Subgroups — #22625145

Order 9344.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989605	C₂	1	2	yes	maximal
2	#17989429	C₂	1	4	yes	maximal, complemented
3	C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556658	C₄	1	4	yes	—
5	#14556648	C₄	1	4	yes	—
6	C₄×#10596833	C₂²	1	4	yes	—
7	C₂×C₈×D₇₃	C₄	1	2	yes	—
8	C₄²×D₇₃	C₂²	1	1	yes	characteristic
9	C₄×#10596831	C₄	1	1	yes	characteristic
10	C₈×Dic₇₃	C₂²	1	2	yes	—
11	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
12	C₂×#10596833	C₂×C₄	1	8	yes	—
13	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
14	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#10596831	C₂×C₄	1	2	yes	—
16	C₈×D₇₃	—	2	4	no	—
17	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
18	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
19	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
20	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×D₇₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₇₃	C₄²	1	2	yes	—
23	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₇₃	C₄²	1	1	yes	characteristic
25	C₂×Dic₇₃	C₂²×C₄	1	2	yes	—
26	C₄×D₇₃	—	2	4	no	—
27	C₄×D₇₃	M₁₆	1	4	yes	—
28	#10596833	—	2	8	no	—
29	C₈×C₇₃	—	2	2	no	—
30	#10596831	—	2	2	no	—
31	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
32	C₂×D₇₃	—	2	2	no	—
33	C₂×D₇₃	#97	1	2	yes	—
34	C₄×C₇₃	—	2	2	no	—
35	C₄×C₇₃	C₂×M₁₆	1	2	yes	—
36	Dic₇₃	#97	1	2	yes	—
37	Dic₇₃	#131	1	4	yes	—
38	C₂×C₇₃	C₂×#97	1	1	yes	characteristic
39	C₂×C₇₃	#405	1	2	yes	—
40	D₇₃	—	2	2	no	—
41	#1452	—	73	1	no	maximal, Sylow
42	C₇₃	#1452	1	1	yes	characteristic, complemented, Sylow
43	#431	—	73	2	no	—
44	C₂×C₄×C₈	—	73	1	no	—
45	#322	—	73	4	no	—
46	C₂²×C₈	—	73	2	no	—
47	C₂×C₄²	—	73	1	no	—
48	C₄⋊C₈	—	73	4	no	—
49	C₂²⋊C₈	—	73	4	no	—
50	C₄×C₈	—	73	4	no	—
51	C₄×C₈	—	73	2	no	—
52	C₄×C₈	—	73	1	no	—
53	C₄×C₈	#64408	1	1	yes	characteristic
54	C₂²×C₄	—	73	1	no	—
55	C₂²×C₄	—	73	2	no	—
56	C₂×C₈	—	73	8	no	—
57	C₂×C₈	—	73	2	no	—
58	C₂×C₈	—	146	4	no	—
59	C₂×C₈	C₂×#64408	1	2	yes	—
60	C₄²	—	73	2	no	—
61	C₄²	—	73	1	no	—
62	C₄²	C₂×#64408	1	1	yes	characteristic
63	C₂³	—	73	1	no	—
64	C₂×C₄	—	73	2	no	—
65	C₂×C₄	—	73	1	no	—
66	C₂×C₄	—	73	4	no	—
67	C₂×C₄	—	146	4	no	—
68	C₂×C₄	C₄×#64408	1	2	yes	—
69	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	146	8	no	—
72	C₈	—	146	2	no	—
73	C₂²	—	73	2	no	—
74	C₂²	—	146	2	no	—
75	C₂²	C₂×C₄×#64408	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	73	2	no	—
78	C₄	—	73	4	no	—
79	C₄	D₇₃⋊M₁₆	1	2	yes	—
80	C₂	—	146	2	no	—
81	C₂	#17989546	1	1	yes	characteristic
82	C₂	#17989550	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂×C₄²
Fitting	C₄×C₈×C₇₃	C₄
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1452
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #17989429	C₂	semidirect
42. C₇₃	#1452	semidirect