Subgroups — C₂³×C₁₁×SD₁₆ #13066413

Order 1408.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×SD₁₆	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×C₁₁	—	2	1	no	—
6	C₂²×Q₈×C₁₁	—	2	7	no	—
7	C₂²×Q₈×C₁₁	C₂²	1	14	yes	complemented
8	C₂²×D₄×C₁₁	—	2	7	no	—
9	C₂²×D₄×C₁₁	C₂²	1	14	yes	—
10	C₂³×C₄×C₁₁	—	2	1	no	—
11	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×SD₁₆	C₂²	1	112	yes	direct product factor
13	C₂²×C₈×C₁₁	C₂²	1	14	yes	complemented
14	C₂⁴×C₁₁	—	2	14	no	—
15	C₂⁴×C₁₁	—	4	8	no	—
16	C₂⁴×C₁₁	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₁₁	—	2	42	no	—
18	C₂×Q₈×C₁₁	C₂³	1	28	yes	complemented
19	C₂×D₄×C₁₁	—	2	42	no	—
20	C₂×D₄×C₁₁	C₂³	1	28	yes	—
21	C₂²×C₄×C₁₁	—	2	14	no	—
22	C₂²×C₄×C₁₁	D₄	1	7	yes	—
23	C₂²×C₄×C₁₁	C₂³	1	7	yes	—
24	C₁₁×SD₁₆	C₂³	1	64	yes	direct product factor
25	C₂×C₈×C₁₁	C₂³	1	28	yes	complemented
26	C₂³×SD₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂³×C₁₁	—	2	28	no	—
28	C₂³×C₁₁	—	4	56	no	—
29	C₂³×C₁₁	SD₁₆	1	8	yes	direct product factor
30	C₂³×C₁₁	C₂×D₄	1	7	yes	—
31	Q₈×C₁₁	—	2	28	no	—
32	Q₈×C₁₁	C₂⁴	1	8	yes	complemented
33	D₄×C₁₁	—	2	28	no	—
34	D₄×C₁₁	C₂⁴	1	8	yes	—
35	C₂×C₄×C₁₁	—	2	28	no	—
36	C₂×C₄×C₁₁	C₂×D₄	1	21	yes	—
37	C₂×C₄×C₁₁	C₂⁴	1	7	yes	—
38	C₈×C₁₁	C₂⁴	1	8	yes	complemented
39	C₂³×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
40	C₂³×D₄	C₂×C₁₁	1	1	yes	characteristic
41	C₂²×SD₁₆	C₂×C₁₁	1	28	yes	direct product factor
42	C₂³×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
43	C₂²×C₁₁	—	2	8	no	—
44	C₂²×C₁₁	—	4	56	no	—
45	C₂²×C₁₁	C₂×SD₁₆	1	28	yes	direct product factor
46	C₂²×C₁₁	C₂²×D₄	1	7	yes	—
47	C₄×C₁₁	—	2	8	no	—
48	C₄×C₁₁	C₂²×D₄	1	7	yes	—
49	C₄×C₁₁	C₂⁵	1	1	yes	characteristic
50	C₂⁵	—	2	1	no	—
51	C₂²×Q₈	—	2	7	no	—
52	C₂²×Q₈	C₂²×C₁₁	1	14	yes	complemented
53	C₂²×D₄	—	2	7	no	—
54	C₂²×D₄	C₂²×C₁₁	1	14	yes	—
55	C₂³×C₄	—	2	1	no	—
56	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic
57	C₂×SD₁₆	C₂²×C₁₁	1	112	yes	direct product factor
58	C₂²×C₈	C₂²×C₁₁	1	14	yes	complemented
59	C₂×C₁₁	—	4	8	no	—
60	C₂×C₁₁	C₂²×SD₁₆	1	14	yes	direct product factor
61	C₂×C₁₁	C₂³×D₄	1	1	yes	characteristic
62	C₂⁴	—	2	14	no	—
63	C₂⁴	—	4	8	no	—
64	C₂⁴	D₄×C₁₁	1	1	yes	characteristic
65	C₂×Q₈	—	2	42	no	—
66	C₂×Q₈	C₂³×C₁₁	1	28	yes	complemented
