Subgroups — #34001284

Order 18688.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625095	C₂	1	1	yes	maximal, characteristic
2	#22625093	C₂	1	1	yes	maximal, characteristic
3	#22608141	C₂	1	1	yes	maximal, characteristic
4	#17989515	—	2	1	no	—
5	#17989513	—	2	1	no	—
6	C₃₂×D₇₃	C₂²	1	1	yes	characteristic
7	#17988306	C₄	1	1	yes	characteristic, complemented
8	C₆₄×C₇₃	C₄	1	1	yes	characteristic, complemented
9	#14556662	—	4	1	no	—
10	#14556660	—	4	1	no	—
11	C₁₆×D₇₃	D₄	1	1	yes	characteristic
12	#14556497	Q₈	1	1	yes	characteristic
13	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
14	#11924038	—	8	1	no	—
15	C₄⋊#64408	—	8	1	no	—
16	C₈×D₇₃	D₈	1	1	yes	characteristic
17	#11924003	Q₁₆	1	1	yes	characteristic
18	C₁₆×C₇₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×#64408	—	16	1	no	—
20	C₄×D₇₃	D₁₆	1	1	yes	characteristic
21	#10596833	—	16	1	no	—
22	C₈×C₇₃	#107	1	1	yes	characteristic
23	#10596831	Q₃₂	1	1	yes	characteristic
24	C₂×D₇₃	SD₆₄	1	1	yes	characteristic
25	#64408	—	32	1	no	—
26	C₄×C₇₃	#366	1	1	yes	characteristic
27	Dic₇₃	SD₆₄	1	1	yes	characteristic
28	#7548	—	73	1	no	maximal, Sylow
29	C₂×C₇₃	#1424	1	1	yes	characteristic
30	D₇₃	—	2	1	no	—
31	M₁₂₈	—	73	1	no	—
32	#1425	—	73	1	no	—
33	#1424	—	73	1	no	—
34	C₇₃	#7548	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃₂	—	73	1	no	—
36	#368	—	146	1	no	—
37	#366	—	146	1	no	—
38	C₆₄	—	73	1	no	—
39	C₆₄	#64408	1	1	yes	characteristic, complemented
40	C₂×C₁₆	—	73	1	no	—
41	#108	—	292	1	no	—
42	#107	—	292	1	no	—
43	C₃₂	—	73	1	no	—
44	C₃₂	C₂×#64408	1	1	yes	characteristic
45	M₁₆	—	584	1	no	—
46	C₂×C₈	—	73	1	no	—
47	C₄⋊C₄	—	584	1	no	—
48	C₁₆	—	73	1	no	—
49	C₁₆	C₄⋊#64408	1	1	yes	characteristic
50	C₂×C₄	—	73	1	no	—
51	C₂×C₄	—	1168	1	no	—
52	C₈	—	73	1	no	—
53	C₈	—	1168	1	no	—
54	C₈	#14556660	1	1	yes	characteristic
55	C₂²	—	73	1	no	—
56	C₄	—	2336	1	no	—
57	C₄	—	73	1	no	—
58	C₄	#17989513	1	1	yes	characteristic
59	C₂	—	146	1	no	—
60	C₂	#22625093	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22625093
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₃₂	C₂×#64408
Fitting	C₆₄×C₇₃	C₄
socle	C₂×C₇₃	#1424
prime radical	C₂×D₇₃	SD₆₄
cosocle	C₃₂×D₇₃	C₂²
hypercenter	C₆₄	#64408
hypocenter	C₇₃	#7548
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ C₆₄

Complements

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

N	H ≅ G/N	type
7. #17988306	C₄	semidirect
8. C₆₄×C₇₃	C₄	semidirect
34. C₇₃	#7548	semidirect
39. C₆₄	#64408	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22625095	2
#22625093	2
#22608141	2
#7548	73