Finite Group Databasebeta

← #45688229

Subgroups — #45688229

Order 33344.

262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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×D521C212yesmaximal, complemented
2#30659740C212yesmaximal, complemented
3#30659737C212yesmaximal, complemented
4#30659735C212yesmaximal, complemented
5#30659732C212yesmaximal, complemented
6#30659730C211yesmaximal, characteristic, complemented
7#30659728C212yesmaximal, complemented
8C2×#22552347C211yesmaximal, characteristic, complemented
9#135×C521C211yesmaximal, characteristic, complemented
10#22552365C2212yes—
11#22552364—22no—
12#22552364C2212yescomplemented
13#22552363—22no—
14#22552363C2212yes—
15Q8×D521C2212yescomplemented
16D4×D521—22no—
17D4×D521C2212yescomplemented
18C2×C4×D521—22no—
19C2×C4×D521C2211yescharacteristic
20Dic2084C2211yescharacteristic, complemented
21#22552354C2212yescomplemented
22#22552353C2212yescomplemented
23#22552352C2212yescomplemented
24#22552351C2212yescomplemented
25D4168C2211yescharacteristic, complemented
26#22552349C2212yescomplemented
27#22552347C2212yescomplemented
28#22552347C2212yescomplemented
29C2×#16861960C2211yescharacteristic, complemented
30#41×C521C2212yescomplemented
31Q16×C521C2211yescharacteristic, complemented
32SD16×C521C2212yescomplemented
33D8×C521C2211yescharacteristic, complemented
34C2×C8×C521C2211yescharacteristic, complemented
35C22×D521—22no—
36C22×D521D411yescharacteristic
37Dic1042—22no—
38Dic1042C2312yes—
39D2084—22no—
40D2084C2312yes—
41C22⋊D521—22no—
42C22⋊D521—22no—
43C22⋊D521—22no—
44C2×Dic521—22no—
45C2×Dic521D411yescharacteristic
46C4×D521—22no—
47C4×D521—22no—
48C4×D521—22no—
49C4×D521D412yes—
50C4×D521C2312yes—
51#16861960C2312yes—
52Q8×C521C2312yes—
53D4×C521—22no—
54D4×C521C2312yes—
55C2×C4×C521—22no—
56C2×C4×C521C2311yescharacteristic
57C8×C521C2311yescharacteristic
58C8×C521C2311yescharacteristic
59C22×C521—22no—
60C22×C521C2×D411yescharacteristic
61C2×D521—22no—
62C2×D521—41no—
63C2×D521—44no—
64C2×D521C2×D412yes—
65C4×C521—22no—
66C4×C521C2×D411yescharacteristic
67C4×C521C2411yescharacteristic
68Dic521—22no—
69Dic521C2×D412yes—
70C2×C521—21no—
71C2×C521—42no—
72C2×C521C22×D411yescharacteristic
73D521—22no—
74D521—42no—
75C521#57511yescharacteristic, complemented, Sylow
76#575—5211nomaximal, Sylow
77C2×#41—5212no—
78#137—5212no—
79#137—5212no—
80AGL(1,ℤ/8)—5212no—
81AGL(1,ℤ/8)—5212no—
82#135—5212no—
83#135—5211no—
84#135D52111yescharacteristic, complemented
85C2×M16—5211no—
86#41—5212no—
87#41—5212no—
88#41—5212no—
89#41—10422no—
90#41—10422no—
91#41C2×D52112yescomplemented
92C2×Q8—5212no—
93C2×D4—5212no—
94C2×D4—10422no—
95C22×C4—5211no—
96C22×C4—10422no—
97Q16—5212no—
98Q16—5211no—
99Q16C2×D52111yescharacteristic, complemented
100SD16—5212no—
101SD16—5212no—
102SD16—5212no—
103SD16C2×D52112yescomplemented
104D8—5212no—
105D8—5211no—
106D8C2×D52111yescharacteristic, complemented
107M16—5212no—
108M16—5212no—
109C2×C8—5211no—
110C2×C8C2×D52111yescharacteristic, complemented
111C23—5211no—
112C23—10422no—
113Q8—5212no—
114Q8—10422no—
115Q8C22×D52112yes—
116D4—22no—
117D4—5212no—
118D4—10422no—
119D4—10422no—
120D4—10422no—
121D4—10422no—
122D4C22×D52112yes—
123C2×C4—22no—
124C2×C4—5211no—
125C2×C4—5212no—
126C2×C4—5212no—
127C2×C4—10422no—
128C2×C4—10422no—
129C2×C4—10422no—
130C2×C4—10422no—
131C2×C4C22×D52111yescharacteristic
132C8—5212no—
133C8C22×D52111yescharacteristic
134C8C22×D52111yescharacteristic
135C22—22no—
136C22—5212no—
137C22—10422no—
138C22—20841no—
139C22—20844no—
140C22D4×D52111yescharacteristic
141C4—22no—
142C4—5212no—
143C4—10422no—
144C4D4×D52111yescharacteristic
145C4C23×D52111yescharacteristic
146C2—21no—
147C2—42no—
148C2—10422no—
149C2—20842no—
150C2C2×D4×D52111yescharacteristic
subgroupG/H
centerC4D4×D521
commutator, cosocleC4×C521C24
FrattiniC4C23×D521
Fitting#135×C521C2
socleC2×C521C22×D4
hypercenter#135D521
hypocenterC521#575
LCSG ▷ C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D521C2semidirect
2. #30659740C2semidirect
3. #30659737C2semidirect
4. #30659735C2semidirect
5. #30659732C2semidirect
6. #30659730C2semidirect
7. #30659728C2semidirect
8. C2×#22552347C2semidirect
9. #135×C521C2semidirect
12. #22552364C22semidirect
15. Q8×D521C22semidirect
17. D4×D521C22semidirect
20. Dic2084C22semidirect
21. #22552354C22semidirect
22. #22552353C22semidirect
23. #22552352C22semidirect
24. #22552351C22semidirect
25. D4168C22semidirect
26. #22552349C22semidirect
27. #22552347C22semidirect
28. #22552347C22semidirect
29. C2×#16861960C22semidirect
30. #41×C521C22semidirect
31. Q16×C521C22semidirect
32. SD16×C521C22semidirect
33. D8×C521C22semidirect
34. C2×C8×C521C22semidirect
75. C521#575semidirect
84. #135D521semidirect
91. #41C2×D521semidirect
99. Q16C2×D521semidirect
103. SD16C2×D521semidirect
106. D8C2×D521semidirect
110. C2×C8C2×D521semidirect

Maximal subgroups

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

subgroupindex
#41×D5212
#306597402
#306597372
#306597352
#306597322
#306597302
#306597282
C2×#225523472
#135×C5212
#575521