Subgroups — C₂³×#4313 #13083317

Order 1408.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#4313	C₂	1	28	yes	maximal, direct product factor
5	C₂⁴×D₁₁	C₄	1	1	yes	characteristic
6	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×Dic₁₁	C₄	1	1	yes	characteristic
8	C₂²×C₄×D₁₁	C₄	1	14	yes	—
9	C₂²×C₄×D₁₁	C₂²	1	14	yes	—
10	C₂²×C₈×C₁₁	C₂²	1	14	yes	complemented
11	C₂²×C₁₁⋊C₈	C₂²	1	14	yes	complemented
12	C₂×#4313	C₂²	1	112	yes	direct product factor
13	C₂⁴×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂³×D₁₁	—	2	8	no	—
15	C₂³×D₁₁	C₂×C₄	1	14	yes	—
16	C₂²×C₄×C₁₁	C₂×C₄	1	7	yes	—
17	C₂²×C₄×C₁₁	C₂³	1	7	yes	—
18	C₂²×Dic₁₁	C₂×C₄	1	14	yes	—
19	C₂×C₄×D₁₁	C₂×C₄	1	84	yes	—
20	C₂×C₄×D₁₁	C₂³	1	28	yes	—
21	C₂×C₈×C₁₁	C₂³	1	28	yes	complemented
22	C₂×C₁₁⋊C₈	C₂³	1	28	yes	complemented
23	#4313	C₂³	1	64	yes	direct product factor
24	C₂³×M₁₆	—	11	1	no	maximal, Sylow
25	C₂³×C₁₁	M₁₆	1	8	yes	complemented
26	C₂³×C₁₁	C₂²×C₄	1	7	yes	—
27	C₂²×D₁₁	—	2	56	no	—
28	C₂²×D₁₁	C₂²×C₄	1	28	yes	—
29	C₂×C₄×C₁₁	C₂²×C₄	1	21	yes	—
30	C₂×C₄×C₁₁	C₂⁴	1	7	yes	—
31	C₂×Dic₁₁	C₂²×C₄	1	28	yes	—
32	C₄×D₁₁	C₂²×C₄	1	56	yes	—
33	C₄×D₁₁	C₂⁴	1	8	yes	—
34	C₈×C₁₁	C₂⁴	1	8	yes	complemented
35	C₁₁⋊C₈	C₂⁴	1	8	yes	complemented
36	C₂⁴×C₄	—	11	1	no	—
37	C₂²×M₁₆	—	11	28	no	—
38	C₂³×C₈	—	11	1	no	—
39	C₂³×C₈	D₁₁	1	1	yes	characteristic, complemented
40	C₂²×C₁₁	C₂×M₁₆	1	28	yes	complemented
41	C₂²×C₁₁	C₂³×C₄	1	7	yes	—
42	C₂×D₁₁	—	2	56	no	—
43	C₂×D₁₁	C₂³×C₄	1	8	yes	—
44	C₄×C₁₁	C₂³×C₄	1	7	yes	—
45	C₄×C₁₁	C₂⁵	1	1	yes	characteristic
46	Dic₁₁	C₂³×C₄	1	8	yes	—
47	C₂⁵	—	11	1	no	—
48	C₂³×C₄	—	11	1	no	—
49	C₂³×C₄	—	11	14	no	—
50	C₂³×C₄	—	11	14	no	—
51	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic
52	C₂×M₁₆	—	11	112	no	—
53	C₂²×C₈	—	11	14	no	—
54	C₂²×C₈	C₂×D₁₁	1	14	yes	complemented
55	C₂×C₁₁	C₂²×M₁₆	1	14	yes	complemented
56	C₂×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
57	D₁₁	—	2	8	no	—
58	C₂⁴	—	11	14	no	—
59	C₂⁴	—	22	8	no	—
60	C₂⁴	C₄×D₁₁	1	1	yes	characteristic
61	C₂²×C₄	—	11	14	no	—
62	C₂²×C₄	—	11	84	no	—
63	C₂²×C₄	—	11	28	no	—
64	C₂²×C₄	C₄×D₁₁	1	7	yes	—
65	C₂²×C₄	C₂²×D₁₁	1	7	yes	—
66	M₁₆	—	11	64	no	—
67	C₂×C₈	—	11	28	no	—
68	C₂×C₈	C₂²×D₁₁	1	28	yes	complemented
69	C₁₁	C₂³×M₁₆	1	1	yes	characteristic, complemented, Sylow
70	C₂³	—	11	28	no	—
71	C₂³	—	22	56	no	—
72	C₂³	#4313	1	8	yes	direct product factor
73	C₂³	C₂×C₄×D₁₁	1	7	yes	—
74	C₂×C₄	—	11	28	no	—
75	C₂×C₄	—	11	56	no	—
76	C₂×C₄	—	11	8	no	—
77	C₂×C₄	C₂×C₄×D₁₁	1	21	yes	—
78	C₂×C₄	C₂³×D₁₁	1	7	yes	—
79	C₈	—	11	8	no	—
80	C₈	C₂³×D₁₁	1	8	yes	complemented
81	C₂²	—	11	8	no	—
82	C₂²	—	22	56	no	—
83	C₂²	C₂×#4313	1	28	yes	direct product factor
84	C₂²	C₂²×C₄×D₁₁	1	7	yes	—
85	C₄	—	11	8	no	—
86	C₄	C₂²×C₄×D₁₁	1	7	yes	—
87	C₄	C₂⁴×D₁₁	1	1	yes	characteristic
88	C₂	—	22	8	no	—
89	C₂	C₂²×#4313	1	14	yes	direct product factor
90	C₂	C₂³×C₄×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₁
Fitting	C₂³×C₈×C₁₁	C₂
socle	C₂⁴×C₁₁	C₂×C₄
prime radical	C₂⁴×D₁₁	C₄
cosocle	C₄×C₁₁	C₂⁵
hypercenter	C₂³×C₈	D₁₁
hypocenter	C₁₁	C₂³×M₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂³×C₈×C₁₁	C₂	semidirect
3. C₂³×C₁₁⋊C₈	C₂	semidirect
4. C₂²×#4313	C₂	direct (N × H)
10. C₂²×C₈×C₁₁	C₂²	semidirect
11. C₂²×C₁₁⋊C₈	C₂²	semidirect
12. C₂×#4313	C₂²	direct (N × H)
21. C₂×C₈×C₁₁	C₂³	semidirect
22. C₂×C₁₁⋊C₈	C₂³	semidirect
23. #4313	C₂³	direct (N × H)
25. C₂³×C₁₁	M₁₆	semidirect
34. C₈×C₁₁	C₂⁴	semidirect
35. C₁₁⋊C₈	C₂⁴	semidirect
39. C₂³×C₈	D₁₁	semidirect
40. C₂²×C₁₁	C₂×M₁₆	semidirect
54. C₂²×C₈	C₂×D₁₁	semidirect
55. C₂×C₁₁	C₂²×M₁₆	semidirect
68. C₂×C₈	C₂²×D₁₁	semidirect
69. C₁₁	C₂³×M₁₆	semidirect
72. C₂³	#4313	direct (N × H)
80. C₈	C₂³×D₁₁	semidirect
83. C₂²	C₂×#4313	direct (N × H)
89. C₂	C₂²×#4313	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×C₄×D₁₁	2
C₂³×C₈×C₁₁	2
C₂³×C₁₁⋊C₈	2
C₂²×#4313	2
C₂³×M₁₆	11

Subgroups — C23×#4313 #13083317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#4313 #13083317