Subgroups — #22612206

Order 9344.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988992	C₂	1	2	yes	maximal
2	#17988413	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556591	—	2	2	no	—
5	#14556525	—	2	2	no	—
6	#14556525	C₂²	1	4	yes	—
7	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
8	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₄₆	—	4	2	no	—
10	C₄⋊Dic₇₃	—	2	4	no	—
11	C₄⋊Dic₇₃	—	4	2	no	—
12	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
14	C₄²×C₇₃	D₄	1	1	yes	characteristic
15	C₁₆×C₇₃	Q₈	1	4	yes	complemented
16	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
17	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
18	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₇₃	—	4	4	no	—
20	Dic₁₄₆	—	8	4	no	—
21	C₈×C₇₃	Q₁₆	1	2	yes	—
22	C₈×C₇₃	C₂×Q₈	1	2	yes	—
23	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
24	C₄×C₇₃	D₁₆	1	2	yes	—
25	C₄×C₇₃	Q₃₂	1	2	yes	—
26	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₇₃	—	8	4	no	—
29	C₂×C₇₃	#500	1	1	yes	characteristic
30	C₂×C₇₃	C₂×D₁₆	1	1	yes	characteristic
31	C₂×C₇₃	C₂×Q₃₂	1	1	yes	characteristic
32	#2252	—	73	1	no	maximal, Sylow
33	C₇₃	#2252	1	1	yes	characteristic, complemented, Sylow
34	#500	—	73	2	no	—
35	#366	—	73	4	no	—
36	C₄×C₁₆	D₇₃	1	1	yes	characteristic
37	C₄⋊Q₈	—	146	2	no	—
38	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
39	#107	—	73	4	no	—
40	#107	—	146	2	no	—
41	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
42	C₂×Q₈	—	292	2	no	—
43	C₂×C₈	D₂₉₂	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
45	C₄⋊C₄	—	292	2	no	—
46	C₄⋊C₄	—	146	4	no	—
47	C₄²	D₂₉₂	1	1	yes	characteristic
48	C₁₆	Dic₁₄₆	1	4	yes	complemented
49	Q₈	—	584	4	no	—
50	C₂×C₄	—	292	4	no	—
51	C₂×C₄	D₅₈₄	1	1	yes	characteristic
52	C₂×C₄	D₅₈₄	1	1	yes	characteristic
53	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
54	C₈	Dic₂₉₂	1	2	yes	—
55	C₈	C₂×Dic₁₄₆	1	2	yes	—
56	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
57	C₄	—	584	4	no	—
58	C₄	D₁₁₆₈	1	2	yes	—
59	C₄	Dic₅₈₄	1	2	yes	—
60	C₄	#14556591	1	1	yes	characteristic
61	C₄	C₂×Dic₂₉₂	1	1	yes	characteristic
62	C₂	#17988992	1	1	yes	characteristic
63	C₂	C₂×D₁₁₆₈	1	1	yes	characteristic
64	C₂	C₂×Dic₅₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₄×C₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	C₄×C₁₆	D₇₃
hypocenter	C₇₃	#2252
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₇₃	Q₈	semidirect
33. C₇₃	#2252	semidirect
48. C₁₆	Dic₁₄₆	semidirect