Subgroups — C₃₂×#64408 #22625034

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989518	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#64408	C₂	1	1	yes	maximal, characteristic
3	C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556664	C₄	1	1	yes	characteristic
5	C₈×#64408	C₄	1	1	yes	characteristic
6	#14556641	C₄	1	2	yes	complemented
7	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
8	#14556497	C₄	1	1	yes	characteristic, complemented
9	C₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
10	#11924036	C₈	1	1	yes	characteristic
11	C₄×#64408	C₈	1	1	yes	characteristic
12	#11924031	C₈	1	2	yes	—
13	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
14	#11924003	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂×#64408	C₁₆	1	2	yes	—
17	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
18	#10596833	C₁₆	1	2	yes	—
19	C₈×C₇₃	C₄²	1	1	yes	characteristic
20	#10596831	C₂×C₈	1	1	yes	characteristic
21	C₂×D₇₃	C₂×C₁₆	1	1	yes	characteristic
22	#64408	C₃₂	1	4	yes	direct product factor
23	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
24	Dic₇₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
26	D₇₃	C₂×C₃₂	1	2	yes	—
27	C₄×C₃₂	—	73	1	no	maximal, Sylow
28	C₇₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	73	1	no	—
30	C₂×C₃₂	—	73	1	no	—
31	C₄×C₁₆	—	73	1	no	—
32	C₂×C₁₆	—	73	1	no	—
33	C₂×C₁₆	—	73	1	no	—
34	C₄×C₈	—	73	1	no	—
35	C₃₂	—	73	2	no	—
36	C₃₂	—	73	1	no	—
37	C₃₂	#64408	1	1	yes	characteristic, direct product factor
38	C₂×C₈	—	73	1	no	—
39	C₂×C₈	—	73	1	no	—
40	C₄²	—	73	1	no	—
41	C₁₆	—	73	2	no	—
42	C₁₆	—	73	1	no	—
43	C₁₆	C₂×#64408	1	1	yes	characteristic
44	C₂×C₄	—	73	2	no	—
45	C₂×C₄	—	73	1	no	—
46	C₈	—	73	2	no	—
47	C₈	—	73	1	no	—
48	C₈	C₄×#64408	1	1	yes	characteristic
49	C₂²	—	73	1	no	—
50	C₄	—	73	4	no	—
51	C₄	—	73	1	no	—
52	C₄	C₈×#64408	1	1	yes	characteristic
53	C₂	—	73	2	no	—
54	C₂	C₁₆×#64408	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃₂	#64408
commutator, hypocenter	C₇₃	C₄×C₃₂
Frattini	C₁₆	C₂×#64408
Fitting	C₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₄×C₁₆
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
6. #14556641	C₄	semidirect
8. #14556497	C₄	semidirect
9. C₃₂×C₇₃	C₄	semidirect
22. #64408	C₃₂	direct (N × H)
28. C₇₃	C₄×C₃₂	semidirect
37. C₃₂	#64408	direct (N × H)

Subgroups — C32×#64408 #22625034

Conjugacy classes of subgroups

Complements

Subgroups — C₃₂×#64408 #22625034