Subgroups — #22607970

Order 9344.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988408	C₂	1	2	yes	maximal
2	#494×C₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556531	—	2	2	no	—
4	C₂×Q₁₆×C₇₃	—	2	2	no	—
5	C₄⋊Q₈×C₇₃	C₄	1	2	yes	—
6	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
7	#11924003	—	4	2	no	—
8	C₂×Q₈×C₇₃	—	2	2	no	—
9	Q₁₆×C₇₃	—	4	2	no	—
10	Q₁₆×C₇₃	—	4	2	no	—
11	C₂×C₈×C₇₃	D₄	1	2	yes	—
12	C₄⋊C₄×C₇₃	—	4	2	no	—
13	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
14	Q₈×C₇₃	—	4	4	no	—
15	C₂×C₄×C₇₃	—	2	1	no	—
16	C₂×C₄×C₇₃	—	4	2	no	—
17	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₈×C₇₃	D₈	1	2	yes	—
19	C₈×C₇₃	SD₁₆	1	2	yes	—
20	C₂²×C₇₃	#100	1	1	yes	characteristic
21	C₄×C₇₃	—	2	2	no	—
22	C₄×C₇₃	—	8	2	no	—
23	C₄×C₇₃	#102	1	2	yes	—
24	C₂×C₇₃	—	2	1	no	—
25	C₂×C₇₃	#331	1	1	yes	characteristic
26	#1358	—	73	1	no	maximal, Sylow
27	C₇₃	#1358	1	1	yes	characteristic, complemented, Sylow
28	#494	D₇₃	1	1	yes	characteristic
29	#364	—	73	2	no	—
30	C₂×Q₁₆	—	2	2	no	—
31	C₄⋊Q₈	Dic₇₃	1	2	yes	—
32	M₃₂	—	146	2	no	—
33	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
34	C₂×Q₈	—	2	2	no	—
35	Q₁₆	—	4	2	no	—
36	Q₁₆	—	4	2	no	—
37	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
38	C₄⋊C₄	—	4	2	no	—
39	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
40	C₁₆	—	292	2	no	—
41	Q₈	—	4	4	no	—
42	C₂×C₄	—	2	1	no	—
43	C₂×C₄	—	4	2	no	—
44	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
45	C₈	#11924013	1	2	yes	—
46	C₈	#11924016	1	2	yes	—
47	C₂²	#14556508	1	1	yes	characteristic
48	C₄	—	2	2	no	—
49	C₄	—	8	2	no	—
50	C₄	#14556512	1	2	yes	—
51	C₂	—	2	1	no	—
52	C₂	#17988331	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988331
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂×C₇₃	#331
hypercenter	#494	D₇₃
hypocenter	C₇₃	#1358
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
27. C₇₃	#1358	semidirect