Subgroups — #22612181

Order 9344.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁₆₈	C₂	1	4	yes	maximal, complemented
2	#17988964	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₈₄	—	2	2	no	—
5	C₂×D₅₈₄	C₂²	1	4	yes	—
6	#14556588	—	2	2	no	—
7	D₁₁₆₈	—	2	8	no	—
8	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
9	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×D₂₉₂	—	2	4	no	—
11	C₂×D₂₉₂	—	4	4	no	—
12	D₅₈₄	—	2	8	no	—
13	D₅₈₄	—	4	4	no	—
14	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
15	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
16	C₄²×C₇₃	D₄	1	1	yes	characteristic
17	C₁₆×C₇₃	D₄	1	4	yes	complemented
18	C₂²×D₇₃	—	4	4	no	—
19	C₂×C₄×C₇₃	D₈	1	2	yes	—
20	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
21	D₂₉₂	—	4	4	no	—
22	D₂₉₂	—	4	4	no	—
23	D₂₉₂	—	8	8	no	—
24	C₈×C₇₃	D₈	1	2	yes	—
25	C₈×C₇₃	C₂×D₄	1	2	yes	—
26	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
27	C₂×D₇₃	—	8	4	no	—
28	C₂×D₇₃	—	8	8	no	—
29	C₄×C₇₃	D₁₆	1	4	yes	complemented
30	C₄×C₇₃	#127	1	1	yes	characteristic
31	C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
32	C₂×C₇₃	#493	1	1	yes	characteristic
33	C₂×C₇₃	C₂×D₁₆	1	2	yes	—
34	D₇₃	—	16	4	no	—
35	#2246	—	73	1	no	maximal, Sylow
36	C₇₃	#2246	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₁₆	—	73	4	no	—
38	#493	—	73	2	no	—
39	C₄×C₁₆	D₇₃	1	1	yes	characteristic, complemented
40	C₂×D₈	—	73	4	no	—
41	C₂×D₈	—	146	2	no	—
42	#127	—	146	2	no	—
43	D₁₆	—	146	8	no	—
44	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
45	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
46	C₂×D₄	—	292	4	no	—
47	C₂×D₄	—	146	4	no	—
48	D₈	—	292	4	no	—
49	D₈	—	146	8	no	—
50	C₂×C₈	D₂₉₂	1	1	yes	characteristic
51	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
52	C₄²	D₂₉₂	1	1	yes	characteristic
53	C₁₆	D₂₉₂	1	4	yes	complemented
54	C₂³	—	292	4	no	—
55	D₄	—	292	4	no	—
56	D₄	—	292	4	no	—
57	D₄	—	584	8	no	—
58	C₂×C₄	D₅₈₄	1	2	yes	—
59	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
60	C₈	D₅₈₄	1	2	yes	—
61	C₈	C₂×D₂₉₂	1	2	yes	—
62	C₂²	—	584	4	no	—
63	C₂²	—	584	8	no	—
64	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
65	C₄	D₁₁₆₈	1	4	yes	complemented
66	C₄	#14556588	1	1	yes	characteristic
67	C₄	C₂×D₅₈₄	1	1	yes	characteristic
68	C₂	—	1168	4	no	—
69	C₂	#17988964	1	1	yes	characteristic
70	C₂	C₂×D₁₁₆₈	1	2	yes	—

	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	#2246
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
1. C₂×D₁₁₆₈	C₂	semidirect
2. #17988964	C₂	semidirect
3. C₄×C₁₆×C₇₃	C₂	semidirect
17. C₁₆×C₇₃	D₄	semidirect
29. C₄×C₇₃	D₁₆	semidirect
36. C₇₃	#2246	semidirect
39. C₄×C₁₆	D₇₃	semidirect
53. C₁₆	D₂₉₂	semidirect
65. C₄	D₁₁₆₈	semidirect