Subgroups — #22625045

Order 9344.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556641	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#14556641	—	2	2	no	—
4	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
5	C₂×#11924003	C₂²	1	1	yes	characteristic
6	C₁₆×D₇₃	—	2	2	no	—
7	C₂×C₁₆×C₇₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
9	C₂×#10596831	C₈	1	1	yes	characteristic
10	C₈×D₇₃	—	2	1	no	—
11	C₈×D₇₃	—	2	1	no	—
12	#11924003	D₄	1	2	yes	—
13	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₇₃	—	2	1	no	—
15	C₂²×D₇₃	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₇₃	C₁₆	1	1	yes	characteristic
18	C₄×D₇₃	—	2	1	no	—
19	C₄×D₇₃	—	2	1	no	—
20	C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₇₃	M₁₆	1	1	yes	characteristic
22	#10596831	—	2	1	no	—
23	C₂²×C₇₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₇₃	—	2	1	no	—
25	C₂×D₇₃	—	2	1	no	—
26	C₂×D₇₃	C₃₂	1	2	yes	complemented
27	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₇₃	M₃₂	1	1	yes	characteristic
29	Dic₇₃	—	2	1	no	—
30	C₂×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
31	C₂×C₇₃	C₂×C₃₂	1	1	yes	characteristic
32	C₂×C₇₃	M₆₄	1	1	yes	characteristic
33	D₇₃	—	2	2	no	—
34	C₂²⋊C₃₂	—	73	1	no	maximal, Sylow
35	C₇₃	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₁₆	—	73	1	no	—
37	C₂×C₃₂	—	73	2	no	—
38	C₂²×C₈	—	73	1	no	—
39	C₂×C₁₆	—	73	1	no	—
40	C₂×C₁₆	—	146	2	no	—
41	C₂×C₁₆	#64408	1	1	yes	characteristic
42	C₃₂	—	146	2	no	—
43	C₂²×C₄	—	73	1	no	—
44	C₂×C₈	—	73	1	no	—
45	C₂×C₈	—	146	1	no	—
46	C₂×C₈	—	146	1	no	—
47	C₂×C₈	C₂×#64408	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	73	2	no	—
50	C₂³	—	73	1	no	—
51	C₂×C₄	—	73	1	no	—
52	C₂×C₄	—	146	1	no	—
53	C₂×C₄	—	146	1	no	—
54	C₂×C₄	#11924036	1	1	yes	characteristic
55	C₈	—	146	1	no	—
56	C₈	C₂²⋊#64408	1	1	yes	characteristic
57	C₈	#11924038	1	1	yes	characteristic
58	C₂²	—	73	2	no	—
59	C₂²	—	146	1	no	—
60	C₂²	—	146	1	no	—
61	C₂²	#14556664	1	1	yes	characteristic
62	C₄	—	146	1	no	—
63	C₄	#14556648	1	1	yes	characteristic
64	C₄	#14556666	1	1	yes	characteristic
65	C₂	—	146	2	no	—
66	C₂	#17989482	1	1	yes	characteristic
67	C₂	#17989518	1	1	yes	characteristic
68	C₂	#17989520	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#64408
commutator	C₂×C₇₃	C₂×C₃₂
Fitting	C₂×C₁₆×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₁₆
hypercenter	C₂×C₁₆	#64408
hypocenter	C₇₃	C₂²⋊C₃₂
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#14556641	C₂	semidirect
26. C₂×D₇₃	C₃₂	semidirect
35. C₇₃	C₂²⋊C₃₂	semidirect