Finite Group Databasebeta

← #28417271

Subgroups — #28417271

Order 14912.

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#21418583C212yesmaximal, complemented
2#21418582C214yesmaximal, complemented
3#21418581C214yesmaximal, complemented
4#21418580C216yesmaximal, complemented
5C2×#16836594C216yesmaximal, complemented
6#41×D233C218yesmaximal, complemented
7C2×#41×C233C211yesmaximal, characteristic, complemented
8#16836595C2218yescomplemented
9#16836594C22112yescomplemented
10#16836594C2214yescomplemented
11#16836594C22112yescomplemented
12#16836594C22112yescomplemented
13#16836593C22124yescomplemented
14C2×Dic466C2216yescomplemented
15Q8×D233C2218yescomplemented
16C2×D932C2216yescomplemented
17C2×C22⋊D233C22112yescomplemented
18D4×D233C22124yescomplemented
19C2×C4×D233C22112yescomplemented
20#41×C233C2214yescomplemented
21#41×C233C2214yescomplemented
22C2×Q8×C233C2211yescharacteristic, complemented
23C2×D4×C233C2213yescomplemented
24C22×C4×C233C2213yescomplemented
25C22×D233C23112yes—
26Dic466C23112yes—
27Dic466C2314yes—
28D932C23112yes—
29D932C2314yes—
30C22⋊D233C23124yes—
31C22⋊D233C2318yes—
32C2×Dic233C23112yes—
33C4×D233C2318yes—
34C4×D233C23124yes—
35C23×C233C2313yes—
36Q8×C233C2314yes—
37D4×C233C23112yes—
38C2×C4×C233C2311yescharacteristic
39C2×C4×C233C2313yes—
40C2×C4×C233C2316yes—
41C2×C4×C233C2316yes—
42C22×C233—43no—
43C22×C233C2411yescharacteristic
44C22×C233C2416yes—
45C2×D233—412no—
46C2×D233C2418yes—
47C4×C233C2411yescharacteristic
48C4×C233C2416yes—
49C4×C233C2411yescharacteristic
50Dic233C2418yes—
51C2×C233—26no—
52C2×C233—21no—
53C2×C233C2511yescharacteristic
54D233—28no—
55C233#58511yescharacteristic, complemented, Sylow
56#585—2331nomaximal, Sylow
572−1+4—2334no—
582−1+4—2332no—
59H(5,𝔽2)—2334no—
60H(5,𝔽2)—2336no—
61C2×#41—2338no—
62C2×#41—2336no—
63C2×#41D23311yescharacteristic, complemented
64#41—2338no—
65#41—23324no—
66#41—23312no—
67#41—2334no—
68#41—23312no—
69#41—23312no—
70#41C2×D23314yescomplemented
71#41C2×D23314yescomplemented
72C2×Q8—2338no—
73C2×Q8—2336no—
74C2×Q8C2×D23311yescharacteristic, complemented
75C2×D4—23312no—
76C2×D4—23324no—
77C2×D4—2336no—
78C2×D4C2×D23313yescomplemented
79C22×C4—23312no—
80C22×C4C2×D23313yescomplemented
81C23—23312no—
82C23C22×D23313yes—
83Q8—23312no—
84Q8—2334no—
85Q8C22×D23314yes—
86D4—23324no—
87D4—2338no—
88D4—23312no—
89D4—2334no—
90D4C22×D233112yes—
91C2×C4—23312no—
92C2×C4—23324no—
93C2×C4—2338no—
94C2×C4C22×D23316yes—
95C2×C4C22×D23313yes—
96C2×C4C22×D23316yes—
97C2×C4C22×D23311yescharacteristic
98C22—43no—
99C22—93212no—
100C22—2338no—
101C22C23×D23316yes—
102C22C23×D23311yescharacteristic
103C4—2338no—
104C4C23×D23316yes—
105C4C23×D23311yescharacteristic
106C4C23×D23311yescharacteristic
107C2—21no—
108C2—26no—
109C2—4668no—
110C2C24×D23311yescharacteristic
subgroupG/H
centerC4C23×D233
commutator, socle, cosocleC2×C233C25
FrattiniC2C24×D233
FittingC2×#41×C233C2
hypercenterC2×#41D233
hypocenterC233#585
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #21418583C2semidirect
2. #21418582C2semidirect
3. #21418581C2semidirect
4. #21418580C2semidirect
5. C2×#16836594C2semidirect
6. #41×D233C2semidirect
7. C2×#41×C233C2semidirect
8. #16836595C22semidirect
9. #16836594C22semidirect
10. #16836594C22semidirect
11. #16836594C22semidirect
12. #16836594C22semidirect
13. #16836593C22semidirect
14. C2×Dic466C22semidirect
15. Q8×D233C22semidirect
16. C2×D932C22semidirect
17. C2×C22⋊D233C22semidirect
18. D4×D233C22semidirect
19. C2×C4×D233C22semidirect
20. #41×C233C22semidirect
21. #41×C233C22semidirect
22. C2×Q8×C233C22semidirect
23. C2×D4×C233C22semidirect
24. C22×C4×C233C22semidirect
55. C233#585semidirect
63. C2×#41D233semidirect
70. #41C2×D233semidirect
71. #41C2×D233semidirect
74. C2×Q8C2×D233semidirect
78. C2×D4C2×D233semidirect
80. C22×C4C2×D233semidirect

Maximal subgroups

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

subgroupindex
#214185832
#214185822
#214185812
#214185802
C2×#168365942
#41×D2332
C2×#41×C2332
#585233