Subgroups — C₂×#17989475 #22626131

Order 9344.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11924031	C₂	1	2	yes	maximal
2	#17989475	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	C₄	1	8	yes	complemented
5	C₂×#11924031	C₂²	1	4	yes	—
6	C₂²×#10596831	C₄	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₄×#10596831	C₄	1	2	yes	—
9	C₄×#10596831	C₂²	1	2	yes	—
10	C₂×C₄²×C₇₃	C₄	1	1	yes	characteristic
11	#11924031	C₂×C₄	1	8	yes	complemented
12	C₂×#10596831	C₈	1	4	yes	—
13	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
14	C₂×#10596831	C₂×C₄	1	4	yes	—
15	C₂×#10596831	C₂×C₄	1	2	yes	—
16	C₂×#10596831	C₂³	1	1	yes	characteristic
17	C₂²×C₄×C₇₃	C₈	1	2	yes	—
18	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄²×C₇₃	C₈	1	2	yes	—
20	C₄²×C₇₃	C₂×C₄	1	2	yes	—
21	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₇₃	—	2	4	no	—
23	C₂×C₄×C₇₃	C₄²	1	2	yes	—
24	C₂×C₄×C₇₃	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	#10596831	C₄²	1	2	yes	—
29	#10596831	C₂×C₈	1	4	yes	—
30	#10596831	C₂²×C₄	1	2	yes	—
31	C₂²×C₇₃	C₄×C₈	1	2	yes	—
32	C₂²×C₇₃	M₃₂	1	4	yes	—
33	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
34	C₄×C₇₃	—	2	4	no	—
35	C₄×C₇₃	C₄×C₈	1	2	yes	—
36	C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₇₃	#346	1	4	yes	complemented
39	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
40	C₂×C₇₃	C₂×M₃₂	1	2	yes	—
41	C₂×#346	—	73	1	no	maximal, Sylow
42	C₇₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₁₆	—	73	2	no	—
44	C₂×C₄×C₈	—	73	1	no	—
45	#346	—	73	4	no	—
46	C₂²×C₈	—	73	1	no	—
47	C₂²×C₈	—	73	1	no	—
48	C₂×C₄²	#64408	1	1	yes	characteristic
49	C₂×C₁₆	—	73	4	no	—
50	C₂×C₁₆	—	73	8	no	—
51	C₄×C₈	—	73	2	no	—
52	C₄×C₈	—	73	2	no	—
53	C₂²×C₄	#10596833	1	2	yes	—
54	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
55	C₂×C₈	—	73	4	no	—
56	C₂×C₈	—	73	4	no	—
57	C₂×C₈	—	73	2	no	—
58	C₂×C₈	—	73	1	no	—
59	C₂×C₈	—	73	1	no	—
60	C₄²	#10596833	1	2	yes	—
61	C₄²	C₂×#64408	1	2	yes	—
62	C₁₆	—	73	8	no	—
63	C₂³	C₂×#10596833	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	C₄×#64408	1	2	yes	—
66	C₂×C₄	C₂×#10596833	1	4	yes	—
67	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
68	C₂×C₄	#11924036	1	2	yes	—
69	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
70	C₈	—	73	4	no	—
71	C₈	—	73	2	no	—
72	C₈	—	73	2	no	—
73	C₂²	C₄×#10596833	1	2	yes	—
74	C₂²	#14556665	1	4	yes	—
75	C₂²	C₂²×#10596833	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	C₄×#10596833	1	2	yes	—
78	C₄	C₂×C₄×#64408	1	1	yes	characteristic
79	C₄	C₂×#11924036	1	1	yes	characteristic
80	C₂	#17989475	1	4	yes	direct product factor
81	C₂	C₂×C₄×#10596833	1	1	yes	characteristic
82	C₂	C₂×#14556665	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×#64408
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂×C₄²×C₇₃	C₄
socle	C₂³×C₇₃	C₂×C₈
hypercenter	C₂×C₄²	#64408
hypocenter	C₇₃	C₂×#346
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #17989475	C₂	direct (N × H)
4. C₂×#11924031	C₄	semidirect
11. #11924031	C₂×C₄	semidirect
38. C₂×C₇₃	#346	semidirect
42. C₇₃	C₂×#346	semidirect
80. C₂	#17989475	direct (N × H)

Subgroups — C2×#17989475 #22626131

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989475 #22626131