Subgroups — #22627030

Order 9344.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556681	C₂	1	2	yes	maximal
2	#17989473	C₂	1	1	yes	maximal, characteristic
3	#14556681	—	2	2	no	—
4	C₂×#11924031	C₄	1	1	yes	characteristic
5	C₂×#11924031	C₂²	1	1	yes	characteristic
6	C₈×Dic₇₃	C₄	1	1	yes	characteristic
7	#11924031	—	2	1	no	—
8	#11924031	D₄	1	1	yes	characteristic
9	#11924031	Q₈	1	1	yes	characteristic
10	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
11	C₄×Dic₇₃	C₈	1	1	yes	characteristic
12	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
13	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
15	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
16	C₈×C₇₃	—	2	1	no	—
17	#10596831	C₄⋊C₄	1	1	yes	characteristic
18	#10596831	M₁₆	1	1	yes	characteristic
19	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
21	C₄×C₇₃	M₃₂	1	1	yes	characteristic
22	Dic₇₃	—	2	1	no	—
23	Dic₇₃	C₃₂	1	2	yes	complemented
24	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₇₃	M₆₄	1	1	yes	characteristic
27	C₄⋊C₃₂	—	73	1	no	maximal, Sylow
28	C₇₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	73	2	no	—
30	C₄×C₁₆	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	C₂×C₁₆	—	73	1	no	—
33	C₄×C₈	—	73	1	no	—
34	C₃₂	—	146	2	no	—
35	C₂×C₈	—	73	1	no	—
36	C₂×C₈	#10596842	1	1	yes	characteristic
37	C₄²	—	73	1	no	—
38	C₁₆	—	73	1	no	—
39	C₁₆	—	73	1	no	—
40	C₁₆	—	146	1	no	—
41	C₂×C₄	—	73	1	no	—
42	C₂×C₄	—	73	1	no	—
43	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	73	1	no	—
46	C₈	—	73	1	no	—
47	C₂²	#14556686	1	1	yes	characteristic
48	C₄	—	73	2	no	—
49	C₄	—	146	1	no	—
50	C₄	C₄⋊#10596842	1	1	yes	characteristic
51	C₄	#14556687	1	1	yes	characteristic
52	C₂	#17989690	1	1	yes	characteristic
53	C₂	#17989694	1	1	yes	characteristic
54	C₂	#17989696	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₃₂
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₁₆
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	C₄⋊C₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
23. Dic₇₃	C₃₂	semidirect
28. C₇₃	C₄⋊C₃₂	semidirect