Subgroups — #34001211

Order 18688.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989426	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₂×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#17989426	—	2	2	no	—
4	C₂×C₁₆×D₇₃	C₄	1	1	yes	characteristic
5	C₂×#14556497	C₂²	1	1	yes	characteristic
6	C₃₂×D₇₃	—	2	2	no	—
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	—	2	1	no	—
34	C₂×D₇₃	C₆₄	1	2	yes	complemented
35	C₄×C₇₃	C₂²⋊C₁₆	1	1	yes	characteristic
36	C₄×C₇₃	M₆₄	1	1	yes	characteristic
37	Dic₇₃	—	2	1	no	—
38	C₂²⋊C₆₄	—	73	1	no	maximal, Sylow
39	C₂×C₇₃	C₂²⋊C₃₂	1	1	yes	characteristic
40	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
41	C₂×C₇₃	M₁₂₈	1	1	yes	characteristic
42	D₇₃	—	2	2	no	—
43	C₂²×C₃₂	—	73	1	no	—
44	C₂×C₆₄	—	73	2	no	—
45	C₇₃	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₁₆	—	73	1	no	—
47	C₂×C₃₂	—	73	1	no	—
48	C₂×C₃₂	—	146	2	no	—
49	C₂×C₃₂	#64408	1	1	yes	characteristic
50	C₆₄	—	146	2	no	—
51	C₂²×C₈	—	73	1	no	—
52	C₂×C₁₆	—	73	1	no	—
53	C₂×C₁₆	—	146	1	no	—
54	C₂×C₁₆	—	146	1	no	—
55	C₂×C₁₆	C₂×#64408	1	1	yes	characteristic
56	C₃₂	—	2	1	no	—
57	C₃₂	—	73	2	no	—
58	C₂²×C₄	—	73	1	no	—
59	C₂×C₈	—	73	1	no	—
60	C₂×C₈	—	146	1	no	—
61	C₂×C₈	—	146	1	no	—
62	C₂×C₈	#11924036	1	1	yes	characteristic
63	C₁₆	—	146	1	no	—
64	C₁₆	C₂²⋊#64408	1	1	yes	characteristic
65	C₁₆	#11924038	1	1	yes	characteristic
66	C₂³	—	73	1	no	—
67	C₂×C₄	—	73	1	no	—
68	C₂×C₄	—	146	1	no	—
69	C₂×C₄	—	146	1	no	—
70	C₂×C₄	#14556664	1	1	yes	characteristic
71	C₈	—	146	1	no	—
72	C₈	#14556648	1	1	yes	characteristic
73	C₈	#14556666	1	1	yes	characteristic
74	C₂²	—	73	2	no	—
75	C₂²	—	146	1	no	—
76	C₂²	—	146	1	no	—
77	C₂²	#17989518	1	1	yes	characteristic
78	C₄	—	146	1	no	—
79	C₄	#17989482	1	1	yes	characteristic
80	C₄	#17989520	1	1	yes	characteristic
81	C₂	—	146	2	no	—
82	C₂	#22625045	1	1	yes	characteristic
83	C₂	#22625099	1	1	yes	characteristic
84	C₂	#22625101	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×#64408
commutator	C₂×C₇₃	C₂×C₆₄
Fitting	C₂×C₃₂×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₃₂
prime radical	C₂²×D₇₃	C₃₂
cosocle	C₂×#14556497	C₂²
hypercenter	C₂×C₃₂	#64408
hypocenter	C₇₃	C₂²⋊C₆₄
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×#17989426	C₂	semidirect
34. C₂×D₇₃	C₆₄	semidirect
45. C₇₃	C₂²⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989426	2
C₂×C₃₂×D₇₃	2
C₂²⋊C₆₄	73