Subgroups — C₂×#4447 #69365

Order 384.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#4447	C₂	1	4	yes	maximal, direct product factor
5	C₂×M₆₄	—	3	1	no	maximal, Sylow
6	C₂×D₃×C₈	C₄	1	1	yes	characteristic
7	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊C₁₆	C₄	1	1	yes	characteristic
9	D₃×C₁₆	C₄	1	2	yes	—
10	D₃×C₁₆	C₂²	1	2	yes	—
11	C₃×C₃₂	C₂²	1	2	yes	complemented
12	C₃⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂²×C₁₆	—	3	1	no	—
14	M₆₄	—	3	4	no	—
15	C₂×C₃₂	—	3	1	no	—
16	C₂×C₃₂	D₃	1	1	yes	characteristic, complemented
17	C₂×C₄×D₃	C₈	1	1	yes	characteristic
18	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₃⋊C₈	C₈	1	1	yes	characteristic
20	D₃×C₈	C₈	1	2	yes	—
21	D₃×C₈	C₂×C₄	1	2	yes	—
22	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₃×C₁₆	C₂³	1	1	yes	characteristic
24	C₃⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×C₈	—	3	1	no	—
26	C₂×C₁₆	—	3	1	no	—
27	C₂×C₁₆	—	3	2	no	—
28	C₂×C₁₆	—	3	2	no	—
29	C₂×C₁₆	C₂×D₃	1	1	yes	characteristic
30	C₃₂	—	3	2	no	—
31	C₃₂	C₂×D₃	1	2	yes	complemented
32	C₂²×D₃	C₁₆	1	1	yes	characteristic
33	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
34	C₂×Dic₃	C₁₆	1	1	yes	characteristic
35	C₄×D₃	C₁₆	1	2	yes	—
36	C₄×D₃	C₂×C₈	1	2	yes	—
37	C₃×C₈	C₂×C₈	1	1	yes	characteristic
38	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
39	C₃⋊C₈	C₂×C₈	1	2	yes	—
40	C₂²×C₄	—	3	1	no	—
41	C₂×C₈	—	3	1	no	—
42	C₂×C₈	—	3	2	no	—
43	C₂×C₈	—	3	2	no	—
44	C₂×C₈	C₄×D₃	1	1	yes	characteristic
45	C₁₆	—	3	2	no	—
46	C₁₆	C₄×D₃	1	1	yes	characteristic
47	C₁₆	C₂²×D₃	1	1	yes	characteristic
48	C₂²×C₃	C₂×C₁₆	1	1	yes	characteristic
49	C₂×D₃	—	2	2	no	—
50	C₂×D₃	C₂×C₁₆	1	2	yes	—
51	C₃×C₄	C₂×C₁₆	1	1	yes	characteristic
52	C₃×C₄	C₂²×C₈	1	1	yes	characteristic
53	Dic₃	C₂×C₁₆	1	2	yes	—
54	C₂³	—	3	1	no	—
55	C₂×C₄	—	3	1	no	—
56	C₂×C₄	—	3	2	no	—
57	C₂×C₄	—	3	2	no	—
58	C₂×C₄	D₃×C₈	1	1	yes	characteristic
59	C₈	—	3	2	no	—
60	C₈	D₃×C₈	1	1	yes	characteristic
61	C₈	C₂×C₄×D₃	1	1	yes	characteristic
62	C₂×C₃	M₆₄	1	2	yes	complemented
63	C₂×C₃	C₂²×C₁₆	1	1	yes	characteristic
64	D₃	—	2	2	no	—
65	C₂²	—	3	2	no	—
66	C₂²	—	6	2	no	—
67	C₂²	D₃×C₁₆	1	1	yes	characteristic
68	C₄	—	3	2	no	—
69	C₄	D₃×C₁₆	1	1	yes	characteristic
70	C₄	C₂×D₃×C₈	1	1	yes	characteristic
71	C₃	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
72	C₂	—	6	2	no	—
73	C₂	#4447	1	2	yes	direct product factor
74	C₂	C₂×D₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₃
commutator	C₂×C₃	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₃
Fitting	C₂×C₃×C₃₂	C₂
socle	C₂²×C₃	C₂×C₁₆
prime radical	C₂²×D₃	C₁₆
cosocle	C₃×C₁₆	C₂³
hypercenter	C₂×C₃₂	D₃
hypocenter	C₃	C₂×M₆₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₃₂	C₂	semidirect
3. C₂×C₃⋊C₃₂	C₂	semidirect
4. #4447	C₂	direct (N × H)
11. C₃×C₃₂	C₂²	semidirect
12. C₃⋊C₃₂	C₂²	semidirect
16. C₂×C₃₂	D₃	semidirect
31. C₃₂	C₂×D₃	semidirect
62. C₂×C₃	M₆₄	semidirect
71. C₃	C₂×M₆₄	semidirect
73. C₂	#4447	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×D₃×C₁₆	2
C₂×C₃×C₃₂	2
C₂×C₃⋊C₃₂	2
#4447	2
C₂×M₆₄	3

Subgroups — C2×#4447 #69365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4447 #69365