Finite Group Databasebeta

← #135×D571 #49143044

Subgroups — #135×D571 #49143044

Order 36544.

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×D571C212yesmaximal, complemented
2#32912717C211yesmaximal, characteristic, complemented
3#32912716C211yesmaximal, characteristic, complemented
4#32912715C212yesmaximal, complemented
5#32912714C212yesmaximal, complemented
6#32912713C211yesmaximal, characteristic, complemented
7Q16×D571C211yesmaximal, characteristic, complemented
8SD16×D571C212yesmaximal, complemented
9D8×D571C211yesmaximal, characteristic, complemented
10C2×C8×D571C211yesmaximal, characteristic, complemented
11#135×C571C211yesmaximal, characteristic, complemented
12#22603734C2212yescomplemented
13#22603733—22no—
14#22603733C2212yescomplemented
15#22603732—22no—
16#22603732C2212yescomplemented
17Q8×D571C2212yes—
18D4×D571—22no—
19D4×D571C2212yes—
20C2×C4×D571—22no—
21C2×C4×D571C2211yescharacteristic
22Dic2284C2211yescharacteristic, complemented
23#22603723C2212yescomplemented
24#22603722C2212yescomplemented
25#22603721C2212yescomplemented
26#22603720C2212yescomplemented
27D4568C2211yescharacteristic, complemented
28#22603718C2212yescomplemented
29C2×C571⋊C8C2211yescharacteristic, complemented
30C8×D571C2211yescharacteristic
31C8×D571C2211yescharacteristic
32C8×D571C2211yescharacteristic, complemented
33C8×D571C2211yescharacteristic, complemented
34#41×C571C2212yescomplemented
35Q16×C571C2211yescharacteristic, complemented
36SD16×C571C2212yescomplemented
37D8×C571C2211yescharacteristic, complemented
38C2×C8×C571C2211yescharacteristic, complemented
39C22×D571—22no—
40C22×D571D411yescharacteristic
41Dic1142—22no—
42Dic1142C2312yes—
43D2284—22no—
44D2284C2312yes—
45C22⋊D571—22no—
46C22⋊D571—22no—
47C22⋊D571—22no—
48C2×Dic571—22no—
49C2×Dic571D411yescharacteristic
50C4×D571—22no—
51C4×D571—22no—
52C4×D571—22no—
53C4×D571D411yescharacteristic
54C4×D571D411yescharacteristic
55C4×D571C2311yescharacteristic
56C4×D571C2311yescharacteristic
57C571⋊C8C2311yescharacteristic
58C571⋊C8C2311yescharacteristic
59Q8×C571C2312yes—
60D4×C571—22no—
61D4×C571C2312yes—
62C2×C4×C571—22no—
63C2×C4×C571C2311yescharacteristic
64C8×C571C2311yescharacteristic
65C8×C571C2311yescharacteristic
66C22×C571—22no—
67C22×C571C2×D411yescharacteristic
68C2×D571—22no—
69C2×D571—22no—
70C2×D571—44no—
71C2×D571C2×D411yescharacteristic
72C2×D571C2×D411yescharacteristic
73C4×C571—22no—
74C4×C571C2×D411yescharacteristic
75C4×C571C2411yescharacteristic
76Dic571—22no—
77Dic571C2×D411yescharacteristic
78Dic571C2×D411yescharacteristic
79C2×C571—21no—
80C2×C571—42no—
81C2×C571C22×D411yescharacteristic
82D571—21no—
83D571—42no—
84D571#13512yesdirect product factor
85C571C2×#13511yescharacteristic, complemented, Sylow
86C2×#135—5711nomaximal, Sylow
87C2×#41—5712no—
88#135—5712no—
89#135—5711no—
90#135—5712no—
91#135—5711no—
92#135—5711no—
