Subgroups — #22625097

Order 9344.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989516	C₂	1	1	yes	maximal, characteristic
2	#17989514	C₂	1	1	yes	maximal, characteristic
3	#17988420	C₂	1	1	yes	maximal, characteristic
4	#14556662	—	2	1	no	—
5	#14556660	—	2	1	no	—
6	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
7	#14556497	C₄	1	1	yes	characteristic, complemented
8	C₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
9	#11924038	—	4	1	no	—
10	C₄⋊#64408	—	4	1	no	—
11	C₈×D₇₃	D₄	1	1	yes	characteristic
12	#11924003	Q₈	1	1	yes	characteristic
13	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#64408	—	8	1	no	—
15	C₄×D₇₃	D₈	1	1	yes	characteristic
16	#10596833	—	8	1	no	—
17	C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
18	#10596831	Q₁₆	1	1	yes	characteristic
19	C₂×D₇₃	SD₃₂	1	1	yes	characteristic
20	#64408	—	16	1	no	—
21	C₄×C₇₃	#107	1	1	yes	characteristic
22	Dic₇₃	SD₃₂	1	1	yes	characteristic
23	C₂×C₇₃	#367	1	1	yes	characteristic
24	D₇₃	—	2	1	no	—
25	#1426	—	73	1	no	maximal, Sylow
26	C₇₃	#1426	1	1	yes	characteristic, complemented, Sylow
27	M₆₄	—	73	1	no	—
28	#368	—	73	1	no	—
29	#367	—	73	1	no	—
30	C₂×C₁₆	—	73	1	no	—
31	#108	—	146	1	no	—
32	#107	—	146	1	no	—
33	C₃₂	—	73	1	no	—
34	C₃₂	#64408	1	1	yes	characteristic, complemented
35	M₁₆	—	292	1	no	—
36	C₂×C₈	—	73	1	no	—
37	C₄⋊C₄	—	292	1	no	—
38	C₁₆	—	73	1	no	—
39	C₁₆	C₂×#64408	1	1	yes	characteristic
40	C₂×C₄	—	584	1	no	—
41	C₂×C₄	—	73	1	no	—
42	C₈	—	584	1	no	—
43	C₈	—	73	1	no	—
44	C₈	C₄⋊#64408	1	1	yes	characteristic
45	C₂²	—	73	1	no	—
46	C₄	—	73	1	no	—
47	C₄	—	1168	1	no	—
48	C₄	#14556660	1	1	yes	characteristic
49	C₂	—	146	1	no	—
50	C₂	#17989514	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989514
commutator	C₁₆×C₇₃	C₂×C₄
Frattini	C₁₆	C₂×#64408
Fitting	C₃₂×C₇₃	C₄
socle	C₂×C₇₃	#367
hypercenter	C₃₂	#64408
hypocenter	C₇₃	#1426
LCS	G ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. #14556497	C₄	semidirect
8. C₃₂×C₇₃	C₄	semidirect
26. C₇₃	#1426	semidirect
34. C₃₂	#64408	semidirect