Finite Group Databasebeta

← #28405385

Subgroups — #28405385

Order 14464.

5992 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.

normal subgroups only

This group has 5992 conjugacy classes of subgroups — too many to draw. Only its 3201 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#20299435C2112yesmaximal, complemented
2#20299434C2115yesmaximal, complemented
3C2×#16813668C2115yesmaximal, complemented
4H(5,𝔽2)×D113C2120yesmaximal, complemented
5#585×C113C211yesmaximal, characteristic, complemented
6#16813670C22130yescomplemented
7#16813669C22120yescomplemented
8#16813668C221120yescomplemented
9#16813668C22160yescomplemented
10#16813667C22190yescomplemented
11C2×#14268648C22130yescomplemented
12C2×#14268647C22145yescomplemented
13#41×D113C221120yescomplemented
14C22×D452C22115yescomplemented
15C2×D4×D113C22190yescomplemented
162−1+4×C113C2216yescomplemented
17H(5,𝔽2)×C113C22110yescomplemented
18C2×#41×C113C22115yescomplemented
19C23×D113C23130yescomplemented
20#14268648C231120yescomplemented
21#14268647C231180yescomplemented
22#14268647C23160yescomplemented
23#14268646C231120yescomplemented
24C2×Dic226C23115yescomplemented
25Q8×D113C23140yescomplemented
26C2×D452C23190yescomplemented
27C2×D452C23145yescomplemented
28C2×C22⋊D113C23190yescomplemented
29D4×D113C231360yescomplemented
30C2×C4×D113C23190yescomplemented
31#41×C113C23160yescomplemented
32#41×C113C23120yescomplemented
33C2×Q8×C113C23115yescomplemented
34C2×D4×C113C23145yescomplemented
35C22×C4×C113C23115yescomplemented
36C23×C113C24115yes—
37C22×D113—830no—
38C22×D113C24190yes—
39Q8×C113C24120yes—
40D4×C113C24160yes—
41C2×C4×C113C24115yes—
42C2×C4×C113C24145yes—
43C22⋊D113C241120yes—
44C2×Dic113C24130yes—
45D452C24190yes—
46D452C24110yes—
47C4×D113C241120yes—
48Dic226C24130yes—
49Dic226C2416yes—
50C22×C113—415no—
51C22×C113C25115yes—
52C2×D113—490no—
53C2×D113C25120yes—
54C4×C113C2511yescharacteristic
55C4×C113C25115yes—
56Dic113C25112yes—
57C2×C113—215no—
58C2×C113C2611yescharacteristic
59D113—220no—
60H(7,𝔽2)—1131nomaximal, Sylow
61C113H(7,𝔽2)11yescharacteristic, complemented, Sylow
62#585—11312no—
63#585—11315no—
64#585D11311yescharacteristic, complemented
65C2×H(5,𝔽2)—11320no—
66C2×H(5,𝔽2)—11315no—
672−1+4—11320no—
682−1+4—11330no—
692−1+4C2×D11316yescomplemented
70H(5,𝔽2)—113120no—
71H(5,𝔽2)—11360no—
72H(5,𝔽2)—11390no—
73H(5,𝔽2)C2×D113110yescomplemented
74C2×#41—113120no—
75C2×#41—11330no—
76C2×#41—11345no—
77C2×#41C2×D113115yescomplemented
78C22×D4—11390no—
79C22×D4—11315no—
80C24—11330no—
81#41—113120no—
82#41—113120no—
83#41—113180no—
84#41—11360no—
85#41C22×D113160yescomplemented
86#41C22×D113120yescomplemented
87C2×Q8—11340no—
88C2×Q8—11315no—
89C2×Q8C22×D113115yescomplemented
90C2×D4—11390no—
91C2×D4—113360no—
92C2×D4—11390no—
93C2×D4—11345no—
94C2×D4C22×D113145yescomplemented
95C22×C4—11390no—
96C22×C4C22×D113115yescomplemented
97C23—11390no—
98C23—90430no—
99C23C23×D113115yes—
100Q8—11330no—
101Q8—1136no—
102Q8C23×D113120yes—
103D4—113120no—
104D4—11390no—
105D4—11310no—
106D4C23×D113160yes—
107C2×C4—11330no—
108C2×C4—113120no—
109C2×C4C23×D113145yes—
110C2×C4C23×D113115yes—
111C22—415no—
112C22—11320no—
113C22—45290no—
114C22C24×D113115yes—
115C4—11312no—
116C4C24×D113115yes—
117C4C24×D11311yescharacteristic
118C2—215no—
119C2—22620no—
120C2C25×D11311yescharacteristic
subgroupG/H
center, FrattiniC2C25×D113
commutator, socle, cosocleC2×C113C26
Fitting#585×C113C2
hypercenter#585D113
hypocenterC113H(7,𝔽2)
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. #20299435C2semidirect
2. #20299434C2semidirect
3. C2×#16813668C2semidirect
4. H(5,𝔽2)×D113C2semidirect
5. #585×C113C2semidirect
6. #16813670C22semidirect
7. #16813669C22semidirect
8. #16813668C22semidirect
9. #16813668C22semidirect
10. #16813667C22semidirect
11. C2×#14268648C22semidirect
12. C2×#14268647C22semidirect
13. #41×D113C22semidirect
14. C22×D452C22semidirect
15. C2×D4×D113C22semidirect
16. 2−1+4×C113C22semidirect
17. H(5,𝔽2)×C113C22semidirect
18. C2×#41×C113C22semidirect
19. C23×D113C23semidirect
20. #14268648C23semidirect
21. #14268647C23semidirect
22. #14268647C23semidirect
23. #14268646C23semidirect
24. C2×Dic226C23semidirect
25. Q8×D113C23semidirect
26. C2×D452C23semidirect
27. C2×D452C23semidirect
28. C2×C22⋊D113C23semidirect
29. D4×D113C23semidirect
30. C2×C4×D113C23semidirect
31. #41×C113C23semidirect
32. #41×C113C23semidirect
33. C2×Q8×C113C23semidirect
34. C2×D4×C113C23semidirect
35. C22×C4×C113C23semidirect
61. C113H(7,𝔽2)semidirect
64. #585D113semidirect
69. 2−1+4C2×D113semidirect
73. H(5,𝔽2)C2×D113semidirect
77. C2×#41C2×D113semidirect
85. #41C22×D113semidirect
86. #41C22×D113semidirect
89. C2×Q8C22×D113semidirect
94. C2×D4C22×D113semidirect
96. C22×C4C22×D113semidirect

Maximal subgroups

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

subgroupindex
#202994352
#202994342
C2×#168136682
H(5,𝔽2)×D1132
#585×C1132
H(7,𝔽2)113