Subgroups — #22627018

Order 9344.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989694	C₂	1	2	yes	maximal
2	C₁₆×#64408	C₂	1	1	yes	maximal, characteristic
3	#14556681	C₄	1	4	yes	complemented
4	#14556664	C₂²	1	1	yes	characteristic
5	C₈×#64408	C₄	1	1	yes	characteristic
6	C₁₆×D₇₃	C₄	1	1	yes	characteristic
7	#11924036	C₈	1	1	yes	characteristic
8	C₄×#64408	C₈	1	1	yes	characteristic
9	#11924031	C₂×C₄	1	2	yes	—
10	C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
11	#11924003	C₈	1	1	yes	characteristic
12	C₁₆×C₇₃	C₈	1	1	yes	characteristic
13	C₂×#64408	C₁₆	1	2	yes	—
14	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
15	#10596833	C₁₆	1	2	yes	—
16	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
17	#10596831	C₄²	1	1	yes	characteristic
18	C₂×D₇₃	C₂×C₁₆	1	1	yes	characteristic
19	#64408	—	2	2	no	—
20	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
21	Dic₇₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₇₃	C₄×C₁₆	1	1	yes	characteristic
23	D₇₃	M₆₄	1	2	yes	—
24	#1397	—	73	1	no	maximal, Sylow
25	C₇₃	#1397	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃₂	—	73	2	no	—
27	C₄×C₁₆	—	73	1	no	—
28	C₂×C₁₆	—	73	1	no	—
29	C₂×C₁₆	—	73	1	no	—
30	C₄×C₈	—	73	1	no	—
31	C₃₂	—	73	4	no	—
32	C₂×C₈	—	73	1	no	—
33	C₂×C₈	—	73	1	no	—
34	C₄²	—	73	1	no	—
35	C₁₆	—	73	2	no	—
36	C₁₆	—	73	1	no	—
37	C₁₆	#10596842	1	1	yes	characteristic
38	C₂×C₄	—	73	1	no	—
39	C₂×C₄	—	73	2	no	—
40	C₈	—	73	2	no	—
41	C₈	—	73	1	no	—
42	C₈	C₂×#10596842	1	1	yes	characteristic
43	C₂²	—	73	1	no	—
44	C₄	—	73	1	no	—
45	C₄	—	146	2	no	—
46	C₄	C₄×#10596842	1	1	yes	characteristic
47	C₂	—	73	2	no	—
48	C₂	#64408⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×#10596842
commutator, socle	C₂×C₇₃	C₄×C₁₆
Fitting	C₁₆×C₇₃	C₈
hypercenter	C₁₆	#10596842
hypocenter	C₇₃	#1397
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
3. #14556681	C₄	semidirect
25. C₇₃	#1397	semidirect