Subgroups — #19132465

Order 5504.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582956	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
4	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
5	#13063236	C₄	1	4	yes	—
6	C₂²×C₈×C₄₃	C₄	1	2	yes	—
7	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₃	—	2	2	no	—
9	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₄₃	—	2	2	no	—
13	C₂×C₈×C₄₃	—	4	2	no	—
14	C₄²×C₄₃	C₂×C₄	1	2	yes	—
15	C₄²×C₄₃	D₄	1	2	yes	—
16	C₂×C₄₃⋊C₈	—	2	4	no	—
17	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	—	2	2	no	—
19	C₂×C₄×C₄₃	—	2	1	no	—
20	C₂×C₄×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	—	4	1	no	—
22	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₈×C₄₃	—	4	2	no	—
27	C₄₃⋊C₈	—	4	4	no	—
28	C₂²×C₄₃	—	2	1	no	—
29	C₂²×C₄₃	—	2	1	no	—
30	C₂²×C₄₃	#95	1	1	yes	characteristic
31	C₂²×C₄₃	#108	1	2	yes	—
32	C₄×C₄₃	—	2	2	no	—
33	C₄×C₄₃	—	2	2	no	—
34	C₄×C₄₃	—	2	1	no	—
35	C₄×C₄₃	#100	1	1	yes	characteristic
36	C₄×C₄₃	#101	1	1	yes	characteristic
37	#1290	—	43	1	no	maximal, Sylow
38	C₂×C₄₃	—	2	2	no	—
39	C₂×C₄₃	H(3,ℤ/4)	1	1	yes	characteristic
40	C₂×C₄₃	#341	1	1	yes	characteristic
41	C₂×C₄₃	#343	1	1	yes	characteristic
42	#432	—	43	2	no	—
43	C₂×C₄⋊C₈	D₄₃	1	1	yes	characteristic
44	C₄₃	#1290	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₈	Dic₄₃	1	2	yes	—
46	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
47	C₄⋊C₈	—	2	2	no	—
48	C₄⋊C₈	—	86	2	no	—
49	C₂²⋊C₈	—	86	2	no	—
50	#97	—	43	4	no	—
51	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
52	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
53	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
54	C₂×C₈	—	2	2	no	—
55	C₂×C₈	—	4	2	no	—
56	C₂×C₈	—	86	4	no	—
57	C₄²	C₄×D₄₃	1	2	yes	—
58	C₄²	C₂²⋊D₄₃	1	2	yes	—
59	C₂³	C₄⋊Dic₄₃	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
65	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
66	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
67	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
68	C₈	—	4	2	no	—
69	C₈	—	172	4	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	C₄₃⋊#95	1	1	yes	characteristic
73	C₂²	#13063261	1	2	yes	—
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	#13063242	1	1	yes	characteristic
78	C₄	#13063244	1	1	yes	characteristic
79	C₂	—	2	2	no	—
80	C₂	#14582656	1	1	yes	characteristic
81	C₂	#14582664	1	1	yes	characteristic
82	C₂	#14582668	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄₃⋊#95
commutator	C₂×C₄×C₄₃	C₄²
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₂×C₄⋊C₈×C₄₃	C₂
socle	C₂²×C₄₃	#95
hypercenter	C₂×C₄⋊C₈	D₄₃
hypocenter	C₄₃	#1290
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
44. C₄₃	#1290	semidirect