Subgroups — C₂×#63388 #10588860

Order 576.

123 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₆	C₂	1	1	yes	maximal, characteristic
3	#63388	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×#829	—	3	1	no	maximal
6	C₂×Q₈×C₉	—	2	1	no	—
7	C₂×Dic₁₈	—	2	1	no	—
8	C₉×Q₁₆	—	2	1	no	—
9	C₉×Q₁₆	C₂²	1	2	yes	—
10	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
11	Dic₃₆	—	2	1	no	—
12	Dic₃₆	C₂²	1	2	yes	—
13	C₉⋊C₁₆	C₂²	1	2	yes	—
14	C₂×C₃×Q₁₆	D₃	1	1	yes	characteristic
15	C₂×Dic₁₂	—	3	1	no	—
16	#829	—	3	4	no	—
17	C₂×C₃⋊C₁₆	—	3	1	no	—
18	Q₈×C₉	—	2	2	no	—
19	Q₈×C₉	—	4	1	no	—
20	C₂×C₄×C₉	—	4	1	no	—
21	C₂×C₄×C₉	D₄	1	1	yes	characteristic
22	C₂×Dic₉	—	4	1	no	—
23	Dic₁₈	—	2	2	no	—
24	Dic₁₈	—	4	1	no	—
25	C₈×C₉	D₄	1	1	yes	characteristic
26	C₈×C₉	C₂³	1	1	yes	characteristic
27	C₂×Q₃₂	—	9	1	no	Sylow
28	C₂×C₃×Q₈	—	2	1	no	—
29	C₂×Dic₆	—	6	1	no	—
30	C₃×Q₁₆	—	2	1	no	—
31	C₃×Q₁₆	C₂×D₃	1	2	yes	—
32	C₂×C₃×C₈	C₂×D₃	1	1	yes	characteristic
33	Dic₁₂	—	3	2	no	—
34	Dic₁₂	—	6	1	no	—
35	C₃⋊C₁₆	—	3	2	no	—
36	C₂²×C₉	D₈	1	1	yes	characteristic
37	C₄×C₉	—	4	2	no	—
38	C₄×C₉	D₈	1	1	yes	characteristic
39	C₄×C₉	C₂×D₄	1	1	yes	characteristic
40	Dic₉	—	4	2	no	—
41	C₂×Q₁₆	—	9	1	no	—
42	C₂×Q₁₆	D₉	1	1	yes	characteristic
43	Q₃₂	—	9	4	no	—
44	C₂×C₁₆	—	9	1	no	—
45	C₃×Q₈	—	2	2	no	—
46	C₃×Q₈	—	4	1	no	—
47	C₂×C₃×C₄	—	4	1	no	—
48	C₂×C₃×C₄	#67	1	1	yes	characteristic
49	C₂×Dic₃	—	12	1	no	—
50	Dic₆	—	6	2	no	—
51	Dic₆	—	12	1	no	—
52	C₃×C₈	#67	1	1	yes	characteristic
53	C₃×C₈	C₂²×D₃	1	1	yes	characteristic
54	C₂×C₉	Q₃₂	1	2	yes	complemented
55	C₂×C₉	C₂×D₈	1	1	yes	characteristic
56	C₂×Q₈	—	2	1	no	—
57	C₂×Q₈	—	18	1	no	—
58	Q₁₆	—	2	1	no	—
59	Q₁₆	—	9	2	no	—
60	Q₁₆	—	18	1	no	—
61	Q₁₆	C₂×D₉	1	2	yes	—
62	C₂×C₈	C₂×D₉	1	1	yes	characteristic
63	C₁₆	—	9	2	no	—
64	C₂²×C₃	#213	1	1	yes	characteristic
65	C₃×C₄	—	4	2	no	—
66	C₃×C₄	#213	1	1	yes	characteristic
67	C₃×C₄	C₂×#67	1	1	yes	characteristic
68	Dic₃	—	12	2	no	—
69	C₉	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	2	2	no	—
71	Q₈	—	4	1	no	—
72	Q₈	—	18	2	no	—
73	Q₈	—	36	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	36	1	no	—
76	C₂×C₄	#611	1	1	yes	characteristic
77	C₈	#611	1	1	yes	characteristic
78	C₈	C₂²×D₉	1	1	yes	characteristic
79	C₂×C₃	#829	1	2	yes	—
80	C₂×C₃	C₂×#213	1	1	yes	characteristic
81	C₂²	#3673	1	1	yes	characteristic
82	C₄	—	4	2	no	—
83	C₄	—	36	2	no	—
84	C₄	#3673	1	1	yes	characteristic
85	C₄	C₂×#611	1	1	yes	characteristic
86	C₃	C₂×#829	1	1	yes	characteristic
87	C₂	#63388	1	2	yes	direct product factor
88	C₂	C₂×#3673	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#3673
commutator, cosocle	C₈×C₉	C₂³
Frattini	C₃×C₈	C₂²×D₃
Fitting	C₂×C₉×Q₁₆	C₂
socle, prime radical	C₂²×C₃	#213
hypercenter	C₂×Q₁₆	D₉
hypocenter	C₉	C₂×Q₃₂
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #63388	C₂	direct (N × H)
54. C₂×C₉	Q₃₂	semidirect
69. C₉	C₂×Q₃₂	semidirect
87. C₂	#63388	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×Q₁₆	2
C₂×Dic₃₆	2
#63388	2
C₂×C₉⋊C₁₆	2
C₂×#829	3

Subgroups — C2×#63388 #10588860

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63388 #10588860