Subgroups — #17989486

Order 4672.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556665	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11924031	C₂	1	1	yes	maximal, characteristic, complemented
3	#14556599	C₂	1	1	yes	maximal, characteristic
4	#11924031	—	2	1	no	—
5	#11924031	—	2	1	no	—
6	#11924028	C₄	1	1	yes	characteristic
7	#11924011	—	2	1	no	—
8	C₂×#10596831	C₂²	1	1	yes	characteristic
9	C₈×D₇₃	—	2	1	no	—
10	M₁₆×C₇₃	C₄	1	1	yes	characteristic
11	C₂×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂²⋊D₇₃	—	2	1	no	—
13	D₂₉₂	C₈	1	1	yes	characteristic
14	C₄×D₇₃	—	2	1	no	—
15	Dic₁₄₆	C₈	1	1	yes	characteristic
16	C₈×C₇₃	—	2	1	no	—
17	#10596831	D₄	1	1	yes	characteristic
18	#10596831	D₄	1	1	yes	characteristic
19	C₂²×C₇₃	M₁₆	1	1	yes	characteristic
20	C₂×D₇₃	—	2	1	no	—
21	C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	Dic₇₃	—	2	1	no	—
24	C₂×C₇₃	—	2	1	no	—
25	C₂×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
26	D₇₃	—	4	1	no	—
27	C₇₃	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	73	1	no	maximal, Sylow
29	#131	—	73	1	no	—
30	M₃₂	—	73	1	no	—
31	C₂×C₁₆	—	73	1	no	—
32	#41	—	73	1	no	—
33	M₁₆	—	146	1	no	—
34	M₁₆	#64408	1	1	yes	characteristic
35	C₂×C₈	—	73	1	no	—
36	C₂×C₈	—	146	1	no	—
37	C₁₆	—	146	1	no	—
38	C₁₆	—	146	1	no	—
39	Q₈	—	73	1	no	—
40	D₄	—	73	1	no	—
41	D₄	—	146	1	no	—
42	C₂×C₄	—	146	1	no	—
43	C₂×C₄	C₂×#64408	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	73	1	no	—
46	C₈	—	73	1	no	—
47	C₂²	—	146	1	no	—
48	C₂²	#11924038	1	1	yes	characteristic
49	C₄	—	146	1	no	—
50	C₄	C₂²⋊#64408	1	1	yes	characteristic
51	C₄	#11924036	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	292	1	no	—
54	C₂	#14556648	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊#64408
commutator	C₄×C₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#64408
Fitting	M₁₆×C₇₃	C₄
socle	C₂×C₇₃	C₂²⋊C₈
prime radical	#11924028	C₄
cosocle	C₂×#10596831	C₂²
hypercenter	M₁₆	#64408
hypocenter	C₇₃	#350
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #14556665	C₂	semidirect
2. C₂×#11924031	C₂	semidirect
27. C₇₃	#350	semidirect

Maximal subgroups

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

subgroup	index
#14556665	2
C₂×#11924031	2
#14556599	2
#350	73