Subgroups — C₂³×D₃₄₄ #19149311

Order 5504.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₇₂	C₂	1	2	yes	maximal, complemented
2	C₂²×D₃₄₄	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×D₄₃	—	2	2	no	—
5	C₂²×D₁₇₂	—	2	14	no	—
6	C₂²×D₁₇₂	C₂²	1	28	yes	complemented
7	C₂×D₃₄₄	C₂²	1	112	yes	direct product factor
8	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₄₃	C₂²	1	14	yes	complemented
10	C₂⁴×C₄₃	D₄	1	1	yes	characteristic
11	C₂³×D₄₃	—	2	28	no	—
12	C₂³×D₄₃	—	4	16	no	—
13	C₂²×C₄×C₄₃	D₄	1	7	yes	—
14	C₂²×C₄×C₄₃	C₂³	1	7	yes	—
15	C₂×D₁₇₂	—	2	84	no	—
16	C₂×D₁₇₂	C₂³	1	56	yes	complemented
17	C₂×C₈×C₄₃	C₂³	1	28	yes	complemented
18	D₃₄₄	C₂³	1	64	yes	direct product factor
19	C₂³×C₄₃	D₈	1	8	yes	complemented
20	C₂³×C₄₃	C₂×D₄	1	7	yes	—
21	C₂²×D₄₃	—	2	56	no	—
22	C₂²×D₄₃	—	4	112	no	—
23	C₂×C₄×C₄₃	C₂×D₄	1	21	yes	—
24	C₂×C₄×C₄₃	C₂⁴	1	7	yes	—
25	D₁₇₂	—	2	56	no	—
26	D₁₇₂	C₂⁴	1	16	yes	complemented
27	C₈×C₄₃	C₂⁴	1	8	yes	complemented
28	C₂²×C₄₃	C₂×D₈	1	28	yes	complemented
29	C₂²×C₄₃	C₂²×D₄	1	7	yes	—
30	C₂×D₄₃	—	2	16	no	—
31	C₂×D₄₃	—	4	112	no	—
32	C₄×C₄₃	C₂²×D₄	1	7	yes	—
33	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
34	C₂³×D₈	—	43	1	no	maximal, Sylow
35	C₂×C₄₃	C₂²×D₈	1	14	yes	complemented
36	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
37	D₄₃	—	4	16	no	—
38	C₂³×D₄	—	43	2	no	—
39	C₂²×D₈	—	43	28	no	—
40	C₂³×C₈	D₄₃	1	1	yes	characteristic, complemented
41	C₄₃	C₂³×D₈	1	1	yes	characteristic, complemented, Sylow
42	C₂⁵	—	86	2	no	—
43	C₂²×D₄	—	43	28	no	—
44	C₂²×D₄	—	86	14	no	—
45	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
46	C₂×D₈	—	43	112	no	—
47	C₂²×C₈	C₂×D₄₃	1	14	yes	complemented
48	C₂⁴	—	86	28	no	—
49	C₂⁴	—	172	16	no	—
50	C₂⁴	D₁₇₂	1	1	yes	characteristic
51	C₂×D₄	—	43	56	no	—
52	C₂×D₄	—	86	84	no	—
53	C₂²×C₄	D₁₇₂	1	7	yes	—
54	C₂²×C₄	C₂²×D₄₃	1	7	yes	—
55	D₈	—	43	64	no	—
56	C₂×C₈	C₂²×D₄₃	1	28	yes	complemented
57	C₂³	—	86	56	no	—
58	C₂³	—	172	112	no	—
59	C₂³	D₃₄₄	1	8	yes	direct product factor
60	C₂³	C₂×D₁₇₂	1	7	yes	—
61	D₄	—	43	16	no	—
62	D₄	—	86	56	no	—
63	C₂×C₄	C₂×D₁₇₂	1	21	yes	—
64	C₂×C₄	C₂³×D₄₃	1	7	yes	—
65	C₈	C₂³×D₄₃	1	8	yes	complemented
66	C₂²	—	86	16	no	—
67	C₂²	—	172	112	no	—
68	C₂²	C₂×D₃₄₄	1	28	yes	direct product factor
69	C₂²	C₂²×D₁₇₂	1	7	yes	—
70	C₄	C₂²×D₁₇₂	1	7	yes	—
71	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
72	C₂	—	172	16	no	—
73	C₂	C₂²×D₃₄₄	1	14	yes	direct product factor
74	C₂	C₂³×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₁₇₂
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₂³×C₈×C₄₃	C₂
socle	C₂⁴×C₄₃	D₄
hypercenter	C₂³×C₈	D₄₃
hypocenter	C₄₃	C₂³×D₈
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×D₁₇₂	C₂	semidirect
2. C₂²×D₃₄₄	C₂	direct (N × H)
3. C₂³×C₈×C₄₃	C₂	semidirect
6. C₂²×D₁₇₂	C₂²	semidirect
7. C₂×D₃₄₄	C₂²	direct (N × H)
9. C₂²×C₈×C₄₃	C₂²	semidirect
16. C₂×D₁₇₂	C₂³	semidirect
17. C₂×C₈×C₄₃	C₂³	semidirect
18. D₃₄₄	C₂³	direct (N × H)
19. C₂³×C₄₃	D₈	semidirect
26. D₁₇₂	C₂⁴	semidirect
27. C₈×C₄₃	C₂⁴	semidirect
28. C₂²×C₄₃	C₂×D₈	semidirect
35. C₂×C₄₃	C₂²×D₈	semidirect
40. C₂³×C₈	D₄₃	semidirect
41. C₄₃	C₂³×D₈	semidirect
47. C₂²×C₈	C₂×D₄₃	semidirect
56. C₂×C₈	C₂²×D₄₃	semidirect
59. C₂³	D₃₄₄	direct (N × H)
65. C₈	C₂³×D₄₃	semidirect
68. C₂²	C₂×D₃₄₄	direct (N × H)
73. C₂	C₂²×D₃₄₄	direct (N × H)

Subgroups — C23×D344 #19149311

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×D₃₄₄ #19149311