Finite Group Databasebeta

← #36374980

Subgroups — #36374980

Order 22336.

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#26013687C212yesmaximal, complemented
2#26013686C214yesmaximal, complemented
3#26013685C214yesmaximal, complemented
4#26013684C216yesmaximal, complemented
5C2×#19150233C216yesmaximal, complemented
6#41×D349C218yesmaximal, complemented
7C2×#41×C349C211yesmaximal, characteristic, complemented
8#19150234C2218yescomplemented
9#19150233C22112yescomplemented
10#19150233C2214yescomplemented
11#19150233C22112yescomplemented
12#19150233C22112yescomplemented
13#19150232C22124yescomplemented
14C2×Dic698C2216yescomplemented
15Q8×D349C2218yescomplemented
16C2×D1396C2216yescomplemented
17C2×C22⋊D349C22112yescomplemented
18D4×D349C22124yescomplemented
19C2×C4×D349C22112yescomplemented
20#41×C349C2214yescomplemented
21#41×C349C2214yescomplemented
22C2×Q8×C349C2211yescharacteristic, complemented
23C2×D4×C349C2213yescomplemented
24C22×C4×C349C2213yescomplemented
25C22×D349C23112yes—
26Dic698C23112yes—
27Dic698C2314yes—
28D1396C23112yes—
29D1396C2314yes—
30C22⋊D349C23124yes—
31C22⋊D349C2318yes—
32C2×Dic349C23112yes—
33C4×D349C2318yes—
34C4×D349C23124yes—
35C23×C349C2313yes—
36Q8×C349C2314yes—
37D4×C349C23112yes—
38C2×C4×C349C2311yescharacteristic
39C2×C4×C349C2313yes—
40C2×C4×C349C2316yes—
41C2×C4×C349C2316yes—
42C22×C349—43no—
43C22×C349C2411yescharacteristic
44C22×C349C2416yes—
45C2×D349—412no—
46C2×D349C2418yes—
47C4×C349C2411yescharacteristic
48C4×C349C2416yes—
49C4×C349C2411yescharacteristic
50Dic349C2418yes—
51C2×C349—26no—
52C2×C349—21no—
53C2×C349C2511yescharacteristic
54D349—28no—
55C349#58511yescharacteristic, complemented, Sylow
56#585—3491nomaximal, Sylow
572−1+4—3494no—
582−1+4—3492no—
59H(5,𝔽2)—3494no—
60H(5,𝔽2)—3496no—
61C2×#41—3498no—
62C2×#41—3496no—
63C2×#41D34911yescharacteristic, complemented
64#41—3498no—
65#41—34924no—
66#41—34912no—
67#41—3494no—
68#41—34912no—
69#41—34912no—
70#41C2×D34914yescomplemented
71#41C2×D34914yescomplemented
72C2×Q8—3498no—
73C2×Q8—3496no—
74C2×Q8C2×D34911yescharacteristic, complemented
75C2×D4—34912no—
76C2×D4—34924no—
77C2×D4—3496no—
78C2×D4C2×D34913yescomplemented
79C22×C4—34912no—
80C22×C4C2×D34913yescomplemented
81C23—34912no—
82C23C22×D34913yes—
83Q8—34912no—
84Q8—3494no—
85Q8C22×D34914yes—
86D4—34924no—
87D4—3498no—
88D4—34912no—
89D4—3494no—
90D4C22×D349112yes—
91C2×C4—34912no—
92C2×C4—34924no—
93C2×C4—3498no—
94C2×C4C22×D34916yes—
95C2×C4C22×D34913yes—
96C2×C4C22×D34916yes—
97C2×C4C22×D34911yescharacteristic
98C22—43no—
99C22—3498no—
100C22—139612no—
101C22C23×D34916yes—
102C22C23×D34911yescharacteristic
103C4—3498no—
104C4C23×D34916yes—
105C4C23×D34911yescharacteristic
106C4C23×D34911yescharacteristic
107C2—21no—
108C2—26no—
109C2—6988no—
110C2C24×D34911yescharacteristic
subgroupG/H
centerC4C23×D349
commutator, socle, cosocleC2×C349C25
FrattiniC2C24×D349
FittingC2×#41×C349C2
hypercenterC2×#41D349
hypocenterC349#585
LCSG ▷ C2×C349 ▷ C349
UCSC1 ◁ C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #26013687C2semidirect
2. #26013686C2semidirect
3. #26013685C2semidirect
4. #26013684C2semidirect
5. C2×#19150233C2semidirect
6. #41×D349C2semidirect
7. C2×#41×C349C2semidirect
8. #19150234C22semidirect
9. #19150233C22semidirect
10. #19150233C22semidirect
11. #19150233C22semidirect
12. #19150233C22semidirect
13. #19150232C22semidirect
14. C2×Dic698C22semidirect
15. Q8×D349C22semidirect
16. C2×D1396C22semidirect
17. C2×C22⋊D349C22semidirect
18. D4×D349C22semidirect
19. C2×C4×D349C22semidirect
20. #41×C349C22semidirect
21. #41×C349C22semidirect
22. C2×Q8×C349C22semidirect
23. C2×D4×C349C22semidirect
24. C22×C4×C349C22semidirect
55. C349#585semidirect
63. C2×#41D349semidirect
70. #41C2×D349semidirect
71. #41C2×D349semidirect
74. C2×Q8C2×D349semidirect
78. C2×D4C2×D349semidirect
80. C22×C4C2×D349semidirect

Maximal subgroups

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

subgroupindex
#260136872
#260136862
#260136852
#260136842
C2×#191502332
#41×D3492
C2×#41×C3492
#585349