67	C₂×D₄	—	2	42	no	—
68	C₂×D₄	C₂³×C₁₁	1	28	yes	—
69	C₂²×C₄	—	2	14	no	—
70	C₂²×C₄	D₄×C₁₁	1	7	yes	—
71	C₂²×C₄	C₂³×C₁₁	1	7	yes	—
72	SD₁₆	C₂³×C₁₁	1	64	yes	direct product factor
73	C₂×C₈	C₂³×C₁₁	1	28	yes	complemented
74	C₁₁	C₂³×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
75	C₂³	—	2	28	no	—
76	C₂³	—	4	56	no	—
77	C₂³	C₁₁×SD₁₆	1	8	yes	direct product factor
78	C₂³	C₂×D₄×C₁₁	1	7	yes	—
79	Q₈	—	2	28	no	—
80	Q₈	C₂⁴×C₁₁	1	8	yes	complemented
81	D₄	—	2	28	no	—
82	D₄	C₂⁴×C₁₁	1	8	yes	—
83	C₂×C₄	—	2	28	no	—
84	C₂×C₄	C₂×D₄×C₁₁	1	21	yes	—
85	C₂×C₄	C₂⁴×C₁₁	1	7	yes	—
86	C₈	C₂⁴×C₁₁	1	8	yes	complemented
87	C₂²	—	2	8	no	—
88	C₂²	—	4	56	no	—
89	C₂²	C₂×C₁₁×SD₁₆	1	28	yes	direct product factor
90	C₂²	C₂²×D₄×C₁₁	1	7	yes	—
91	C₄	—	2	8	no	—
92	C₄	C₂²×D₄×C₁₁	1	7	yes	—
93	C₄	C₂⁵×C₁₁	1	1	yes	characteristic
94	C₂	—	4	8	no	—
95	C₂	C₂²×C₁₁×SD₁₆	1	14	yes	direct product factor
96	C₂	C₂³×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₁	D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₁₁
prime radical	C₂³×D₄×C₁₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×C₁₁	C₂	semidirect
3. C₂²×C₁₁×SD₁₆	C₂	direct (N × H)
4. C₂³×C₈×C₁₁	C₂	semidirect
7. C₂²×Q₈×C₁₁	C₂²	semidirect
12. C₂×C₁₁×SD₁₆	C₂²	direct (N × H)
13. C₂²×C₈×C₁₁	C₂²	semidirect
18. C₂×Q₈×C₁₁	C₂³	semidirect
24. C₁₁×SD₁₆	C₂³	direct (N × H)
25. C₂×C₈×C₁₁	C₂³	semidirect
26. C₂³×SD₁₆	C₁₁	direct (N × H)
29. C₂³×C₁₁	SD₁₆	direct (N × H)
32. Q₈×C₁₁	C₂⁴	semidirect
38. C₈×C₁₁	C₂⁴	semidirect
39. C₂³×Q₈	C₂×C₁₁	semidirect
41. C₂²×SD₁₆	C₂×C₁₁	direct (N × H)
42. C₂³×C₈	C₂×C₁₁	semidirect
45. C₂²×C₁₁	C₂×SD₁₆	direct (N × H)
52. C₂²×Q₈	C₂²×C₁₁	semidirect
57. C₂×SD₁₆	C₂²×C₁₁	direct (N × H)
58. C₂²×C₈	C₂²×C₁₁	semidirect
60. C₂×C₁₁	C₂²×SD₁₆	direct (N × H)
66. C₂×Q₈	C₂³×C₁₁	semidirect
72. SD₁₆	C₂³×C₁₁	direct (N × H)
73. C₂×C₈	C₂³×C₁₁	semidirect
74. C₁₁	C₂³×SD₁₆	direct (N × H)
77. C₂³	C₁₁×SD₁₆	direct (N × H)
80. Q₈	C₂⁴×C₁₁	semidirect
86. C₈	C₂⁴×C₁₁	semidirect
89. C₂²	C₂×C₁₁×SD₁₆	direct (N × H)
95. C₂	C₂²×C₁₁×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×C₁₁	2
C₂³×D₄×C₁₁	2
C₂²×C₁₁×SD₁₆	2
C₂³×C₈×C₁₁	2
C₂³×SD₁₆	11

Subgroups — C23×C11×SD16 #13066413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₁×SD₁₆ #13066413