Subgroups — #19132569

Order 5504.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583017	C₂	1	1	yes	maximal, characteristic
2	#14582720	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063347	C₄	1	1	yes	characteristic
5	#13063331	—	2	1	no	—
6	#13063265	—	2	1	no	—
7	#13063261	C₄	1	1	yes	characteristic
8	#13063253	—	2	1	no	—
9	C₄×C₈×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	#10621898	—	2	1	no	—
12	C₂×C₈×C₄₃	—	2	2	no	—
13	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
15	C₄²×C₄₃	D₄	1	1	yes	characteristic
16	#10621877	—	2	1	no	—
17	Dic₁₇₂	C₈	1	1	yes	characteristic, complemented
18	D₃₄₄	C₈	1	1	yes	characteristic, complemented
19	#10621873	—	2	1	no	—
20	#10621872	—	4	1	no	—
21	C₈×D₄₃	—	4	1	no	—
22	C₄₃⋊C₁₆	—	4	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₄₃	—	4	1	no	—
26	D₁₇₂	—	2	1	no	—
27	C₄×D₄₃	—	4	1	no	—
28	Dic₈₆	—	2	1	no	—
29	C₈×C₄₃	—	2	4	no	—
30	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₄₃	M₁₆	1	1	yes	characteristic
32	C₈×C₄₃	D₈	1	1	yes	characteristic
33	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
34	C₄₃⋊C₈	—	4	1	no	—
35	C₂²×C₄₃	#104	1	1	yes	characteristic
36	C₂×D₄₃	—	4	1	no	—
37	C₄×C₄₃	—	2	2	no	—
38	C₄×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₄₃	#102	1	1	yes	characteristic
40	Dic₄₃	—	4	1	no	—
41	#1335	—	43	1	no	maximal, Sylow
42	C₂×C₄₃	—	2	1	no	—
43	C₂×C₄₃	D₄⋊C₈	1	1	yes	characteristic
44	D₄₃	—	8	1	no	—
45	#443	—	43	1	no	—
46	#364	—	43	1	no	—
47	C₈²	D₄₃	1	1	yes	characteristic, complemented
48	C₄₃	#1335	1	1	yes	characteristic, complemented, Sylow
49	#135	—	43	1	no	—
50	#131	—	86	1	no	—
51	M₃₂	—	86	1	no	—
52	#108	—	43	1	no	—
53	#104	—	86	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
56	#41	—	86	1	no	—
57	Q₁₆	—	43	1	no	—
58	SD₁₆	—	86	1	no	—
59	D₈	—	43	1	no	—
60	M₁₆	—	86	1	no	—
61	M₁₆	—	172	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	172	1	no	—
64	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
65	C₂×C₈	D₁₇₂	1	1	yes	characteristic
66	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
67	C₁₆	—	172	1	no	—
68	Q₈	—	86	1	no	—
69	D₄	—	86	1	no	—
70	D₄	—	172	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	172	1	no	—
73	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
74	C₈	—	2	4	no	—
75	C₈	—	172	1	no	—
76	C₈	C₈×D₄₃	1	1	yes	characteristic
77	C₈	#10621872	1	1	yes	characteristic
78	C₈	#10621873	1	1	yes	characteristic
79	C₈	D₃₄₄	1	1	yes	characteristic
80	C₂²	—	172	1	no	—
81	C₂²	#13063253	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	172	1	no	—
84	C₄	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
85	C₄	#13063247	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	344	1	no	—
88	C₂	#14582628	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₃₄₄
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂×C₄₃	D₄⋊C₈
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1335
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #14582720	C₂	semidirect
3. C₈²×C₄₃	C₂	semidirect
17. Dic₁₇₂	C₈	semidirect
18. D₃₄₄	C₈	semidirect
47. C₈²	D₄₃	semidirect
48. C₄₃	#1335	semidirect