Subgroups — #32973794

Order 18688.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988420	C₂	1	1	yes	maximal, characteristic
2	#22608142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₇₃	C₄	1	1	yes	characteristic
5	#17988420	—	2	1	no	—
6	#17988420	—	2	1	no	—
7	C₂×#14556497	C₄	1	1	yes	characteristic
8	#17988306	—	2	1	no	—
9	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
10	C₆₄×C₇₃	—	2	1	no	—
11	C₂×C₈×D₇₃	C₈	1	1	yes	characteristic
12	C₂×#11924003	C₈	1	1	yes	characteristic
13	C₁₆×D₇₃	—	2	1	no	—
14	C₁₆×D₇₃	—	2	1	no	—
15	#14556497	—	2	1	no	—
16	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₇₃	D₄	1	1	yes	characteristic
18	C₃₂×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	C₁₆	1	1	yes	characteristic
20	C₂×#10596831	C₁₆	1	1	yes	characteristic
21	C₈×D₇₃	—	2	1	no	—
22	C₈×D₇₃	—	2	1	no	—
23	#11924003	—	2	1	no	—
24	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
27	C₂²×D₇₃	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
30	C₄×D₇₃	—	2	1	no	—
31	C₄×D₇₃	—	2	1	no	—
32	C₈×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₇₃	M₃₂	1	1	yes	characteristic
34	#10596831	—	2	1	no	—
35	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
36	C₂×D₇₃	—	2	1	no	—
37	C₂×D₇₃	—	4	1	no	—
38	C₄×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₄×C₇₃	M₆₄	1	1	yes	characteristic
40	Dic₇₃	—	2	1	no	—
41	#7513	—	73	1	no	maximal, Sylow
42	C₂×C₇₃	—	2	1	no	—
43	C₂×C₇₃	C₂²⋊C₃₂	1	1	yes	characteristic
44	D₇₃	—	4	1	no	—
45	C₂×M₆₄	—	73	1	no	—
46	M₁₂₈	—	73	1	no	—
47	M₁₂₈	D₇₃	1	1	yes	characteristic, complemented
48	C₇₃	#7513	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	73	1	no	—
50	M₆₄	—	146	1	no	—
51	M₆₄	—	146	1	no	—
52	C₂×C₃₂	—	73	1	no	—
53	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
54	C₆₄	—	2	1	no	—
55	C₆₄	—	146	1	no	—
56	C₂²×C₈	—	73	1	no	—
57	C₂×C₁₆	—	73	1	no	—
58	C₂×C₁₆	—	146	1	no	—
59	C₂×C₁₆	—	146	1	no	—
60	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
61	C₃₂	—	146	1	no	—
62	C₃₂	D₂₉₂	1	1	yes	characteristic
63	C₃₂	C₂²⋊D₇₃	1	1	yes	characteristic
64	C₂²×C₄	—	73	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	146	1	no	—
67	C₂×C₈	—	146	1	no	—
68	C₂×C₈	C₈×D₇₃	1	1	yes	characteristic
69	C₁₆	—	146	1	no	—
70	C₁₆	#11924005	1	1	yes	characteristic
71	C₁₆	#11924011	1	1	yes	characteristic
72	C₂³	—	73	1	no	—
73	C₂×C₄	—	73	1	no	—
74	C₂×C₄	—	146	1	no	—
75	C₂×C₄	—	146	1	no	—
76	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
77	C₈	—	146	1	no	—
78	C₈	#14556503	1	1	yes	characteristic
79	C₈	#14556530	1	1	yes	characteristic
80	C₂²	—	292	1	no	—
81	C₂²	—	146	1	no	—
82	C₂²	C₃₂×D₇₃	1	1	yes	characteristic
83	C₄	—	146	1	no	—
84	C₄	#17988366	1	1	yes	characteristic
85	C₄	#17988420	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	292	1	no	—
88	C₂	#22608068	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	#11924005
commutator	C₂²×C₇₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₇₃×M₁₂₈	C₂
socle	C₂×C₇₃	C₂²⋊C₃₂
prime radical	C₂²×D₇₃	C₃₂
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	M₁₂₈	D₇₃
hypocenter	C₇₃	#7513
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #22608142	C₂	semidirect
3. C₇₃×M₁₂₈	C₂	semidirect
47. M₁₂₈	D₇₃	semidirect
48. C₇₃	#7513	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988420	2
#22608142	2
C₇₃×M₁₂₈	2
#7513	73