Subgroups — #34033111

Order 18688.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626993	C₂	1	1	yes	maximal, characteristic
2	#22626991	C₂	1	1	yes	maximal, characteristic
3	#22625041	C₂	1	1	yes	maximal, characteristic
4	#17989691	—	2	1	no	—
5	#17989676	—	2	1	no	—
6	#17989520	C₄	1	1	yes	characteristic
7	#17989474	C₂²	1	1	yes	characteristic
8	#17988420	C₄	1	1	yes	characteristic
9	#14556688	—	4	1	no	—
10	C₄⋊#10596842	—	4	1	no	—
11	#14556664	Q₈	1	1	yes	characteristic
12	C₈×#64408	D₄	1	1	yes	characteristic
13	#14556641	—	2	1	no	—
14	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
15	#14556497	C₈	1	1	yes	characteristic, complemented
16	C₃₂×C₇₃	C₈	1	1	yes	characteristic, complemented
17	C₂×#10596842	—	8	1	no	—
18	#11924040	—	8	1	no	—
19	#11924036	SD₁₆	1	1	yes	characteristic
20	C₄×#64408	SD₁₆	1	1	yes	characteristic
21	#11924031	—	2	1	no	—
22	C₈×D₇₃	C₄⋊C₄	1	1	yes	characteristic
23	#11924003	M₁₆	1	1	yes	characteristic
24	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
25	C₂×#64408	—	2	1	no	—
26	#10596842	—	16	1	no	—
27	C₄×D₇₃	#106	1	1	yes	characteristic
28	#10596833	—	2	1	no	—
29	C₈×C₇₃	C₄⋊C₈	1	1	yes	characteristic
30	#10596831	#108	1	1	yes	characteristic
31	C₂×D₇₃	#365	1	1	yes	characteristic
32	#64408	—	4	1	no	—
33	C₄×C₇₃	#334	1	1	yes	characteristic
34	Dic₇₃	#365	1	1	yes	characteristic
35	#7457	—	73	1	no	maximal, Sylow
36	C₂×C₇₃	#1368	1	1	yes	characteristic
37	D₇₃	—	2	1	no	—
38	#1398	—	73	1	no	—
39	#1369	—	73	1	no	—
40	#1368	—	73	1	no	—
41	C₇₃	#7457	1	1	yes	characteristic, complemented, Sylow
42	M₆₄	—	73	1	no	—
43	M₆₄	—	73	1	no	—
44	#364	—	146	1	no	—
45	#346	—	73	1	no	—
46	#334	—	146	1	no	—
47	M₃₂	—	292	1	no	—
48	C₂×C₁₆	—	73	1	no	—
49	C₂×C₁₆	—	73	1	no	—
50	C₄⋊C₈	—	292	1	no	—
51	C₄×C₈	—	73	1	no	—
52	C₃₂	—	73	1	no	—
53	C₃₂	—	146	1	no	—
54	C₃₂	#10596842	1	1	yes	characteristic, complemented
55	C₂×C₈	—	584	1	no	—
56	C₂×C₈	—	73	1	no	—
57	C₂×C₈	—	73	1	no	—
58	C₄²	—	73	1	no	—
59	C₁₆	—	584	1	no	—
60	C₁₆	—	73	1	no	—
61	C₁₆	—	146	1	no	—
62	C₁₆	C₂×#10596842	1	1	yes	characteristic
63	C₂×C₄	—	73	1	no	—
64	C₂×C₄	—	146	1	no	—
65	C₈	—	73	1	no	—
66	C₈	—	1168	1	no	—
67	C₈	—	146	1	no	—
68	C₈	C₄⋊#10596842	1	1	yes	characteristic
69	C₂²	—	73	1	no	—
70	C₄	—	292	1	no	—
71	C₄	—	73	1	no	—
72	C₄	#17989676	1	1	yes	characteristic
73	C₂	—	146	1	no	—
74	C₂	#22626991	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22626991
commutator	C₁₆×C₇₃	C₂×C₈
Frattini	C₁₆	C₂×#10596842
Fitting	C₃₂×C₇₃	C₈
socle	C₂×C₇₃	#1368
prime radical	C₂×D₇₃	#365
cosocle	#17989474	C₂²
hypercenter	C₃₂	#10596842
hypocenter	C₇₃	#7457
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
15. #14556497	C₈	semidirect
16. C₃₂×C₇₃	C₈	semidirect
41. C₇₃	#7457	semidirect
54. C₃₂	#10596842	semidirect

Maximal subgroups

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

subgroup	index
#22626993	2
#22626991	2
#22625041	2
#7457	73