Finite Group Databasebeta

← #44442912

Subgroups — #44442912

Order 29504.

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#28414166C212yesmaximal, complemented
2#28414165C214yesmaximal, complemented
3#28414164C214yesmaximal, complemented
4#28414163C216yesmaximal, complemented
5C2×#20301501C216yesmaximal, complemented
6#41×D461C218yesmaximal, complemented
7C2×#41×C461C211yesmaximal, characteristic, complemented
8#20301502C2218yescomplemented
9#20301501C22112yescomplemented
10#20301501C2214yescomplemented
11#20301501C22112yescomplemented
12#20301501C22112yescomplemented
13#20301500C22124yescomplemented
14C2×Dic922C2216yescomplemented
15Q8×D461C2218yescomplemented
16C2×D1844C2216yescomplemented
17C2×C22⋊D461C22112yescomplemented
18D4×D461C22124yescomplemented
19C2×C4×D461C22112yescomplemented
20#41×C461C2214yescomplemented
21#41×C461C2214yescomplemented
22C2×Q8×C461C2211yescharacteristic, complemented
23C2×D4×C461C2213yescomplemented
24C22×C4×C461C2213yescomplemented
25C22×D461C23112yes—
26Dic922C23112yes—
27Dic922C2314yes—
28D1844C23112yes—
29D1844C2314yes—
30C22⋊D461C23124yes—
31C22⋊D461C2318yes—
32C2×Dic461C23112yes—
33C4×D461C2318yes—
34C4×D461C23124yes—
35C23×C461C2313yes—
36Q8×C461C2314yes—
37D4×C461C23112yes—
38C2×C4×C461C2311yescharacteristic
39C2×C4×C461C2313yes—
40C2×C4×C461C2316yes—
41C2×C4×C461C2316yes—
42C22×C461—43no—
43C22×C461C2411yescharacteristic
44C22×C461C2416yes—
45C2×D461—412no—
46C2×D461C2418yes—
47C4×C461C2411yescharacteristic
48C4×C461C2416yes—
49C4×C461C2411yescharacteristic
50Dic461C2418yes—
51C2×C461—26no—
52C2×C461—21no—
53C2×C461C2511yescharacteristic
54D461—28no—
55C461#58511yescharacteristic, complemented, Sylow
56#585—4611nomaximal, Sylow
572−1+4—4614no—
582−1+4—4612no—
59H(5,𝔽2)—4614no—
60H(5,𝔽2)—4616no—
61C2×#41—4618no—
62C2×#41—4616no—
63C2×#41D46111yescharacteristic, complemented
64#41—4618no—
65#41—46124no—
66#41—46112no—
67#41—4614no—
68#41—46112no—
69#41—46112no—
70#41C2×D46114yescomplemented
71#41C2×D46114yescomplemented
72C2×Q8—4618no—
73C2×Q8—4616no—
74C2×Q8C2×D46111yescharacteristic, complemented
75C2×D4—46112no—
76C2×D4—46124no—
77C2×D4—4616no—
78C2×D4C2×D46113yescomplemented
79C22×C4—46112no—
80C22×C4C2×D46113yescomplemented
81C23—46112no—
82C23C22×D46113yes—
83Q8—46112no—
84Q8—4614no—
85Q8C22×D46114yes—
86D4—46124no—
87D4—4618no—
88D4—46112no—
89D4—4614no—
90D4C22×D461112yes—
91C2×C4—46112no—
92C2×C4—46124no—
93C2×C4—4618no—
94C2×C4C22×D46116yes—
95C2×C4C22×D46113yes—
96C2×C4C22×D46116yes—
97C2×C4C22×D46111yescharacteristic
98C22—43no—
99C22—184412no—
100C22—4618no—
101C22C23×D46116yes—
102C22C23×D46111yescharacteristic
103C4—4618no—
104C4C23×D46116yes—
105C4C23×D46111yescharacteristic
106C4C23×D46111yescharacteristic
107C2—21no—
108C2—26no—
109C2—9228no—
110C2C24×D46111yescharacteristic
subgroupG/H
centerC4C23×D461
commutator, socle, cosocleC2×C461C25
FrattiniC2C24×D461
FittingC2×#41×C461C2
hypercenterC2×#41D461
hypocenterC461#585
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #28414166C2semidirect
2. #28414165C2semidirect
3. #28414164C2semidirect
4. #28414163C2semidirect
5. C2×#20301501C2semidirect
6. #41×D461C2semidirect
7. C2×#41×C461C2semidirect
8. #20301502C22semidirect
9. #20301501C22semidirect
10. #20301501C22semidirect
11. #20301501C22semidirect
12. #20301501C22semidirect
13. #20301500C22semidirect
14. C2×Dic922C22semidirect
15. Q8×D461C22semidirect
16. C2×D1844C22semidirect
17. C2×C22⋊D461C22semidirect
18. D4×D461C22semidirect
19. C2×C4×D461C22semidirect
20. #41×C461C22semidirect
21. #41×C461C22semidirect
22. C2×Q8×C461C22semidirect
23. C2×D4×C461C22semidirect
24. C22×C4×C461C22semidirect
55. C461#585semidirect
63. C2×#41D461semidirect
70. #41C2×D461semidirect
71. #41C2×D461semidirect
74. C2×Q8C2×D461semidirect
78. C2×D4C2×D461semidirect
80. C22×C4C2×D461semidirect

Maximal subgroups

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

subgroupindex
#284141662
#284141652
#284141642
#284141632
C2×#203015012
#41×D4612
C2×#41×C4612
#585461