Subgroups — #34033153

Order 18688.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22627036	C₂	1	2	yes	maximal
2	#22625037	C₂	1	1	yes	maximal, characteristic
3	#17989669	C₄	1	4	yes	complemented
4	#17989518	C₂²	1	1	yes	characteristic
5	C₁₆×#64408	C₄	1	1	yes	characteristic
6	C₃₂×D₇₃	C₄	1	1	yes	characteristic
7	#14556664	C₈	1	1	yes	characteristic
8	C₈×#64408	C₈	1	1	yes	characteristic
9	#14556641	C₂×C₄	1	2	yes	—
10	C₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
11	#14556497	C₈	1	1	yes	characteristic
12	C₃₂×C₇₃	C₈	1	1	yes	characteristic
13	#11924036	C₁₆	1	1	yes	characteristic
14	C₄×#64408	C₁₆	1	1	yes	characteristic
15	#11924031	C₁₆	1	2	yes	—
16	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic
17	#11924003	C₄²	1	1	yes	characteristic
18	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
19	C₂×#64408	—	2	1	no	—
20	C₄×D₇₃	C₂×C₁₆	1	1	yes	characteristic
21	#10596833	—	2	1	no	—
22	C₈×C₇₃	C₄×C₈	1	1	yes	characteristic
23	#10596831	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₇₃	M₆₄	1	1	yes	characteristic
25	#64408	—	4	1	no	—
26	C₄×C₇₃	C₄×C₁₆	1	1	yes	characteristic
27	Dic₇₃	M₆₄	1	1	yes	characteristic
28	#7511	—	73	1	no	maximal, Sylow
29	C₂×C₇₃	#1397	1	1	yes	characteristic
30	D₇₃	—	2	1	no	—
31	M₁₂₈	—	73	2	no	—
32	#1397	—	73	1	no	—
33	C₇₃	#7511	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃₂	—	73	1	no	—
35	C₂×C₃₂	—	73	1	no	—
36	C₄×C₁₆	—	73	1	no	—
37	C₆₄	—	73	4	no	—
38	C₂×C₁₆	—	73	1	no	—
39	C₂×C₁₆	—	73	1	no	—
40	C₄×C₈	—	73	1	no	—
41	C₃₂	—	73	2	no	—
42	C₃₂	—	73	1	no	—
43	C₃₂	#10596842	1	1	yes	characteristic
44	C₂×C₈	—	73	1	no	—
45	C₂×C₈	—	73	1	no	—
46	C₄²	—	73	1	no	—
47	C₁₆	—	73	2	no	—
48	C₁₆	—	73	1	no	—
49	C₁₆	C₂×#10596842	1	1	yes	characteristic
50	C₂×C₄	—	73	1	no	—
51	C₂×C₄	—	146	1	no	—
52	C₈	—	73	1	no	—
53	C₈	—	146	1	no	—
54	C₈	C₄×#10596842	1	1	yes	characteristic
55	C₂²	—	73	1	no	—
56	C₄	—	292	1	no	—
57	C₄	—	73	1	no	—
58	C₄	#64408⋊C₁₆	1	1	yes	characteristic
59	C₂	—	146	1	no	—
60	C₂	#22627018	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#10596842
commutator	C₄×C₇₃	C₄×C₁₆
Frattini	C₁₆	C₂×#10596842
Fitting	C₃₂×C₇₃	C₈
socle	C₂×C₇₃	#1397
prime radical	C₂×D₇₃	M₆₄
cosocle	#17989518	C₂²
hypercenter	C₃₂	#10596842
hypocenter	C₇₃	#7511
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
3. #17989669	C₄	semidirect
33. C₇₃	#7511	semidirect

Maximal subgroups

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

subgroup	index
#22627036	2
#22625037	2
#7511	73