Finite Group Databasebeta

← #16840598

Subgroups — #16840598

Order 3904.

810 conjugacy classes of subgroups; only the 443 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 443 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#14519825C212yesmaximal, complemented
2#14519824C214yesmaximal, complemented
3#14519823C214yesmaximal, complemented
4#14519822C216yesmaximal, complemented
5C2×#11758222C216yesmaximal, complemented
6#41×D61C218yesmaximal, complemented
7C2×#41×C61C211yesmaximal, characteristic, complemented
8#41×C61C2214yescomplemented
9#41×C61C2214yescomplemented
10C2×Q8×C61C2211yescharacteristic, complemented
11C2×D4×C61C2213yescomplemented
12C22×C4×C61C2213yescomplemented
13C2×C22⋊D61C22112yescomplemented
14#11758226C2218yescomplemented
15Q8×D61C2218yescomplemented
16#11758224C22124yescomplemented
17D4×D61C22124yescomplemented
18#11758222C22112yescomplemented
19#11758222C2214yescomplemented
20#11758222C22112yescomplemented
21#11758222C22112yescomplemented
22C2×D244C2216yescomplemented
23C2×C4×D61C22112yescomplemented
24C2×Dic122C2216yescomplemented
25C23×C61C2313yes—
26C22×D61C23112yes—
27Q8×C61C2314yes—
28D4×C61C23112yes—
29C2×C4×C61C2316yes—
30C2×C4×C61C2316yes—
31C2×C4×C61C2311yescharacteristic
32C2×C4×C61C2313yes—
33C22⋊D61C2318yes—
34C22⋊D61C23124yes—
35C2×Dic61C23112yes—
36D244C2314yes—
37D244C23112yes—
38C4×D61C2318yes—
39C4×D61C23124yes—
40Dic122C2314yes—
41Dic122C23112yes—
42C22×C61—43no—
43C22×C61C2416yes—
44C22×C61C2411yescharacteristic
45C2×D61—412no—
46C2×D61C2418yes—
47C4×C61C2411yescharacteristic
48C4×C61C2416yes—
49C4×C61C2411yescharacteristic
50Dic61C2418yes—
51C2×C61—26no—
52C2×C61—21no—
53C2×C61C2511yescharacteristic
54D61—28no—
55#585—611nomaximal, Sylow
56C61#58511yescharacteristic, complemented, Sylow
572−1+4—614no—
582−1+4—612no—
59H(5,𝔽2)—614no—
60H(5,𝔽2)—616no—
61C2×#41—618no—
62C2×#41—616no—
63C2×#41D6111yescharacteristic, complemented
64#41—618no—
65#41—6124no—
66#41—6112no—
67#41—614no—
68#41—6112no—
69#41—6112no—
70#41C2×D6114yescomplemented
71#41C2×D6114yescomplemented
72C2×Q8—618no—
73C2×Q8—616no—
74C2×Q8C2×D6111yescharacteristic, complemented
75C2×D4—6112no—
76C2×D4—6124no—
77C2×D4—616no—
78C2×D4C2×D6113yescomplemented
79C22×C4—6112no—
80C22×C4C2×D6113yescomplemented
81C23—6112no—
82C23C22×D6113yes—
83Q8—6112no—
84Q8—614no—
85Q8C22×D6114yes—
86D4—6124no—
87D4—618no—
88D4—6112no—
89D4—614no—
90D4C22×D61112yes—
91C2×C4—6112no—
92C2×C4—6124no—
93C2×C4—618no—
94C2×C4C22×D6116yes—
95C2×C4C22×D6113yes—
96C2×C4C22×D6116yes—
97C2×C4C22×D6111yescharacteristic
98C22—43no—
99C22—618no—
100C22—24412no—
101C22C23×D6116yes—
102C22C23×D6111yescharacteristic
103C4—618no—
104C4C23×D6116yes—
105C4C23×D6111yescharacteristic
106C4C23×D6111yescharacteristic
107C2—21no—
108C2—26no—
109C2—1228no—
110C2C24×D6111yescharacteristic
subgroupG/H
centerC4C23×D61
commutator, socle, cosocleC2×C61C25
FrattiniC2C24×D61
FittingC2×#41×C61C2
hypercenterC2×#41D61
hypocenterC61#585
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14519825C2semidirect
2. #14519824C2semidirect
3. #14519823C2semidirect
4. #14519822C2semidirect
5. C2×#11758222C2semidirect
6. #41×D61C2semidirect
7. C2×#41×C61C2semidirect
8. #41×C61C22semidirect
9. #41×C61C22semidirect
10. C2×Q8×C61C22semidirect
11. C2×D4×C61C22semidirect
12. C22×C4×C61C22semidirect
13. C2×C22⋊D61C22semidirect
14. #11758226C22semidirect
15. Q8×D61C22semidirect
16. #11758224C22semidirect
17. D4×D61C22semidirect
18. #11758222C22semidirect
19. #11758222C22semidirect
20. #11758222C22semidirect
21. #11758222C22semidirect
22. C2×D244C22semidirect
23. C2×C4×D61C22semidirect
24. C2×Dic122C22semidirect
56. C61#585semidirect
63. C2×#41D61semidirect
70. #41C2×D61semidirect
71. #41C2×D61semidirect
74. C2×Q8C2×D61semidirect
78. C2×D4C2×D61semidirect
80. C22×C4C2×D61semidirect

Maximal subgroups

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

subgroupindex
#145198252
#145198242
#145198232
#145198222
C2×#117582222
#41×D612
C2×#41×C612
#58561