Subgroups — #34033120

Order 18688.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626997	C₂	1	2	yes	maximal
2	C₃₂×#64408	C₂	1	1	yes	maximal, characteristic
3	#17989677	—	2	2	no	—
4	#17989518	C₄	1	1	yes	characteristic
5	C₁₆×#64408	C₂²	1	1	yes	characteristic
6	C₃₂×D₇₃	C₄	1	1	yes	characteristic
7	C₄⋊#10596842	—	4	2	no	—
8	#14556664	Q₈	1	1	yes	characteristic
9	C₈×#64408	D₄	1	1	yes	characteristic
10	#14556641	—	2	1	no	—
11	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
12	#14556497	C₈	1	1	yes	characteristic, complemented
13	C₃₂×C₇₃	C₈	1	1	yes	characteristic, complemented
14	C₂×#10596842	—	8	2	no	—
15	#11924036	Q₁₆	1	1	yes	characteristic
16	C₄×#64408	D₈	1	1	yes	characteristic
17	#11924031	—	2	1	no	—
18	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
19	#11924003	M₁₆	1	1	yes	characteristic
20	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₂×#64408	D₁₆	1	1	yes	characteristic
22	C₂×#64408	Q₃₂	1	1	yes	characteristic
23	#10596842	—	16	2	no	—
24	C₄×D₇₃	#107	1	1	yes	characteristic
25	#10596833	—	2	1	no	—
26	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
27	#10596831	#108	1	1	yes	characteristic
28	C₂×D₇₃	#366	1	1	yes	characteristic
29	#64408	—	2	1	no	—
30	#64408	SD₆₄	1	2	yes	—
31	C₄×C₇₃	#335	1	1	yes	characteristic
32	Dic₇₃	#368	1	1	yes	characteristic
33	#7461	—	73	1	no	maximal, Sylow
34	C₂×C₇₃	#1371	1	1	yes	characteristic
35	D₇₃	#1424	1	1	yes	characteristic
36	D₇₃	#1425	1	1	yes	characteristic
37	C₄×C₃₂	—	73	1	no	—
38	#1371	—	73	2	no	—
39	C₇₃	#7461	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃₂	—	73	1	no	—
41	C₂×C₃₂	—	73	1	no	—
42	C₄×C₁₆	—	73	1	no	—
43	#335	—	146	2	no	—
44	C₂×C₁₆	—	73	1	no	—
45	C₂×C₁₆	—	73	1	no	—
46	C₄⋊C₈	—	292	2	no	—
47	C₄×C₈	—	73	1	no	—
48	C₃₂	—	73	1	no	—
49	C₃₂	—	146	1	no	—
50	C₃₂	#10596842	1	1	yes	characteristic, complemented
51	C₂×C₈	—	584	2	no	—
52	C₂×C₈	—	73	1	no	—
53	C₂×C₈	—	73	1	no	—
54	C₄²	—	73	1	no	—
55	C₁₆	—	73	1	no	—
56	C₁₆	—	146	1	no	—
57	C₁₆	C₂×#10596842	1	1	yes	characteristic
58	C₂×C₄	—	73	1	no	—
59	C₂×C₄	—	73	1	no	—
60	C₂×C₄	—	73	1	no	—
61	C₈	—	73	1	no	—
62	C₈	—	1168	2	no	—
63	C₈	—	146	1	no	—
64	C₈	C₄⋊#10596842	1	1	yes	characteristic
65	C₂²	—	73	1	no	—
66	C₄	—	73	2	no	—
67	C₄	—	73	1	no	—
68	C₄	—	146	1	no	—
69	C₄	#17989677	1	1	yes	characteristic
70	C₂	—	73	1	no	—
71	C₂	—	73	1	no	—
72	C₂	#22626997	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22626997
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₁₆	C₂×#10596842
Fitting	C₃₂×C₇₃	C₈
socle	C₂×C₇₃	#1371
prime radical	C₂×D₇₃	#366
cosocle	C₁₆×#64408	C₂²
hypercenter	C₃₂	#10596842
hypocenter	C₇₃	#7461
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
12. #14556497	C₈	semidirect
13. C₃₂×C₇₃	C₈	semidirect
39. C₇₃	#7461	semidirect
50. C₃₂	#10596842	semidirect

Maximal subgroups

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

subgroup	index
#22626997	2
C₃₂×#64408	2
#7461	73