Finite Group Databasebeta

← #26012327

Subgroups — #26012327

Order 11072.

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#19149727C212yesmaximal, complemented
2#19149726C214yesmaximal, complemented
3#19149725C214yesmaximal, complemented
4#19149724C216yesmaximal, complemented
5C2×#14583826C216yesmaximal, complemented
6#41×D173C218yesmaximal, complemented
7C2×#41×C173C211yesmaximal, characteristic, complemented
8#14583827C2218yescomplemented
9#14583826C22112yescomplemented
10#14583826C2214yescomplemented
11#14583826C22112yescomplemented
12#14583826C22112yescomplemented
13#14583825C22124yescomplemented
14C2×Dic346C2216yescomplemented
15Q8×D173C2218yescomplemented
16C2×D692C2216yescomplemented
17C2×C22⋊D173C22112yescomplemented
18D4×D173C22124yescomplemented
19C2×C4×D173C22112yescomplemented
20#41×C173C2214yescomplemented
21#41×C173C2214yescomplemented
22C2×Q8×C173C2211yescharacteristic, complemented
23C2×D4×C173C2213yescomplemented
24C22×C4×C173C2213yescomplemented
25C22×D173C23112yes—
26Dic346C23112yes—
27Dic346C2314yes—
28D692C23112yes—
29D692C2314yes—
30C22⋊D173C23124yes—
31C22⋊D173C2318yes—
32C2×Dic173C23112yes—
33C4×D173C2318yes—
34C4×D173C23124yes—
35C23×C173C2313yes—
36Q8×C173C2314yes—
37D4×C173C23112yes—
38C2×C4×C173C2316yes—
39C2×C4×C173C2316yes—
40C2×C4×C173C2311yescharacteristic
41C2×C4×C173C2313yes—
42C22×C173—43no—
43C22×C173C2411yescharacteristic
44C22×C173C2416yes—
45C2×D173—412no—
46C2×D173C2418yes—
47C4×C173C2411yescharacteristic
48C4×C173C2416yes—
49C4×C173C2411yescharacteristic
50Dic173C2418yes—
51C2×C173—26no—
52C2×C173—21no—
53C2×C173C2511yescharacteristic
54D173—28no—
55C173#58511yescharacteristic, complemented, Sylow
56#585—1731nomaximal, Sylow
572−1+4—1734no—
582−1+4—1732no—
59H(5,𝔽2)—1734no—
60H(5,𝔽2)—1736no—
61C2×#41—1738no—
62C2×#41—1736no—
63C2×#41D17311yescharacteristic, complemented
64#41—1738no—
65#41—17324no—
66#41—17312no—
67#41—1734no—
68#41—17312no—
69#41—17312no—
70#41C2×D17314yescomplemented
71#41C2×D17314yescomplemented
72C2×Q8—1738no—
73C2×Q8—1736no—
74C2×Q8C2×D17311yescharacteristic, complemented
75C2×D4—17312no—
76C2×D4—17324no—
77C2×D4—1736no—
78C2×D4C2×D17313yescomplemented
79C22×C4—17312no—
80C22×C4C2×D17313yescomplemented
81C23—17312no—
82C23C22×D17313yes—
83Q8—17312no—
84Q8—1734no—
85Q8C22×D17314yes—
86D4—17324no—
87D4—1738no—
88D4—17312no—
89D4—1734no—
90D4C22×D173112yes—
91C2×C4—17312no—
92C2×C4—17324no—
93C2×C4—1738no—
94C2×C4C22×D17316yes—
95C2×C4C22×D17313yes—
96C2×C4C22×D17316yes—
97C2×C4C22×D17311yescharacteristic
98C22—43no—
99C22—1738no—
100C22—69212no—
101C22C23×D17316yes—
102C22C23×D17311yescharacteristic
103C4—1738no—
104C4C23×D17316yes—
105C4C23×D17311yescharacteristic
106C4C23×D17311yescharacteristic
107C2—21no—
108C2—26no—
109C2—3468no—
110C2C24×D17311yescharacteristic
subgroupG/H
centerC4C23×D173
commutator, socle, cosocleC2×C173C25
FrattiniC2C24×D173
FittingC2×#41×C173C2
hypercenterC2×#41D173
hypocenterC173#585
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #19149727C2semidirect
2. #19149726C2semidirect
3. #19149725C2semidirect
4. #19149724C2semidirect
5. C2×#14583826C2semidirect
6. #41×D173C2semidirect
7. C2×#41×C173C2semidirect
8. #14583827C22semidirect
9. #14583826C22semidirect
10. #14583826C22semidirect
11. #14583826C22semidirect
12. #14583826C22semidirect
13. #14583825C22semidirect
14. C2×Dic346C22semidirect
15. Q8×D173C22semidirect
16. C2×D692C22semidirect
17. C2×C22⋊D173C22semidirect
18. D4×D173C22semidirect
19. C2×C4×D173C22semidirect
20. #41×C173C22semidirect
21. #41×C173C22semidirect
22. C2×Q8×C173C22semidirect
23. C2×D4×C173C22semidirect
24. C22×C4×C173C22semidirect
55. C173#585semidirect
63. C2×#41D173semidirect
70. #41C2×D173semidirect
71. #41C2×D173semidirect
74. C2×Q8C2×D173semidirect
78. C2×D4C2×D173semidirect
80. C22×C4C2×D173semidirect

Maximal subgroups

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

subgroupindex
#191497272
#191497262
#191497252
#191497242
C2×#145838262
#41×D1732
C2×#41×C1732
#585173