Subgroups — C₂×(C₂×D₃)⋊C₄ #927

Order 96.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊C₄	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	1	yes	characteristic
7	C₂²×D₃	—	2	2	no	—
8	C₂²×D₃	—	2	2	no	—
9	C₂²×D₃	C₄	1	4	yes	complemented
10	C₂²×D₃	C₂²	1	2	yes	—
11	C₂×C₃×C₄	—	2	2	no	—
12	C₂×C₃×C₄	C₂²	1	2	yes	complemented
13	C₂×Dic₃	—	2	2	no	—
14	C₂×Dic₃	C₂²	1	2	yes	complemented
15	C₂⁴	—	3	1	no	—
16	C₂²×C₄	—	3	1	no	—
17	C₂²×C₄	D₃	1	1	yes	characteristic, complemented
18	C₂²⋊C₄	—	3	4	no	—
19	C₂²×C₃	C₂×C₄	1	2	yes	—
20	C₂²×C₃	D₄	1	2	yes	—
21	C₂²×C₃	D₄	1	2	yes	—
22	C₂²×C₃	C₂³	1	1	yes	characteristic
23	C₂×D₃	—	2	8	no	—
24	C₂×D₃	—	2	2	no	—
25	C₂×D₃	—	2	2	no	—
26	C₂×D₃	C₂×C₄	1	4	yes	complemented
27	C₃×C₄	—	2	2	no	—
28	Dic₃	—	2	2	no	—
29	C₂³	—	3	4	no	—
30	C₂³	—	3	2	no	—
31	C₂³	—	6	2	no	—
32	C₂³	—	6	2	no	—
33	C₂³	C₂×D₃	1	1	yes	characteristic
34	C₂×C₄	—	2	2	no	—
35	C₂×C₄	—	3	2	no	—
36	C₂×C₄	—	6	2	no	—
37	C₂×C₄	C₂×D₃	1	2	yes	complemented
38	C₂×C₃	C₂²⋊C₄	1	4	yes	complemented
39	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃	C₂×D₄	1	1	yes	characteristic
42	D₃	—	2	4	no	—
43	C₂²	—	3	4	no	—
44	C₂²	—	6	8	no	—
45	C₂²	—	6	2	no	—
46	C₂²	—	6	2	no	—
47	C₂²	C₄×D₃	1	2	yes	—
48	C₂²	D₁₂	1	2	yes	—
49	C₂²	#67	1	2	yes	—
50	C₂²	C₂²×D₃	1	1	yes	characteristic
51	C₄	—	2	2	no	—
52	C₄	—	6	2	no	—
53	C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	6	4	no	—
55	C₂	(C₂×D₃)⋊C₄	1	4	yes	direct product factor
56	C₂	C₂×C₄×D₃	1	1	yes	characteristic
57	C₂	C₂×D₁₂	1	1	yes	characteristic
58	C₂	C₂×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃
commutator	C₂×C₃	C₂²×C₄
Frattini	C₂²	C₂²×D₃
Fitting	C₂²×C₃×C₄	C₂
socle	C₂³×C₃	C₂²
prime radical	C₂³×D₃	C₂
cosocle	C₂²×C₃	C₂³
hypercenter	C₂²×C₄	D₃
hypocenter	C₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄	C₂	semidirect
3. C₂²×Dic₃	C₂	semidirect
4. (C₂×D₃)⋊C₄	C₂	direct (N × H)
9. C₂²×D₃	C₄	semidirect
12. C₂×C₃×C₄	C₂²	semidirect
14. C₂×Dic₃	C₂²	semidirect
17. C₂²×C₄	D₃	semidirect
26. C₂×D₃	C₂×C₄	semidirect
37. C₂×C₄	C₂×D₃	semidirect
38. C₂×C₃	C₂²⋊C₄	semidirect
53. C₃	C₂×C₂²⋊C₄	semidirect
55. C₂	(C₂×D₃)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃	2
C₂²×C₃×C₄	2
C₂²×Dic₃	2
(C₂×D₃)⋊C₄	2
C₂×C₂²⋊C₄	3

Subgroups — C2×(C2×D3)⋊C4 #927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₂×D₃)⋊C₄ #927