Subgroups — #34034483

Order 18688.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627035	C₂	1	3	yes	maximal, complemented
2	C₂×#17989669	C₂	1	3	yes	maximal, complemented
3	#22626354	C₂	1	1	yes	maximal, characteristic
4	#17989669	C₂²	1	1	yes	characteristic
5	#17989669	C₂²	1	3	yes	—
6	#17989519	C₄	1	3	yes	—
7	C₂×#14556641	C₂²	1	3	yes	—
8	#17989004	C₄	1	1	yes	characteristic
9	#14556641	C₂×C₄	1	3	yes	—
10	#14556641	C₂³	1	1	yes	characteristic
11	#14556531	C₈	1	3	yes	—
12	C₂×#11924003	C₂×C₄	1	3	yes	—
13	#131×C₇₃	C₈	1	1	yes	characteristic
14	#11924003	C₂×C₈	1	3	yes	—
15	#11924003	C₂²×C₄	1	1	yes	characteristic
16	#41×C₇₃	C₁₆	1	1	yes	characteristic
17	M₁₆×C₇₃	C₁₆	1	3	yes	—
18	C₂×C₈×C₇₃	C₂×C₈	1	3	yes	—
19	Q₈×C₇₃	C₃₂	1	1	yes	characteristic
20	D₄×C₇₃	C₃₂	1	3	yes	—
21	C₂×C₄×C₇₃	C₂×C₁₆	1	3	yes	—
22	C₈×C₇₃	C₂×C₁₆	1	3	yes	—
23	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
24	C₂²×C₇₃	C₂×C₃₂	1	3	yes	—
25	C₄×C₇₃	C₂×C₃₂	1	3	yes	—
26	C₄×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
27	#13737	—	73	1	no	maximal, Sylow
28	C₂×C₇₃	—	2	3	no	—
29	C₂×C₇₃	C₂²×C₃₂	1	1	yes	characteristic
30	#2258	—	73	1	no	—
31	M₁₂₈	—	73	3	no	—
32	C₂×C₆₄	—	73	3	no	—
33	C₇₃	#13737	1	1	yes	characteristic, complemented, Sylow
34	#504	—	73	1	no	—
35	M₆₄	—	73	3	no	—
36	C₂×C₃₂	—	73	3	no	—
37	C₆₄	—	73	1	no	—
38	C₆₄	—	73	3	no	—
39	#131	#10596842	1	1	yes	characteristic
40	M₃₂	—	73	3	no	—
41	C₂×C₁₆	—	73	3	no	—
42	C₃₂	—	73	1	no	—
43	C₃₂	—	73	3	no	—
44	#41	#11924040	1	1	yes	characteristic
45	M₁₆	#11924040	1	3	yes	—
46	C₂×C₈	C₂×#10596842	1	3	yes	—
47	C₁₆	—	73	3	no	—
48	C₁₆	—	73	1	no	—
49	Q₈	#14556681	1	1	yes	characteristic
50	D₄	#14556681	1	3	yes	—
51	C₂×C₄	C₂×#11924040	1	3	yes	—
52	C₈	C₂×#11924040	1	3	yes	—
53	C₈	C₂²×#10596842	1	1	yes	characteristic
54	C₂²	C₂×#14556681	1	3	yes	—
55	C₄	C₂×#14556681	1	3	yes	—
56	C₄	C₂²×#11924040	1	1	yes	characteristic
57	C₂	—	2	3	no	—
58	C₂	C₂²×#14556681	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₃₂
Fitting	#131×C₇₃	C₈
prime radical	#41×C₇₃	C₁₆
cosocle	#14556641	C₂³
hypercenter	#131	#10596842
hypocenter	C₇₃	#13737
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #22627035	C₂	semidirect
2. C₂×#17989669	C₂	semidirect
33. C₇₃	#13737	semidirect

Maximal subgroups

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

subgroup	index
#22627035	2
C₂×#17989669	2
#22626354	2
#13737	73