Subgroups — #22609549

Order 9344.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988992	C₂	1	4	yes	maximal
2	#17988967	C₂	1	2	yes	maximal
3	C₈²×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₉₂	—	2	4	no	—
5	#14556591	C₂²	1	4	yes	—
6	#14556525	—	2	8	no	—
7	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₇₃	C₂²	1	2	yes	—
9	C₂×Dic₁₄₆	—	2	4	no	—
10	Dic₂₉₂	—	4	8	no	—
11	C₄⋊Dic₇₃	—	2	8	no	—
12	C₂×C₈×C₇₃	D₄	1	2	yes	—
13	C₂×C₈×C₇₃	D₄	1	4	yes	—
14	C₄²×C₇₃	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
17	C₂×Dic₇₃	—	4	4	no	—
18	Dic₁₄₆	—	4	8	no	—
19	C₈×C₇₃	D₈	1	4	yes	—
20	C₈×C₇₃	Q₁₆	1	8	yes	complemented
21	C₂²×C₇₃	#127	1	1	yes	characteristic
22	C₄×C₇₃	C₂×D₈	1	2	yes	—
23	C₄×C₇₃	C₂×Q₁₆	1	4	yes	—
24	Dic₇₃	—	8	4	no	—
25	C₂×C₇₃	#493	1	1	yes	characteristic
26	C₂×C₇₃	#494	1	2	yes	—
27	#1713	—	73	1	no	maximal, Sylow
28	C₇₃	#1713	1	1	yes	characteristic, complemented, Sylow
29	#500	—	73	4	no	—
30	#494	—	73	2	no	—
31	C₈²	D₇₃	1	1	yes	characteristic
32	C₂×Q₁₆	—	146	4	no	—
33	C₄⋊Q₈	—	73	4	no	—
34	#107	—	146	8	no	—
35	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
36	C₄×C₈	C₂×D₇₃	1	2	yes	—
37	C₂×Q₈	—	146	4	no	—
38	Q₁₆	—	292	8	no	—
39	C₂×C₈	D₂₉₂	1	2	yes	—
40	C₂×C₈	D₂₉₂	1	4	yes	—
41	C₄⋊C₄	—	146	8	no	—
42	C₄²	C₂²×D₇₃	1	1	yes	characteristic
43	Q₈	—	292	8	no	—
44	C₂×C₄	—	292	4	no	—
45	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
46	C₂×C₄	C₂×D₂₉₂	1	2	yes	—
47	C₈	D₅₈₄	1	4	yes	—
48	C₈	Dic₂₉₂	1	8	yes	complemented
49	C₂²	#14556588	1	1	yes	characteristic
50	C₄	—	584	4	no	—
51	C₄	C₂×D₅₈₄	1	2	yes	—
52	C₄	C₂×Dic₂₉₂	1	4	yes	—
53	C₂	#17988964	1	1	yes	characteristic
54	C₂	#17988967	1	2	yes	—

	subgroup	G/H
center	C₂²	#14556588
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	C₈²×C₇₃	C₂
socle	C₂²×C₇₃	#127
hypercenter	C₈²	D₇₃
hypocenter	C₇₃	#1713
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₇₃	Q₁₆	semidirect
28. C₇₃	#1713	semidirect
48. C₈	Dic₂₉₂	semidirect