Subgroups — #19136904

Order 5504.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583331	C₂	1	2	yes	maximal, complemented
2	Dic₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582738	C₂	1	2	yes	maximal, complemented
4	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	—	2	2	no	—
7	Dic₃₄₄	C₂²	1	2	yes	—
8	#13063270	—	2	2	no	—
9	D₆₈₈	C₂²	1	2	yes	—
10	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
12	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
13	#10621898	—	4	2	no	—
14	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
15	Dic₁₇₂	—	2	2	no	—
16	D₃₄₄	—	2	2	no	—
17	#10621873	—	4	2	no	—
18	C₁₆×C₄₃	D₄	1	1	yes	characteristic
19	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
21	C₂²⋊D₄₃	—	8	2	no	—
22	D₁₇₂	—	4	2	no	—
23	C₄×D₄₃	—	8	2	no	—
24	Dic₈₆	—	4	2	no	—
25	C₈×C₄₃	D₈	1	1	yes	characteristic
26	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
28	C₂×D₄₃	—	8	2	no	—
29	C₄×C₄₃	D₁₆	1	1	yes	characteristic
30	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
31	Dic₄₃	—	8	2	no	—
32	#2262	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
35	D₄₃	—	16	2	no	—
36	#508	—	43	2	no	—
37	Q₆₄	—	43	1	no	—
38	SD₆₄	—	43	2	no	—
39	D₃₂	—	43	1	no	—
40	C₂×C₃₂	D₄₃	1	1	yes	characteristic, complemented
41	C₄₃	#2262	1	1	yes	characteristic, complemented, Sylow
42	#135	—	86	2	no	—
43	Q₃₂	—	43	2	no	—
44	SD₃₂	—	86	2	no	—
45	D₁₆	—	43	2	no	—
46	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
47	C₃₂	C₂×D₄₃	1	1	yes	characteristic
48	C₃₂	C₂×D₄₃	1	1	yes	characteristic
49	#41	—	172	2	no	—
50	Q₁₆	—	86	2	no	—
51	SD₁₆	—	172	2	no	—
52	D₈	—	86	2	no	—
53	C₂×C₈	D₁₇₂	1	1	yes	characteristic
54	C₁₆	D₁₇₂	1	1	yes	characteristic
55	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
56	Q₈	—	172	2	no	—
57	D₄	—	344	2	no	—
58	D₄	—	172	2	no	—
59	C₂×C₄	—	344	2	no	—
60	C₂×C₄	D₃₄₄	1	1	yes	characteristic
61	C₈	D₃₄₄	1	1	yes	characteristic
62	C₈	C₂×D₁₇₂	1	1	yes	characteristic
63	C₂²	—	344	2	no	—
64	C₂²	D₆₈₈	1	1	yes	characteristic
65	C₄	—	344	2	no	—
66	C₄	D₆₈₈	1	1	yes	characteristic
67	C₄	C₂×D₃₄₄	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	688	2	no	—
70	C₂	C₂×D₆₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₆₈₈
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₁₆
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	#2262
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #14583331	C₂	semidirect
2. Dic₆₈₈	C₂	semidirect
3. #14582738	C₂	semidirect
4. D₁₃₇₆	C₂	semidirect
5. C₂×C₃₂×C₄₃	C₂	semidirect
40. C₂×C₃₂	D₄₃	semidirect
41. C₄₃	#2262	semidirect