Subgroups — #32973668

Order 18688.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22608065	C₂	1	1	yes	maximal, characteristic
2	#22608007	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1373	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556497	C₄	1	1	yes	characteristic
5	C₂×#14556497	C₄	1	1	yes	characteristic
6	#17988408	—	2	1	no	—
7	#364×C₇₃	—	2	1	no	—
8	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	#14556531	—	4	1	no	—
10	#14556497	—	2	1	no	—
11	#14556497	C₈	1	2	yes	—
12	M₃₂×C₇₃	—	4	1	no	—
13	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
16	#11924003	—	8	1	no	—
17	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
19	C₄²×C₇₃	Q₁₆	1	1	yes	characteristic
20	C₁₆×C₇₃	—	2	1	no	—
21	C₁₆×C₇₃	—	8	1	no	—
22	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	#107	1	1	yes	characteristic
26	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
27	C₈×C₇₃	#108	1	1	yes	characteristic
28	C₈×C₇₃	SD₃₂	1	1	yes	characteristic
29	C₈×C₇₃	SD₃₂	1	1	yes	characteristic
30	C₂²×C₇₃	#368	1	1	yes	characteristic
31	C₄×C₇₃	—	4	1	no	—
32	C₄×C₇₃	#335	1	1	yes	characteristic
33	C₄×C₇₃	#367	1	1	yes	characteristic
34	#7464	—	73	1	no	maximal, Sylow
35	C₂×C₇₃	—	2	1	no	—
36	C₂×C₇₃	#1372	1	1	yes	characteristic
37	#1397	—	73	1	no	—
38	#1373	—	73	1	no	—
39	#1373	D₇₃	1	1	yes	characteristic
40	C₇₃	#7464	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃₂	—	73	1	no	—
42	C₂×C₃₂	—	73	1	no	—
43	#364	—	2	1	no	—
44	#364	—	146	1	no	—
45	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
46	M₃₂	—	4	1	no	—
47	M₃₂	—	292	1	no	—
48	C₂×C₁₆	Dic₁₄₆	1	1	yes	characteristic
49	C₂×C₁₆	C₄×D₇₃	1	1	yes	characteristic
50	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
51	C₃₂	—	73	2	no	—
52	C₃₂	—	146	1	no	—
53	C₂×C₈	#11924007	1	1	yes	characteristic
54	C₂×C₈	#11924013	1	1	yes	characteristic
55	C₄²	#11924018	1	1	yes	characteristic
56	C₁₆	—	2	1	no	—
57	C₁₆	—	8	1	no	—
58	C₁₆	—	584	1	no	—
59	C₁₆	C₈×D₇₃	1	1	yes	characteristic
60	C₁₆	#11924011	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#14556524	1	1	yes	characteristic
63	C₈	#14556520	1	1	yes	characteristic
64	C₈	#14556526	1	1	yes	characteristic
65	C₈	#14556534	1	1	yes	characteristic
66	C₈	#14556535	1	1	yes	characteristic
67	C₂²	#17988416	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#17988339	1	1	yes	characteristic
70	C₄	#17988414	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#22608004	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17988414
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₇₃×#1373	C₂
socle	C₂×C₇₃	#1372
prime radical	C₂²×C₇₃	#368
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	#1373	D₇₃
hypocenter	C₇₃	#7464
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
40. C₇₃	#7464	semidirect

Maximal subgroups

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

subgroup	index
#22608065	2
#22608007	2
C₇₃×#1373	2
#7464	73