Finite Group Databasebeta

← #31824299

Subgroups — #31824299

Order 17984.

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#22582927C212yesmaximal, complemented
2#22582926C214yesmaximal, complemented
3#22582925C214yesmaximal, complemented
4#22582924C216yesmaximal, complemented
5C2×#17985138C216yesmaximal, complemented
6#41×D281C218yesmaximal, complemented
7C2×#41×C281C211yesmaximal, characteristic, complemented
8#17985139C2218yescomplemented
9#17985138C22112yescomplemented
10#17985138C2214yescomplemented
11#17985138C22112yescomplemented
12#17985138C22112yescomplemented
13#17985137C22124yescomplemented
14C2×Dic562C2216yescomplemented
15Q8×D281C2218yescomplemented
16C2×D1124C2216yescomplemented
17C2×C22⋊D281C22112yescomplemented
18D4×D281C22124yescomplemented
19C2×C4×D281C22112yescomplemented
20#41×C281C2214yescomplemented
21#41×C281C2214yescomplemented
22C2×Q8×C281C2211yescharacteristic, complemented
23C2×D4×C281C2213yescomplemented
24C22×C4×C281C2213yescomplemented
25C22×D281C23112yes—
26Dic562C23112yes—
27Dic562C2314yes—
28D1124C23112yes—
29D1124C2314yes—
30C22⋊D281C23124yes—
31C22⋊D281C2318yes—
32C2×Dic281C23112yes—
33C4×D281C2318yes—
34C4×D281C23124yes—
35C23×C281C2313yes—
36Q8×C281C2314yes—
37D4×C281C23112yes—
38C2×C4×C281C2311yescharacteristic
39C2×C4×C281C2313yes—
40C2×C4×C281C2316yes—
41C2×C4×C281C2316yes—
42C22×C281—43no—
43C22×C281C2411yescharacteristic
44C22×C281C2416yes—
45C2×D281—412no—
46C2×D281C2418yes—
47C4×C281C2411yescharacteristic
48C4×C281C2416yes—
49C4×C281C2411yescharacteristic
50Dic281C2418yes—
51C2×C281—26no—
52C2×C281—21no—
53C2×C281C2511yescharacteristic
54D281—28no—
55C281#58511yescharacteristic, complemented, Sylow
56#585—2811nomaximal, Sylow
572−1+4—2814no—
582−1+4—2812no—
59H(5,𝔽2)—2814no—
60H(5,𝔽2)—2816no—
61C2×#41—2818no—
62C2×#41—2816no—
63C2×#41D28111yescharacteristic, complemented
64#41—2818no—
65#41—28124no—
66#41—28112no—
67#41—2814no—
68#41—28112no—
69#41—28112no—
70#41C2×D28114yescomplemented
71#41C2×D28114yescomplemented
72C2×Q8—2818no—
73C2×Q8—2816no—
74C2×Q8C2×D28111yescharacteristic, complemented
75C2×D4—28112no—
76C2×D4—28124no—
77C2×D4—2816no—
78C2×D4C2×D28113yescomplemented
79C22×C4—28112no—
80C22×C4C2×D28113yescomplemented
81C23—28112no—
82C23C22×D28113yes—
83Q8—28112no—
84Q8—2814no—
85Q8C22×D28114yes—
86D4—28124no—
87D4—2818no—
88D4—28112no—
89D4—2814no—
90D4C22×D281112yes—
91C2×C4—28112no—
92C2×C4—28124no—
93C2×C4—2818no—
94C2×C4C22×D28116yes—
95C2×C4C22×D28113yes—
96C2×C4C22×D28116yes—
97C2×C4C22×D28111yescharacteristic
98C22—43no—
99C22—2818no—
100C22—112412no—
101C22C23×D28116yes—
102C22C23×D28111yescharacteristic
103C4—2818no—
104C4C23×D28116yes—
105C4C23×D28111yescharacteristic
106C4C23×D28111yescharacteristic
107C2—21no—
108C2—26no—
109C2—5628no—
110C2C24×D28111yescharacteristic
subgroupG/H
centerC4C23×D281
commutator, socle, cosocleC2×C281C25
FrattiniC2C24×D281
FittingC2×#41×C281C2
hypercenterC2×#41D281
hypocenterC281#585
LCSG ▷ C2×C281 ▷ C281
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #22582927C2semidirect
2. #22582926C2semidirect
3. #22582925C2semidirect
4. #22582924C2semidirect
5. C2×#17985138C2semidirect
6. #41×D281C2semidirect
7. C2×#41×C281C2semidirect
8. #17985139C22semidirect
9. #17985138C22semidirect
10. #17985138C22semidirect
11. #17985138C22semidirect
12. #17985138C22semidirect
13. #17985137C22semidirect
14. C2×Dic562C22semidirect
15. Q8×D281C22semidirect
16. C2×D1124C22semidirect
17. C2×C22⋊D281C22semidirect
18. D4×D281C22semidirect
19. C2×C4×D281C22semidirect
20. #41×C281C22semidirect
21. #41×C281C22semidirect
22. C2×Q8×C281C22semidirect
23. C2×D4×C281C22semidirect
24. C22×C4×C281C22semidirect
55. C281#585semidirect
63. C2×#41D281semidirect
70. #41C2×D281semidirect
71. #41C2×D281semidirect
74. C2×Q8C2×D281semidirect
78. C2×D4C2×D281semidirect
80. C22×C4C2×D281semidirect

Maximal subgroups

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

subgroupindex
#225829272
#225829262
#225829252
#225829242
C2×#179851382
#41×D2812
C2×#41×C2812
#585281