Subgroups — #22625048

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556641	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989004	C₂	1	1	yes	maximal, characteristic
4	#14556641	—	2	1	no	—
5	#14556641	—	2	1	no	—
6	#14556531	—	2	1	no	—
7	#14556531	C₄	1	1	yes	characteristic
8	C₂×#11924003	—	2	1	no	—
9	C₂×#11924003	C₂²	1	1	yes	characteristic
10	#131×C₇₃	C₄	1	1	yes	characteristic
11	#11924003	—	2	1	no	—
12	#11924003	D₄	1	1	yes	characteristic
13	#11924003	D₄	1	1	yes	characteristic
14	#41×C₇₃	C₈	1	1	yes	characteristic
15	M₁₆×C₇₃	—	2	1	no	—
16	M₁₆×C₇₃	C₈	1	1	yes	characteristic
17	C₂×C₈×C₇₃	—	2	1	no	—
18	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
19	Q₈×C₇₃	C₁₆	1	1	yes	characteristic
20	D₄×C₇₃	—	2	1	no	—
21	D₄×C₇₃	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₇₃	—	2	1	no	—
23	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
24	C₈×C₇₃	—	2	1	no	—
25	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₇₃	M₁₆	1	1	yes	characteristic
27	C₂²×C₇₃	—	2	1	no	—
28	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
29	C₄×C₇₃	—	2	1	no	—
30	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	—	4	1	no	—
34	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	#1401	—	73	1	no	maximal, Sylow
36	C₇₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	73	1	no	—
38	M₆₄	—	73	1	no	—
39	C₂×C₃₂	—	73	1	no	—
40	#131	#64408	1	1	yes	characteristic
41	M₃₂	—	73	1	no	—
42	M₃₂	—	146	1	no	—
43	C₂×C₁₆	—	73	1	no	—
44	C₂×C₁₆	—	146	1	no	—
45	C₃₂	—	146	1	no	—
46	C₃₂	—	146	1	no	—
47	#41	#10596833	1	1	yes	characteristic
48	M₁₆	—	2	1	no	—
49	M₁₆	#10596833	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×#64408	1	1	yes	characteristic
52	C₁₆	—	73	1	no	—
53	C₁₆	—	73	1	no	—
54	C₁₆	—	146	1	no	—
55	Q₈	#11924031	1	1	yes	characteristic
56	D₄	—	2	1	no	—
57	D₄	#11924031	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	C₂²⋊#64408	1	1	yes	characteristic
62	C₈	#11924037	1	1	yes	characteristic
63	C₂²	—	2	1	no	—
64	C₂²	#14556665	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₂²⋊#10596833	1	1	yes	characteristic
67	C₄	C₂×#11924031	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	C₂²⋊#11924031	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#64408
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₂×C₈	C₂×#64408
Fitting	#131×C₇₃	C₄
socle	C₂×C₇₃	C₂²⋊C₁₆
hypercenter	#131	#64408
hypocenter	C₇₃	#1401
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #131

Complements

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

N	H ≅ G/N	type
1. #17989519	C₂	semidirect
2. C₂×#14556641	C₂	semidirect
36. C₇₃	#1401	semidirect