Subgroups — #19136910

Order 5504.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583331	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582738	C₂	1	2	yes	maximal, complemented
4	D₁₃₇₆	C₂	1	2	yes	maximal, complemented
5	C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063347	—	2	1	no	—
7	C₂×D₃₄₄	—	2	1	no	—
8	Dic₃₄₄	C₂²	1	1	yes	characteristic, complemented
9	#13063270	—	2	1	no	—
10	D₆₈₈	—	2	1	no	—
11	D₆₈₈	C₂²	1	2	yes	—
12	D₆₈₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₃₂×C₄₃	C₂²	1	2	yes	complemented
15	#10621898	—	4	1	no	—
16	C₂×D₁₇₂	—	4	1	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	Dic₁₇₂	—	2	1	no	—
19	D₃₄₄	—	2	2	no	—
20	D₃₄₄	—	2	1	no	—
21	D₃₄₄	—	4	1	no	—
22	#10621873	—	4	1	no	—
23	C₁₆×C₄₃	D₄	1	1	yes	characteristic
24	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×D₄₃	—	8	1	no	—
26	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
27	C₂²⋊D₄₃	—	8	1	no	—
28	D₁₇₂	—	4	1	no	—
29	D₁₇₂	—	4	2	no	—
30	D₁₇₂	—	8	1	no	—
31	C₄×D₄₃	—	8	1	no	—
32	Dic₈₆	—	4	1	no	—
33	C₈×C₄₃	D₈	1	1	yes	characteristic
34	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
36	C₂×D₄₃	—	8	2	no	—
37	C₂×D₄₃	—	8	1	no	—
38	C₂×D₄₃	—	16	2	no	—
39	C₄×C₄₃	D₁₆	1	1	yes	characteristic
40	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
41	Dic₄₃	—	8	1	no	—
42	#2263	—	43	1	no	maximal, Sylow
43	C₂×C₄₃	—	2	1	no	—
44	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
45	D₄₃	—	16	1	no	—
46	D₄₃	—	16	2	no	—
47	#508	—	43	1	no	—
48	C₂×D₁₆	—	43	1	no	—
49	SD₆₄	—	43	2	no	—
50	D₃₂	—	43	2	no	—
51	M₆₄	D₄₃	1	1	yes	characteristic, complemented
52	C₄₃	#2263	1	1	yes	characteristic, complemented, Sylow
53	#135	—	86	1	no	—
54	C₂×D₈	—	86	1	no	—
55	Q₃₂	—	43	1	no	—
56	SD₃₂	—	86	1	no	—
57	D₁₆	—	43	2	no	—
58	D₁₆	—	43	1	no	—
59	D₁₆	—	86	1	no	—
60	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
61	C₃₂	C₂×D₄₃	1	2	yes	complemented
62	#41	—	172	1	no	—
63	C₂×D₄	—	172	1	no	—
64	Q₁₆	—	86	1	no	—
65	SD₁₆	—	172	1	no	—
66	D₈	—	86	2	no	—
67	D₈	—	86	1	no	—
68	D₈	—	172	1	no	—
69	C₂×C₈	D₁₇₂	1	1	yes	characteristic
70	C₁₆	D₁₇₂	1	1	yes	characteristic
71	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
72	C₂³	—	344	1	no	—
73	Q₈	—	172	1	no	—
74	D₄	—	344	1	no	—
75	D₄	—	344	1	no	—
76	D₄	—	172	2	no	—
77	D₄	—	172	1	no	—
78	C₂×C₄	—	344	1	no	—
79	C₂×C₄	D₃₄₄	1	1	yes	characteristic
80	C₈	D₃₄₄	1	1	yes	characteristic
81	C₈	C₂×D₁₇₂	1	1	yes	characteristic
82	C₂²	—	344	1	no	—
83	C₂²	—	344	2	no	—
84	C₂²	—	688	2	no	—
85	C₂²	D₆₈₈	1	1	yes	characteristic
86	C₄	—	344	1	no	—
87	C₄	D₆₈₈	1	1	yes	characteristic
88	C₄	C₂×D₃₄₄	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	688	2	no	—
91	C₂	—	688	1	no	—
92	C₂	C₂×D₆₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₆₈₈
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₄₃×M₆₄	C₂
socle	C₂×C₄₃	C₂×D₁₆
hypercenter	M₆₄	D₄₃
hypocenter	C₄₃	#2263
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
1. #14583331	C₂	semidirect
2. C₂×D₆₈₈	C₂	semidirect
3. #14582738	C₂	semidirect
4. D₁₃₇₆	C₂	semidirect
5. C₄₃×M₆₄	C₂	semidirect
8. Dic₃₄₄	C₂²	semidirect
12. D₆₈₈	C₂²	semidirect
14. C₃₂×C₄₃	C₂²	semidirect
51. M₆₄	D₄₃	semidirect
52. C₄₃	#2263	semidirect
61. C₃₂	C₂×D₄₃	semidirect