Subgroups — #22624952

Order 9344.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989510	C₂	1	1	yes	maximal, characteristic
2	#17989510	C₂	1	1	yes	maximal, characteristic
3	#17988986	C₂	1	1	yes	maximal, characteristic
4	#14556665	—	2	1	no	—
5	#14556665	—	2	1	no	—
6	#14556583	C₄	1	1	yes	characteristic
7	#14556524	—	2	1	no	—
8	#14556522	—	2	1	no	—
9	C₄×#10596831	C₂²	1	1	yes	characteristic
10	#125×C₇₃	C₄	1	1	yes	characteristic
11	#11924031	—	4	1	no	—
12	#11924031	—	4	1	no	—
13	C₂×#10596831	D₄	1	1	yes	characteristic
14	C₂×#10596831	D₄	1	1	yes	characteristic
15	C₄⋊Dic₇₃	—	2	1	no	—
16	#11924007	—	4	1	no	—
17	C₄⋊C₄×C₇₃	—	2	1	no	—
18	C₄⋊C₄×C₇₃	—	4	1	no	—
19	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₇₃	—	2	1	no	—
21	C₂×C₄×C₇₃	—	4	1	no	—
22	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₇₃	—	4	1	no	—
24	#10596831	SD₁₆	1	1	yes	characteristic
25	#10596831	SD₁₆	1	1	yes	characteristic
26	#10596831	Q₁₆	1	1	yes	characteristic
27	#10596831	Q₁₆	1	1	yes	characteristic
28	C₂²×C₇₃	#100	1	1	yes	characteristic
29	C₄×C₇₃	—	4	1	no	—
30	C₄×C₇₃	—	8	1	no	—
31	C₄×C₇₃	#103	1	1	yes	characteristic
32	C₄×C₇₃	#103	1	1	yes	characteristic
33	Dic₇₃	—	8	1	no	—
34	C₂×C₇₃	—	2	1	no	—
35	C₂×C₇₃	#333	1	1	yes	characteristic
36	#1366	—	73	1	no	maximal, Sylow
37	C₇₃	#1366	1	1	yes	characteristic, complemented, Sylow
38	#499	—	73	1	no	—
39	#364	—	73	1	no	—
40	#364	—	73	1	no	—
41	#125	—	73	1	no	—
42	#125	#64408	1	1	yes	characteristic
43	M₃₂	—	146	1	no	—
44	M₃₂	—	146	1	no	—
45	#107	—	146	1	no	—
46	#106	—	146	1	no	—
47	C₄×C₈	—	73	1	no	—
48	C₂×C₈	—	73	1	no	—
49	C₂×C₈	—	73	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	4	1	no	—
52	C₄⋊C₄	—	292	1	no	—
53	C₄⋊C₄	—	146	1	no	—
54	C₄²	C₂×#64408	1	1	yes	characteristic
55	C₁₆	—	292	1	no	—
56	C₁₆	—	292	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	—	292	1	no	—
60	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
61	C₈	—	73	1	no	—
62	C₈	—	73	1	no	—
63	C₈	—	73	1	no	—
64	C₈	—	73	1	no	—
65	C₂²	#14556651	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	8	1	no	—
68	C₄	—	584	1	no	—
69	C₄	#14556654	1	1	yes	characteristic
70	C₄	#14556654	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#17989447	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989447
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	#125×C₇₃	C₄
socle	C₂×C₇₃	#333
hypercenter	#125	#64408
hypocenter	C₇₃	#1366
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
37. C₇₃	#1366	semidirect