Subgroups — #22624843

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11924031	C₂	1	2	yes	maximal
2	C₈×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924031	C₄	1	4	yes	—
4	C₄×#10596831	C₄	1	1	yes	characteristic
5	C₄×#10596831	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
7	#11924031	C₈	1	8	yes	complemented
8	C₂×#10596831	C₈	1	2	yes	—
9	C₂×#10596831	C₂×C₄	1	2	yes	—
10	C₂×C₈×C₇₃	C₈	1	2	yes	—
11	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₇₃	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₇₃	—	2	2	no	—
16	#10596831	—	2	2	no	—
17	#10596831	C₂×C₈	1	4	yes	—
18	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₇₃	C₄×C₈	1	2	yes	—
20	C₄×C₇₃	M₃₂	1	2	yes	—
21	C₄×C₇₃	M₃₂	1	2	yes	—
22	C₂×C₇₃	C₈²	1	1	yes	characteristic
23	C₂×C₇₃	#346	1	1	yes	characteristic
24	C₂×C₇₃	#346	1	1	yes	characteristic
25	#1311	—	73	1	no	maximal, Sylow
26	C₇₃	#1311	1	1	yes	characteristic, complemented, Sylow
27	C₄×C₁₆	—	73	2	no	—
28	C₈²	—	73	1	no	—
29	C₂×C₁₆	—	73	4	no	—
30	C₄×C₈	—	73	1	no	—
31	C₄×C₈	—	73	1	no	—
32	C₄×C₈	#64408	1	1	yes	characteristic
33	C₂×C₈	—	73	2	no	—
34	C₂×C₈	—	73	2	no	—
35	C₂×C₈	#10596833	1	2	yes	—
36	C₄²	C₂×#64408	1	1	yes	characteristic
37	C₁₆	—	73	8	no	—
38	C₂×C₄	C₄×#64408	1	1	yes	characteristic
39	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
40	C₂×C₄	#11924036	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	—	73	4	no	—
43	C₈	—	146	2	no	—
44	C₂²	C₄×#10596833	1	1	yes	characteristic
45	C₄	C₈×#64408	1	2	yes	—
46	C₄	#14556665	1	2	yes	—
47	C₄	#14556666	1	2	yes	—
48	C₂	C₈×#10596833	1	1	yes	characteristic
49	C₂	#17989475	1	1	yes	characteristic
50	C₂	#17989476	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×#64408
commutator	C₂×C₇₃	C₈²
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₄×C₈
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1311
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. #11924031	C₈	semidirect
26. C₇₃	#1311	semidirect