Subgroups — #19132578

Order 5504.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583029	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₈₆	C₄	1	1	yes	characteristic
5	C₂×C₄₃⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₄₃⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₄₃⋊C₈	—	2	1	no	—
8	#13063235	—	2	1	no	—
9	C₂×C₁₆×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₈₆	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₄₃	C₈	1	1	yes	characteristic
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₄×Dic₄₃	—	2	1	no	—
18	C₂×C₄₃⋊C₈	—	2	1	no	—
19	C₁₆×C₄₃	—	2	2	no	—
20	C₄₃⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
24	C₂×Dic₄₃	—	2	1	no	—
25	C₂×Dic₄₃	—	2	1	no	—
26	Dic₈₆	—	4	1	no	—
27	C₈×C₄₃	—	2	1	no	—
28	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
29	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
30	C₄₃⋊C₈	—	4	1	no	—
31	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₄×C₄₃	—	2	1	no	—
33	C₄×C₄₃	—	2	1	no	—
34	C₄×C₄₃	#103	1	1	yes	characteristic
35	C₄×C₄₃	#104	1	1	yes	characteristic
36	Dic₄₃	—	4	1	no	—
37	Dic₄₃	—	4	1	no	—
38	#1338	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	Q₈⋊C₈	1	1	yes	characteristic
40	C₂×C₄₃	#349	1	1	yes	characteristic
41	C₂×C₄₃	#350	1	1	yes	characteristic
42	#446	—	43	1	no	—
43	C₄⋊C₁₆	—	43	1	no	—
44	#346	D₄₃	1	1	yes	characteristic
45	C₄₃	#1338	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₈	—	43	1	no	—
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	86	1	no	—
49	C₄⋊C₈	—	43	1	no	—
50	C₄⋊C₈	—	86	1	no	—
51	#97	—	86	1	no	—
52	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
53	C₂×Q₈	—	43	1	no	—
54	C₂×C₈	—	86	1	no	—
55	C₂×C₈	D₁₇₂	1	1	yes	characteristic
56	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
57	C₄⋊C₄	—	43	1	no	—
58	C₄⋊C₄	—	86	1	no	—
59	C₄²	—	86	1	no	—
60	C₄²	C₄×D₄₃	1	1	yes	characteristic
61	C₁₆	—	2	2	no	—
62	C₁₆	—	172	1	no	—
63	Q₈	—	172	1	no	—
64	C₂×C₄	—	86	1	no	—
65	C₂×C₄	—	86	1	no	—
66	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
67	C₂×C₄	#10621872	1	1	yes	characteristic
68	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	172	1	no	—
71	C₈	#10621873	1	1	yes	characteristic
72	C₈	Dic₁₇₂	1	1	yes	characteristic
73	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	—	172	1	no	—
77	C₄	—	172	1	no	—
78	C₄	#13063250	1	1	yes	characteristic
79	C₄	#13063253	1	1	yes	characteristic
80	C₂	#14582631	1	1	yes	characteristic
81	C₂	#14582680	1	1	yes	characteristic
82	C₂	#14582684	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#346	C₂
socle	C₂²×C₄₃	C₂²⋊C₈
hypercenter	#346	D₄₃
hypocenter	C₄₃	#1338
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
45. C₄₃	#1338	semidirect