Subgroups — #34033123

Order 18688.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626998	C₂	1	2	yes	maximal
2	#22625037	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	SD₃₂	1	2	yes	—
22	#10596842	—	16	2	no	—
23	C₄×D₇₃	#107	1	1	yes	characteristic
24	#10596833	—	2	1	no	—
25	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
26	#10596831	#108	1	1	yes	characteristic
27	C₂×D₇₃	#367	1	1	yes	characteristic
28	#64408	—	2	2	no	—
29	C₄×C₇₃	#335	1	1	yes	characteristic
30	Dic₇₃	#368	1	1	yes	characteristic
31	#7463	—	73	1	no	maximal, Sylow
32	C₂×C₇₃	#1372	1	1	yes	characteristic
33	D₇₃	#1426	1	2	yes	—
34	#1397	—	73	1	no	—
35	#1372	—	73	2	no	—
36	C₇₃	#7463	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃₂	—	73	1	no	—
38	C₂×C₃₂	—	73	1	no	—
39	C₄×C₁₆	—	73	1	no	—
40	#335	—	146	2	no	—
41	C₂×C₁₆	—	73	1	no	—
42	C₂×C₁₆	—	73	1	no	—
43	C₄⋊C₈	—	292	2	no	—
44	C₄×C₈	—	73	1	no	—
45	C₃₂	—	73	1	no	—
46	C₃₂	—	146	1	no	—
47	C₃₂	#10596842	1	1	yes	characteristic, complemented
48	C₂×C₈	—	584	2	no	—
49	C₂×C₈	—	73	1	no	—
50	C₂×C₈	—	73	1	no	—
51	C₄²	—	73	1	no	—
52	C₁₆	—	73	1	no	—
53	C₁₆	—	146	1	no	—
54	C₁₆	C₂×#10596842	1	1	yes	characteristic
55	C₂×C₄	—	73	1	no	—
56	C₂×C₄	—	73	2	no	—
57	C₈	—	73	1	no	—
58	C₈	—	1168	2	no	—
59	C₈	—	146	1	no	—
60	C₈	C₄⋊#10596842	1	1	yes	characteristic
61	C₂²	—	73	1	no	—
62	C₄	—	73	1	no	—
63	C₄	—	146	2	no	—
64	C₄	#17989677	1	1	yes	characteristic
65	C₂	—	73	2	no	—
66	C₂	#22626998	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22626998
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₁₆	C₂×#10596842
Fitting	C₃₂×C₇₃	C₈
socle	C₂×C₇₃	#1372
prime radical	C₂×D₇₃	#367
cosocle	C₁₆×#64408	C₂²
hypercenter	C₃₂	#10596842
hypocenter	C₇₃	#7463
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
36. C₇₃	#7463	semidirect
47. C₃₂	#10596842	semidirect

Maximal subgroups

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

subgroup	index
#22626998	2
#22625037	2
#7463	73