Subgroups — C₂×#14582734 #19136892

Order 5504.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#14582734	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₄₄	—	2	1	no	—
6	D₆₈₈	—	2	1	no	—
7	D₆₈₈	C₂²	1	2	yes	complemented
8	C₄₃⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₈×C₄₃	—	2	1	no	—
10	D₁₆×C₄₃	—	2	1	no	—
11	D₁₆×C₄₃	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₄₃	—	4	1	no	—
14	C₂×D₁₇₂	—	4	1	no	—
15	D₈×C₄₃	—	2	2	no	—
16	D₈×C₄₃	—	4	1	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	D₃₄₄	—	2	2	no	—
19	D₃₄₄	—	4	1	no	—
20	C₁₆×C₄₃	D₄	1	1	yes	characteristic
21	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
22	C₂³×C₄₃	—	8	1	no	—
23	C₂²×D₄₃	—	8	1	no	—
24	D₄×C₄₃	—	4	2	no	—
25	D₄×C₄₃	—	8	1	no	—
26	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
27	D₁₇₂	—	4	2	no	—
28	D₁₇₂	—	8	1	no	—
29	C₈×C₄₃	D₈	1	1	yes	characteristic
30	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄₃	—	8	2	no	—
32	C₂²×C₄₃	—	16	2	no	—
33	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
34	C₂×D₄₃	—	8	2	no	—
35	C₂×D₄₃	—	16	2	no	—
36	C₄×C₄₃	D₁₆	1	1	yes	characteristic
37	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
38	C₂×D₃₂	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	—	16	2	no	—
40	C₂×C₄₃	D₃₂	1	2	yes	complemented
41	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
42	D₄₃	—	16	2	no	—
43	C₂×D₁₆	—	43	1	no	—
44	C₂×D₁₆	D₄₃	1	1	yes	characteristic, complemented
45	D₃₂	—	43	4	no	—
46	C₂×C₃₂	—	43	1	no	—
47	C₄₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	—	86	1	no	—
50	D₁₆	—	2	1	no	—
51	D₁₆	—	43	2	no	—
52	D₁₆	—	86	1	no	—
53	D₁₆	C₂×D₄₃	1	2	yes	complemented
54	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
55	C₃₂	—	43	2	no	—
56	C₂×D₄	—	4	1	no	—
57	C₂×D₄	—	172	1	no	—
58	D₈	—	2	2	no	—
59	D₈	—	4	1	no	—
60	D₈	—	86	2	no	—
61	D₈	—	172	1	no	—
62	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
63	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
64	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
65	C₂³	—	8	1	no	—
66	C₂³	—	344	1	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	1	no	—
69	D₄	—	344	1	no	—
70	D₄	—	172	2	no	—
71	C₂×C₄	#10621882	1	1	yes	characteristic
72	C₈	#10621882	1	1	yes	characteristic
73	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
74	C₂²	—	8	2	no	—
75	C₂²	—	16	2	no	—
76	C₂²	—	344	2	no	—
77	C₂²	—	688	2	no	—
78	C₂²	#13063266	1	1	yes	characteristic
79	C₄	#13063266	1	1	yes	characteristic
80	C₄	C₂×#10621882	1	1	yes	characteristic
81	C₂	—	16	2	no	—
82	C₂	—	688	2	no	—
83	C₂	#14582734	1	2	yes	direct product factor
84	C₂	C₂×#13063266	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063266
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×D₁₆×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×D₁₆	D₄₃
hypocenter	C₄₃	C₂×D₃₂
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₆₈₈	C₂	semidirect
2. #14582734	C₂	direct (N × H)
3. C₂×C₄₃⋊C₃₂	C₂	semidirect
4. C₂×D₁₆×C₄₃	C₂	semidirect
7. D₆₈₈	C₂²	semidirect
8. C₄₃⋊C₃₂	C₂²	semidirect
11. D₁₆×C₄₃	C₂²	semidirect
40. C₂×C₄₃	D₃₂	semidirect
44. C₂×D₁₆	D₄₃	semidirect
47. C₄₃	C₂×D₃₂	semidirect
53. D₁₆	C₂×D₄₃	semidirect
83. C₂	#14582734	direct (N × H)

Subgroups — C2×#14582734 #19136892

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582734 #19136892