Finite Group Databasebeta

← #45691007

Subgroups — #45691007

Order 33472.

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

normal subgroups only

This group has 268 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#30660419C212yesmaximal, complemented
2#30660400C214yesmaximal, complemented
3#30660398C212yesmaximal, complemented
4#30660396C212yesmaximal, complemented
5C2×D4184C211yesmaximal, characteristic, complemented
6D8×D523C212yesmaximal, complemented
7#30660379C211yesmaximal, characteristic, complemented
8#135×C523C211yesmaximal, characteristic, complemented
9#22552642C2214yescomplemented
10#22552641—22no—
11#22552641C2211yescharacteristic
12C2×D2092—22no—
13C2×D2092C2212yescomplemented
14D4×D523—24no—
15D4×D523C2214yescomplemented
16#22552628C2214yescomplemented
17D4184C2212yescomplemented
18D4184C2212yescomplemented
19#22552626C2214yescomplemented
20#22552625C2211yescharacteristic, complemented
21#22552624C2212yescomplemented
22C8×D523C2212yescomplemented
23#41×C523C2212yescomplemented
24Q16×C523C2211yescharacteristic, complemented
25SD16×C523C2212yescomplemented
26D8×C523C2211yescharacteristic, complemented
27C2×C8×C523C2211yescharacteristic, complemented
28C22×D523—22no—
29C22×D523—24no—
30Dic1046D411yescharacteristic
31D2092—24no—
32D2092—22no—
33D2092D411yescharacteristic
34D2092C2314yes—
35C22⋊D523—24no—
36C22⋊D523D412yes—
37C4×D523—24no—
38C4×D523C2312yes—
39C523⋊C8C2312yes—
40Q8×C523C2312yes—
41D4×C523—22no—
42D4×C523C2312yes—
43C2×C4×C523—22no—
44C2×C4×C523C2311yescharacteristic
45C8×C523C2311yescharacteristic
46C8×C523C2311yescharacteristic
47C22×C523—22no—
48C22×C523C2×D411yescharacteristic
49C2×D523—24no—
50C2×D523—84no—
51C2×D523—82no—
52C2×D523C2×D412yes—
53C4×C523—22no—
54C4×C523C2×D411yescharacteristic
55C4×C523C2411yescharacteristic
56Dic523C2×D412yes—
57C2×C523—21no—
58C2×C523—42no—
59C2×C523C22×D411yescharacteristic
60D523—22no—
61D523—44no—
62C523#57611yescharacteristic, complemented, Sylow
63#576—5231nomaximal, Sylow
64H(5,𝔽2)—5232no—
65AGL(1,ℤ/8)—5232no—
66AGL(1,ℤ/8)—5234no—
67#135—5232no—
68#135D52311yescharacteristic, complemented
69C2×D8—5232no—
70C2×D8—5231no—
71#131—5231no—
72#41—5231no—
73#41—5234no—
74#41—10462no—
75#41C2×D52312yescomplemented
76C2×D4—5234no—
77C2×D4—5232no—
78C2×D4—10462no—
79C2×D4—10464no—
80Q16C2×D52311yescharacteristic, complemented
81SD16—5234no—
82SD16C2×D52312yescomplemented
83D8—5234no—
84D8—5232no—
85D8—5232no—
86D8C2×D52311yescharacteristic, complemented
87M16—5231no—
88M16—5232no—
89C2×C8—5232no—
90C2×C8C2×D52311yescharacteristic, complemented
91C23—10464no—
92C23—10462no—
93Q8—5231no—
94Q8C22×D52312yes—
95D4—22no—
96D4—5232no—
97D4—5231no—
98D4—5234no—
99D4—10464no—
100D4—10464no—
101D4—10462no—
102D4C22×D52312yes—
103C2×C4—22no—
104C2×C4—5232no—
105C2×C4—10464no—
106C2×C4C22×D52311yescharacteristic
107C8—5232no—
108C8C22×D52311yescharacteristic
109C8C22×D52311yescharacteristic
110C22—22no—
111C22—5232no—
112C22—10464no—
113C22—41842no—
114C22—41844no—
115C22D4×D52311yescharacteristic
116C4—22no—
117C4—5232no—
118C4D4×D52311yescharacteristic
119C4C23×D52311yescharacteristic
120C2—21no—
121C2—42no—
122C2—10462no—
123C2—20924no—
124C2C2×D4×D52311yescharacteristic
subgroupG/H
centerC2C2×D4×D523
commutator, cosocleC4×C523C24
FrattiniC4C23×D523
Fitting#135×C523C2
socleC2×C523C22×D4
hypercenter#135D523
hypocenterC523#576
LCSG ▷ C4×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #30660419C2semidirect
2. #30660400C2semidirect
3. #30660398C2semidirect
4. #30660396C2semidirect
5. C2×D4184C2semidirect
6. D8×D523C2semidirect
7. #30660379C2semidirect
8. #135×C523C2semidirect
9. #22552642C22semidirect
13. C2×D2092C22semidirect
15. D4×D523C22semidirect
16. #22552628C22semidirect
17. D4184C22semidirect
18. D4184C22semidirect
19. #22552626C22semidirect
20. #22552625C22semidirect
21. #22552624C22semidirect
22. C8×D523C22semidirect
23. #41×C523C22semidirect
24. Q16×C523C22semidirect
25. SD16×C523C22semidirect
26. D8×C523C22semidirect
27. C2×C8×C523C22semidirect
62. C523#576semidirect
68. #135D523semidirect
75. #41C2×D523semidirect
80. Q16C2×D523semidirect
82. SD16C2×D523semidirect
86. D8C2×D523semidirect
90. C2×C8C2×D523semidirect

Maximal subgroups

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

subgroupindex
#306604192
#306604002
#306603982
#306603962
C2×D41842
D8×D5232
#306603792
#135×C5232
#576523