Subgroups — C₂×#3775 #64238

Order 288.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#627	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#625	C₂	1	1	yes	maximal, characteristic
3	C₂×#622	C₂	1	1	yes	maximal, characteristic, complemented
4	#3775	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₃×D₃	—	2	1	no	—
6	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₃	—	2	1	no	—
8	#627	—	2	1	no	—
9	#627	C₂²	1	2	yes	complemented
10	#625	—	2	1	no	—
11	#625	C₂²	1	2	yes	—
12	#622	C₂²	1	2	yes	complemented
13	C₂×#67	—	6	1	no	—
14	C₂×Dic₆	—	6	1	no	—
15	C₂²×C₃²	D₄	1	1	yes	characteristic
16	C₂×C₃×D₃	—	2	2	no	—
17	C₂×C₃×D₃	—	4	2	no	—
18	C₃⋊Dic₃	D₄	1	1	yes	characteristic
19	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
20	C₃×Dic₃	—	2	2	no	—
21	C₂×SD₁₆	—	9	1	no	maximal, Sylow
22	C₂³×C₃	—	6	1	no	—
23	C₂²×D₃	—	2	1	no	—
24	C₂×C₃×C₄	—	6	1	no	—
25	#67	—	6	2	no	—
26	#67	—	6	2	no	—
27	C₂×Dic₃	—	2	1	no	—
28	C₂×Dic₃	—	6	1	no	—
29	C₂×Dic₃	—	6	1	no	—
30	Dic₆	—	6	2	no	—
31	Dic₆	—	6	2	no	—
32	C₂×C₃²	SD₁₆	1	2	yes	complemented
33	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
34	C₃×D₃	—	4	2	no	—
35	C₂×Q₈	—	9	1	no	—
36	C₂×D₄	—	9	1	no	—
37	SD₁₆	—	9	4	no	—
38	C₂×C₈	—	9	1	no	—
39	C₂²×C₃	—	2	1	no	—
40	C₂²×C₃	—	2	1	no	—
41	C₂²×C₃	—	6	2	no	—
42	C₂²×C₃	—	12	2	no	—
43	C₂×D₃	—	2	2	no	—
44	C₂×D₃	—	4	2	no	—
45	C₃×C₄	—	6	2	no	—
46	Dic₃	—	2	2	no	—
47	Dic₃	—	6	1	no	—
48	Dic₃	—	6	1	no	—
49	Dic₃	—	6	1	no	—
50	Dic₃	—	6	1	no	—
51	C₃²	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
52	C₂³	—	6	1	no	—
53	Q₈	—	9	2	no	—
54	Q₈	—	18	1	no	—
55	D₄	—	9	2	no	—
56	D₄	—	18	1	no	—
57	C₂×C₄	—	6	1	no	—
58	C₂×C₄	—	9	1	no	—
59	C₈	—	9	2	no	—
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	2	1	no	—
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	—	12	2	no	—
65	D₃	—	4	2	no	—
66	C₂²	—	6	2	no	—
67	C₂²	—	12	2	no	—
68	C₂²	GO⁺(4,𝔽₂)	1	1	yes	characteristic
69	C₄	—	6	2	no	—
70	C₄	—	9	1	no	—
71	C₄	—	9	1	no	—
72	C₃	—	2	1	no	—
73	C₃	—	2	1	no	—
74	C₂	—	12	2	no	—
75	C₂	#3775	1	2	yes	direct product factor
76	C₂	C₂×GO⁺(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	GO⁺(4,𝔽₂)
commutator, cosocle	C₃⋊Dic₃	C₂³
Frattini	C₂	C₂×GO⁺(4,𝔽₂)
Fitting, socle	C₂²×C₃²	D₄
prime radical	C₂×#625	C₂
hypocenter	C₃²	C₂×SD₁₆
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#627	C₂	semidirect
3. C₂×#622	C₂	semidirect
4. #3775	C₂	direct (N × H)
9. #627	C₂²	semidirect
12. #622	C₂²	semidirect
32. C₂×C₃²	SD₁₆	semidirect
51. C₃²	C₂×SD₁₆	semidirect
75. C₂	#3775	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×#627	2
C₂×#625	2
C₂×#622	2
#3775	2
C₂×SD₁₆	9

Subgroups — C2×#3775 #64238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3775 #64238