Subgroups — #578⋊C₉ #10589562

Order 576.

127 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴⋊C₉	C₂	1	2	yes	maximal, complemented
2	#131⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#578	C₃	1	1	yes	maximal, characteristic
4	#41⋊C₉	C₂²	1	1	yes	characteristic
5	C₂×Q₈⋊C₉	—	2	2	no	—
6	C₉×D₈	—	4	1	no	maximal
7	C₃×2₋¹⁺⁴	C₂×C₃	1	2	yes	—
8	C₃×#137	—	3	2	no	—
9	C₃×#135	—	3	1	no	—
10	C₂×C₃×Q₁₆	—	3	1	no	—
11	C₃×#131	C₂×C₃	1	1	yes	characteristic
12	D₄×C₉	—	4	2	no	—
13	Q₈⋊C₉	D₄	1	1	yes	characteristic
14	C₈×C₉	—	4	1	no	—
15	#578	C₉	1	1	yes	characteristic, complemented, Sylow
16	C₃×#41	—	3	2	no	—
17	C₃×#41	—	6	2	no	—
18	C₃×#41	C₂²×C₃	1	1	yes	characteristic
19	C₂×C₃×Q₈	—	2	2	no	—
20	C₂×C₃×Q₈	—	3	2	no	—
21	C₃×Q₁₆	—	3	2	no	—
22	C₃×Q₁₆	—	3	1	no	—
23	C₃×SD₁₆	—	3	2	no	—
24	C₃×D₈	A₄	1	1	yes	characteristic
25	C₃×M₁₆	—	3	1	no	—
26	C₂×C₃×C₈	—	3	1	no	—
27	C₂²×C₉	—	8	2	no	—
28	C₄×C₉	—	4	1	no	—
29	2₋¹⁺⁴	C₂×C₉	1	2	yes	complemented
30	#137	—	3	2	no	—
31	#135	—	3	1	no	—
32	C₂×Q₁₆	—	3	1	no	—
33	#131	C₂×C₉	1	1	yes	characteristic, complemented
34	C₃×Q₈	—	3	2	no	—
35	C₃×Q₈	—	6	2	no	—
36	C₃×Q₈	C₃×D₄	1	1	yes	characteristic
37	C₃×D₄	—	3	1	no	—
38	C₃×D₄	—	6	2	no	—
39	C₃×D₄	C₂×A₄	1	2	yes	—
40	C₂×C₃×C₄	—	3	1	no	—
41	C₂×C₃×C₄	—	6	2	no	—
42	C₂×C₃×C₄	—	6	2	no	—
43	C₃×C₈	—	3	1	no	—
44	C₃×C₈	C₂×A₄	1	1	yes	characteristic
45	C₂×C₉	—	4	1	no	—
46	C₂×C₉	—	16	2	no	—
47	#41	—	3	2	no	—
48	#41	—	6	2	no	—
49	#41	C₂²×C₉	1	1	yes	characteristic
50	C₂×Q₈	—	2	2	no	—
51	C₂×Q₈	—	3	2	no	—
52	Q₁₆	—	3	2	no	—
53	Q₁₆	—	3	1	no	—
54	SD₁₆	—	3	2	no	—
55	D₈	C₂²⋊C₉	1	1	yes	characteristic
56	M₁₆	—	3	1	no	—
57	C₂×C₈	—	3	1	no	—
58	C₂²×C₃	—	2	2	no	—
59	C₂²×C₃	—	3	1	no	—
60	C₃×C₄	—	3	1	no	—
61	C₃×C₄	—	6	2	no	—
62	C₃×C₄	C₂²×A₄	1	1	yes	characteristic
63	C₉	—	4	1	no	Sylow
64	Q₈	—	3	2	no	—
65	Q₈	—	6	2	no	—
66	Q₈	D₄×C₉	1	1	yes	characteristic
67	D₄	—	3	1	no	—
68	D₄	—	6	2	no	—
69	D₄	C₂×C₂²⋊C₉	1	2	yes	—
70	C₂×C₄	—	3	1	no	—
71	C₂×C₄	—	6	2	no	—
72	C₂×C₄	—	6	2	no	—
73	C₈	—	3	1	no	—
74	C₈	C₂×C₂²⋊C₉	1	1	yes	characteristic
75	C₂×C₃	—	4	2	no	—
76	C₂×C₃	—	6	1	no	—
77	C₂×C₃	D₄×A₄	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	—	3	1	no	—
80	C₄	—	3	1	no	—
81	C₄	—	6	2	no	—
82	C₄	C₂²×C₂²⋊C₉	1	1	yes	characteristic
83	C₃	#578⋊C₃	1	1	yes	characteristic
84	C₂	—	4	2	no	—
85	C₂	—	6	1	no	—
86	C₂	D₄×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	D₄×A₄
commutator	#41	C₂²×C₉
Frattini	C₃×C₄	C₂²×A₄
Fitting, prime radical	C₃×#578	C₃
cosocle	C₃×#41	C₂²×C₃
hypercenter	C₃×D₈	A₄
hypocenter	Q₈	D₄×C₉
LCS	G ▷ #41 ▷ Q₈
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₈

Complements

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴⋊C₉	C₂	semidirect
2. #131⋊C₉	C₂	semidirect
15. #578	C₉	semidirect
29. 2₋¹⁺⁴	C₂×C₉	semidirect
33. #131	C₂×C₉	semidirect

Maximal subgroups

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

subgroup	index
2₋¹⁺⁴⋊C₉	2
#131⋊C₉	2
C₃×#578	3
C₉×D₈	4

Subgroups — #578⋊C9 #10589562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #578⋊C₉ #10589562