Subgroups — #32973656

Order 18688.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14556497	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₇₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×#14556497	—	2	1	no	—
5	C₄×#11924003	C₄	1	1	yes	characteristic
6	C₈×#10596831	C₄	1	1	yes	characteristic
7	C₂×C₃₂×C₇₃	—	2	1	no	—
8	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×#11924003	—	2	1	no	—
10	C₄×#10596831	C₈	1	1	yes	characteristic
11	C₄×#10596831	C₈	1	1	yes	characteristic
12	#14556497	—	4	1	no	—
13	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	Q₈	1	1	yes	characteristic
15	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₇₃	—	4	1	no	—
17	C₂×#10596831	—	2	1	no	—
18	C₂×#10596831	C₁₆	1	1	yes	characteristic
19	C₂×#10596831	C₁₆	1	1	yes	characteristic
20	#11924003	—	2	2	no	—
21	C₂×C₈×C₇₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	M₁₆	1	1	yes	characteristic
23	C₄²×C₇₃	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₇₃	—	2	1	no	—
25	C₁₆×C₇₃	D₈	1	1	yes	characteristic
26	C₁₆×C₇₃	Q₁₆	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₁₆	1	1	yes	characteristic
29	C₂×C₄×C₇₃	M₃₂	1	1	yes	characteristic
30	C₈×C₇₃	—	2	1	no	—
31	C₈×C₇₃	#107	1	1	yes	characteristic
32	C₈×C₇₃	#108	1	1	yes	characteristic
33	#10596831	—	2	2	no	—
34	#10596831	—	2	1	no	—
35	#10596831	C₃₂	1	2	yes	complemented
36	C₂²×C₇₃	C₄⋊C₁₆	1	1	yes	characteristic
37	C₄×C₇₃	—	2	1	no	—
38	C₄×C₇₃	#335	1	1	yes	characteristic
39	C₄×C₇₃	#364	1	1	yes	characteristic
40	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₇₃	M₆₄	1	1	yes	characteristic
42	#7458	—	73	1	no	maximal, Sylow
43	C₂×C₇₃	#1370	1	1	yes	characteristic
44	C₂×C₇₃	C₄⋊C₃₂	1	1	yes	characteristic
45	C₂×C₇₃	#1422	1	1	yes	characteristic
46	C₄⋊C₃₂	—	73	1	no	—
47	C₄⋊C₃₂	D₇₃	1	1	yes	characteristic
48	C₈×C₁₆	—	73	1	no	—
49	C₇₃	#7458	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃₂	—	2	1	no	—
51	C₂×C₃₂	—	146	1	no	—
52	C₄×C₁₆	—	73	1	no	—
53	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
54	C₈²	—	73	1	no	—
55	C₂×C₁₆	—	146	1	no	—
56	C₂×C₁₆	Dic₁₄₆	1	1	yes	characteristic
57	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
58	C₄×C₈	—	73	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
61	C₃₂	—	4	1	no	—
62	C₃₂	—	292	1	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	146	1	no	—
66	C₂×C₈	#11924007	1	1	yes	characteristic
67	C₂×C₈	#11924011	1	1	yes	characteristic
68	C₄²	C₈×D₇₃	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	—	146	2	no	—
71	C₁₆	#11924013	1	1	yes	characteristic
72	C₁₆	#11924018	1	1	yes	characteristic
73	C₂×C₄	#14556520	1	1	yes	characteristic
74	C₂×C₄	C₁₆×D₇₃	1	1	yes	characteristic
75	C₂×C₄	#14556530	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	73	2	no	—
78	C₈	—	146	2	no	—
79	C₈	—	146	1	no	—
80	C₈	#14556524	1	1	yes	characteristic
81	C₈	#14556526	1	1	yes	characteristic
82	C₂²	#17988405	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	#17988339	1	1	yes	characteristic
85	C₄	#17988407	1	1	yes	characteristic
86	C₄	C₃₂×D₇₃	1	1	yes	characteristic
87	C₄	#17988420	1	1	yes	characteristic
88	C₂	#22608000	1	1	yes	characteristic
89	C₂	#22608126	1	1	yes	characteristic
90	C₂	#22608128	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₇₃
commutator	C₄×C₇₃	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₇₃
Fitting	C₇₃×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₇₃	C₄⋊C₁₆
cosocle	C₄×C₁₆×C₇₃	C₂²
hypercenter	C₄⋊C₃₂	D₇₃
hypocenter	C₇₃	#7458
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
35. #10596831	C₃₂	semidirect
49. C₇₃	#7458	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14556497	2
C₁₆×#10596831	2
C₇₃×C₄⋊C₃₂	2
#7458	73