Subgroups — #32973870

Order 18688.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22612240	C₂	1	1	yes	maximal, characteristic
2	#22608142	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#1424	C₂	1	1	yes	maximal, characteristic, complemented
4	#17989019	—	2	1	no	—
5	Dic₁₁₆₈	C₄	1	1	yes	characteristic, complemented
6	#17988426	—	2	1	no	—
7	D₂₃₃₆	C₄	1	1	yes	characteristic, complemented
8	#17988306	—	2	1	no	—
9	C₂×C₃₂×C₇₃	C₂²	1	1	yes	characteristic
10	#366×C₇₃	—	2	1	no	—
11	#14556613	—	4	1	no	—
12	Dic₅₈₄	—	2	1	no	—
13	#14556536	—	4	1	no	—
14	D₁₁₆₈	—	2	1	no	—
15	C₂×C₁₆×C₇₃	D₄	1	1	yes	characteristic
16	#107×C₇₃	—	4	1	no	—
17	C₃₂×C₇₃	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₇₃	D₄	1	1	yes	characteristic
19	#11924028	—	8	1	no	—
20	Dic₂₉₂	—	4	1	no	—
21	#11924017	—	8	1	no	—
22	D₅₈₄	—	4	1	no	—
23	C₂×C₈×C₇₃	D₈	1	1	yes	characteristic
24	C₄⋊C₄×C₇₃	—	8	1	no	—
25	C₁₆×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₇₃	SD₁₆	1	1	yes	characteristic
27	C₂×C₄×C₇₃	—	16	1	no	—
28	C₂×C₄×C₇₃	D₁₆	1	1	yes	characteristic
29	C₂²⋊D₇₃	—	16	1	no	—
30	D₂₉₂	—	8	1	no	—
31	C₄×D₇₃	—	16	1	no	—
32	Dic₁₄₆	—	8	1	no	—
33	C₈×C₇₃	#102	1	1	yes	characteristic
34	C₈×C₇₃	SD₃₂	1	1	yes	characteristic
35	C₂²×C₇₃	D₃₂	1	1	yes	characteristic
36	C₂×D₇₃	—	16	1	no	—
37	C₄×C₇₃	—	32	1	no	—
38	C₄×C₇₃	#357	1	1	yes	characteristic
39	C₄×C₇₃	SD₆₄	1	1	yes	characteristic
40	Dic₇₃	—	16	1	no	—
41	#7540	—	73	1	no	maximal, Sylow
42	C₂×C₇₃	—	2	1	no	—
43	C₂×C₇₃	#1415	1	1	yes	characteristic
44	D₇₃	—	32	1	no	—
45	#2262	—	73	1	no	—
46	M₁₂₈	—	73	1	no	—
47	#1424	D₇₃	1	1	yes	characteristic, complemented
48	C₇₃	#7540	1	1	yes	characteristic, complemented, Sylow
49	#508	—	146	1	no	—
50	Q₆₄	—	73	1	no	—
51	SD₆₄	—	146	1	no	—
52	D₃₂	—	73	1	no	—
53	C₂×C₃₂	C₂×D₇₃	1	1	yes	characteristic
54	#366	—	2	1	no	—
55	C₆₄	—	146	1	no	—
56	#135	—	292	1	no	—
57	Q₃₂	—	146	1	no	—
58	SD₃₂	—	292	1	no	—
59	D₁₆	—	146	1	no	—
60	C₂×C₁₆	C₂²⋊D₇₃	1	1	yes	characteristic
61	#107	—	4	1	no	—
62	C₃₂	C₄×D₇₃	1	1	yes	characteristic
63	C₃₂	D₂₉₂	1	1	yes	characteristic
64	#41	—	584	1	no	—
65	Q₁₆	—	292	1	no	—
66	SD₁₆	—	584	1	no	—
67	D₈	—	292	1	no	—
68	C₂×C₈	#11924013	1	1	yes	characteristic
69	C₄⋊C₄	—	8	1	no	—
70	C₁₆	#11924005	1	1	yes	characteristic
71	C₁₆	#11924015	1	1	yes	characteristic
72	Q₈	—	584	1	no	—
73	D₄	—	584	1	no	—
74	D₄	—	1168	1	no	—
75	C₂×C₄	—	16	1	no	—
76	C₂×C₄	—	1168	1	no	—
77	C₂×C₄	#14556532	1	1	yes	characteristic
78	C₈	#14556511	1	1	yes	characteristic
79	C₈	#14556534	1	1	yes	characteristic
80	C₂²	—	1168	1	no	—
81	C₂²	#17988422	1	1	yes	characteristic
82	C₄	—	32	1	no	—
83	C₄	—	1168	1	no	—
84	C₄	#17988387	1	1	yes	characteristic
85	C₄	#17988424	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	2336	1	no	—
88	C₂	#22608108	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22608108
commutator	C₃₂×C₇₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₇₃
Fitting	C₇₃×#1424	C₂
socle	C₂×C₇₃	#1415
prime radical	#22612240	C₂
cosocle	C₂×C₃₂×C₇₃	C₂²
hypercenter	#1424	D₇₃
hypocenter	C₇₃	#7540
LCS	G ▷ C₃₂×C₇₃ ▷ C₁₆×C₇₃ ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1424

Complements

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

N	H ≅ G/N	type
2. #22608142	C₂	semidirect
3. C₇₃×#1424	C₂	semidirect
5. Dic₁₁₆₈	C₄	semidirect
7. D₂₃₃₆	C₄	semidirect
47. #1424	D₇₃	semidirect
48. C₇₃	#7540	semidirect

Maximal subgroups

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

subgroup	index
#22612240	2
#22608142	2
C₇₃×#1424	2
#7540	73