Subgroups — C₂³×#11924040 #22627176

Order 9344.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11924040	C₂	1	14	yes	maximal, direct product factor
2	C₂³×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924040	C₂²	1	28	yes	direct product factor
4	C₂²×#10596833	C₄	1	7	yes	—
5	C₂²×#10596833	C₂²	1	7	yes	—
6	C₂³×Dic₇₃	C₄	1	1	yes	characteristic
7	#11924040	C₂³	1	8	yes	direct product factor
8	C₂×#10596833	C₂×C₄	1	21	yes	—
9	C₂×#10596833	C₂³	1	7	yes	—
10	C₂²×Dic₇₃	C₈	1	7	yes	—
11	C₂²×Dic₇₃	C₂×C₄	1	7	yes	—
12	C₂⁴×C₇₃	C₈	1	1	yes	characteristic
13	C₂³×C₇₃	C₁₆	1	8	yes	complemented
14	C₂³×C₇₃	C₂×C₈	1	7	yes	—
15	C₂×Dic₇₃	C₂×C₈	1	21	yes	—
16	C₂×Dic₇₃	C₂²×C₄	1	7	yes	—
17	#10596833	C₂²×C₄	1	7	yes	—
18	#10596833	C₂⁴	1	1	yes	characteristic
19	C₂²×C₇₃	C₂×C₁₆	1	28	yes	complemented
20	C₂²×C₇₃	C₂²×C₈	1	7	yes	—
21	Dic₇₃	C₂²×C₈	1	7	yes	—
22	Dic₇₃	C₂³×C₄	1	1	yes	characteristic
23	C₂×C₇₃	C₂²×C₁₆	1	14	yes	complemented
24	C₂×C₇₃	C₂³×C₈	1	1	yes	characteristic
25	C₂³×C₁₆	—	73	1	no	maximal, Sylow
26	C₇₃	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂³×C₈	—	73	1	no	—
28	C₂²×C₁₆	—	73	14	no	—
29	C₂³×C₄	—	73	1	no	—
30	C₂²×C₈	—	73	7	no	—
31	C₂²×C₈	—	73	7	no	—
32	C₂×C₁₆	—	73	28	no	—
33	C₂⁴	#10596842	1	1	yes	characteristic
34	C₂²×C₄	—	73	7	no	—
35	C₂²×C₄	—	73	7	no	—
36	C₂×C₈	—	73	21	no	—
37	C₂×C₈	—	73	7	no	—
38	C₁₆	—	73	8	no	—
39	C₂³	#11924040	1	8	yes	direct product factor
40	C₂³	C₂×#10596842	1	7	yes	—
41	C₂×C₄	—	73	7	no	—
42	C₂×C₄	—	73	21	no	—
43	C₈	—	73	1	no	—
44	C₈	—	73	7	no	—
45	C₂²	C₂×#11924040	1	28	yes	direct product factor
46	C₂²	C₂²×#10596842	1	7	yes	—
47	C₄	—	73	1	no	—
48	C₄	—	73	7	no	—
49	C₂	C₂²×#11924040	1	14	yes	direct product factor
50	C₂	C₂³×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴	#10596842
commutator, hypocenter	C₇₃	C₂³×C₁₆
Frattini	C₂	C₂³×#10596842
Fitting, socle	C₂⁴×C₇₃	C₈
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂²×#11924040	C₂	direct (N × H)
3. C₂×#11924040	C₂²	direct (N × H)
7. #11924040	C₂³	direct (N × H)
13. C₂³×C₇₃	C₁₆	semidirect
19. C₂²×C₇₃	C₂×C₁₆	semidirect
23. C₂×C₇₃	C₂²×C₁₆	semidirect
26. C₇₃	C₂³×C₁₆	semidirect
39. C₂³	#11924040	direct (N × H)
45. C₂²	C₂×#11924040	direct (N × H)
49. C₂	C₂²×#11924040	direct (N × H)

Subgroups — C23×#11924040 #22627176

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×#11924040 #22627176