Subgroups — #22624839

Order 9344.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989590	C₂	1	2	yes	maximal
2	#17988610	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924037	C₄	1	4	yes	—
4	#14556658	—	2	2	no	—
5	C₄⋊#10596833	—	2	2	no	—
6	C₂×#11924012	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
8	#14556520	—	2	2	no	—
9	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
10	#11924037	—	4	4	no	—
11	C₂×#10596833	—	2	4	no	—
12	C₂²×Dic₇₃	C₂×C₄	1	2	yes	—
13	#11924012	—	4	1	no	—
14	C₂×#10596831	—	2	1	no	—
15	C₄×Dic₇₃	D₄	1	1	yes	characteristic
16	C₄×Dic₇₃	D₄	1	2	yes	—
17	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
18	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
19	M₁₆×C₇₃	—	4	1	no	—
20	C₂×C₈×C₇₃	—	2	1	no	—
21	C₂³×C₇₃	C₄²	1	1	yes	characteristic
22	C₂×C₄×C₇₃	—	2	1	no	—
23	C₂×C₄×C₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
26	C₂×Dic₇₃	—	2	2	no	—
27	C₂×Dic₇₃	—	2	2	no	—
28	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
29	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
30	#10596833	—	4	4	no	—
31	C₈×C₇₃	—	4	1	no	—
32	#10596831	—	4	1	no	—
33	C₂²×C₇₃	—	2	2	no	—
34	C₂²×C₇₃	—	2	1	no	—
35	C₂²×C₇₃	#95	1	1	yes	characteristic
36	C₄×C₇₃	—	2	1	no	—
37	C₄×C₇₃	#100	1	1	yes	characteristic
38	C₄×C₇₃	#101	1	1	yes	characteristic
39	Dic₇₃	—	2	2	no	—
40	Dic₇₃	#100	1	2	yes	—
41	Dic₇₃	#101	1	2	yes	—
42	C₂×C₇₃	—	4	1	no	—
43	C₂×C₇₃	#343	1	2	yes	—
44	C₂×C₇₃	#343	1	1	yes	characteristic
45	#1309	—	73	1	no	maximal, Sylow
46	C₇₃	#1309	1	1	yes	characteristic, complemented, Sylow
47	#423	—	73	2	no	—
48	#423	—	73	1	no	—
49	C₂×M₁₆	—	73	4	no	—
50	C₂×M₁₆	—	73	1	no	—
51	C₂×M₁₆	#64408	1	1	yes	characteristic
52	C₂×C₄²	—	73	1	no	—
53	C₄⋊C₈	—	146	2	no	—
54	C₄⋊C₈	—	146	2	no	—
55	C₄⋊C₈	—	146	2	no	—
56	C₂²×C₄	—	73	2	no	—
57	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
58	M₁₆	—	4	1	no	—
59	M₁₆	—	292	1	no	—
60	M₁₆	—	292	4	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	146	4	no	—
63	C₂×C₈	—	146	1	no	—
64	C₄²	—	73	2	no	—
65	C₄²	—	73	1	no	—
66	C₄²	—	73	1	no	—
67	C₂³	C₄×#64408	1	1	yes	characteristic
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	73	2	no	—
71	C₂×C₄	—	73	2	no	—
72	C₂×C₄	—	146	2	no	—
73	C₂×C₄	—	146	2	no	—
74	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
76	C₈	—	4	1	no	—
77	C₈	—	292	4	no	—
78	C₈	—	292	1	no	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	1	no	—
81	C₂²	(C₂×#64408)⋊C₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	73	2	no	—
84	C₄	—	73	2	no	—
85	C₄	—	146	2	no	—
86	C₄	#14556651	1	1	yes	characteristic
87	C₄	#14556652	1	1	yes	characteristic
88	C₂	—	4	1	no	—
89	C₂	#17989466	1	2	yes	—
90	C₂	#17989467	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×#64408)⋊C₄
commutator	C₂³×C₇₃	C₄²
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂²×C₇₃	#95
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#1309
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
46. C₇₃	#1309	semidirect