Subgroups — #17989504

Order 4672.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556666	C₂	1	1	yes	maximal, characteristic, complemented
2	#14556659	C₂	1	1	yes	maximal, characteristic, complemented
3	#14556614	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#64408	—	2	1	no	—
5	#11924031	—	2	1	no	—
6	#11924029	—	2	1	no	—
7	#11924015	—	2	1	no	—
8	D₅₈₄	C₄	1	1	yes	characteristic, complemented
9	C₈×D₇₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#64408	—	4	1	no	—
12	Q₈×C₇₃	—	2	1	no	—
13	D₂₉₂	—	2	1	no	—
14	D₂₉₂	—	4	1	no	—
15	C₄×D₇₃	—	4	1	no	—
16	C₄×D₇₃	D₄	1	1	yes	characteristic
17	C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
18	#10596831	D₄	1	1	yes	characteristic
19	C₂×D₇₃	—	4	1	no	—
20	C₂×D₇₃	D₈	1	1	yes	characteristic
21	#64408	—	8	1	no	—
22	C₄×C₇₃	—	4	1	no	—
23	C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₇₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₇₃	#102	1	1	yes	characteristic
26	D₇₃	—	2	1	no	—
27	D₇₃	—	8	1	no	—
28	C₇₃	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	73	1	no	maximal, Sylow
30	#135	—	73	1	no	—
31	M₃₂	—	73	1	no	—
32	#106	—	73	1	no	—
33	#41	—	146	1	no	—
34	Q₁₆	#64408	1	1	yes	characteristic, complemented
35	SD₁₆	—	146	1	no	—
36	D₈	—	73	1	no	—
37	C₂×C₈	—	73	1	no	—
38	C₄⋊C₄	—	146	1	no	—
39	C₁₆	—	146	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	292	1	no	—
42	D₄	—	146	1	no	—
43	C₂×C₄	—	292	1	no	—
44	C₂×C₄	—	292	1	no	—
45	C₂×C₄	—	73	1	no	—
46	C₈	—	73	1	no	—
47	C₈	C₂×#64408	1	1	yes	characteristic
48	C₂²	—	292	1	no	—
49	C₂²	—	73	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	584	1	no	—
52	C₄	—	73	1	no	—
53	C₄	C₂²⋊#64408	1	1	yes	characteristic
54	C₂	—	584	1	no	—
55	C₂	—	146	1	no	—
56	C₂	#14556653	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14556653
commutator	C₈×C₇₃	C₂×C₄
Frattini	C₈	C₂×#64408
Fitting	Q₁₆×C₇₃	C₄
socle	C₂×C₇₃	#102
prime radical	#14556614	C₂
cosocle	C₈×D₇₃	C₂²
hypercenter	Q₁₆	#64408
hypocenter	C₇₃	#360
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #14556666	C₂	semidirect
2. #14556659	C₂	semidirect
8. D₅₈₄	C₄	semidirect
10. Q₁₆×C₇₃	C₄	semidirect
28. C₇₃	#360	semidirect
34. Q₁₆	#64408	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14556666	2
#14556659	2
#14556614	2
#360	73