Subgroups — C₂×#14582736 #19136895

Order 5504.

112 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
2	#14582736	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₃₂×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	—
8	C₄₃⋊C₃₂	C₂²	1	2	yes	complemented
9	C₂×Q₁₆×C₄₃	—	2	1	no	—
10	Q₃₂×C₄₃	—	2	1	no	—
11	Q₃₂×C₄₃	C₂²	1	2	yes	complemented
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₄₃	—	4	1	no	—
14	C₂×D₁₇₂	—	4	1	no	—
15	Q₁₆×C₄₃	—	2	2	no	—
16	Q₁₆×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	C₂²×D₄₃	—	8	1	no	—
23	Q₈×C₄₃	—	4	2	no	—
24	Q₈×C₄₃	—	8	1	no	—
25	C₂×C₄×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	D₁₆	1	1	yes	characteristic
32	C₂×D₄₃	—	8	2	no	—
33	C₂×D₄₃	—	16	2	no	—
34	C₄×C₄₃	—	8	2	no	—
35	C₄×C₄₃	D₁₆	1	1	yes	characteristic
36	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
37	C₂×SD₆₄	—	43	1	no	maximal, Sylow
38	C₂×C₄₃	SD₆₄	1	2	yes	complemented
39	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
40	D₄₃	—	16	2	no	—
41	C₂×Q₃₂	D₄₃	1	1	yes	characteristic, complemented
42	C₂×D₁₆	—	43	1	no	—
43	SD₆₄	—	43	4	no	—
44	C₂×C₃₂	—	43	1	no	—
45	C₄₃	C₂×SD₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂×Q₁₆	—	2	1	no	—
47	C₂×D₈	—	86	1	no	—
48	Q₃₂	—	2	1	no	—
49	Q₃₂	C₂×D₄₃	1	2	yes	complemented
50	D₁₆	—	43	2	no	—
51	D₁₆	—	86	1	no	—
52	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
53	C₃₂	—	43	2	no	—
54	C₂×Q₈	—	4	1	no	—
55	C₂×D₄	—	172	1	no	—
56	Q₁₆	—	2	2	no	—
57	Q₁₆	—	4	1	no	—
58	D₈	—	86	2	no	—
59	D₈	—	172	1	no	—
60	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
61	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
62	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
63	C₂³	—	344	1	no	—
64	Q₈	—	4	2	no	—
65	Q₈	—	8	1	no	—
66	D₄	—	344	1	no	—
67	D₄	—	172	2	no	—
68	C₂×C₄	—	8	1	no	—
69	C₂×C₄	#10621882	1	1	yes	characteristic
70	C₈	#10621882	1	1	yes	characteristic
71	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
72	C₂²	—	344	2	no	—
73	C₂²	—	688	2	no	—
74	C₂²	#13063266	1	1	yes	characteristic
75	C₄	—	8	2	no	—
76	C₄	#13063266	1	1	yes	characteristic
77	C₄	C₂×#10621882	1	1	yes	characteristic
78	C₂	—	688	2	no	—
79	C₂	#14582736	1	2	yes	direct product factor
80	C₂	C₂×#13063266	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063266
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×Q₃₂×C₄₃	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	C₂×Q₃₂	D₄₃
hypocenter	C₄₃	C₂×SD₆₄
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
2. #14582736	C₂	direct (N × H)
3. C₂×C₄₃⋊C₃₂	C₂	semidirect
4. C₂×Q₃₂×C₄₃	C₂	semidirect
8. C₄₃⋊C₃₂	C₂²	semidirect
11. Q₃₂×C₄₃	C₂²	semidirect
38. C₂×C₄₃	SD₆₄	semidirect
41. C₂×Q₃₂	D₄₃	semidirect
45. C₄₃	C₂×SD₆₄	semidirect
49. Q₃₂	C₂×D₄₃	semidirect
79. C₂	#14582736	direct (N × H)

Subgroups — C2×#14582736 #19136895

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582736 #19136895