Subgroups — #17989505

Order 4672.

62 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	#14556661	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#11924038	—	2	1	no	—
5	#11924031	—	2	1	no	—
6	D₄×D₇₃	—	2	1	no	—
7	D₅₈₄	C₄	1	1	yes	characteristic
8	#11924013	—	2	1	no	—
9	C₈×D₇₃	C₂²	1	1	yes	characteristic
10	D₈×C₇₃	C₄	1	1	yes	characteristic
11	C₂²×D₇₃	—	4	1	no	—
12	D₄×C₇₃	—	2	1	no	—
13	C₂²⋊D₇₃	—	4	1	no	—
14	D₂₉₂	—	2	1	no	—
15	C₄×D₇₃	D₄	1	1	yes	characteristic
16	#10596833	—	4	1	no	—
17	C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
18	#10596831	D₄	1	1	yes	characteristic
19	C₂²×C₇₃	—	4	1	no	—
20	C₂×D₇₃	—	4	1	no	—
21	C₂×D₇₃	—	8	2	no	—
22	C₂×D₇₃	SD₁₆	1	1	yes	characteristic
23	C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₇₃	D₈	1	1	yes	characteristic
25	C₂×C₇₃	—	8	1	no	—
26	C₂×C₇₃	#102	1	1	yes	characteristic
27	D₇₃	—	2	1	no	—
28	D₇₃	—	8	1	no	—
29	C₇₃	#361	1	1	yes	characteristic, complemented, Sylow
30	#361	—	73	1	no	maximal, Sylow
31	C₂×D₈	—	73	1	no	—
32	M₃₂	—	73	1	no	—
33	#108	—	73	1	no	—
34	C₂×D₄	—	146	1	no	—
35	D₈	—	73	1	no	—
36	D₈	—	146	1	no	—
37	D₈	#64408	1	1	yes	characteristic
38	M₁₆	—	146	1	no	—
39	C₂×C₈	—	73	1	no	—
40	C₁₆	—	146	1	no	—
41	C₂³	—	292	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	292	1	no	—
44	D₄	—	146	1	no	—
45	C₂×C₄	—	73	1	no	—
46	C₈	—	292	1	no	—
47	C₈	—	73	1	no	—
48	C₈	C₂×#64408	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	292	1	no	—
51	C₂²	—	584	2	no	—
52	C₂²	—	73	1	no	—
53	C₄	—	73	1	no	—
54	C₄	C₂²⋊#64408	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	584	1	no	—
57	C₂	—	146	1	no	—
58	C₂	#14556653	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14556653
commutator	C₈×C₇₃	C₂×C₄
Frattini	C₈	C₂×#64408
Fitting	D₈×C₇₃	C₄
socle	C₂×C₇₃	#102
prime radical	D₈×D₇₃	C₂
cosocle	C₈×D₇₃	C₂²
hypercenter	D₈	#64408
hypocenter	C₇₃	#361
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #14556666	C₂	semidirect
2. #14556661	C₂	semidirect
29. C₇₃	#361	semidirect

Maximal subgroups

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

subgroup	index
#14556666	2
#14556661	2
D₈×D₇₃	2
#361	73