Finite Group Databasebeta

← #16840564

Subgroups — #16840564

Order 3904.

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#14519823C212yesmaximal, complemented
2#14519804C214yesmaximal, complemented
3#14519802C212yesmaximal, complemented
4#14519800C212yesmaximal, complemented
5C2×D488C211yesmaximal, characteristic, complemented
6D8×D61C212yesmaximal, complemented
7#14519783C211yesmaximal, characteristic, complemented
8#135×C61C211yesmaximal, characteristic, complemented
9#41×C61C2212yescomplemented
10#11758226C2214yescomplemented
11D4×D61—24no—
12D4×D61C2214yescomplemented
13#11758222—22no—
14#11758222C2211yescharacteristic
15C2×D244—22no—
16C2×D244C2212yescomplemented
17Q16×C61C2211yescharacteristic, complemented
18SD16×C61C2212yescomplemented
19D8×C61C2211yescharacteristic, complemented
20C2×C8×C61C2211yescharacteristic, complemented
21#11758201C2214yescomplemented
22#11758199C2214yescomplemented
23#11758194C2211yescharacteristic, complemented
24D488C2212yescomplemented
25D488C2212yescomplemented
26#11758189C2212yescomplemented
27C8×D61C2212yescomplemented
28C22×D61—22no—
29C22×D61—24no—
30Q8×C61C2312yes—
31D4×C61—22no—
32D4×C61C2312yes—
33C2×C4×C61—22no—
34C2×C4×C61C2311yescharacteristic
35C22⋊D61—24no—
36C22⋊D61D412yes—
37D244—24no—
38D244—22no—
39D244D411yescharacteristic
40D244C2314yes—
41C4×D61—24no—
42C4×D61C2312yes—
43Dic122D411yescharacteristic
44C8×C61C2311yescharacteristic
45C8×C61C2311yescharacteristic
46#92418C2312yes—
47C22×C61—22no—
48C22×C61C2×D411yescharacteristic
49C2×D61—24no—
50C2×D61—84no—
51C2×D61—82no—
52C2×D61C2×D412yes—
53C4×C61—22no—
54C4×C61C2×D411yescharacteristic
55C4×C61C2411yescharacteristic
56Dic61C2×D412yes—
57C2×C61—21no—
58C2×C61—42no—
59C2×C61C22×D411yescharacteristic
60D61—22no—
61D61—44no—
62#576—611nomaximal, Sylow
63C61#57611yescharacteristic, complemented, Sylow
64H(5,𝔽2)—612no—
65AGL(1,ℤ/8)—612no—
66AGL(1,ℤ/8)—614no—
67#135—612no—
68#135D6111yescharacteristic, complemented
69C2×D8—612no—
70C2×D8—611no—
71#131—611no—
72#41—611no—
73#41—614no—
74#41—1222no—
75#41C2×D6112yescomplemented
76C2×D4—614no—
77C2×D4—612no—
78C2×D4—1222no—
79C2×D4—1224no—
80Q16C2×D6111yescharacteristic, complemented
81SD16—614no—
82SD16C2×D6112yescomplemented
83D8—614no—
84D8—612no—
85D8—612no—
86D8C2×D6111yescharacteristic, complemented
87M16—611no—
88M16—612no—
89C2×C8—612no—
90C2×C8C2×D6111yescharacteristic, complemented
91C23—1224no—
92C23—1222no—
93Q8—611no—
94Q8C22×D6112yes—
95D4—22no—
96D4—612no—
97D4—611no—
98D4—614no—
99D4—1224no—
100D4—1224no—
101D4—1222no—
102D4C22×D6112yes—
103C2×C4—22no—
104C2×C4—612no—
105C2×C4—1224no—
106C2×C4C22×D6111yescharacteristic
107C8—612no—
108C8C22×D6111yescharacteristic
109C8C22×D6111yescharacteristic
110C22—22no—
111C22—612no—
112C22—1224no—
113C22—4882no—
114C22—4884no—
115C22D4×D6111yescharacteristic
116C4—22no—
117C4—612no—
118C4D4×D6111yescharacteristic
119C4C23×D6111yescharacteristic
120C2—21no—
121C2—42no—
122C2—1222no—
123C2—2444no—
124C2C2×D4×D6111yescharacteristic
subgroupG/H
centerC2C2×D4×D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
Fitting#135×C61C2
socleC2×C61C22×D4
hypercenter#135D61
hypocenterC61#576
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #14519823C2semidirect
2. #14519804C2semidirect
3. #14519802C2semidirect
4. #14519800C2semidirect
5. C2×D488C2semidirect
6. D8×D61C2semidirect
7. #14519783C2semidirect
8. #135×C61C2semidirect
9. #41×C61C22semidirect
10. #11758226C22semidirect
12. D4×D61C22semidirect
16. C2×D244C22semidirect
17. Q16×C61C22semidirect
18. SD16×C61C22semidirect
19. D8×C61C22semidirect
20. C2×C8×C61C22semidirect
21. #11758201C22semidirect
22. #11758199C22semidirect
23. #11758194C22semidirect
24. D488C22semidirect
25. D488C22semidirect
26. #11758189C22semidirect
27. C8×D61C22semidirect
63. C61#576semidirect
68. #135D61semidirect
75. #41C2×D61semidirect
80. Q16C2×D61semidirect
82. SD16C2×D61semidirect
86. D8C2×D61semidirect
90. C2×C8C2×D61semidirect

Maximal subgroups

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

subgroupindex
#145198232
#145198042
#145198022
#145198002
C2×D4882
D8×D612
#145197832
#135×C612
#57661