Finite Group Databasebeta

← #16840563

Subgroups — #16840563

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#14519822C212yesmaximal, complemented
2#14519803C212yesmaximal, complemented
3#14519801C214yesmaximal, complemented
4#14519799C211yesmaximal, characteristic, complemented
5#14519796C212yesmaximal, complemented
6D8×D61C212yesmaximal, complemented
7#14519783C211yesmaximal, characteristic, complemented
8C2×D8×C61C211yesmaximal, characteristic, complemented
9C2×D4×C61C2212yescomplemented
10C2×C22⋊D61—24no—
11#11758224—22no—
12#11758224C2214yescomplemented
13D4×D61—22no—
14D4×D61C2214yescomplemented
15#11758222C2211yescharacteristic
16#11758222C2212yescomplemented
17D8×C61C2212yescomplemented
18D8×C61C2212yescomplemented
19C2×C8×C61C2211yescharacteristic, complemented
20#11758200C2214yescomplemented
21#11758199C2214yescomplemented
22#11758194C2211yescharacteristic, complemented
23Dic244C2211yescharacteristic, complemented
24D488C2211yescharacteristic, complemented
25#11758190C2212yescomplemented
26#11758189C2212yescomplemented
27C8×D61C2212yescomplemented
28C23×C61—22no—
29C22×D61—24no—
30D4×C61—22no—
31D4×C61C2314yes—
32C2×C4×C61C2311yescharacteristic
33C22⋊D61—22no—
34C22⋊D61—24no—
35C22⋊D61—24no—
36C22⋊D61D412yes—
37C2×Dic61—24no—
38D244D411yescharacteristic
39D244C2312yes—
40C4×D61—22no—
41C4×D61C2312yes—
42Dic122D411yescharacteristic
43Dic122C2312yes—
44C8×C61C2311yescharacteristic
45C8×C61C2311yescharacteristic
46#92418C2312yes—
47C22×C61—24no—
48C22×C61—82no—
49C22×C61C2×D411yescharacteristic
50C2×D61—22no—
51C2×D61—84no—
52C2×D61C2×D412yes—
53C4×C61C2×D411yescharacteristic
54C4×C61C2411yescharacteristic
55Dic61—22no—
56Dic61C2×D412yes—
57C2×C61—21no—
58C2×C61—44no—
59C2×C61C22×D411yescharacteristic
60D61—22no—
61D61—42no—
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#135—611no—
69C2×D8—612no—
70C2×D8D6111yescharacteristic, complemented
71#131—611no—
72#41—611no—
73#41—614no—
74#41—612no—
75#41—1222no—
76C2×D4—614no—
77C2×D4—1222no—
78C2×D4—1224no—
79C2×D4C2×D6112yescomplemented
80Q16—611no—
81SD16—614no—
82SD16—612no—
83D8—614no—
84D8—611no—
85D8C2×D6112yescomplemented
86D8C2×D6112yescomplemented
87M16—611no—
88M16—612no—
89C2×C8—612no—
90C2×C8C2×D6111yescharacteristic, complemented
91C23—22no—
92C23—1224no—
93Q8—611no—
94Q8—612no—
95D4—22no—
96D4—612no—
97D4—611no—
98D4—612no—
99D4—1224no—
100D4—1224no—
101D4—1222no—
102D4C22×D6114yes—
103C2×C4—612no—
104C2×C4—1224no—
105C2×C4—1222no—
106C2×C4C22×D6111yescharacteristic
107C8—612no—
108C8C22×D6111yescharacteristic
109C8C22×D6111yescharacteristic
110C22—24no—
111C22—82no—
112C22—612no—
113C22—1222no—
114C22—4884no—
115C22D4×D6111yescharacteristic
116C4—612no—
117C4—1222no—
118C4D4×D6111yescharacteristic
119C4C23×D6111yescharacteristic
120C2—21no—
121C2—44no—
122C2—1222no—
123C2—2442no—
124C2C2×D4×D6111yescharacteristic
subgroupG/H
centerC2C2×D4×D61
commutator, cosocleC4×C61C24
FrattiniC4C23×D61
FittingC2×D8×C61C2
socleC2×C61C22×D4
hypercenterC2×D8D61
hypocenterC61#576
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #14519822C2semidirect
2. #14519803C2semidirect
3. #14519801C2semidirect
4. #14519799C2semidirect
5. #14519796C2semidirect
6. D8×D61C2semidirect
7. #14519783C2semidirect
8. C2×D8×C61C2semidirect
9. C2×D4×C61C22semidirect
12. #11758224C22semidirect
14. D4×D61C22semidirect
16. #11758222C22semidirect
17. D8×C61C22semidirect
18. D8×C61C22semidirect
19. C2×C8×C61C22semidirect
20. #11758200C22semidirect
21. #11758199C22semidirect
22. #11758194C22semidirect
23. Dic244C22semidirect
24. D488C22semidirect
25. #11758190C22semidirect
26. #11758189C22semidirect
27. C8×D61C22semidirect
63. C61#576semidirect
70. C2×D8D61semidirect
79. C2×D4C2×D61semidirect
85. D8C2×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
#145198222
#145198032
#145198012
#145197992
#145197962
D8×D612
#145197832
C2×D8×C612
#57661