Subgroups — C₂×#63510 #10589920

Order 576.

399 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#41	C₂	1	1	yes	maximal, characteristic
2	#63510	C₂	1	8	yes	maximal, direct product factor
3	C₂×#3667	C₂	1	3	yes	maximal, complemented
4	C₂²×C₉⋊C₈	C₂	1	3	yes	maximal, complemented
5	C₂×#948	—	3	1	no	maximal
6	C₉×#41	C₄	1	4	yes	—
7	C₉×#41	C₂²	1	4	yes	—
8	C₂×Q₈×C₉	C₄	1	1	yes	characteristic
9	C₂×D₄×C₉	C₄	1	3	yes	—
10	C₂²×C₄×C₉	C₂²	1	3	yes	—
11	#3667	C₂²	1	12	yes	complemented
12	C₂×C₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₉⋊C₈	C₂²	1	3	yes	—
14	C₂×C₉⋊C₈	C₂²	1	12	yes	complemented
15	C₂×C₃×#41	D₃	1	1	yes	characteristic
16	#948	—	3	8	no	—
17	C₂×#208	—	3	3	no	—
18	C₂²×C₃⋊C₈	—	3	3	no	—
19	C₂³×C₉	C₂×C₄	1	3	yes	—
20	Q₈×C₉	C₂×C₄	1	4	yes	—
21	D₄×C₉	C₂×C₄	1	12	yes	—
22	C₂×C₄×C₉	C₂×C₄	1	3	yes	—
23	C₂×C₄×C₉	C₂×C₄	1	6	yes	—
24	C₂×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₉	C₂³	1	6	yes	—
26	C₉⋊C₈	C₂³	1	2	yes	—
27	C₉⋊C₈	C₂³	1	6	yes	—
28	C₂×#131	—	9	1	no	Sylow
29	C₃×#41	Dic₃	1	4	yes	—
30	C₃×#41	C₂×D₃	1	4	yes	—
31	C₂×C₃×Q₈	Dic₃	1	1	yes	characteristic
32	C₂×C₃×D₄	Dic₃	1	3	yes	—
33	C₂²×C₃×C₄	C₂×D₃	1	3	yes	—
34	#208	—	3	12	no	—
35	C₂×C₃⋊C₈	—	3	1	no	—
36	C₂×C₃⋊C₈	—	3	3	no	—
37	C₂×C₃⋊C₈	—	3	12	no	—
38	C₂²×C₉	—	2	6	no	—
39	C₂²×C₉	C₂²×C₄	1	6	yes	—
40	C₂²×C₉	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
42	C₄×C₉	C₂²×C₄	1	6	yes	—
43	C₄×C₉	C₂⁴	1	1	yes	characteristic
44	C₂×#41	D₉	1	1	yes	characteristic
45	#131	—	9	8	no	—
46	C₂×M₁₆	—	9	3	no	—
47	C₂²×C₈	—	9	3	no	—
48	C₂³×C₃	C₂×Dic₃	1	3	yes	—
49	C₃×Q₈	C₂×Dic₃	1	4	yes	—
50	C₃×D₄	C₂×Dic₃	1	12	yes	—
51	C₂×C₃×C₄	C₂×Dic₃	1	3	yes	—
52	C₂×C₃×C₄	C₂×Dic₃	1	6	yes	—
53	C₂×C₃×C₄	C₂²×D₃	1	6	yes	—
54	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
55	C₃⋊C₈	—	3	2	no	—
56	C₃⋊C₈	—	3	6	no	—
57	C₂×C₉	—	2	6	no	—
58	C₂×C₉	#131	1	2	yes	complemented
59	C₂×C₉	C₂³×C₄	1	1	yes	characteristic
60	#41	Dic₉	1	4	yes	—
61	#41	C₂×D₉	1	4	yes	—
62	C₂×Q₈	Dic₉	1	1	yes	characteristic
63	C₂×D₄	Dic₉	1	3	yes	—
64	C₂²×C₄	C₂×D₉	1	3	yes	—
65	M₁₆	—	9	12	no	—
66	C₂×C₈	—	9	12	no	—
67	C₂×C₈	—	9	1	no	—
68	C₂×C₈	—	9	3	no	—
69	C₂²×C₃	—	2	6	no	—
70	C₂²×C₃	C₂²×Dic₃	1	6	yes	—
71	C₂²×C₃	C₂²×Dic₃	1	1	yes	characteristic
72	C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
73	C₃×C₄	C₂²×Dic₃	1	6	yes	—
74	C₃×C₄	C₂³×D₃	1	1	yes	characteristic
75	C₉	C₂×#131	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂×Dic₉	1	3	yes	—
77	Q₈	C₂×Dic₉	1	4	yes	—
78	D₄	C₂×Dic₉	1	12	yes	—
79	C₂×C₄	C₂×Dic₉	1	3	yes	—
80	C₂×C₄	C₂×Dic₉	1	6	yes	—
81	C₂×C₄	C₂²×D₉	1	6	yes	—
82	C₂×C₄	C₂²×D₉	1	1	yes	characteristic
83	C₈	—	9	2	no	—
84	C₈	—	9	6	no	—
85	C₂×C₃	—	2	6	no	—
86	C₂×C₃	#948	1	2	yes	—
87	C₂×C₃	C₂³×Dic₃	1	1	yes	characteristic
88	C₂²	—	2	6	no	—
89	C₂²	C₂²×Dic₉	1	6	yes	—
90	C₂²	C₂²×Dic₉	1	1	yes	characteristic
91	C₄	C₂²×Dic₉	1	1	yes	characteristic
92	C₄	C₂²×Dic₉	1	6	yes	—
93	C₄	C₂³×D₉	1	1	yes	characteristic
94	C₃	C₂×#948	1	1	yes	characteristic
95	C₂	—	2	6	no	—
96	C₂	#63510	1	2	yes	direct product factor
97	C₂	C₂³×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₉
commutator	C₂×C₉	C₂³×C₄
Frattini	C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#41	C₂
socle	C₂²×C₃	C₂²×Dic₃
prime radical	C₂×C₃×#41	D₃
cosocle	C₄×C₉	C₂⁴
hypercenter	C₂×#41	D₉
hypocenter	C₉	C₂×#131
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #63510	C₂	direct (N × H)
3. C₂×#3667	C₂	semidirect
4. C₂²×C₉⋊C₈	C₂	semidirect
11. #3667	C₂²	semidirect
14. C₂×C₉⋊C₈	C₂²	semidirect
58. C₂×C₉	#131	semidirect
75. C₉	C₂×#131	semidirect
96. C₂	#63510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#41	2
#63510	2
C₂×#3667	2
C₂²×C₉⋊C₈	2
C₂×#948	3

Subgroups — C2×#63510 #10589920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63510 #10589920