Finite Group Databasebeta

← #36378623

Subgroups — #36378623

Order 22592.

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#26015040C212yesmaximal, complemented
2#26015039C214yesmaximal, complemented
3#26015038C214yesmaximal, complemented
4#26015037C216yesmaximal, complemented
5C2×#19150737C216yesmaximal, complemented
6#41×D353C218yesmaximal, complemented
7C2×#41×C353C211yesmaximal, characteristic, complemented
8#19150738C2218yescomplemented
9#19150737C22112yescomplemented
10#19150737C2214yescomplemented
11#19150737C22112yescomplemented
12#19150737C22112yescomplemented
13#19150736C22124yescomplemented
14C2×Dic706C2216yescomplemented
15Q8×D353C2218yescomplemented
16C2×D1412C2216yescomplemented
17C2×C22⋊D353C22112yescomplemented
18D4×D353C22124yescomplemented
19C2×C4×D353C22112yescomplemented
20#41×C353C2214yescomplemented
21#41×C353C2214yescomplemented
22C2×Q8×C353C2211yescharacteristic, complemented
23C2×D4×C353C2213yescomplemented
24C22×C4×C353C2213yescomplemented
25C22×D353C23112yes—
26Dic706C23112yes—
27Dic706C2314yes—
28D1412C23112yes—
29D1412C2314yes—
30C22⋊D353C23124yes—
31C22⋊D353C2318yes—
32C2×Dic353C23112yes—
33C4×D353C2318yes—
34C4×D353C23124yes—
35C23×C353C2313yes—
36Q8×C353C2314yes—
37D4×C353C23112yes—
38C2×C4×C353C2311yescharacteristic
39C2×C4×C353C2313yes—
40C2×C4×C353C2316yes—
41C2×C4×C353C2316yes—
42C22×C353—43no—
43C22×C353C2411yescharacteristic
44C22×C353C2416yes—
45C2×D353—412no—
46C2×D353C2418yes—
47C4×C353C2411yescharacteristic
48C4×C353C2416yes—
49C4×C353C2411yescharacteristic
50Dic353C2418yes—
51C2×C353—26no—
52C2×C353—21no—
53C2×C353C2511yescharacteristic
54D353—28no—
55C353#58511yescharacteristic, complemented, Sylow
56#585—3531nomaximal, Sylow
572−1+4—3534no—
582−1+4—3532no—
59H(5,𝔽2)—3534no—
60H(5,𝔽2)—3536no—
61C2×#41—3538no—
62C2×#41—3536no—
63C2×#41D35311yescharacteristic, complemented
64#41—3538no—
65#41—35324no—
66#41—35312no—
67#41—3534no—
68#41—35312no—
69#41—35312no—
70#41C2×D35314yescomplemented
71#41C2×D35314yescomplemented
72C2×Q8—3538no—
73C2×Q8—3536no—
74C2×Q8C2×D35311yescharacteristic, complemented
75C2×D4—35312no—
76C2×D4—35324no—
77C2×D4—3536no—
78C2×D4C2×D35313yescomplemented
79C22×C4—35312no—
80C22×C4C2×D35313yescomplemented
81C23—35312no—
82C23C22×D35313yes—
83Q8—35312no—
84Q8—3534no—
85Q8C22×D35314yes—
86D4—35324no—
87D4—3538no—
88D4—35312no—
89D4—3534no—
90D4C22×D353112yes—
91C2×C4—35312no—
92C2×C4—35324no—
93C2×C4—3538no—
94C2×C4C22×D35316yes—
95C2×C4C22×D35313yes—
96C2×C4C22×D35316yes—
97C2×C4C22×D35311yescharacteristic
98C22—43no—
99C22—3538no—
100C22—141212no—
101C22C23×D35316yes—
102C22C23×D35311yescharacteristic
103C4—3538no—
104C4C23×D35316yes—
105C4C23×D35311yescharacteristic
106C4C23×D35311yescharacteristic
107C2—21no—
108C2—26no—
109C2—7068no—
110C2C24×D35311yescharacteristic
subgroupG/H
centerC4C23×D353
commutator, socle, cosocleC2×C353C25
FrattiniC2C24×D353
FittingC2×#41×C353C2
hypercenterC2×#41D353
hypocenterC353#585
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26015040C2semidirect
2. #26015039C2semidirect
3. #26015038C2semidirect
4. #26015037C2semidirect
5. C2×#19150737C2semidirect
6. #41×D353C2semidirect
7. C2×#41×C353C2semidirect
8. #19150738C22semidirect
9. #19150737C22semidirect
10. #19150737C22semidirect
11. #19150737C22semidirect
12. #19150737C22semidirect
13. #19150736C22semidirect
14. C2×Dic706C22semidirect
15. Q8×D353C22semidirect
16. C2×D1412C22semidirect
17. C2×C22⋊D353C22semidirect
18. D4×D353C22semidirect
19. C2×C4×D353C22semidirect
20. #41×C353C22semidirect
21. #41×C353C22semidirect
22. C2×Q8×C353C22semidirect
23. C2×D4×C353C22semidirect
24. C22×C4×C353C22semidirect
55. C353#585semidirect
63. C2×#41D353semidirect
70. #41C2×D353semidirect
71. #41C2×D353semidirect
74. C2×Q8C2×D353semidirect
78. C2×D4C2×D353semidirect
80. C22×C4C2×D353semidirect

Maximal subgroups

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

subgroupindex
#260150402
#260150392
#260150382
#260150372
C2×#191507372
#41×D3532
C2×#41×C3532
#585353