Subgroups — C₁₆×#10596833 #22624840

Order 9344.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989473	C₂	1	1	yes	maximal, characteristic
2	C₈×#10596833	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	C₄	1	2	yes	—
5	C₄×#10596833	C₄	1	2	yes	—
6	C₂×#11924003	C₄	1	1	yes	characteristic
7	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
9	C₂×#10596833	C₈	1	4	yes	—
10	#11924031	C₈	1	4	yes	complemented
11	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
13	#11924003	C₈	1	2	yes	complemented
14	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₈	1	2	yes	complemented
16	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
17	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
18	#10596833	C₁₆	1	8	yes	direct product factor
19	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
20	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
21	#10596831	C₂×C₈	1	2	yes	—
22	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
23	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
24	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
25	Dic₇₃	C₂×C₁₆	1	4	yes	—
26	C₂×C₇₃	C₈²	1	1	yes	characteristic
27	C₂×C₇₃	C₄×C₁₆	1	2	yes	—
28	C₈×C₁₆	—	73	1	no	maximal, Sylow
29	C₇₃	C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₄×C₁₆	—	73	1	no	—
31	C₄×C₁₆	—	73	1	no	—
32	C₈²	—	73	1	no	—
33	C₂×C₁₆	—	73	2	no	—
34	C₂×C₁₆	—	73	1	no	—
35	C₂×C₁₆	#64408	1	1	yes	characteristic
36	C₄×C₈	—	73	2	no	—
37	C₄×C₈	—	73	1	no	—
38	C₂×C₈	—	73	4	no	—
39	C₂×C₈	—	73	1	no	—
40	C₂×C₈	C₂×#64408	1	1	yes	characteristic
41	C₄²	—	73	1	no	—
42	C₁₆	—	73	4	no	—
43	C₁₆	—	73	2	no	—
44	C₁₆	#10596833	1	2	yes	direct product factor
45	C₂×C₄	—	73	2	no	—
46	C₂×C₄	C₄×#64408	1	1	yes	characteristic
47	C₈	—	73	8	no	—
48	C₈	—	73	2	no	—
49	C₈	C₂×#10596833	1	1	yes	characteristic
50	C₈	#11924036	1	1	yes	characteristic
51	C₂²	C₈×#64408	1	1	yes	characteristic
52	C₄	—	73	4	no	—
53	C₄	C₈×#64408	1	1	yes	characteristic
54	C₄	C₄×#10596833	1	1	yes	characteristic
55	C₂	C₈×#10596833	1	1	yes	characteristic
56	C₂	C₁₆×#64408	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₁₆	#64408
commutator, hypocenter	C₇₃	C₈×C₁₆
Frattini	C₂×C₈	C₂×#64408
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₈
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
10. #11924031	C₈	semidirect
13. #11924003	C₈	semidirect
15. C₁₆×C₇₃	C₈	semidirect
18. #10596833	C₁₆	direct (N × H)
29. C₇₃	C₈×C₁₆	semidirect
44. C₁₆	#10596833	direct (N × H)

Subgroups — C16×#10596833 #22624840

Conjugacy classes of subgroups

Complements

Subgroups — C₁₆×#10596833 #22624840