Subgroups — #22625001

Order 9344.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#108	C₂	1	2	yes	maximal
2	C₂×#14556530	C₂	1	1	yes	maximal, characteristic
3	D₇₃⋊M₁₆	—	2	2	no	—
4	#14556662	—	2	2	no	—
5	#14556661	C₄	1	4	yes	—
6	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
7	#14556530	—	2	2	no	—
8	C₂×#11924003	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
10	#11924038	—	2	4	no	—
11	#11924037	—	4	2	no	—
12	#11924036	—	4	2	no	—
13	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
14	C₂×#10596831	Q₈	1	1	yes	characteristic
15	C₈×D₇₃	C₂×C₄	1	2	yes	—
16	C₈×D₇₃	D₄	1	2	yes	—
17	#11924003	—	2	1	no	—
18	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₇₃	—	2	1	no	—
20	C₂²×D₇₃	Q₁₆	1	1	yes	characteristic
21	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×Dic₇₃	D₈	1	1	yes	characteristic
23	C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
24	C₄×D₇₃	SD₁₆	1	2	yes	—
25	#10596833	—	4	4	no	—
26	C₈×C₇₃	C₄²	1	1	yes	characteristic
27	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	#10596831	C₄⋊C₄	1	2	yes	—
29	C₂²×C₇₃	#107	1	1	yes	characteristic
30	C₂×D₇₃	—	4	1	no	—
31	C₂×D₇₃	#103	1	2	yes	—
32	C₄×C₇₃	#95	1	1	yes	characteristic
33	C₄×C₇₃	#106	1	1	yes	characteristic
34	Dic₇₃	#102	1	2	yes	—
35	C₂×C₇₃	—	2	1	no	—
36	C₂×C₇₃	#340	1	1	yes	characteristic
37	D₇₃	—	2	2	no	—
38	#1385	—	73	1	no	maximal, Sylow
39	C₇₃	#1385	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₃₂	—	73	1	no	—
41	C₂×#108	—	73	2	no	—
42	C₂×M₁₆	—	146	2	no	—
43	C₂²×C₈	—	73	1	no	—
44	M₃₂	—	146	2	no	—
45	C₂×C₁₆	—	73	1	no	—
46	C₂×C₁₆	#64408	1	1	yes	characteristic
47	#108	—	73	4	no	—
48	#108	—	146	2	no	—
49	C₂²×C₄	—	73	1	no	—
50	M₁₆	—	292	2	no	—
51	M₁₆	—	146	4	no	—
52	C₂×C₈	—	292	2	no	—
53	C₂×C₈	—	73	1	no	—
54	C₂×C₈	—	73	2	no	—
55	C₂×C₈	—	73	2	no	—
56	C₂×C₈	C₂×#64408	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	146	1	no	—
59	C₂³	—	73	1	no	—
60	C₂×C₄	—	73	1	no	—
61	C₂×C₄	—	73	2	no	—
62	C₂×C₄	—	73	2	no	—
63	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
64	C₈	—	292	4	no	—
65	C₈	—	73	2	no	—
66	C₈	C₄×#64408	1	1	yes	characteristic
67	C₈	C₂²⋊#64408	1	1	yes	characteristic
68	C₂²	—	292	1	no	—
69	C₂²	—	73	2	no	—
70	C₂²	#14556660	1	1	yes	characteristic
71	C₄	—	73	2	no	—
72	C₄	(C₂×#64408)⋊C₄	1	1	yes	characteristic
73	C₄	#14556659	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	146	2	no	—
76	C₂	#17989461	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556659
commutator	C₈×C₇₃	C₄²
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂×C₇₃	#340
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	#1385
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
39. C₇₃	#1385	semidirect