1072no—
105C2×D4—1072no—
106C2×D4—2142no—
107C22×C4—1071no—
108C22×C4—2142no—
109Q16—1072no—
110Q16—1071no—
111Q16C2×D10711yescharacteristic, complemented
112SD16—1072no—
113SD16—1072no—
114SD16—1072no—
115SD16C2×D10712yescomplemented
116D8—1072no—
117D8—1071no—
118D8C2×D10711yescharacteristic, complemented
119C2×C8—1071no—
120C2×C8—1071no—
121C2×C8—1071no—
122C2×C8—1071no—
123C2×C8—1071no—
124C2×C8C2×D10711yescharacteristic, complemented
125C23—1071no—
126C23—2142no—
127Q8—1072no—
128Q8—2142no—
129Q8C22×D10712yes—
130D4—22no—
131D4—1072no—
132D4—2142no—
133D4—2142no—
134D4—2142no—
135D4—2142no—
136D4C22×D10712yes—
137C2×C4—22no—
138C2×C4—1071no—
139C2×C4—1071no—
140C2×C4—1071no—
141C2×C4—1071no—
142C2×C4—1071no—
143C2×C4—2142no—
144C2×C4—2142no—
145C2×C4—2142no—
146C2×C4—2142no—
147C2×C4C22×D10711yescharacteristic
148C8—1071no—
149C8—1071no—
150C8C22×D10711yescharacteristic
151C8C22×D10711yescharacteristic
152C22—22no—
153C22—1071no—
154C22—1071no—
155C22—4284no—
156C22—2142no—
157C22—2142no—
158C22D4×D10711yescharacteristic
159C4—22no—
160C4—1071no—
161C4—1071no—
162C4—2142no—
163C4D4×D10711yescharacteristic
164C4C23×D10711yescharacteristic
165C2—21no—
166C2—42no—
167C2—1072no—
168C2—4282no—
169C2—2141no—
170C2C2×D4×D10711yescharacteristic
subgroupG/H
centerC4D4×D107
commutatorC4×C107C24
FrattiniC4C23×D107
Fitting#135×C107C2
socleC2×C107C22×D4
hypercenter#135D107
hypocenterC107C2×#135
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D107C2semidirect
2. #16812132C2semidirect
3. #16812131C2semidirect
4. #16812130C2semidirect
5. #16812129C2semidirect
6. #16812128C2semidirect
7. Q16×D107C2semidirect
8. SD16×D107C2semidirect
9. D8×D107C2semidirect
10. C2×C8×D107C2semidirect
11. #135×C107C2semidirect
12. #13133819C22semidirect
14. #13133818C22semidirect
16. #13133817C22semidirect
22. Dic428C22semidirect
23. #13133808C22semidirect
24. #13133807C22semidirect
25. #13133806C22semidirect
26. #13133805C22semidirect
27. D856C22semidirect
28. #13133803C22semidirect
29. C2×C107⋊C8C22semidirect
32. C8×D107C22semidirect
33. C8×D107C22semidirect
34. #41×C107C22semidirect
35. Q16×C107C22semidirect
36. SD16×C107C22semidirect
37. D8×C107C22semidirect
38. C2×C8×C107C22semidirect
84. D107#135direct (N × H)
85. C107C2×#135semidirect
93. #135D107direct (N × H)
103. #41C2×D107semidirect
111. Q16C2×D107semidirect
115. SD16C2×D107semidirect
118. D8C2×D107semidirect
124. C2×C8C2×D107semidirect