Subgroups — #17989708

Order 4672.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556688	C₂	1	1	yes	maximal, characteristic, complemented
2	#14556687	C₂	1	2	yes	maximal, complemented
3	#14556686	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11924040	C₂	1	2	yes	maximal, complemented
5	#14556678	C₂	1	1	yes	maximal, characteristic
6	#11924040	C₂²	1	1	yes	characteristic
7	#11924040	C₂²	1	2	yes	—
8	#11924040	C₂²	1	1	yes	characteristic
9	#11924038	C₄	1	1	yes	characteristic
10	#11924037	C₄	1	2	yes	—
11	#11924036	C₂²	1	1	yes	characteristic
12	C₂×#10596833	C₂²	1	2	yes	—
13	#11924027	C₄	1	1	yes	characteristic
14	D₄×C₇₃	C₈	1	1	yes	characteristic
15	C₂²⋊D₇₃	C₈	1	2	yes	—
16	C₂×Dic₇₃	C₂×C₄	1	2	yes	—
17	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
18	Dic₁₄₆	C₈	1	1	yes	characteristic
19	#10596833	C₂×C₄	1	2	yes	—
20	#10596833	C₂×C₄	1	1	yes	characteristic
21	#10596833	C₂³	1	1	yes	characteristic
22	C₂²×C₇₃	C₂×C₈	1	2	yes	—
23	C₂×D₇₃	C₂×C₈	1	1	yes	characteristic
24	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
25	Dic₇₃	C₂×C₈	1	2	yes	—
26	Dic₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₇₃	—	2	2	no	—
28	C₂×C₇₃	C₂²×C₈	1	1	yes	characteristic
29	D₇₃	—	2	1	no	—
30	C₇₃	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	73	1	no	maximal, Sylow
32	#131	—	73	1	no	—
33	M₃₂	—	73	2	no	—
34	M₃₂	—	73	1	no	—
35	C₂×C₁₆	—	73	2	no	—
36	C₂×C₁₆	—	73	1	no	—
37	#41	—	73	1	no	—
38	M₁₆	—	73	2	no	—
39	M₁₆	—	73	1	no	—
40	C₂×C₈	—	73	2	no	—
41	C₂×C₈	—	73	1	no	—
42	C₁₆	—	73	1	no	—
43	C₁₆	—	73	2	no	—
44	C₁₆	—	73	1	no	—
45	Q₈	—	73	1	no	—
46	D₄	—	73	2	no	—
47	D₄	#10596842	1	1	yes	characteristic
48	C₂×C₄	—	73	2	no	—
49	C₂×C₄	—	73	1	no	—
50	C₈	—	73	1	no	—
51	C₈	—	73	2	no	—
52	C₈	—	73	1	no	—
53	C₂²	—	73	1	no	—
54	C₂²	C₂×#10596842	1	2	yes	—
55	C₄	—	73	1	no	—
56	C₄	—	73	2	no	—
57	C₄	C₂×#10596842	1	1	yes	characteristic
58	C₂	—	2	2	no	—
59	C₂	—	146	1	no	—
60	C₂	C₂²×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₈
Fitting	D₄×C₇₃	C₈
prime radical	#11924027	C₄
cosocle	#10596833	C₂³
hypercenter	D₄	#10596842
hypocenter	C₇₃	#504
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #14556688	C₂	semidirect
2. #14556687	C₂	semidirect
3. #14556686	C₂	semidirect
4. C₂×#11924040	C₂	semidirect
30. C₇₃	#504	semidirect

Maximal subgroups

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

subgroup	index
#14556688	2
#14556687	2
#14556686	2
C₂×#11924040	2
#14556678	2
#504	73