Subgroups — #22624849

Order 9344.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989475	C₂	1	1	yes	maximal, characteristic
2	#17989475	C₂	1	1	yes	maximal, characteristic
3	#17988309	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	C₄	1	2	yes	—
5	C₂×#11924031	C₄	1	2	yes	—
6	C₄×#10596831	C₄	1	1	yes	characteristic
7	C₄×#10596831	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
9	#11924031	—	2	2	no	—
10	#11924031	C₈	1	4	yes	complemented
11	C₂×#10596831	—	2	1	no	—
12	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
13	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₇₃	—	2	1	no	—
15	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
19	C₈×C₇₃	—	4	1	no	—
20	#10596831	—	4	1	no	—
21	#10596831	C₂×C₈	1	2	yes	—
22	#10596831	M₁₆	1	2	yes	—
23	C₂²×C₇₃	#97	1	1	yes	characteristic
24	C₄×C₇₃	—	2	1	no	—
25	C₄×C₇₃	—	2	1	no	—
26	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
27	C₄×C₇₃	#97	1	1	yes	characteristic
28	C₂×C₇₃	#322	1	1	yes	characteristic
29	C₂×C₇₃	#347	1	1	yes	characteristic
30	C₂×C₇₃	#347	1	1	yes	characteristic
31	#1313	—	73	1	no	maximal, Sylow
32	C₇₃	#1313	1	1	yes	characteristic, complemented, Sylow
33	#346	—	73	1	no	—
34	#346	—	73	1	no	—
35	#322	—	73	1	no	—
36	C₂×C₁₆	—	73	2	no	—
37	C₂×C₁₆	—	73	2	no	—
38	C₄×C₈	—	73	1	no	—
39	C₄×C₈	—	73	1	no	—
40	C₄×C₈	#64408	1	1	yes	characteristic
41	C₂×C₈	—	2	1	no	—
42	C₂×C₈	—	73	1	no	—
43	C₂×C₈	—	73	1	no	—
44	C₂×C₈	—	146	1	no	—
45	C₄²	C₂×#64408	1	1	yes	characteristic
46	C₁₆	—	73	4	no	—
47	C₁₆	—	146	2	no	—
48	C₂×C₄	C₄×#64408	1	1	yes	characteristic
49	C₂×C₄	#11924037	1	1	yes	characteristic
50	C₂×C₄	#11924038	1	1	yes	characteristic
51	C₈	—	4	1	no	—
52	C₈	—	292	1	no	—
53	C₈	—	73	2	no	—
54	C₈	—	73	2	no	—
55	C₂²	#14556646	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	C₈×#64408	1	1	yes	characteristic
59	C₄	#14556645	1	1	yes	characteristic
60	C₂	#17989429	1	1	yes	characteristic
61	C₂	#17989479	1	1	yes	characteristic
62	C₂	#17989480	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#64408
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₄²	C₂×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	#97
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1313
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
10. #11924031	C₈	semidirect
32. C₇₃	#1313	semidirect