Subgroups — #22627162

Order 9344.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989696	C₂	1	2	yes	maximal, complemented
2	#17989695	C₂	1	2	yes	maximal, complemented
3	#17989694	C₂	1	2	yes	maximal, complemented
4	C₂×#14556664	C₂	1	1	yes	maximal, characteristic
5	#14556681	C₂²	1	4	yes	complemented
6	#14556664	C₄	1	1	yes	characteristic
7	#14556664	C₄	1	1	yes	characteristic
8	#14556664	C₂²	1	1	yes	characteristic
9	#14556664	C₂²	1	1	yes	characteristic
10	C₂×#11924031	C₄	1	1	yes	characteristic
11	C₂×#11924031	C₂²	1	1	yes	characteristic
12	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
13	#11924031	C₂×C₄	1	1	yes	characteristic
14	#11924031	C₂×C₄	1	1	yes	characteristic
15	#11924031	C₂×C₄	1	1	yes	characteristic
16	#11924031	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₈×D₇₃	C₈	1	1	yes	characteristic
20	C₈×D₇₃	C₈	1	1	yes	characteristic
21	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
22	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
24	C₂²×D₇₃	C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
27	C₄×D₇₃	C₁₆	1	1	yes	characteristic
28	C₄×D₇₃	C₁₆	1	1	yes	characteristic
29	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
30	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
33	#10596831	C₂×C₈	1	1	yes	characteristic
34	#10596831	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
36	C₂×D₇₃	—	2	2	no	—
37	C₂×D₇₃	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₇₃	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
41	Dic₇₃	C₂×C₁₆	1	1	yes	characteristic
42	Dic₇₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₇₃	—	2	1	no	—
44	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
45	D₇₃	—	2	1	no	—
46	D₇₃	M₆₄	1	2	yes	complemented
47	C₂×M₆₄	—	73	1	no	maximal, Sylow
48	C₇₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	73	1	no	—
50	M₆₄	—	73	2	no	—
51	M₆₄	—	73	2	no	—
52	C₂×C₃₂	—	73	2	no	—
53	C₂²×C₈	—	73	1	no	—
54	C₂×C₁₆	—	73	1	no	—
55	C₂×C₁₆	—	73	1	no	—
56	C₂×C₁₆	—	73	1	no	—
57	C₂×C₁₆	—	73	1	no	—
58	C₂×C₁₆	—	73	1	no	—
59	C₂×C₁₆	—	73	1	no	—
60	C₃₂	—	73	4	no	—
61	C₂²×C₄	—	73	1	no	—
62	C₂×C₈	—	73	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	#10596842	1	1	yes	characteristic
68	C₁₆	—	73	1	no	—
69	C₁₆	—	73	1	no	—
70	C₁₆	—	73	1	no	—
71	C₁₆	—	73	1	no	—
72	C₂³	—	73	1	no	—
73	C₂×C₄	—	73	1	no	—
74	C₂×C₄	—	73	1	no	—
75	C₂×C₄	—	73	1	no	—
76	C₂×C₄	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
79	C₈	—	73	1	no	—
80	C₈	—	73	1	no	—
81	C₈	C₂×#10596842	1	1	yes	characteristic
82	C₈	C₂×#10596842	1	1	yes	characteristic
83	C₂²	—	73	1	no	—
84	C₂²	—	73	1	no	—
85	C₂²	—	146	2	no	—
86	C₂²	#14556686	1	1	yes	characteristic
87	C₄	—	73	1	no	—
88	C₄	—	73	1	no	—
89	C₄	#14556686	1	1	yes	characteristic
90	C₄	C₂²×#10596842	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	73	2	no	—
93	C₂	—	146	1	no	—
94	C₂	C₂×#14556686	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₁₆
Frattini	C₄	C₂²×#10596842
Fitting	C₂×C₈×C₇₃	C₈
hypercenter	C₂×C₈	#10596842
hypocenter	C₇₃	C₂×M₆₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #17989696	C₂	semidirect
2. #17989695	C₂	semidirect
3. #17989694	C₂	semidirect
5. #14556681	C₂²	semidirect
46. D₇₃	M₆₄	semidirect
48. C₇₃	C₂×M₆₄	semidirect