Subgroups — #22627087

Order 9344.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556686	C₂	1	2	yes	maximal
2	#17989681	C₂	1	4	yes	maximal, complemented
3	C₄×#11924036	C₂	1	1	yes	maximal, characteristic
4	#14556686	C₄	1	8	yes	complemented
5	C₂×#11924040	C₂²	1	4	yes	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₄×#10596833	C₄	1	2	yes	—
9	C₄×#10596833	C₂²	1	2	yes	—
10	C₄²×D₇₃	C₄	1	1	yes	characteristic
11	#11924040	C₂×C₄	1	8	yes	complemented
12	#11924036	C₈	1	4	yes	—
13	#11924036	C₂×C₄	1	4	yes	—
14	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
15	C₂×#10596833	C₂×C₄	1	2	yes	—
16	C₂×#10596833	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₇₃	C₈	1	2	yes	—
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₇₃	C₈	1	1	yes	characteristic
20	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
21	C₄²×C₇₃	C₈	1	1	yes	characteristic
22	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
24	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
26	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×D₇₃	—	2	4	no	—
28	C₄×D₇₃	C₄²	1	2	yes	—
29	C₄×D₇₃	C₂×C₈	1	2	yes	—
30	#10596833	C₄²	1	2	yes	—
31	#10596833	C₂×C₈	1	4	yes	—
32	#10596833	C₂²×C₄	1	2	yes	—
33	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
34	C₂×D₇₃	C₄×C₈	1	2	yes	—
35	C₂×D₇₃	M₃₂	1	4	yes	—
36	C₄×C₇₃	—	2	2	no	—
37	C₄×C₇₃	C₄×C₈	1	2	yes	—
38	Dic₇₃	—	2	2	no	—
39	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
40	Dic₇₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₇₃	C₂×M₃₂	1	2	yes	—
43	D₇₃	#346	1	4	yes	complemented
44	C₂×#346	—	73	1	no	maximal, Sylow
45	C₇₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₁₆	—	73	2	no	—
47	C₂×C₄×C₈	—	73	1	no	—
48	#346	—	73	4	no	—
49	C₂²×C₈	—	73	1	no	—
50	C₂²×C₈	—	73	1	no	—
51	C₂×C₄²	—	73	1	no	—
52	C₂×C₁₆	—	73	4	no	—
53	C₂×C₁₆	—	73	8	no	—
54	C₄×C₈	—	73	2	no	—
55	C₄×C₈	—	73	2	no	—
56	C₂²×C₄	—	73	1	no	—
57	C₂²×C₄	—	73	2	no	—
58	C₂×C₈	—	73	1	no	—
59	C₂×C₈	—	73	2	no	—
60	C₂×C₈	—	73	1	no	—
61	C₂×C₈	—	73	4	no	—
62	C₂×C₈	—	73	4	no	—
63	C₄²	—	73	2	no	—
64	C₄²	—	73	1	no	—
65	C₄²	#10596842	1	1	yes	characteristic
66	C₁₆	—	73	8	no	—
67	C₂³	—	73	1	no	—
68	C₂×C₄	—	73	1	no	—
69	C₂×C₄	—	73	2	no	—
70	C₂×C₄	—	73	2	no	—
71	C₂×C₄	—	73	2	no	—
72	C₂×C₄	—	146	4	no	—
73	C₂×C₄	C₂×#10596842	1	2	yes	—
74	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
75	C₈	—	73	2	no	—
76	C₈	—	73	2	no	—
77	C₈	—	73	4	no	—
78	C₂²	—	73	2	no	—
79	C₂²	—	73	4	no	—
80	C₂²	C₂²×#10596842	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	73	1	no	—
83	C₄	—	73	1	no	—
84	C₄	—	146	2	no	—
85	C₄	C₄×#10596842	1	2	yes	—
86	C₂	—	73	4	no	—
87	C₂	C₂×C₄×#10596842	1	1	yes	characteristic
88	C₂	#17989706	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₂²	C₂²×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₄²	#10596842
hypocenter	C₇₃	C₂×#346
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #17989681	C₂	semidirect
4. #14556686	C₄	semidirect
11. #11924040	C₂×C₄	semidirect
43. D₇₃	#346	semidirect
45. C₇₃	C₂×#346	semidirect