Subgroups — C₂×#63656 #10592879

Order 576.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#3746	C₂	1	1	yes	maximal, characteristic
3	#63656	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	C₂×#829	—	3	4	no	maximal
6	C₂×C₃²×Q₈	—	2	1	no	—
7	C₂×#634	—	2	1	no	—
8	C₃²×Q₁₆	—	2	1	no	—
9	C₃²×Q₁₆	C₂²	1	2	yes	—
10	C₂×C₃²×C₈	C₂²	1	1	yes	characteristic
11	#3746	—	2	1	no	—
12	#3746	C₂²	1	2	yes	—
13	C₃⋊(C₃⋊C₁₆)	C₂²	1	2	yes	—
14	C₂×C₃×Q₁₆	D₃	1	4	yes	—
15	C₂×Dic₁₂	—	3	4	no	—
16	#829	—	3	16	no	—
17	C₂×C₃⋊C₁₆	—	3	4	no	—
18	C₃²×Q₈	—	2	2	no	—
19	C₃²×Q₈	—	4	1	no	—
20	C₂×C₃²×C₄	—	4	1	no	—
21	C₂×C₃²×C₄	D₄	1	1	yes	characteristic
22	C₂×C₃⋊Dic₃	—	4	1	no	—
23	#634	—	2	2	no	—
24	#634	—	4	1	no	—
25	C₃²×C₈	D₄	1	1	yes	characteristic
26	C₃²×C₈	C₂³	1	1	yes	characteristic
27	C₂×Q₃₂	—	9	1	no	Sylow
28	C₂×C₃×Q₈	—	2	4	no	—
29	C₂×Dic₆	—	6	4	no	—
30	C₃×Q₁₆	—	2	4	no	—
31	C₃×Q₁₆	C₂×D₃	1	8	yes	—
32	C₂×C₃×C₈	C₂×D₃	1	4	yes	—
33	Dic₁₂	—	3	8	no	—
34	Dic₁₂	—	6	4	no	—
35	C₃⋊C₁₆	—	3	8	no	—
36	C₂²×C₃²	D₈	1	1	yes	characteristic
37	C₃²×C₄	—	4	2	no	—
38	C₃²×C₄	D₈	1	1	yes	characteristic
39	C₃²×C₄	C₂×D₄	1	1	yes	characteristic
40	C₃⋊Dic₃	—	4	2	no	—
41	C₂×Q₁₆	—	9	1	no	—
42	C₂×Q₁₆	C₃⋊D₃	1	1	yes	characteristic
43	Q₃₂	—	9	4	no	—
44	C₂×C₁₆	—	9	1	no	—
45	C₃×Q₈	—	2	8	no	—
46	C₃×Q₈	—	4	4	no	—
47	C₂×C₃×C₄	—	4	4	no	—
48	C₂×C₃×C₄	#67	1	4	yes	—
49	C₂×Dic₃	—	12	4	no	—
50	Dic₆	—	6	8	no	—
51	Dic₆	—	12	4	no	—
52	C₃×C₈	#67	1	4	yes	—
53	C₃×C₈	C₂²×D₃	1	4	yes	—
54	C₂×C₃²	Q₃₂	1	2	yes	complemented
55	C₂×C₃²	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×C₃⋊D₃	1	2	yes	—
62	C₂×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
63	C₁₆	—	9	2	no	—
64	C₂²×C₃	#213	1	4	yes	—
65	C₃×C₄	—	4	8	no	—
66	C₃×C₄	#213	1	4	yes	—
67	C₃×C₄	C₂×#67	1	4	yes	—
68	Dic₃	—	12	8	no	—
69	C₃²	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	#638	1	1	yes	characteristic
77	C₈	#638	1	1	yes	characteristic
78	C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
79	C₂×C₃	#829	1	8	yes	complemented
80	C₂×C₃	C₂×#213	1	4	yes	—
81	C₂²	#3753	1	1	yes	characteristic
82	C₄	—	4	2	no	—
83	C₄	—	36	2	no	—
84	C₄	#3753	1	1	yes	characteristic
85	C₄	C₂×#638	1	1	yes	characteristic
86	C₃	C₂×#829	1	4	yes	complemented
87	C₂	#63656	1	2	yes	direct product factor
88	C₂	C₂×#3753	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#3753
commutator, cosocle	C₃²×C₈	C₂³
Frattini	C₈	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×Q₁₆	C₂
socle, prime radical	C₂²×C₃²	D₈
hypercenter	C₂×Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×Q₃₂
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
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. #63656	C₂	direct (N × H)
54. C₂×C₃²	Q₃₂	semidirect
69. C₃²	C₂×Q₃₂	semidirect
79. C₂×C₃	#829	semidirect
86. C₃	C₂×#829	semidirect
87. C₂	#63656	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×C₃²×Q₁₆	2
C₂×#3746	2
#63656	2
C₂×C₃⋊(C₃⋊C₁₆)	2
C₂×#829	3

Subgroups — C2×#63656 #10592879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63656 #10592879