Subgroups — #22608072

Order 9344.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989003	C₂	1	1	yes	maximal, characteristic
2	#17988421	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556597	C₄	1	1	yes	characteristic
5	#14556531	C₄	1	1	yes	characteristic
6	#14556530	—	2	1	no	—
7	C₁₆×D₇₃	—	2	1	no	—
8	#14556497	—	2	1	no	—
9	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₇₃	—	2	1	no	—
11	#11924028	C₈	1	1	yes	characteristic
12	#11924012	C₈	1	1	yes	characteristic
13	#11924011	—	2	1	no	—
14	C₈×D₇₃	—	2	1	no	—
15	#11924003	—	2	1	no	—
16	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₇₃	D₄	1	1	yes	characteristic
18	C₁₆×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₇₃	—	2	1	no	—
21	D₂₉₂	C₁₆	1	1	yes	characteristic
22	C₄×D₇₃	—	2	1	no	—
23	Dic₁₄₆	C₁₆	1	1	yes	characteristic
24	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₇₃	M₁₆	1	1	yes	characteristic
26	#10596831	—	2	1	no	—
27	C₂²×C₇₃	M₃₂	1	1	yes	characteristic
28	C₂×D₇₃	—	2	1	no	—
29	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
31	Dic₇₃	—	2	1	no	—
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₇₃	—	4	1	no	—
35	#1401	—	73	1	no	maximal, Sylow
36	C₇₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	73	1	no	—
38	M₆₄	—	73	1	no	—
39	C₂×C₃₂	D₇₃	1	1	yes	characteristic, complemented
40	#131	—	73	1	no	—
41	M₃₂	—	73	1	no	—
42	M₃₂	—	146	1	no	—
43	C₂×C₁₆	—	146	1	no	—
44	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	146	1	no	—
47	#41	—	73	1	no	—
48	M₁₆	—	73	1	no	—
49	M₁₆	—	146	1	no	—
50	C₂×C₈	—	146	1	no	—
51	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
52	C₁₆	—	146	1	no	—
53	C₁₆	D₂₉₂	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
55	Q₈	—	73	1	no	—
56	D₄	—	73	1	no	—
57	D₄	—	146	1	no	—
58	C₂×C₄	—	146	1	no	—
59	C₂×C₄	C₈×D₇₃	1	1	yes	characteristic
60	C₈	—	146	1	no	—
61	C₈	#11924005	1	1	yes	characteristic
62	C₈	#11924011	1	1	yes	characteristic
63	C₂²	—	146	1	no	—
64	C₂²	#14556530	1	1	yes	characteristic
65	C₄	—	146	1	no	—
66	C₄	#14556503	1	1	yes	characteristic
67	C₄	C₁₆×D₇₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	292	1	no	—
70	C₂	#17988366	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₂₉₂
commutator	C₄×C₇₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₇₃
Fitting	C₂×C₃₂×C₇₃	C₂
socle	C₂×C₇₃	C₂²⋊C₁₆
hypercenter	C₂×C₃₂	D₇₃
hypocenter	C₇₃	#1401
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #17988421	C₂	semidirect
3. C₂×C₃₂×C₇₃	C₂	semidirect
36. C₇₃	#1401	semidirect
39. C₂×C₃₂	D₇₃	semidirect