Subgroups — #34001947

Order 18688.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22625644	C₂	1	3	yes	maximal
2	#22625127	C₂	1	3	yes	maximal
3	C₈²×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄×#11924036	C₂²	1	3	yes	—
5	C₄²×#64408	C₂²	1	1	yes	characteristic
6	#17989452	C₄	1	12	yes	—
7	#17989429	C₄	1	12	yes	complemented
8	C₄×C₈×D₇₃	C₂²	1	3	yes	—
9	C₈×#10596831	C₄	1	3	yes	complemented
10	C₈²×C₇₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#11924036	C₂×C₄	1	6	yes	—
12	C₂×C₄×#64408	C₂×C₄	1	6	yes	—
13	C₄×#10596833	C₂×C₄	1	12	yes	—
14	C₂×C₈×D₇₃	C₂×C₄	1	6	yes	—
15	C₄²×D₇₃	C₂³	1	1	yes	characteristic
16	C₄×#10596831	C₂×C₄	1	3	yes	—
17	C₈×Dic₇₃	C₂×C₄	1	6	yes	—
18	C₄×C₈×C₇₃	C₂×C₄	1	3	yes	—
19	C₂²×#64408	C₄²	1	4	yes	—
20	#11924036	—	2	12	no	—
21	C₂×#10596833	C₄²	1	12	yes	—
22	C₄×#64408	—	2	12	no	—
23	C₂×C₄×D₇₃	C₂²×C₄	1	3	yes	—
24	C₂×#10596831	C₄²	1	6	yes	—
25	C₈×D₇₃	—	2	12	no	—
26	C₄×Dic₇₃	C₂²×C₄	1	3	yes	—
27	C₂×C₈×C₇₃	C₄²	1	6	yes	—
28	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
30	C₂×#64408	—	2	12	no	—
31	C₂×C₄×C₇₃	C₂×C₄²	1	3	yes	—
32	C₂×Dic₇₃	C₂×C₄²	1	3	yes	—
33	C₄×D₇₃	#131	1	12	yes	—
34	#10596833	—	2	12	no	—
35	C₈×C₇₃	—	2	6	no	—
36	#10596831	—	2	6	no	—
37	C₂²×C₇₃	C₄³	1	1	yes	characteristic
38	C₂×D₇₃	#405	1	6	yes	—
39	#64408	—	4	4	no	—
40	C₄×C₇₃	#405	1	6	yes	—
41	Dic₇₃	#405	1	6	yes	—
42	#7845	—	73	1	no	maximal, Sylow
43	C₂×C₇₃	#1726	1	3	yes	—
44	D₇₃	#1454	1	4	yes	—
45	#1744	—	73	3	no	—
46	C₂×#322	—	73	3	no	—
47	C₂×C₈²	—	73	1	no	—
48	C₇₃	#7845	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₄×C₈	—	73	3	no	—
50	C₂×C₄×C₈	—	73	3	no	—
51	C₄³	—	73	1	no	—
52	#336	—	73	12	no	—
53	#322	—	73	12	no	—
54	C₈²	—	73	3	no	—
55	C₈²	#64408	1	1	yes	characteristic, complemented
56	C₂²×C₈	—	73	6	no	—
57	C₂²×C₈	—	73	6	no	—
58	C₂×C₄²	—	73	1	no	—
59	C₂×C₄²	—	73	6	no	—
60	C₄×C₈	—	73	12	no	—
61	C₄×C₈	—	73	6	no	—
62	C₄×C₈	—	73	3	no	—
63	C₄×C₈	C₂×#64408	1	3	yes	—
64	C₂²×C₄	—	73	3	no	—
65	C₂²×C₄	—	73	4	no	—
66	C₂×C₈	—	73	12	no	—
67	C₂×C₈	—	73	6	no	—
68	C₂×C₈	—	146	12	no	—
69	C₂×C₈	—	146	12	no	—
70	C₂×C₈	C₄×#64408	1	6	yes	—
71	C₄²	—	73	3	no	—
72	C₄²	—	146	12	no	—
73	C₄²	C₂²×#64408	1	1	yes	characteristic
74	C₂³	—	73	1	no	—
75	C₂×C₄	—	73	3	no	—
76	C₂×C₄	—	73	12	no	—
77	C₂×C₄	—	146	12	no	—
78	C₂×C₄	C₂×C₄×#64408	1	3	yes	—
79	C₈	—	2	6	no	—
80	C₈	—	146	12	no	—
81	C₈	—	146	6	no	—
82	C₂²	—	73	6	no	—
83	C₂²	C₄²×#64408	1	1	yes	characteristic
84	C₄	—	292	4	no	—
85	C₄	—	73	6	no	—
86	C₄	#17989550	1	6	yes	—
87	C₂	—	73	4	no	—
88	C₂	#22625587	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₄³
Fitting	C₈²×C₇₃	C₄
prime radical	C₂²×D₇₃	C₂×C₄²
cosocle	C₄²×D₇₃	C₂³
hypercenter	C₈²	#64408
hypocenter	C₇₃	#7845
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
7. #17989429	C₄	semidirect
9. C₈×#10596831	C₄	semidirect
10. C₈²×C₇₃	C₄	semidirect
48. C₇₃	#7845	semidirect
55. C₈²	#64408	semidirect

Maximal subgroups

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

subgroup	index
#22625644	2
#22625127	2
C₈²×D₇₃	2
#7845	73