Subgroups — #22627031

Order 9344.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989695	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	—	2	1	no	—
15	C₈×C₇₃	C₁₆	1	2	yes	—
16	#10596831	C₄⋊C₄	1	1	yes	characteristic
17	#10596831	M₁₆	1	1	yes	characteristic
18	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
19	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
21	Dic₇₃	—	2	2	no	—
22	C₂×C₇₃	—	2	1	no	—
23	C₂×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
24	#1422	—	73	1	no	maximal, Sylow
25	C₇₃	#1422	1	1	yes	characteristic, complemented, Sylow
26	M₆₄	—	73	2	no	—
27	C₄×C₁₆	—	73	1	no	—
28	C₂×C₁₆	—	73	1	no	—
29	C₂×C₁₆	—	73	1	no	—
30	C₄×C₈	—	73	1	no	—
31	C₃₂	—	146	2	no	—
32	C₂×C₈	—	73	1	no	—
33	C₂×C₈	#10596842	1	1	yes	characteristic
34	C₄²	—	73	1	no	—
35	C₁₆	—	73	1	no	—
36	C₁₆	—	73	1	no	—
37	C₁₆	—	146	1	no	—
38	C₂×C₄	—	146	1	no	—
39	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
40	C₈	—	73	1	no	—
41	C₈	—	73	1	no	—
42	C₈	#11924040	1	2	yes	—
43	C₂²	#14556688	1	1	yes	characteristic
44	C₄	—	146	2	no	—
45	C₄	C₄⋊#10596842	1	1	yes	characteristic
46	C₄	C₂×#11924040	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊#11924040	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#10596842
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₂×C₈×C₇₃	C₈
socle	C₂×C₇₃	C₄⋊C₁₆
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	#1422
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
25. C₇₃	#1422	semidirect