93#135D57111yescharacteristic, direct product factor
94C2×Q16—5711no—
95C2×SD16—5712no—
96C2×D8—5711no—
97C22×C8—5711no—
98#41—5712no—
99#41—5712no—
100#41—5712no—
101#41—11422no—
102#41—11422no—
103#41C2×D57112yescomplemented
104C2×Q8—5712no—
105C2×D4—5712no—
106C2×D4—11422no—
107C22×C4—5711no—
108C22×C4—11422no—
109Q16—5712no—
110Q16—5711no—
111Q16C2×D57111yescharacteristic, complemented
112SD16—5712no—
113SD16—5712no—
114SD16—5712no—
115SD16C2×D57112yescomplemented
116D8—5712no—
117D8—5711no—
118D8C2×D57111yescharacteristic, complemented
119C2×C8—5711no—
120C2×C8—5711no—
121C2×C8—5711no—
122C2×C8—5711no—
123C2×C8—5711no—
124C2×C8C2×D57111yescharacteristic, complemented
125C23—5711no—
126C23—11422no—
127Q8—5712no—
128Q8—11422no—
129Q8C22×D57112yes—
130D4—22no—
131D4—5712no—
132D4—11422no—
133D4—11422no—
134D4—11422no—
135D4—11422no—
136D4C22×D57112yes—
137C2×C4—22no—
138C2×C4—5711no—
139C2×C4—5711no—
140C2×C4—5711no—
141C2×C4—5711no—
142C2×C4—5711no—
143C2×C4—11422no—
144C2×C4—11422no—
145C2×C4—11422no—
146C2×C4—11422no—
147C2×C4C22×D57111yescharacteristic
148C8—5711no—
149C8—5711no—
150C8C22×D57111yescharacteristic
151C8C22×D57111yescharacteristic
152C22—22no—
153C22—5711no—
154C22—5711no—
155C22—11422no—
156C22—11422no—
157C22—22844no—
158C22D4×D57111yescharacteristic
159C4—22no—
160C4—5711no—
161C4—5711no—
162C4—11422no—
163C4D4×D57111yescharacteristic
164C4C23×D57111yescharacteristic
165C2—21no—
166C2—42no—
167C2—5712no—
168C2—11421no—
169C2—22842no—
170C2C2×D4×D57111yescharacteristic
subgroupG/H
centerC4D4×D571
commutator, cosocleC4×C571C24
FrattiniC4C23×D571
Fitting#135×C571C2
socleC2×C571C22×D4
hypercenter#135D571
hypocenterC571C2×#135
LCSG ▷ C4×C571 ▷ C2×C571 ▷ C571
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D571C2semidirect
2. #32912717C2semidirect
3. #32912716C2semidirect
4. #32912715C2semidirect
5. #32912714C2semidirect
6. #32912713C2semidirect
7. Q16×D571C2semidirect
8. SD16×D571C2semidirect
9. D8×D571C2semidirect
10. C2×C8×D571C2semidirect
11. #135×C571C2semidirect
12. #22603734C22semidirect
14. #22603733C22semidirect
16. #22603732C22semidirect
22. Dic2284C22semidirect
23. #22603723C22semidirect
24. #22603722C22semidirect
25. #22603721C22semidirect
26. #22603720C22semidirect
27. D4568C22semidirect
28. #22603718C22semidirect
29. C2×C571⋊C8C22semidirect
32. C8×D571C22semidirect
33. C8×D571C22semidirect
34. #41×C571C22semidirect
35. Q16×C571C22semidirect
36. SD16×C571C22semidirect
37. D8×C571C22semidirect
38. C2×C8×C571C22semidirect
84. D571#135direct (N × H)
85. C571C2×#135semidirect
93. #135D571direct (N × H)
103. #41C2×D571semidirect
111. Q16C2×D571semidirect
115. SD16C2×D571semidirect
118. D8C2×D571semidirect
124. C2×C8C2×D571semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×D5712
#329127172
#329127162
#329127152
#329127142
#329127132
Q16×D5712
SD16×D5712
D8×D5712
C2×C8×D5712
#135×C5712
C2×#135571