Subgroups — C₂×#17989695 #22627161

Order 9344.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989695	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14556681	C₂	1	2	yes	maximal, complemented
3	C₂²×#11924031	C₂	1	1	yes	maximal, characteristic
4	#14556681	C₂²	1	4	yes	complemented
5	C₂×#11924031	C₄	1	2	yes	—
6	C₂×#11924031	C₄	1	1	yes	characteristic
7	C₂×#11924031	C₂²	1	1	yes	characteristic
8	C₂×#11924031	C₂²	1	2	yes	—
9	C₂²×#10596831	C₄	1	1	yes	characteristic
10	#11924031	C₂×C₄	1	1	yes	characteristic
11	#11924031	C₂×C₄	1	2	yes	—
12	#11924031	C₂³	1	1	yes	characteristic
13	C₂×#10596831	C₈	1	2	yes	—
14	C₂×#10596831	C₈	1	1	yes	characteristic
15	C₂×#10596831	C₂×C₄	1	2	yes	—
16	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
18	C₂³×C₇₃	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₃	C₁₆	1	2	yes	—
20	C₂×C₄×C₇₃	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
22	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	#10596831	C₂×C₈	1	1	yes	characteristic
24	#10596831	C₂×C₈	1	2	yes	—
25	#10596831	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₇₃	—	2	2	no	—
27	C₂²×C₇₃	C₂×C₁₆	1	2	yes	—
28	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
29	C₄×C₇₃	C₂×C₁₆	1	2	yes	—
30	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
32	C₂×C₇₃	—	2	2	no	—
33	C₂×C₇₃	M₆₄	1	2	yes	complemented
34	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
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	2	no	—
44	C₂×C₁₆	—	73	1	no	—
45	C₃₂	—	73	4	no	—
46	C₂²×C₄	#10596842	1	1	yes	characteristic
47	C₂×C₈	—	73	2	no	—
48	C₂×C₈	—	73	2	no	—
49	C₂×C₈	—	73	1	no	—
50	C₂×C₈	—	73	1	no	—
51	C₁₆	—	73	1	no	—
52	C₁₆	—	73	2	no	—
53	C₁₆	—	73	1	no	—
54	C₂³	#11924040	1	1	yes	characteristic
55	C₂×C₄	#11924040	1	1	yes	characteristic
56	C₂×C₄	#11924040	1	2	yes	—
57	C₂×C₄	C₂×#10596842	1	2	yes	—
58	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
59	C₈	—	73	1	no	—
60	C₈	—	73	1	no	—
61	C₈	—	73	2	no	—
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#11924040	1	2	yes	—
64	C₂²	C₂×#11924040	1	1	yes	characteristic
65	C₄	C₂×#11924040	1	2	yes	—
66	C₄	C₂×#11924040	1	1	yes	characteristic
67	C₄	C₂²×#10596842	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#17989695	1	2	yes	direct product factor
70	C₂	C₂²×#11924040	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #17989695	C₂	direct (N × H)
2. C₂×#14556681	C₂	semidirect
4. #14556681	C₂²	semidirect
33. C₂×C₇₃	M₆₄	semidirect
36. C₇₃	C₂×M₆₄	semidirect
69. C₂	#17989695	direct (N × H)

Subgroups — C2×#17989695 #22627161

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989695 #22627161