Subgroups — C₂×#14556686 #17989704

Order 4672.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556686	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11924040	C₂	1	2	yes	maximal, complemented
3	C₂×#11924036	C₂	1	1	yes	maximal, characteristic
4	#11924040	C₂²	1	4	yes	complemented
5	#11924036	C₄	1	2	yes	—
6	#11924036	C₂²	1	2	yes	—
7	C₂×#10596833	C₄	1	1	yes	characteristic
8	C₂×#10596833	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₇₃	C₄	1	1	yes	characteristic
10	C₂²×D₇₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₇₃	C₈	1	1	yes	characteristic
12	C₂×Dic₇₃	C₂×C₄	1	1	yes	characteristic
13	C₄×D₇₃	C₈	1	2	yes	—
14	C₄×D₇₃	C₂×C₄	1	2	yes	—
15	#10596833	C₂×C₄	1	2	yes	—
16	#10596833	C₂×C₄	1	1	yes	characteristic
17	#10596833	C₂³	1	1	yes	characteristic
18	C₂²×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₂×D₇₃	C₁₆	1	4	yes	complemented
20	C₂×D₇₃	C₂×C₈	1	2	yes	—
21	C₄×C₇₃	C₂×C₈	1	2	yes	—
22	Dic₇₃	C₂×C₈	1	1	yes	characteristic
23	Dic₇₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₇₃	C₂×C₁₆	1	2	yes	complemented
25	C₂×C₇₃	C₂²×C₈	1	1	yes	characteristic
26	D₇₃	C₂×C₁₆	1	4	yes	complemented
27	C₇₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₁₆	—	73	1	no	maximal, Sylow
29	C₂²×C₈	—	73	1	no	—
30	C₂×C₁₆	—	73	2	no	—
31	C₂×C₁₆	—	73	4	no	—
32	C₂²×C₄	—	73	1	no	—
33	C₂×C₈	—	73	1	no	—
34	C₂×C₈	—	73	1	no	—
35	C₂×C₈	—	73	2	no	—
36	C₂×C₈	—	73	2	no	—
37	C₁₆	—	73	4	no	—
38	C₂³	—	73	1	no	—
39	C₂×C₄	—	73	1	no	—
40	C₂×C₄	—	73	2	no	—
41	C₂×C₄	—	73	2	no	—
42	C₂×C₄	#10596842	1	1	yes	characteristic
43	C₈	—	73	1	no	—
44	C₈	—	73	2	no	—
45	C₈	—	73	1	no	—
46	C₂²	—	73	4	no	—
47	C₂²	—	73	2	no	—
48	C₂²	C₂×#10596842	1	1	yes	characteristic
49	C₄	—	73	1	no	—
50	C₄	—	73	1	no	—
51	C₄	C₂×#10596842	1	2	yes	—
52	C₂	—	73	4	no	—
53	C₂	#14556686	1	2	yes	direct product factor
54	C₂	C₂²×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#10596842
commutator, hypocenter	C₇₃	C₂²×C₁₆
Frattini	C₂	C₂²×#10596842
Fitting	C₂×C₄×C₇₃	C₈
socle	C₂²×C₇₃	C₂×C₈
prime radical	C₂²×D₇₃	C₈
cosocle	#10596833	C₂³
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #14556686	C₂	direct (N × H)
2. C₂×#11924040	C₂	semidirect
4. #11924040	C₂²	semidirect
19. C₂×D₇₃	C₁₆	semidirect
24. C₂×C₇₃	C₂×C₁₆	semidirect
26. D₇₃	C₂×C₁₆	semidirect
27. C₇₃	C₂²×C₁₆	semidirect
53. C₂	#14556686	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14556686	2
C₂×#11924040	2
C₂×#11924036	2
C₂²×C₁₆	73

Subgroups — C2×#14556686 #17989704

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14556686 #17989704