Subgroups — C₂×#63742 #10593509

Order 576.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#622	C₂	1	1	yes	maximal, characteristic
2	C₂×#3724	C₂	1	2	yes	maximal
3	#63742	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
5	C₂²×C₃×Dic₃	—	2	2	no	—
6	C₂×#622	C₄	1	4	yes	complemented
7	C₂×#622	C₂²	1	2	yes	—
8	#3724	—	2	2	no	—
9	#3724	C₂²	1	4	yes	—
10	C₂×Dic₃⋊C₄	—	6	2	no	—
11	C₂³×C₃²	D₄	1	1	yes	characteristic
12	C₂×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
13	C₂×C₃⋊Dic₃	D₄	1	1	yes	characteristic
14	C₂×C₃⋊Dic₃	Q₈	1	2	yes	—
15	C₂×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
16	C₂×C₃×Dic₃	—	2	4	no	—
17	C₂×C₃×Dic₃	—	4	4	no	—
18	#622	C₂×C₄	1	4	yes	complemented
19	C₂×#106	—	9	1	no	maximal, Sylow
20	C₂²×C₃×C₄	—	6	2	no	—
21	C₂²×Dic₃	—	2	2	no	—
22	C₂²×Dic₃	—	6	2	no	—
23	Dic₃⋊C₄	—	6	4	no	—
24	Dic₃⋊C₄	—	6	4	no	—
25	C₂²×C₃²	C₄⋊C₄	1	2	yes	—
26	C₂²×C₃²	SD₁₆	1	4	yes	—
27	C₂²×C₃²	C₂×D₄	1	1	yes	characteristic
28	C₃⋊Dic₃	C₄⋊C₄	1	2	yes	—
29	C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
30	C₃⋊Dic₃	C₂×Q₈	1	1	yes	characteristic
31	C₃×Dic₃	—	4	4	no	—
32	C₂²×C₈	—	9	1	no	—
33	C₂×C₄⋊C₄	—	9	2	no	—
34	#106	—	9	4	no	—
35	C₂³×C₃	—	2	2	no	—
36	C₂×C₃×C₄	—	6	4	no	—
37	C₂×C₃×C₄	—	12	4	no	—
38	C₂×Dic₃	—	2	4	no	—
39	C₂×Dic₃	—	4	4	no	—
40	C₂×Dic₃	—	6	4	no	—
41	C₂×Dic₃	—	6	2	no	—
42	C₂×Dic₃	—	6	4	no	—
43	C₂×Dic₃	—	6	2	no	—
44	C₂×C₃²	#106	1	4	yes	complemented
45	C₂×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₃²	C₂×SD₁₆	1	2	yes	—
47	C₂²×C₄	—	6	2	no	—
48	C₂²×C₄	—	9	1	no	—
49	C₂×C₈	—	9	2	no	—
50	C₂×C₈	—	9	4	no	—
51	C₄⋊C₄	—	9	4	no	—
52	C₄⋊C₄	—	18	2	no	—
53	C₂²×C₃	—	2	2	no	—
54	C₂²×C₃	—	2	4	no	—
55	C₂²×C₃	—	2	4	no	—
56	C₂²×C₃	—	2	4	no	—
57	C₃×C₄	—	12	4	no	—
58	Dic₃	—	4	4	no	—
59	Dic₃	—	6	4	no	—
60	Dic₃	—	6	2	no	—
61	Dic₃	—	6	2	no	—
62	C₃²	C₂×#106	1	1	yes	characteristic, complemented, Sylow
63	C₂³	GO⁺(4,𝔽₂)	1	1	yes	characteristic
64	C₂×C₄	—	6	4	no	—
65	C₂×C₄	—	9	1	no	—
66	C₂×C₄	—	9	1	no	—
67	C₂×C₄	—	9	2	no	—
68	C₂×C₄	—	9	2	no	—
69	C₂×C₄	—	12	4	no	—
70	C₈	—	9	4	no	—
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	—	2	2	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	2	8	no	—
75	C₂²	#3773	1	2	yes	—
76	C₂²	#3775	1	4	yes	—
77	C₂²	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic
78	C₄	—	9	1	no	—
79	C₄	—	9	1	no	—
80	C₄	—	9	2	no	—
81	C₄	—	12	4	no	—
82	C₃	—	2	2	no	—
83	C₂	#63742	1	4	yes	direct product factor
84	C₂	C₂×#3773	1	1	yes	characteristic
85	C₂	C₂×#3775	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂³	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₂²×C₄
Frattini	C₂²	C₂×GO⁺(4,𝔽₂)
Fitting, socle, prime radical	C₂³×C₃²	D₄
cosocle	C₂×C₃⋊Dic₃	C₂³
hypocenter	C₃²	C₂×#106
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
3. #63742	C₂	direct (N × H)
6. C₂×#622	C₄	semidirect
18. #622	C₂×C₄	semidirect
44. C₂×C₃²	#106	semidirect
62. C₃²	C₂×#106	semidirect
83. C₂	#63742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#622	2
C₂×#3724	2
#63742	2
C₂×#106	9

Subgroups — C2×#63742 #10593509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#63742 #10593509