Subgroups — C₂×#17989681 #22627086

Order 9344.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11924040	C₂	1	2	yes	maximal
2	#17989681	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×#10596833	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924040	C₄	1	8	yes	complemented
5	C₂×#11924040	C₂²	1	4	yes	—
6	C₂²×#10596833	C₄	1	1	yes	characteristic
7	C₂²×#10596833	C₂²	1	1	yes	characteristic
8	C₄×#10596833	C₄	1	2	yes	—
9	C₄×#10596833	C₂²	1	2	yes	—
10	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
11	#11924040	C₂×C₄	1	8	yes	complemented
12	C₂×#10596833	C₈	1	4	yes	—
13	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
14	C₂×#10596833	C₂×C₄	1	4	yes	—
15	C₂×#10596833	C₂×C₄	1	2	yes	—
16	C₂×#10596833	C₂³	1	1	yes	characteristic
17	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
18	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₇₃	C₈	1	2	yes	—
20	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
22	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	2	2	no	—
24	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
25	C₂×Dic₇₃	—	2	2	no	—
26	C₂×Dic₇₃	C₄²	1	2	yes	—
27	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
28	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
30	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
31	#10596833	C₄²	1	2	yes	—
32	#10596833	C₂×C₈	1	4	yes	—
33	#10596833	C₂²×C₄	1	2	yes	—
34	C₂²×C₇₃	C₄×C₈	1	2	yes	—
35	C₂²×C₇₃	M₃₂	1	2	yes	—
36	C₂²×C₇₃	M₃₂	1	2	yes	—
37	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₇₃	—	2	2	no	—
39	Dic₇₃	—	2	2	no	—
40	Dic₇₃	C₄×C₈	1	2	yes	—
41	Dic₇₃	C₂×C₄²	1	1	yes	characteristic
42	Dic₇₃	C₂²×C₈	1	1	yes	characteristic
43	C₂×C₇₃	#346	1	4	yes	complemented
44	C₂×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
45	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
46	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
47	C₂×#346	—	73	1	no	maximal, Sylow
48	C₇₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	73	2	no	—
50	C₂×C₄×C₈	—	73	1	no	—
51	#346	—	73	4	no	—
52	C₂²×C₈	—	73	1	no	—
53	C₂²×C₈	—	73	1	no	—
54	C₂×C₄²	—	73	1	no	—
55	C₂×C₁₆	—	73	8	no	—
56	C₂×C₁₆	—	73	4	no	—
57	C₄×C₈	—	73	2	no	—
58	C₄×C₈	—	73	2	no	—
59	C₂²×C₄	—	73	1	no	—
60	C₂²×C₄	—	73	1	no	—
61	C₂²×C₄	#10596842	1	1	yes	characteristic
62	C₂×C₈	—	73	4	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	4	no	—
66	C₂×C₈	—	73	1	no	—
67	C₄²	—	73	2	no	—
68	C₄²	—	73	2	no	—
69	C₁₆	—	73	8	no	—
70	C₂³	C₂×#10596842	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	73	2	no	—
73	C₂×C₄	—	73	2	no	—
74	C₂×C₄	—	73	1	no	—
75	C₂×C₄	—	73	1	no	—
76	C₂×C₄	—	73	2	no	—
77	C₂×C₄	—	146	2	no	—
78	C₂×C₄	C₂×#10596842	1	2	yes	—
79	C₈	—	73	2	no	—
80	C₈	—	73	2	no	—
81	C₈	—	73	4	no	—
82	C₂²	C₄×#10596842	1	2	yes	—
83	C₂²	#14556687	1	2	yes	—
84	C₂²	#14556688	1	2	yes	—
85	C₂²	C₂²×#10596842	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	73	1	no	—
88	C₄	—	73	1	no	—
89	C₄	—	73	2	no	—
90	C₄	—	146	2	no	—
91	C₂	#17989681	1	4	yes	direct product factor
92	C₂	C₂×C₄×#10596842	1	1	yes	characteristic
93	C₂	C₂×#14556687	1	1	yes	characteristic
94	C₂	C₂×#14556688	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#10596842
commutator	C₂×C₇₃	C₂×C₄×C₈
Frattini	C₂²	C₂²×#10596842
Fitting	C₂²×C₄×C₇₃	C₈
socle	C₂³×C₇₃	C₂×C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	C₂×#346
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #17989681	C₂	direct (N × H)
4. C₂×#11924040	C₄	semidirect
11. #11924040	C₂×C₄	semidirect
43. C₂×C₇₃	#346	semidirect
48. C₇₃	C₂×#346	semidirect
91. C₂	#17989681	direct (N × H)

Subgroups — C2×#17989681 #22627086

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17989681 #22627086