Subgroups — #34001213

Order 18688.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625100	C₂	1	2	yes	maximal, complemented
2	C₂×#17988420	C₂	1	1	yes	maximal, characteristic
3	#17989426	—	2	2	no	—
4	C₂×C₁₆×D₇₃	C₄	1	1	yes	characteristic
5	#17988420	—	2	2	no	—
6	C₂×#14556497	C₂²	1	1	yes	characteristic
7	C₂×C₃₂×C₇₃	C₄	1	1	yes	characteristic
8	C₂×C₈×D₇₃	C₈	1	1	yes	characteristic
9	C₂×#11924003	C₈	1	1	yes	characteristic
10	C₁₆×D₇₃	—	2	1	no	—
11	C₁₆×D₇₃	—	2	1	no	—
12	#14556497	D₄	1	2	yes	—
13	C₂×C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₃₂×C₇₃	—	2	1	no	—
15	C₂×C₄×D₇₃	C₁₆	1	1	yes	characteristic
16	C₂×#10596831	C₁₆	1	1	yes	characteristic
17	C₈×D₇₃	—	2	1	no	—
18	C₈×D₇₃	—	2	1	no	—
19	#11924003	—	2	1	no	—
20	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
21	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₆×C₇₃	M₁₆	1	1	yes	characteristic
23	C₂²×D₇₃	C₃₂	1	1	yes	characteristic
24	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×Dic₇₃	C₃₂	1	1	yes	characteristic
26	C₄×D₇₃	—	2	1	no	—
27	C₄×D₇₃	—	2	1	no	—
28	C₈×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
29	C₈×C₇₃	M₃₂	1	1	yes	characteristic
30	#10596831	—	2	1	no	—
31	C₂²×C₇₃	C₂×C₃₂	1	1	yes	characteristic
32	C₂×D₇₃	—	2	1	no	—
33	C₂×D₇₃	—	4	1	no	—
34	C₄×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	C₄×C₇₃	M₆₄	1	1	yes	characteristic
36	Dic₇₃	—	2	1	no	—
37	#7513	—	73	1	no	maximal, Sylow
38	C₂×C₇₃	—	2	1	no	—
39	C₂×C₇₃	C₂²⋊C₃₂	1	1	yes	characteristic
40	D₇₃	—	4	1	no	—
41	C₂×M₆₄	—	73	1	no	—
42	M₁₂₈	—	73	2	no	—
43	C₇₃	#7513	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₁₆	—	73	1	no	—
45	M₆₄	—	146	2	no	—
46	C₂×C₃₂	—	73	1	no	—
47	C₂×C₃₂	#64408	1	1	yes	characteristic
48	C₆₄	—	146	2	no	—
49	C₂²×C₈	—	73	1	no	—
50	C₂×C₁₆	—	73	1	no	—
51	C₂×C₁₆	—	146	1	no	—
52	C₂×C₁₆	—	146	1	no	—
53	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
54	C₃₂	—	2	1	no	—
55	C₃₂	—	73	2	no	—
56	C₂²×C₄	—	73	1	no	—
57	C₂×C₈	—	73	1	no	—
58	C₂×C₈	—	146	1	no	—
59	C₂×C₈	—	146	1	no	—
60	C₂×C₈	#11924036	1	1	yes	characteristic
61	C₁₆	—	146	1	no	—
62	C₁₆	C₂²⋊#64408	1	1	yes	characteristic
63	C₁₆	#11924038	1	1	yes	characteristic
64	C₂³	—	73	1	no	—
65	C₂×C₄	—	73	1	no	—
66	C₂×C₄	—	146	1	no	—
67	C₂×C₄	—	146	1	no	—
68	C₂×C₄	#14556664	1	1	yes	characteristic
69	C₈	—	146	1	no	—
70	C₈	#14556648	1	1	yes	characteristic
71	C₈	#14556666	1	1	yes	characteristic
72	C₂²	—	292	1	no	—
73	C₂²	—	146	1	no	—
74	C₂²	#17989518	1	1	yes	characteristic
75	C₄	—	146	1	no	—
76	C₄	#17989482	1	1	yes	characteristic
77	C₄	#17989520	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	292	1	no	—
80	C₂	#22625045	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#64408
commutator	C₂²×C₇₃	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#64408
Fitting	C₂×C₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₂²⋊C₃₂
prime radical	C₂²×D₇₃	C₃₂
cosocle	C₂×#14556497	C₂²
hypercenter	C₂×C₃₂	#64408
hypocenter	C₇₃	#7513
LCS	G ▷ C₂²×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
1. #22625100	C₂	semidirect
43. C₇₃	#7513	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22625100	2
C₂×#17988420	2
#7513	73