Subgroups — #32973868

Order 18688.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988306	C₂	1	1	yes	maximal, characteristic, complemented
2	#22608135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2262	C₂	1	1	yes	maximal, characteristic
4	#17988417	—	2	1	no	—
5	#17988306	—	2	1	no	—
6	#508×C₇₃	—	2	1	no	—
7	Q₆₄×C₇₃	C₄	1	1	yes	characteristic
8	SD₆₄×C₇₃	—	2	1	no	—
9	D₃₂×C₇₃	C₄	1	1	yes	characteristic
10	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
11	#14556527	—	4	1	no	—
12	#135×C₇₃	—	4	1	no	—
13	Q₃₂×C₇₃	—	2	1	no	—
14	SD₃₂×C₇₃	—	4	1	no	—
15	D₁₆×C₇₃	—	2	1	no	—
16	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
17	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₇₃	D₄	1	1	yes	characteristic
19	#11924012	—	8	1	no	—
20	#41×C₇₃	—	8	1	no	—
21	Q₁₆×C₇₃	—	4	1	no	—
22	SD₁₆×C₇₃	—	8	1	no	—
23	D₈×C₇₃	—	4	1	no	—
24	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
25	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₇₃	SD₁₆	1	1	yes	characteristic
27	Q₈×C₇₃	—	8	1	no	—
28	D₄×C₇₃	—	8	1	no	—
29	D₄×C₇₃	—	16	1	no	—
30	C₂×C₄×C₇₃	—	16	1	no	—
31	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
32	C₈×C₇₃	#102	1	1	yes	characteristic
33	C₈×C₇₃	SD₃₂	1	1	yes	characteristic
34	#10596831	—	16	1	no	—
35	C₂²×C₇₃	—	16	1	no	—
36	C₂²×C₇₃	SD₆₄	1	1	yes	characteristic
37	C₄×C₇₃	—	16	1	no	—
38	C₄×C₇₃	#357	1	1	yes	characteristic
39	C₄×C₇₃	D₃₂	1	1	yes	characteristic
40	#7539	—	73	1	no	maximal, Sylow
41	C₂×C₇₃	—	2	1	no	—
42	C₂×C₇₃	—	32	1	no	—
43	C₂×C₇₃	#1415	1	1	yes	characteristic
44	#2262	D₇₃	1	1	yes	characteristic
45	C₂×C₆₄	—	73	1	no	—
46	#1425	—	73	1	no	—
47	C₇₃	#7539	1	1	yes	characteristic, complemented, Sylow
48	#508	—	2	1	no	—
49	Q₆₄	Dic₇₃	1	1	yes	characteristic
50	SD₆₄	—	2	1	no	—
51	D₃₂	Dic₇₃	1	1	yes	characteristic
52	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
53	#368	—	146	1	no	—
54	C₆₄	—	146	1	no	—
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
60	#108	—	292	1	no	—
61	C₃₂	C₂×Dic₇₃	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₇₃	1	1	yes	characteristic
63	#41	—	8	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	8	1	no	—
66	D₈	—	4	1	no	—
67	M₁₆	—	584	1	no	—
68	C₂×C₈	#11924013	1	1	yes	characteristic
69	C₁₆	C₂²⋊Dic₇₃	1	1	yes	characteristic
70	C₁₆	#11924016	1	1	yes	characteristic
71	Q₈	—	8	1	no	—
72	D₄	—	8	1	no	—
73	D₄	—	16	1	no	—
74	C₂×C₄	—	16	1	no	—
75	C₂×C₄	#14556532	1	1	yes	characteristic
76	C₈	—	1168	1	no	—
77	C₈	#14556512	1	1	yes	characteristic
78	C₈	#14556535	1	1	yes	characteristic
79	C₂²	—	16	1	no	—
80	C₂²	#17988425	1	1	yes	characteristic
81	C₄	—	16	1	no	—
82	C₄	#17988388	1	1	yes	characteristic
83	C₄	#17988422	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	32	1	no	—
86	C₂	#22608109	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17988422
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting, prime radical	C₇₃×#2262	C₂
socle	C₂×C₇₃	#1415
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	#2262	D₇₃
hypocenter	C₇₃	#7539
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. C₂×#17988306	C₂	semidirect
2. #22608135	C₂	semidirect
47. C₇₃	#7539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988306	2
#22608135	2
C₇₃×#2262	2
#7539	73