Subgroups — C₂×#17989696 #22627163

Order 9344.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989696	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14556681	C₂	1	2	yes	maximal, complemented
3	C₂×#14556664	C₂	1	1	yes	maximal, characteristic
4	#14556681	C₂²	1	4	yes	complemented
5	#14556664	C₄	1	2	yes	—
6	#14556664	C₂²	1	2	yes	—
7	C₂×#11924031	C₄	1	1	yes	characteristic
8	C₂×#11924031	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
10	#11924031	C₂×C₄	1	2	yes	—
11	#11924031	C₂×C₄	1	1	yes	characteristic
12	#11924031	C₂³	1	1	yes	characteristic
13	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
14	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
15	C₈×D₇₃	C₈	1	2	yes	—
16	C₈×D₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₇₃	C₈	1	1	yes	characteristic
18	C₂²×D₇₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
20	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
21	C₄×D₇₃	C₁₆	1	2	yes	—
22	C₄×D₇₃	C₂×C₈	1	2	yes	—
23	C₈×C₇₃	C₂×C₈	1	2	yes	—
24	#10596831	C₂×C₈	1	1	yes	characteristic
25	#10596831	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
27	C₂×D₇₃	—	2	2	no	—
28	C₂×D₇₃	C₂×C₁₆	1	2	yes	—
29	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
30	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
31	Dic₇₃	C₂×C₁₆	1	2	yes	—
32	C₂×C₇₃	M₆₄	1	2	yes	complemented
33	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
34	D₇₃	—	2	2	no	—
35	C₂×M₆₄	—	73	1	no	maximal, Sylow
36	C₇₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
37	C₂²×C₁₆	—	73	1	no	—
38	M₆₄	—	73	4	no	—
39	C₂×C₃₂	—	73	2	no	—
40	C₂²×C₈	—	73	1	no	—
41	C₂×C₁₆	—	73	1	no	—
42	C₂×C₁₆	—	73	2	no	—
43	C₂×C₁₆	—	73	1	no	—
44	C₂×C₁₆	—	73	2	no	—
45	C₃₂	—	73	4	no	—
46	C₂²×C₄	—	73	1	no	—
47	C₂×C₈	—	73	1	no	—
48	C₂×C₈	—	73	2	no	—
49	C₂×C₈	—	73	2	no	—
50	C₂×C₈	#10596842	1	1	yes	characteristic
51	C₁₆	—	73	2	no	—
52	C₁₆	—	73	1	no	—
53	C₁₆	—	73	1	no	—
54	C₂³	—	73	1	no	—
55	C₂×C₄	—	73	1	no	—
56	C₂×C₄	—	73	2	no	—
57	C₂×C₄	—	73	2	no	—
58	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
59	C₈	—	73	1	no	—
60	C₈	—	73	1	no	—
61	C₈	C₂×#10596842	1	2	yes	—
62	C₂²	—	73	2	no	—
63	C₂²	—	146	2	no	—
64	C₂²	#14556686	1	1	yes	characteristic
65	C₄	—	73	2	no	—
66	C₄	#14556686	1	1	yes	characteristic
67	C₄	C₂²×#10596842	1	1	yes	characteristic
68	C₂	—	146	2	no	—
69	C₂	#17989696	1	2	yes	direct product factor
70	C₂	C₂×#14556686	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #17989696	C₂	direct (N × H)
2. C₂×#14556681	C₂	semidirect
4. #14556681	C₂²	semidirect
32. C₂×C₇₃	M₆₄	semidirect
36. C₇₃	C₂×M₆₄	semidirect
69. C₂	#17989696	direct (N × H)

Subgroups — C2×#17989696 #22627163

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989696 #22627163