Finite Group Databasebeta

← #11761403

Subgroups — #11761403

Order 1056.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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#10587283C211yesmaximal, characteristic, complemented
2C11×#239C211yesmaximal, characteristic, complemented
3C3×#4343C211yesmaximal, characteristic, complemented
4#10587239C213yesmaximal, complemented
5D3×D44C213yesmaximal, complemented
6D11×D12C213yesmaximal, complemented
7#10587233C213yesmaximal, complemented
8#67042—31nomaximal, Hall
9C2×D3×D11C2216yescomplemented
10C3×Q8×C11C2211yescharacteristic, complemented
11D132C2213yescomplemented
12C4×D33C2213yescomplemented
13C11×D12C2213yescomplemented
14C4×D3×C11C2213yescomplemented
15C3×D44C2213yescomplemented
16C3×C4×D11C2213yescomplemented
17#63143C2211yescharacteristic, complemented
18#63142C2213yescomplemented
19#63141C2213yescomplemented
20#63140C2213yescomplemented
21C11×#41—31no—
22#4343—31no—
23#4343D311yescharacteristic, complemented
24D4×D11—33no—
25D4×D11—33no—
26#4339—33no—
27C2×D44—33no—
28C2×D33C2313yes—
29C2×D3×C11C2313yes—
30C2×C3×D11C2313yes—
31D3×D11—46no—
32C3×C4×C11C2313yes—
33Dic33C2311yescharacteristic
34C3×Dic11C2311yescharacteristic
35C11×Dic3C2311yescharacteristic
36#1009—111nomaximal, Hall
37C22×D11—36no—
38Q8×C11C2×D311yescharacteristic, complemented
39D4×C11—33no—
40C2×C4×C11—33no—
41C22⋊D11—33no—
42C22⋊D11—33no—
43D44—33no—
44D44—33no—
45D44C2×D313yescomplemented
46C4×D11—33no—
47C4×D11C2×D313yescomplemented
48Dic22—31no—
49C2×C3×C11C2411yescharacteristic
50D33—23no—
51C3×D11—23no—
52D3×C11—23no—
53C3×#41—111no—
54#239—111no—
55#239D1111yescharacteristic, complemented
56D3×D4—113no—
57D3×D4—113no—
58#235—113no—
59C2×D12—113no—
60C22×C11—33no—
61C2×D11—33no—
62C2×D11—126no—
63C2×D11C22×D313yes—
64C4×C11—31no—
65C4×C11C22×D313yes—
66Dic11—31no—
67Dic11C22×D311yescharacteristic
68C3×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
69H(5,𝔽2)—331noSylow
70C22×D3—116no—
71C3×Q8C2×D1111yescharacteristic, complemented
72C3×D4—113no—
73C2×C3×C4—113no—
74#67—113no—
75#67—113no—
76D12—113no—
77D12—113no—
78D12C2×D1113yescomplemented
79C4×D3—113no—
80C4×D3C2×D1113yescomplemented
81Dic6—111no—
82C2×C11—63no—
83C2×C11C23×D311yescharacteristic
84D11—23no—
85D11—63no—
86#41—31no—
87#41—111no—
88#41—333no—
89#41—331no—
90C2×D4—333no—
91C2×D4—333no—
92C2×D4—333no—
93C22×C3—113no—
94C2×D3—113no—
95C2×D3—446no—
96C2×D3C22×D1113yes—
97C3×C4—111no—
98C3×C4C22×D1113yes—
99Dic3—111no—
100Dic3C22×D1111yescharacteristic
101C11#100911yescharacteristic, complemented, Sylow
102C23—336no—
103Q8—331no—
104Q8D3×D1111yescharacteristic, complemented
105D4—33no—
106D4—113no—
107D4—333no—
108D4—333no—
109D4—333no—
110D4—333no—
111C2×C4—33no—
112C2×C4—113no—
113C2×C4—333no—
114C2×C3—223no—
115C2×C3C23×D1111yescharacteristic
116D3—23no—
117D3—223no—
118C22—33no—
119C22—113no—
120C22—333no—
121C22—1326no—
122C4—31no—
123C4—111no—
124C4—331no—
125C4C2×D3×D1113yes—
126C3#6704211yescharacteristic, complemented, Sylow
127C2—63no—
128C2—223no—
129C2—663no—
130C2C22×D3×D1111yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D11
commutator, socle, cosocleC2×C3×C11C24
FittingC3×Q8×C11C22
hypercenterQ8D3×D11
hypocenterC3×C11H(5,𝔽2)
LCSG ▷ C2×C3×C11 ▷ C3×C11
UCSC1 ◁ C2 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. #10587283C2semidirect
2. C11×#239C2semidirect
3. C3×#4343C2semidirect
4. #10587239C2semidirect
5. D3×D44C2semidirect
6. D11×D12C2semidirect
7. #10587233C2semidirect
9. C2×D3×D11C22semidirect
10. C3×Q8×C11C22semidirect
11. D132C22semidirect
12. C4×D33C22semidirect
13. C11×D12C22semidirect
14. C4×D3×C11C22semidirect
15. C3×D44C22semidirect
16. C3×C4×D11C22semidirect
17. #63143C22semidirect
18. #63142C22semidirect
19. #63141C22semidirect
20. #63140C22semidirect
23. #4343D3semidirect
38. Q8×C11C2×D3semidirect
45. D44C2×D3semidirect
47. C4×D11C2×D3semidirect
55. #239D11semidirect
68. C3×C11H(5,𝔽2)semidirect
71. C3×Q8C2×D11semidirect
78. D12C2×D11semidirect
80. C4×D3C2×D11semidirect
101. C11#1009semidirect
104. Q8D3×D11semidirect
126. C3#67042semidirect

Maximal subgroups

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

subgroupindex
#105872832
C11×#2392
C3×#43432
#105872392
D3×D442
D11×D122
#105872332
#670423
#100911